Encyclopedia of Glass Science, Technology, History and Culture 9781118799420

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Encyclopedia of Glass Science, Technology, History, and Culture

Encyclopedia of Glass Science, Technology, History, and Culture Volume I

Pascal Richet Institut de Physique du Globe de Paris, Paris, France Earth and Environmental Sciences, Ludwig-Maximilians-Universität, Munich, Germany

Editorial advising Reinhard Conradt UniglassAC GmbH, Aachen, Germany

Akira Takada University College London, London, UK Ehime University, Matsuyama, Japan

Infography Joël Dyon Institut de Physique du Globe, Paris, France

Copyright © 2021 by The American Ceramic Society. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions. The right of Pascal Richet to be identified as the editor of this work has been asserted in accordance with law. Registered Office John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA Editorial Office 111 River Street, Hoboken, NJ 07030, USA For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com. Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats. Limit of Liability/Disclaimer of Warranty In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication data applied for ISBN: 978-1-118-79942-0 Cover Design: Wiley Cover Images: Courtesy of S. Di Pierro, Saint-Gobain Research Paris; Christian Patzig, Fraunhofer Institute for Microstructure of Materials and Systems, Halle Germany; Dominique de Ligny, Friedrich Alexander Universität Erlangen-Nürnberg; Nicolas Villeneuve, Université de La Réunion Set in 10/12pt Warnock by SPi Global, Pondicherry, India

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Contents List of Contributors Preface xxxi

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Volume I

1 2

General Introduction 1 Pascal Richet, Reinhard Conradt and Akira Takada A Historical Random Walk 2 Some Basic Concepts of Glass Science 7

Section I. 1.1 1 2 3 4 5 1.2 1 2 3 4 5 1.3 1 2 3 4 5 6 7 1.4 1 2 3 4 5 6 7

Glassmaking

23

Glass Production: An Overview 25 Reinhard Conradt Introduction 25 Industrially Manufactured Glasses 26 Process-controlling Properties 28 Glass Composition – its Relevance to Glass Properties Perspectives 36

34

Raw Materials for Glassmaking: Properties and Constraints Simonpietro Di Pierro Introduction 39 Raw-material Specifications 40 From Raw Materials to Melt 45 Special Raw Materials 48 Perspectives 50 Fusion of Glass 53 Reinhard Conradt Introduction 53 Overview of Industrial Processes 54 Batch Preparation 54 The Conversion of Batch into Melt 57 Fining, Refining, Homogenization 62 Energetics of Glass Melting 63 Perspectives 64 Primary Fabrication of Flat Glass Toru Kamihori Introduction 67 Overview 68 Updraw Processes 70 Roll Out Process 71 Float Process 72 Downdraw Processes 77 Perspectives 78

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1.5 1 2 3 4 5 6 7 8 1.6 1 2 3 4 5 1.7 1 2 3 4 5 6

Fabrication of Glass Containers 81 Christian Roos Introduction 81 Principles of Glass-Container Forming 82 Glass-Container Forming Processes 84 Making of the Gob: Forehearth, Feeder, and Shears 87 IS-Forming Machine 88 Hot-End Handling, Hot-End Coating, and Annealing 91 Cold-End Handling and Inspection 91 Perspectives 92 Continuous Glass Fibers for Reinforcement Hong Li and James C. Watson Introduction 95 Commercial Glass Fibers 95 Manufacturing of Glass Fibers 100 Markets and Applications 106 Perspectives 108

Simulation in Glass Processes 111 Patrick J. Prescott and Bruno Purnode Introduction 111 A Brief Overview 111 Fundamental Phenomena, Governing Equations, and Simulation Tools Simulations in Glass Manufacturing Processes: A Few Examples 117 Simulation Data Management 123 Perspectives 125

Section II. 2.1 1 2 3 4 5 6 7 8 2.2 1 2 3 4 5 6 7 2.3 1 2 3 4 5 6

95

Structure

127

Basic Concepts of Network Glass Structure 129 Alex C. Hannon Introduction 129 The Zachariasen–Warren Random Network Model Silica – The Archetypal Glass 131 Microcrystalline Models 133 Modifiers and Non-Bridging Oxygens 133 Intermediate-Range Order 137 Chalcogenide Glasses 138 Perspectives 139 Structural Probes of Glass 141 Grant S. Henderson Introduction 141 Diffraction (Scattering) 143 X-ray Absorption Techniques 147 Nuclear Magnetic Resonance Spectroscopy Vibrational Spectroscopies 151 Other Techniques 155 Perspectives 157

130

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Microstructure Analysis of Glasses and Glass Ceramics Christian Patzig and Thomas Höche Introduction 159 Scanning Electron Microscopy 160 Transmission Electron Microscopy 163 Scanning Probe Microscopy 168 X-Ray Microscopy 170 Perspectives 170

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2.4 1 2 3 4 5 6 7 8 2.5 1 2 3 4 5 6 7 2.6 1 2 3 4 5 6 7 2.7 1 2 3 4 5 6 7 2.8 1 2 3 4 5 6 2.9 1 2 3 4 5 6

Short-range Structure and Order in Oxide Glasses 173 Jonathan F. Stebbins Introduction 173 One-component Oxide Glass Formers 173 Modifying the Network: Silicates and Phosphates 175 Modifying the Network: Borates and Germanates 176 Network Cations in Aluminosilicates 177 Short-range Order and Modifier Cations 178 Interactions of Network Modifiers and Network Order/Disorder 178 Perspectives 180 The Extended Structure of Glass 183 George Neville Greaves Introduction 183 Extended Structure of Glass: The Need for a Multiplicity of Techniques Structural Order over Different Length Scales 187 Structural Aspects of Density Fluctuations 190 Models of Glass Structure 191 Structural Heterogeneity in Glasses 192 Perspectives 194

185

Structure of Chemically Complex Silicate Systems 197 Bjorn Mysen Introduction 197 Glass and Melt Polymerization 197 Metal Oxide–SiO2 Systems 199 Aluminum and Aluminate 202 Ferric and Ferrous Iron 203 Minor Components in Silicate Glasses and Melts 205 Perspectives 205 Topological Constraint Theory of Inorganic Glasses 207 Prabhat K Gupta Introduction 207 Concepts of the Topological Constraint Theory 208 Polyhedral Constraint Theory 210 The Bond Constraint Theory 212 Temperature-Dependent Constraints 214 Topological Constraint Theory, Thermodynamics, and the Potential Energy Landscape Formalism Perspectives 218 Atomistic Simulations of Glass Structure and Properties 221 Akira Takada Introduction 221 Basics of Numerical Simulations 222 Monte-Carlo Simulations 224 Molecular Dynamics Simulations 225 Modeling: Simulation Techniques and Examples 226 Perspectives 230 First-principles Simulations of Glass-formers Walter Kob and Simona Ispas Introduction 233 Ab Initio Simulations 234 Structural Properties 236 Vibrational Properties 238 Calculations of NMR Spectra 241 Perspectives 241

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Section III. Physics of Glass 3.1 1 2 3 4 5 6 7 3.2 1 2 3 4 5 6 7 3.3 1 2 3 4 5 6 7 8 3.4 1 2 3 4 5 6 7 3.5 1 2 3 4 5 3.6 1 2 3 4

245

Glass Formation 249 Michael I. Ojovan Introduction 249 Glass and Relaxation 250 Kinetic Theory of Vitrification The Viscosity Factor 252 Structural Factors 253 Glass-Liquid Transition 255 Perspectives 258

250

Thermodynamics of Glasses 261 Jean-Luc Garden and Hervé Guillou Introduction 261 Basics of Nonequilibrium Thermodynamics 261 Supercooled Liquids 263 Glass as a Nonequilibrium Substance 264 Nonequilibrium Thermodynamics of the Glass Transition Physical Aging 269 Perspectives 270

266

The Glass Transition and the Entropy Crisis 273 Purushottam D. Gujrati Introduction 273 Important Concepts and Theories 273 Nonsingular Glass Phenomenology 277 Nonequilibrium Formulation: Brief Review 278 Nonequilibrium Relaxation in Internal Equilibrium 280 The Free Volume and the Communal Entropy 281 The Unifying Approach for Glasses 283 Perspectives 285 Atomic Vibrations in Glasses 287 Bernard Hehlen and Benoît Rufflé Introduction 287 Atomic Vibrations in Disordered Solids 288 Vibrations and Thermal Properties 289 Inelastic Spectroscopy in Glasses 291 Vibrational Spectra 292 The Boson Peak 296 Perspectives 298 Density of Amorphous Oxides 301 Michael J. Toplis Introduction 301 Measuring the Density of Amorphous Oxides Measured Density Variations 305 Practical Applications 309 Perspectives 309

302

Thermodynamic Properties of Oxide Glasses and Liquids Pascal Richet and Dominique de Ligny Introduction 313 Thermodynamic Functions 314 Low-temperature Heat Capacity and Entropy 318 High-temperature Properties 322

313

Contents

5 6

Reaction Thermodynamics 326 Perspectives 327

3.7

Structural and Stress Relaxation in Glass-Forming Liquids Ulrich Fotheringham Introduction 331 Structural Relaxation: A Few Examples 331 Structural Relaxation 332 Shear Viscoelasticity 339 Bulk Viscoelasticity 344 Perspectives 346

1 2 3 4 5 6 3.8 1 2 3 4 5 6 7 8 3.9 1 2 3 4

331

Hyperquenched Glasses: Relaxation and Properties 349 Yuanzheng Yue Introduction 349 Fictive Temperature and Cooling Rates 349 Sub-Tg Relaxation 351 Anomalous Relaxation 352 Modeling of Sub-Tg Relaxation 353 Boson Peak 354 Resolving Glass Problems Via Hyperquenching-Annealing Calorimetry Perspectives 357

354

Polyamorphism and Liquid–Liquid Phase Transitions 359 Paul F. McMillan and Martin C. Wilding Introduction 359 Liquid–Liquid Phase Transitions and Polyamorphism 359 Classic Systems Exhibiting Polyamorphism 365 Perspectives 369

3.10 Pressure-Induced Amorphization 371 Paul F. McMillan, Denis Machon and Martin C. Wilding 1 Introduction 371 2 First Observation of PIA: Metastable Melting vs. Mechanical Destabilization of Ice Ih 3 SiO2 and AlPO4: “Memory Glass” Effects 373 4 SnI4 and Cu2O: Examples of Compositionally Driven Instability 373 5 Nanocrystalline Materials 374 6 Zeolites as Examples of “Perfect Glass” Formation 375 7 Configurational Energy Landscapes 376 8 Perspectives 377 3.11 Mechanical Properties of Inorganic Glasses 379 Russell J. Hand 1 Introduction 379 2 The Importance of Flaws 379 3 Moduli and Hardness 380 4 Fracture Toughness and Strength 383 5 Flaws and Strength 385 6 Chemically Assisted Crack Growth – Stress Corrosion 387 7 Improving the Practical Strength of Glass 388 8 Perspectives 389 3.12 Strengthening of Oxide Glasses 391 K. Stefan R. Karlsson and Lothar Wondraczek 1 Introduction 391 2 Strength and Stresses 391 3 Elimination of Surface Flaws 393 4 Thermal Strengthening 395

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Chemical Strengthening 398 Strengthening by Coating 401 Perspectives 402

3.13 Radiation Effects in Glass 405 Nadège Ollier, Sylvain Girard and Sylvain Peuget 1 Introduction 405 2 Point Defects 406 3 Vitreous Phase Stability and Bubble Formation 408 4 Glass Network Evolution Under Irradiation 408 5 Optical Properties 409 6 RIA and Emission 409 7 Effect on Mechanical Properties 411 8 Mitigation of Radiation Effects 412 9 Perspectives 412 3.14 Amorphous Ices 415 Robert F. Tournier 1 Introduction 415 2 Ice Phase Transitions 416 3 Predictions of Glass–Glass and Liquid–Liquid Transitions 418 4 Numerical Applications to Water 421 5 Supercluster Formation at the Glass Transition of Strong Liquids 6 Perspectives 426

426

Section IV. Transport Properties 429 4.1 1 2 3 4 5 6 7 8 9 4.2 1 2 3 4 5 6 4.3 1 2 3 4 5 6 7 8

Viscosity of Glass-Forming Melts 431 Joachim Deubener Introduction 431 General Aspects and Definitions 432 Structural Aspects 433 Technological Aspects 434 Temperature Dependence of Viscosity 437 Composition Dependence 440 Dependence on Time and Strain Rate 444 Dependence on Microstructure 445 Perspectives 447 Ionic and Electronic Transport 453 Jean-Louis Souquet Introduction 453 Ionic Conductivity and Diffusion 454 Ionic Transport Mechanisms 455 Ionic Transport Above the Glass Transition: An Entropic Mechanism Electronically Conductive Glasses 459 Perspectives 462 Diffusion in Oxide Glass-forming Systems 465 Huaiwei Ni and Nico de Koker Introduction 465 Physical and Chemical Description of Diffusion 465 Experimental Methods for Determining Diffusivity 467 Influence on Diffusivity of Species Properties 467 Compositional Control 470 Temperature and Pressure Effects 472 Insights from Molecular Dynamics Simulations 473 Perspectives 474

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Contents

4.4 1 2 3 4 5 6 4.5 1 2 3 4 5 4.6 1 2 3 4 5 6 7

Chemical Diffusion in Multicomponent Glass-forming Systems Mathieu Roskosz and Emmanuelle Gouillart Introduction 477 Conceptual and Experimental Approaches 478 Tracer vs. Chemical Diffusion 479 Diffusion in Multicomponent Systems 480 Available Chemical Diffusion Data 482 Perspectives 484 Thermal Diffusivity and Conductivity of Glasses and Melts 487 Anne Hofmeister and Alan Whittington Introduction 487 Theory 487 Measurement Techniques 490 Thermal Diffusivity and Conductivity Data: Key Variables 493 Perspectives 499 Atomistic Simulations of Transport Properties 501 Junko Habasaki Introduction 501 MD Simulations: Conditions and Potentials 501 Dynamics 502 Insights into Dynamic Heterogeneities 505 Mixed Alkali Effect 508 Glass Transition and Thermodynamic Scaling 509 Perspectives 509

Section V. 5.1 1 2 3 4 5 6 7 8 9 10 5.2 1 2 3 4 5 6 5.3 1 2 3 4 5

Chemistry of Glass

511

Chemical Analyses and Characterization of Glass Thomas Bach, Reiner Haus and Sebastian Prinz Introduction 515 Gravimetry and Glass Digestion 517 X-Ray Fluorescence 517 Inductively Coupled Plasma Methods 518 Atomic Absorption Spectroscopy 520 Microprobe Analyses 521 Special Elements 521 Resistance to Chemical Attack 523 Analyses of Glass Defects 525 Perspectives 525

515

Phase Equilibria and Phase Diagrams in Oxide Systems Ilya Veksler Introduction 529 Thermodynamic Principles 530 Basic Topological Types of Binary T–x Diagrams 532 Ternary Diagrams 537 Some Phase Diagrams for Glass-Forming Systems 538 Perspectives 541 Thermodynamic Models of Oxide Melts Giulio Ottonello Introduction 545 General Considerations 546 Thermodynamic Models 548 First-Principles Calculations 555 Perspectives 556

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5.4 1 2 3 4 5 5.5 1 2 3 4 5 5.6 1 2 3 4 5 6 5.7 1 2 3 4 5 6 7 8 5.8 1 2 3 4 5 5.9 1 2 3 4 5 6 7 8

Nucleation, Growth, and Crystallization in Inorganic Glasses 559 Edgar D. Zanotto, Jürn W. P. Schmelzer and Vladimir M. Fokin Introduction 559 Crystal Nucleation and Classical Nucleation Theory 560 Basic Models of Crystal Growth in Supercooled Liquids 564 Overall Crystallization and Glass-forming Ability: The Johnson–Mehl–Avrami–Kolmogorov Approach 565 Perspectives 567 Solubility of Volatiles 571 Bjorn Mysen Introduction 571 Principles and Concepts 571 Reactive Volatiles in Silicate Glass and Melt 573 Nonreactive Volatiles in Silicate Glass and Melt 578 Perspectives 579 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses Reid F. Cooper Introduction 581 Oxidation/Reduction Thermodynamics 581 Oxidation/Reduction Kinetics 586 Open-System Redox Dynamics 586 Closed-System (or Internal) Redox Dynamics 593 Perspectives 595 Optical Basicity: Theory and Application 597 John A. Duffy Introduction: The Need for a Suitable Basicity Scale for Oxide Melts Theoretical Foundation of Optical Basicity 597 Redox Equilibria in Network Melts 600 Optical Basicity and Electronic Polarizability 601 Chemical Reactions: Changes in Structure and Bonding 601 High and Low Optical–Basicity Materials 604 Optical Basicity and Electronegativity 604 Perspectives 606

581

597

The Glass Electrode and Electrode Properties of Glasses 609 Anatolii A. Belyustin and Irina S. Ivanovskaya Introduction 609 Types and Properties of Glass Electrodes 610 Glass Structure as Viewed by the Glass Electrode 612 Theories of the Glass Electrode 614 Perspectives 616 Electrochemistry of Oxide Melts 619 Christian Rüssel Introduction 619 Thermodynamics of Redox Equilibria 619 Experimental Aspects 620 Standard Potentials and Equilibrium Constants 621 Diffusion Coefficients 623 Voltammetric Sensors: Quantitative Determinations of Polyvalent Elements Impedance Spectroscopy 625 Perspectives 626

624

5.10 Glass/Metal Interactions 629 Carine Petitjean, Pierre-Jean Panteix, Christophe Rapin, Michel Vilasi, Eric Schmucker and Renaud Podor 1 Introduction 629 2 Wetting, Sticking, and Adhesion Phenomena 629

Contents

3 4 5 6

Control of High-Temperature Chemical Interactions at the Metal/Molten Glass Interface Characterization of the Glass/Metal Interaction 632 Corrosion of Metals and Alloys by Molten Glass 635 Perspectives 638

631

5.11 Durability of Commercial-type Glasses 639 Marie-Hélène Chopinet, Hervé Montigaud, Patrice Lehuédé and Sylvie Abensour 1 Introduction 639 2 Chemical Processes and Parameters 639 3 Alteration as Related to Glass Composition 641 4 Post-Production Corrosion of Flat and Container Glass 642 5 Characterization Methods 644 6 Protection Methods 645 7 Perspectives 645 5.12 Mechanisms of Glass Corrosion by Aqueous Solutions 647 Roland Hellmann 1 Introduction 647 2 Early Models 648 3 Leached-layer Model 648 4 Coupled Interfacial Dissolution-Reprecipitation (CIDR) 652 5 Rates of Dissolution and Element Release 657 6 Perspectives 660 Section VI. Glass and Light 6.1 1 2 3 4 5 6 7 6.2 1 2 3 4 5 6 7 8 6.3 1 2 3 4 5 6 6.4 1 2

663

Optical Glasses 665 Alix Clare Introduction 665 Basic Features 666 Transmitted Light Tin 667 Glass Properties 670 Glass Responses 671 Interaction of Optical Components with Light Perspectives 674

673

The Color of Glass 677 Georges Calas, Laurence Galoisy and Laurent Cormier Introduction 677 Background on Color Processes 677 Crystal-Field-Driven Glass Color 681 Variation of Glass Coloration 685 Temperature Dependence of the Optical Absorption Spectra of Glasses: Thermochromism Charge-Transfer Processes: From Amber Glasses to Lunar Glasses 688 Absorption by Organized Clusters and Nanophases 689 Perspectives 690 Photoluminescence in Glasses 693 Lothar Wondraczek Introduction 693 Inelastic Light Scattering Through Photoluminescence Photoluminescence and Glass Chemistry 697 Efficiency, Lifetime, and Quenching Effects 700 Applications 701 Perspectives 702 Optical Fibers 705 John Ballato Introduction 705 Optical Properties and Fiber Designs

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Glasses 711 Fabrication 714

3 4 5 6

Optical Fiber Optical Fiber Applications Perspectives

6.5

Fluoride and Chalcogenide Glasses for Mid-infrared Optics Bruno Bureau and Jacques Lucas Introduction 721 Glass Transparency in the Infrared Region 721 Fluoride Glasses: Formation and Structure 723 Applications of Fluoride Glasses 724 Chalcogenide Glasses 726 Chalcogenide Glass Applications 730 Perspectives 732

1 2 3 4 5 6 7 6.6 1 2 3 4 5 6 6.7 1 2 3 4 5 6 7 8 6.8 1 2 3 4 5 6 6.9 1 2 3 4

718 718

Optoelectronics: Active Chalcogenide Glasses 735 Jong Heo and Kai Xu Introduction 735 Active Chalcogenide Glasses Doped with Rare-Earth Ions Optical Fiber Amplifiers 736 Mid-Infrared Lasers 739 Chalcogenide Quantum Dots 743 Perspectives 747 Modification Technologies of Glass Surfaces 751 İlkay Sökmen, Sener Oktik and Klaus Bange Introduction 751 Hot-End Processes in Glass Production 752 Cleaning 754 Strengthening 756 Modification of the Surface Topography 757 Structuring and Texturing 757 Applications 758 Perspectives 760 Thin-Film Technologies for Glass Surfaces Sener Oktik, İlkay Sökmen and Klaus Bange Introduction 763 Deposition Techniques 764 Thin Films 766 Transparent Conducting Oxides 767 Miscellaneous Uses 772 Perspectives 772

763

Glass for Lighting 775 Hiroki Yamazaki and Shigeru Yamamoto Introduction 775 Glass for Incandescent and Electric Discharge Lamps Glass for Solid-State Lighting 781 Perspectives 784

6.10 Screens and Displays 787 Kei Maeda 1 Introduction 787 2 Cathode-Ray Tubes 788 3 Glasses for Flat-Panel Displays 4 Liquid-Crystal Displays 793 5 Plasma-Display Panels 794

790

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6 7 8

Organic Light-Emitting Diodes Device Configuration 795 Perspectives 796

795

Volume II Section VII. Inorganic Glass Families 7.1 1 2 3 4 5 6 7.2 1 2 3 4 5 6 7 8 9 7.3 1 2 3 4 5 6 7 8 9 7.4 1 2 3 4 5 6 7 7.5 1 2 3 4 5 6

799

Extraterrestrial Glasses 801 Guy Libourel Introduction 801 Chondrules: The Oldest Glasses of the Solar System The Lunar Glass-Bead Factory 805 Cosmic Spherules 808 Terrestrial Versus Extraterrestrial 810 Perspectives 811

802

Geological Glasses 815 Cristina P. De Campos and Kai-Uwe Hess Introduction 815 Compositional Diversity of Natural Glasses 815 Fulgurites: The Petrified Lightnings 817 Impact-Related Glasses 817 The Basalt Factory 820 Siliceous Glasses 822 The Fate of Natural Glasses 825 Compositional vs. Rheological Variability 826 Perspectives 828 Corrosion of Natural Glasses in Seawater 831 Roland Hellmann Introduction 831 From Basalt Glass to Palagonite 831 Seafloor Basalt Alteration by Abiotic and Biotic Processes 832 Alteration Enhancement by Microorganism Metabolic Processes Biotic Corrosion Models 833 Abiotic Corrosion Models 836 The Abiotic vs. Biotic Alteration Debate 838 Which Mechanism Controls Basalt Glass Corrosion? 839 Perspectives 840 Metallurgical Slags 843 Kenneth C. Mills Introduction 843 Basic Constraints: A Summary 844 From Composition to Reactivity 846 Slag Properties 847 Transport Properties 849 Thermodynamic Properties 853 Perspectives 854 Water Glass 857 Hans Roggendorf Introduction 857 Fabrication of Water Glass 857 Materials and Chemical Stability and Structure Properties of Water Glass 863 Applications of Water Glass 863 Perspectives 864

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7.6 1 2 3 4 5 6 7.7 1 2 3 4 5 6 7 8 7.8 1 2 3 4 5 6 7 8 9 7.9 1 2 3 4 5 6 7 8

Borosilicate Glasses 867 Randall E. Youngman Introduction 867 Borosilicate Applications 867 Vycor: A Composition–Structure Case Study 870 Structural Aspects 871 Temperature and Pressure Variations of Network Structure Perspectives 876

874

Glass for Pharmaceutical Use 879 Daniele Zuccato and Emanuel Guadagnino Introduction 879 Glass Products and Types 879 Production of Pharmaceutical Glasses and Containers 880 Physical Resistance 882 Chemical Resistance 883 Surface Interactions with Pharmaceutical Products 885 Internal/External Treatments for Chemical/Mechanical Resistance Perspectives 888

887

Oxynitride Glasses 891 Stuart Hampshire and Michael J. Pomeroy Introduction 891 Solubility of Nitrogen in Glasses 891 Glass Formation in M–Si–Al–O–N Systems and Its Representation 892 Structure of Oxynitride Glasses 893 Effects of Composition on Properties 895 Oxynitride Glass–Ceramics 898 Phosphorus Oxynitride Glasses 899 Lower-Temperature Preparation Methods 899 Perspectives 899 Phosphate Glasses 901 Andrew James Parsons Introduction 901 Structure 902 Synthesis 904 Physical Properties 906 Optical Properties 908 Chemical Properties 911 Other Applications 914 Perspectives 914

7.10 Bulk Metallic Glasses 919 Dmitri V. Louzguine-Luzgin and Akihisa Inoue 1 Introduction 919 2 Glass Formation 920 3 Structure 923 4 Mechanical Properties 925 5 Deformation Behavior at Room Temperature 927 6 Magnetism: Properties and Applications 931 7 Other Properties and Applications 932 8 Perspectives 934 7.11 Glass-Ceramics 937 Monique Comte 1 Introduction 937 2 History and Present Uses of Glass-Ceramics

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3 4 5

Properties of Glass-Ceramics 943 Examples of Glass-Ceramics 945 Perspectives 949

Section VIII. Organically Related Glasses 951 8.1 1 2 3 4 5 6 7 8.2 1 2 3 4 5 8.3 1 2 3 4 5 6 7 8.4 1 2 3 4 5 6 7 8 8.5 1 2 3 4 5 8.6 1 2 3 4

Biogenic Silica Glasses 955 Jacques Livage and Pascal Jean Lopez Introduction 955 A Slowly Awakening Scientific Interest 956 Biogenic Silica 958 The Low-Temperature Silica Factories 962 Biomimetism and Applications 963 Biogenic Silica in the Global Ecosystem 964 Perspectives 964 Sol–Gel Process and Products 969 Rui M. Almeida and M. Clara Gonçalves Introduction 969 Sol–Gel Processing 970 Advantages and Drawbacks of the Sol–Gel Process Sol–Gel Products and Applications 974 Perspectives 978

974

Silica Aerogels 981 Wim J. Malfait, Jannis Wernery, Shanyu Zhao, Samuel Brunner, and Matthias M. Koebel Introduction 981 Synthesis 982 Properties 983 Applications 986 Markets and Industrial Production 986 Silica Hybrid Aerogels, Aerogel Composites, and Non-silica Aerogels 988 Perspectives 988 Bioactive Glasses 991 Delia S. Brauer and Julian R. Jones Introduction 991 Melt-Derived Bioactive Glasses 991 Bioactive Sol–Gel Glasses 993 Degradation and Apatite Formation 994 Biological Response 996 Therapeutic Ions in Bioactive Glasses 997 Applications of Bioglasses 998 Perspectives 1001 Dental Glass-Ceramics 1005 Wolfram Höland and Marcel Schweiger Introduction 1005 History and Present Uses of Dental Glass-Ceramics 1006 Properties of Dental Glass-Ceramics 1006 Examples of Dental Glass-Ceramics 1007 Perspectives 1010 Relaxation Processes in Molecular Liquids 1013 Thomas Blochowicz, Ernst A. Rössler and Michael Vogel Introduction 1013 From the Boiling Point Down to the Glass Transition 1015 Binary Glass-Forming Liquids 1021 Secondary Relaxations 1024

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Plastic and Glassy Crystals Perspectives 1027

8.7

Physics of Polymer Glasses 1031 Jean-Pierre Cohen-Addad Introduction 1031 Polymeric Chains 1032 Polymeric Liquids 1033 Polymer Transformations 1036 Glass Transitions and Aging 1036 Polymer Products 1039 Perspectives 1040

1 2 3 4 5 6 7 8.8 1 2 3 4 5 8.9 1 2 3 4 5 6

Introduction to Polymer Chemistry Oliver Weichold Introduction 1043 Polymer Synthesis 1045 Polymerization Processes 1050 The Solid State 1052 Perspectives 1054

1043

Hybrid Inorganic–Organic Polymers 1057 Karl-Heinz Haas and Gerhard Schottner Introduction 1057 Sol–Gel for Hybrid Materials 1057 Coatings 1061 Particles 1065 Bulk Materials, Fibers, and Composites 1065 Perspectives 1066

Section IX. Environmental and Other Issues 9.1 1 2 3 4 5 6 9.2 1 2 3 4 5 9.3 1 2 3 4 5 6 7

1069

Structural Glass in Architecture 1071 Freek Bos and Christian Louter Introduction 1071 Scheme Design 1071 Float-Glass Processing for Structural Applications Design and Detailing 1077 Connections 1079 Perspectives 1083

1074

Tempered and Laminated Glazing for Cars 1091 René Gy Introduction 1091 A Brief History from the Early Twentieth Century to Today’s Huge Market Glazing Functions 1092 Manufacturing 1097 Perspectives 1101 Stone and Glass Wool 1103 Yuanzheng Yue and Mette Solvang Introduction 1103 Classification of Man-Made Vitreous Wool 1104 Fiber Spinning Technologies 1104 Melt Viscosity and Fiber Spinnability 1106 Physical Properties of Stone and Glass Wool 1108 Biopersistence and Biodurability 1110 Perspectives 1111

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9.4 1 2 3 4 5 6 7 9.5 1 2 3 4 5 6 7 9.6 1 2 3 4 9.7 1 2 3 4 5 6 7 9.8 1 2 3 4 5 9.9 1 2 3 4 5 6 7

Glasses for Solar-energy Technologies Joachim Deubener and Gundula Helsch Introduction 1113 The Energy Problem 1113 Solar Electricity 1114 Solar Heat 1117 Solar Fuels 1120 Solar Water Treatments 1121 Perspectives 1122

1113

Sulfide-glass Electrolytes for All-solid-state Batteries Akitoshi Hayashi and Masahiro Tatsumisago Introduction 1125 Classification of All-solid-state Batteries 1126 Sulfide Glasses 1127 Sulfide Glasses as Solid Electrolytes 1128 Bulk-type Batteries with Sulfide Electrolytes 1130 Interfacial Design 1131 Perspectives 1133

1125

The World of the Flat-glass Industry: Key Milestones, Current Status, and Future Trends Bernard J. Savaëte Introduction 1135 A Short Overview: Processes and Products 1135 The Float-glass World 1139 Perspectives 1145 Design and Operation of Glass Furnaces Christoph Jatzwauk Introduction 1147 The Furnace Families 1148 Melter 1152 Heat Management 1155 Furnace Design 1159 NOx Emissions 1161 Perspectives 1162

1147

Physics and Modeling of Glass Furnaces Reinhard Conradt and Erik Muijsenberg Introduction 1165 Furnace Parameters 1166 The Physics of Glass Furnaces 1166 Modeling of Glass Furnaces 1173 Perspectives 1176

1165

Glass Cullet: Sources, Uses, and Environmental Benefits Nicola Favaro and Stefano Ceola Introduction 1179 Basic Features of Cullet 1180 Glass Recycling 1182 Separation Technologies 1184 Miscellaneous 1186 Environmental Aspects 1187 Perspectives 1188

9.10 Immobilization of Municipal and Industrial Waste Soraya Heuss-Aßbichler and Athanasius P. Bayuseno 1 Introduction 1191

1191

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Municipal Solid Waste Incineration Residues 1192 Environmental Impact of MSWI Residues 1199 Special Residues 1201 Perspectives 1203

9.11 Nuclear Waste Vitrification 1205 Olivier Pinet, Etienne Vernaz, Christian Ladirat, and Stéphane Gin 1 Introduction 1205 2 History of Nuclear Waste Vitrification 1205 3 Nuclear Glasses 1206 4 Long-Term Stability of Nuclear Glass 1209 5 Industrial Implementation of Nuclear Waste Vitrification 1213 6 Perspectives 1217 9.12 The International Commission on Glass (ICG) 1219 John M. Parker 1 Introduction: Origins of ICG and Founding Members 1219 2 ICG as an Organization 1219 3 The ICG Committees 1222 4 Public Activities 1223 5 Perspectives 1228 Section X.

History

1231

10.1 Obsidian in Prehistory 1237 Robert H. Tykot 1 Introduction 1237 2 Geological Formation, Properties, and Sources 1238 3 Obsidian Use in Prehistory 1238 4 Obsidian Studies 1240 5 Provenance Analysis Methods 1241 6 The Issue of Obsidian Sources: The European Region 1243 7 Obsidian Artifacts Studied in the Western Mediterranean 1243 8 Obsidian Trade and Socioeconomic Systems 1245 9 Conclusions and Closing Perspectives 1247 10.2 Ancient Glass, Late Bronze Age 1249 Andrew J. Shortland and Patrick Degryse 1 Introduction 1249 2 Early Glass: From Faience to Glassmaking 1250 3 Chemical Composition: The Analytical Standpoint 4 Material Sources 1254 5 The Issue of Provenance 1255 6 The Isotopic Clues 1256 7 Perspectives 1258

1251

10.3 Roman Glass 1261 Ian C. Freestone 1 Introduction 1261 2 Glass Synthesis 1261 3 Provenance and Location of Glassmaking 1263 4 Color Generation and Control 1265 5 Secondary Production and Consumption 1267 6 Recycling, Shifts in Production, and Decline 1269 7 Perspectives 1270 10.4 Glass and the Philosophy of Matter in Antiquity Marco Beretta 1 Introduction 1273 2 Near Eastern Views on Glass 1273

1273

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3 4 5 6

The Glass of the Greek Philosophers Glass and Alchemy 1276 The Byzantine Connection 1280 Perspectives 1282

1275

10.5 Ancient Glassworking 1285 E. Marianne Stern 1 Introduction 1285 2 Basic Features of Glass Shaping 1286 3 Early Shaping Methods 1288 4 The Slow Blowing Revolution 1295 5 Decoration 1297 6 Special Techniques 1299 7 Secondary Glassworking 1302 8 A Short Retrospective Overview 1304 9 Perspectives 1305 10.6 Glazes and Enamels 1309 Philippe Colomban 1 Introduction 1309 2 Preparation and Thermal Constraints 1311 3 Composition and Microstructure 1312 4 Coloration 1316 5 Enamels 1320 6 Glazes 1322 7 Perspectives 1324 10.7 Venetian Glass 1327 Marco Verità 1 Introduction 1327 2 Raw Materials and Glassmaking 1328 3 The Origins of Venetian Glass 1329 4 Venetian Renaissance Glass 1331 5 Façon de Venise Glass and Competition 1337 6 Other Italian Glassmaking Traditions 1337 7 Perspectives 1338 10.8 Stained Glass Windows 1341 John M. Parker and David Martlew 1 Introduction 1341 2 Making Glass Sheets 1342 3 Social Context 1346 4 Glass Decoration 1348 5 Leading 1352 6 Later Trends: Nineteenth to Twentieth Century 7 Conservation 1356 8 Perspectives 1357

1354

10.9 Furnaces and Glassmaking Processes: From Ancient Tradition to Modernity 1361 Marie-Hélène Chopinet and Pascal Richet 1 Introduction 1361 2 The Written Sources 1362 3 Furnaces 1364 4 Plate Glass 1372 5 Container Glass 1375 6 Perspectives 1381 10.10 Glass, the Wonder Maker of Science Pascal Richet 1 Introduction 1387

1387

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2 3 4 5 6

The Source of Optics 1388 The Enabler of Chemistry 1395 Hotness and Air Weight Measured 1399 From Electrostatics to Subatomic Physics 1404 Perspectives 1408

10.11 A History of Glass Science 1413 Pascal Richet 1 Introduction 1413 2 Glass: An Impossible Definition? 1414 3 The Origins 1415 4 The Early Modern Period (Sixteenth to Eighteenth Centuries) 5 The Chemical Revolution 1420 6 The Crystal Connection 1421 7 The Multiple Roots of Glass Science 1423 8 Perspectives 1433 10.12 Glass Museums 1441 Dedo von Kerssenbrock-Krosigk 1 Introduction 1441 2 The Invention of the Glass Museum 1442 3 Glass Museums 1443 4 Types of Glass Collections 1443 5 The Corning Museum of Glass 1450 6 Glass Museums: Purpose and Concerns 1451 7 Perspectives 1452 11.1 Postface – A Personal Retrospective C. Austen Angell Subject Index 1463 Name Index 1489

1457

1418

xxiii

List of Contributors Functions and affiliations at the time of publication of the Encyclopedia Abensour, Sylvie Analytical Chemistry Group Manager Expertise Department on Crystalline and Composite Materials, Saint-Gobain Research Paris 39 Quai Lucien Lefranc, 93300 Aubervilliers, France – 5.11: Durability of Commercial-type Glasses.

Almeida, Rui M. Catedrático, Departamento de Engenharia Química, CQE Instituto Superior Técnico Universidade de Lisboa Av. Rovisco Pais 1049-001 Lisboa, Portugal – 8.2: Sol-gel Processes and Products.

Angell, C. Austen Regent’s Professor, School of Molecular Sciences Arizona State University Tempe, AZ 85287-1604, USA – 11.1: Postface – A Personal Retrospective.

Bach, Thomas Head of Laboratory, Dorfner Analysenzentrum und Anlagenplanungsgesellschaft mbH (ANZAPLAN) Scharhof 1, 92242 Hirschau, Germany – 5.1: Chemical Analyses and Characterization of Glass.

Belyustin, Anatolii A. (deceased) Former Professor of Physical Chemistry, Chemistry Institute c/o Saint Petersburg State University Physical Chemistry Department, Saint Petersburg State University, Universitetskii prospect, 26, Petrodvorets 198504 Saint Petersburg, Russia – 5.8: The Glass Electrode and Electrode Properties of Glasses.

Beretta, Marco Professor of History of Science Dipartimento di Filosofia e Comunicazione Università di Bologna, via Zamboni 38, 40126 Bologna, Italy – 10.4: Glass and the Philosophy of Matter in Antiquity.

Blochowicz, Thomas Privatdozent, Institut für Festkörperphysik Technische Universität Darmstadt, Hochschulstraße 6-8 64289 Darmstadt, Germany – 8.6: Relaxation Processes in Molecular Liquids.

Bos, Freek Assistant Professor Concrete Structures Unit Structural Design, Department of the Built Environment, Eindhoven University of Technology (TU/e), PO Box 513, 5600 MB Eindhoven The Netherlands – 9.1: Structural Glass in Architecture.

Ballato, John, J. E. Sirrine Endowed Chair in Optical Fiber, and Professor Department of Materials Science and Engineering and the Center for Optical Materials Science and Engineering Technologies (COMSET) Clemson University, Clemson SC 29631, USA – 6.4: Optical Fibers.

Brauer, Delia S.

Bange, Klaus

Brunner, Samuel

Consultant, MK Consulting GmbH, Burgunderstr. 8, 55270 Jugenheim, Germany – 6.7: Modification Technologies of Glass Surfaces; 6.8: Thin-Film Technologies for Glass Surfaces.

Research Scientist, Laboratory for Building Energy Materials and Components, EMPA Überlandstrasse 129, 8600 Dübendorf Switzerland – 8.3: Silica Aerogels.

Bayuseno, Athanasius P.

Bureau, Bruno

Professor, Centre for the Waste Management Department of Mechanical Engineering Diponegoro University, Tembalang Campus Semarang 50275, Indonesia – 9.10: Immobilization of Municipal and Industrial Waste.

Professor, Université de Rennes I, Verres et Céramiques Institut des Sciences Chimiques, UMR-CNRS 6226 35700 Rennes, France – 6.5: Fluoride and Chalcogenide Glasses for Mid-infrared Optics.

Professor for Bioactive Glasses Otto Schott Institute of Materials Research Friedrich Schiller University Jena Fraunhoferstr. 6, 07743 Jena, Germany – 8.4: Bioactive Glasses.

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List of Contributors

Calas, Georges Professor, Institut de Mineralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université UMR CNRS 7590, Muséum National d’Histoire Naturelle, IRD, 4 Place Jussieu 75005 Paris, France – 6.2: The Color of Glass.

Ceola, Stefano Researcher, Stazione Sperimentale del Vetro Via Briati 10, 30141 Venice, Italy – 9.9: Glass Cullet: Sources, Uses, and Environmental Benefits.

Chopinet, Marie-Hélène Former Senior Research Engineer Saint-Gobain Research Paris, 90 rue Duhesme 75018 Paris, France – 5.11: Durability of Commercial-type Glasses; 10.9: Furnaces and Glassmaking Processes: From Ancient Tradition to Modernity.

Clare, Alix Professor, Kazuo Inamori School of Engineering Alfred University, Alfred, NY 14802, USA – 6.1: Optical Glasses. Cohen-Addad, Jean-Pierre (deceased) Former Professor, Laboratoire LiPhy Université J. Fourier, Grenoble 38402 Saint-Martin d’Hères, France – 8.7: Physics of Polymer Glasses.

Colomban, Philippe

de Campos, Cristina P., Visiting Professor Earth and Environmental Sciences Ludwig-Maximillians-Universität LMU Theresienstr. 41/III Munich 80333, Germany – 7.2: Geological Glasses.

Degryse, Patrick Professor, Department of Earth and Environmental Sciences – Geology, Center for Archaeological Sciences KU Leuven, Celestijnenlaan 200E Box 2408, BE-3001, Leuven Belgium and Faculty of Archaeology Universiteit Leiden, Leiden the Netherlands – 10.2: Ancient Glass Late Bronze Age.

de Koker, Nico Research Fellow, Department of Civil Engineering University of Stellenbosch, 7600, South Africa – 4.3: Diffusion in Oxide Glass-forming Systems.

de Ligny, Dominique Chair of Glass and Ceramics Department of Materials Science and Engineering Friedrich Alexander Universität Erlangen-Nürnberg Martensstr. 5, 91058 Erlangen, Germany – 3.6: Thermodynamic Properties of Oxide Glasses and Liquids.

Deubener, Joachim

Emeritus Research Director, CNRS Laboratory “From Molecule to Nano-object: Reactivity, Interaction & Spectroscopies,” Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France – 10.6: Glazes and Enamels.

Professor of Glass Science and Engineering Institute of Non-Metallic Materials Clausthal University of Technology 38678 Clausthal-Zellerfeld, Germany – 4.1: Viscosity of Glass-forming Melts; 9.4: Glass for Solar-energy Technologies.

Comte, Monique

Di Pierro, Simonpietro

Research Engineer, Advanced Materials Research Group, Corning European Technology Center Corning SAS, 77210 Avon, France – 7.11: Glass-Ceramics.

Director, Expertise Department on Crystalline and Composite Materials, Saint-Gobain Research Paris 39 Quai Lucien Lefranc 93300 Aubervilliers, France – 1.2: Raw Materials for Glass Making: Properties and Constraints.

Conradt, Reinhard Uniglass AC GmbH, Nizzaallee 75 52072 Aachen, Germany, President Deutsche Glastechnische Gesellschaft Former Professor of Glass and Ceramic Composites RWTH Aachen University, Aachen 52072, Germany – General Introduction; 1.1: Glass Production: An Overview; 1.3: Fusion of Glass; 9.8: Physics and Modeling of Glass Furnaces.

Cooper, Reid F. Professor, Department of Earth, Environmental and Planetary Sciences, Brown University, Box 1946, Providence RI 02912, USA – 5.6: Redox Thermodynamics and Kinetics in Silicate Melts and Glasses.

Cormier, Laurent Research Director, Institut de Mineralogie de Physique des Matériaux et de Cosmochimie Sorbonne Université, UMR CNRS 7590, Muséum National d’Histoire Naturelle, IRD, 4 Place Jussieu 75005 Paris, France – 6.2: The Color of Glass.

Duffy, John A. (deceased) Former Emeritus Professor of Chemistry University of Aberdeen, Old Aberdeen AB24 3UE Scotland, UK – 5.7: Optical Basicity: Theory and Application.

Dyon, Joël Designer and Project Manager Institut de Physique du Globe de Paris 1 rue Jussieu, 75005 Paris, France.

Favaro, Nicola Laboratory Director, Stazione Sperimentale del Vetro Via Briati 10, 30141 Venice, Italy – 9.9: Glass Cullet: Sources Uses, and Environmental Benefits.

Fokin, Vladimir M. Senior Research Fellow Vavilov State Optical Institute ul. Babushkina 36-1, 193 171 Saint Petersburg, Russia – 5.4: Nucleation, Growth, and Crystallization in Inorganic Glasses.

List of Contributors

Fotheringham, Ulrich

Guillou, Hervé

Senior Principal Scientist Central Research and Technology Development Schott AG, 55014 Mainz, Germany – 3.7: Structural Shear, and Stress Relaxation in Glass-forming Liquids.

Maître de conférences, CNRS Institut Néel and Université de Grenoble Alpes 38042 Grenoble, France – 3.2: Thermodynamics of Glasses.

Freestone, Ian, C. Professor, Institute of Archaeology, University College London 31–34 Gordon Square, London WC1H 0PY, UK – 10.3: Roman Glass.

Professor, Department of Physics Department of Polymer Science The University of Akron, Akron OH 44325, USA – 3.3: The Glass Transition and the Entropy Crisis.

Galoisy, Laurence

Gupta, Prabhat K.

Maître de conférences, Institut de Mineralogie de Physique des Matériaux et de Cosmochimie Sorbonne Université, UMR CNRS 7590 Muséum National d’Histoire Naturelle, IRD 4 Place Jussieu, 75005 Paris, France – 6.2: The Color of Glass.

Emeritus Professor, Department of Materials Science and Engineering The Ohio State University, Columbus OH 43235, USA – 2.7: Topological Constraint Theory of Inorganic Glasses.

Garden, Jean-Luc R&D Engineer, CNRS, Institut Néel and Université de Grenoble Alpes, F-38042 Grenoble, France – 3.2: Thermodynamics of Glasses.

Gujrati, Purushottam D.

Gy, René Department Manager, Thermomechanics & Modelling Saint-Gobain Research Paris, 39 Quai Lucien Lefranc 93302 Aubervilliers, France – 9.2: Tempered and Laminated Glazing for Cars.

Haas, Karl-Heinz

Research Director, CEA DEN/DTCD Marcoule 30207 Bagnols sur Cèze, France – 9.11: Nuclear Waste Vitrification.

Research Scientist, Fraunhofer-Institut für Silicatforschung, Neunerplatz 2, D-97082 Wuerzburg Germany – 8.9: Hybrid Inorganic–Organic Polymers.

Girard, Sylvain

Habasaki, Junko

Professor, Laboratoire Hubert Curien, Univ Lyon UJM Saint-Etienne, CNRS, IOGS, UMR 5516 18 rue du professuer Benoît Lauras 42000 Saint-Etienne, France – 3.13: Radiation Effects in Glass.

Assistant Professor, School of Materials and Chemical Technology, Tokyo Institute of Technology 4259 Nagatsuta-chi, Yokohama, Kanagawa 226-8502 Japan – 4.6: Atomistic Simulations of Transport Properties.

Gonçalves, M. Clara

Hampshire, Stuart

Professora auxiliar, Departamento de Engenharia Química, CQE, Instituto Superior Técnico Universidade de Lisboa Av. Rovisco Pais 1049-001 Lisboa, Portugal – 8.2: Sol-gel Processes and Products.

Emeritus Professor of Materials Science Materials and Surface Science Institute University of Limerick, Limerick V94 T19PX, Ireland – 7.8: Oxynitride Glasses.

Hand, Russell J.

Gouillart, Emmanuelle

Professor of Glass Science & Engineering Department of Materials Science & Engineering University of Sheffield, Sir Robert Hadfield Building Mappin Street, Sheffield S1 3JD, UK – 3.11: Mechanical Properties of Inorganic Glasses.

Gin, Stéphane

Director, CNRS-Saint-Gobain Laboratory of Glass Surface and Interfaces, Saint-Gobain Research Paris 39 quai Lucien Lefranc, 93303 Aubervilliers cédex, France – 4.4: Chemical Diffusion in Multicomponent Glass-forming Systems.

Greaves, Neville G. (deceased) Distinguished Research Fellow Department of Materials Science and Metallurgy University of Cambridge, Cambridge CB3 0FS, UK – 2.5: The Extended Structure of Glass.

Guadagnino, Emanuel European Pharmacopeia Expert, Italian Delegate via Paolo Erizzo 20, Venezia (Ve) 30126, Italy – 7.7: Glass for Phamaceutical Use.

Hannon, Alex C. Research Scientist, ISIS Facility R3, Rutherford Appleton Laboratory Chilton, Didcot, Oxon OX11 0QX, UK – 2.1: Basic Concepts of Network Glass Structure.

Haus, Reiner Managing Director, Dorfner Analysenzentrum und Anlagenplanungsgesellschaft mbH (ANZAPLAN), Scharhof 1, 92242 Hirschau, Germany – 5.1: Chemical Analyses and Characterization of Glass.

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Hayashi, Akitoshi

Höland, Wolfram

Professor, Department of Applied Chemistry Faculty of Engineering, Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai Osaka 599-8531, Japan – 9.5: Sulfide Glass Electrolytes for All-solid-state Batteries.

Former Head of Fundamental Research on Glass and Ceramics, Ivoclar Vivadent AG, R&D, Bendererstr. 2, 9494 Schaan, Principality of Liechtenstein – 8.5: Dental Glass Ceramics.

Hehlen, Bernard

Professor, International Institute of Green Materials, Josai International University, Togane 283-8555, Japan; School of Materials Science and Engineering Tianjin University, Tianjin 300072, China; Department of Physics, King Abdulaziz University, Jeddah 22254, Saudi Arabia; National University of Science and Technology (MISIS), Leninsky prosp. 4 Moscow 119049, Russia – 7.10: Bulk Metallic Glasses.

Professor, Laboratoire Charles Coulomb, UMR 5221 CNRS, Université de Montpellier, 34095 Montpellier, France – 3.4: Atomic Vibrations in Glasses.

Hellmann, Roland Senior Scientist, ISTerre- Geochemistry Group CNRS, Université Grenoble Alpes 38058 Grenoble Cedex 9, France – 5.12: Mechanisms of Glass Corrosion by Aqueous Solutions; 7.3: Corrosion of Natural Glasses in Seawater.

Helsch, Gundula Senior Scientist, Institute of Non-Metallic Materials, Clausthal University of Technology Zehnterstraße 2a, 38678 Clausthal-Zellerfeld, Germany – 9.4: Glass for Solar-energy Technologies.

Inoue, Akihisa

Ispas, Simona Maître de conférences, Laboratoire Charles Coulomb Université de Montpellier, CNRS, 34095 Montpellier France – 2.9: First-principles Simulations of Glass Formers.

Ivanovskaya, Irina, S.

Professor, Department of Earth Sciences, University of Toronto 22 Russell St., Toronto, Ontario M5S 3B1, Canada – 2.2: Structural Probes of Glass.

Former Senior Researcher, Chemistry Institute c/o Saint Petersburg State University Physical Chemistry Department, Saint Petersburg State University Universitetskii prospect, 26, Petrodvorets 198504 Saint Petersburg, Russia – 5.8: The Glass Electrode and Electrode Properties of Glasses.

Heo, Jong

Jatzwauk, Christoph

Professor, Department of Materials Science and Engineering Pohang University of Science and Technology (POSTECH), Gyeongbuk 790784, Republic of Korea – 6.6: Optoelectronics: Active Chalcogenide Glasses.

Managing Director F.I.C. Germany GmbH Eichenstraße 51, 92637 Weiden, Germany – 9.7: Design and Operation of Glass Furnaces.

Henderson, Grant S.

Hess, Kai-Uwe Academic Staff, Department for Earth and Environmental Science, Ludwig-Maximilians Universität München, Theresienstr. 41/III, 80333 Munich, Germany – 7.2: Geological Glasses.

Heuss-Aßbichler, Soraya Professor, Section of Mineralogy Petrology and Geochemistry Department for Earth and Environmental Science Ludwig-Maximilians Universität München Theresienstr. 41/III, 80333 Munich, Germany – 9.10: Immobilization of Municipal and Industrial Waste.

Höche, Thomas

Jones, Julian R. Professor of Biomaterials, Department of Materials, Imperial College London, Exhibition Road, London SW7 2AZ, UK – 8.4: Bioactive Glasses.

Kamihori, Toru Deputy General Manager, Director, Glass Process Division, AGC Inc., Innovative Technology Laboratories Technology General Division, 1-1 Suehiro-cho Tsurumi-ku, Yokohama-shi Kanagawa 230-0045, Japan – 1.4: Primary Fabrication of Flat Glass.

Karlsson, K. Stefan R. Senior Scientist, RISE Glass (Former Glafo) Division of Built Environment, RISE Research Institutes of Sweden, SE-351 96 Växjö, Sweden – 3.12: Strengthening of Oxide Glasses.

Head of the Optical Materials and Technologies Department, Fraunhofer Institute for Microstructure of Materials and Systems IMWS Walter-Huelse-Strasse 1, D-06120 Halle (Saale), Germany – 2.3: Microstructure Analysis of Glasses and Glass Ceramics.

Kob, Walter

Hofmeister, Anne

Head, Laboratory for Building Energy Materials and Components, EMPA, Überlandstrasse 129 8600 Dübendorf, Switzerland – 8.3: Silica Aerogels.

Research Professor, Department of Earth and Planetary Sciences Washington University, St. Louis, MO 63130, USA – 4.5: Thermal Diffusivity and Conductivity of Glasses and Melts.

Professor, Laboratoire Charles Coulomb, Université de Montpellier CNRS, 34095 Montpellier, France – 2.9: First-principles Simulations of Glass Formers.

Koebel, Mathias M.

List of Contributors

Ladirat, Christian

Machon, Denis

Deputy Manager of Waste Containment and Vitrification Service, Commissariat à l’Énergie Atomique DEN/DTCD Marcoule, 30207 Bagnols sur Cèze, France – 9.11: Nuclear Waste Vitrification.

Maître de conférences, Institut Lumière Matière Université Claude Bernard Lyon 1, 10 rue Ada Byron 69622 Villeurbanne Cedex, France – 3.10: Pressure-Induced Amorphization.

Lehuédé, Patrice

McMillan, Paul F.

Free Researcher, Centre de Recherche et Restauration des Musées de France, 14, quai François Mitterrand 75001 Paris, France – 5.11: Durability of Commercial-type Glasses.

Sir William Ramsay Professor of Chemistry Christopher Ingold Laboratory, Department of Chemistry, University College London, 20 Gordon Street London WC1H 0AJ, UK – 3.9: Polyamorphism and Liquid–Liquid Phase Transitions; 3.10: Pressure-Induced Amorphization.

Li, Hong Senior Scientist, Nippon Electric Glass US, Fiber Glass Science & Technology, PPG Industries, 940 Washburn Switch Rd., Shelby, NC 28150-9089, USA – 1.6: Continuous Glass Fibers for Reinforcement.

Libourel, Guy Professor, Université Côte d’Azur, Observatoire de la Côte d’Azur CNRS, UMR 7293 Lagrange, Boulevard de l’Observatoire CS34229, 06304 Nice Cedex 4, France – 7.1: Extraterrestrial Glasses.

Livage, Jacques Emeritus Professor, Collège de France and French Academy of Sciences Laboratoire de Chimie de la Matière Condensée de Paris CNRS, UMR-7574, 4 place Jussieu, 75252 Paris Cedex 05 France – 8.1: Biogenic Silica Glasses.

Lopez, Pascal Jean Research Director and Director of the Observatoire HommesMilieux Port Caraïbe, Biologie des Organismes Aquatiques et Écosystèmes (BOREA), UMR CNRS 7208 Muséum National d’Histoire Naturelle, Sorbonne Université; IRD207 Université Caen Normandie; and Université des Antilles, 75005 Paris, France – 8.1: Biogenic Silica Glasses.

Maeda, Kei Fellow, Asahi Glass Company Inc. Research Center, 1150 Hazawa-cho, Kanagawaku Yokohama 221-8755, Japan – 6.10: Screens and Displays.

Malfait, Wim J. Group Leader Superinsulation Materials, Laboratory for Building Energy Materials and Components, EMPA Überlandstrasse 129, 8600 Dübendorf, Switzerland – 8.3: Silica Aerogels.

Martlew, David (deceased) Glass Technologist, 15 Cecil Drive, Eccleston, St Helens, UK – 10.8: Stained Glass Windows.

Mills, Kenneth C. (deceased) Former Professor, Department of Materials Imperial College, London SW7 2AZ, England, UK – 7.4: Metallurgical Slags.

Montigaud, Hervé R&D Engineer, Associate Researcher Surface du Verre et Interfaces Saint-Gobain Research Paris, UMR 125 CNRS 39 Quai Lucien Lefranc, 93303 Aubervilliers Cedex, France – 5.11: Durability of Commercial-type Glasses.

Louter, Christian

Muijsenberg, Erik

Professor of Building Construction Institute of Building Construction Faculty of Civil Engineering Technische Universität Dresden 01062 Dresden, Germany – 9.1: Structural Glass in Architecture.

Vice-president, Glass Service a.s Rokytnice 60, 75501 Vsetin, Czech Republic – 9.8: Physics and Modeling of Glass Furnaces.

Louzguine-Luzgin, Dmitri V. Professor, Principal Investigator, Laboratory Director, WPI Advanced Institute for Materials Research and AIST-Tohoku Mathematics for Advanced Materials – Open Innovation Laboratory, Tohoku University Aoba-Ku, Sendai 980-8577, Japan – 7.10: Bulk Metallic Glasses.

Lucas, Jacques Emeritus Professor, French Academy of Sciences, Université de Rennes I Verres et Céramiques, Institut des Sciences Chimiques UMR-CNRS 6226, 35700 Rennes, France – 6.5: Fluoride and Chalcogenide Glasses for Mid-infrared Optics.

Mysen, Bjorn Senior Staff Member, Geophysical Laboratory Carnegie Institution for Science, 5251 Broad Brach Rd Washington, DC 20015, USA – 2.6: Structure of Chemically Complex Silicate Systems; 5.5: Solubility of Volatiles.

Ni, Huaiwei Professor of Geochemistry, CAS Key Laboratory of Crust-Mantle Materials and Environments School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China – 4.3: Diffusion in Oxide Glass-forming Systems.

Ojovan, Michael I. Professor, Department of Materials, Imperial College London London SW7 2AZ, UK – 3.1: Glass Formation.

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List of Contributors

Oktik, Sener

Podor, Renaud

Chief Technology Officer, Türkiye Şişe ve Cam Fabrikaları A.Ş., Science and Technology Center Cumhuriyet Mah. Şişecam Yolu Sok. No:2 41400 Gebze-Kocaeli, Turkey – 6.7: Modification Technologies of Glass Surfaces; 6.8: Thin-Film Technologies for Glass Surfaces.

Research Engineer CNRS, Institut de Chimie Séparative de Marcoule, UMR 5257; Bât. 426, BP 17171, 30207 Bagnols sur Cèze Cédex, France – 5.10: Glass/Metal Interactions.

Ollier, Nadège Research Scientist, Laboratoire des Solides Irradiés Ecole polytechnique, CNRS, CEA, 91128 Palaiseau Cedex, France – 3.13: Radiation Effects in Glass.

Pomeroy, Michael J. Professor, Materials Science and Technology, Materials and Surface Science Institute, University of Limerick Limerick V94 T19PX, Ireland – 7.7: Oxynitride Glasses.

Prescott, Patrick J. Ottonello, Giulio Former Chair of Geochemistry, Laboratorio di Geochimica at DISTAV, University of Genoa Corso Europa 26: 16132 Genova, Italy – 5.3: Thermodynamic Models of Oxide Melts.

Panteix, Pierre-Jean Research Engineer, CNRS, Institut Jean Lamour UMR 7198; Campus ARTEM, 2 allée André Guinier BP 50840, 54011 Nancy Cedex, France – 5.10: Glass/Metal Interactions.

Parker, John M. MA (Cantab), FSGT, FIMMM, CEng Professor Emeritus Department of Materials Science and Engineering Sheffield University Sir Robert Hadfield Building, Mappin Street Sheffield S10 5TX, UK – 9.12: The International Commission on Glass (ICG); 10.8: Stained Glass Windows.

Parsons, Andrew James Senior Research Fellow, Faculty of Engineering University of Nottingham, University Park Nottingham NG7 2RD, UK – 7.9: Phosphate Glasses.

Patzig, Christian Senior Research Scientist, Fraunhofer Institute for Microstructure of Materials and Systems IMWS Walter-Huelse-Strasse 1, D-06120 Halle (Saale), Germany – 2.3: Microstructure Analysis of Glasses and Glass Ceramics.

Senior Engineer, Owens Corning Science & Technology Center, Granville, OH 43023, USA – 1.7: Simulation in Glass Processes.

Prinz, Sebastian Business Development Director, Dorfner Analysenzentrum und Anlagenplanungsgesellschaft mbH (ANZAPLAN), Scharhof 1, 92242 Hirschau, Germany – 5.1: Chemical Analyses and Characterization of Glass.

Purnode, Bruno Senior Research Associate Owens Corning Science & Technology Center Granville, OH 43023, USA – 1.7: Simulation in Glass Processes.

Rapin, Christophe Professor, Université de Lorraine Institut Jean Lamour UMR 7198 Campus ARTEM, 2 Allée André Guinier, BP 50840 54011 Nancy Cedex, France – 5.10: Glass/Metal Interactions.

Richet, Pascal Senior Physicist, Institut de Physique du Globe de Paris 1 rue Jussieu, 75005 Paris, France – Preface; General and Section Introductions; 3.6: Thermodynamic Properties of Oxide Glasses and Liquids; 10.9: Furnaces and Glassmaking Processes: from Ancient Tradition to Modernity; 10.10: Glass, the Wonder Maker of Science; 10.11: A History of Glass Science; Indexes.

Roggendorf, Hans

Maître de conférences, Université de Lorraine Institut Jean Lamour UMR 7198, Campus ARTEM, 2 Allée André Guinier, BP 50840, 54011 Nancy Cedex, France – 5.10: Glass/Metal Interactions.

Professor, Nonmetallic-inorganic Materials, Martin-LutherUniversität Halle-Wittenberg, Institute of Physics D-06099 Halle (Saale), Von-Danckelmann-Platz 3 Germany – 7.5: Water Glass.

Peuget, Sylvain

Roos, Christian

Senior Research Scientist, Commissariat à l’Énergie Atomique, Nuclear Energy Division, BP 17171, 30207 Bagnols-sur-Ceze Cedex, France – 3.13: Radiation Effects in Glass.

Professor, Department of Mineral Engineering, RWTH Aachen Nizzaallee 75, Aachen, Germany – 1.5: Fabrication of Glass Containers.

Roskosz, Mathieu

Pinet, Olivier

Professor, Cosmochimie, IMPMC, CNRS UMR 7590, Muséum National d’Histoire Naturelle, 57 rue Cuvier, 75231 Paris Cedex 05, France – 4.4: Chemical Diffusion in Multicomponent Glass-forming Systems.

Petitjean, Carine

Head of Research Laboratory for the Development of Conditioning Matrices, Commissariat à l’Énergie Atomique, DEN/DTCD Marcoule, 30207 Bagnols sur Cèze, France – 9.11: Nuclear Waste Vitrification.

List of Contributors

Rössler, Ernst A.

Souquet, Jean-Louis

Emeritus Professor, Experimentalphysik II Universität Bayreuth, 95441 Bayreuth, Germany – 8.6: Relaxation Processes in Molecular Liquids.

Emeritus Professor, Laboratoire d’électrochimie et de physicochimie des matériaux et des interfaces PHELMA, BP 75, 38402 Saint Martin d’Hères Cedex France – 4.2: Ionic and Electronic Transport.

RufflÉ, Benoît Professor, Laboratoire Charles Coulomb, UMR 5221 CNRS Université de Montpellier, 34095 Montpellier, France – 3.4: Atomic Vibrations in Glasses.

Rüssel, Christian Professor, Otto-Schott-Institut, Jena University Fraunhoferstr. 6, 07743 Jena, Germany – 5.9: Electrochemistry of Oxide Melts.

Savaëte, Bernard Founder and President, BJS.Différences 33 Rue Jules Ferry, 92400 Courbevoie, France – 9.6. The World of the Flat-glass Industry: Key Milestones, Current Status and Future Trends.

Schmelzer, Jürn W.P. Leading Research Scientist (retired), Institut für Physik Universität Rostock, Wismarsche Str. 43-45 18057 Rostock, Germany – 5.4: Nucleation Growth, and Crystallization in Inorganic Glasses.

Schmucker, Éric Research Scientist, Commissariat à l’Énergie Atomique, Université Paris-Saclay, 91191 Gif-sur-Yvette, France – 5.10: Glass/Metal Interactions.

Schottner, Gerhard Research Scientist, Fraunhofer-Institut für Silicatforschung, Neunerplatz 2, D-97082 Wuerzburg Germany – 8.9: Hybrid Inorganic–Organic Polymers.

Schweiger, Marcel Director, Inorganic Chemistry R&D, Ivoclar Vivadent AG, R&D, Bendererstr. 2, 9494 Schaan, Principality of Liechtenstein – 8.5: Dental Glass Ceramics.

Shortland, Andrew J. FSA FGS, Professor of Archaeological Science, Director Cranfield Forensic Institute, Director of Research Cranfield Defence and Security Cranfield University Wilts SN6 8LA, UK – 10.2: Ancient Glass Late Bronze Age.

Sökmen, Ilkay Surface Technologies Manager, Türkiye Şişe ve Cam Fabrikaları A. Ş., Science and Technology Center Cumhuriyet Mah. Şişecam Yolu Sok. No:2 41400 Gebze-Kocaeli, Turkey – 6.7: Modification Technologies of Glass Surfaces; 6.8: Thin-Film Technologies for Glass Surfaces.

Solvang, Mette Chief Engineer, Group Research & Development Rockwool International A/S, 2640 Hedehusene Denmark – 9.3: Stone and Glass Wool.

Stebbins, Jonathan F. Professor, Department of Geological Sciences Stanford University, Stanford, CA 94305-2115, USA – 2.4: Short-range Structure and Order in Oxide Glasses.

Stern, E. Marianne Independent Researcher, Nieuwe Passeerdersstr. 186 1016XP Amsterdam, The Netherlands – 10.5: Ancient Glassworking.

Takada, Akira Visiting Professor, University College London Gower Street, London W1E 6BT, UK, and Ehime University, 10-13 Dogo-Himata Matsuyama, Ehime 790-8577 Japan. Former Junior Fellow Research Center, AGC Inc., 1150 Hazawa-cho Yokohama 221-8755, Japan – General Introduction; 2.8: Atomistic Simulations of Glass Structure and Properties.

Tatsumisago, Masahiro Professor, Department of Applied Chemistry, Faculty of Engineering, Osaka Prefecture University 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan – 9.5: Sulfide Glass Electrolytes for All-solid-state Batteries.

Toplis, Michael J. Research Director, CNRS, Institut de recherche en astrophysique et planétologie, Observatoire Midi Pyrénées, Université de Toulouse, 31400 Toulouse, France – 3.5: Density of Amorphous Oxides.

Tournier, Robert F. Emeritus Research Director, Institute of Engineering Institut Néel and CNRS, Grenoble INP 38042 Grenoble, Université de Grenoble Alpes, France – 3.14: Amorphous Ices.

Tykot, Robert H. Past President, Society for Archaeological Sciences Professor, Department of Anthropology Director, Laboratory for Archaeological Science & Technology University of South Florida, Tampa, FL 33620, USA – 10.1: Obsidian in Prehistory.

Veksler, Ilya Research Scientist, GFZ German Research Centre for Geosciences, Telegrafenberg, 14473 Postdam, Germany – 5.2: Phase Equilibria and Phase Diagrams in Oxide Systems.

Verità, Marco LAMA Laboratory, Università IUAV di Venezia 30135 Venice, Italy and Retired Researcher Stazione Sperimentale del Vetro, Murano, Venice Castello 3371, 30122 Venice, Italy – 10.7: Venetian Glass.

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List of Contributors

Vernaz, Étienne

Wondraczek, Lothar

Former Research Director, Commissariat à l’Énergie Atomique, DEN/DTCD Marcoule 30207 Bagnols sur Cèze, France – 9.11: Nuclear Waste Vitrification.

Professor, Otto Schott Institute of Materials Research University of Jena, Fraunhoferstrasse 6, 07743 Jena Germany – 3.12: Strengthening of Oxide Glasses; 6.3: Photoluminescence in Glasses.

Vilasi, Michel Professor, Université de Lorraine, Institut Jean Lamour UMR 7198 Campus ARTEM, 2 Allée André Guinier BP 50840, 54011 Nancy Cedex, France – 5.10: Glass/Metal Interactions.

Vogel, Michael Professor, Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstraße 6-8, 64289 Darmstadt Germany – 8.6: Relaxation Processes in Molecular Liquids.

von Kerssenbrock-Krosigk, Dedo Head, Glass Museum Hentrich, Kunstpalast Ehrenhof 4-5, 40479 Düsseldorf, Germany – 10.12: Glass Museums.

Watson, James C. Former Associate Director Nippon Electric Glass US, Fiber Glass Science & Technology, PPG Industries, Inc., 940 Washburn Switch Rd., Shelby, NC 28150-9089, USA – 1.6: Continuous Glass Fibers for Reinforcement.

Xu, Kai Professor, State Key Laboratory of Silicate Materials for Architectures (SMART) Wuhan University of Technology Wuhan 430070, China – 6.6: Optoelectronics: Active Chalcogenide Glasses.

Yamamoto, Shigeru Executive Technical Adviser, Nippon Electric Glass 7-1, Seiran 2-Chome, Otsu, Shiga 520-8639, Japan – 6.9: Glass for Lighting.

Yamazaki, Hiroki Group General Manager, Nippon Electric Glass 7-1, Seiran 2-Chome, Otsu, Shiga 520-8639, Japan – 6.9: Glass for Lighting.

Youngman, Randall E. Research Scientist, Science & Technology Division Corning Incorporated, Corning, NY 14831, USA – 7.6: Borosilicate Glasses.

Weichold, Oliver

Yue, Yuanzheng

Professor, Engineered Polymer Composites, Institute of Building Materials Science, RWTH Aachen University Schinkelstrasse 3, 52062 Aachen, Germany – 8.8: Introduction to Polymer Chemistry.

Professor, Department of Chemistry and Bioscience Aalborg University, 9220 Aalborg, Denmark – 3.8. Hyperquenched Glasses: Relaxation and Properties; 9.3: Stone and Glass Wool.

Wernery, Jannis

Zanotto, Edgar D.

Group Leader Building Integration Laboratory for Building Energy Materials and Components, EMPA, Überlandstrasse 129, 8600 Dübendorf, Switzerland – 8.3: Silica Aerogels.

Professor of Materials Science, Center for Research Technology, and Education in Vitreous Materials (CeRTEV), Department of Materials Engineering Federal University of São Carlos, 13.565-905 São Carlos, SP, Brazil –5.4: Nucleation Growth, and Crystallization in Inorganic Glasses.

Whittington, Alan Professor, Department of Geological Sciences The University of Texas at San Antonio One UTSA Circle, San Antonio, TX 78249, USA – 4.5: Thermal Diffusivity and Conductivity of Glasses and Melts.

Wilding, Martin C. Research Fellow, University of Manchester at Harwell Harwell Science and Innovation Campus Didcot, Oxfordshire OX11 0DE, UK – 3.9: Polyamorphism and Liquid–Liquid Phase Transitions; 3.10: Pressure-Induced Amorphization.

Zhao, Shanyu Research Scientist, Laboratory for Building Energy Materials and Components, EMPA Überlandstrasse 129, 8600 Dübendorf, Switzerland – 8.3: Silica Aerogels.

Zuccato, Daniele Senior Expert Quality, Pharmaceutical Systems Schott AG, Hattenbergstraße 10, 55122 Mainz, Germany – 7.7: Glass for Phamaceutical Use.

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When art meets glassmaking: the visit of the Duchess of Berry (1798–1870) in 1824 to the plate-glass factory of the Royal Manufacture of Saint-Gobain as depicted by Édouard Pingret (1788–1869). The stifling heat, the noise of the furnaces, and the danger for the workers of the molten glass poured from the pot and spread with the steel roller on the large table (Chapter 10.9) have all vanished. Only the theatrical aspect of the scene remains, highlighted by the tall curtain, the duchess’s light-colored dress echoing the worker’s white smocks, and the children watching the show from the balcony. Source: Photo courtesy Saint-Gobain Archives.

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The Encyclopedia has been designed to satisfy the needs and curiosity of a broad audience interested in the nature, properties, fabrication, and history of glass and looking for consistent, comprehensive, and up-to-date information in a single book. More than 100 chapters involving even more glass experts have been written in a perspective that combines the various aspects of this unique material, be they scientific, technological, industrial, historical, or cultural. Whether coming from academia or industry, the authors have in common a long practice of glass. Their goal is to be informative without being pedantic, to be concrete without being boring, and to give a balanced overview of the field – in a word, to allow a large readership to understand both the amazing properties of the vitreous state and its pecularities compared with those of other states of matter. Excluding the socalled spin glasses and other kinds of disordered physical systems, the Encyclopedia restricts itself to what is now termed structural glass. In all chapters, the authors discuss glass from a materials-science standpoint, but their purpose is not to review in any detail the latest advances of interest to specialists only. Rather, in the form of scholarly introductions, it is to present every topic at a uniform level and in a self-consistent manner. In this way, the main points will be grasped and key information of fundamental or practical use will be made available. The neophyte reader will then be able to consult the specialized literature and, in particular, the select bibliography appended to each chapter. This approach does not imply that only elementary features are presented, but that concepts are appropriately introduced and any technical information clearly explained so as to avoid the common defect underlined in 1911 by the astronomer Percival Lowell (1855–1916) who emphasized in Mars and its Canals that “nothing in any branch of science is so little known as its articulation, — how the skeleton of it is put together, and what may be the mode of attachment of its muscles.” Whereas a very few chapters give a flavor of current technicalities involved in glass research, newly investigated topics are also considered with the goal of ensuring that the Encyclopedia remains a useful reference over an extended period of time. Although those views that are at this moment very speculative are generally not discussed at length, they may be stated in the final Perspectives of the chapters. Given the diversity of topics treated, the name of Encyclopedia (Kuklos paideia, cycle of enlightenments, in Greek) is particularly appropriate. The surprising fact is that such a reference work was not existing at all for glass, in general, even though more than hundreds of thousands of encyclopedias have now been devoted to any topic worth of attention, including glass art in particular. The

Encyclopedia consists of 10 sections preceded by a general introduction and concluded by a postface. It begins with glassmaking and continues with structural, physical, and chemical properties. The stage is then set to turn to issues pertaining to light, to the main inorganic glass families, to organically related glasses, to environmental and other industrial issues, and, finally, to the main facets of the rich glass history. Even in more than 100 chapters, it has not been possible to deal with every important topic relevant to glass. A few more chapters would have been welcomed, but their advantages would not have outweighted the inconvenience of a longer publication time, especially for the Encyclopedia contributors. Each section is preceded by a short introduction summarizing in a few sentences the contents of its chapters for helping readers to decide which ones fit their own interest best. Another purpose of these introductions is to show that, from the first to the last, the chapters are telling a consistent story. Although efforts have been made to avoid overlap, some limited duplication was inevitable to make sure that most contributions could be read independently of the others. Of course, boundaries between chapters or sections are not always clearcut, so that some arbitrariness has been involved in their delineation. And whereas the scientific and technology contents of the chapters will probably speak for themselves, it might be useful to note that historical aspects are dealt with not only in the last section but also elsewhere each time they can help to open deeper perspectives. As for the Culture included in the title of the Encyclopedia, it is explicitly treated only in the very last chapter but pervades a great many others, for example, in the history section where beautiful pieces of art are in particular reproduced. At the end of this endeavor, it is now a pleasure to acknowledge (i) the encouragement initially provided by R. Conradt, N.G. Greaves, J. Livage, J. Lucas, B. Mysen, A. Takada, and Y. Yue when the project took shape; (ii) the warm welcome this project received through G. Geiger and A. Lekhwani when submitted to the American Ceramic Society and John Wiley & Sons; (iii) the invaluable help then brought all the way by Reinhard Conradt and Akira Takada through their constant advice, support, friendship, and careful reviewing work; (iv) the great many graphics and pictures neatly prepared by Joël Dyon to highlight the matter presented in numerous chapters; (v) the efforts of 151 authors working in 23 countries who participated in this ambitious endeavor and went responsively throughout an editorial process aimed at ensuring an overall homogeneity of style and content, and incorporated in their texts the relevant historical and cultural aspects evoked by the Encyclopedia title; (vi) the thoughtful comments and apt observations provided

Preface

by nearly 200 reviewers whose names are included at the beginning of every chapter to recognize publicly their contributions; (vii) the original pictures or help in different matters generously provided by colleagues, friends, and institutions whose names are mentioned at the relevant places; (viii) the Humbold Stifftung, the Ludwig-Maximilans-Universität, and Donald Dingwell for the fruitful work done in Munich; (ix) the so many things about glass or high-temperature techniques and processes discussed over the years with T. Atake, J.-L. Bernard, Y. Bottinga, R. Conradt, K.-U. Hess, R. Kerner, B. Mysen, G. Ottonello, J.-P. Petitet, J. Roux, A. Sipp, J.F. Stebbins, A. Takada, C. Téqui, and other colleagues too numerous to be mentioned; (x) the Table of ion data compiled by J.F. Stebbins, the help provided at various stages of this study by É. Fareau, B. Gasparyan, K.U. Hess, A. Hofmeister, K. Meliksetian, B. Mysen, and M. Wolf as well as thoughtful comments by J.M. Parker and R.F. Tournier on the section introductions; (xi) and finally Michael Leventhal who oversaw the project at Wiley, Stefanie Volk for copy editing and Viniprammia Premkumar for smooth and responsive production of the book. The Encyclopedia is dedicated to them and to all people whose efforts throughout the ages made glass the astonishing, ubiquitous material it has become.

Select Additional Reading The Vitreous State Bach, H. and Krause, D. (eds.) (1992–2020). Schott Series on Glass and Ceramics, 7 vols. Berlin: Springer. Binder, K. and Kob, W. (2011). Glassy Materials and Disordered Solids, 2nd ed. Singapore: World Scientific. Blanshard, J.M.V. and Lillford, P.J. (1994). Glassy Sate in Food. Loughborough: Nottingham University Press. Donth, E. (2001). The Glass Transition. Berlin: Springer. Doremus, R.H. (1994). Glass Science, 2e. New York: Wiley. Gutzow, I. and Schmelzer, J. (2013). The Vitreous State: Thermodynamics, Structure, Rheology, Crystallization. Heidelberg: Springer. Kerner, R. (2006). Models of Agglomeration and Glass Transition. London: Imperial College Press. Leuzzi, L. and Nieuwenhuizen, L. (2008). Thermodynamics of the Glassy State. New York: Taylor & Francis. Mackenzie, J.D. (ed.) (1960–1964). Modern Aspects of the Vitreous State, 3 vols. London: Butterworth. Nemilov, S.V. (1995). Thermodynamic and Kinetic Aspects of the Vitreous State. Boca Raton, FL: CRC Press. Rawson, H. (1967). Inorganic Glass Systems. London: Academic Press. Scholze, H. (1991). Glass. Nature, Structure, and Properties. New York: Springer.

Shelby, J.E. (1997). Introduction to Glass Science and Technology. Cambridge: Royal Society of Chemistry. Simmons, C.J. and El-Bayoumi, O.H. (1993). Experimental Techniques of Glass Science. Westerville, OH: American Ceramic Society. Varshneya, A. (2014). Fundamentals of Inorganic Glasses. Sheffield: Society of Glass Technology. Zarzycki, J. (ed.) (1991). Glasses and Amorphous Materials. Materials Science and Technology. Weinheim: VCH. Zarzycki, J. (1991). Glasses and the Vitreous State. Cambridge: Cambridge University Press.

Glass Systems and Properties Affatigato, M. (ed.) (2014). Modern Glass Characterisation. Hoboken, NJ: Wiley. Bange, K., Durán, A., and Parker, J.M. (eds.) (2014). Making Glass Better: ICG Roadmaps of Glass R&D with a 25-Year Horizon. Madrid: Cyan. Cable, M. and Parker, J.M. (1992). High-Performance Glasses. Glasgow: Blackie. Carroll, M.R. and Holloway, J.R. (eds.) (1994). Volatiles in Magmas. Reviews in Mineralogy, 30. Washington, DC: Mineralogical Society of America. Cowie, J.M.G. and Arrighi, V. (2008). Polymers: Chemistry and Physics of Modern Materials, 3e. Boca Raton, FL: CRC Press. Ebewele, R.O. (2000). Polymer Science and Technology. Boca Raton, FL: CRC Press. Louzguine-Luzgin, D.V. (2018). Metallic Glasses and Their Composites. Materials Research Forum LLC: Millersville, PA. Musgraves, J.D., Hu, J., and Calvez, L. (2019). Springer Handbook of Glass. Berlin: Springer. Mysen, B.O. and Richet, P. (2018). Silicate Glasses and Melts, 2nd ed. Amsterdam: Elsevier. Odian, G. (2004). Principles of Polymerization, 4e. Hoboken, NJ: Wiley-Interscience. Painter, P.C. and Coleman, M.M. (2009). Essentials of Polymer Science and Engineering. Lancaster, PA: DEStech Publishing. Paul, A. (1990). Chemistry of Glass, 2e. London: Chapman and Hall. Pye, L.D., Montenero, A., and Joseph, I. (2005). Properties of Glass-Forming Melts. Boca Raton, FL: CRC Press. Rao, K.J. (2002). Structural Chemistry of Glasses. Oxford: Elsevier. Richardson, F. (1974). Physical Chemistry of Melts in Metallurgy, 2 vols. London: Academic Press. Suryanarayana, C. and Inoue, A. (2011). Bulk Metallic Glasses. Boca Raton, FL: CRC Press. Stebbins, J.F., McMillan, P., and Dingwell, D.B. (eds.) (1995). Structure, Dynamics and Properties of Silicate Melts.

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Reviews in Mineralogy, 32. Washington, DC: Mineralogical Society of America. Takada, A., Parker, J.M., Durán, A., and Bange, K. (eds.) (2018). Teaching Glass Better. Madrid: Cyan. Tomozawa, M. and Doremus, R.H. (eds.) (1977–1985). Treatise on Materials 2. Science and Technology: Glass IIV. New York: Academic Pressn. Uhlmann, D.R. and Kreidl, N.J. (1983–1990). Glass Science and Technology, 1. Glass-Forming Systems; 2. Processing; 3. Viscosity and Relaxation; 4A. Structure, Microstructure, and Properties; 4B. Advances in Structural Analysis; 5. Elasticity and Strength in Glass. New York: Academic Press. Vogel, W. (1994). Glass Chemistry, 2e. New York: Springer. Wolf, M.B. (1984). Chemical Approach to Glass. Amsterdam: Elsevier. Zanotto, E.D. (2013). Crystals in Glass: A Hidden Beauty. Hoboken, NJ: Wiley.

Compilations of Glass Data Bansal, N.P. and Doremus, R.H. (1986). Handbook of Glass Properties. Orlando: Academic Press. Mazurin, O.V., Streltsina, M.V., and Shvaiko-Shvaikovskaya, T.P. (1987). Handbook of Glass Data. Part A. Silica Glass and Binary Silicate Glasses. Amsterdam: Elsevier. Mazurin, O.V., Streltsina, M.V., and Shvaiko-Shvaikovskaya, T.P. (1987). Handbook of Glass Data. Part C. Ternary Silicate Glasses. Amsterdam: Elsevier.

Mazurin, O.V., Streltsina, M.V., and Shvaiko-Shvaikovskaya, T.P. (1993). Handbook of Glass Data. Part E. SingleComponent, Binary, and Ternary Oxide Glasses: Supplements to Parts A, B, C, and D. Amsterdam: Elsevier. Turkdogan, E.T. (1983). Physicochemical Properties of Molten Slags and Glasses. London: The Metals Society.

Glass Art Various authors. Histoire du verre. Paris: Massin; F. Slitine (2005). L’Antiquité; Du Pasquier, J. (2005). Le Moyen Age and (2007). Les chefs-d’oeuvre de l’Islam; Bellanger, J. (2006). L’Aube des temps modernes 1453–1672 and (2008) Du Baroque aux lumières; Ennès, (2006). Au carrefour de l’art et de l’industrie. Le XIXe siècle. Hérold, M. and David., V. (eds) (2014). Vitrail, Ve-XXIe siècle. Paris: Editions du Patrimoine. Koob, S. (2006). Conservation and Care of Glass Objects. London: Archetype Publications. Page, J.-A. (ed.) (2006). The Art of Glass: Toledo Museum of Art. Toledo and London: Toledo Museum of Art and D. Giles Ltd. Ricke, H. (2002). Glass Art: Reflections of the Centuries. Masterpieces from the Glasmuseum Hentrich in Museum Kunst Palast. Düsseldorf, Munich: Prestel. Tait, H. (ed.) (1991). Five Thousand Years of Glass. London: The British Museum. Weiß, G. (1966). Ullstein Gläserbuch. Eine Kultur- und Technikgeschichte des Glases. Berlin: Frankfurt am Main and Vienna: Ullstein.

1

General Introduction Pascal Richet,1 Reinhard Conradt2 and Akira Takada3,4 1

Institut de Physique du Globe de Paris, Paris, France UniglassAC GmbH, Aachen, Germany 3 University College London, London, UK 4 Ehime University, Matsuyama, Japan 2

Figure 1 Obsidian core found in the sixth to fifth millennia BCE Aknashen Neolithic site in Armenia. As indicated by the flake scars, large flakes were detached in a single final strike by an experienced stone knapper. Source: Photo P. Richet. Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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General Introduction

1

A Historical Random Walk

1.1 The Glass Age “Among the so many, so varied products, which attest to the industrial genius of mankind, there are very few that have uses as numerous as glass, whose properties are so wonderful,” pointed out in 1868 Georges Bontemps (1799–1883), a famous nineteenth-century glassmaker [1], who added: “no matter could replace glass in the most important of its uses.” At the same time, the great popularizer Louis Figuier (1818–1894) stated that it would be too long to list “the services that glass provides to science, the arts, industry, domestic needs, to the individual acts of man in society, to the poor and the rich, to the ignorant and to the learned.” Stressing that “household economics, science, civilization, progress and well-being, we owe almost all this to glass,” Figuier concluded that “born with primitive societies, glass will only disappear with civilization” [2]. Certainly, Bontemps and Figuier could not have guessed that organic polymers known as plastics would replace mineral glass in some of its traditional uses. Ironically, however, not only has mineral glass found many more, such as light guide in optical fibers (Chapter 6.4) or scaffold for bone regeneration (Chapter 8.4) to name only two of the latest, but most organic polymers are also glasses in the physical sense of the term. Since its very first origins, the vitreous state has thus opened astonishing ways to create original materials, to satisfy the most diverse needs and even to discover the world at large. Unlike other well-established materials, glass has gone through more developments in the past 50 years than in two millennia from both industrial and technological standpoints. Whether overwhelming in the glazing of skyscrapers or hidden in telecommunication networks, glass has become still more ubiquitous in the modern environment than at Bontemps and Figuier’s time so that claiming that we are now living in the Glass Age is not an overstatement [3, 4]. Whereas original glass compositions have, for instance, been designed for innovative lighting, screen, and display applications (Chapters 6.9 and 6.10), even the traditional products used for glazing and containers are now taking advantage of various new functionalities (Chapters 6.7 and 6.8). But what might be the most fascinating modern feature of glass is the way in which the material can be engineered to satisfy the most opposite requirements. Long celebrated for light transmission (Chapter 6.1), glass can be made opaque to a wide range of electromagnetic radiations from infrared to X-ray wavelengths through addition of appropriately absorbing elements (Chapters 3.13 and 6.2). Chemical inertness is

another major traditional asset of glass, which is in contrast purposely avoided in water glass (Chapter 7.5) and bioactive glasses (Chapter 8.4) whose usefulness rests on their intrinsically high chemical reactivity. And whereas extremely low impurity levels are required in optical fibers and other optoelectronic devices (Chapters 6.3–6.6), storage of municipal and nuclear waste relies on the capacity of glass matrices to incorporate large amounts of a great many elements (Chapters 9.10 and 9.11). Additional examples are not needed here to illustrate further the point as they will be found in numbers in the Encyclopedia. It is more appropriate to stress that most of these engineering developments have relied on the improved understanding of the glassy state brought by a better knowledge of its physical, chemical, and structural properties. What a long way has therefore been traveled since man made acquaintance with a strange, dark rock differing from all others by its luster and especially, when split into pieces, by its extremely sharp edges that even flint could not match!

1.2 An Economic Forerunner Obsidian (Figure 1), a natural glass found in volcanic provinces in various parts of the Earth, has been known from time immemorial. From arrowheads (Figure 2) to blades of any kinds and purposes (Figure 3), its unique properties made it so valuable to hunter-gatherers that it was the very first item to be extensively exchanged over long distances [5]. Well before any man-made object was produced, obsidian thus embodied at an early stage of human evolution the economic notion of competitive advantage, which eventually resulted in its real trade (Chapter 10.1). At the heart of a dynamic corridor between Eurasia and Africa, present-day Armenia played a significant role in this history as a material source for a wide area in the Near East, initially through moving communities that were carrying their tools with them [6]. Armenia is also important because of the new light it has recently shed on the far-reaching issue of the expansion of archaic Homo sapiens out of Africa. According to a claim often made, this expansion followed the important technical change from bifacial to Levallois technique of stone knapping (Figure 3, cf. [7] for their differences). At the Nor Geghi-I site, near Yerevan, both types of tools actually coexist within alluvial sediments sandwiched in between lava flows dated to

1 A Historical Random Walk

Figure 2 The delicate stone knapping of an arrowhead made possible by obsidian in Pre-Colombian present-day Arizona. Source: Photo courtesy Alexandra Navrotsky.

441 000 ± 6 000 and 197 000 ± 7 000 years [8]. From a fundamental standpoint, the synchronic use of both techniques by a single human group at this site thus indicates instead that, after human dispersion, the transition occurred independently within geographically distinct areas. From a practical standpoint, the change allowed better tools to be obtained so much faster from a large core (Figure 1) and with little waste. One could in fact conclude from the incredibly high abundance of artifacts buried in a Middle-Paleolithic site such as Barozh 12 [9], next to the Arteni Complex Volcano (Eastern Armenia), that the concept of disposable object was born with obsidian in the Paleolithic!

(a)

(b)

Man-made glass appeared considerably later, only three and a half millennia ago in the Late Bronze Age in a wide area ranging from the Near East to Egypt and Greece (Chapter 10.2). The vividly colored but expensive material newly produced was originally the preserve of elites who had recognized its aesthetic and practical interest. After 15 centuries of technical improvements and decreases of production costs, it became a basic commodity in the Roman Empire as acknowledged by Petronius (first century CE) in the Satyricon where one of his characters uttered: “You will forgive me if I say that personally I prefer glass; glass does not smell. If it were not so breakable I should prefer it to gold; as it is, it is so cheap” [10]. This chemical inertness achieved at reduced cost was of course one of the early assets of glass. As we now know, others were resulting from its lack of long-range atomic order, which makes forming in the most diverse shapes and sizes possible, produces optical isotropy, gives much flexibility in terms of raw materials and coloring elements thanks to the almost limitless extent of its solid solutions, and is at the source of mechanical properties in principle limited only by the strength of interatomic bonds thanks to the lack of weak grain boundaries. How was it figured out that glass could completely lose its vivid colors, which first attracted man’s interest, we do not know. The transparency now so closely associated

(c)

Figure 3 The striking stone-knapping difference between a biface (left) and Levallois point and blade, all made from obsidian (right); length: 20 cm: (a) Acheulean hand axe produced by serial removal of small flakes with a soft hammer (Kuchak-3 open-air site, Aparan Depression, Central Armenia); (b) Levallois Mousterian point, with its plano-convex profile, produced before the repreparation of core convexities, and the recurrent method, in which multiple Levallois flakes are detached before repreparation (Barozh-12 open-air site, Ararat Depression, Eastern Armenia); (c) Regular flake of the Chalcolithic period produced by pressure flaking from a prismatic core with the aid of a lever (Mastara-1 settlement, Ararat Depression). Source: Photos courtesy Boris Gasparyan.

3

4

General Introduction

with glass was first achieved for very special pieces such as cups made in Achaemenid Persia in the fifth century BCE (Chapter 10.0, Figure 1a). But it took several more centuries before transparency became common. The existence of pure, natural carbonates commonly termed natron was the key ingredient to achieve it at a large scale at the beginning of our era [11]. Especially in the Levant, the competitive edge acquired by glassmakers thanks to this substance was such that it led to the establishment of a world market: finished items and glass ingots were traded along well-established commercial routes to be exported as far as East Africa and India [12], the ingots to be shaped locally in small workshops (Chapter 10.3). A first glimpse at globalization?

1.3 A Multifaceted Material Glass has always aroused much curiosity by its virtue of embodying almost unlimited possibilities for transforming matter. Until the end of the nineteenth century, industrial illustrations of such transformations were the metamorphoses undergone by the large glass pieces that were first blown before being opened and flattened to yield flat panes with the neat fire finish required for transparency (Chapter 10.8). Nowadays, who has never been captivated by the work of a blower, by the action of a delicately controlled fire that gives birth to the most surprising shapes and, in a way, makes the material living for an instant? Even the proverbial brittleness of glass is part of this powerful imaginative world: its fracture indeed seems as unpredictable as it is dramatic, as illustrated by a tempered drinking glass suddenly exploding after several bounces when falling onto the ground. To this kind of amazement also contributed early the miracles wrought by glass ever since it first restored sight to visually impaired people in the thirteenth century (Chapter 10.10). It is thus no wonder that Leonardo da Vinci (1452–1519) devoted efforts to design a device for machining eyeglasses. Shortly after, the transparent glazing of windows opened houses on the outside world at about the same time as the telescope and the microscope led to the discovery of the universe from the infinitely large to the infinitely small (Chapter 10.10). Grinding of optical lenses was then extensively practiced by Galileo Galilei (1564–1642) himself and considered a trade worth earning a living by the eminent philosopher Baruch Spinoza (1632–1677). That glassmaking had something special is actually indicated by the fact that, in France, it was long the only trade that the nobility could practice as gentlemen glassmakers without losing its special status.

To acknowledge all what civilization was owing to this material, the polymath and glassmaker Mikhail Vasilyevich Lomonosov (1711–1765) wrote in Russia a long poem entitled Letter on the use of Glass. “A whole year would hardly suffice me to reach the end of worthy praise for Glass” [13], Lomonosov thus claimed when mentioning not only the telescope, the microscope, or the barometer, but also the thrilling electrical researches of his time based on the accumulation of charges on the glass disks of electrostatic machines (Chapter 10.10). Such was the interest raised by the vitreous (positive) and resinous (negative) electricities “that people of all genders and ranks were then begging for the favor of being subjected to electric shock, to the point that the noble and courageous Professor Georg Matthias Bose (1710–1761) said with philosophical heroism: I would not regret dying of an electric shock, since the account of my death would provide the subject of an article in the Memoirs of the Royal Academy of Sciences of Paris” [14]. Could this admirable philosophical heroism have been elicited by a material other than glass? At the same period, glass became the source of another kind of emotions when the famous Benjamin Franklin (1706–1790) was inspired by “the sweet tone that is drawn from a drinking glass, by passing a wet finger around the rim” [15] to design in 1761 the glass armonica whereby it was a set of overlapping wet glass cones of different sizes that was rotating to emit a sweet, ethereal, or pathetic tone through the friction of fingers. The instrument met with rapid success such that, beginning with Wolfgang Amadeus Mozart (1756–1791) [16], quite a few great composers wrote short pieces for it. The fashion for glass was such that a German living in Paris named Beyer presented in 1785 to the Académie des Sciences his forte-piano with glass plates, acted upon by woolcovered hammers, which Franklin christened glass-cord [17]. And it was a flute made from lead-crystal glass that the Parisian instrument maker Claude Laurent (d. 1848) patented in 1806 and produced in white, cobalt-blue, and uranium-green hues; in spite of its weight, its musical qualities and reduced temperature-induced pitch changes ensured its popularity for several decades [18]. This select series of anecdotes probably makes it unnecessary to emphasize again the importance of glass in daily and social life stressed above by Bontemps and Figuier. It might in contrast be useful to mention that the antique tradition or ornamental glass was revived at the same period by Georges Frédéric Strass (1701–1773), who became the French King’s jeweler, when he invented strass, or rhinestone, a high-lead crystal glass bearing various metal oxides that is still made today to imitate precious stones.

1 A Historical Random Walk

1.4

The Silica Paradoxes

1.4.1 Biogenic Silica vs. Flint

Historically, glass owes its importance to silicates. But what substances could have replaced silicate glasses in their diversity of uses on a silicon-free planet? The question would be moot if carbon – the next of kin of silicon in the Periodic Table – and, therefore, life and human beings would have also been lacking. More seriously, however, reflecting on the origin of the silica sources used in glassmaking is not a futile exercise. It is not widely known that 15 billion tons of biogenic silica glass are yearly produced in seawater by diatoms, sponges, and some other living organisms. Such a biological production has major effects on the Earth’s global ecosystem and has now become a biomimetic source of inspiration for designing wholly new materials (Chapter 8.1). Interestingly, biogenic silica also had noteworthy implications for glassmaking because of its recycling into the opal or microcrystalline quartz of flint. Flint, or chert as it is called in geology, is commonly found as abundant nodules horizontally embedded in limestone (Figure 4). Its deposition thus requires carbonate Figure 4 The abundant beds of black flint present in a 80-m high limestone cliff of the English Channel at the Pointe du Chicard in Yport (Normandy). Same beds of the Upper Cretaceous used in the past for making flint glass in England on the other side of the Channel. Height visible on the picture: 10 m. Source: Photo P. Richet.

dissolution followed by silica precipitation and, thus, percolating waters undersaturated with respect to calcium carbonates but oversaturated with respect to silica. Without going into the details of the process and of its control by pH and geological context [19, 20], it will suffice here to state that biogenic silica accumulating at the bottom of the sea is the source of the dissolved silica that reprecipitates as flint. And it happens that flint was the raw material used in England from the seventeenth century to remedy the lack of sand pure enough for making optical glass and luxury ware (Chapter 10.10). In passing, one can also note that silica has been biogenically produced relatively late in evolution compared with calcite and aragonite, the main CaCO3 polymorphs, but then met with immense success especially with diatoms. A major reason was the advantages of an amorphous compared with a crystalline substance in terms of optical or mechanical properties for the materials protecting the living organisms (Chapter 8.1); amorphous calcium carbonates do exist, but they serve instead as intermediate reaction steps, which are short lived and thus end up crystallizing [21], which is not surprising as molten CaCO3 is

5

General Introduction

2

1.65 T– O distance (Å)

6

3

4

5

6

1

Figure 5 The strong contrast between the potential energy changes induced by variations of Si–O distances and S–O–Si angles indicated by the calculated surfaces of constant energy of H6Si2O7 clusters. Source: After [23].

1.60 1 1 unit =14 kJ/mol 1.55

3 5 4 8 7

2

6 120

140

160

180

T–O–T angle (°)

not itself a good glass-forming liquid. Interestingly, formation of biogenic silica would have first been a way to evacuate toxic Si at too high concentrations from cells. By a twist of evolutionary history, it would have become a protecting device so efficient for organisms [22] that it has since then played a major role in the global ecosystem, causing, for instance, the Si concentrations to be so low in seawater. 1.4.2 A Quantum-Chemical Factory: The Production of Silica Sand

Although glassmaking would have been possible without sand, it is unlikely that flint would have led to the invention of glass as it requires thorough grinding to become a reactive raw material. Regardless of grinding costs, it is also doubtful that flint would have been a silica resource widespread and convenient enough for an expanding glass industry. The fundamental importance of silica sand thus remains undisputed. Geologically, sand is produced via the weathering of granite and related SiO2-rich igneous rocks. The most abundant rock of the Earth’s crust, granite is made up of quartz and alkali [(Na,K)AlSi3O8] and plagioclase [(Nax,Ca1 − x)Al2 − xSi2 + xO8] feldspars. Whereas feldspars progressively transform into clay under the action of meteoric waters, quartz resists and accumulates as sand either on the spot or downstream. The very presence of quartz at the Earth’s surface appears to be a clear geochemical anomaly, however, which thus deserves some explanation. With typical 75 wt % SiO2, the melts from which granite crystallizes represent the end products of magma differentiation (Chapter 7.2). Owing to their very high viscosities, they rarely rise up to the Earth’s surface to erupt as obsidian flows but crystallize slowly instead at some depth to yield large-grained rocks. These melts are the last produced after partial crystallization of primary magmas, which form themselves deep in the Earth’s mantle by partial melting of SiO2-poor, MgO-rich rocks (~45 wt % for both oxides, along with ~7 % FeO, 2 % Al2O3, 1 % CaO, and a few ‰ at most alkali oxides). Because oxygen bonds more

strongly with silicon than with the other elements (Table A.1), one might think that SiO2-rich minerals should be the most refractory. As a result, the SiO2 content of primary magmas should be lower than that of their source rock and decrease further through partial crystallization on their way up to the Earth’s surface. Such a trend is opposite to the SiO2 increase observed. It is in contrast consistent with the fact that cristobalite, the high-temperature polymorph of SiO2 at room pressure, is less refractory than lime (CaO), periclase (MgO), and even forsterite (Mg2SiO4) whose melting temperatures are about 600, 800, and 175 higher than the 2000 K of cristobalite, respectively. The paradox lies in the fact that bond strengths are usually considered within the framework of ionic forces, which are by definition nondirectional. Now, directionality is an inherent feature of Si–O bonding in view of its markedly covalent character. Because electron delocalization through polymerization and creation of Si–O–Si linkages is not large enough to constrain geometrically the arrangements of the SiO4 tetrahedra, the same energy variations are, for instance, caused in H6Si2O7 clusters by a small 0.02 Å change of the Si–O bond length and by a large 20 modification of the O–Si–O inter-tetrahedral angles (Figure 5). Bending of these linkages is thus so easy that configurational rearrangements take place without involving much energy [24]. The fact is most simply illustrated by the transitions of α-quartz and α-cristobalite to their dynamically disordered β-forms near 573 and 250 C, respectively. Hence, fusion of these minerals does not require the breaking of bonds involved in ionic crystals. The SiO2 enrichment and resulting quartz crystallization induced by magma differentiation are thus mainly driven by the sp3 hybridization of silicon orbitals, which causes largely polymerized crystals to melt at temperatures much lower than would be expected from the Si–O and Al–O bond strengths [24]. In other words, the existence of silica sand originates in a quantum-chemical effect, without which glassmaking would not have existed.

2 Some Basic Concepts of Glass Science

2 Some Basic Concepts of Glass Science 2.1

From Metastability to Relaxation

The silica issue illustrates how answers to apparently simple problems can require in-depth analyses for which theoretical concepts presented in various chapters of the Encyclopedia should prove useful. To help readers whose knowledge of the glassy state is minimal, however, the rest of this introduction will be devoted to a brief presentation of some basic concepts pertaining to glass and nonequilibrium systems, which will thus not need to be commented upon in specific chapters. In preamble, it would be useful to define precisely what a glass is before discussing any of its properties. In accordance with its intrinsically disordered nature, however, glass might be pleasantly defined as a material that is difficult to define in an unambiguous or fully consistent manner. In Chapter 10.11, a glass is nonetheless defined as a macroscopically homogeneous amorphous solid whose properties (physical, chemical, or structural) vary with its preparation conditions. Usual definitions differ depending on whether the emphasis is put on the disordered atomic structure of the material or on the existence of a glass transition separating a solid material at lower temperature from a supercooled liquid at higher temperatures. Because glass structures depend on the type of system considered, they are described in widely different ways for oxides, metals, or organic polymers so that they do not lend themselves to a brief, general presentation. Although a glass transition cannot always be observed, its phenomenology and its implications on glass properties are in contrast common not only to all glass-forming liquids, but also to partially disordered systems such as plastic crystals. In view of their dual practical and theoretical importance, the main features of the glass transition will thus be summarized here in a qualitative way. Without making any reference to recent advances in the field, the purpose is simply to describe the phenomenology of vitrification and its effects on physical properties, to introduce some of the groundbreaking concepts that have been proposed to account for them, and to highlight some simplifying features thanks to which intrinsically complex glass problems become more tractable. A main source of difficulty is that the time parameter must be considered because of the kinetic nature of the glass transition. In the backdrop is the way in which the Gibbs free energy of a glass-forming liquid would be minimized under given experimental conditions and, thus, the kinetics at which physical properties relax after changes in intensive thermodynamic variables (Chapter 3.7). The largest and most rapid decrease of the Gibbs free energy would of course be ensured by crystallization. To bypass it, it has been known from time immemorial that a melt must be cooled rapidly enough.

Other things being equal, vitrification is favored by large freezing-point depressions near eutectic compositions, which result in increased viscosities and reduced thermodynamic driving forces for crystallization. With very few exceptions (e.g. [25]), however, supercooled liquids do crystallize more or less rapidly upon prolonged annealing. Perhaps also influenced by the early twentieth-century conception that glasses were supercooled liquids (Chapter 10.11), a commonly held assumption is that any glass would eventually crystallize. This assumption is in fact plainly contradicted by the 4.6-billion year old glasses found in meteorites (Chapter 7.1). What has ensured their long-term preservation has been the extremely dry conditions of extraterrestrial space, which have prevented them from weathering. Since their SiO2poor compositions would make them prime candidates for ready devitrification, the almost infinite metastability enjoyed by these glasses is especially significant. The crystallization issue will thus be left aside in the following. 2.2

Relaxation: Phenomenological Aspects

Atomic mobility is the hallmark of the molten state as illustrated by the ready flow of a liquid adjusting to the shape of its container. Contrary to crystals where atomic positions are fixed and strongly constrained by long-range symmetry, liquids are characterized by dynamic disorder, i.e. by unceasing atomic rearrangements. This structural incompatibility between a crystal and a liquid makes any progressive transformation of one phase into the other impossible. In contrast, the vitrification of liquids is clearly a continuous process during which disordered structures become frozen in as revealed by progressively increasing viscosities, which eventually becomes so high that the materials have mechanically become a solid. At high temperatures, the liquid is in internal thermodynamic equilibrium because its properties are time independent and uniquely determined by two intensive variables, usually taken to be pressure and temperature. At high viscosities, however, this simplicity no longer holds true as seen if one exerts a stress on the liquid at constant temperature or change the temperature at constant stress (Figure 6a). For a window glass [26], a constant, equilibrium shear viscosity is, for example, reached more rapidly in the former case than in the latter but this difference does not need to be commented upon here because pressure and temperature changes are of a different nature. Of greater importance is that Boltzmann superposition principle (Chapter 10.11) applies because, if both perturbations are simultaneously exerted, the response of the system is the sum of the two individual responses (Figure 6a). In practice, temperature changes matter most. When high viscosities are measured at successively lower temperatures and then at higher temperatures (Figure 6b), two conclusions follow: (i) the time needed to reach the

7

General Introduction

20

(a) 14.0

16 1

2

log η (Pa.s)

log η (Pa•s)

13.8

13.6

12

8

13.4 3

4

13.2

Window glass Window glass

0

13.0 0

400

800

1200

4

6

8

1600

Time (min)

10

12

14.5 777 K

τY = − Y t − Y e

14.0 788 K 13.5

∂Y ∂t ,

13.0 Window glass 12.5 400

800

1200

1600

16

2000

2400

Time (min)

Figure 6 Viscosity relaxation of window glass (Source: Data from [26]). (a) Time dependence of the viscosity at 788 K after: (1) application of a 110 MPa stress; (2) a temperature change from 819 to 788 K with this stress; (3) exerting simultaneously these stress and temperature changes. (b) Attainment of the equilibrium viscosity; sample equilibrated at 795 K, then quickly brought for equilibration at 788 K and at 777 K (open symbols) before following the same procedure for reversing the equilibrium values first measured at 788 and 795 K (open symbols).

constant equilibrium values increases tremendously with decreasing temperatures; (ii) the approach to equilibrium is slower when the sample was previously equilibrated at a lower than at a higher temperature. Hence, the rate at which these changes occur depends not only on temperature but also on the thermal history of the sample, i.e. on the instantaneous structure as well. Because thermodynamic equilibrium is reached when the structure has adjusted to the new intensive parameters, the process is termed structural relaxation. To characterize the rate at which the shear viscosity (η) or any other property Y approaches a new equilibrium value, Ye, one defines the relaxation time, τY, as

1

where Yt is the value actually measured at time t. If τY were constant, the relaxation would be exponential: Y t − Y e = Y 0 − Y e exp − t τY ,

795 K

0

14

104/T (K–1)

Figure 7 Viscosity of window glass; solid line VFT fit to the data; dashed line: Arrhenius fit made to the high-temperature measurements; arrow: onset of departure from the equilibrium viscosity; solid squares and line: isostructural viscosities. Source: Data from [26, 27].

(b)

log η (Pa•s)

8

2

where Y0 is the initial Y value, so that after a time τY, the variation of Y would be a fraction 1/e of the initial departure from the equilibrium value. Regardless of the actual non-exponential nature of relaxation, measurements, for example, made on window glass at 777 K point to relaxation times much higher than one hour (Figure 6b). A measurement performed in only a few minutes would thus refer to a fixed configuration, i.e. to a glass. Depending on the timescale of the experiment, one observes that the nature of response is thus either liquid- or solid-like. The glass transition range is that temperature interval where, depending on the timescale of the experiment performed, time-dependent observations are made. It signals the change from the liquid state, where a great many different atomic configurations are unceasingly explored, to another state where atoms become trapped in fixed positions and properties become again time independent. In statistical–mechanical jargon, this change is said to represent the loss of ergodicity and, thus, of internal thermodynamic equilibrium. Experimentally, the loss of equilibrium can be readily followed by viscometry. Over an interval as wide as 10–1015.5 Pa.s, the viscosity of a glass-forming melt can be reproduced empirically with the Vogel–Fulcher– Tammann (VFT) equation (Chapters 4.1 and 10.11): log η = A + B T − T 1 ,

3

where A, B, and T1 are constants (Figure 7). If only hightemperature measurements are considered, then a simpler Arrhenius equation is generally adequate, viz.

2 Some Basic Concepts of Glass Science

4

where η0 is a pre-exponential term and ΔHη the activation enthalpy for viscous flow. Consistent with the aforementioned effects of thermal history (Figure 6b), the increasing departure of the viscosities from an Arrhenius fit made to the high-temperature data (Figure 7) indicates that, independently of any thermal-energy decrease, the structural rearrangements induced by lower temperatures progressively hinders viscous flow. The effect is still more apparent when measurements are made rapidly such that structural relaxation does not take place. Under these conditions, the isoconfigurational viscosity is indeed lower than the viscosity of the equilibrium supercooled liquid at the same temperature (Figure 7). 2.3

(a) 6

5 103 Δl/l

log η = log η0 + ΔH η RT ,

4 Tg

3

E glass 2 350

400

450

500

550

600

T (°C)

(b)

The Glass Transition

2.3.1 Standard Glass-Transition Temperature

For the experimental timescales of the order of a few minutes typical of measurements of macroscopic properties, one observes that, regardless of chemical composition, time-dependent results begin to be observed when the viscosity becomes higher than about 1012 Pa. For convenience and comparison purposes, one defines the standard glasstransition temperature, Tg, as the temperature at which the viscosity of the liquid reaches this value of 1012 Pa.s.

Liquid V

Glass

V0 = f(T)

2.3.2 Volume Effects

The enhanced thermal expansion coefficient observed upon heating of a glass rod in dilatometry experiments is one of the most familiar manifestations of the glass transition (Figure 8a). The marked increase over an interval of about 50 K is rapidly followed by sample collapse because the viscosity rapidly decreases so much that the sample begins to flow under its own weight before structural relaxation is complete. As a result, the volume thermal expansion coefficient [α = 1/V (∂V/∂T)P = 3/l (∂l/ ∂T)P] may be rigorously determined from the slope of the dilatometry curve for the glass, but not for the supercooled liquid. In dilatometry experiments, one usually defines the glass-transition temperature as the intersection of the tangents to the lower- and higher-temperature curves. This temperature generally differs somewhat from the standard Tg simply because the glass transition depends on the particular experimental conditions of the experiment. With respect to enthalpimetry, dilatometry has the advantage of yielding absolute values of the property of interest, namely, the volume (and density). The influence of thermal history on density can thus be readily determined (which is why it was observed as early as in 1845, cf. Chapter 10.11). In contrast, the thermal expansion coefficient of glasses generally does not markedly

T

Figure 8 Volume effects of the glass transition. (a) Linear thermal expansion coefficient of E glass (Chapter 1.6) heated at 10 K/min; l = sample length (Source: Data from [28]). (b). Dependence of the volume of a glass on its fictive temperature.

depend on thermal history. At least above room temperature. The volumes of glasses produced at different cooling rates will then plot as a series of parallel lines (Figure 8b). To characterize the state of the glass, it suffices to know the temperature at which equilibrium was lost, which is directly given by the intersection of the glass and supercooled volumes (Figure 8b). This parameter is called the fictive temperature (T), which thus represents the temperature at which the configuration of the glass would be that of the equilibrium liquid (Chapter 10.11). Knowing T , it is then straightforward to determine the glass volume as a function of the fictive temperature, for example, at room temperature (Figure 8b). 2.3.3 Frequency Dependence

For exploring further the kinetics of the glass transition, one can vary the experimental timescale not only through

9

General Introduction

changes of the heating rate for a given technique, but through changes of the technique itself. In view of their relative simplicity, acoustic measurements of the adiabatic compressibility are especially interesting in this respect. For an isotropic solid, this compressibility is related to the velocities of compressional (vp) and transverse (vs) acoustic waves by: βS = 1 ρ vp 2 – 4 3vs 2 ,

vp decreases markedly and becomes frequency-dependent. With respect to dilatometry or calorimetry experiments, the glass transition shifts from about 500 to 900 C, with a difference of about 50 between the measurements made at 1 and 5.6 MHz. At higher temperatures, equilibrium values of the compressibility are finally measured near 1100 C when the ultrasonic velocity becomes independent of frequency. Experiments can be made at even shorter timescales when hypersonic sound velocities are measured by Brillouin inelastic scattering of photons by phonons (Chapter 2.2). At the timescales of the order of 10−10 seconds of these interactions, the glass transition shifts to higher still temperatures. For calcium aluminosilicates (Figure 9b), relaxed compressional velocities are typically observed only above 2200 C [30] where they begin to match the values determined by ultrasonic methods (Figure 9b). The first effect noticed when the temperature is increased is a slight kink (at around 750 C in Figure 9b), which disappears if the velocities are plotted against the volume of the sample instead of its temperature. This kink thus signals the increase in thermal expansion at the volume glass transition, whereas structural relaxation at the extremely short timescale of Brillouin scattering experiments becomes significant only at much higher temperatures. Interestingly, the shear sound velocities can then be measured for the supercooled liquid

5

where ρ is the density. In a liquid of low viscosity, the attenuation of compressional waves is so rapid that one can usually consider that these waves do not propagate at all, in which case the compressibility reduces to βS = 1 ρvp 2

6

Acoustic measurements are typically made with transducers working at MHz frequencies. Under these conditions, the response of the material to the compression exerted adiabatically by the acoustic waves is probed at timescales of the order of 10−6 seconds. To be induced by an acoustic wave, configurational changes must thus take place at timescales at least 106–107 shorter than those of dilatometry or calorimetry experiments. Their onset is thus correlatively observed at much higher temperatures. For a sodium silicate (Figure 9a), they are revealed above 700 C by a temperature interval where (a)

(b) 4500

7

4000

6 V∞

Tg Vp (km/s)

Vp (m/s)

10

3500

3 3000

Vp 0

1

5 Brillouin scattering

5.6 MHz

2 4

Ultrasonics Na2Si2O5 3

2500 700

900

1100 T (°C)

1300

0

500

1000

1500

2000

2500

T (°C)

Figure 9 Frequency dependence of the glass transition range. (a) Compressional acoustic-wave velocities of sodium disilicate measured at the frequencies (MHz) indicated (Source: Data from [29]); larger width of the glass transition range than in dilatometry because of the actual distribution of relaxation times. (b) Compressional hypersonic sound velocities measured for 36 SiO2 16 Al2O3 48 CaO melt (mol %) by Brillouin scattering and ultrasonic methods. Source: Data from [30, 31].

2 Some Basic Concepts of Glass Science

180

2200 Brillouin

160

Tg (°C)

1900

Liquid

Tg(°C)

1600

1300

140

120

100

Glass

a. Polystyrene 80 0

Ultrasonics 1000

–10

1

1.5

2

2.5

3

P (kbar)

Viscometry

Figure 11 Pressure dependence of the glass transition of atactic polystyrene. Source: Zero-frequency Brillouin scattering data from [33].

CaAl2Si2Oδ 700 –15

0.5

–5 log timescale (s)

0

5

Figure 10 Time dependence of the boundary between the glass and liquid phases of CaAl2Si2O8. Source: Data from [32].

hypersurface in the pressure–temperature–composition–timescale space.

2.3.4 An Irreversible Transition

well above the standard glass-transition temperature as long as its viscosity is not too low [32]. The material is not really a “glass” because its configuration changes rapidly with temperature, but a “glass-like” material whose solid-like part of its acoustic properties may be probed. Finally, another noteworthy feature of the glass transition range is its markedly increasing width apparent from Figures 8b to 9a and b, which originates in the fact that a distribution of relaxation times, and not a single time, must be considered. Complete relaxation is thus controlled by the slowest mechanisms whose retarding effects are the greatest for the shortest experimental timescales. In conclusion, the question as to whether a given substance is a liquid or a glass cannot be answered if the observational timescale is not specified. One must consider instead that the transition between the two kinds of phases is represented by a curve in the timescale– temperature plane (Figure 10). The picture is actually still more complex because the glass transition also depends on pressure. With the exception of some open 3-D network structures, Tg generally increases with pressure because an increasing compaction makes configurational rearrangements more difficult. At constant timescale, the glass transition is thus represented by another curve in the pressure–temperature plane (Figure 11). And the description is still more complex if the effects of composition are also considered. If all factors are dealt with together, the glass transition then becomes a

The glass transition was first signaled by anomalous increases of the heat capacity, and its kinetic nature by the dependence of these anomalies on the thermal histories of the samples investigated (Chapter 10.11). Such effects are clearly apparent in early Cp measurements made on B2O3 (Figure 12a) where three different temperature intervals are distinguished [34]. Above about 270 C, the liquid phase is in internal thermodynamic equilibrium because its heat capacity is uniquely defined by temperature (and pressure). In the 270–100 C interval, internal equilibrium is lost as Cp is no longer defined by temperature only. The measurements made upon heating and cooling differ and Cp differences of up to 20% are found between samples initially cooled rapidly and slowly. Also noteworthy is the fact that the observed Cp hysteresis prevents a reversible thermodynamic pathway from being followed. It points instead to the creation of entropy through cycling in this interval and, therefore, demonstrates the irreversibility of the glass–liquid transformation. Below 100 C, Cp depends again only on temperature. If integrated from 270 to 100 C, however, the Cp and Cp/T differences between the rapidly and slowly cooled samples represent enthalpy and entropy differences, respectively. These are constant below 100 C as the glass Cp does not depend sensitively on thermal history. They can be readily calculated for any two glasses, like a volume difference, if their fictive temperatures are known (Chapter 3.6). An important conclusion then follows: the existence of an entropy difference at 0 K between

11

General Introduction

(a) 7 Liquid 6 Cp (cal/mol °C)

5 R 4

S Glass

3

0

B2O3 100

50

150

200

250

300

350

T (°C)

p. lip .

(b)

Su

12

lq1l H1

H2

heating, the situation is more complicated because relaxation resumes at the temperature at which it vanished on cooling, but its first effect is to lower the enthalpy of the glass to bring it closer to the equilibrium values of the supercooled liquid (Figure 12b). At higher temperatures, the enthalpy curve of the material has already crossed that of the supercooled liquid when relaxation becomes almost complete at the timescale of the experiment. The heat capacity then increases rapidly (Figure 12b) in a way that depends on thermal history. The rise is highest for samples initially cooled down at the slowest rates, whose enthalpy is initially the lowest, or for samples heated at the highest rates. If the heating and cooling rates are increased, the transition shifts to higher temperatures because the decrease of the experimental timescale must be matched by an analogous decrease of the relaxation time (Figure 12b). Determination of a glass-transition temperature is more complicated in calorimetry than in dilatometry because of the complex shapes of the observed Cp variations or even of the endothermic peaks recorded in thermal analysis. This temperature may, for instance, be taken as the inflection point of the Cp increase upon heating, but it can alternatively be defined in different ways so that is generally needed to specify which particular one has been selected [35].

Tʹ lq1l>lq2l

lq2l lq1l

Cp T

Figure 12 Irreversibility of the glass transition: heat capacity hysteresis measured for boron oxide upon cooling and upon heating of a slowly (S) and rapidly (R) cooled glass [34]. (b) Enthalpy and Cp differences between glasses cooled at different rates q; Sup. liq.: enthalpy of the equilibrium supercooled liquid.

two samples implies that glasses have a residual entropy at 0 K: hence, glasses do not obey the third Law of thermodynamics because of the irreversible nature of the glass transition (cf. Chapters 3.6 and 10.11). In more detail, the Cp hysteresis results from the observed contrast between a smooth decrease upon cooling and sharp increases upon heating followed by overshoots right at the end of the transition (Figure 12a). The former decrease simply points to the progressive loss of atomic mobility with decreasing temperatures. Upon

2.3.5 The Case of Plastic Crystals

This description of the glass transition applies to a variety of kinetically controlled processes in crystals. Plastic crystals, characterized by low entropy of fusion and an unusually high plasticity, are good examples of disordered systems with three-dimensional long-range order. When the high-temperature form of cyclohexanol (ChI), for instance, crystallizes at 299 K, the C6H12O molecules order in a face-centered cubic lattice but their regular shape allows them to maintain orientational mobility by rotations around the lattice points. It is through a transition to the low-temperature polymorph (ChII), which is stable below 265 K, that this dynamics vanishes and the orientational disorder disappears [36]. With rapid cooling rates, the ChI form can be obtained metastably and kept for long periods of time below 180 K. On further cooling, a transition is eventually observed near 160 K (Figure 13). The orientational disorder of C6H12O molecules is then frozen in within the crystal. In contrast to the ChII form, whose entropy is zero at 0 K, ChI has a residual entropy of 4.7 J/mol K. The similarity with the glass transition phenomenology is such that the name of glassy crystals has been proposed for crystals where rotation of molecular groups is freed above a glass-like transition temperature and gives rise to relaxation

2 Some Basic Concepts of Glass Science

2.4

250

Configurational Properties

2.4.1 Equivalence of Relaxation Kinetics

Cp (J/molK)

Tf 150 100

Tg

50 Cyclohexanol 0

0

100

200

300

400

T (K)

Figure 13 The calorimetric signature of orientational disorder in cyclohexanol plastic crystal. Measurements made upon heating with a gap from slightly above the glass-transition temperature Tg and the melting temperature Tf because of rapid transformation into the stable, ordered polymorph. Source: Data from [36].

phenomena much more complex than summarized here (Chapter 8.6). 2.3.6 Maxwell Model

In view of the continuous pathway between the liquid and glass states, glass-forming liquids cannot be purely Newtonian when they approach the glass transition. In fact, they are viscoelastic, with an elastic component that becomes increasingly important near Tg. More precisely, application of a shear stress first causes an elastic strain, which would be recovered if the stress were released, and then a viscous deformation. The response of a viscous melt subjected to stress thus is made up of an instantaneous, elastic response along with a delayed response. By combining the simplest representations of elasticity and viscous flow, Maxwell model has as a mechanical analogue a spring and a dash pot placed in series [37]. Its important result is that, if stresses are applied at low frequencies, as usually the case in viscometry, then a simple relationship holds between the viscosity, relaxation time, and shear modulus at infinite frequency (G∞), η = G∞τ

7

The fact that the glass transition is observed at values close to 1012 Pa.s for widely different kinds of liquids thus indicate that G∞ also weakly depends on composition, with a mean value of about 10 GPa, which varies by less than a factor of 10 with either temperature or composition at least for oxide glass-forming liquids [38, 39]. Compared with the tremendous variations of viscosity with temperature and composition, G∞ thus is almost constant. If the viscosity is known, structural relaxation times can be readily estimated from Eq. (7).

It is usually more difficult to account for the kinetics of a reaction than for its thermodynamics. Relaxation in glassforming systems does not depart from this rule. Whereas a single-order parameter such as the fictive temperature may be appropriate for characterizing the volume or enthalpy of a glass, relaxation kinetics requires models much too complex to be discussed here (see Chapter 3.7). One can nonetheless have a first look at the mechanisms involved in relaxation by examining whether their kinetics varies or not with the particular property considered. As done for viscosity, the kinetics of volume equilibration can, for instance, be measured by isothermal dilatometry experiments. If samples with the same thermal history are studied, comparisons between the relaxation kinetics of different properties can be made in terms of normalized variables Y = Yt – Y ∞

Y 0 – Y∞ ,

8

where Yt, Y∞, and Y0 are the property Y at time t, initial time, and equilibrium, respectively. To within experimental errors, experiments on E glass, for example, show in this way the same kinetics for viscosity and volume (Figure 14). More general conclusions are readily derived from comparison between different glass-transition temperatures even though these are not necessarily defined in the same way in different kinds of measurements. What is important is that they be defined consistently and refer to samples with the same thermal histories. For volume 1.0

0.5 (Yt –Y∞)/(Y0 –Y∞)

200

Viscosity 0.0

–0.5

Volume E glass

–1.0

0

2000

1000

3000

Time (min)

Figure 14 Kinetics of equilibration for the viscosity and volume of E glass. Differences between the ascending branches mainly due to the uncertainties on the Y0 values caused by unrecorded relaxation during the initial thermal equilibration of the sample. Source: Data from [28].

13

General Introduction

and enthalpy, the latter condition is fulfilled in dilatometry experiments and differential thermal analyses performed simultaneously, whose results can also be compared with standard glass-transition temperatures (Figure 15). The close 1 : 1 correspondences found in this way for the three temperatures of silicates, calcium aluminosilicates, titanosilicates, and borosilicates over a 400 K

interval thus confirm the equivalence of the relaxation kinetics for differing properties [28]. In other words, one must conclude that the same configurational changes are involved in enthalpy, volume, or viscosity relaxation at least in oxide systems, which illustrates their overall cooperative nature.

2.4.2 Vibrational vs. Configurational Relaxation (a) 1200 Ca76.11 Ca12.44 Ca50.25 Ca0.39

1100

Ab Ca42.14

1000 T12(K)

Di E

900

NTS4 KTS2 BNC WG

800 NS4

700 700

900

800

1000

1100

1200

TDTA (K)

(b) 1200

Ca76.11 Ca12.44 Ca50.25 Ca0.39

1100

Ab Ca42.14

1000

Di

TDil (K)

14

The equivalence of relaxation kinetics allows an important distinction to be made between vibrational and configurational contributions to the properties of glass-forming liquids. In preamble, one should note that relaxation in solids does not need to be specifically addressed, as long as macroscopic properties are concerned, because it takes place at the 10−14 –10−12 seconds timescale of atomic vibrations. This instantaneous vibrational response persists in liquids where it combines with the configurational response whose timescale markedly decreases with increasing temperatures (Figure 16). For volume, isothermal dilatometry experiments near the glass transition may yield these two contributions (Figure 17) whose relative magnitudes directly reflect the increase in thermal expansion at the glass transition [40]. For the compressibility, another approach may take advantage of experiments made at different timescales. As described above, in certain temperature ranges, ultrasonic measurements yield the equilibrium adiabatic compressibility whereas Brillouin scattering experiments probe only its vibrational part. The configurational compressibility is then given by the difference between these two results [32]. That such determinations are actually scarce is not too problematic for second-order thermodynamic properties because, at least as a first approximation, one can assume that the vibrational contribution is represented by the glass property and the configurational one by the variations of these

E

NTS4

900

Y1

KTS2 BNC WG

Y2

800

Y3

NS4

700 700

800

(a) ΔY

900

1000

1100

1200

TDTA (K)

Figure 15 Equivalence of the relaxation kinetics for the enthalpy, volume, and viscosity illustrated by 1 : 1 correlations between the relevant glass-transition temperatures determined by differential thermal analysis (DTA), dilatometry (dil), and viscometry (vis, i.e. standard Tg). BNC: sodium borosilicate; WG: window glass; E: E glass; Ab: NaAlSi3O8; Di: CaMgSi2O6; N:Na2O; S: SiO2; T: TiO2; Ca.xx. yy: xx mol % SiO2, yy % Al2O3. Source: Data from [28].

Y4 T

(b) ΔT Time

Figure 16 Relative importance of configurational and vibrational relaxation with increasing temperatures for a given property Y (a) after instantaneous temperature jumps ΔT (b). Source: Data from [40].

2 Some Basic Concepts of Glass Science

(a)

αconf CaMgSi2O6

980

MC

αvib

C

Potential energy

T (K)

985

975 970

(b) 32

IG Strong

C IG

MC Fragile

Cpvib

30

Cpconf

ΔI (μm)

Vib. Distance

28

Figure 18 One-dimensional schematic representation of interatomic potentials. Inset: potential-energy landscape for a strong and a fragile liquid (Source: After [42]). C: crystal; IG: ideal glass; MC: metastable crystal.

Conf.

26

24 1600

2000

2400

2800

3200

Time (min)

Figure 17 Vibrational and configurational contributions to the volume change of CaMgSi2O6 liquid after an abrupt temperature decrease from 982 to 972 K. Source: Data from [40], cf. Chapter 3.5.

properties at the glass transition. In silicate systems, the configurational heat capacity can thus be written C conf T = C pl − C pg T g , pl

9

where the subscripts l and g refer to the liquid and glass phases, respectively, and a further simplification arises from the fact that Cpg(Tg) may be considered to be the Dulong–Petit harmonic limit of 3 R/g atom (R = gas constant) the isochoric heat capacity [41].

2.4.3 A Microscopic Picture

The vibrational/configurational split can be simply illustrated by a schematic one-dimensional representation of interatomic potentials (Figure 18). Contrary to crystals, where these potentials have a long-range symmetry, glasses have essentially a short-range order because the bond angles and distances between next-nearest neighbor atoms are not constant but spread over a range of values. The minima of potential energy, which determine the glass configuration, are separated by barriers with varying heights and shapes [43]. When thermal energy is delivered to the glass, the subsequent temperature rise is associated only with increasing amplitudes of vibration of atoms within their potential energy wells. Like for any solid, the heat capacity of the glass is, therefore, only vibrational in nature.

At sufficiently high temperature, thermal energy increases to the point that atoms can overcome the barriers that separate their own from the neighboring potential energy wells (Figure 18). This onset of atomic mobility signals structural relaxation. If the relaxation time is longer than the experimental timescale, however, only the vibrational heat capacity is measured. If the temperature is increased further, or if time is sufficient for the new equilibrium configuration to be attained during the measurement, then the configurational heat capacity is also measured. When integrated over all atoms, the configurational heat capacity represents the energy differences between the minima of the potential energy wells that are explored as temperature increases (Figure 18). The glass transition can thus be viewed as the point from which atoms begin to explore positions characterized by higher potential energies. Regardless of the complexity of this process at a microscopic level, this spreading of configurations over states of higher and higher potential energy is the main feature of atomic mobility. As a consequence, configurational heat capacities are positive. This feature, in turn, is consistent with the fact that any configurational change must cause an entropy rise when the temperature increases as required by Le Chatelier principle. As for relaxation times, they decrease with rising temperatures because large thermal energies allow potential energy barriers to be overcome more easily. Another general feature of interatomic potentials is their anharmonic nature: displacements of the vibrating atoms from their equilibrium positions are not strictly proportional to the forces exerted on them. Because increasing vibrational amplitudes result in increasing interatomic distances (Figure 18), the thermal expansion

15

General Introduction

coefficient is generally positive for glasses. In the liquid, it increases markedly when even greater interatomic distances result from configurational changes. 2.4.4 Compressibility and Permanent Compaction

An important difference between crystals and liquids concerns the effects of pressure on their structures. The former are stable as long as the variations in their bond angles and distances induced remain consistent with their long-range symmetry. A transition to a new phase takes place when this constraint is no longer respected. In contrast, the lack of long-range order makes a wide diversity of densification mechanisms possible in a liquid, whose structure thus keeps constantly adjusting to varying pressures through changes in short-range order characterized by shorter equilibrium distances and steeper slopes around the minima pictured in Figure 18. The compressibility is thus greater for a liquid than for its isochemical crystal. It is also made up of vibrational and configurational contributions. Because the shape of interatomic potentials determines the vibrational energy levels, compression is termed vibrational for the elastic part of the deformation. As for the configurational contribution, it is related to the aforementioned changes in the potential energy wells. If a liquid is quenched as a glass at high pressure, the final glass recovered after decompression will be denser than its counterpart formed at room pressure because only the vibrational part of the compression is eventually recovered (Figure 19). But permanent densification can also be achieved at room temperature through compression of a glass at a few tens of kbar (Chapter 10.11). The effects of pressure and temperature on the properties of glasses are thus of a different nature since the kinetics

of pressure- and temperature-induced configurational modifications are markedly different for given frequencies or experimental timescales. This dissimilarity mainly originates in the fact that the shape of potential energy wells varies little with temperature, but significantly with pressure. If a high kinetic energy is needed to overcome potential barriers at constant pressure, the changes in these barriers with pressure can lead by themselves to new configurational states, at low temperatures, if the pressure is high enough. 2.4.5 Kauzmann Paradox

When viscous liquids escape crystallization, why do they eventually vitrify instead of remaining in the supercooled liquid state? One answer to this question is purely kinetic and relies only on increasingly long relaxation times on cooling. If experiments could last forever, any glass would eventually relax to the equilibrium state. Then, the glass transition would result only from the limited timescale of feasible measurements. A simple thermodynamic argument known as Kauzmann’s paradox [45] indicates that this answer is incorrect. At its basis is the existence of a configurational contribution that causes the heat capacity of a supercooled liquid to be generally higher than that of an isochemical crystal and its entropy to decrease faster than that of a crystal when the temperature is lowered (Figure 20). If the entropy is extrapolated to temperatures 80

1 bar 0.88

Tg

60

S (J/mol K)

0.90

V (cm3/g)

16

Tk

Se

40

0.86 Liquid 20 0.84

0.82

800 bar

Tg Tk o-Terphenyl (× 0.1)

Glass Polyvinyl acetate

0.80 240

270

300

330

360

0 390

T (K)

Figure 19 Permanent compaction of polyvinyl acetate after compression at 800 bar (80 MPa) in the liquid state. Source: Data from [44].

0

100

200

300

400

500

T (K)

Figure 20 Kauzmann catastrophe for amorphous selenium and ortho-terphenyl (C8H14). Differences between the glass transition and Kauzmann temperatures indicating the smallness of the Cp extrapolations performed. Source: Data from [46, 47].

2 Some Basic Concepts of Glass Science

configurational entropy increases, the cooperative rearrangements of the structure required for mass transfer can take place independently in smaller and smaller regions of the liquid. Within this picture, relaxation is determined by the topology of potential energy wells in an n-dimensional space and, particularly, by the density and relative depths of these wells as may be illustrated in a 1-d representation of such a potential-energy landscape (Figure 18, insets).

1.8

1.6 ΔCp/Cp

below the glass transition range, it becomes lower than that of the crystal at a temperature TK, which is high enough for such an extrapolation to remain reasonable. Although this situation is not thermodynamically forbidden, it seems unlikely that an amorphous phase could have a lower entropy than an isochemical crystal. The conclusion is that an amorphous phase cannot exist below TK. The temperature of such an entropy catastrophe constitutes the lower bound to the metastability limit of the supercooled liquid. As internal equilibrium cannot be reached below TK, the liquid must undergo a phase transition before reaching it. This is, of course, the glass transition. In its original form, Kauzmann’s paradox implicitly neglects possible differences in vibrational entropy between the amorphous and crystalline phases. This simplification is actually incorrect but it does not detract from the gist of the argument, for taking into account such differences would only shift TK slightly. A more rigorous statement of the paradox is that the catastrophe would occur when the configurational entropy of the supercooled liquid vanishes.

1.2

1.0

2.4.6 Potential Energy Landscape: Ideal Glass and Fragility

τ = Ae exp Be TS

,

0.4

0.8

0.4

0.6

1.2

1.6

0.8

1

12

10

8

6 log η (Pa.s)

Among the great many statistical mechanical models that have attempted to account for the glass transition and solve Kauzmann’s paradox, the early one proposed by Gibbs and Di Marzio [48] is of special interest. It predicts that the supercooled liquid would transform to an ideal glass through a second-order transition at the temperature T0 at which its configurational entropy would vanish. Since then, the existence and the nature of such a transformation have been much debated. This debate notwithstanding, the important point for our discussion is the result subsequently derived by Adam and Gibbs [49] on the basis of a lattice model of polymers. This result is a very simple relationship between relaxation times and the configurational entropy of the melt, viz. conf

1.4

4

2

10

where Ae is a pre-exponential term and Be is approximately a constant proportional to the Gibbs free energy barriers hindering the cooperative rearrangements of the structure. Qualitatively, this theory assumes that structural rearrangements would be impossible in a liquid with zero configurational entropy so that relaxation time would be infinite. If two configurations only were available for an entire liquid volume, mass transfer would require a simultaneous displacement of all structural entities. The probability for such a cooperative event would be extremely small, but not zero, and the relaxation times would be extremely high, but no longer infinite. When

0

–2

Tg/T

Figure 21 Fragility as a measure of the extent of temperatureinduced configurational changes in inorganic and organic glassforming liquids: correlations between relative Cp increases at the glass transition and deviations of viscosities from Arrhenius laws (Source: After [52]). Lower panel, from top to bottom: SiO2, GeO2, BeF3, ZnCl3, LiCH3COO, 4 Ca[(NO3)]2 4 H2O, o-terphenyl, glycerol (C3H8O3), and H2SO4 3 H2O.

17

18

General Introduction

A simple distinction can then be made between strong and fragile liquids [43, 50]. For the former, a low density of wells translates into a small configurational heat capacity and entropy and thus, in small departures from an Arrhenian temperature-dependence of relaxation times as given by Eq. (7); for the former, the high density of wells is in contrast associated with high configurational heat capacities and entropies, and marked deviations from Arrhenian temperature dependences. Owing to the simple proportionality between relaxation times and viscosity, this difference may be simply visualized in plots of viscosities as a function of Tg/T where Tg is the standard glass-transition temperature [51]. A well-known sketch (Figure 21) illustrates the point for a variety of inorganic and organic glass-forming liquids [52]. As particularly exemplified in Chapter 4.1, this duality between fragile and strong liquids will be a recurrent theme in many other chapters of the Encyclopedia to which the reader is thus referred.

10 11

12 13

14

15

References 16 1 Bontemps, G. (1868). Guide du verrier. Traité historique

2

3 4 5

6

7

8

9

et pratique de la fabrication des verres, cristaux, vitraux, 1. Paris: Librairie du dictionnaire des arts et manufactures (trans. Cable, M. (2008). Bontemps on Glass Making. Sheffield: Society of Glass Technology). Figuier, L. (1873). Les Merveilles de l’industrie ou description des principales industries modernes [The Wonders of Industry or Description of the Main Modern Industries], vol. 1, 156–157. Paris: Furne, Jouvet et Cie. Richet, P. (2000). L’Âge du verre [The Glass Age]. Paris: Gallimard. Morse, D.L. and Evenson, J.W. (2016). Welcome to the glass age. Int. J. Appl. Glass Sci. 7: 409–412. Cann, J.R. and Renfrew, C. (1964). The characterization of obsidian and its application to the Mediterranean region. Proc. Prehist. Soc. 30: 111–133. Gasparyan, B. and Arimura, M. (eds.) (2014). Stone Age of Armenia. A Guide-Book to the Stone Age Archaeology in the Republic of Armenia. Kamazawa: Kamazawa University. Shea, J.J. (2013). Stone Tools in the Paleolithic and Neolithic near East: A Guide. Cambridge: Cambridge University Press. Adler, D.S., Wilkinson, K.N., Bloc, S. et al. (2014). Early Levallois technology and the lower to middle Paleolithic transition in the southern Caucasus. Science 345: 1609–1613. Glauberman, P., Gasparian, B., Wilkinson, K. et al. (2016). Introducing Barozh 12: a middle Palaeolithic open-air site on the edge of the Ararat depression,

17

18 19 20 21

22

23

24

25

Armenia. ARAMAZD, Armenian J. Near-East. Stud. 9 (2016): 7–20. Petronius Arbiter, 51 (repr. 1987). Satyricon (trans. M. Heseltine). Cambridge: Harvard University Press. Shortland, A., Schachner, L., Freestone, I., and Tite, M. (2006). Natron as a flux in the early vitreous materials industry: sources, beginings and reasons for decline. J. Archaeol. Sci. 33: 521–530. Stern, E.M. (1999). Roman glass blowing in a cultural context. Am. J. Archaeol. 103: 441–484. Lomonosov, M.V. (1967). Pis’mo o pol’ze stekla (trans. H.B. Segel, Letter on the Use of Glass, 209–220 in The Literature of Eighteenth-Century Russia). New York: E.P. Dutton & Co. Figuier, L. (1868). Les Merveilles de la science ou Description populaire des inventions modernes [The Wonders of Science or Popular Description of Modern Inventions], vol. I, 463. Paris: Furne, Jouvet et Cie. Franklin, B. (1769). Letter to Giambatista Beccaria. In: Experiments and Observations on Electricity, Made at Philadelphia in America, to Which Are Added Letters and Papers on Philosophical Subjects, 4e, 427–433. London: D. Henry. Mozart, W.A. Adagio in C for armonica (K. 356); Adagio and Rondo in C minor for armonica, flute, oboe, viola and cello (K. 617). Cohen, A. (1981). Music in the French Royal Academy of Sciences: A Study in the Evolution of Musical Thought. Princeton University Press: Princeton. Powell, A. (2002). The Flute. Yale: Yale University Press. Knauth, P. (1979). A model for the origin of chert in limestone. Geology 7: 274–277. Hesse, R. (1989). Silica diagenesis: origin of inorganic and replacement cherts. Earth Sci. Rev. 26: 253–284. Bots, P., Benning, L.G., Rodriguez-Blanco, J.-D. et al. (2012). Mechanistic insights into the crystallization of amorphous calcium carbonate (ACC). Cryst. Growth Design 12: 3806–3814. Marron, A.O., Ratcliffe, S., Wheeler, G.L. et al. (2016). The evolution of silicon transport in eukaryotes. Mol. Biol. Evol. 33: 3226–3248. Gibbs, G.V., Meagher, E.P., Newton, M.D., and Swanson, D.K. (1981). A comparison of experimental and theoretical bond length and angle variations for minerals and inorganic solids, and molecules. In: Structure and Bonding in Crystals (eds. M. O’Keefe and A. Navrotsky), 195–225. New York: Academic Press. Richet, P. and Ottonello, G. (2014). The earth as a multiscale quantum-mechanical system. C. R. Geosci. 346: 317–325. Zanotto, E.D. and Cassar, D.R. (2017). The microscopic origin of the extreme glass-forming ability of albite and B2O3. Sci. Rep. 7: 43022. https://doi.org/10.1038/ srep43022.

References

26 Sipp, A., Neuville, D.R., and Richet, P. (1997).

27

28

29

30

31

32

33

34

35

36

37

Viscosity, configurational entropy and relaxation kinetics of borosilicate melts. J. Non Cryst. Solids 211: 281–293. Mazurin, O.V., Startsev, Y.K., and Potselueva, L.N. (1979). Temperature dependences of the viscosity of some glasses at a constant structural temperature. Sov. J. Glass Phys. Chem. 5: 68–79. Sipp, A. and Richet, P. (2002). Equivalence of the kinetics of volume, enthalpy and viscosity relaxation in glass-forming silicate liquids. J. Non Cryst. Solids 298: 202–212. Nikonov, A.M., Bogdanov, V.N., Nemilov, S.V. et al. (1982). Structural relaxation in binary alkalisilicate melts. Fyz. Khim. Stekla 8: 694–703. Vo-Thanh, D., Bottinga, Y., Polian, A., and Richet, P. (2005). Sound velocity in alumino-silicate liquids determined up to 2550 K from Brillouin spectroscopy: glass transitions and crossover temperatures. J. Non Cryst. Solids 351: 61–68. Webb, S. and Courtial, P. (1996). Compressibility of melts in the system CaO-Al2O3-SiO2. Geochim. Cosmochim. Acta 60: 75–86. Askarpour, V., Manghnani, M.H., and Richet, P. (1993). Elastic properties of diopside, anorthite and grossular glasses and liquids: a Brillouin scattering study up to 1400 K. J. Geophys. Res. B98: 17683–17689. Stevens, J.R., Coakley, R.W., Chau, K.W., and Hunt, J.L. (1986). The pressure variation of the glass transition temperature in atactic polystyrene. J. Chem. Phys. 84: 1006–1014. Thomas, S.B. and Parks, G.S. (1931). Studies on glass. VI. Some specific heat data on boron trioxide. J. Phys. Chem. 35: 2091–2102. Hutchinson, J.M. (2009). Determination of the glass transition temperature. Methods correlation and structural heterogeneity. J. Therm. Anal. Calorim. 98: 578–589. Adachi, K., Suga, H., and Seki, S. (1968). Phase changes in crystalline and glassy-crystalline cyclohexanol. Bull. Chem. Soc. Jpn. 41: 1073–1087. Maxwell, J.C. (1868). On the dynamical theory of gases. Philos. Mag. 35: 129–145. and 185–217.

38 Dingwell, D.B. and Webb, S.L. (1989). Structural relaxation

39 40

41

42

43

44

45

46

47

48 49

50 51 52

in silicate melts and non-Newtonian melt rheology in geologic processes. Phys. Chem. Minerals 16: 508–516. Mysen, B. and Richet, P. (2005). Silicate Glasses and Melts. Properties and Structure. Amsterdam: Elsevier. Toplis, M.J. and Richet, P. (2000). Equilibrium expansivity of silicate liquids in the glass transition range. Contrib. Mineral. Petrol. 139: 672–683. Richet, P., Robie, R.A., and Hemingway, B.S. (1986). Lowtemperature heat capacity of diopside glass (CaMgSi2O6): a calorimetric test of the configurationalentropy theory applied to the viscosity of liquid silicates. Geochim. Cosmochim. Acta 50: 1521–1533. Angell, C.A. (1985). Strong and fragile liquids. In: Relaxation in Complex Systems (eds. K.L. Ngai and G.B. Wright), 3–11. Arlington, VA: Office Naval Research. Goldstein, M. (1969). Viscous liquids and the glass transition: a potential energy barrier picture. J. Chem. Phys. 51: 3728–3739. McKinney, J.E. and Goldstein, M. (1974). PVT relationships for liquid and glassy poly(vinyl acetate). J. Res. N.B.S. 78A: 331–353. Kauzmann, W. (1948). The nature of the glassy state and the behavior of liquids at low temperature. Chem. Rev. 43: 219–256. Chang, S.S. and Bestul, A.B. (1972). Heat capacity and thermodynamic properties of o-terphenyl crystal, glass, and liquid. J. Chem. Phys. 56: 503–516. Chang, S.S. and Bestul, A.B. (1974). Heat capacities of selenium crystal (trigonal), glass, and liquid from 5 to 360 K. J. Chem. Therm. 6: 325–344. Gibbs, J.H. and Di Marzio, E. (1958). Nature of the glass transition and the glassy state. J. Chem. Phys. 28: 373–383. Adam, G. and Gibbs, J.H. (1965). On the temperature dependence of cooperative relaxation properties in glassforming liquids. J. Chem. Phys. 43: 139–146. Angell, C.A. (1997). Entropy and fragility in supercooling liquids. J. Res. NIST 102: 171–185. Laughlin, W.T. and Uhlmann, D.R. (1972). Viscous flow in simple organic liquids. J. Phys. Chem. 76: 2317–2325. Angell, C.A. and Sichina, W. (1976). Thermodynamics of the glass transition: empirical aspects. Ann. N. Y. Acad. Sci. 279: 53–67.

19

20

General Introduction

Appendix A Table A.1 Coordination numbers, effective ionic radii, field strengths, and electronegativities of some cations and anions of interest in oxide glasses. Source: Compilation courtesy J.F. Stebbins.

Coordinationa

Ionic radiusb (Å)

Field strengthb

Electronegativityc

O2−

2, 6

1.35, 1.40

–

3.5

F1−

2, 6

1.29, 1.33

–

4.0

6

1.81

–

3.0

4, 6

0.49, 0.55

0.88, 0.82

1.8

4, 6

0.47, 0.62

0.90, 0.77

1.6

Anions

Cl

1−

Cations Network formersd Fe3+ Ga3+ Al

3+

4, 6

0.39, 0.54

0.98, 0.83

1.5

Te4+

3, 4e

0.52, 0.66

1.13, 0.98

2.1

Ti4+

4, 6

0.42, 0.61

1.26, 1.03

1.5

Ge4+

4, 6

0.39, 0.53

1.31, 1.12

1.8

4+

4, 6

0.26, 0.40

1.52, 1.29

1.8

B3+

3, 4

0.01, 0.11

1.60, 1.41

2.0

4

0.17

2.14

2.1

Si P

5+

Modifier to intermediate: alkalis and alkaline earths Cs1+

8

1.74

0.10

0.7

Rb1+

8

1.61

0.11

0.8

1+

8

1.51

0.12

0.8

Na1+

6

1.02

0.18

0.9

K

Li

1+

4, 6

0.59, 0.76

0.26, 0.22

1.0

Ba2+

8

1.42

0.26

0.9

Sr2+

8

1.26

0.29

1.0

Ca2+

6, 8

1.00, 1.12

0.36, 0.33

1.0

4, 6

0.57, 0.72

0.53, 0.46

1.2

4

0.27

0.75

1.5

1.26

0.29

1.8

Mg

2+

Be2+

Modifier to intermediate: selected others Sn2+ Pb

2+

8e

0.98, 1.29

0.37, 0.28

1.9

Mn2+

6

0.83f

0.42

1.5

Fe2+

6

0.78f

0.44

1.8

Zn2+

4, 6

0.60, 0.74

0.52, 0.45

1.6

2+

Ni

4, 8

e

4, 6

0.55, 0.69

0.55, 0.48

1.9

La3+

8

1.16

0.47

1.1

Nd3+

8

1.11

0.49

1.1

Er3+

8

1.00

0.54

1.2

3+

8

1.02

0.53

1.2

Sc3+

6

0.75

0.67

1.3

0.76

0.67

1.9

0.84

0.83

1.4

Y

3+

4

Zr4+

8

Sb

e

Appendix A

Table A.1 (Continued) Coordination

Ionic radiusb (Å)

Field strengthb

Electronegativityc

6

0.89

0.79

1.7

4, 6

0.41, 0.59

1.92, 1.58

1.8

a

U4+ Mo

6+

a

Common coordination numbers; others may occur. Five-coordinate states are also known for many cations listed with 4 and 6 coordination (e.g. Al, Si, Ti, Ni), which have intermediate radii and field strengths. b Cation field strength, valence divided by square of cation–oxygen distance, with the radius of the latter taken as 1.36 Å, the typical value for threecoordinated O. c Pauling electronegativity, from Pauling, L. (1970). General Chemistry. San Francisco: W.H. Freeman. d “Network former” description is generally most appropriate for lower coordination numbers. e Lone-pair electronic structure may lead to lower coordination than expected from radius. f Radii for high spin electronic state. g Effective ionic radius, from Shannon, R.D. (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst. A32, 751–767.

Table A.2 S.I. units and physical constants. Symbol

Value

Unit

Speed of light

c

2.999 792 458 108

m/s

Gravitation constant

G

6.674 08 (31) 10−11

m3/kg/s

Planck constant

h

6.626070 10−34

J/s

4.135669 2 (12) 10−15

eV s

9.109383 56 (11) 10−31

kg

Universal constants

Masses Electron

me

−27

Proton

mp

1.672621898 (21) 10

Neutron

mn

1.674927471 (21) 10−27

Avogadro number

NA

6.022140857 (74) 1023

Faraday constant

F

9.648533212331001 84 104

C/mol

Ideal gas constant

R

8.3144598 (48)

J/mol/K

kg kg

Physical constants

Boltzmann constant Stefan–Boltzmann constant Molar volume of ideal gases (at 273.15 K and 1 atm)

−23

k

1.380649 10

J/K

k/hc

69.503 87 (59)

m−1/K

σ

5.670367 (13) 10−8

W/m2/K4 −3

Vm

22. 413 962 (13) 10

eV

1.6021766208 (98) 10−19

m3

Conversion factors Electron-Volt Standard atmosphere

atm

3

101. 325 10

J Pa

Numbers in brackets denote the uncertainties in the final decimal places. Reported values by definition exact when no uncertainties are mentioned.

21

23

Section I. Glassmaking

Figure 1 The initial melting step in the making of float glass: the 1-m deep bath of raw materials melted by the flames of a cross-fired furnace (Chapter 9.7). Pulls ranging from 500 to 1000 tons/ day and mean residence times of at least 24 hours. Electro-fused refractory materials made up of alumina-zirconia-silica in contact with the melt, and of alumina and alumina-silica elsewhere (cf. Chapter 9.8). Source: Photo courtesy Simonpietro Di Pierro, Saint-Gobain Research Paris.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

24

Section I. Glassmaking

Compared with crude steel (1700 million tons/year worldwide) and especially with cement (4300 Mtons), glass (about 120 Mtons) is produced in relatively small quantities. In terms of product value or volume, however, the imbalance is significantly reduced since the cost of cement is about one sixth of that of window glass and steel about three times as dense. But what differentiates glass most from these other two inorganic pillars of modern civilization is the remarkable diversity of its uses illustrated throughout the Encyclopedia. In Europe, for which the data are the most readily available, the 35 Mtons produced in 2017 were split into container (21.4), flat (10.1), domestic (1.3), reinforcement (0.7), and other (1.1) glass. For both container and flat glass, the world market is estimated to be in the 60–80 billion $ range and is expected to keep growing in the years to come at yearly rates higher than 5% on average, with large geographical differences (cf. Chapter 9.6). And growth rates should be higher still for new products such as the smart glass used in a variety of electronic devices (cf. Chapter 6.10), whose market should increase by a factor of 3 from 2017 to 2023 from the current few billion $ per year. Like cement and steel producers, glassmakers sell more than 90% of their production to other industries. Most uses of glass are nonetheless familiar to anyone. These are summarized in the first chapter of this section where R. Conradt points out their strong dependence on chemical composition of the glasses and on their ensuing physical properties, explaining that the reason why the stilldominant soda-lime silicates were empirically found so early in the history of glassmaking is simply because they lie close to the eutectic of the Na2O–CaO–SiO2 system. Even though glass is now made in many different ways for different applications, the traditional procedure of making it by cooling of a batch melted at high temperatures remains by far prevailing. As one readily realizes when looking at the original glazing of late-nineteenthcentury buildings, the long-standing problem faced by glassmakers was to achieve chemical homogeneity. The mass production of defect-free glass is a relatively recent achievement. It has resulted from better furnaces (Figure 1; Chapters 9.7 and 9.8), higher melting temperatures, and more carefully selected raw materials. In the Chapter 1.2, S. Di Pierro thus discusses the importance of the specifications, sources, and management of raw materials needed to avoid high rejection costs after

melting operations that must be as fast as possible for economic reasons (Chapter 1.2). Being common to most glassmaking processes, fusion itself is then reviewed by R. Conradt from a dual thermodynamic and kinetic standpoint; the account includes not only the fundamental reaction and dissolution steps of the batch ingredients but also the fining and homogenization of the melt produced (Chapter 1.3). The second part of the section is devoted to the making of three basic products. Flat glass is dealt with by T. Kamihori. He begins with the first mechanical methods devised at the turn of the nineteenth and twentieth centuries, turns to the famous float process, which revolutionized the flat-glass industry in the 1960s, and ends with the recent downdraw processes widely used to produce new glasses for electronic applications with ever stricter quality specifications (Chapter 1.4). Container glass is considered by C. Roos who briefly presents the first forming devices designed at the beginning of the twentieth century before describing the various ways in which a bottle is now shaped with Individual Section machines at extremely high rates and may then be protected by treatments such as coating to enhance resistance to breakage (Chapter 1.5). In the next chapter, the drawing of continuous glass fibers for the relatively small but important reinforcement market is considered by H. Li and J. Watson in terms of both processes and composition evolutions driven by the need to improve chemical and physical properties (Chapter 1.6). That computer modeling of glassmaking has become an important tool to save time and money in the design or improvements of plants is explained by P. Prescott and B. Purnode in the final chapter of this section, which shows that, in industry too, fundamental insights and an accurate knowledge of the physical properties of melts have become badly needed (Chapter 1.7). Other processes and their products are too diverse to be gathered into a common chapter. Hence, they are described along with some of their important applications: the secondary fabrication of flat glass in Chapter 9.2, the making of thermal insulation fibers in Chapter 9.3, of sol–gel products in Chapter 8.2, of glass tubes in Chapter 7.7, and of light bulbs in Chapter 6.9. Other fabrication issues are dealt with in chapters devoted to modern furnaces (Chapters 9.7 and 9.8), cullet recycling (Chapter 9.9), and the history of glassmaking processes (Chapters 10.5, 10.7, and 10.8).

25

1.1 Glass Production: An Overview Reinhard Conradt RWTH Aachen University, Aachen, Germany

1

Introduction

The term “glass” may either refer to a special state of matter in general or to a group of industrially manufactured materials. The chart in Figure 1 presents, from a chemical point of view, an overview of a large number of systems that can be easily transferred into the glassy state. In this chart, special emphasis is given to the industrially relevant group of silicate glasses because, by volume or mass, the vast majority of the glasses produced belong to it. Nonsilicate oxide glasses and other inorganic nonmetallic glasses, nevertheless, play an essential role in the production of highly specialized functional materials such as optical fibers (Chapter 6.4). The group of “other glasses” comprises materials of very different nature. Within this group, metallic glasses (Chapter 7.11) are finding a variety of practical applications whereas organic glasses (Chapters 8.7 and 8.8) have long played a major role at the industrial scale. No attempt is made here to present a concise definition of the glassy state in general. From a practical point of view, however, glasses comprise a group of noncrystalline homogeneous and isotropic materials characterized by the absence of any microstructure. Thus, in contrast to (poly)crystalline materials, the bulk properties of which are essentially tailored via their microstructure, those of glasses are chiefly designed via their chemical composition; by contrast, thermal treatment has a comparatively small “fine-tuning” effect, which may, nevertheless, become crucial for specific products (e.g. optical or strong glasses).

Reviewers: Joachim Deubener, TU Clausthal University, ClausthalZellerfeld, Germany Yuanzheng Yue, Aalborg University, Aalborg, Denmark

At the atomic scale, the very same bonding interactions are present in isochemical condensed phases, i.e. in liquids, glasses, and crystalline polymorphs. Therefore, the chemical and electronic properties of glasses resemble those of their crystalline counterparts – with the reservation that glasses typically possess larger molar volumes, higher entropies, and higher (less negative) enthalpies of formation. In other words, they are thermodynamically less stable than crystals. Nevertheless, their macroscopic properties reflect in essence the same dependences on chemical composition as their crystalline counterparts. Without mentioning a host of other polymorphs, SiO2 may, for example, exist under ambient conditions as quartz, cristobalite, or vitreous silica; thermodynamic stability decreases in the given order. The same applies to hydrolytic stability, a macroscopic property for which all SiO2 polymorphs nonetheless stand out by comparison with other oxides. In general, information on atomic bond strengths, compound formation energies, and phase equilibria in a system of a given chemical composition may serve as reliable guidelines to explore the relation between the chemical composition of a glass and its macroscopic properties. It would go too far to draw the same conclusion for the relation between the chemical composition and the short-range order structure. Although there is ample experimental proof for such a relation in many systems [1], the general claim may be misleading, even erroneous is specific instances. Yet, in any case, the energetics pertaining to a specific glass structure is in general very close to that of an isochemical crystalline system. Energetics, in turn, is the key factor governing the relation between the chemical composition of a glass and its macroscopic properties. For this reason, equilibrium phase diagrams ([2, 3], Chapter 5.2) and thermochemical databases [4–9] are most helpful tools in the design of glass compositions with desired properties.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

26

1.1 Glass Production: An Overview

Glasses by chemistry

Non-oxide glasses

Oxide glasses

Silicate glasses

Non-silicate glasses

Inorganic nonmetals

Other glasses

Soda lime silicates

Borates

Chalcogenides

Organic glasses

Aluminosilicates

Phosphates

Halogenides

Metallic glasses

Borosilicates

Germanates

Oxynitrides

Molecular glasses

Lead silicates

Tellurites

Spin glasses

Silica (“quartz”)

Figure 1 Glass-forming systems, classified by chemical composition.

The industrial synthesis of glasses can also be based on a large systematic collection of experimental data of the properties of glass-forming systems [10–14]. Because at a microscopic level, atomic interactions are primarily pairwise (Chapter 2.7), one can in particular make use of empirical composition–property relations [15–20] of the type P = Σaj pj + bj pj 2 +

,

1

where P denotes a macroscopic property, pj is the mol or weight fraction of component j, and the aj and bj coefficients are sets of empirical parameters representing the contribution of component j to the property P of the glass.

2

• • •

Industrially Manufactured Glasses

• •

2.1 Properties of Manufactured Glasses in General In addition to the influence of chemical composition, it is the homogeneity, isotropy, and absence of any microstructure that brings about the main features shared by most industrially manufactured glasses. This group of materials stands out from others by

•

aesthetics; historically, the fact that glass was looking like gems has been the predominant driving force for the invention of glass as a material (Chapter 10.2). Aesthetic requirements today remain an important aspect, technically expressed as quality since, for instance, the presence of a single blister calls for the rejection of a 3 × 6 m sheet of flat glass.

•

its suitability for large-scale continuous primary forming as sheets, rods, tubes, and fibers. its extreme variability of shapes in discontinuous forming, comprising shapes with undercut. optical transparency. By virtue of their electronic and ionic properties, homogeneity, and absence of any microstructure, most glasses have an excellent transparency in the visible range. A standard float glass (4 mm thick) is transparent for light at wavelengths from 300 to 3500 nm, covering the entire visible (400–760 nm) and the near-IR ranges, the reflection losses of a standard glass sheet remaining slightly lower than 8%. an extremely wide and continuous compositional variability. Glasses can also easily incorporate functional components such as colorants. an extremely smooth surface, which originally allowed glass not to “smell” the odors of the substances it was storing. Today an as-received float glass possesses a roughness (root mean squared [RMS] value) of approximately 0.5 nm on the atmosphere side, and 1 nm on the tin-bath contact side. Even after an extended exposure to water or humid air at room temperature, RMS remains well below 10 nm. This makes glasses ideal substrates for metal and other functional coatings. excellent dielectric properties. Lead silicate glasses used in the back part of cathode-ray tubes reach dielectric constants of 20. It is true, this number does not match the extremely high values of functional ceramics (polycrystalline TiO2 ≈ 100, BaTiO3 ≈ 1000). When it comes to breakthrough voltages, however, the lack of any microstructure confers a clear advantage to glasses over polycrystalline materials: polycrystalline alumina withstands less than 8–9 kV/mm, whereas alkali-free

2 Industrially Manufactured Glasses

• •

glasses reach 40 kV/mm, like natural mica; glass ceramics doped with BaTiO3 crystals may even reach values higher than 400 kV/mm. excellent chemical durability against most chemicals. This is especially the case for silicate glasses in the low-pH range (i.e. with strong acids), making them excellent materials for chemical-process plants. an extremely high stiffness and intrinsic strength, both again by virtue of the absence of any microstructure. With a tensile strength of up to 4000 MPa (glass fibers), glass ranges among the strongest materials available. Its proverbial fragility is not a matter of strength, but of vulnerability of its surface and of low fracture toughness (Chapter 3.11).

It is a combination of the above features which gives glass such a prominent and indispensable place in the world of materials.

Other glass, comprising specialty glass Soluble glass (water glass)

For chemicals and detergents

Foam glass

For thermal insulation

Laboratory and industry

Lab ware glasses Glasses for process plants Electrode glasses

Artificial lighting

Incandescent lamps Gas-discharge lamps Semiconductor light sources Reflectors

Pharmaceutics and medicine

Ampoules and vials Antibacterial glasses Bioactive glasses

Optics

Eyeglasses

2.2 Classification of Glasses by Commercial Branches

Cameras, microscopes, telescopes

From a technical point of view, glasses are classified in terms of applications rather than chemical composition. The following list presents the most important groups of industrial products under this aspect.

Telecommunication fibers

Fiber optics and endoscopy Laser glasses Electronics and energy generation

Glass hollowware Container glass

Substrate glasses and display glasses

Flaconnage

Glasses for thermal power generation

Stemware, kitchenware, vases

Flat glass Architectural glass

Radiation protection

Radiation shielding windows

Silica (“quartz”) glass

For high-T processing

Glass for personal security and property protection Glass for photovoltaic application Fire-resistant glass

Sealing glasses Soldering and passivation glasses

Bottles (flint, green, amber) Preserving jars

Tableware

Electronic tubes

High-energy radiation detection windows For silicon crystal growth

Automotive glass

For silicon-wafer handling

Decorative interior glass and mirrors

For optical fibers

Fiber glass Continuous fibers (textile; reinforcement)

Multi-purpose (E) Acid resistant (A, C, E-CR) Alkali resistant (AR) High strength (R, S) Dielectric (D)

Fibers for thermal and acoustic insulation

Glasswool, stonewool

The pie chart in Figure 2 provides a rough overview of the shares of these categories by amounts of worldwide production. The figures given are estimates based on an evaluation of multiple sources for the time span 2003–2008. By absolute amounts, the 2005 world production reached about 124 million metric tons (31 in the European Union, 8 in Germany). Since then, an average annual increase of about 3.5% is observed. Whereas the production is more or less leveling off in most industrialized countries, the PR of China is among the main

27

28

1.1 Glass Production: An Overview

driving markets for this increase as its 2005 output of flat glass already accounted for more than 50% of the world production (cf. Chapter 9.6). For each type of glass products listed above, a typical chemical composition range has been adopted worldwide. The compositions of container and flat glass have never been developed by a scientific approach. Rather, they have remained pretty the same ever since the beginnings of glass makings (Chapter 10.2). Compositions have thus been very early constrained by the availability of affordable raw materials, the need to prevent water corrosion, and the highest temperatures reached in furnaces. A systematic scientific approach to glass compositions did not begin before the nineteenth century, chiefly promoted by the work of individuals such as Fraunhofer,

Container

Faraday, Harcourt, Abbé, or Schott (Chapter 10.11). Since then, this scientific approach has remained the basis for designing not only the compositions of most specialty glasses but also to improve those of existing products. For example, there is a quest among the producers of continuous fibers for completely new compositions with outstanding mechanical or chemical properties such as high modulus for lightweight construction composites or extreme alkali resistance for concrete reinforcement. In other cases, the driving force for development stems from environmental or health concerns and legislation. As examples, lead and arsenic oxides are being replaced in the formulae of optical glasses, solder and sealant glasses, and even in crystal tableware, whereas insulation-fiber compositions have been reformulated to avoid any confusion with asbestos fibers whose cancerogenic potency is well known. The typical composition ranges of current glass products are summarized in Table 1.

3

44/50/58

Process-controlling Properties

3.1 Viscosity

29/25/23 12/15/11 15/10/8 Flat

Fibers Others

Figure 2 Glass production by branches; figures in % in the sequence world/United States/Europe.

Among all the properties of a glass-forming substance, the viscosity–temperature relationship is by far the most important practically in glass making. Referring to Chapter 4.1 for an in-depth review of this topic, here we will consider it from a simpler technological point of view. The main feature then is that the viscosity of a glass-forming liquid extends over a range of 12–14 orders of magnitude, which thus involves large rheology changes in the temperature range relevant to glass manufacturing

Table 1 Typical compositions of industrial glasses comprising main oxides only (no colorants or impurities); compositional ranges from multiple sources (e.g. [13]) or typical individual examples (wt %).

Oxide

Container glass

Float glass

Crystal glass

Display glass

E fiber glass

Glass wool

Stonewool

Lowα glass

Soluble glass

SiO2

66–75

70–74

66.0

65.0

52–60

56–66

35–48

70–81

66–77

1–3

0.5–1.5

18.0

12–16

0–6

12–28

1.0

0–9

3–9

TiO2 Al2O3

1.0 2.0

0–3

Fe2O3

2.5–5

3–12

B2O3

10–15

MgO

0–4

0–4

4.0

7.0

0.5–4.5

1–5

2–11

1.0

CaO

8–12

7–10

6.0

6.0

16–24

5–11

10–28

1.0

BaO

2.0

3.0

ZnO

3.0 0–2

13–17

1–6

4–8

0–2

1–6

0–3

Li2O

0–1

Na2O

11–15

12–14

K2O

0–2

0–1

0–1 8.0

23–34

3 Process-controlling Properties

Table 2 Viscosity ranges of industrially manufactured glasses. Viscosity as log η, η in dPa s

Process range, technological meaninga

Melting 2.0

Typical of a soda-lime silicate glass melt at 1450 C

3.0

Transfer to forming area Volume relaxation time is 4.0 may in contrast be vitrified at moderately low cooling rates. Of great interest, therefore, is the possibility to predict the viscosity of a glass melt as a function of its temperature

and chemical composition. From measurements performed for a variety of samples, sets of incremental factors have been empirically derived by regression analysis for this purpose. The left-hand part of Table 3 presents such a widely used database [19] with which the effect of additions of individual oxides (by weight and molar amounts, respectively) have been calculated for a sodalime silicate. The temperature T(n.n) at which viscosity reaches 10n.n dPa s is thus calculated as T n n = a SiO2 + 100

a j

y j y SiO2 , 3

where y(j) is the weight fraction of oxide j. Helpful guidelines for the design of the viscosity curve of a mass-produced glass may be derived from the graphs of Figure 4. For example, replacement of 1 wt % SiO2 by 1 wt % Li2O to yield a glass 73 wt % SiO2, 10 CaO, 16 Na2O, 1 Li2O lowers the temperature at log η = 4.0 and 13.0, relative to the base glass, by 45 and 29 K, respectively. Among the alkali oxides, lithia is the strongest liquidus flux; it significantly lowers viscosity at all levels. Boron oxide has a similarly strong effect, however, at hightemperature only. So it reduces the working range (the

Table 3 Empirical factors for the calculation of viscosities [19] and elastic properties [21, 22] (units revisited) from composition. Viscosity

Elastic properties

a(j) for T(2.0) ( C)

T(4.0) ( C)

T(6.0) ( C)

Validity range (wt %)

V(j) (cm3/mol)

SiO2

1847.80

1249.70

962.90

60–77a

28.0

64.5

TiO2

−4.00

−4.00

−4.00

0–8b

29.2

86.7

b

ZrO2

8.65

7.96

8.16

0–8

30.2

97.1

Al2O3

8.32

5.23

4.01

0–8a

42.8

134.0

−21.62

−11.97

−6.42

0–14a

41.6

77.8

—c

—

—

B2O3 - “-

a

U(j) (GPa)

Oxide j

0.5122

0.3182

0.1900

MgO

−5.87

−0.12

0.91

15.2

83.7

CaO

−11.27

−3.99

−0.74

4–13a

18.8

64.9

BaO

−5.67

−3.04

−1.88

0–17

b

26.2

40.6

ZnO

−5.37

−1.99

−0.71

0–9b

15.8

41.5

PbO

−4.85

−3.17

−2.24

0–12

23.4

17.6

Li2O

−35.54

−30.04

−26.45

0–3a

16.0

80.4

Na2O

−12.65

−9.19

−7.06

10–17

22.4

37.3

K2O

−5.93

−4.17

−3.53

0–9a

37.6

23.4

Error

±4.7 K

±3.4 K

±3.2 K

—

n.s.

n.s.

0–6

a

b

a

Combinations of these oxides, plus one. Oxide only, keep the error within the given ± range. c For boron oxide, the factors in the second row are square terms; thus, the sum for each T(n.n) has to be expanded by a term 10 000 a(B2O3) [y(B2O3)/ y(SiO2)]2. b

3 Process-controlling Properties

By weight 0

By molar amounts

K2O

0

Na2O

PbO

K2O

–20 –20

Na2O Li2O

–40

PbO B2O3

Li2O

B2O3

ΔT in K

–40 –60 20

20

ZrO2

ZrO2

Al2O3

CaO MgO

0

ZnO

–20

Al2O3

BaO

ZnO

MgO

0 BaO

CaO

–20 0

8

16 0

8

16

0

8

16 0

8

16

log η, η in dPa·s

Figure 4 Temperature change brought about by a replacement of 1% of SiO2 by another oxide in the base glass composition 74SiO2, 10CaO, 16Na2O; left side: for oxide amounts by wt; right side: for molar amounts.

“length”) of a glass. In the language of glass technologists, boron oxide makes a glass “short.” Lime strongly reduces viscosity at high temperatures; the effect is almost as strong as with soda. Thus, if viscosity needs to be lowered in this range, inexpensive limestone as a calcium carrier raw material may be used instead of expensive soda ash as a sodium carrier. Also note that lime, quite in contrast to magnesia, makes a glass “short.” One can thus extend the working range of a glass by manipulating its CaO/ MgO ratio. Alumina makes at the same time a glass more viscous and “longer.” Although not giving any in-depth scientific understanding, these empirical tools undoubtedly have their merits in glass technology. 3.2

Liquidus Temperatures

Most industrial glass-melting processes run in a continuous way 365 days per year over periods of 2–15 years. This operation time depends on the type of glass and on the corrosion wear of both the refractory lining of the melting tank and channels guiding the melt to the working stations. A maximum temperature of about 1500 C is needed to achieve homogenous fusion; at the exit of the furnace, the melt still is at about 1350 C. This temperature makes it necessary to cool steadily the melt down to T(3.0) while keeping a safety margin ΔT above the liquidus temperature Tliq of the particular composition to prevent precipitation of crystals. This

yields a constraint of a minimum temperature of T(3.0) + ΔT required to ensure a crystal-free glass. This constraint is especially critical for continuous glass fiber production (Chapter 1.5), but it applies to any other process as well before the forming step. Traditionally, liquidus temperatures have been determined experimentally to be represented graphically for simple-enough systems in the form of phase diagrams (Chapter 5.2, [2]). For complex compositions of industrial interest, they are generally determined with a gradient furnace whereby a series of 5–10 samples are heated for typically 24 hours in a temperature gradient spanning the expected range of Tliq. After quenching, the samples are examined by optical microscopy. The liquidus temperature is then bracketed by the treatment temperatures of the last homogeneous glass and that of the first sample in which crystallites are observed. In a more accurate approach, samples from the gradient furnace containing tiny amounts of crystals are reheated in a heating-stage microscope at a rate well below 1 K/min, and the temperature at which the last crystal dissolves is adopted as Tliq. Thanks to the progress made in thermodynamic modeling of melts (Chapter 5.3), an increasingly useful approach is to predict liquidus temperatures with one of the dedicated softwares designed to calculate phase equilibria relevant to glass making (e.g. 20). Empirically, however, simple rules have long been known to predict

31

1.1 Glass Production: An Overview

the alkali oxide that most strongly decreases viscosity is the least effective in lowering liquidus. Only boron and lead oxides cause strong decreases of both viscosity and liquidus. This may shed some light on the technological challenge raised by the replacement of lead oxide in the glass formulae of modern tableware and solder glasses. In ternary systems, the Na2O–CaO–SiO2 and CaO– Al2O3–SiO2 phase diagrams are especially important as they serve as references for soda-lime and most stonewool and reinforcement-fiber glasses, respectively (Figure 6).

the effects on a given oxide on liquidus temperatures. Illustrating again the predominantly pairwise nature of atomic interactions, they rely particularly on the topology of binary phase diagrams (Figure 5). The tremendous freezing-point depressions of SiO2 brought about by addition of alkali oxides as well as by boron and lead oxides are in fact so conspicuous that they have historically been at the basis of the development of glass technology. As illustrated by a comparison made between Li2O and K2O (Figures 4 and 5), of particular interest is the fact that

Figure 5 Liquidus lines of binary silicate systems (left: by wt, right: by mol); all systems comprising a divalent oxide, except BaO, show an extended stable miscibility gap; data source [2].

1800 Two liquids

Two liquids

BaO

1600

MgO

CaO

MgO

ZnO

1400

CaO

T in°C

BaO

ZnO

SrO

SrO

FeO

1200

Li2O

FeO Li2O

1000 Cs2O

800

Rb2O

Rb2O,

Na2O Na2O

PbO B2O3

Cs2O

PbO K2O

K2O B2O3

600 20

40

60

80

100

40

60

80

100

mol % SiO2

wt % SiO2

System Na2O–CaO–SiO2

System CaO–Al2O3SiO2

20 0 15 00 00 14 13

30

TR 16-10-74

25

13 0

0

0

10 5

0

2

14 0

CS

CR

1100 Na O 2 ·Ca O·5 S iO

15

CR

0

1200

CS

1000 950

NC3S6

CAS2

TR 1184

900

N

2C

S

3

10

0 130

wt % CaO

32

850 5

20

750

65 Na2O·2 SiO2

85

0

70

0

0

874

80

NS2

By experiment. TEU = 1170 °C 23.5 CaO 14.5 Al2O3 62.0 SiO2 1500

Q 75

50

3 Na2O·8 SiO2 wt % SiO2

55

1400 60

65

Figure 6 Ternary phase diagrams in versions of technological relevance; shorthand notation: N = Na2O, C = CaO, A = Al2O3, S = SiO2, Q = quartz, TR = tridymite, CR = cristbobalite; left: the basic system of all commercial hollowware and flat glasses; the triangles mark the positions of the compounds, Na2O 2 SiO2: the circle the position of the base glass 74 SiO2, 10 CaO, 16 Na2O; data source [2]. Right: the basic system of reinforcementfiber glasses; industrial compositions flock around the eutectic; calculation using FactSage® [23].

3 Process-controlling Properties

Figure 7 Miscibility gaps. (a) Extension of stable gaps in ternary borosilicate systems with different oxides as third component; the area shaded in gray refers to BaO; (b) isotherms of the (metastable) subliquidus immiscibility dome in the system Na2O–B2O3–SiO2.

(a)

SiO2

80

20

Na2O 20 30

10 850

(b)

550

80 755

60

40

60

750 700

60

40

650 600

ZnO PbO 20

40

BaO

CaO

80

20

MgO

20

40

60

80

550 500

70

80 590 90

B2O3

Me oxide

From Figure 6a, it is easy to understand why, in Antiquity (Chapter 10.3), glasses with silica contents of 70–74 wt % and amounts of lime not exceeding 12 wt % were already mass produced: Thanks to typical T(3.0) values of 1200 ± 10 C, it is comparatively easy to comply for them with the constraint Tmin = T(3.0) + ΔT. The particular composition “16-10-74” has been investigated in many scientific studies. It may be considered as a reference and the mother of all mass-produced glasses, including of course today’s float glass. That the Tmin constraint represents in contrast a real challenge for CaO–Al2O3–SiO2-based glasses is readily apparent in Figure 6b where only a narrow range around the ternary eutectic between tridymite [SiO2], wollastonite [CaSiO3], and anorthite [CaAl2Si2O8] qualifies for a successful production. In passing, note that Figure 6b has been calculated by using the thermochemical software and databases FactSage® [23]. The experimental position of the mentioned eutectic is also marked, thus displaying the degree of accuracy that may be expected from the calculation of liquidus for more complex compositions. 3.3

Liquid–liquid unmixing

If phase separation within a condensed system most commonly takes place via partial crystallization, it can also occur as liquid–liquid unmixing (Chapter 5.2). Ternary systems containing boron oxide illustrate that the phenomenon should certainly not be overlooked in glassforming systems. For ternary borosilicates, the boundaries of the composition domains where such an unmixing

takes place stably, i.e. above the liquidus, are indicated in Figure 7a. If temperature is represented in a third dimension, these domains define the base areas of immiscibility domes that eventually terminate at upper critical points at their tops. The isotherms of the immiscibility dome in the system Na2O–B2O3–SiO2, which is the base composition of all borosilicate glasses, are drawn in Figure 7b. Here, in contrast to Figure 7a, the entire dome comprising its upper critical point (755 C at composition 25-05-70 by wt) is located below the liquidus surface. Hence, liquid unmixing cannot take place during the initial melting step, but at lower temperatures during the forming process. This is one of the reasons why, in order to minimize phaseseparation effects, pharmaceutical and low-expansion borosilicate glasses are designed around a composition of 80 wt % silica. The system Li2O–B2O3–SiO2 (not shown here) displays a similar topology. It is only with glasses known under the trade name Vycor Glass that liquid unmixing is exploited on purpose. Here, after forming by conventional technology to the desired shape, phase separation develops upon annealing at an appropriate temperature to yield two interconnected phases, namely an Na2O- and B2O3-rich glass along with another one that contains more than 96 wt % SiO2. Then the former is leached out by a hot strong mineral acid, leaving behind a nanoporous skeleton of highSiO2 glass. This material may then be used directly as filter, for example, or sintered at temperatures below 1300 C to fabricate dense and almost pure silica glass articles much more readily than with pure SiO2.

33

1.1 Glass Production: An Overview

The numerical calculation of liquid–liquid immiscibility ranges in multicomponent systems (e.g. by using the software and databases mentioned in Section 3.2) is even more challenging than the calculation of solid–liquid equilibria. This is because available experimental data hardly reach beyond what has been sketched in the present section, and such a narrow base of information does not allow to fine-tune the parameters used in the calculations.

4 Glass Composition – its Relevance to Glass Properties 4.1 Property Optimization Both search and optimization of glass formulae begin with a given profile of target glass properties. In the following, three properties will be addressed as examples typically targeted in glass development, namely the elastic properties, the thermal expansion coefficient, and the chemical durability. From a scientific point of view, such a task should rest on deep insights on the relationships between chemical composition, glass structure, and glass properties. It is only from such a fundamental approach that ground-breaking developments of novel glasses with outstanding properties may be expected. But this goal is still a matter of fundamental research as expounded in the following chapters where this most challenging issue is pursued. For the time being, however, only few manageable tools and procedures of this kind are available for the technological community. To optimize properties, technologists thus rely largely on empirical approaches whereby, as applied to glass viscosity in Section 3.1, they use incremental oxide factors derived by statistical means from large numbers of experiments. One has, however, to keep in mind that these approaches represent only interpolations of what is already known. Hence, limited areas in compositional space leading to truly outstanding properties should be easily overlooked so that developments similar to the famous low-expansion metallic alloy Invar are very unlikely to be found this way.

(74–x) SiO2 10 CaO 16 Na2O plus addition x of oxide of labeled cation 3 P

at x = 0, E = 65.4 GPa Change ΔE of Young’s modulus in GPa

34

B 2

Li Zr

Mg Al Ti 1 Ca

0

Ba Zn, Pb

Na

K

–1 0

1

2

3

4

x in wt %

Figure 8 Change of Young’s modulus E in the base glass composition 74 SiO2 10 CaO 16 Na2O upon the replacement of x wt % silica by another oxide.

E= ρ

V j U j

x j

M j

x j

4

x j,

where x(j) and M(j) are the mole fraction and molar mass of oxide j, respectively, and ρ the density of the glass. As for Poisson’s ratio μ, it is calculated as μ = 0 5 – 0 278 ρ

V j

x j

M j

x j 5

The manner in which Young’s modulus varies when a glass composition of (74 − x)SiO2, 10 CO, 16 Na2O (by wt) is modified by an addition of x wt % of another oxide is illustrated in Figure 8. Young’s modulus can be raised by the addition of P, Li, B, Zr, Mg, and Al oxides, and in contrast lowered by oxides of heavy mono- and divalent ion oxides. True, such small additions do not yield major overall effects but the tendency is clearly shown.

4.2 Elastic Properties

4.3 Thermal Expansion Coefficient

Incremental oxide factors for the calculation of the elastic properties from the composition compiled in the righthand part of Table 3 are taken from a widely accepted earlier publication [21]; for the sake of clarity, they have been adjusted with respect to the units used, i.e. to cm3/mol for volume, and to GPa for modulus increments. Young’s modulus E is then calculated with

Incremental oxide factors for the calculation of the thermal expansion coefficient are compiled in Table 4. Again, the factors are taken from a widely accepted earlier publication [24], see also [15]. When inspecting the entries in Table 4, the reader will notice a number of conditions that have to be obeyed for specific compositions. These conditions reflect intrinsic structural changes, which

4 Glass Composition – its Relevance to Glass Properties

Table 4 Empirical factors for the calculation of the thermal expansion coefficient α20–300 in ppm/K; it is calculated from the molar fractions of oxides j like α20–300 = x(j) α(j). Increment α(j)

SiO2

10.5–10 x(SiO2) 3.8

Condition

x(SiO2) > 0.67 Otherwise

TiO2

10.5–15 x(SiO2)

ZrO2

−6.0

Al2O3

−3.0

B2O3

−1.26 φ

φ95 % SiO2; H2O, Al2O3, RO, R2O, Fe2O3

Quartz, free-water, mica, feldspars

Arena – Sable – Sabbia – Sand

20–200€/T

Sandstone

>95 % SiO2; H2O, Al2O3, RO, R2O, Fe2O3

Quartz, mica, feldspars, FeTi-oxides, free-water

Arenisca – Grès – Arenaria – Sandstein

Quartzite

>95 % SiO2; H2O, Al2O3, RO, R2O, Fe2O3

Quartz, mica, feldspars, FeTi-oxides

Cuarcita – Quartzite – Quarzite – Quarzit

Feldspar (concentrates from greywacke, arkose, pegmatite, granite, etc.)

17–20 % Al2O3; 11–15 % R2O; 98 % CaO, H2O

CaO, Ca(OH)2

Cal – Chaux – Calce – gebranntes Kalk

Marble

56 % CaO, 44 % CO2, MgO, SiO2

Calcite CaCO3, dolomite, quartz

Marmol – Marbre – Marmo – Marmor

Wollastonite

48 % CaO, 52 % SiO2

Wollastonite CaSiO3

Dolomite

30 % CaO, 22 % MgO, 47 % CO2, SiO2

Dolomite CaMg(CO3)2

MgO

Li2O

B2O3

BaO

80–450 €/T Dolomie – Dolomie – Dolomia – Dolomit

20–40 €/T 250–400 €/T

Magnesite

48 % MgO, 52 % CO2, CaO

Magnesite MgCO3

Talc

32 % MgO, 63 % SiO2, 98 % As2O5

Sb-oxide

>98 % Sb2O5

>2500 €/T

Se, Co, Cu, Cd, Mn

Prices only indicative as actual quotations strongly depend on quality (grain size distribution, iron content, and overall impurities), volumes, transportation costs (quarry-to-plant distance and transportation mode) and, of course, market-price fluctuations. RO = CaO and MgO; R2O = Na2O + K2O.

1.2 Raw Materials for Glassmaking: Properties and Constraints

Figure 1 Comparison between the compositions of the main raw materials used in glassmaking and those of some important glass products as projected in the pseudo-ternary Al2O3–R2O + CaO–SiO2 diagram.

Al2O3 wt % 0,0 Rocks Glasses

0,1

Bauxites 0,2

0,3 0,4 0,5

Kaolin

0,6

Basalt Reinforcement Opal fibers Glasswool

0,9

1,0 Limestone Dolomite R2O + CaO wt % Marble Na-K carbonates

Windows Mirrors SiO2wt % Windshields Bottles Solar panels

10 000

Dolomit e

helin

Quartz -sand Na e e-sy -sulfat e enite Quartz Cok -sand e (coars e Fe ) lds Lim pa Ph es r ton on oli e te

1000

-ca Na

ite ux Ba

80

rbo

nat

60

Fe-oxyde

anite

rbo

na

te

40

Colem

Li-

ca

20

μm

100

Nep

10 0

Sandstone Quartzite

Basalt

0,8

Gypsum

Nepheline-syenite Phonolite Feldspars Glass-ceramics Granite Pegmatite Pharmaceuticals

Anorthosite Rockwool

0,7

Sieve cumulate refusal (%)

44

100 Quartz-sand (fine)

Quartz-sand (coarse)

Na-carbonate

Limestone

Dolomite

Basalt

Phonolite

Bauxite

Na-sulfate

Coke

Nepheline-syenite

Feldspar

Fe-oxyde

Colemanite

Li-carbonate

Figure 2 Sieve particle size distribution (PSD) curves of the main raw materials used in glassmaking ( 13

285 0

1021 0.64

0

40 mol % SiO2

80

59

60

1.3 Fusion of Glass

(a)

(b)

(c)

(d)

Figure 4 Early stages of batch melting, manually sketched after the scanning electron microscopy micrograph. (a) Open-pore stage with granular solids and gas, the gas composition being dominated by the equilibrium between CO2 and O2 from trapped air and the furnace atmosphere. (b) Closed-pore stage with the development of a widespread primary liquid, a large ratio s of effective liquid interface (solid/liquid and solid/gas) and liquid volume, and a gas composition dominated by CO2, redox active materials, and polyvalent ions in the primary melt. (c) Reaction-foam stage characterized by large volumes of granular solids, bubbles, and melt, and by progressive melting of solids and decreasing s ratios. (d) Rough-melt stage, the melt being the predominant phase coexisting with considerable amounts of bubbles and undissolved grains and showing on top a seam of the primary foam formed.

bottom side, typically in an almost symmetrical way as the heat fluxes from above and below are of the same order of magnitude. The release of gases is in contrast asymmetric since those from the upper parts readily escape whereas those coming from the lower parts remain trapped below the batch. In a successful primary melting process, the majority of solids are digested, only a minor part being released to the rough melt. This requires good batch mixing and a well-balanced granulometry of the raw materials. The issue can be tested at the lab scale by so-called batch-free time crucible tests. In these simple tests, batch samples of 50–100 g are exposed to a laboratory furnace at 1400 C and the progress of melting is inspected visually after a given time.

4.3 Sand Dissolution All solids surviving primary batch melting have to dissolve in the viscous rough melt by slow diffusion processes under comparatively low driving chemical forces. This is one of the reasons why, even today, long dwell times are required for the fusion process. By mass, the sand represents the major part of solids that have to dissolve in this way. The process suffers from an especially unfavorable feature (Figure 5): the decrease of the silica concentration from the sand grain to the melt phase represents a strong chemical gradient that causes the grain to be surrounded by a seam of melt with a high viscosity and a low basicity. This gradient affects not only

4 The Conversion of Batch into Melt

wt % retained on sieve Solid reaction layer

Glass melt

40

Sand 1 Sand 2

30 Sand grain 20

Bubble cluster

10 Liquid diffusion seam 0

Figure 5 Schematic view of a dissolving sand grain; the grain is surrounded by a solid reaction layer (e.g. tridymite) followed by a liquid high-viscosity diffusion seam with decreasing SiO2 concentration, hence decreasing acidity, from inside to outside; gas bubbles – mostly O2 – precipitate at the interface solid/liquid; upon complete dissolution of the sand grain, a bubble cluster remains in the melt.

mass transport but also the solubility of gases, which generally decreases with decreasing basicity (cf. Chapter 5.7). Thus, gases dissolved in the rough melt tend to form bubbles around a dissolving sand grain. In addition, temperature-induced reduction of ferric iron takes place as described by the reaction 7 1 5− Fe2 + + O2 − + O2 2 Fe3 + O4 2 2 describing how firm [Fe3+O4] oxygen complexes give rise to the weak [Fe2+O6] complexes formed by ferrous iron. The equilibrium constant of the reaction is given by Kp =

Fe2 + Fe3 +

O2 −

7 2

P O2

1 2

3

so that, at constant redox state, tiny oxygen bubbles emerge at the boundary of the dissolving grain. Any dissolving sand grain leaves behind it a cluster of small bubbles, removal of these bubbles makes sense only if their generation is over. This is one of the reasons why sand dissolution and the fining process need to take place in separate parts of the furnace. In summary, successful sand dissolution is a prerequisite for successful fining. Even apparently small differences in the grain-size distributions of sands have a big impact in this respect. This statement will be demonstrated for two different sands. Let us assume that a spherical sand grain with radius r dissolves according to Jander’s kinetics: α r, t = 1 − 1 −

t t∗ r

3

, t∗ r =

r2 4 D

4

63

90

125 180 250 Mesh width of sieves in μm

355

Figure 6 Grain-size distributions of two different glass-grade sand qualities as determined with sieves of increasing mesh width.

Here, α(r,t) denotes the turnover, with 0 ≤ α(r,t) ≤ 1 and D a diffusion coefficient. The grain-size distribution is mathematically represented by a log-normal distribution, the differential form of which reads q r =

1 exp − 2π σ r

1 r ln r 50 2 σ

2

,

5

where r50 is the median radius of the particle size distribution and σ = ½ ln(r84/r16) is the standard deviation denoting the width of the distribution; 16 and 84% by mass of the sand are contained in the fraction smaller than r16 and r84, respectively. The values of r50 and σ are determined by an evaluation of the sieve analysis (Figure 6). Both sand qualities have an identical median d50 = 2 r50 = 180 μm, but different σ. An ensemble of grains with a size distribution q(r) then dissolves according to the equation r=

∞

4Dt

α r, t q r dr

q r dr +

At = 0

r=

6

4Dt

where 0 ≤ A(t) ≤ 1 denotes the reaction turnover of the entire ensemble. The results for the two selected sand qualities upon isothermal dissolution are shown in Figure 7 as obtained with the solution of Eq. (18) given in the Appendix. At first sight, both kinds of sands dissolve in about the same manner. But on closer

61

1.3 Fusion of Glass Melt viscosity: 150dPa·s corresponding to 1400°C

1.0 100

r in mm =

Size-distributed glass-grade sands 0.8

Monodisperse sand grains with d50 1.000

0.6

Sand 1: σ = 0.283

0.4

0.998

0.996 0

5

Limit of random dense spherical packing ϕmax = 0.64, foam formation

5 2

1

1 0.1

0.5

Sand 2: σ = 0.354 0.2

0.01

0.2

0.0

10 vSLIP in m/h

Turnover α (t)

62

d50 = 180 μm

0.1

D = 1·10–13m2/s 10 15 t in hours

1E-3 0.0

20

0.2

0.4

0.6

0.8

1.0

Volume fraction ϕ of bubbles

Figure 7 Dissolution turnover of the two sands of Figure 6 as a function of process time for isothermal diffusion with D = 1 10−13 m2/s. Inset: magnification of the results for nearly complete dissolution.

Figure 8 Rising velocity vSLIP of bubble swarms in a melt at a viscosity of 150 dPa s as a function of bubble radius r and volume fraction ϕ of bubbles.

ηeff = η 1 − ϕ ϕmax inspection (see inset), the difference does become large toward the very end of the process since Sand 2 needs significantly many more hours than Sand 1 to reach a 99.9% dissolution level, which is crucial for glass quality.

5

5.1 Physical Fining As noted above, the ideal onset of fining takes place when sand dissolution is complete. Physically, fining relies on two simultaneous processes, namely bubble removal by buoyancy and coalescence of small bubbles to form larger ones. The latter is driven by the release of energy associated with the excess internal pressure of a bubble relative to ambient. As given by Laplace’s formula, this excess pressure is ΔP = 2σ/r for a bubble of radius r with a surface tension σ so that the energy gained amounts to about 3.5 σ r when two bubbles of identical size merge. As for the buoyancy velocity v0 of a single bubble in a melt of viscosity η, it is given by a modification of Stokes’ law for dispersed phases with mobile boundaries known as Hadamard’s law: v0 = Δρ g r 2 3η,

where ϕmax = 0.64 is the maximum value of ϕ as given by random close spherical packing. But the density decrease caused by the presence of bubbles, which is proportional to 1 − ϕ/ϕmax, must also be taken into account. The rising velocity vSLIP of an individual bubble within a bubble swarm of volume fraction ϕ thus is vSLIP = v0 η ηeff = Δρ g r 2 3η 1 − ϕ ϕmax

Fining, Refining, Homogenization

7

where g is the gravitation constant and Δρ the density difference between the melt and bubble. For a melt with a volume fraction ϕ of bubbles, the effective viscosity becomes

8

2

9

The situation is illustrated in Figure 8 for a viscosity of 150 dPa s, which is that of a typical float glass melt near 1400 C. Up to a volume fraction of 0.4, bubbles bigger than 0.5 mm in radius safely escape during the available process time, whereas those smaller than 0.1 mm hardly reach any noticeable rising velocity. They rather rest relative to the environment. An especially critical situation occurs when the volume fraction approaches the limit ϕmax. In this case, bubbles of any size become stagnant so that a foam forms on top of the melt in the fining area as observed in a glass of beer. Hence, this problem calls for utmost care in the design of the chemical part of the fining process, and especially of the amount of fining agent used.

5.2 Chemical Fining As indicated by old glass specimens, bubbles cannot be completely eliminated with only physical fining. In a somewhat paradoxical way, better results are achieved if additional bubbles are produced within the melt at a sufficiently high, yet not too high, volume fraction to coalesce with the bubbles formed or entrapped during

6 Energetics of Glass Melting

melting. The process is known as chemical fining as it involves reactions with gas-releasing substances. For reasons of cost, chemical compatibility, and effectiveness, the most widely used agent is sodium sulphate (Na2SO4). By experience, 4 kg of Na2SO4 are added per ton of produced glass. During the early stages of batch melting, the sulfate dissolves in the melt. Under oxidizing conditions, it decomposes at 1400–1450 C according to the reaction Na2 SO4

Na2 O + SO2 g + O2 g ,

10

where the braces {−} denote the state “dissolved in the melt.” Under reducing conditions, sodium sulphate reacts with the Na2S formed during primary batch melting as follows: 3 Na2 SO4 + Na2 S

4 Na2 O + 4 SO2 g 11

The latter reaction already occurs at temperatures slightly below 1400 C. Oxygen fining is an alternative option. The agent typically used is Sb2O3; it is added to the batch in amounts of 3–5 kg per 1000 kg of sand, in combination with a four- to eightfold amount of NaNO3 [5]. At the moderately low temperatures of primary batch melting, Sb2O3 converts to {Sb2O5} provided that a sufficiently high oxygen partial pressure in the batch is established (Figure 4, stage b). This is achieved by the action of NaNO3, which decomposes at batch melting temperatures to release oxygen: 2 NaNO3

Na2 O + NOx + 5 − x O2

12

At increasing temperatures, the higher valences of polyvalent ions become increasingly unstable (see Chapter 5.6) so that the fining reaction actually reads Sb2 O5

Sb2 O3 + O2 g

13

The release of oxygen bubbles reaches its maximum at about 1300 C and extends beyond 1400 C. The negative side effect of this procedure is the formation of the NOx pollutant. A simple calculation will finally explain why experience and empirical knowledge still play the predominant role in the allotment of fining agents. As used in the batch in Table 4, a mass of 4 kg of Na2SO4 represents 56.3 mol of SO2, which, at 1400 C, 1 bar, would fill a volume of 7.6 m3. Now, 1 ton of melt, by contrast, fills 0.4 m3 only. Obviously, only a very minor part of the nominal SO2 ends up in gas bubbles otherwise a foam instead of a clear melt would be obtained. The major part of SO2 is in fact lost during batch melting, by evaporation from the melt surface, or is retained in the glass. Thus, the proper

allotment of fining rests on the small difference between sulfate input and the above losses. One of the rare attempts to perform a detailed sulfur balance of a glass furnace revealed that approximatively 0.25–0.3 kg of the sulfate added per t of glass are released in the form of fining bubbles [6].

5.3

Homogeneization

After the fining process, the melt is cooled down and homogenized thermally in a steady way. Small residual bubbles resorb themselves because the solubilities of most volatile species strongly decrease with increasing temperatures (Chapter 5.5). For this reason, care has to be taken to prevent local temperature rises from happening during the homogenization process otherwise the so-called reboil bubbles would form in the melt and could not be removed in any way. Among dissolved gases, N2 distinguishes itself by its decreasing solubility with decreasing temperatures. Thus, N2-containing bubbles escaping the fining process appear as very tiny bubbles called seeds in the final glass. Their number per unit mass of glass represents an important quality criterion. In container glass, a few tens of seeds per 100 g of glass are accepted. Float glass requires a much higher quality (one visible defect per 20 m2 already is considered a high defect density) and hence, much longer dwell times (approx. 1.5–2 days vs. 1 day for container glass) in the melting compartment.

6

Energetics of Glass Melting

The amount of energy involved in the fusion of glass is an issue of great interest to the glass industry. Referring to comprehensive quantitative treatments ([7, 8] and Chapter 9.8), we will give only a brief sketch of this issue within the scope of this chapter. The approach rests on the fact that, at constant pressure, the heat (enthalpy) transferred to or drawn from a system is thermodynamically the variation of a state function: as such, the intrinsic energy demand depends only on the initial and final states of the system and it can be determined without any consideration of what is going on along the process road. The initial enthalpy state is given by the sum of standard enthalpies H i at 25 C, 1 bar, of the individual raw materials i, weighted by their respective amounts mi in the batch: H

BATCH

= Σ mi H

i

14

The final enthalpy is given by the standard enthalpies of the batch gases g, H GASES = Σ mg H g, and of the glass,

63

64

1.3 Fusion of Glass

H GLASS, plus the heat content ΔH(Tex) of the glass at the exit temperature Tex. The standard enthalpy difference between inputs and products constitutes the chemical energy demand ΔH

chem

=H

BATCH

–H

GASES

–H

GLASS

15

The heat content of the melt at Tex is given by ΔH(Tex). For convenience, all enthalpy values are inserted in absolute figures, disregarding the minus sign given in thermochemical tables. The overall intrinsic heat demand Hex (exploited heat of the process) is given by H ex = 1 – yCULLET

ΔH

chem

+ ΔH T ex ,

16

where yCULLET denotes the weight fraction of cullet per amount of glass produced. It is true, real raw materials typically do not contain their main mineral phase only, but also contain minor amounts of side minerals. For example, a real quartz sand may contain, beside its main phase quartz, minor amounts of feldspar minerals, magnetite, spinel, etc.; a natural dolomite is typically composed of different minerals forming solid solutions in the system Ca– Mg–FeII–CO3 with an overall composition not too far from the pure phase CaMg(CO3)2. An accurate determination of the enthalpy values H i of real raw materials would thus require the evaluation of multicomponent phase diagrams. However, such an approach would hardly be accepted by the technological community. Beyond this, the gain of accuracy against a simpler approach is minor only. Thus, with the reservation to a more rigorous treatment [7, 8], only the enthalpy values H i of pure raw materials are given here in units of MJ/kg: Raw material i

Enthalpy H i in MJ/kg

Pure quartz sand

15.150

Pure albite (NaAlSi3O8)

14.952

Pure dolomite CaMg(CO3)2

12.549

Pure calcite CaCO3

12.058

Soda ash

10.659

Sodium sulfate

9.782

Carbon

0.000

Calumite®

13.561

For the batch gases, the following values hold: CO2: 8.941; H2O: 13.422; SO2: 4.633; O2: 0.000. The energy calculation for the real glass composition of Table 2 (where the tiny amount of TiO2 has been allotted to SiO2) is summarized in Table 5. The position of the

glass composition in the phase diagram in units of kg of equilibrium compounds per t of glass is found by the following simplified procedure: NAS6 = 51.440 Al2O3 – 55.697 K2O, KAS6 = 59.102 K2O, hm = 6 Fe2O3, FS = 7.345 Fe2O3, MS = 24.907 MgO, NC3S6 = 35.112 CaO, NS2 = 29.386 Na2O + 19.346 K2O – 17.867 Al2O3 – 10.824 CaO, S = difference to 1000 kg. Oxide amounts are to be inserted in wt %. For the components k, the shorthand notation hm = FeO Fe2O3, F = Fe2O3, M = MgO, C = CaO, N = Na2O, K = K2O, S = SiO2 is used. Column m(k) in Table 5 lists the resulting amounts of the constitutional components of the glass. By this procedure, one finds that the standard enthalpies of formation of the glass and melt are 14 189.7 MJ/t at room temperature and 12 665.9 MJ/t at 1300 C, respectively. The enthalpy physically stored in the melt at 1300 C relative to the glass at 25 C is thus 1523.8 MJ/t. By the weighted sum of the heat capacity of compounds k, the latter value can be adjusted to any other exit temperature of the melt. For the batch given in Table 4, column “mII(i)”, a chemical energy demand of ΔH chem = 461.8 MJ/t is obtained. Fusion of the selected batch with 50% cullet (yCULLET = 0.5) thus requires an intrinsic energy demand of H ex = 1 – yCULLET = 1745 7 MJ t

ΔH

chem

+ ΔH T ex 17

A well-constructed and operated melting furnace (end port, air-gas fired) reaches an efficiency of heat exploitation ηex of 48%. Thus, the actual energy demand Hin of the melting process amounts to Hin = Hex/ηex = 3637 MJ/t. This result is very much in line with industrial experience. Calculations of this kind are of high importance for the evaluation of glass furnace performance [9], for furnace design, as well as for the energy optimization of batch and glass compositions.

7

Perspectives

Although the energetics of the fusion process may be considered as satisfactorily assessed, the kinetic aspects of fusion are not yet well enough understood. The efficiency of heat exploitation ηex of a furnace varies according to a hyperbolic law of the type ηex = 1/(A + B p) with the production rate p (t/h). Thus, furnaces are preferentially operated at the highest achievable rates. The limits for p are determined by the rate of heat transfer or the time

References

Table 5 Calculation scheme for the energetics of a soda-lime silicate glass (composition in wt %).a Oxide

wt %

Compound k

H

k,GL

MJ/kg

Hk,1300

cP,k,L

m(k)

m(k) H

MJ/kg

kJ/kg K

kg/t

MJ/kg

k,GL

m(k) Hk,1300

MJ/kg

SiO2

71.84

hm

4.4313

3.0196

0.9217

0.18

0.8

0.5

Al2O3

1.50

FS

8.7888

7.3999

1.0589

0.22

1.9

1.6

Fe2O3

0.03

MS

14.9599

13.2740

1.4582

74.47

1114.1

988.5

MgO

2.99

NS2

13.4194

11.6862

1.4335

284.99

3824.4

3330.4

CaO

9.47

NC3S6

14.0278

12.6137

1.3301

332.51

4664.4

4194.2

Na2O

13.96

NAS6

14.7131

13.2234

1.2358

65.46

963.2

865.6

KAS6

14.0258

12.5775

1.3755

12.41

174.1

156.1

S

15.0023

13.6179

1.4347

229.75

3446.9

3128.8

Sum 1000.00

H GLASS 14 189.7

K2O

0.21

Sum

100.00

H1300,MELT 12 665.9

ΔH1300 1523.8 a

H k,GL = standard enthalpy of component k in the glassy state; Hk,1300 = enthalpy of k in the liquid state at 1300 C; cP,k,L = isobaric heat capacity of liquid k; m(k) = equilibrium amount of k in the multicomponent phase diagram; H GLASS = standard enthalpy of the resulting glass; H1300,MELT = enthalpy of the melt at 1300 C; ΔH1300 = heat content of the melt at 1300 C relative to the glass at 25 C. b hm = FeO Fe2O3, F = Fe2O3, M = MgO, C = CaO, N = Na2O, K = K2O, S = SiO2.

demand of the fusion process required to achieve an acceptable glass quality. As of now, however, one does not even known which of the above constraints controls the melting rate. As a matter of fact, the answer depends on both furnace and batch design. A better understanding of redox and acid base reactions in real furnaces is also desired. Although these reactions are well understood at the laboratory scale, the transfer to a real production situation is still set by experience rather than by scientific principles. In view of the large impact of these reactions on glass quality, progress in this area would be highly appreciated. Finally, the glass industry is engaged in a quest to lower its overall energy consumption to decrease its operating costs and to satisfy increasingly stringent legislation imposed on high-temperature industrial processes. The design of faster conversion batches is becoming important in this respect. Conventional glass formulae and batch recipes are no longer taken for granted. Efforts are in particular made to design batches that would melt along reaction pathways ensuring higher turnover rates than current randomly mixed batches. Progress may be achieved with selective batching, granulation processes bringing the reaction partners into close contact at the μm scale, preparation of core-shell type pellets, or selective preheating of specific raw-material combinations of the batch. In each case, of course, a prerequisite would be that the obtained energy savings are not offset by increased batch costs.

Appendix The results plotted in Figure 7 for the dissolution of an ensemble of grains have been obtained from the analytical solution to the integral A(t) of Eq. (6) given by: 1 1 3y s2 1 s erfc erfc ln y + exp ln y + 4 2 s 2 s 2 3y2 1 ln y + s exp s2 erfc − s 2 y3 9s2 1 3s + ln y + , exp erfc s 2 2 4

A t = 1−

y=

4 D t , s= r 50

2 σ

18 Here, erfc(z) denotes the complementary Gaussian error function of argument z, while y and s are used as abbreviations in the formula. It is true that sand dissolution does not proceed isothermally at a constant diffusion coefficient D in a real fusion process, but the utmost importance of the grain-size distribution for a successful fusion process is nonetheless demonstrated clearly.

References 1 Cable, M. (1998). A century of development in glass

melting. J. Am. Ceram. Soc. 81: 1083–1094.

65

66

1.3 Fusion of Glass

2 Simpson, W. and Myers, D.D. (1978). The redox number

6 Müller-Simon, H. (1999). Sulfate fining in soda

concept and its use by the glass technologists. Glass Technol. 19: 82–85. 3 Nemecˇ, L. and Cincibusová, P. (2009). Glass melting and its innovation potentials: the potential role of glass flow in the sand dissolution process. Ceramics Silikaty 53: 145–155. 4 Nemecˇ, L., Jebavá, M., and Dyrcˇíková, P. (2013). Glass melting phemomena, their ordering and melting space utilization. Ceramics Silikaty 57: 275284. 5 Jebsen-Marwedel, H. and Brückner, R. (1980). Glastechnische Fabrikationsfehler, “Pathologische” Ausnahmezustände des Werkstoffes Glas und ihre Behebung; Eine Brücke zwischen Wissenschaft, Technologie und Praxis, 229. Berlin: Springer.

lime silicate glasses (in German). In: HVG Course 1999, 45–72. Offenbach: Deutsche Glastechnische Gesellschaft. 7 Conradt, R. (2008). The industrial glass melting process, Chapter II:24. In: The SGTE Casebook. Thermodynamics at Work (ed. K. Hack). Boca Raton: CRC Press. 8 Conradt, R. (2010). Thermodynamics of glass melting. In: Fiberglass and Glass Technology – Energy-Friendly Compositions and Applications (eds. F.T. Wallenberger and P.A. Bingham), 385–412. Berlin: Springer. 9 Conradt, R. (2019). Prospects and physical limits of processes and technologies in glass melting. J. Asian Ceram. Soc. 7: 377–396.

67

1.4 Primary Fabrication of Flat Glass Toru Kamihori Production Technology Center, Asahi Glass Co., Ltd., Yokohama-shi, Kanagawa, Japan

1

Introduction

Flat glass is ubiquitous in the modern world, from the facades of high-rise buildings to the large windows of automobiles, the solar power generation systems, and the various kinds of displays that are now integral components of daily life. Not only did these new applications cause a tremendous increase of the world production from less than 7 105 in the early 1960s to 59 106 metric tons in 2014 (then with an annual growth rate of 7%), but they have also yielded dramatic improvements in glass quality and functionalities. For a glass material that had been manufactured for 2000 years with very little change, the industrial evolution observed during the last 50 years has been incredibly rapid indeed! As experienced by ancient Roman glassmakers, flat glass made by pouring the melt on a solid substrate has a surface that is not smooth enough to ensure good transparency. Until the beginning of the twentieth century, flat glass had for this reason to be produced out of hollow glass to keep the defect-free surface conferred by fire polish. As made in this way with either the crown or the cylinder process (Chapter 10.8), production of flat glass was very labor-intensive, restricted to relatively small sheets and subject to wastage when cut into pieces for use. Besides, it did not yield high-quality products as is obvious to anyone looking at an old window where objects are often seen distorted through the glass in which defects and streaks are also generally present as a result of the detrimental effects of temperature or composition heterogeneities that could not be avoided during the melting and forming processes.

Reviewers: S. Inoue, National Institute for Materials Science, Tsukuba-shi, Ibaraki, Japan T. Yano, Tokyo Institute of Technology, Meguro-ku, Tokyo, Japan

Mechanization was pioneered from 1894 to 1916 by J. H. Lubbers at the American Window Glass company. Glass cylinders of constant diameter and wall thickness began in 1904 to be blown successfully with a wellcontrolled low-pressure air flow issued for 15–18 minutes from a machine that was dubbed iron lung [1]. Making much bigger cylinders, which eventually reached 1 m in diameter and more than 13 m in length (Figure 1), did reduce considerably cost and labor (whence the very strong Union opposition met by the new process), but did not result in consistently good quality because of the wavy surface and optical distortion induced by the flattening stage. Thanks to updraw processes designed in Belgium and in the United States, it then became possible in the following decade to bypass the hollowglass step. But these processes remained discontinuous because devitrified material had to be removed periodically from the production line. A true revolution in glass producing thus occurred when the float process was introduced in the 1950s to produce sufficiently good flat glass to make the grinding and polishing steps ensuring high-quality sheets obsolete. Production became in addition completely continuous, which allowed the productivity to be considerably increased without affecting surface quality. Because of the very large amount of glass produced, however, the float process may be impractical when production volumes are small or the glass composition has to be changed frequently. For specialties such as crown glass for niche markets or new glass for electronics markets, older processes are thus still used or new ones have been designed to achieve in particular a high flexibility of throughput and broad ranges of thickness and width. In this chapter, we will review the various processes that have been designed to achieve these goals, beginning with the first developed ones whose interest is now only historical. The early processes are denoted as updraw because

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

68

1.4 Primary Fabrication of Flat Glass

Figure 1 Very large glass cylinders blown mechanically with the Lubbers process for flat-glass production [2].

the glass was drawn upward, in contrast to the downdraw processes, which have subsequently been developed for specialty glasses. No attention at all will be paid to the synthesis of the glass itself, which is described in Chapter 1.3. The emphasis will thus be put on the forming process and on the material parameters such as viscosity, density, heat capacity, and surface tension that control it. For more detailed descriptions, the reader will be referred to the available technical literature [1–9].

2

Overview

The main features of past and current processes are summarized in Table 1. Although updraw processes are no longer used for commodity applications, it remains worthwhile to examine their mechanisms and forming principles from a technological viewpoint. For flat-glass forming, the essential requirement is to achieve the constant desired thickness, which now ranges from around 25 mm to less than 50 μm, with the specified width at a commercially admissible cost. Additionally, a flatter and smoother surface is requested. The essential forming defects are mainly of two kinds depending on whether they are derived from locally uneven deformation or undesirable stress. The former is caused by viscosity heterogeneity of glass originating from chemical impurities

or temperature irregularity, and the latter is caused by fluctuation of forming condition or stress imbalance. Architectural glass must, for instance, satisfy appropriate transparency and reflection, but glass for automobiles and electronics products has to meet much more demanding quality specifications even for thinner glass whose production becomes increasingly difficult. In all forming processes, two distinct steps are involved once the glass has been melted at about 1500 C, refined, and homogenized in the melting tank. The first is its delivery under conditions at which the temperature, thickness, and flow rate must be as stable and uniform as possible throughout its whole width at a viscosity of about 102–103 Pa s (i.e. at 1200–1000 C for soda-lime silicate). In the second step, the more viscous molten glass cooled down to a temperature at which the viscosity is 103−106.65 Pa s (i.e. at 1050–700 C for soda-lime silicate) is stretched in the longitudinal direction, while minimizing simultaneous narrowing of the glass ribbon. In both glass delivering and stretching systems, properties of the molten glass such as surface tension, gravitational force, and tensile stresses are critical factors, whereas the kinetic aspects of the process are tightly controlled by means of drawing chambers, débiteuses, draw bars, rolls, float baths, slots, fusion pipes, etc. Besides, heat management through variously devised heaters and coolers is another fundamental aspect because glass properties vary very strongly with temperature. In addition to physical effects, one must also take into account chemical factors such as possible devitrification and chemical reactions between the glass and other materials, which may themselves depend on glass composition. Since annealing follows forming, the conditions of the former process are greatly influenced by those of the latter. The formed glass ribbon is cooled down and conveyed to an annealing lehr where the decreasing glass temperature is carefully controlled so that residual stresses caused by viscoelasticity are relaxed between the annealing and strain points (1012 Pa s, 570 C, and 1013.6 Pa s, 530 C, respectively, in soda-lime silicate), and breakage caused by thermal stresses is minimized upon cooling down to room temperature. Finally, optical devices are installed at the downstream part of production line to detect in the glass at room temperature any visible defects such as bubbles, stones, streaks, etc., which originate either from the melting tank or the forming process. These defects are at once clearly marked on the glass ribbon and their positions are usually electronically recorded for optimized cutting either at the end of the production line or by the user according to its specific application. For flat glass to be used in buildings, any 10 m2-sheet must, for instance, have fewer than three defects with a maximum size of 1 mm (which would be tantamount to finding fewer than three coins on a football field!).

2 Overview

Table 1 Comparison of forming processes. Mechanism Step 1: Preliminary forming (Molten glass delivering)

Step 2: Main forming (Stretching)

Category

Process

Updraw process

Fourcault process

Glass flow toward débiteuse and upward flow through débiteuse slot

Colburn process

Current situation

Advantage

Disadvantage

Upward drawing against gravity by pairs of rolls

Earliest continuous production Smaller investment

Quality (Draw lines) Cyclic operation

Glass flow toward drawing point and upward flow from free surface

Upward drawing against gravity by pair of knurled rolls and bending roll

Higher output Wide range of thickness

Low surface quality Complex operation

Pittsburg Pennvernon process

Glass flow around draw bar and upward flow above draw bar

Upward drawing against gravity by pairs of rolls

Better surface quality Longer cycle

Distortion Thickness deviation

Asahi process

Glass flow toward Asahi blocks and upward flow through gap between Asahi blocks

Upward drawing against gravity by pairs of rolls

Smaller investment Longer cycle

Cyclic operation

Roll out process

Continuous double roll process

Horizontal glass flow through forehearth

Pressing by pair of rolls

Value added with patterns and wires Versatility Smaller investment

Limited applications

Popular for patterned glass, wired glass, and specialty glass

Float process

For thinner sheet (Top roll process)

Viscous flow with equilibrium thickness in upstream area of bath

Horizontally stretching by conveyor rolls and top rolls

Large-scale production (productivity) Quality (flatness) Flexibility for thickness and width

Large investment Constraint of chemical elements in glass

Widely operating in the world for various applications

For thicker sheet(Fender process)

Viscous flow with restricted width by pair of fenders

Cooling to appropriate temperature in fender area (without stretching)

+ Thicker and larger sheet

Slot downdraw process

Glass flow toward slot and downward flow through slot

Stretching by pairs of rolls and gravity with anchored to slot

Thinner glass Small-scale production

Flatness and surface quality Limited width

Customized/ modified process operating for specialty glass

Fusion downdraw process

Glass flow through trough and over weirs, downward flow on both sides of fusion pipe

Stretching by pairs of rolls and gravity with anchored to root

Thinner glass High surface quality

Minute control required (temperature, glass flow) Constraint of liquidus viscosity

Popular for specialty glass

Downdraw process

Almost obsolete for commodity applications Customized/ modified process operating for specialty glass

69

70

1.4 Primary Fabrication of Flat Glass

3

Updraw Processes

3.1 Fourcault The first manufacturing method successfully industrialized and commercialized was invented from 1901 in Belgium by É. Gobbe and É. Fourcault and finally implemented industrially in 1912 by É. Fourcault in his family company in Charleroi. With this process, the molten glass was drawn vertically through a débiteuse into a continuous glass ribbon. The débiteuse, a rectangular refractory piece with a spindle-shaped slot at the center, was immersed into the molten glass. The molten glass flowing up from the slot was drawn upward and immediately cooled by the coolers while conveyed upward by pairs of rolls in a such a manner that its width was kept constant. The formed glass was annealed along the way and finally cut off at the top of the 8–10 m drawing tower (Figure 2). The flow rate was controlled by the immersion depth of the débiteuse, the shape of the slot, and the cooling exerted, whereas the thickness of the sheet was determined by the drawing speed. The advantages of this process were many. Not only could production be made with several drawing machines for a single glass tank, but wide ranges of thickness (1–8 mm) and width (1.5–2.5 m) were possible for glass sheets formed with a relatively uniform thickness. In terms of disadvantages, continuous operation was impossible because of the need after about two weeks of operation to remove the devitrified glass that was accumulating around the slot of the débiteuse and on the inner surfaces of the drawing kiln. Whereas the former devitrified

Glass sheet Drawing tower

Typical slot shape of Débiteuse

material was causing draw lines, the latter changed the flow rate and flow pattern toward the débiteuse. In addition, it was impossible to maintain a completely stable throughput because of bubble formation at the beginning of a drawing cycle and draw-line problems and instability toward the end [1, 3–6].

3.2 Colburn At the same time the Fourcault process was being developed, the American inventor I. W. Colburn (1861–1917) was experimenting vertical drawing without a débiteuse. His first patent was taken in 1902 but the company he founded in 1906 to produce glass went bankrupt five years later. Working thereafter for the Toledo Glass Company, which had bought his patent, Colby was eventually successful in 1913. With his process, the molten glass introduced into a shallow drawing chamber was drawn upward from the free surface, its edges being gripped and driven by pairs of knurled rolls, and cooled immediately. After being reheated by a gas burner, the formed glass was brought horizontally by a bending roll and conveyed to a horizontal annealing lehr (Figure 3). Since the surface condition and flatness of the bending roll directly determined the quality of the glass sheet, the choice of an appropriate metal as well as the surface treatment and temperature control of the bending roll were crucial. Typically, two drawing chambers were mounted on one glass tank. The 0.9–6 mm thickness range obtained was similar to that of the Fourcault process, but devitrification on the débiteuse was avoided and a much larger width of up to 4.2 m could be obtained, thanks to the horizontally conveying process. But the price to be paid was a lower glass quality because of thickness variations, optical distortions, and surface defects [1, 3–6].

Rolls

Coolers Depressor mechanism

Canal coolers

Bending rolls Débiteuse Canal

Knurled rolls Molten glass

Kiln

Molten glass

Figure 2 Sketch of Fourcault process in cross section. The molten glass flows up through the débiteuse slot and is drawn upward [3].

Drawing chamber

Figure 3 Sketch of Colburn process in a bird’s-eye perspective. The molten glass is drawn upward from the free surface and bended horizontally by a bending roll [6].

4 Roll Out Process

3.3

Pittsburg Pennvernon

A process similar to that of Fourcault was developed and introduced by the Pittsburg Plate Glass Company in 1926. In this Pittsburg Pennvernon process, the molten glass was not drawn through a débiteuse but upward from the free surface right above a drawbar, which was a long and thin refractory part immersed below the glass surface. The ribbon width was kept constant because the glass was cooled by edge folks and coolers. After being annealed and cooled in the drawing tower, the glass ribbon was cut off at the top of the tower (Figure 4). The drawbar served to anchor the drawing point and to ensure uniform temperature and glass flow rate across its width. In addition, ell blocks served to homogenize the drawing temperature by keeping the glass melt covered. The operation cycle was much longer than that of the Fourcault process with a better surface quality and without devitrification complications. Typically, the thickness range was 1–8 mm with a width of up to 3.2 m, but the disadvantages were thickness variations resulting from temperature fluctuations and inhomogeneities in chemical composition caused by drawing of the glass directly from its surface [3–6].

3.4

Asahi

The most recent updraw process has been developed by Asahi Glass Company around 1970 to overcome in a new way the disadvantages of the Fourcault process [5, 6, 8]. With it, a pair of hourglass-shaped rolls, called “Asahi blocks,” is immersed into the molten glass instead of a débiteuse

(Figure 5). The trick then is to make the Asahi blocks rotatable to renew the parting line where the glass leaves from the refractory and devitrification takes place. As a result, much longer drawing periods of up to 2–4 months can be achieved. An additional advantage is that thinner sheets down to 1.1–0.7 mm can be produced, especially for electronics applications, with a width of 1.5–2 m, thanks to the forming stability derived from the Asahi blocks.

4

Roll Out Process

The continuous double-roll process was developed in the United States in an effort led by the Ford Motor Company to meet a growing demand from the automotive industry. As delivered from the forehearth, the molten glass was pressed to a given thickness, cooled rapidly by a watercooled pair of rotating rolls, and then conveyed into a horizontal annealing lehr. The thickness was determined mainly by the gap between the rolls, whereas the output was fixed by the rotating speed of the rolls. As made by Pilkington Brothers in the 1920s, this process was then improved to manufacture plate glass through online grinding after annealing, followed by polishing of the cut plates. The process was further developed by Saint-Gobain in the 1950s to grind and polish on line the glass ribbon (Chapter 10.9). Along with a waste of about 20% of the glass, very high investment and operating costs were major disadvantages of these mechanical methods, however, which in fact prompted Pilkington to develop the float process as described in Section 5.

Figure 4 Sketch of the Pittsburg Pennvernon process in cross section. The molten glass is drawn upward from the free surface right above the drawbar immersed below the glass surface [3].

Drawing tower Rolls

Glass sheet

Ell blocks Edge rolls

Coolers Edge forks

Shutoff block

Molten glass

Skim bar

Drawbar

71

72

1.4 Primary Fabrication of Flat Glass

Glass sheet Drawing tower Rolls Coolers Parting line Canal coolers

Canal

As to wire-reinforced glass, it is produced in two ways depending on whether the wire is simply inserted into a molten glass (single-pass process, Figure 6) or sandwiched between two glass layers (double-pass process). Although more complex, the latter process has advantages over the former in terms of larger output, wider width, and higher quality, and better suitability for subsequent conversion into polished wired glass because the wire mesh is always precisely located at the center in the thickness direction [1, 3–8].

Asahi blocks

5

Kiln

Float Process

Molten glass

5.1 Principle

Figure 5 Sketch of the Asahi process in cross section. The rotatable Asahi blocks are immersed into molten glass instead of the débiteuse, and enable the parting line to be renewed where devitrification takes place [6].

Because the float process was not designed at all for patterned and wire-reinforced glass, the continuous roll out process, with which these products have been produced since the 1920s, has escaped oblivion (Chapter 10.9). Thanks to its versatility and facility for customization, it has even found new special applications, for instance, to make cover glasses for solar cells with excellent light diffusion through patterned textures on the surface. Usually the pattern is impressed on the lower surface by the lower roll, which is engraved. Generally the thickness range is 2–7 mm for the patterned and 8–25 mm for the polished glass.

Figure 6 Sketch of single-pass wire roll out process (upper part insertion process). The wire is inserted into the molten glass, which is pressed and cooled by rotating water-cooled rolls [8].

Wire Dumper Guide roll Top roll Forehearth

Molten glass Lip tile

Lower roll

When it was invented in the 1950s, the float process turned out to be an epoch-making method to produce flat glass with a smooth surface without any additional polishing. Its production cost was low enough to make possible an extensive use of the material in buildings and automobiles, which is one of the hallmarks of current civilization. The basic process of making flat glass on a molten metal was in fact patented in various ways as early as in 1848 in England by H. Bessemer, of steel-converter fame, and then several times in the United States by W. Heal and J. H. Forrest (1902 and then in 1925), and by Halbert K. Hitchcock (1905 and 1925), but a great many technical problems had to be solved before the process could be made practical. Through a seven-year expensive research program of Pilkington Brothers in the United Kingdom, which in its last stage included 13 months of production that had to be discarded, all these problems had eventually been overcome in July 1958 by a team led by L.A.B. Pilkington (no relationship with the Company’s owners) and K. Bickerstaff. The following year it

5 Float Process

even became possible to produce with the same process the distortion-free glasses needed for mirrors, thus abolishing the long-standing distinction between window and polished-plate glass (Chapter 10.9). Although the float process became continuously profitable only in 1963, the previous year it began to be licensed all over the world by Pilkington Brothers in rapidly expanding markets. Within a decade, the good optical quality of float glass resulted in a vanishing share for other sheet- and plate-glass processes. As of 2015, more than 400 float plants are operated worldwide, units being up to about 500 m long (Figure 7). With a typical size of about 25 × 60 m, melting tanks are bigger than Olympic swimming pools to produce 600 metric tons (and even up to 1300 tons in the biggest plants) of flat glass per day with an investment cost ranging from 70 to 200 million dollars or euros, depending on actual size, location, and product complexity. As for the inflation-adjusted production cost (cf. Chapter 9.6), it has been almost continuously decreasing by a factor of 4 from 1965 to reach today a range of 200–300 dollars or euros per ton (Chapter 9.6), raw materials and energy accounting both for about 20% of it. When a molten glass is poured onto a clean molten metal bath, it floats, thanks to its much lower density, spreads out, and thins to the point where the gravitational forces and the surface tensions among the glass, molten metal, and atmosphere are in equilibrium to reach the so-called equilibrium thickness. The lower and especially the upper surfaces of the molten glass are fire-polished, perfectly flat, and parallel except at the edges. The float process is based on this principle. Among metals or alloys

that are liquid between 600 and 1050 C, the relevant temperature range for glass forming, pure tin was the obvious choice because of its low melting temperature of 232 C, high density of about 6.5 g/cm3 at 1000 C, low vapor pressure of about 10−7 atm at 1000 C, high boiling point of 2602 C, low reactivity with silicates in the metallic state, and not too high cost (about 20 dollars/kg as of 2015). The aforementioned equilibrium thickness Te is given by T e 2 = 2ρt S ga + S gt − S ta

,

1

where Sga, Sgt, and Sta are the surface tensions at the glass–atmosphere, glass–molten tin, and tin–atmosphere interfaces, respectively, g is the gravitational constant and ρt and ρg are the density of the molten tin and glass, respectively (Table 2). For soda-lime silicate glass floating on clean molten tin under a nitrogen-hydrogen atmosphere, Te is 6.9 mm (Figure 8), a thickness that is actually insensitive to small changes in the chemical compositions of the atmosphere, metal bath, or glass [1, 3–9].

5.2

Float Bath

The float bath contains several metric tons of molten glass. It is a large unit with a length of up to more than 50 m enclosed by a steel shell that is lined with thick insulating and nonreactive refractory materials and holds a pool of molten tin whose depth is 50–100 mm and total amount is up to more than 200 metric tons kept at temperatures decreasing from about 1000 to 600 C from the

Large plate lift-off devices Continuous ribbon of glass

gρg ρt − ρg

Small plate lift-off devices

Cross cutters

Cooling lehr (coating chamber) Float bath Melting furnace

Raw material feed

Figure 7 Overview of a float-glass plant (scale not right: size of the right-hand side, for instance, much exaggerated) http://www. glassforeurope.com/en/industry/float-process.php

73

74

1.4 Primary Fabrication of Flat Glass

Table 2 List of symbols regarding equilibrium thickness mechanism. Symbol

Denotation

Te

Equilibrium thickness

ρt

Density of molten tin

ρg

Density of molten glass

Sga

Surface tension at glass–atmosphere interface

Sgt

Surface tension at glass–molten tin interface

Sta

Surface tension at tin–atmosphere interface

g

Gravitational constant

out from the bath either to receive appropriate reflective, low-emissivity, solar-control, self-cleaning, or other specific coatings (Chapters 6.7 and 6.8) or to enter directly the annealing lehr at the temperature at which the viscosity is about 1010 Pa s (i.e. about 600 C for soda-lime silicate). At the end of the lehr, whose length can reach 120 m, the ribbon is finally cooled down to room temperature and brought into the cutting area. Whereas both edges are cut out (to be recycled as cullet) because of the imprint left by the top rolls, the ribbon itself is cut either according to customers’ specifications or as standard sheets, for instance, 6.0 × 3.21 m in Europe where tools used in the flat-glass transportation industry have been fitted to this size (which, by the way, is too large to allow flat glass to be shipped in containers).

Atmosphere Equilibrium thickness Sga Sta

Molten glass Sgt Molten tin

Figure 8 Equilibrium thickness of floating glass on the molten tin when the gravitational forces and surface tensions are balanced [3].

hot to the cold end (Figure 9). A reducing gas mixture made up of 2–8% hydrogen and 98–92% nitrogen is supplied at a high rate of the order of 103 m3/h from above to the bath to prevent oxidation of the molten tin and to maintain a positive pressure difference with the atmosphere at the bath exit where leakages are highest. The heaters, coolers, and other devices are installed and inserted in the bath. The molten glass is continuously supplied from the furnace conditioner via a canal where its flow rate is precisely controlled by an adjustable gate called a tweel. It arrives to a ceramic spout lip, which is an inlet of the float bath, through which it falls freely onto the molten tin. After many years of struggle at Pilkington Brothers to achieve excellent quality, the design and engineering of the inlet area were an outstanding invention to force the contaminated molten glass in contact with the refractory lip to flow outwardly so as to be brought forward at the outer edges of the ribbon [9]. Once poured onto the tin bath with a thickness of about 50 mm, the glass spreads out and thins to its equilibrium thickness in the upstream area in the float bath. As formed to the required thickness and width in the forming area (see Section 5.3), the glass ribbon is taken

5.3 Thinner (Top-Roll Process) and Thicker (Fender Process) Glass Ribbons For forming thin sheets, the molten glass with its initial equilibrium thickness in the upstream area in the bath is subjected at the same time to longitudinal and lateral forces. The former are exerted by conveyor rolls that stretch the ribbon from the annealing lehr and pull it at a typical speed of up to 25 m per minute. The latter are exerted outwardly on the ribbon edges by pairs of top rolls, which are water-cooled rotating gears, to reduce the narrowing of the glass ribbon because the imposed longitudinal stretching reduces not only its thickness but also its width (Figure 10a). In parallel, the glass ribbon is cooled down to prevent it from returning to its equilibrium thickness until its width is constant at the end of the forming area. In view of the fundamental influence of viscosity within the glass ribbon upon stretching and thinning, the temperature distribution and the top-roll operations must be controlled very tightly to ensure a good forming quality. Besides, keeping the glass ribbon as wide as possible is important to maximize productivity. For producing float glass thicker than the equilibrium thickness, a pair of water-cooled carbon fenders serves as slipping guides to the flowing glass in the bath (Figure 10b). The glass thus proceeds with a restricted width and a large thickness. As it passes down the fender area, the effects of gravitational forces and surface tensions make both its upper and lower surfaces flat and thickness uniform. The glass is then cooled to an appropriate temperature in the downstream area of the fender where its viscosity is high enough not to allow width changes. In contrast to what is taking place in the top-roll process, stretching is not significant at all and there is no drive to return to the equilibrium thickness because there is no glass–tin–atmosphere interface in the fender area.

5 Float Process

Figure 9 Sketch of the tin bath part of the float process: (a) on vertical plane along centerline; (b) on horizontal plane. A reducing nitrogen–hydrogen gas mixture is supplied from above. Heaters and coolers are installed [10].

(a) Nitrogen/hydrogen

Steel shell

Refractory Heaters

Tweel

Coolers Canal Spout lip

Molten glass

Steel shell

Refractory

Molten tin

Rolls

(b)

Glass ribbon

Centerline

Figure 10 Sketch of the float process: (a) for sheets thinner than the equilibrium thickness, where the glass is stretched, from its edges by top rolls and from its downstream part by conveyor rolls; (b) for sheets thicker than the equilibrium thickness, where water-cooled carbon fenders serve as slipping guides to glass flowing [7].

(a)

Glass ribbon

Top rolls

Centerline

Coolers Rolls

(b)

Glass ribbon Carbon fenders

Centerline

5.4

A Complex Industrial Problem

In spite of the simplicity of its principles, the float process is not readily implemented because flow in both tin and glass and heat transfer among tin, glass, and the radiative field are really complex processes. Glass

forming is mainly determined by parameters such as the glass flow rate, conveyor speed, rotating speed and angle of top rolls, and by the viscosity distribution within the glass ribbon. It goes without saying that the viscosity of the glass strongly depends on temperature, but the temperature distribution in the bath is itself influenced

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1.4 Primary Fabrication of Flat Glass

5.5 Trends in Float Production The float process is advantageous because it yields excellent flatness, high flexibility with regard to thickness and

3.0MM

4.0MM

5.0MM

6.0MM

Shape of glass ribbon

7.0MM

by radiative heat transfer, the flow of molten tin, and the glass forming conditions. Radiative heat transfer is predominant in the bath at temperatures higher than 600 C, but the flowing molten tin also contributes markedly to heat transfer as a result of its high heat capacity, high thermal conductivity (about 50 times higher than that of the glass), and low kinematic viscosity (about 8 times lower than that of water), whereas the glass flow carries a large amount of convective heat. On the other hand, molten tin flows by traction from the glass ribbon (i.e. velocity distribution) and buoyancy convection (i.e. temperature distribution in the bath). In order to understand forming conditions, one thus needs to understand the whole set of processes taking place in the bath since glass forming, heat transfer in the bath, and flow of molten tin affect one another in a very complex manner. As summarized by C.K. Edge [4], the float bath thus is “a remarkable entity which, although first envisioned as a finisher of glass surfaces, also functions as a container, a conveyor, a forming unit, a chemical reactor and a heat exchanger.” In view of this complexity, valuable information has been drawn from mathematical simulations not only of the glass forming mechanisms, but also of the temperature field and the mutually related dynamics of the molten tin and glass ribbon. As examples, calculations with finite-element methods of the thickness contour over the glass ribbon and of the lateral thickness distribution of the ribbon at the bath exit are shown in Figures 11 and 12 [10]. The rather good agreement of such model values with the temperatures, thicknesses, or ribbon shapes that can be measured on line illustrates how simulations can be used to optimize the operating conditions, to design new facilities, and to check new ideas for process improvement and development. From a chemical standpoint, potentially annoying impurities are oxygen from leaks or the N2–H2 gas mix, and sulfur originating from the molten glass. Both deteriorate productivity and glass quality if they induce alteration on the bottom surface of the glass caused by reactions with tin, and contamination adhesion on top and bottom surfaces (Chapter 5.6). In the so-called oxygen and sulfur cycles (Figure 13), SnO and SnS vapors form, condense, and precipitate, the former as SnO2 and the latter as SnS (which is ultimately reduced to Sn particles). Thanks to extensive research, however, these impurities are now carefully managed through monitoring, sealing, cleaning, atmosphere controlling on flow and pressure, etc.

Centerline of bath

Figure 11 Shape and thickness distribution of a 2 mm thick floatglass ribbon calculated with an integrated glass-forming model [10]. Forming (i.e. shape, thickness, and velocity distributions of the glass ribbon) and the flow of molten tin are first calculated for a given temperature distribution of the glass ribbon. Heat transfer (i.e. the temperature distribution) in the float bath then is simulated, and the whole calculation is iteratively repeated until convergence is reached for the three interrelated mechanisms.

3.5 Glass thickness at bath exit (mm)

76

Calculated 3.0

Measured

2.5

2.0

1.5 0.0

0.2

0.4

0.6

0.8

1.0

Distance from centerline

Figure 12 Simulated thickness distribution at the exit of the bath for 2 mm thick glass ribbon. The lateral distance is normalized [10].

width, and high productivity owing to completely continuous operation during the whole lifetime of the melting furnace, which can now reach up to two decades. Ever since its conception, plenty of technological improvements have been conducted for achieving higher throughput, larger width, and higher still quality, the thickness currently extending down to less than 0.4 mm and up to around 25 mm. Originally the float process was designed to produce glass sheets for architectural window and mirrors. Since the 1970s, the technology has evolved to meet other demands, especially that emerging from automotive

6 Downdraw Processes

disk drive (HDD) substrates, and other products such as touch panels and display covers that are then chemically strengthened.

Air leaks

(a) +H2

SnO vapur

H2O vapur

6

+H2

6.1 SnO2 Glass ribbon

SnO O dissolved in Sn

(b) Condensate H2S

Slot Downdraw

It was for forming thin glass sheets that the slot downdraw process was developed in the 1940s. As driven by pairs of rolls, the molten glass is pulled downward through an accurately dimensioned narrow slot, made of platinum, which is fixed at the bottom of the forehearth. The glass sheet pulled from the slot is then gripped on its edges to prevent narrowing (Figure 14). The suitability of this process for making thin glass stems from the fact that a viscous molten glass can be pulled downward with a higher speed than if it were just subjected to free fall [3, 7, 11].

SnS vapur

6.2 +H2

Downdraw Processes

Glass ribbon

S dissolved in Sn

Figure 13 The complex interactions of impurities with the atmosphere, tin bath, and glass ribbon in the float process: (a) oxygen cycle; (b) sulfur cycle. Source: After Pilkington [9].

market for higher optical quality and thinner sheets along with higher throughput to keep production costs reasonable. In addition, the float process has contributed to the growing solar generation market with products such as mirrors for solar power systems and cover glasses for photovoltaics. In the early 1980s, the float process achieved production of ultrathin glass of less than 1.1 mm for twisted nematic (TN)/super TN (STN) liquid crystal display (LCD) substrates, touch panels, and other electronics products with a remarkably high quality for flatness, thickness constancy, defect level, etc. Beginning in the 1990s, the float process has been producing flat glass of various kinds of compositions other than the traditional soda-lime silicate. Examples are alkali-free glass for thin film transistor (TFT) LCD substrate, high strain-point glass for plasma display panel (PDP) and solar panel substrates, specialty glasses for heat-resistant products, hard

Fusion Downdraw

The slot downdraw process has disadvantages in terms of imperfect flatness and other defects caused by slot deformation and foreign contamination on the inside of the slot. It was to overcome them that the fusion downdraw process was developed by Corning [3, 5, 7, 11]. As sketched in Figure 15, the well-stirred molten glass is delivered through a conduit tube to one end of a rectangular trough that is the upper part of a fusion pipe. The molten glass flows over the weirs uniformly along the full length of the trough and then runs down on both sides of the fusion pipe. Two glass streams join and merge together at the “root,” which is a bottom apex of the fusion pipe. A pair of rolls grips the edges of the glass sheet just below the root to prevent the sheet from becoming narrower as it is stretched downward. The glass sheet is then cooled down while its edges are still held by pulling rolls as it proceeds through a vertical annealing lehr, and is finally conveyed to the cutoff station. The distinguishing advantage of the fusion downdraw process thus is that the glass is formed without touching anything except air so that one obtains a smooth and defect-free fire-polished surface. To be achieved, however, this result requires a highly homogeneous molten glass and a minute control of the distribution of glass temperature and flow. Since the 1960s, the fusion downdraw process has produced photochromic glass, heat-resistant glass, and glass for chemically strengthening. It provides ultrathin specialty glass of less than 1.1 mm thickness used for electrical capacitors, microscope slides, optical filters, touch panels, micro electronic mechanical systems (MEMS),

77

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1.4 Primary Fabrication of Flat Glass

thanks to its excellent surface quality. To meet the market demand for larger size substrates, the width has been extended up to around 3 m. In addition, the downdraw process is applied to specialty glass for emerging chemically strengthened products such as touch panels and display covers.

Stirrer

Molten glass

Forehearth

7

Slot

Rolls

Annealer

Figure 14 Sketch of slot downdraw process in cross section. The molten glass is pulled downward through a narrow slot driven by rolls [7].

substrates of TN LCD, and thin film solar cells. Besides, production of alkali-free glass for TFT LCD substrate was started in 1984 by Corning. Although the specifications are in this case much more severe, the fusion glass can also be used for TFT LCD substrate without polishing,

Perspectives

Over the years the demand for flat glass has paralleled the growth of the global economy. In addition to architectural applications, the automotive, solar energy, and electronics especially flat panel display (FPD) application markets have all been at the same time growing and an important source of new, value-added products (Chapter 6.10). Recently, glass sheets for chemically strengthened components such as cover glass for displays and ultrathin glass for touch panels have emerged as important products driven by the explosive diffusion of mobile phones and tablets with touch sensors [12]. These trends are supposed to continue and affect markets such as appliance, transportation, interior architecture, and many others. The important role of flat glass keeps increasing in these domains as well as in the field of information and communication, optics, healthcare, and so forth. Further improvements will thus be made to meet new specifications and respond to various market demands. From an industrial perspective, however, not only the cost and quality of the glass itself but also controllability, investment size, yield, delivery time, versatility, cost of post-processing, and other factors of the manufacturing process have to be taken into consideration for each application. Therefore, an overall and comprehensive understanding of the forming process remains a key issue.

Figure 15 Sketch of fusion downdraw process in a bird’s-eye perspective. Molten glass flows over weirs and run down on both sides of fusion pipe. Two glass streams join and merge together at the root and are stretched downward [3].

Weir Trough

Fusion pipe

Conduit tube

Molten glass Rolls Root

References

For new applications, work is in particular being conducted on ultrathin flexible glass (0.2 mm–30 μm) and on rolled glass for flexible display, OLED lighting, and organic thin-film solar cell to take advantage of unique features of glass such as bendability, impermeability to gas, transparency, surface quality, chemical and thermal durability, and so on [13]. Such products are not yet on the mass market because the fundamental technologies are not mature, but flexible and rolled glasses are nonetheless expected to come out in the near future. The applications to the field of health care, electrical and optical packaging, MEMS, and so forth are anticipated to become more popular as well [14]. The relevant information can be found on the websites of glass manufacturers. Two directions for development of the forming process can be followed. One is to improve further currently existing processes in terms of flatness, thickness, width, productivity, controllability, cost, versatility, facility lifetime, etc. The other direction is to add values through online introduction of other features such as coating and surface treatment (cf. Chapters 6.7 and 6.8). A closer match and harmonization between forming process and glass composition and properties might be also attractive. As for forming commodity glass, invention of a novel process surpassing float with regard to energy consumption and investment costs would be desirable. For specialty glasses, innovative processes with higher quality and lower cost will of course also be sought after. Advances in basic science, simulation methods, sensing procedures, and information technology are presumed to become still more important either in operation and engineering or in development and innovation. Moreover, newly developed materials could make other innovative progress possible. In this respect, could unprecedented innovations based on novel mechanism make the processes described in this chapter obsolete in a near future? Their advantages should be considerable to write off the capital invested in current production plants all over the world. But would those innovations give rise to new applications and create new markets? A never ending challenge will change the world [15, 16].

2 Yates, R.F. (May 1921). Revolutionizing the glass-

blowing industry. Popular Monthly: 30–32. 3 Hynd, W.C. (1984). Flat glass manufacturing processes.

4

5 6

7

8

9 10

11 12

13

14

15

References 16 1 Cable, M. (2004). The development of flat glass

manufacturing processes. Trans. Newcomen Soc. 74: 19–43.

In: Glass: Science and Technology, Vol. 2, Processing I (eds. D.R. Uhlmann and N.J. Kreidl), 45–106. New York: Academic Press, Inc. Yunker, R.W. (1984). Flat glass manufacturing processes, and C.K. Edge, Update. In: The Handbook of Glass Manufacture, 3rd ed., vol. 2 (ed. F.V. Tooley), 683–714 and p. 714/1–714/21. New York: Ashlee Publishing Co. Cable, M. (1999). Mechanization of glass manufacture. J. Am. Ceram. Soc. 82: 1093–1012. Mishima, Y. (1985). Flat glass forming, float process. In: Glass Encyclopedia [in Japanese] (ed. S. Sakka), 276–283. Tokyo: Asakura Shoten. Abe, Y., Inaba, H., Okamoto, F. et al. (2010). Glass forming. In: Glass Engineering Handbook [in Japanese] (eds. M. Yamane, I. Yasui, M. Wada, et al.), 354–364. Tokyo: Asakura Shoten. Mori, T. (2007). Historical Development of Flat Glass Manufacturing Technologies, Research Report on technological systematization [in Japanese], vol. 9. National Science Museum: Tokyo. Pilkington, L.A.B. (1969). The float glass process. Proc. Roy. Soc. London A314: 1–25. Kamihori, T., Iga, M., Kakihara, S., and Mase, H. (1994). An integrated mathematical model of float process. J. Non-Cryst. Solids 177: 363–371. Ellison, A. and Cornejo, I.A. (2010). Glass substrates for liquid crystal displays. Int. J. Appl. Glass Sci. 1: 87–103. Lee, M.Y.M. (March/April 2013). Glass part 3: new generation of specialty glass for LCDs and AMOLEDs. Gases Instrum: 1–6. Plichta, A., Habeck, A., Knoche, S. et al. (2005). Flexible glass substrates. In: Flexible Flat Panel Displays (ed. G.P. Crawford), 35–56. Chichester, UK: Wiley. Schröder, H., Brusberg, L., Arndt-Staufenbiel, N. et al. (2011). Glass panel processing for electrical and optical packaging. In: 61st IEEE Electronic Components and Technology Conference Proceedings, 625–633. IEEE: Piscataway, NJ. Bange, K., Jain, H., and Pantano, C.G. (2014). Making Glass Better. Functional Glasses: properties and Applications for Energy and Information. Madrid: International Commission on Glass. Bange, K. and Weissenberger-Eibl, M. (2010). Making Glass Better, an ICG Roadmap with a 25 Year Glass R&D Horizon. Madrid: International Commission on Glass.

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1.5 Fabrication of Glass Containers Christian Roos IPGR – International Partners in Glass Research, Bülach, Switzerland

1

Introduction

At the beginning of the twentieth century, glass-container manufacturing still was a strenuous business, involving much manual labor and sweat. In 1903, Michael J. Owens developed in Ohio the world’s first fully automatic glassforming machine (Chapter 10.9). The concept consisted of a rotating machine that sucked glass from a pool of melt into forming molds. A preform of the final container (the so-called “parison”) was first produced, and then transferred into a second mold where the parison was blown to its final shape to form the container itself. This truly revolutionary concept gave major advantages over semiautomatic methods since it cut labor costs by 80% and also led to the end of child labor in glassmanufacturing companies. But this concept still had its drawbacks because the machine itself was expensive and cumbersome and a true monster of tons of rotated, lowered, and lifted metal. In 1915, Karl E. Peiler and F. Goodwin Smith established a fully automatic press-and-blow rotary machine, which was fed with glass from above by an automatic paddle-needle gob-feeder (Chapter 10.9). Although this design resulted in a much less complex forming cycle, the machine was still a rotating system that involved again much mechanics and moving metal. And, most importantly, as soon as one section of a rotating machine experienced any problem, the machine as a whole had to be stopped. Hence, yield was significantly decreased when the complete machine had to be paused because only one section was experiencing problems.

Reviewers: A.J. Faber, Celsian Glass & Solar, Eindhoven, The Netherlands C. van Reijmersdal, Bucher Emhart Glass S.A., Niderwenigen, Switzerland

With gob-feeding getting more and more sophisticated, a search began for a more efficient forming process. In 1924, F. Goodwin Smith and Henry W. Ingle developed a totally new concept for automated glass-container forming: the ISmachine, where “IS” stands for Individual Section. The machine sections were no longer arranged in a circle but in a row. This meant that each section of the forming machine operated independently from the others. Hence, if failure occurred in one section, just this section and not the complete machine had to be stopped and fixed. This made production much more efficient and flexible. Production speed and container quality also were greatly increased. With 4 individual sections in the first IS-machine, the concept was soon improved and enhanced from initially 4 single gob sections (in total, therefore, 4 containers in one complete machine cycle) to nowadays 12 sectionsystems with multi-gob delivery to each section. In the most recent form, IS-machines can consist of 12 sections, with 4 forming molds per section (quad-gob system), summing up to 48 containers produced in one machine cycle. Looking at a modern IS-machine, however, one should nonetheless recognize the basic features that were designed when the concept was first developed. As shown in Figure 1, one section is made of the following zones, which will be explained more in detail later in this chapter: 1) Delivery equipment, consisting of scoop, trough, and deflector. 2) Blank-side with plunger, neck-ring, guide-ring, moldhalves. and baffle. 3) Invert with invert-arm holding neck-ring and guide-ring. 4) Blow-side with bottom-plate, blow-head, and moldhalves. 5) Take-out with tongs, dead-plate, and pusher to conveyor belt.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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1.5 Fabrication of Glass Containers

Trough Deflector

Take-out

Blow-head Blow-molds Invert

Baffle

Pusher

Conveyor

Blank molds Plunger

Invert-arm Guide-ring Neck-ring

Dead-plate Bottom-plate

Figure 1 Schematic overview of one section of an Individual-section machine (here Narrow-Neck Press & Blow process, double-gob set-up).

Several major improvements have been implemented in the forming process since its beginnings. We will, for instance, describe how, following the Press & blow (PB) and Blow & blow (BB) processes, the Narrow-neck press & blow (NNPB) process has recently met with much success because of its more efficient forming. And it should also be stressed that the original pneumatic control of IS-machines has given way to servo-electric devices with which higher precision and reliability has been achieved.

2 Principles of Glass-Container Forming Before a glass can be formed, it usually has to be melted out of the respective raw materials. The melting of container glass bears some peculiarities such as a high usage of foreign (external) recycled cullet or auxiliary devices such as batch and cullet preheaters. Because these features and the basics of the melting of container glass are described elsewhere in Chapter 1.3, we will focus solely on forming. Glass containers for mass-market are formed with the aid of molds in which the molten glass is blown or pressed. The forming process consists of two steps. First a “parison” is made in cast-iron “blank-molds.” Then, in the second step, this parison is formed into the final container in “blow-molds” that are made of either cast iron or aluminum bronze.

2.1 Heat Management in Glass-Container Forming A basic feature of the forming process is that it is highly non-isothermal. On the one hand, temperature differences over the dimensions of the glass component are present and on the other, the glass experiences a great change in temperature and thus in glass properties. As a result, the forming process has of course to be designed to cope with these changes, which are the largest for viscosity. When the gob enters the mold in the first forming step, it has a bulk temperature of about 1050 C. The mold itself has a temperature of 450–520 C at the end of the parison forming cycle, depending on forming conditions and container type. The glass–metal interface temperature TC, which is a very important parameter for the forming, is almost constant (Figure 2) because of the short contact time t of only a few seconds between the gob and mold material. It depends on the temperature of the glass T1, on that of the contact material (mold) T2, and on the thermal conductivity λ, heat capacity Cp, and density ρ of both the glass and the mold material [1–3]. For soda-lime-silica glass, at the relevant temperatures these values can be taken as λ ≈ 10 W/m K, Cp ≈ 870 J/ kg K, and ρ ≈ 2500 kg/m3. For laminar cast iron, appropriate parameters are λ ≈ 55 W/m K, Cp ≈ 500 J/kg K, and ρ ≈ 7300 kg/m3. From these values, one can estimate TC with:

2 Principles of Glass-Container Forming

2.2 Interface Interactions in Glass-Container Forming

T1

Contact material

Glass

TC

t2 t1 t0 T2

Figure 2 Temperature gradients and interface temperature between contact-material and glass over time.

T1 – TC = T C − T2

λ cp ρ

mold

λ cp ρ

glass

1

One finds in this way that temperatures of 1050 C for the gob and 470 C for the blank mold yield an interface temperature of ca. 614 C if no oxide layer resulting from corrosion of the mold is present and if the heat balance of the blank mold is correctly managed. A certain cooling of the glass during the forming process is mandatory to achieve a stable enough product that does not lose shape in subsequent processes (handling, coating, etc.). If cooling is not applied correctly, too low a viscosity will prevent the parison from maintaining its shape and, thus, correct dimensions from being achieved and the final container from conforming to its specifications. In glasscontainer forming, this stabilization is realized, thanks to the surface layer of the parison that cools down through contact with the mold. Heat transfer thus is, in general, an important aspect in the forming of container glass. Not only large amounts of heat need to be removed from the glass, but heat transfer must be controlled locally to avoid internal tension that would build up if the shrinking rate were variable throughout the glass. The average heat transfer Q0 − t during the short contact period t between the glass and mold can be calculated according to Q0 − t =

λg ∙ λm λg

λm ∕ c p ∙ ρ

m

+ λm

λg ∕ cp ∙ ρ

∙ g

2 T1 − T2 π∙t 2

where m designates the mold and g denotes glass properties. With the aforementioned parameters, one, for instance, finds a very large average heat transfer of 647 kW/m2 for a typical forming cycle for which t = 6 seconds.

Whenever a glass container is formed through contact with a solid material, such as a mold or roller, the interface between the two bodies is a crucial point. From the preceding presentation, it appears that problematic situations occur when the interface temperature is either too high or too low. If cooling of the mold is not rapid enough in relation to the gob temperature, the interface temperature between the gob and mold increases and at a certain point the glass begins to stick to the mold. The sticking temperature has a lower bound at which the glass still can be separated from the mold without significant damage. Nevertheless, reaching this lower bound leads to process failure because sticking of the glass causes a bad loading and a inhomogeneous temperature distribution, which themselves give rise to defects in the final container. At the upper sticking temperature, removing the glass from the contact material inevitably leads to damages of the glass, like checks or torn-out pieces. The glass sticking temperature is widely independent of the type of the contact material. It is basically a function of the interface temperature TC, but surface conditioning of the contact material may play a role as well. Sticking appears when the viscosity of the glass at the interface becomes lower than 108.8 Pa s [4, 5]. For an average container-glass composition that means sticking begins to take place when the interface temperature TC between the gob and mold becomes higher than ~ 645 C. The interface temperature of about 614 C calculated above is lower than the sticking temperature. However, it can easily happen in production that this temperature increases locally such that sticking of the glass does occur. This may happen because of changed cooling conditions, cooling failure, or the growth of an oxide layer on the molds, which significantly decreases thermal conductivity. The friction coefficient μ between the glass and contact material plays a crucial role during forming. A low dynamic friction between the contact material and the glass favors a good gob-loading and glass-forming. Often the molds and the finish equipment are coated with a lubricant that decreases the friction. This so-called swabbing process is widely used in glass-container manufacturing. The swabbing lubricant mainly consists of graphite with various additives. Periodically, the molds are swabbed automatically by robot or by human hand to allow precise and stable forming. The swabbing intervals depend on the respective machine setup and container produced and can range between 15 minutes and several hours. The effect of swabbing on the friction coefficient is a temporary decrease in friction as well as a change in the heat-transfer characteristics between the glass and mold.

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1.5 Fabrication of Glass Containers

There are also different permanent and nonpermanent coatings available that can be applied to the mold and forming equipment to extend or even avoid the swabbing. Important physical aspects of gob-loading, including models of the mechanics of gob/blank-mold interaction and of dynamical friction, have been extensively discussed in papers to which we refer for further details [e.g. 6, 7]. 2.3 Deformation Rates in Glass-Container Forming As already pointed out, in container-glass manufacturing, the gob is first formed into the parison, and then the parison into the final container. The (de-)formation of both the gob and parison depends on the actual viscosity of the glass. A low forming- or interface-temperature leads to a high viscosity at the glass surface. Hence the glass surface starts to get “brittle.” If such a glass is then subjected to high deformation rates, as it happens not only upon pressing and blowing but also earlier in the process upon gob-cutting, it can experience too high tensile or shear stresses. The critical tensile stress σ c (in MPa) that a hot soda-lime-silica glass can sustain at a given temperature T may be estimated from an empirically derived correlation [8]: σc =

4 8 ∙ 103 T

3

Hot fracture occurs if the tensile stresses exceed this critical value. The maximum velocity vmax at which a glass container with a thickness d can be formed at viscosity η without experiencing hot fracture can be approximated by: vmax =

σc ∙ d 4η

4

One thus concludes that at temperatures of about 1000 C, deformation velocities of ca. 500 m/s are, for instance, possible without hot fracture for a 2 cm-thick soda-lime-silica glass layer. At 900 C, the maximum allowed velocity is already down to 100 m/s and is lower than 10 m/s at 800 C. Below 700 C the risk of defects caused by hot fracture becomes significant. Because usually such defects cannot be inverted (“healed”) in later forming steps, care must be taken to prevent them from appearing.

3

Glass-Container Forming Processes

3.1 Glass Composition For cost reasons, glass containers are made out of sodalime-silica glass whenever special constraints do not

apply. An exception is, for instance, laboratory ware for which borosilicate glass is used instead (Chapter 7.7). Even though the forming process needs to be adapted to account for the specific properties of each glass type, the principles at work are similar for given kinds of containers. Three different forming processes are applied, namely BB, PB, and NNPB. Their main differences concern blank-side forming where the parison is made, the subsequent forming steps to make the final container being identical. As a matter of fact, many containers can be produced with more than one process so that there is much overlap between them in terms of product range. 3.2 Blow & Blow Process The BB process is the oldest and remains still widely used in manufacturing of large and heavy containers such as wine or sparkling wine bottles. The gob is loaded into the blank mold, often via a funnel (Figure 3a). After loading, the mold is closed with a baffle and a settle-blow is applied from above through the baffle (Figure 3b). The settle-blow presses the glass gob deeper into the mold and down to the finish equipment, which basically consists of a neck-ring, a guide-ring, and a short plunger. On loading, the plunger is in upper position. In this very first step, the opening, sealing surface, and thread (if present) are thus formed before the bulk of the container itself, which represents an important difference with respect to the other forming processes. In the current IS-machines, the loading speed of the gob is often so high that the finish is already formed at the gob-loading step, which would make the settle-blow unnecessary for the finish forming. This step is nonetheless maintained in the process to guarantee a constant heat transfer between the glass and the blank, from cycle to cycle, before counter-blow. During settle-blow, a vacuum can be applied through cavities in the molds to support the parison and finish forming. Some modern BB ISmachines work without a funnel. They control the switch between settle-blow and counter-blow by a valve in the baffle to exhaust the compressed air that is used for settle-blow. After settle-blow, the baffle is quickly lifted, the funnel is removed, and the baffle settles again and closes the blank-mold completely. A counter-blow is applied from the down side through the formed finish, blowing the glass fully into the mold shape and forming the parison (Figure 3c). This two-step blowing process with settle-blow and counter-blow on the blank-side causes an inhomogeneity in the container because of different contact times between the glass and the mold above and below the loading line. Such an inhomogeneity can be seen as a horizontal, optical streak in the body of the containers. It is called

3 Glass-Container Forming Processes

(a)

(b)

(c)

(d)

Figure 3 (a–d) Blow & blow process, blank-side.

settle- or feeder-wave and can be reduced in several ways, but not fully avoided. When looking at a final container, the existence or nonexistence of a settle-wave thus indicates whether or not the container has been produced with the BB process. After the parison has been formed, the baffle is removed (Figure 3d), the mold opens, and the parison is transferred via the invert mechanism to the blow-side. The final forming of the container is in principle the same for all three forming processes. The following description will thus apply to all of them. When transfer to the blow-side is over, the parison lengthens into the blow-mold as determined by its viscosity and the machine parameters. This causes the outside of the parison to be reheated by the heat stored in the hot inside and temperature to homogenize within the parison (Figure 4a). This reheat is essential to ensure that the container is to be precisely formed to its intended shape. The blow-mold is

then closed, leaving the finish outside. The invert-tongs open and the container is released from the invert. Directly after releasing, the blow-head with a blowingtube is placed on top of the finish (Figure 4b). Through this blow-head, the final-blow is applied, giving the parison the final shape of the container (Figure 4c). Strictly speaking, the reheat ends when the final-blow is triggered. After the container has been released by the blow-mold, a take-out grips it by its finish (Figure 4d) and places it over a dead-plate through which air is blown from below to cool it further. Finally the container is transferred via a pusher onto a conveyor belt. 3.3

Press & Blow Process

The PB process is used for wide-mouth containers of all weights, such as jars and baby-food containers. It differs

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1.5 Fabrication of Glass Containers

(a)

(b)

(c)

(d)

Figure 4 (a–d) Forming of the final container at the blow-side (same for all processes).

significantly from the BB process at the blank-side. After loading the gob (Figure 5), the blank-mold is closed fully by the baffle and a plunger presses in an upward movement the glass from below into the mold (Figure 5b). The plungers usually are made out of tungsten carbide (WC) or another hard metal to ensure a long lifetime. In contrast to BB-forming, the process causes the finish to be formed at the end of the blank-mold process (Figure 5c) and no disturbance such as settle-wave is introduced into the parison because it is formed by a single (smooth) motion at the blank-side. As in BB, the baffle is removed after the parison has been formed, the mold opens (Figure 5d), and the parison is transferred to the blow-side to get its final shape as described above.

3.4 Narrow-Neck & Blow Process The NNPB process is mainly used for lighter containers such as beer bottles, small water and juice containers, and other lightweight containers. It is the most advanced forming process because it yields not only the highest machine speeds but also a homogeneous glass distribution in the final container. It is similar to the PB process in that the gob is not blown into the parison but pressed via a plunger. After loading the gob (Figure 6), the mold is closed fully by the baffle and a plunger smaller in diameter than in PB presses in an upward movement the glass into the mold (Figure 6b). The plungers are also made out of tungsten-carbide. As with PB, the finish is formed at the end of the blank-mold process (Figure 6c). Again, the baffle is removed after the parison has been formed,

4 Making of the Gob: Forehearth, Feeder, and Shears

(a)

(b)

(c)

(d)

Figure 5 (a–d) Press & blow process, blank-side.

the mold opens (Figure 6d), and the parison is transferred to the blow-side. Restrictions in usage of the NNPB process are due to the plunger dimensions and finish openings and the corresponding cavities pressed into the parison. The parisons are usually shorter for NNPB than for BB if the same final container shape is to be produced (e.g. a 0.33 l beverage bottle). Another significant difference between NNPB and BB is that the required gob temperature is from around 20 to 50 C higher in NNPB because of difficult pressing conditions. This difference in consequence leads to different thermal requirements during the process in terms of mold-cooling and reheat-timing.

4 Making of the Gob: Forehearth, Feeder, and Shears Most forming processes take place at a viscosity of 102– 104 Pa s. Hence, for soda-lime-silica containers, the glass

needs to be cooled from melting and fining at ca. 1500 C and a viscosity of 10 Pa s down to ca. 1050 C and a viscosity of 103 Pa s. This quite demanding task is accomplished in the forehearth. The forehearth is directly connected to the working-end and ensures the required homogeneity of the glass while bringing it to the desired temperature and viscosity. After the forehearth, a feeder enables glass-portioning and gob pre-shaping (Figure 7). It consists of a refractory tube and one or more plunger(s) that are moving periodically up and down. The tube is rotating to homogenize the melt in this final stage. With each upward stroke of the plunger, the glass stream is released from the shear blades in order to cut a gob without having a glass stream loaded on top of these shears. For a single-, double-, triple-, or quad-gob setup, the respective number of plungers operates simultaneously in the feeder, hence as many openings in the orifice ring are required. The final gob shape is influenced by the sizes of the orifice ring and plunger, and by the shape, height, and motion profile of the plunger.

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1.5 Fabrication of Glass Containers

(a)

(b)

(c)

(d)

Figure 6 (a–d) Narrow-neck press & blow process, blank-side.

Glass-stream from forehearth Tube Plunger(s) Spout

Orifice-ring with opening

Glass-stream to shears

Figure 7 Cross section of a modern feeder (double-gob setup). Source: Courtesy Bucher Emhart Glass.

The originally continuous glass stream is cut by the shears right after it has been “pre-shaped” by the feeder and plunger and has passed though the openings of the

orifice ring. The gob needs to be completely separated from the glass stream by the shears to prevent any glass fibers from being attached to it. Any misaligned or poorly operating shear will result in shear marks and, consequently, in defects in the final container. For shears, the materials most commonly used are steel (cheap, but short-lived) and hard alloys such as WC (more expensive, but long-lived). In all cases, the shears are cooled by a shear-spray, a mixture of water and cooling fluids.

5

IS-Forming Machine

5.1 General Principles Rotational forming machines are nowadays used only in some rare cases. The principles of glass-container forming will thus be described for IS-machines, with which almost glass containers are made. Derivatives of the ISmachine such as the Emhart RIS and Heye H 1–2

5 IS-Forming Machine

machines have been developed in the past but are hardly in use any longer [9]. They work with two molds on the blow-side forming, which are loaded alternately. This approach is advantageous in terms of longer reheat and more homogeneous glass thickness distribution but is much more complicated, expensive, and prone to jamming. In a narrow sense, IS-machines consist of a gobdistributor and delivery equipment, blank-side forming, invert, blow-side forming, and take-out and have several identical sections aligned in a row (Figure 1). The only differences between sections are the individual delivery (as different distances from gob-cut to mold need to be overcome) and the distance of the section to the annealing lehr. The differences in delivery distances cause different gob speeds and different gob arrival-times at loading and thus require different section-timings. The differences in distance to the annealing lehr may cause different containers temperatures at the hot-end coating and at lehr entrance. When entering the lehr, there is, for example, a difference of 50 K or more in surface temperature between containers from section 1 and from section 12, which are the farthest from the annealing zone. The IS-machines in principle can be adapted to all three forming processes that have been mentioned earlier. To a certain extent the machines can be converted between a triple-gob setup to a quad-gob setup or, given another machine construction, from a triple-gob setup into a double-gob setup. How widely a machine can be adapted depends on different parameters, especially on the inner-section distance, which describes the possible center distances of the molds to each other within one section. The type of setup to be used depends on different parameters such as the size and weight of the container to be produced, desired machine speed, and portfolio of the respective glass-manufacturing plant. 5.2

The IS-Machine Families

The IS-machines can be separated into three groups: 1) Pneumatic-controlled IS-machines with angular mold-opening. 2) Pneumatic-controlled IS-machines with parallel mold-opening. 3) Servo-electric-controlled IS-machines with parallel mold-opening. In the earliest types of IS-machines, all movements are controlled by pneumatic valves. The mold opening and closing is in an angular motion, which means that in a multi-gob setup at the blank-mold-side, the inner blanks are more widely opened than the outer blanks, causing difference in radiation between the glass and the open

blanks. At the blow-side, the inner molds are not opened as wide as the outer molds, which may lead to difficulties in machine accuracy and forming. A significant step forward, therefore, was the introduction of pneumatic-controlled IS-machines with parallel mold-opening and closing. Here the mold-halves from the inner, middle, and outer cavity open in a parallel motion to each other. This leads to more comparable conditions between the molds of a given section. Furthermore, the parallel closing and opening is more precise, leading to a more reliable forming. In the color section of this Encyclopedia, a picture of a modern pneumatic-controlled IS-machine is shown. The next logical improvement was to exchange the pneumatic-controlled movement for a servo-electriccontrolled motion to take advantage of the enhanced stability, reliability, and precision of servo-electric drives. In this way, motions are much more easily cushioned and are gentler for the hinges, molds, and also for the glass itself. In the latest generation of IS-machines, mold opening and closing, plunger motion, invert, blow-head, take-out, pusher, and other parts are thus servo controlled. The machine speed is a general parameter to describe the production performance for a given container. It is expressed as the cavity rate (C), namely the number of containers produced per minute (cpm) for each cavity considering the total numbers of cavities (NS) of the ISmachine: C=

cpm NS

5

For a 12-section machine with a triple-gob setup and container output of 324 containers per minute, the cavity rate C is, for instance, 324/12 × 3= 9. Hence, a 12-section IS-machine with a triple-gob setup producing 240 containers per minute is running a lower cavity rate than a 10-section IS-machine with the same triple-gob setup producing the same number of containers per minute. Highly efficient IS-machines can go up to cavity rates of 25 for small container sizes. This rate translates to production speeds of more than 700 containers per minute. In general, one can state that the higher the gob weight and the larger the container size, the lower is the corresponding cavity rate. As illustrated in Figure 8 for 0.3-l beverage bottles, the performance of IS forming machines has steadily improved since their inception in the 1920s. In 90 years, one forming line has been producing 26 times more containers per minute. And in the same period the weight of such containers could be decreased from more than 300 to less than 170 g. These figures show vividly the very strong potential that this forming process had when it was invented.

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1.5 Fabrication of Glass Containers 624 600 Containers per minute (cpm)

90

0.3 I beverage bottle 540

500 420 400 300

300 180

200 100

100 48

24 0 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 Year

Figure 8 Performance increase of IS forming machines over the years in containers per minute.

the bottom of the container upward before the invert leads to the proper upright formed final container. Upon forming of the parison, the mold is always cooled by air to allow fast heat extraction from the glass. As already explained, this is necessary to have a stable parison with a high enough viscosity after the mold has opened. If the parison is too hot and hence has a too low viscosity, it may collapse after opening the mold, causing section failure. Different mold-cooling techniques are available. Most dominant are inside-mold cooling systems, where air is lead through channels in the mold either from below or from above and an older technique called stack-cooling. Here, fins are attached to the outside of the mold and the mold is streamed by air. This version is less efficient than inside mold cooling so that it usually leads to lower machine speeds.

5.3 Delivery Equipment

5.5 Invert and Reheat

The delivery equipment consists of the gob-distributor (also called scoop), the trough, and the deflector. After the gob has been cut, it falls into the scoop which distributes the gobs to the different sections in the forming machine. The gobs slide through the respective troughs and then are redirected by the deflectors into the blank-molds. Although the delivery section looks like a simple part of the IS-machine, it bears considerable neuralgic points. The gob temperature decreases during the delivery but the upward side of the gob loses less heat than the side in contact with the metal delivery, which in some cases is in addition cooled and lubricated. Forming problems can thus happen if the gob acquires a nonuniform temperature profile. The speed of the gob when it leaves the deflector is also an important parameter. When leaving the deflector, the gob is loaded into the mold. The higher the speed of the gob, the more beneficial it is for a good loading. Too slow a gob speed may lead to incorrect loading and hence to problems in the forming process or defects in the final container. In extreme cases, the gob is not fully loaded into the mold and the upper end of the gob is caught by the baffle. This leads to immediate failure of the respective section. The average gob speed at loading is between 6.5 and 7.5 m/s.

After forming of the parison, the blank-mold opens and the parison is transferred via an invert to the blow-side. The invert consists of an invert-arm in which the finish equipment with neck-ring and guide-ring is fixed. As soon as the blank-mold opens and invert takes place, the so-called reheat starts. During the blank-side process, the glass-surface has been cooled down, especially through the contact with the molds and blowing air. The glass viscosity rises in this way, which is necessary to give the parison a certain rigidity to move it without deformation. After having been released from the blank-mold, the outer parts of the parison get reheated from the hotter inner part through thermal conduction, which is in fact needed to lower again surface viscosity before the last forming step that will give the container its final shape.

5.4 Blank-Side Forming At the blank-side the three different forming processes come to play as explained in Section 3. Molds at the blank-side are usually made of laminar cast-iron. The glass gob is loaded into these molds and is formed into the parison. Because of process-sequence, the parison is formed upside down, the finish facing downward and

5.6 Blow-Mold Forming The forming of the final container in the blow-mold is from a mechanical point of view identical for all three forming processes (BB, PB, and NNPB) as explained in Section 3. As with parison forming at the blank-side, final blowing at the blow-side can also be aided by vacuum. A main task for the blow-mold is to extract as much heat from the container as fast as possible to increase its viscosity, stabilize its shape, and avoid deformations during take-out and transport of the container after it has been released from the blow-molds. Because of this need to extract large amounts of heat in a short time, blow-molds often are made out of aluminum-bronze, which has much higher heat conductivity than cast-iron, hence allowing faster heat removal from the container.

7 Cold-End Handling and Inspection

A picture of a triple-gob setup in the color-section of this Encyclopedia shows the parisons just having arrived at the blow-side and the final containers just having been removed from the blow-mold and placed over the deadplate by the take-out.

6 Hot-End Handling, Hot-End Coating, and Annealing The conveyor belt transports the container to the annealing lehr for stress-relaxation. Once the container has left the IS-machine, a first inspection often takes place with cameras that record the infrared images of the hot containers. From these images, defects can be identified and immediate corrections of the process can be initiated. This is very beneficial as the feedback between defects and applied corrections is direct and without the time delay that would occur if the container were first annealed and then inspected. Before entering the annealing lehr, the outside body (not the finish) of the containers receives a hot-end coating of a 5–15 nm thickness. Even so thin, the hot-end coating serves different important functions. It first saturates the highly reactive surface bonds that are present at the surface of the new glass container. It also provides a surface suitable for good adhesion of the cold-end coating, which is applied later. Furthermore, it may slightly increase the strength of the container by disabling surface flaws that have been introduced during the forming process. As precursor for hot-end coating most frequently used is monobutyltin-trichloride, C4H9SnCl3 (MBTC) or tintetrachloride, which both gives rise to a SnO2 coating on the container. The process is chemical vapor deposition under air at atmospheric pressure (atmospheric CVD) and is supported by the moisture of the air. The reactions that take place are: For MBTC C4 H9 SnCl3 + 3 H2 O + 6 5 O2 SnO2 + 3 HCl + 4 CO2 + 6 H2 O 6 For SnCl4 SnCl4 + 2 H2 O

SnO2 + 4 HCl

7

Other precursors based on titanium or titaniumsilicium are also in development to yield a TiO2 or TiO2-SiO2 coating. As explained, after forming and hot-end transport, the containers from different sections experience different cooling whereas the surfaces of a given container cool faster than its bulk, the rate being higher for the outer than for the inner surface. These differences create tensile stresses in

the container, which can lead to spontaneous breakage. Containers are thus reheated in the glass transition range in a continuous-annealing lehr long enough to ensure complete stress relaxation. The annealing times depend on the size of the containers, but are typically between 45 and 60 minutes. The containers can then cool down to room temperature homogeneously.

7

Cold-End Handling and Inspection

When they leave the annealing lehr, containers have a temperature between 80 and 120 C. They are coated a second time in a spray process. The main purpose of this cold-end coating is to protect the container against scratches upon further handling and later at the filling line. Usually a polyethylene wax is used to decrease surface friction, hence making the containers less susceptible to scratches when being handled or touching one another. The cold-end coating also serves to provide a surface suitable for good adhesion of the label, which is usually fixed at the filler. After application of the cold-end coating, another inspection takes place in a highly automated way such that additional inspection by human eye is applied only in rare cases. Most inspection systems are based on various sophisticated optical systems, each checking for a certain type or group of potential defects that include flaws, scratches, cracks, blisters, seeds, loose or stuck glass particles, or dimensional errors of the container. Because special attention is paid to the finish of the container, mechanical inspection systems are, for instance, applied for testing that it is free of obstacles. Finally, random checks are made offline, e.g. to check that the strength exceeds definite values that depend on the kind of container. For impact strength, usually a minimum lot-size of 30 containers is tested on a shift, daily or some other regular basis, depending on the container made and plant procedures. The container is hit by a pendulum of a certain weight – depending on the chosen specification and domain of the container – in a well-defined matter until it breaks. As for the burst pressure strength, which is especially relevant for carbonated liquids such as sparkling wine, water, and champagne, the container is filled with water and its pressure is increased until breakage. Also here, due to the Weibull-characteristics of brittle materials, a minimum of at least 30 containers should be tested. After inspection, the containers are pelletized, wrapped, and prepared for shipment.

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1.5 Fabrication of Glass Containers

8

Perspectives

With the introduction of PET and other plastic containers, the glass industry has experienced a severe loss in market share for certain types of products such as juice, water, and milk. After years now the market seems balanced and the container-glass industry could maintain a quite stable production level of ca. 65 million tons worldwide, which amounts to ca. 200 billion containers in 2012. Recently, however, disadvantages of plastic containers have been recognized. Because of the leaching of endocrine-active substances, phthalates and other substances into the container content [10, 11] and the dispersion of plastic waste on land and especially in the oceans [12], glass might even be able to gain more acceptance from the consumer. Here, glass can play out it strengths as, among other positive aspects, it is fully inert and can be 100% recycled. Furthermore, glass in a landfill does not pose any threat to the environment as it degrades to the components it was made of. Nevertheless, glass has also its well-known drawbacks and a positive future of container glass strongly depends on the capabilities to overcome them. First, there is the fact that glass containers are energy-intensive to produce. Emission control, CO2-trading, rising energy costs, and other environmental regulation force the glass-industry to push limits farther (Chapter 9.7). As processes are already highly optimized, there are no more “low-hanging fruits.” Although the effort that has to be made financially and risk-wise increases exponentially with the possible benefit that can be gained, the container-glass industry is aware of the need of innovations. The increasing number of batch and cullet preheaters or the latest concepts to

allow heat recovery for oxy-fuel fired furnaces illustrate the kind of efforts made to keep shifting the limits. Other weak points are the fact that glass containers are brittle and mostly regarded as heavy. In specific instances, however, weight is considered a positive aspect of glass packaging. For example, think of the smooth texture, the reassuring heft, and the feel of value when lifting a glass bottle of wine or perfume. Nevertheless, many investigations have been carried out to decrease the weight of glass containers while increasing their strength. Coatings based on silica-sol-gels (Chapter 8.2) can, for instance, increase the strength of glass containers by 20% or more. Besides, most impressive are current developments which aim at thermal strengthening of containers. After forming, the containers are reheated and then cooled from both inside and outside much faster and in a much more controlled way than in an annealing lehr. In this manner, compressive stresses at the inner and outer surface are introduced, which significantly increase the strength of the glass so that containers can be lightweighted further or be reused. The key to this development is to control the cooling very precisely and to adjust the balance between compressive stresses at the surface and tensile stresses in the bulk of the container (Chapters 3.7 and 3.12). Innovations are also targeted in the field of glasscontact materials. Coatings for enabling a full nonswabbing production of all types of containers are investigated, but this task is still unsolved. Furthermore, it is highly desirable to avoid all lubricants that are currently used in shear-, trough-, and mold-lubrication. This would allow a full “dry-gob” delivery that would give considerable advantages over current process.

Figure 9 A modern pneumatic-controlled 12section double-gob individual-section machine; on the left, the conveyor belt evacuating the newly blown bottles (courtesy Bucher Emhart Glass).

References

References 1 Carslaw, H.S. and Jaeger, J.C. (1986). Conduction of Heat

in Solids, 2e. Oxford, UK: Oxford University Press. 2 Rieser, D., Manns, P., Spieß, G., and Kleer, G. (2004).

3 4

5

6

7

Figure 10 Parison just before blow-mold closing and final container on the blow-mold-side. Source: Courtesy Bucher Emhart Glass.

Concerning the IS-machine itself (Figures 9 and 10), a significant improvement would be to ensure a more precise and controlled forming process and, hence, a more homogeneous wall-thickness distribution in the final container. This could, for instance, be achieved by a direct gob-loading without the need of a delivery or by a forming process, which would allow a more precise reheat to have a more homogeneous final container forming. Because cost competition with alternative packaging is one of the biggest drivers and deciders for innovations, however, all the aforementioned approaches and concepts will have to distinguish themselves not only by their technical feasibility but also by their economic efficiency.

8 9 10

11

12

Investigations on sticking temperature and wear of mold materials and wear of coatings. In: Advances in Fusion and Processing of Glass, Part IV (eds. J.R. Varner, T.P. Seward and H.A. Schaeffer), 281–289. Hoboken: Wiley. Eales, J. (1977). Manual and Databook of Glass Technology Calculations. Holon, Israel: Ordentlich. Falipou, M., Donnet, C., Maréchal, F., and Charenton, J.-C. (1997). Sticking temperature investigations of glass/metal contacts – determination of influencing parameters. Glass Sci. Technol. 70: 137–140. Rieser, D., Spieß, G., and Manns, P. (2008). Investigations on glass-to-mold sticking in the hot forming process. J. Non Cryst. Solids 354: 1393–1397. Manns, P., Döll, W., and Kleer, G. (1995). Glass in contact with mould materials for container production. Glass Sci. Technol. 68: 389–399. Falipou, M., Zahouani, H., and Donnet, C. (1999). Effect of surface morphology upon friction of a metal substrate sliding against hot viscous melt under extreme conditions. In: Lubrication at the Frontier: The Role of the Interface and Surface Layers in the Thin Film and Boundary Regime (eds. D. Dowson, M. Priest, C.M. Taylor, et al.), 91–99. Amsterdam: Elsevier. Coenen, M. (1978). Festigkeit von Glasschmelzen. Glastech. Ber. 51: 17–20. Schaeffer, H.A. (2010). Hohlglas, Glass Hollowware. Munich: Deutsches Museum. Muncke, J. (2009). Exposure to endocrine disrupting compounds via the food chain: is packaging a relevant source? Sci. Total Environ. 407: 4549–4559. Sax, L. (2010). Polyethylene terephthalate may yield endocrine disruptors. Environ. Health Perspect. 118: 445–448. Moore, C.J. (2008). Synthetic polymers in the marine environment: a rapidly increasing, long-term threat. Environ. Res. 108: 131–139.

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1.6 Continuous Glass Fibers for Reinforcement Hong Li and James C. Watson Fiber Glass Science and Technology, PPG Industries, Inc., Shelby, NC, USA

1

Introduction

Numerous examples of the use of glass drawn as fibers can be found throughout history. The early Egyptians wrapped glass fibers over clay vessels and then fused them to form glass vessels. Venetian glass blowers in the sixteenth and seventeenth centuries used glass fibers to decorate elaborate glass articles. Glass fibers were even used as fabric elements in fashion garments in the late nineteenth century. It was in the mid-1930s, however, that two key developments created the means for glass fibers to become the base for a new industry based on composites–organic polymers reinforced with glass fibers, more commonly known as glass reinforced plastics, or GRP. The first was improvements in the process of manufacturing glass fibers at the Owens-Illinois Glass Company so that commercial fibers could be made in a multifilament strand form that met basic material handling requirements for downstream processing into composite structures [1]. The second was the development of polymeric resin systems by DuPont and others that could be combined readily with glass fibers. These glass-fiber reinforced polymer–matrix composites offered key material advantages over conventional metallic materials, including light weight, stiffness, and strength, and resistance to corrosion and fatigue. Today, glass fibers have become the most widely used and cost-effective reinforcing fibers in the arena of commercial polymer–matrix composites. Early melt spun processes producing discontinuous fibers have evolved to today’s large-scale direct melt continuous fiberforming operations. One of the first needs for continuous fibers was for insulation of electrical wires for hightemperature applications, leading to the development Reviewers: R. Conradt, RWTH University of Aachen, Aachen, Germany J. Thomason, The University of Strathclyde, Glasgow, Scotland, UK

of a new glass composition based on a CaO–Al2O3– SiO2–B2O3 system that met the electrical requirements and subsequently became known as E-glass. Because these fibers also exhibited excellent mechanical properties and could be made in relatively high-volume manufacturing operations, the original E-glass compositions rapidly spread into many composite applications. Today, the glass fiber reinforcement spectrum has grown to include an increasing array of specialty glass compositions that are targeted for key expanding markets in electronics, transportation, corrosion, construction, and in energy management. Prior to 2000, most major glass fibers manufacturers were concentrated in North America and Western Europe. Today, fiberglass production facilities are flourishing in China and beginning to spread to other regions of the world to satisfy a constantly growing demand of GRP. It is the intent of this overview to provide insight into the technology that is associated with the continuing success of glass as a reinforcing fiber. Fiberglass technology associated with both material characteristics and manufacturing processes are described at a high level.

2

Commercial Glass Fibers

2.1 History of Fiberglass Development and Glass Chemistry 2.1.1 Fiber Types

Reinforcement glass fibers can be broadly divided into two categories – general-purpose and premium specialpurpose fibers. The former are known as E-glass and subject to specific compositional ranges as defined by recognized standards such as ASTM D578 [2]. Historically, E-glass fibers have been predominant in the commercial production of fiberglass products for use as

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

1.6 Continuous Glass Fibers for Reinforcement

reinforcements in various industrial polymer–matrix composites applications. Other types of fibers that have been used in special purpose and low-volume applications include S-glass, R-glass, D-glass, ultrapure silica fibers, and hollow fibers [3]. Continuous glass fibers for composite reinforcement have been categorized by the specific properties required for end-use applications (Figure 1). An overview of the historical timeline of the development and commercial use of these major glass types is represented on the horizontal axis. Further detail on the typical oxides and oxide ranges, physical and mechanical properties, and processing-related properties that are characteristic of the major glass types used in glass fibers are listed in Tables 1 and 2, respectively. More specific examples of recent developments in the areas of D-, S-, and R-glasses are also included. 2.1.2 E-Glass

First commercialized in the late 1930s [1], E-glass fiber remains the most widely used class of fiberglass for GRP materials [3, 4]. Its composition primarily lies within the ternary CaO–Al2O3–SiO2 system with B2O3 and F2 contents that vary from 0 to 10 wt % and 0 to 2 wt %, respectively. For much of its history, E-glass fiber production incorporated B2O3 in commercial compositions at levels of 7–8 wt %, which provided an optimal balance of melting and fiber-forming characteristics, mechanical properties, and electrical properties. Over time, however, increasingly restrictive environmental emissions requirements for particulates have been driving costs up for emission control systems. Countries such as Canada and Norway were leaders in the push to improve environmental conditions, leading to the introduction of the first boron-free commercial glass fibers. These glasses had in addition excellent corrosion resistance under strongly acidic conditions [7]. They have been designated as E-corrosion resistant (E-CR) glass fibers in the late

High strength High modulus High dielectric performance Alkaline resistance Acid corrosion resistance Electrical insulation/acid corrosion resistance

1970s. Over time, optimizations of minor oxide components such as TiO2, ZnO, and MgO served to improve their cost and manufacturing efficiencies while also providing proprietary regions in the compositional space as their use was growing rapidly. In key areas outside of the corrosion markets, however, there was resistance to move to low-boron compositions. The electronics industry, dominated by E-glass fabrics used in printed wiring boards (PWB), relied on the unique value set of electrical consistency, dimensional stability, processing predictability, and low cost provided by conventional E-glass over many years and resisted any change in the E-glass standards. The aerospace industry also resisted the change, based on a well-defined history of performance of conventional E-glass and a desire to minimize any risk, however small, which might be incurred by what was perceived as a significant material change. As a consequence of these developments, commercial E-glass fibers today fall into two major categories: low or zero B2O3 levels for general reinforcements, and higher B2O3 levels (>5%) for electronic and aerospace applications. The distinction between these categories is clearly defined in ASTM D578 [2]. 2.1.3 C-Glass

Other reinforcement fibers containing B2O3 were developed in the early 1940s as C-glass, which has limited use as discontinuous fiber products for roofing materials. Continuous boron-free variants of C-glass fibers with improved chemical resistance to acids came to market in the mid-1960s. The composition is primarily composed of Na2O, CaO, Al2O3, and SiO2. The absence of boron resulted in improved acid resistance; the mechanical performance (strength and modulus) of C-glass fiber is inferior to those of both E-glass and E-CR glass, however, so that applications of this glass in the reinforcements industry have been limited to nonstructural uses Figure 1 History of commercial continuous fiberglass development (most active period in development shown and beyond 2015 most intensive research areas projected are S, R, and D glass fibers) and standard nomenclature/ classification based on their key properties used in commercial applications [4].

S R

Type of glass fibers

96

Good electrical performance and general industry application

D AR C E-CR E

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 Year

2 Commercial Glass Fibers

Table 1 Composition of glass fibers found in literature and/or commercial market [2–6]. SiO2 (wt %)

Al2O3 (wt %)

MgO (wt %)

CaO (wt %)

SrO (wt %)

BaO (wt %)

B2O3 (wt %)

R2O (wt %)

F2 (wt %)

ZrO2 (wt %)

E including E-CR C (China)a C (Europe)

52–62

12–16

0–5

16–25

—

—

0–10

0–2

0–2

—

67.0 53–65

6.2 3.8–16

4.2 2.4–3.8

9.5 14–16

—

—

0 3–6

12 7–9

33.3 mol% in the MgO–SiO2 binary. As containerless melting and quenching methods have made the formation of very low silica glasses possible (even into the “sub-orthosilicate” range, e.g. lower silica than in Mg2SiO4), it has become possible to quantify more clearly this most basic aspect of silicate structure [6]. In “modified,” ambient-pressure silicate glasses, only tiny fractions of SiO5 groups have been detected in a few alkali silicates. However, high pressures, or high P2O5 contents, can lead to the formation of substantial fractions of both SiO5 and SiO6, which will contribute to the overall network disorder as well as to density increase. For example, both an unusual high-pressure crystalline phase of CaSi2O5 and its glassy equivalent clearly have all three Si coordinations (Figure 5). A number of insitu, high-pressure studies, particularly by Raman spectroscopy, have suggested that considerable structural relaxation, and reversion to lower network cation coordination, can take place on decompression of a glass, even at ambient temperature. A few of these have probably also taken samples above Tg at high pressure. The small cationic radius and high charge of P5+ makes P2O5 another well-known network-forming oxide. Over wide

Glass, x8

Glass

SiO4 SiO5

SiO6

Crystal

–50

–100

–150

–200

ppm

Figure 5 Silicate structural groups in a high-pressure, triclinic crystalline phase of CaSi2O5 and in its isochemical glass quenched from the melt at 10 GPa, showing the correspondence of signals for Si with 4, 5, and 6 oxygen neighbors in 29Si MAS NMR spectra. Source: Modified from [7].

ranges of composition, two-component and more complex phosphate liquids are stable and can be quenched to glasses. These have been extensively studied, particularly by vibrational spectroscopy and 31P MAS NMR. All phosphorus is present in PO4 tetrahedra. As in silicate glasses, these are linked together to form chains of varying length as well as more complex structures. The roles of BO and modifier oxides in phosphate glasses are analogous to those in silicates, as are the considerations of anionic speciation discussed in Section 7.2.

4 Modifying the Network: Borates and Germanates Contrary to what is found in ambient-pressure silicates and phosphates, a different type of network modification takes place when oxides of low-valence cations are initially added to B2O3 or to GeO2, facilitated by the energetically “easy” transitions of network cations between two (BO3, BO4) or even three (GeO4, GeO5, GeO6) coordination states. Instead of only forming NBOs, the added oxide ion serves primarily to increase the coordination number of the network cation so that the network remains fully connected by BO, if the definition of the latter is expanded to include linkages with the highercoordinated network cations. (It is important to note, of course, that oxygen bridges between network cations may be energetically quite distinct, and have differing implications for bulk properties, as the network cation coordination varies.) If NBOs do form, their concentrations are much lower than produced in the corresponding silicate equilibria. The “modifier” cations are coordinated primarily by BO, some of which will have partial negative formal charges, e.g. −1/4 on the BO linking a BO3 with a BO4 group. This mechanism (Figure 4) predominates up to about 20–30 mol% modifier oxide, at which point the formation of “normal” NBOs, as in silicates, begins to become important. At least part of this turnover may result from the difficulty of packing enough low-charge modifier cations around BOs with higher formal charges, i.e. −1/2 on the link between two BO4 groups, and in turn this can be affected by the cation field strength and dilution of the borate network by silica. At higher modifier contents, much or even most of the network cation coordination returns to the lower state, BO3 or GeO4. These compositionally induced transitions in the network cation coordination are generally mirrored in the structures of the binary crystals, and result in strongly nonlinear property– composition relationships in both the melts and glasses, e.g. density and glass transition temperature.

5 Network Cations in Aluminosilicates

This mechanism is most precisely defined in alkali borate glasses, for which 11B NMR has long been applied to measure directly BO3 and BO4 contents [8]. Raman spectroscopy can also detect this coordination shift, and can be more readily applied at high temperatures and pressures. The structural transition with composition can be symbolized by the reaction, which incorporates the reaction of O2− with BOs to form NBOs: BO3 + NBO = BO4

2

This reaction can also be taken as a statement of chemical equilibrium among melt species. Shifts with temperature have been determined from both in-situ, hightemperature vibrational and NMR spectroscopy and studies of glasses prepared at different cooling rates and thus with different fictive temperatures [9]. The lower coordination state (left hand side) is generally favored at higher temperature, meaning that the enthalpy change for the reaction as written is negative. In boronrich systems, this coordination change can be a major contributor to the overall configurational heat capacity and enthalpy of the liquid; changes in the abundances and mixing of the boron coordinations will clearly affect the configurational entropy as well. At least in borosilicate glasses, modifier cations with higher field strengths tend to favor the formation of NBOs and thus lower boron coordination numbers. Spectroscopy on quenched, decompressed glasses has shown that this mechanism leads to boron coordination increase at high pressure [10]; a few in-situ studies by X-ray and other methods have observed this process more directly. Analogous structural transitions that take place as modifier oxides are added to GeO2. Alkali germanate glasses and melts have density maxima at roughly 15–20% M2O, the compositions near which crystal structures are made up of mixtures of GeO4, GeO6, and even GeO5 groups. Although these groups cannot be individually quantified in glasses as readily as those in boroncontaining compositions, XRD and neutron diffraction demonstrate the accompanying changes in mean Ge–O distances. Also, 17O NMR can distinguish BOs, NBOs, and other species in germanates and confirms the transition from a primarily “borate-like” mechanism at low modifier contents (mixed low- and high-coordination of Ge, most or all BO in the broad sense of the term) to a “silicate-like” mechanism (GeO4 and “normal” NBO formation) at high modifier contents. Germanate crystals, glasses, and melts are often considered as at least rough analogs for silicates at elevated pressures. If the changes in network cation coordination with composition are as complex in silicate melts at high pressures, then highly nonlinear compositional effects on melt properties may be expected.

5

Network Cations in Aluminosilicates

In most readily formed multicomponent oxide glasses, Al3+ is a network former predominantly present as AlO4 tetrahedra. The latter are compositionally equivalent to AlO4/2 if oxygen sharing is taken into account. Because the alumina chemical component (Al2O3 or AlO3/2) has insufficient oxygen to form this species, one NBO, if present, will be converted to a BO for each added Al cation. Simple models of aluminosilicate melt structure have long assumed that, when alumina contents become large enough to balance all of modifier oxides (e.g. moles of Al2O3 = moles of Na2O or CaO), NBO contents are reduced to zero and the glass or melt structure is comprised entirely of fully connected tetrahedra, by analogy with framework aluminosilicate crystals such as feldspars (e.g. NaAlSi3O8, CaAl2Si2O8). This is a good approximation in some systems, especially those with alkali oxide modifiers only, and is supported by long-known changes in properties with composition as well as diffraction and spectroscopic data. As alumina is added to alkali silicate melts and glasses, for example, the alkali cations are coordinated by fewer NBOs and more BOs, some of which will have partial negative formal charges, e.g. −1/4 for Si–O–Al and −1/2 for Al–O–Al. This change in role can be described as a transition from “network-modifying” to “charge-compensating” cation. However, detailed spectroscopic studies, especially by 27 Al and 17O NMR and Raman, show that the structure can be more complex than indicated by this model, particularly in systems with modifier cations of high field strength. In Ca and Mg aluminosilicates, for example, significant concentrations of AlO5 (typically 4–8% of Al cations) and even small amounts of AlO6 groups are present throughout most of the glass-forming regions [11]. Some NBOs also persist well into the peraluminous compositional range (e.g. with moles of Al2O3 > CaO). Trivalent modifier cations such as Y3+ and La3+ promote this shift in Al coordination, which increases even more obviously in peraluminous compositions and in aluminoborates and aluminophosphates. The mixing of these Al coordinations in the network must contribute to configurational entropy and related properties. As noted in Section 3, the distinction between “bridging” and “nonbridging” oxygens becomes blurred as network cations increase in coordination number and their bonds to oxygen lengthen and weaken, complicating simple structure–property hypotheses. A few in-situ X-ray diffraction and Raman studies, and more detailed research on quenched, decompressed glasses, have clearly shown increases in Al coordination with pressure, which occurs more readily than for Si. NMR studies of glasses quenched

177

2.4 Short-range Structure and Order in Oxide Glasses

from high-pressure melts have shown that Al coordination increase is promoted by modifier cations with higher field strength [10].

6 Short-range Order and Modifier Cations The relatively large, low-charge cations that can serve as “network modifiers” in oxide glasses comprise much of the periodic table, so that their behavior can only be generally summarized here. Information about their local structural environments has been most commonly obtained from XAS, both XANES and EXAFS [12], from optical spectroscopy for many transition metal and rare earth cations, from Mössbauer for Fe2+ and Fe3+, and from modeling of neutron and X-ray diffraction data. In a few cases, notably for 6,7Li, 23Na, 25Mg, and 207Pb, NMR has begun to contribute as well. In a number of oxide glass systems, the possibilities of substitution of isotopes of modifier cations with different neutron scattering cross sections (e.g. 44Ca–40Ca) has allowed cationspecific pair distribution functions to be derived from differential measurements, which can give unique details of ordering out to several cation shells. All of these types of data usually indicate some disorder in the first shell and, in some cases, mixes of cation coordination. Most commonly, coordination numbers are similar to those of known crystals or somewhat lower, as can be expected from the lower densities of the glass and liquid phases. Fitting of EXAFS data for some modifier cations has provided important clues about cation first neighbors and on whether these mix randomly, which can be important not only for thermodynamic models but for optical and magnetic properties. In systems with strong nuclear dipolar couplings, such as for 23Na and 7Li in alkali silicate and borate glasses, detailed studies of NMR line shapes and relaxation can give estimates of mean distances among the modifier cations [13]. With these data one can discriminate between models of random, spatially homogenous distributions and of nonrandom arrangements with shorter average cation–cation separations. The latter feature is found in models in which modifiers are clustered in regions with relatively high NBO concentrations, for example, those in 2-D “channels” thought to be important in ion transport [1]. The coordination number of a given modifier cation often depends on glass composition. For example, the coordination number of an alkali cation should increase as the fraction of coordinating oxygens that are NBO (vs. BO) decreases with increasing silica or alumina content, and thus the negative charge per oxygen is reduced. This type of change has been measured by 23Na NMR and other methods. In cases where glass color is caused by electronic transitions in cations such as transition

4

60 εapp (L/mol/cm)

178

5

40

20 6 0 15 000

cm–1

25 000

Figure 6 Optical spectra for glasses in which Ni2+ coordination changes from primarily 4 to 5 to 6 coordinated as alkali content is decreased. The bulk glass color changes from purple to brown to green. Source: Modified from [14].

metals and rare earths, changing site geometry or coordination number with composition can have dramatic visible and spectroscopic consequences (Figure 6). If more than one modifier cation is present in the system, that with the higher field strength can outcompete another with a lower field strength for coordination by NBOs, displacing the latter cations into sites with higher coordination number (and/or to those with more BOs) as composition changes. This type of site ordering is probably part of the explanation for the commonly seen “mixed alkali” effects, where cation diffusion and ionic conductivity can be slowed by orders of magnitude relative to those in single-modifier compositions. At higher temperatures, increased disorder with respect to modifier cations can be a major contributor to configurational entropies and is marked, for example, by the enhancement of the entropy of fusion of diopside (CaMgSi2O6) relative to those of enstatite (Mg2Si2O6) and wollastonite (Ca2Si2O6) [2]. The charges and sizes of network-modifier cations, as in part captured by their field strength and reflected by their coordination numbers, can have huge effects on the network structure of oxide glasses and on both glass and melt properties. When the coordination of the network cation can readily change, as for boron and aluminum in some systems, higher field-strength modifiers can either decrease (B) or increase (Al) the network cation coordination, again probably through a process of formation of and/or competition for NBOs. These effects are much less well known, but could be expected in germanates and in high-pressure silicates.

7 Interactions of Network Modifiers and Network Order/Disorder 7.1 Order and Disorder of Bridging and Non-bridging Oxygens In oxide glasses with more than one type of networkforming cation, NBOs and BOs could be equally

7 Interactions of Network Modifiers and Network Order/Disorder

distributed on all such cations, or could be ordered in some way. The latter is generally the case. Raman spectra of aluminosilicates have suggested that most NBOs are on Si and that most AlO4 groups thus have four BO, when composition permits. This result has been directly confirmed by 17O NMR in Ca aluminosilicates. Comparable studies in a few borosilicates have observed B-NBO and the predominant Si-NBO. For systems with more than one type of modifier cation, large differences in size or charge might be expected to lead to some kind of ordering. This can be sampled by methods that “see” the coordination environments of oxygen species directly. For example, both one- and two-2-D 17O NMR spectra have shown that chemical shift distributions in mixed Na/K and mixed Ca/Mg silicate glasses are consistent with random distributions of the two cations around the NBOs, consistent with deductions from viscosity measurements and estimated configurational entropies. In contrast, the large field-strength difference between K+ and Mg2+ leads to a concentration of the latter around the available NBO sites. This approach has shown the considerable complexity of order/disorder patterns that can occur in the distributions of modifier- and charge-compensator cations around both NBO and BO sites in a number of other mixed-cation silicates and aluminosilicates. Decreases in this type of ordering might be expected from entropic considerations at higher temperatures in the liquids.

7.2

Qn Speciation

In silicate and phosphate glasses, the best-known aspect of network order/disorder, as affected by the modifier cations, involves the distributions of the NBOs. One can sample these distributions by counting the proportions of “Qn” species, defined as tetrahedral groups with n BOs and 4-n NBOs. Such measurements were originally done by Raman spectroscopy [2]. At least in some simple systems such as alkali silicates and phosphates, these proportions can often be readily quantified by 29Si or 31P NMR; such results can be used to evaluate cross sections for vibrational spectroscopy as well. In both approaches, peak fitting and associated assumptions about line shapes are usually required and can lead to some ambiguity. An early and important question was whether the number of Qn species present in a glass was the minimum derived from stoichiometry (in general two, but only one at special compositions), or whether entropy induced a greater variety. The clear detection of Q2, Q3, and Q4 species in glasses such as Na2Si2O5, which could contain only Q3 as in the crystal, confirmed the latter view. Simple equilibria among Qn species can be defined for n = 1, 2, 3: 2Qn = Qn − 1 + Qn + 1

3

Apparent equilibrium constants kn for such reactions have been evaluated from Raman and NMR data on glasses, including 2-D 29Si NMR on Ca and Mg silicates [15]. Higher field-strength modifiers push these reactions to the right (increasing kn), presumably favoring the concentration of more NBOs around some Si sites and thus better local charge balance for small, highly charged modifiers. More Q4 species are also generated, which correlates with higher thermodynamic activities of silica as deduced from phase diagrams [5]. In the range of observed speciation, greater kn values lead to greater contributions to the configurational entropy if models of random mixing of the Qn species are considered. But enhanced ordering of NBOs around higher field-strength cations could counter this effect to some degree and, in the extreme, could lead to cation clustering and even incipient phase separation. Shifts of such equilibria have been measured with both in-situ high-temperature Raman spectroscopy and NMR on glasses with increasing fictive temperatures, the results from the two methods often agreeing well. Estimated enthalpies of reaction are usually positive, but are less so for higher fieldstrength cations. If a random model is assumed (which can in some cases be tested by NMR methods yielding spatial correlations of different species), mixing of observed Qn populations can contribute a substantial fraction of the calorimetrically determined entropy differences between glasses and crystals. Complementary to these results for glasses in the normal, high-silica, glass-forming range are the recent findings for orthosilicate (e.g. Mg2SiO4) and even “sub-orthosilicate” glasses formed by quenching in laser-heated, gaslevitated, containerless melting systems. Here, significant concentrations of Q1 species can be observed by Raman and 29Si NMR, requiring as well the presence of nonstoichiometric “free oxide” ions. Direct evidence for the latter can be seen in 17O NMR spectra [6].

7.3

Order/Disorder in Network Linkages

The distribution of network cations (e.g. Si4+, Al3+, B3+, P5+) around BO in multicomponent oxide glasses and melts is in principle relatively simple to characterize, as each BO has only two such neighbors. This is a quite important problem, though, as it defines the extent of disorder among the various network components as well as the partitioning of partial charges on the BO, which in turn affects ordering of modifier or charge-compensator cations. Multiplequantum 17O NMR has allowed such distributions to be directly quantified in some systems, through direct counting of proportions of different linkages among network species. In crystalline, framework aluminosilicates such as feldspars and zeolites, diffraction and NMR studies have generally shown that Al–O–Al linkages are “avoided”, if

179

2.4 Short-range Structure and Order in Oxide Glasses

stoichiometry allows, leading to a high degree of ordering when Al/Si = 1, as for example in anorthite (CaAl2Si2O8) and nepheline (NaAlSiO4) in which all the oxygens are present as Si–O–Al linkages. This ordering presumably is related to the energetic and/or geometric unfavorability of bringing enough of the charge-compensating cations close to the relatively highly charged (formally −1/2) Al–O–Al linkages. There are notable exceptions for disordered crystals formed by rapid devitrification of glasses (e.g. cordierite Mg2Al5Si4O18 and β-eucryptite LiAlSiO4), and stable tetrahedral framework compounds containing only Al–O–Al linkages are well known (e.g. CaAl2O4). Triple-quantum 17O NMR spectra of alkali aluminosilicate glasses can fully resolve Si–O–Si, Si–O–Al, and Al– O–Al sites. This has enabled more precise formulations of the thermodynamics of equilibria such as: 2Si − O − Al = Si − O − Si + Al − O − Al

4

In terms of distributions of residual negative charges on oxygens, this reaction is analogous to that for the Al-free system (Eq. 3), as one species on the right has a reduced net negative charge (Si–O–Si or Qn + 1) whereas the other has an enhanced charge concentration (Al–O–Al or Qn −1 ). In NaAlSiO4 glass, the observation of about 10% of Al–O–Al confirmed that aluminum avoidance is not perfect, but also that this aspect of the structure is closer to ordered than to fully disordered, at least near the glass transition temperature. Further studies of other Na, Li, and Ca aluminosilicates, complemented by 29Si NMR spectra, showed that the concentration of negative charge, now in the form of Al–O–Al linkages, is favored by higher field-strength cations (as for the distribution of Qn species in Al-free silicates) [5]. Thermodynamic modeling of the effects of Al/Si ratio on speciation predicted heats of reactions that are consistent with solution

calorimetry and that were, for a few compositions, confirmed by observed increases in Al/Si disorder in glasses with higher fictive temperatures, making a larger contribution to configurational heat capacity. Subsequent extensive work on high-pressure aluminosilicates has begun to elucidate the much more complex linkages among not only tetrahedral network species but fiveand six-coordinated Al and Si, where the mixing of all of these network species presumably contributes to increases in configurational entropy [16]. The same experimental approach can, in some borosilicate glass compositions, quantify the extent of mixing of boron and silicon network cations, which can be much greater than considered in early models based primarily on 11B NMR data (Figure 3). In compositions with modifier oxides, the structure is further complicated by the presence of both BO3 and BO4 groups. As for aluminosilicates, relatively highly charged B–O–B linkages between two of the latter seem to be at least partially “avoided.” When pairs of network cations are present that can have strong nuclear dipolar couplings, notably 11B and 27Al, or 27 Al and 31P, double-resonance NMR methods can reveal their relative proximities and even the correlations of species with multiple coordination environments, for example of BO3 groups with AlO4 [17]. These findings again can provide important constraints on mixing and contributions to order/disorder.

8

Perspectives

Technical advances continue to increase the quality, depth, and breadth of information that can be obtained about short-range structure and order in oxide glasses, for example, microscale XAS, X-ray Raman, improved

16 Ca–Ca

Si–Ca

20 Mg–Ca

Si–Mg gij(r)

180

Mg–Mg O–O

8

10 Ca–O

Si–Si

Si–O

Mg–O 0

0 0

2

4 r (Å)

6

8

0

2

4 r (Å)

6

8

Figure 7 Partial pair distribution functions gij(r) calculated from a “reverse Monte Carlo” model combining X-ray and neutron diffraction data for various CaSiO3–MgSiO3 glasses. Source: Reprinted with permission from [18].

References

neutron scattering facilities, and NMR at higher magnetic fields and with methods that allow better measurements of internuclear distances and connectivities. Combination of experimental data from different methods, to yield consistent models, is especially powerful, as illustrated in Figure 7 [18]. Some of these approaches are now feasible for in-situ studies of high-temperature liquids and even of liquids at high pressure and temperature. Advances in theory are beginning to allow accurate forward calculation of spectra (e.g. vibrational and NMR) from structural models [19]. This information can then be combined with experimental data to obtain much more complete views of structure, quantitative extent of disorder, and their links to thermodynamic properties that depend critically on configurational entropy, such as viscosity, heat capacity, and the bulk free energy. As researchers move beyond model-dependent fitting and interpretation of spectra of glasses to more complete theoretical analyses, our understanding of the true complexities of these fascinating and useful materials will expand enormously.

9

10

11

12

13

References 1 Greaves, G.N. and Sen, S. (2007). Inorganic glasses, glass-

2 3

4

5

6

7

8

forming liquids and amorphizing solids. Adv. Phys. 56: 1–166. Mysen, B.O. and Richet, P. (2018). Silicate Glasses and Melts, 2e. Amsterdam: Elsevier. Kroeker, S.K., Rice, D., and Stebbins, J.F. (2002). Disordering during melting: an oxygen-17 NMR study of crystalline and glassy CaTiSiO5 (titanite). Am. Mineral. 87: 572–579. Warren, B.E. and Biscoe, J. (1938). Fourier analysis of Xray patterns of soda-silica glass. J. Am. Ceram. Soc. 21: 259–265. Stebbins, J.F. (2016). Glass structure, melt structure and dynamics: some concepts for petrology. Am. Mineral. 101: 753–768. Stebbins, J.F. (2017). “Free” oxide ions in silicate melts: thermodynamic considerations and probable effects of temperature. Chem. Geol. 461: 2–12. Stebbins, J.F. and Poe, B.T. (1999). Pentacoordinate silicon in high-pressure crystalline and glassy phases of calcium disilicate (CaSi2O5). Geophys. Res. Lett. 26: 2521–2523. Silver, A.H. and Bray, P.J. (1958). Nuclear magnetic resonance absorption in glass. 1. Nuclear quadrupolar

14 15

16

17

18

19

effects in boron oxide, soda-boric oxide, and borosilicate glass. J. Chem. Phys. 29: 984–990. Wu, J. and Stebbins, J.F. (2013). Temperature and modifier cation field strength effects on aluminoborosilicate glass network structure. J. NonCryst. Solids 362: 73–81. Bista, S., Stebbins, J.F., Wu, J., and Gross, T.M. (2017). Structural changes in calcium aluminoborosilicate glasses recovered from pressures of 1.5 to 3.0 GPa: Interactions of two network species with coordination number increases. J. Non-Cryst. Solids 478: 50–57. Neuville, D.R., Cormier, L., and Massiot, D. (2006). Al coordination and speciation in calcium aluminosilicate glasses: effects of composition determined by Al-27 MQMAS NMR and Raman spectroscopy. Chem. Geol. 229: 173–185. Brown, G.E. Jr., Farges, F., and Calas, G. (1995). X-ray scattering and x-ray spectroscopy studies of silicate melts. In: Structure, Dynamics, and Properties of Silicate Melts (eds. J.F. Stebbins, P.F. McMillan and D.B. Dingwell), 317–410. Washington, DC: Mineralogical Soc iety of America. Eckert, H. (1994). Structural studies of non-crystalline solids using solid state NMR. New experimental approaches and results. In: Solid-State NMR IV. Methods and Applications of Solid-State NMR (ed. B. Blümich), 127–202. Berlin: Springer-Verlag. Galoisy, L. (2006). Structure-property relationships in industrial and natural glasses. Elements 2: 293–297. Davis, M.C., Sanders, K.J., Grandinetti, P.J. et al. (2011). Structural investigations of magnesium silicate glasses by 29 Si 2D magic-angle flipping NMR. J. Non-Cryst. Solids 357: 2787–2795. Lee, S.K., Fei, Y., Cody, G.D., and Mysen, B.O. (2003). Order and disorder in sodium silicate glasses and melts at 10 GPa. Geophys. Res. Lett. 30: 1845–1849. Chan, J.C.C., Bertmer, M., and Eckert, H. (1999). Site connectivities in amorphous materials studied by double-resonance NMR of quadrupolar nuclei: high resolution 11B – 27Al spectroscopy of aluminoborate glasses. J. Am. Chem. Soc. 121: 5238–5248. Cormier, L. and Cuello, G.J. (2013). Structural investigation of glasses along the MgSiO3-CaSiO3 join: diffraction studies. Geochim. Cosmochim. Acta 122: 498–510. Angeli, F., Villain, O., Schuller, S. et al. (2011). Insight into sodium silicate glass structural organization by multinuclear NMR combined with first-principles calculations. Geochim. Cosmochim. Acta 75: 2453–2469.

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2.5 The Extended Structure of Glass George Neville Greaves Department of Metallurgy and Materials Science, University of Cambridge, Cambridge, UK

1

Introduction

The structure of glass stretches from atomic dimensions and local short-range order (SRO), which is often similar to that of the crystalline state, through intermediate-range order (IRO) and long-range order (LRO) on the nanoscale, which has no parallel in periodic materials. Sometimes IRO and LRO are grouped together as mediumrange order (MRO). Glasses have a monolithic structure, which in principle can extend indefinitely from the atomic scale, via the mesoscale to macroscopic dimensions. The extended structure of glass even encompasses the thousands of square meters emerging from the float process, the quenched field of volcanic obsidian, the kilometers of optical fiber, or the reels of metallic glass tape. Contrary to received wisdom, glasses are in general practically defect-free relative to crystalline materials. The fraction of broken bonds in fiber-quality silica, for instance, is a few parts per million. In generating the macroscale, the self-similar configurations of SRO extend virtually continuously everywhere. The extended structures of glasses generally define their functionality. In silicate and aluminosilicate glasses, for example, tetrahedral bonding through corner-sharing oxygens ensures that the gap between the occupied oxygen p states and unoccupied antibonding sp3 levels is retained everywhere (this is the so-called HOMO– LUMO gap between the highest occupied and lowest unoccupied molecular orbitals). The existence of relatively few mid-gap defect states in turn guarantees visible and UV transparency for windows, optical components, laser glasses, etc. In metallic glasses, the cohesive potential between the delocalized electron gas and the ion cores Reviewers: J. F. Stebbins, Geological Sciences, Stanford University, Stanford, CA, USA A. Takada, Research Center, Asahi Glass Co. Ltd., Yokohama, Japan

is maintained isotropically throughout the bulk. These features underwrite electrical conductivity and, without the dislocations of crystalline metals, extremely high levels of mechanical hardness and toughness. Likewise, the spin–spin exchange interaction is retained in aperiodic metallic structures, supporting the ferromagnetism exploited in low-loss magnetic metallic glass-transformer cores. Additionally, because most glass formers – either metallic or not – derive from reasonably strong liquids, they have a wide supercooled liquid range and exhibit superplasticity at the softening point (108 Pa s) but virtual rigidity at the glass transition (1012 Pa s). Through Newtonian viscous flow, their monolithic structures enable the easy fabrication of components with essentially any shape, from the industrial dimensions of windscreens down to those of MEMS and nanotechnology. By contrast, in crystalline materials even the largest industrial single crystals are extremely small by comparison to glass sheet. Large-area crystalline films comprise micron-sized powders such that the facets of polycrystals generate a microstructure of interlacing grain boundaries where functionality generally resides. For example, the ductility of metals, the hardness of ceramics, the strength of steels, and the mesoscale magnetism of metal films mainly derive from the properties of grain boundaries that are often structurally disordered and anisotropic. By comparison glasses are structurally isotropic, and the cracks that affect their mechanical strength are usually restricted to the surface where the atomic structure terminates. The extended structure of glass links the SRO of atoms, molecules, and metallic clusters and geometrically underpins its intrinsic isotropic properties – optical, electronic, dielectric, electrolytic, magnetic, mechanical, etc. This can be visualized through computer-simulated structures (Figure 1), where the open network of a silicate glass is contrasted with the dense close-packed arrangement of a metallic glass.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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(a)

(b)

Si

O

Na

K

Ni

P

Figure 1 Visualizing the extended atomic structure characteristic of glass. (a) Molecular dynamics simulation of the network structure of NaKSi2O5 glass [1, 2]; Na and K atoms are dispersed within depolymerized silicate network, forming percolating alkali channels. (b) Reverse Monte Carlo simulation of the close-packed structure of the metal-metalloid glass Ni80P20 [3, 4]; P atoms also cluster, forming percolating channels through the Ni dense random packed structure. The scale bars indicate the start of long range order (LRO). Source: (b) Reproduced from [4] © 2006 Nature Publications.

The respective atomic volumes are 7 and 11 Å3 and are typical of these very different families of glass, but where each share an extended defect-free structure. Reviews of network glasses and metallic glasses can be found in [1, 3], respectively. In this chapter we consider how several experimental techniques are required to access the extended structure of glass (Section 2), from diffraction and inelastic spectroscopies that reveal relationships between SRO, IRO, and LRO structure and dynamics, to microscopy that probes the average projected structure in real space. We then turn to the different types of structural order that characterize network and metallic glasses (Section 3): starting with the SRO, progressing through the configurations of adjacent local structural units that define IRO, and extending through MRO to LRO, the topology of larger agglomerations – clusters, rings, channels, and chains. Beyond these dimensions are those of density fluctuations (DFs) (Section 4), frozen into glasses from the liquid state, which reflect the degree of non-ergodicity frozen in at the glass transition. In particular, DFs are the agents at supercooled temperatures that promote phase separation, either in density or in composition. Models of extended glass structure (Section 5) are next described and include conceptual models, devised before the advent of computational methods but still useful heuristically, and large computerized models that have been developed since.

Using this approach, we show how structural heterogeneity in glasses (Section 6) can be modeled in terms of minority-component channels percolating through the majority network or metallic structure. Here, as elsewhere, the extended structure of glass is linked with its applications. Finally, we outline perspectives for future work (Section 7).

Acronyms AFM BO BP CN CRN DAS NMR DF DFT DRPHS EXAFS HR TEM INS IXS IRO

atomic force microscopy bridging oxygens boson peak coordination number continuous random network dynamic-angle spinning nuclear magnetic resonance density fluctuations density functional theory dense random packing of hard spheres extended X-ray absorption fine structure high-resolution transmission electron microscopy inelastic neutron scattering inelastic X-ray scattering intermediate-range order

2 Extended Structure of Glass: The Need for a Multiplicity of Techniques

long-range order magic angle spinning nuclear magnetic resonance molecular dynamics medium-range order modified random network nanobeam electron diffraction nonbridging oxygens phase-separated glasses reverse Monte Carlo short-range order vibrational density of states

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In addressing the extended structure of glasses, a wide portfolio of techniques has developed [1, 3, 5]. For many years the principal experimental method has been X-ray and neutron scattering [6], initially concentrating on the radial distribution function (RDF) from which the radially averaged local structure T(r) can be determined, as illustrated in Figure 2 for silica glass and the metallic glass Ca60Mg25Cu15. The maxima identify interatomic correlations, first between nearest neighbors (SRO) defining the polyhedral or icosahedral building units and then between adjacent units (MRO or IRO), as spelt out in the cartoons. The SRO and IRO in glasses are often similar to their crystalline cousins. On the other hand, topology influences LRO – ring statistics for network glasses [1] and icosahedral packing for metallic glasses ([3], Chapter 7.10) – where mismatching frustrates crystallization. Attention has subsequently shifted to the measured scattered intensity i(Q) from which the static structure factor S(Q) is obtained, which leads to T(r) via Fourier transform [1]. The scattering vector Q is defined by Q = 4πsinθ/λ, where θ is the scattering angle and λ the wavelength of the scattering particles. The i(Q) for the two exemplar glasses are plotted in Figure 3. Two important features are located early on for Q < 5 Å−1: the first sharp diffraction peak (FSDP), for which the spacing 2π/QFSDP is a metric for IRO, and the principal peak (PP), which is directly related to the average nearestneighbor distance 2π/QPP [6, 7]. Both the FSDP and the PP are features common to network glasses as well as metallic glasses (Figure 3). With high-intensity spallation neutron sources, the Q-range reliably reaches 50 Å−1, enabling the T(r) to be confidently measured to 20 Å, embracing SRO with LRO.

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Figure 2 Contrast between the radially averaged local structure T(r) of directionally and metallically bonded structures as exemplified by the network glass SiO2 (a) and the bulk metallic glass Ca60Mg25Cu15 (b). The short (SRO), intermediate (IRO), long (LRO), and medium (MRO) range orders are identified alongside 2-D schematics of local atomic arrangements. Note the difference in the widths of atomic shells reflecting the bonding strength of covalent networks compared to the dense metallic random packings. Source: Courtesy of A. Hannon (http://alexhannon.co.uk/ DBindex.htm).

Compared with diffraction techniques used for crystalline materials, diffuse scattering methods seriously underdetermine the extended structure of glass, even for monatomic systems. Other independent structural measurements are needed in order to increase the credibility of atomistic models. Although X-ray and neutron S (Q) s are independent measures of the same radially averaged structure, until recently X-ray measurements lacked the extensive Q-range of neutron instruments. However, with the arrival of high-energy X-ray scattering [8], both methods are now compatible and are generally applied sequentially to the same material. Most glasses, though, are multicomponent, which adds chemical complexity to the radial averaging of

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three-dimensional (3-D) arrays. More chemically selective techniques are thus generally required, even though isotopic neutron scattering can assist when different isotopes of an element are available [6]. Accordingly, neutron and X-ray scattering are now increasingly complemented by spectroscopies, like magic- and dynamic-angle spinning nuclear magnetic resonance (MAS NMR and DAS NMR), and extended X-ray absorption fine structure (EXAFS) [1, 5, 9]. As these are element specific and increase the mix of independent measurements of the same structure, they add rigor to models of extended glass structure derived from computational methods such as reverse Monte Carlo (RMC) and molecular dynamics

(MD) [1, 10–12]. Moreover, expressed as S(Q), the credibility of predictions of atomic arrangements in glasses can be judged against experimental data quality. Compared to the direct analysis of experimental RDFs, which dates back to the 1930s, these new combinations of experiment and computational modeling now offer impressive insight into the nature of the extended structure glasses, on the scale of 30 Å or more (Figure 1). Often glasses with equivalent local structure lead to images that at first glance appear to be quite dissimilar (Figure 4). The tetrahedral glass network of silica may thus be contrasted with that of amorphous ZIF-8 – one of a newly discovered family of hybrid glasses derived from organic–inorganic materials [14, 15]. The extended structure of silica is perpetuated through corner-sharing SiO4 tetrahedra (SRO) via bridging oxygens (BOs), IRO ultimately extending to LRO comprising rings of different size (Figure 4). The geometry of amorphous ZIF-8 [Zn(C4H5N2)2] develops in a similar way, with Zn atoms tetrahedrally coordinated to 2-methylimidazolate bridges that form into silica-like rings, despite the atomic volume being hugely different, viz. the 11.1 Å3 of SiO2 compared with the 73.4 Å3 of amorphous Zn(C4H5N2)2. In adding further confidence to modeling extended glass structure, studies of dynamic properties, using inelastic spectroscopies like inelastic neutron scattering (INS) and Raman spectroscopy, have played an important part [1, 5, 16] – principally in highlighting stretching and bending optic mode vibrations between the atom pairs in network glasses and providing fingerprints of the polyhedra and small molecular groups that constitute SRO and aspects of IRO. At lower frequencies, inelastic spectroscopies like INS access acoustic modes that are generically subsumed into the boson peak, ubiquitous in the glassy state [1, 5, 17–19]. Derived from the localized collective vibrations of groups of atoms, the boson peak relates to the dynamics of MRO and LRO considered to be the source of fast β relaxation [1, 7]. Located at the bottom of the vibrational density of states (VDOS) in the THz region (1 THz = 4.1 meV), the boson peak is generally accepted as comprising quasi-localized transverse vibrational modes (Chapter 3.4 [16, 18]). These vibrations also enhance the specific heat Cp at low temperatures above the Debye threshold – typically around 10 K. Using either INS or excess Cp reveals that the boson peak intensity is directly related to glass density (Figure 5a–d [18, 19]). For zeolites, which share compositions with silicate and aluminosilicates but have characteristically low densities, the different cage-like units that define their nanoporous structures resonate at different THz frequencies [16]. As the temperature or pressure is increased, these subunits collapse [1] through a process of decelerated melting [21], and a glass, similar in density to a melt-quenched glass, is formed

3 Structural Order over Different Length Scales

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enthalpy, which can be reduced by annealing Figure 5f [20]. As annealing increases, the glass density, νBP, also increases while IBP decreases (compare Figure 5e and f). Whereas inelastic scattering S(ω) measures the VDOS integrated over Q, and the structure factor S(Q) timeaveraged atomic distributions, both derive from the dynamic structure factor S(Q,ω), which through comparisons with experiment affords a global view of the structure and dynamics of glassy systems and melts over extended regions of space and time. Related to S(Q,ω) is the intermediate scattering function F(Q,t), which registers structural relaxation from liquid to glass as a function of time [1]. In the limit t ∞ F(Q,t)/S(Q) yields the non-ergodicity factor f(Q,T), which is particularly relevant in the present context as it records the degree to which a liquid departs from thermodynamic equilibrium as it is supercooled (Section 4.1). It is readily measured using inelastic X-ray scattering (IXS). Structural relaxation is dominated by fast β processes at high temperatures, with slow α processes emerging through the supercooled region, only to be frozen out at the glass transition Tg. Microscopy has always played a part in glass structure determination, albeit as a distant companion to diffraction and spectroscopy techniques. It originally provided qualitative evidence for IRO [7]. But the SRO and LRO of network glasses can now be imaged [1, 22] with the emergence of atomic-scale resolution by atomic force microscopy (AFM) and high-resolution transmission electron microscopy (HRTEM). With nanobeam electron diffraction (NBED), images can also be obtained for the variety of icosahedral clusters present in metallic glasses [23] (Figure 6).

3 Structural Order over Different Length Scales Figure 4 Visualization of MD simulations of two tetrahedral glasses with vastly different atomic volumes but both conforming to the CRN prescription [13]. (a) SiO2 glass (11.1 Å3). (b) Hybrid glass ZIF-8 (Zn(C4H5N2)2) (73.4 Å3). Source: Images courtesy of J. Du (a) and W. Chen (b).

with a single boson peak (Figure 5e). In particular, atomic volume and peak intensity IBP are correlated, with the peak frequency νBP shifting to higher values as the atomic volume falls. As for metallic glasses (Chapter 7.10), these also exhibit soft collective vibrations whose origins are similar to oxide glasses boson peaks [3, 20]. If these are accessed from low-temperature Cp experiments, then the enthalpy captured at supercooled temperatures can also be recorded. A direct link exists between IBP and the glass

3.1

Network Glasses

Network-oxide glass formers like SiO2, GeO2, P2O5, and B2O3 [1] are defined by three- or fourfold directionally bonded polyhedra comprising hybridized units measuring ~2.5 Å, similar to nearest-neighbor arrangements in crystalline polymorphs [1]. For low-density hybrid glasses like a-ZIF-4 and a-ZIF-8, tetrahedral units are much larger, measuring about 9.5 Å [14]. Generally, SRO polyhedra are comparatively rigid, with variations in bond angle of less than 10%. The IRO is located between 3 and 4 Å for oxides increasing to 13 Å for hybrid glasses, covering correlation distances between SRO polyhedra (Figure 2 [1, 7, 14]). In oxide glasses the interpolyhedral distance is defined by the BO that is also hybridized, with interpolyhedral angles ranging from around 145 for SiO2, 130 for

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GeO2, and P2O5 to 120 for B2O3 (Figures 1 and 4 [1]). The imidazolate bridge between metal nodes in a-ZIFs is ~145 [14]. On average, the rigidity of tetrahedral and bridging angles is similar. In network glasses LRO begins at around 6 Å – the width of a typical sixfold ring (Figures 1 and 4) – and continues as far as out as features in the RDF can be discerned (Figure 2). Providing a direct link with a multiplicity of rings of corner-sharing polyhedra with different sizes, LRO is perpetuated through modest variations in bond angles, as illustrated in Figure 6 with the two-dimensional (2-D) distributions directly observed for silica [1, 22]. Combinations of experimental RDFs with computer simulations afford 3-D models of network topology where rings are often puckered in conformations foreign to crystalline geometries through variation and twisting of dihedral angles (Figures 1 and 4). The network statistics in SiO2 glass include five-, six-, and sevenfold rings, as illustrated schematically in Figure 7, in contrast to the

sixfold ring topology of crystalline silicates. In addition, three- and fourfold rings are also found, but in much smaller proportions [1, 6]. They have been identified with the oxygen “defects” that give rise to breathing modes in Raman spectra [1]. These miniature rings increase in number when pressure is applied, for example, in indentation experiments. The converse applies in B2O3 glass where the network is less 3-D than in SiO2 and where Raman spectra are instead dominated by the threefold boroxol ring feature [1]. Pressure causes boroxol rings to break up into buckled ribbons, the dimensionality decreasing further. Another consequence of LRO in network glasses is the quasiperiodic alignment of groups of caged voids associated with the aperiodic network of rings (Figure 7) to which the FSDP at QFSDP (Figure 2) is attributed [7]. In glass formers like SiO2 and B2O3, 2π/QFSDP distances lie around 4 Å. In chalcogenide glasses, such as As2S3 and GeSe2, SRO polyhedra are larger (~4 Å), leading to

3 Structural Order over Different Length Scales

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Figure 6 Direct observation of the atomic structures of glasses. (a) Atomic force microscopy image from freshly fractured silica in ultra-high vacuum, revealing a 2-D projection of the near-surface structure and showing SRO and fragments of rings – solid and dotted lines – contributing to LRO [24]. (b) Atomic resolution transmission electron microscope image of a graphene-supported silica bilayer, showing SRO and extensive LRO network with a variety of ring structures [22], consistent with Zachariasen’s CRN [13] (Figure 7a). (c) Nanobeam electron diffraction patterns of Zr0.667Ni0.333 metallic glass [23] (left), with their simulated patterns (right) in terms of the icosohedra shown in (d). The different SRO reflect the variety of icosohedra in Bernal’s DRPHS model of liquid metals [25] (Figure 7b). Source: (a) Reproduced from [24] © (2004) Elsevier; (b) reproduced from [22] © (2012) ACS; (c, d) reproduced from [23] © Nature Publications.

larger quasiperiodic void separations (~6 Å). In all cases FSDP distances decrease as pressure is applied but also become more dispersed, the FSDP peak widening and decreasing in intensity with increasing glass density [7]. Importantly these changes in the FSDP properties of network glasses with pressure correlate with those of the boson peak [17], where νBP increases and IBP decreases with increasing pressure and therefore density, supporting the view that the BP comprises collective atomic motion of large groups of atoms whose breathing frequency increases as their size shrinks. Furthermore, excess Cp in glasses is attributed to a double-well vibrational potential, which, in silica, can be modeled through the librational twisting of pairs of tetrahedral units, underscoring how the dynamics of IRO promote buckling of rings across LRO in network structures. 3.2

Metallic Glasses

In metallic glasses (Chapter 7.10) bonding is directionless and SRO comprises clusters of atoms around 3 Å in

diameter [11, 12]. Coordination numbers (CN) are between 10 and 11 – much greater than in directionally bonded glasses. With respect to crystalline metals, the CNs of metallic glasses exceed 8, the value for bcc structure (8), but fall short of 10, the CNs for fcc and hcp structures. Atomic cluster units in metallic glasses are around 5 Å apart, similar to interpolyhedral IRO distances in network glasses. The interatomic correlations between neighboring cluster units are identifiable out to around 15 Å (Figure 2), similar to the establishment of LRO in network glasses. In these densely packed metallic structures, however, the geometry of bond angles and dihedral angles and ring topology is absent. The sequence from IRO to LRO is usually collectively described as MRO [4], but is less well understood than in network glasses. Furthermore, compared to supercooled network systems, where high shear viscosity and low atomic diffusion stem from the existence of open structures, the glassforming ability of densely packed metallic melts is imprecisely understood. In searching for melt compositions that are suitably viscous for conventional glass

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Figure 7 Simple two-dimensional models of glass structure created from sparse (a) and dense (b) packing of spheres. (a) The continuous random network (CRN) model of Zachariasen [13] representing a network glass comprising threefold coordinated cations and bridging anions. Different ring sizes (3, 4, 5, 6, 7, 8) perpetuating extended range order are shown. (b) The dense random packing of atomic spheres (DRPHS) model of Bernal [25] showing variations in icosahedral packing, viz. 5, 6, and 7, that promote homogeneous noncrystalline extended range order.

quenching, those associated with deep eutectics can be a guide, but not exclusively so [4, 23]. An overriding requirement, though, resides in achieving the highest atomic packing density in the supercooled state, which is often achieved by “dissolving” smaller atoms. The atomic size ratio for solute to solvent atoms, which yields the most efficient packing, is frequently found to be approximately 0.9 [4]. For complicated high-density geometries, different packing arrangements in metallic glasses are now modeled with computer simulations – mainly RMC, but also ab initio MD – the aim being to analyze the variety and

number of different Voronoi polyhedra present [23]. For an atomic size ratio of 0.9, SRO is predominantly icosahedral, the geometry for tessellated quasicrystal structures. In glasses with pronounced chemical order and atomic size ratio lower than 0.9, pentagonal biprisms replace icosahedra as the dominant Voronoi polyhedra. Because they embody fivefold symmetry, icosahedrons and pentagonal biprisms frustrate crystalline close packing and represent the geometric counterparts to oddmembered rings in directionally bonded glasses with open structures. Metallic glasses, like network glasses, are less dense than their crystalline counterparts, the additional free volume being a throwback from the configurational diversity of the supercooled liquid. In contrast to that of network glasses, though, the FSDP in metallic glasses (Figure 3) is considered to derive from scattering from voids interspersed within the SRO of atomic clusters (Figure 7). In Ca–Mg–Cu glasses, QFSDP is, for example, about 1.2 Å−1, and the FSDP correlation length about 5 Å (Figure 3). In multicomponent alloys QFSDP is affected by the size distribution of the different metals and its intensity by density. In Ni–Zr–Al, QFSDP is, for example, about 0.9 Å−1 with a FSDP correlation length of about 7 Å. Also found in metallic glasses, the excess THz modes at the onset of the VDOS and linear low-temperature specific heat first observed in oxide glasses at THz frequencies [7] appear to have a common origin in the behavior of collective transverse acoustic modes at the Ioffe–Regel limit, where the phonon mean free path equates with its wavelength [19]. At this point vibrations no longer propagate, which suggests that LRO vibrations are localized. Demonstrated by computer simulation of Lennard-Jones glass models, collective vibrations in these close-packed structures replicate the scaling down of IBP with density referred to earlier and the increase in νBP.

4 Structural Aspects of Density Fluctuations 4.1 Non-ergodicity and Elastic Moduli Beyond the length scales of LRO and MRO are the DFs characteristic of the liquid state. They originate from the dynamics of the liquid state in thermodynamic response to temperature and pressure. Whereas liquids are in equilibrium and ergodic above the melting point, supercooled liquids are non-ergodic at Tg, which is reflected in the size of the non-ergodicity factor f(Q,T) (Section 2). In particular f(Q 0,T) is related to the magnitude of DFs, and as T Tg, a dynamic crossover occurs to non-ergodicity – typically ~1.2Tg. On vitrification DFs increase in amplitude and eventually become frozen in.

5 Models of Glass Structure

In glasses the spatial extent and amplitude of DFs can be determined from IXS and S(0) [1]. In glass formers DFs are typically ≥20 Å in scale, their amplitude being proportional to the melt compressibility κ, which is greater for network glasses than metallic glasses, for example, reflecting the considerable differences in atomic packing (Figure 7). In network glasses like silica, light scattering from DFs limits losses in fiber-optic applications [7]. Interestingly the amplitude of DFs is inversely related to Poisson’s ratio, which is smaller for oxide glasses, which are usually brittle, than for many metallic glasses, which are tough [17]. 4.2

Polyamorphism and Phase Separation

At high degrees of supercooling, liquid–liquid phase transitions have been observed, a phenomenon now commonly referred to as polyamorphism ([26], Chapter 3.9). These phase transitions have been observed in water, supercooled oxides, semiconductors, and metallic alloys, leading to new types of glass, such as low- and highdensity amorphous phases – LDA and HDA respectively – each differing in density and entropy but sharing the same composition [1, 14, 21, 26]. In some multicomponent supercooled oxide liquids, on the other hand, atomic diffusion can result in the coexistence of liquids with different compositions, the analogue of multiple phases in crystalline systems. On cooling these lead to phase-separated glasses (PSG) – the bestknown being borosilicates [7]. Pyrex, for example, combines low thermal expansion with high mechanical strength, whereas Vycor glass owes its special open microporous structure to the continuous silicate phase that is left when the borate phase has been leached out. In summary, the extended structure of glass connects all of the various ordered regions present on different length scales and underpins the diverse global properties of the glassy state.

5 5.1

Models of Glass Structure Conceptual Models

Two conceptual models have proved very influential over the years in picturing the overarching aperiodic structure of glass. Zachariasen’s continuous random network (CRN), devised for oxide glasses, dates from 1932 [13]. In 1960 Bernal introduced the dense random packing of hard spheres (DRPHS) to describe the structure of liquid metals [25], which has been applied widely to glassy metals once these had been discovered. Both constructs of glass structure, for insulators and metals, respectively, came in advance of experimental techniques that have

since illuminated their strengths as well as their shortcomings. The two models are illustrated in Figure 7, reduced to 2-D arrangements. Presented in this way, they reveal a common basis for constructing aperiodic arrays from contiguous spheres. They markedly differ, however, because each sphere touches just three neighbors in the CRN, resulting in a more open network structure than with the DRPHS where the number of neighboring spheres lies between five and seven. Taken together, though, both the CRN and DRPHS noncrystalline schemes yield a lower density than for their crystalline counterparts, and voids are seen to align mimicking the quasiperiodicity attributed to the FSDP (dashed curves in Figure 7). The increased free volume derives from variations in packing. As such, both CRN and DRPHS offer respective snapshots of the glassy state without informing on the quenching process during which the configurational entropy is generated. With the CRN each sphere embodies the SRO surrounding individual atoms: MO3 units, for example, mimic SiO4 tetrahedra in silica glass or BO3 and BO4 polyhedra in borate glasses (Figure 7). The SRO units are interconnected to create cornersharing networks of directionally bonded atoms perpetuating indefinitely, which in addition provides a conceptual representation of the extended structures of network glass formers. Although amorphous semiconductors were not yet discovered in 1932, the CRN is equally applicable to chalcogenide glasses like As2S3 and also to elemental semiconductors like amorphous As and Ge [7]. In all cases fixed CNs and bond lengths are prescribed by the tenets of the CRN. Usually these parameters are informed from crystalline structures even though space group symmetry is broken by variations in bond angles. Distortions between SRO units lead to rings of atoms of different sizes (Figure 7), including odd-membered rings seldom found in the crystalline state. Because of the bond angle flexibility of the CRN, point defects, like vacancies and interstitials, can formally be avoided, which is consistent with the observation that optical-quality glass is almost free of point defects. By contrast Bernal’s DRPHS structure is the geometric outcome of the random packing of spheres, originally ball bearings in a can [25], each representing a metal atom (Figure 7). Designed to model elemental liquid metals, the DRPHS became an approximate structure for glassy metallic alloys where components have similar atomic radii, such as Pd80Si20. Nearest-neighbor distances in densely packed structures scale with metallic radii, but the packing scheme in three dimensions incorporates icosahedral units avoiding dense-packed crystalline arrangements. By analogy with the CRN, Bernal’s model is free from dislocations that render crystalline metals prone to mechanical damage, which qualitatively explains the

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exceptional toughness of metallic glasses. Moreover, as the main contribution to metallic electrical resistivity at ambient temperature is governed by the scattering of electrons by irregularities in the positions of core ions, the DRPHS supports the greater electrical resistivity of glassy metals compared to than crystalline metals, enabling the low-loss of metglas magnetic transformer cores. The major success of the Zachariasen and Bernal models has been in reconciling SRO with the extended structure of the glassy state. These model structures are isotropic and homogeneous by definition, however, and as such they fail to account for DFs observed almost universally in network as well as in metallic glasses. The solution to this drawback can only be solved through the computer modeling of large 3-D melt-quenched structures.

In simulating glass structure with MD and DFT, crystalline ensembles are typically “melted” at, say, 5000 K over 10’s of ps until thermodynamic equilibrium is reached, after which they are cooled at ~1 K/ps, through the supercooled regime and glass transition, to a glass at ambient temperature. At each stage the SRO of bond lengths and bond angles of polyhedra in directionally bonded systems, and bond lengths and icosahedral geometry in metallic systems, can be catalogued and compared with experiment. Likewise, one can examine directly IRO and LRO such as ring statistics in covalent structures and MRO, for example, the icosahedral variety, in metallic alloyed structures. Moreover, dynamic properties like ion diffusivities can be predicted as a function of temperature and pressure, the same applying to vibrational modes that determine the VDOS – not least the manyatom cooperative motion responsible for the boson peak.

5.2 Computational Modeling of Extended Structure

6

Atomistic modeling of liquids and solids goes back over 50 years. Over the interim period three main approaches have been developed in relation to glass-forming materials (Chapters 2.7 and 2.8): (i) MD, where empirical potentials describing the repulsive and attractive interactions between atoms are used in conjunction with classical dynamics to explore P–T phase space; (ii) RMC, in which sequential adjustments in atomic positions are made to improve agreement with the experimental structure factor S(Q); and (iii) density functional theory (DFT) based on all-electron quantum mechanical methods that replace the empirical potential in MD. At the present time ensembles 300 Å in size are feasible with MD and RMC, whereas ab initio DFT MD, which is computationally more demanding, is currently limited to systems of about 15 Å. Empirical 2- and 3-body potentials are formally ionic but have been successful for predicting the structure and dynamics of liquids and glasses where chemical bonding is predominantly directional in character such as in feldspar compositions ([27], Figure 8). Interestingly, RMC and latterly DFT have been used for metallically bonded systems as well ([4] Figure 1). Neutron S(Q) data from single experiments were originally used with RMC, together with simple constraints, such as nearest interatomic approach, CN, etc., to avoid unphysical SRO [10]. Now other sources of data are used in conjunction, the most common being high-energy X-ray diffraction [8], but these have been augmented by other sources of data – notably EXAFS and MAS NMR spectra [10]. From large models, LRO effects such as clustering, channels, and other sources of heterogeneity can be examined.

The conceptual CRN and DRPHS models for glass structure [15, 16] are based on single-type polyhedra or atoms, respectively, and predict extended range order to be homogeneous everywhere. Because these models are constructed statically, not dynamically, DFs are also excluded. A geometric consequence of introducing more than one size of polyhedron or atom type is microsegregation in the packing of the minority component, first as clusters, which then coalesce into channels above the percolation limit (~20%). This evolution was originally predicted from the 2-D modified random network (MRN) model [9] and later from 3-D MD simulated structures [2]. Interestingly, a similar clustering is also evident in computer-simulated metallic glass structures, such as the metalloid P in the RMC model for Ni0.8P0.2 metallic glass, where this microsegregation can be seen threading through the close-packed Ni structure ([12] Figure 1). For MRN structures (Figure 8), channels are defined by nonbridging oxygens (NBOs) resulting in silicons, for example, being surrounding by mixtures of BOs and NBOs, which can be readily identified by 29Si MAS NMR [1, 28]. In aluminosilicate glasses, aluminums occupy tetrahedral sites AlO4−1 [1] where the extra charge is compensated for by adjacent modifier cations like alkalis or alkaline earths. For fully compensated compositions, like those of feldspars, glasses, silicon, and aluminum tetrahedra are corner-shared via BOs, adopting a CRN-like geometry that is categorized as a compensated continuous random network (CCRN) [28]. Alkali channels have also been predicted in aluminosilicate melts and glasses, like the nepheline family (NaxK1−xAlSiO4)

Structural Heterogeneity in Glasses

6 Structural Heterogeneity in Glasses

(a)

(b)

Si O K

(c)

Modified random network (MRN)

(d)

K2Si2O5

Na K

Na0.25K0.75AISiO4

(Agl)0.6–(Ag2O–2B2O3)0.4

Figure 8 Microsegregation in network glasses. (a) Modified random network (MRN) used to model oxide glasses [9]. Cation modifier channels clearly seen percolating through the two-dimensional network, 3-D microsegregation later confirmed with MD methods [2]. (b) Isosurfaces delineating K+ conducting pathways in MD simulated K2Si2O5 disilicate glass, with cutaway showing adjacent interweaving modified silicate network. (c) Alkali channels in MD simulated aluminosilicate Na0.25K0.75AlSiO4 [27]. (d) Ag+1 channels in the superionic glass (AgI)0.6–(Ag2O–2B2O3)0.4 separated from anion borohalide pockets. Source: (a) Reproduced from [9] © (1985) Elsevier; (b) image courtesy Z. Zhou; (c) reproduced from [27] © (2017) Nature Publications; (d) reproduced from [10] © 2001 Institute of Physics.

(Figure 8), confirmed by MD modeling, which also reproduces the way the viscosity changes with composition [27]. Modifier channels were envisaged from the start as supporting ionic diffusion, such as that of alkali ions migrating through oxide glasses [28]. The use of isosurfaces to delineate channels (Figure 8) helps visualize the separation of mobile ions from the surrounding network. The presence of well-defined channels explains the additional FSDP observed, for example, in modified silicate glasses around 0.8 Å−1, which can be attributed to correlations between alkalis with a quasiperiodicity of about 8 Å [1]. Other evidence comes from EXAFS and MAS NMR experiments. There is now much support for the idea of reconciling structural heterogeneity with transport properties [28]. For example, the mixed alkali effect, where the mixing of different mobile alkalis in the same glass drastically affects the mobility of both, can be understood in terms of the

segregation of alkalis packing within channels, diluting the diffusivity of each ([2], Chapter 4.6). The huge fall in the average ionic mobility with alkali mixing reduces the ionic conductivity of glass and increases its corrosion resistance and other related transport properties [28]. Fast-ion conducting glasses based on silver salts, like AgI dissolved in oxide and sulfide matrices, have unusually high ionic conductivities at ambient temperature, exceeding those of binary alkali silicates and borosilicates by three or four decades, making them attractive as possible electrolytes for solid-state batteries. For these systems RMC modeling has been interpreted in terms of the MRN and the high diffusivity of Ag+1 along percolating channels that are approximately one-dimensional (Figure 8). Like for conventional modified oxide glasses, the FSDP is often structured for fast-ion conducting glasses with Ag–Ag and anion–anion components, the former with a quasiperiodicity approaching 10 Å. This is illustrated for (AgI)0.6–(Ag2O–2B2O3)0.4 glass in

193

194

2.5 The Extended Structure of Glass

Figure 8 where the topology of ion transport channels can be clearly seen. As the AgI content increases, extending the composition range (and with it the ionic conductivity), the halide component “pushes apart” the remaining network, which also becomes more disordered. The FSDP is dominated by Ag–Ag quasiperiodicity so that this is the feature that correlates with superionic diffusivity within glass-forming compositions [10]. In these examples, structural heterogeneity is manifest both in the IRO related to the FSDP and topologically over LRO and beyond to embody the extended structure of glass.

7

Perspectives

For the future, the ideas about the extended structure of glass, introduced separately in this chapter, need eventually to be consolidated into a holistic description. This is implicit in the conceptual MRN, CRN, and DRPHS models [9, 13, 25] whose fixed geometries are infinitely perpetuated through rings of different sizes and modifier channels for insulating network glasses and through variations in icosahedra for densely packed metallic glasses. Nevertheless, for the last two decades of research, SRO, IRO, and LRO/MRO have been loosely defined in terms of static geometry between basic atomic building units, correlations between adjacent units, and more distant neighbors. This has created demarcations, often based on different experimental techniques, that avoids the central issue. The extended structure of glass should rather be seen as a continuous development from the microscopic atomic level through mesoscopic dimensions to the macroscopic scale relevant to applications. The challenge in glass science is to associate, in a quantitative way, atomic structure with functionality [1, 3, 7]. In particular, heterogeneity is a common feature of functional glasses but is incompletely understood at the level of static structures. It has its antecedents in the rheology of the supercooled state and the dynamics of the glass transition. Empirical correlations have been reported, often controversially received, between the fragility m of supercooled liquids at the glass transition and solidstate properties such as Poisson’s ratio, between m and IBP, and between m and f(0,T) [1]. Underlying all these relationships is the role played by DFs, which increase in amplitude at the dynamic crossover ~1.2Tg [26] and are frozen into the glassy state as α relaxation dynamics slow down. They appear to be central to nucleation processes, whether these are crystallization, phase separation, or polyamorphism. DFs have the dimensions of the acoustic wavelengths of the boson peak, which underscores, again, the cooperative nature of the many-atom

fast β dynamics in the condensation of glasses and their functionality. Finally, the important technical drivers in meeting the challenge raised by the prospect of understanding the extended structure of glass as a predictor of functionality are the advances in experimental technology. First are those coming from light and particle beams in materials science – spallation neutron sources, coherent X-ray sources, electron nanobeams, and atomic-scale microscopy. These tools have already escalated in intensity and diversity in recent years, increasingly driven by the needs of the biosciences, where similar issues exist in handling complexity and aperiodicity on a grand scale. Second, and as important, are advances in highperformance computing and the visualization of big data sets. Year on year larger and larger simulations are reported, sizes for MD, currently reaching several million atoms, already on a length scale commensurate with DFs. Ab initio techniques, which are the most reliable for predicting functionality, necessarily lag behind, but are currently heading toward the thousand atom mark – all of which concurs with the forward thinking of Alder and Wainwright, over 50 years ago, that “the behaviour of systems of many interacting particles cannot, in general, be dealt with theoretically in an exact way […] Since these difficulties are not conceptual but mathematical, highspeed computers are well-suited to deal with them” [29].

Acknowledgments Warm thanks are due to A. Takada and J.F. Stebbins for most careful reviews of this chapter.

References 1 Greaves, G.N. and Sen, S. (2007). Inorganic glasses, glass-

2 3 4

5 6

forming liquids and amorphizing solids. Adv. Phys. 56: 1–166. Vessal, B. et al. (1992). Cation microsegregation and ionic mobility in mixed alkali glasses. Nature 356: 504–507. Suryanayana, C. and Inoue, A. (2017). Bulk Metallic Glasses. Boca Raton: CRC Press. Sheng, H.W., Luo, W.K., Alamgir, F.M. et al. (2006). Atomic packing and short-to-medium-range order in metallic glasses. Nature 439: 419–425. Affatigato, M. (ed.) (2014). Modern Glass Characterisation. Hoboken, NJ: Wiley. Fischer, H.E., Barnes, A.C., and Salmon, P.S. (2006). Neutron and X-ray diffraction studies of liquids and glasses. Rep. Prog. Phys. 69: 233–269.

References

7 Elliott, S.R. (1990). Physics of Amorphous Materials. New 8

9 10 11

12

13 14

15

16

17

York: Wiley. Benmore, C.J. (2012). A review of high energy X-ray diffraction from glasses and liquids. ISRN Mater. Sci. 2012: 852905. (19 pages). Greaves, G.N. (1985). EXAFS and the structure of glass. J. Non-Cryst. Solids 71: 203–217. McGreevy, R.L. (2001). Reverse Monte Carlo modelling. J. Phys.: Condens. Matter 13: R877–R913. Smith, W., Greaves, G.N., and Gillan, M.J. (1995). Computer simulation of sodium disilicate glass. J. Chem. Phys. 103: 3091–3097. Zeng, Q., Sheng, H., Ding, Y. et al. (2011). Long range topological order in metallic glass. Science 332: 1404–1406. Zachariasen, W.H. (1932). The atomic arrangement in glass. J. Am. Chem. Soc. 54: 3841–3851. Greaves, G.N. (2019). Hybrid glasses: from metal organic frameworks and coordination polymers to hybrid perovskites. In: Springer Handbook of Glass (eds. J.D. Musgraves, J. Hu and L. Calvez). Cham: Springer. Bennett, T.D. et al. (2015). Hybrid glasses from strong and fragile metal-organic framework liquids. Nat. Commun. 6: 1–7. Greaves, G.N., Meneau, F., Majérus, O. et al. (2005). Identifying the vibrations that destabilise crystals and which characterise the glassy state. Science 308: 1299–1302. Greaves, G.N., Greer, A.L., Lakes, R.S., and Rouxel, T. (2011). Poisson’s ratio and modern materials. Nat. Mater. 10: 823–837.

18 Chumakov, A.I. et al. (2014). Role of disorder in the

19

20

21 22 23 24

25 26 27

28

29

thermodynamics and atomic dynamics of glasses. Phys. Rev. Lett. 112: 025502. Shintani, H. and Tanaka, H. (2008). Universal link between the boson peak and transverse phonons in glass. Nat. Mater. 7: 870–877. Luo, P., Li, Y.Z., Bai, H.Y. et al. (2016). Memory effect manifested by a boson peak in metallic glass. Phys. Rev. Lett. 116: 175901. Wondraczek, L. et al. (2018). Kinetics of decelerated melting. Adv. Sci. 5 (5): 1700850. Huang, P.Y. et al. (2012). Direct imaging of a twodimensional silica glass. Nano Lett. 12: 1081–1086. Hirata, A. et al. (2011). Direct observation of local atomic order in a metallic glass. Nat. Mater. 10: 28–33. Frischat, G.H., Poggemann, J.-F., and Heide, E. (2004). Nanostructure and atomic structure of glass seen by atomic force microscopy. J. Non-Cryst. Solids 345–346: 197–202. Bernal, J.D. (1960). Geometry of the structure of monatomic liquids. Nature 185: 68–70. Stanley, H.E. (ed.) (2013). Liquid polyamorphism. Adv. Chem. Phys. 152: 1–611. Le Losq, C. et al. (2017). Percolation channels: a universal idea to describe the atomic structure and dynamics of glasses and melts. Sci. Rep. 7: 16490. Greaves, G.N. and Ngai, K.L. (1995). Reconciling ionic transport properties with atomic structure in oxide glasses. Phys. Rev., B 52: 6358–6380. Adler, B.J. and Wainwright, T.E. (1959). Studies in molecular dynamics. 1. General method. J. Chem. Phys. 31: 459–466.

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197

2.6 Structure of Chemically Complex Silicate Systems Bjorn Mysen Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC, USA

1

Introduction

Chemically complex silicate glasses and melts include natural magmatic liquids as well as many commercial glasses. Magmatic rocks sometimes also are used for commercial purposes with slight compositional adjustment made to optimize processes or material properties and reduce costs (e.g. rock wool, Chapter 9.3). Glass families such as boro- and phosphosilicates are specifically dealt with in Chapters 7.6 and 7.9, respectively. The chemically complex glasses and melts considered here are mainly aluminosilicates with Si4+ and Al3+ as the main network-formers and alkali metals, alkaline earths, and Fe2+ the dominant network-modifiers. Their structure, properties, and structure/property relations can be described with the aid of information obtained with compositionally simpler unary, binary, and ternary compositions and composition joins (Figure 1). The principal composition variables are metal oxide/silica, alumina/silica, and types and proportions of metal cations with different electronic properties (see also [1]). The structural environment changes when pressure during melting is sufficiently high to cause oxygen coordination changes of Al3+ and Si4+ (≥6 GPa). High-pressure data are so limited, however, that a survey will not be very informative and high-pressure industrial processes are virtually nonexistent. Pressure will not, therefore, be discussed here.

2

Glass and Melt Polymerization

The degree of polymerization of the aluminosilicate network affects most glass and melt properties. Melt Reviewers: J.F. Stebbins, Geological and Environmental Sciences, Stanford University, Stanford, CA, USA A. Takada, Research Center, Asahi Glass Co. Ltd., Yokohama, Japan

polymerization can be expressed as the proportion of nonbridging oxygen (NBO) per tetrahedrally coordinated cations (T), NBO/T. The NBO/T can be calculated from the chemical composition of a glass and melt, provided that types and proportions of network-forming cations are known. Then, NBO/T = (2 O–4 T)/T, where T and O are atomic proportions of tetrahedral cations and oxygen, respectively, and T is given a formal charge of 4 can be readily calculated. The principal network-formers (tetrahedral cations) in complex glasses and melts are Si4+ and Al3+. These will be discussed first.

2.1

SiO2

In nature, the SiO2 concentration in some cases can exceed 80 wt % although in the most common magma, basalt, the SiO2 range is 45–55 wt %. By comparison, most commercial glasses have from 50 to 70 wt % SiO2 contents (Table 1). From the relatively small enthalpy, entropy, and volume of fusion (ΔH, ΔS, and ΔV) of crystalline SiO2 polymorphs (see [2] for review of data), it may be inferred that silica melt and glass retain a three-dimensional structure of interconnected SiO4 tetrahedra that exist in its crystalline polymorphs (quartz, tridymite, and cristobalite). From vibrational, X-ray, and NMR spectroscopic studies, one also concludes that the SiO2 glass structure is essentially fully polymerized [3]. Vibrational spectroscopic spectra recorded at temperature above that of the glass transition of silica glass (1208 C) do not reveal significant structural differences between glass and supercooled liquid. There is an asymmetric distribution of intertetrahedral angles, ranging from ~120 to 180 (Figure 2) with a maximum between 145 and 155 [4]. A 145–155 Si─O─Si angle is that expected in a threedimensionally interconnected SiO2 glass structure

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

198

2.6 Structure of Chemically Complex Silicate Systems

The coexistence of distinct structural units has important consequences because it has been invoked to account for the unusual properties of SiO2 glass such as a room-temperature density maximum for glass quenched from temperatures near 1505 C. Besides, a density minimum is observed near 950 C for structurally relaxed glass. The anomalous pressure- and temperature-dependence of SiO2 glass compressibility, with maxima near 3 GPa and 100 K, respectively, can also be modeled with two coexisting three-dimensional structures in SiO2 glass.

SiO2 10

90 80

20

Meta-aluminous

30 40 50 60

70 60 50 40 30

70 80

Peralkaline

Peraluminous

20

2.2 Al2O3 10

90 10

20

30

Mn+On/2

40

50

60

70

80

Mn+AlnO2n

90 Al2O3

(Mn+: K+, Na+, Li+, Ca2+, Mg2+, etc.)

Figure 1 Compositional environment of complex silicate melts and glasses. Peralkaline denotes compositional range where there is excess metal cations (alkali metals + alkaline earths) over that necessary for charge-balance of tetrahedrally coordinated Al3+. Meta-aluminous compositions are those where the proportion of alkali metals + alkaline earths is exactly equal to that needed for charge-balance of tetrahedrally coordinated Al3+. Peraluminous compositions are those where there is excess Al3+ over that which can be charge-balanced with alkali metals + alkaline earths.

consisting predominantly of six-membered rings. The somewhat asymmetric Si─O─Si angle distribution (Figure 2) suggests that more than one exists in SiO2 glass. Rings with three or four SiO4 tetrahedra coexisting with six-membered rings are those most commonly suggested.

The second most important network-forming component in complex aluminosilicate glasses and melts is Al2O3 (Table 1). Its concentration range in most natural magma and commercial applications (5–20 wt % Al2O3) can have profound influence on glass and melt properties compared with pure SiO2. These include better glassforming ability of melts, improved durability, lower viscosity, and lower thermal expansion. The type of metal cations serving to charge-balance tetrahedrally coordinated Al3+ is central to understanding the structural roles of Al3+ in silicate melts and glasses and, therefore, their physicochemical properties. Charge-balance commonly is achieved with alkali metals and alkaline earths (as in feldspar structures, for example). With an alkali metal, M+, one Al3+ can be charge-balanced provided that XM+ ≥ XAl3+, whereas for alkaline earths, the requirement is 0.5 XM2+ ≥ XAl3+, where XM+, XAl3+, and XM2+ are atomic fractions of the respective cations. The structural environment near alkalis and alkaline earths depends on whether these ions play a

Table 1 Oxide composition (wt %) of common commercial glasses and glass of common magmatic rocks with additional data from http:// Earthchem.org.

SiO2

Window glass

Pyrex

Glass wool

Rockwool

Rhyolite

Dacite

Andesite

Basalt

Phonolite

72.6

81.1

65

46.6

72.18

65.13

57.51

50.29

56.56

TiO2 Al2O3

0.6

B2O3 FeO(T)

0.43 22

2.5

2.4

0.39

0.64

0.93

2.06

0.87

13.3

13.23

15.67

16.93

14.79

19.31

10.6

2.90

4.73

7.08

10.94

4.02

0.10

0.82

0.05

0.03

1.05

0.48

1.03

1.82

2.5

1.86

4.5

0.8

0.2

3.6

0.3

CaO

8.7

1.1

8

1.53

1.47

1.85

1.38

2.28

Na2O

14.3

1.5

16.5

5.6

4.03

0.81

0.77

0.55

1.57

K2 O

0.2

0.7

1.4

3.76

0.96

0.86

0.38

1.01

NBO/T

0.79

0.62

0.99

0.08

0.18

0.36

0.72

0.22

MnO MgO

Source: Modified from [1]

0.00

2.5

9.1 10

3 Metal Oxide–SiO2 Systems

K

Cristoballite

s

SiO

2

s gla

gla

Angle distribution function

ss

O2 Si

Enthalpy of solution (kJ/mol)

10

Na

5

SiO

2 –M

AIO

2

0

Li

Ba SiO

2 –M

AI

–5

2O 4

0.50

0.75

1.00

1.25

Sr

Ca 1.50

Z/r2

120

140

Intertetrahedral angle,

160

180

(Si–O–Si)o

Figure 2 Distribution of intertetrahedral angle, ∠(Si–O–Si)o, in SiO2 glass from fitting of 29Si MAS NMR spectra to an angle distribution function. Note that the maximum corresponds to that of cristobalite at its liquidus temperature (1723 C), and is also similar to that obtained from X-ray diffraction of SiO2 glass. A recent 17 O NMR two-dimensional dynamic angle study resulted in 147 [3]. These angle distributions are consistent with a SiO2 glass structure comprising predominantly six-membered rings of threedimensionally interconnected SiO4 tetrahedra.

charge-balancing or a network-modifying role [5]. The type and proportion of charge-balancing cations also are important because of their different effect on the energetics of the O─Al bonds and, therefore, on glass and melt properties. This is seen, for example, in enthalpy of solution (Figure 3), viscosity, and also in melt and glass density, compressibility, and thermal expansion. The glass structure along SiO2–MAlO2 joins (M = alkali metal as charge-balancing cation – meta-aluminosilicate; see Figure 1) is a continuous evolution of the SiO2 glass structure with substitution of Al3+ for Si4+ in tetrahedral coordination and with only a very small percentage or fraction of a percent of Al3+ in different structural roles. There is marginally more Al3+ in such roles in glasses along the SiO2–CaAl2O4 join [7]. The K+, Na+, and Ca2+ are the dominant chargebalancers in natural magmatic liquids (Figure 4). For melts and glasses with multiple potential cations for Al3+ charge-balance, thermodynamic data can be used to establish relative stability of aluminate complexes. There is near equal stability of (KAl)4+ and (NaAl)4+ charge-balance followed by (Ca0.5Al)4+. In natural rocks, the proportion of Ca2+ relative to (Na+ + K+) decreases with increasing SiO2 concentration so that in rhyolite melt, for example, alkalis dominate over Ca+ for

Figure 3 Energetics of Al,Si substitution along metaaluminosilicate joins as a function of ionization potential, Z/r2, of metal cation that serves to charge-balance Al3+ in tetrahedral coordination (ionic radius, r, assumed that of six-coordinated metal cations – data from [6]). Heat of solution of glasses in molten lead borate solution is used as a measure of the substitution energetics. Simple and systematic relations with Z/r2 are evident, but with distinct separation of relationships for cations with different charge-balancing cations. This difference stems from different substitution mechanisms of Al3+ for Si4+ depending on whether the charge-balance is accomplished with monovalent or divalent cations.

charge-balancing of Al3+. For less silica-rich melts, the main charge-balancing cation is Ca2+. For commercial glass such as glass wool, Na+ is the principal chargebalancing cation for tetrahedral Al3+, whereas in rock wool with a composition more akin to natural basalt (Table 1; see also [1], chapter 18), alkali metals and Ca2+ serve to charge-balance Al3+ together. Somewhat similar structural features can be found in the glass containment of incinerated household waste.

3 3.1

Metal Oxide–SiO2 Systems General Remarks

In order to characterize the structure of depolymerized, chemically complex aluminosilicate glasses and melts (Figure 1), it is first necessary to describe the structure of simple binary metal oxide–silica compositions. With this information, one can then consider multicomponent metal oxide silicate and aluminosilicate glasses and melts. The metal oxides in multicomponent metal oxide– silica systems usually are K2O, Na2O, CaO, and MgO. In Al-free silicate glasses such as window and container glass, for example, these oxides serve only as

199

2.6 Structure of Chemically Complex Silicate Systems

100

Basalt melt Ca

Distribution (%)

80

60

40

20

Na + K 0

0.4

0.8

1.2

1.6

NBO/T of melt

Rhyolite melt 100

Na + K 80

Distribution (%)

200

60 40 20

Ca

the volume of pure SiO2 (27.3 cm3/mol) because some of the oxygen in these glasses and melts are nonbridging (NBO) and the partial molar volume of NBO is slightly less than that of bridging oxygen. In metal oxide silicate, the partial molar volume of SiO2 is independent of composition, however, over wide composition range [8]. Systematic relations between metal/silicon ratio can also be seen in other physical and chemical properties such as viscosity, conductivity, thermal expansion, and compressibility of glasses and melts [1]. In ternary and more complex metal oxide silica melts, the values of most properties cannot be described as linear combinations of the endmembers (mixed alkali effect). For example, window glass, which is essentially a mixture of Ca- and Na-silicate components, is in this category. This behavior is related to the steric effects that govern metal cation ordering among different NBO in ternary and more complex metal oxide–SiO2 glasses and melts. Ordering affects configurational and mixing properties and, therefore, rheological and thermodynamic properties. The greater the contrast in electronic properties such as their electrical charge and ionic radius of the network-modifying cations, the greater the effect of mixing on melt and glass properties. This ultimately leads to liquid immiscibility in SiO2-rich metal oxide–SiO2 melts. In fact, at given temperature the width of the immiscibility gap is a positive function, Z/r2 (Z = formal electrical charge, r = ionic radius), of the metal cation.

0 0.0

0.2

0.4

0.6

NBO/T of melt Figure 4 Summary of distribution of charge-balancing cations (Na+ + K+ and Ca2+) in natural magmatic liquids of basalt and rhyolite melt compositions as a function of the NBO/T of the melts. The summary was developed from chemical data in http:// Earthchem.org. This web site contains a compilation of analyses of rocks in the published literature, where the individual rock names are those given in the source of the database. As seen in Figure 5, for each of these types of rocks, the NBO/T of their melts comprises a wide range. See Table 1 for average compositions of basalt and rhyolite.

network-modifiers. Glass used in television and computer monitors and in optical fibers comprises additional network-modifying cations including rare earths, large alkaline earths (Sr2+ and Ba2+) and, sometimes, transition metals. In natural magmatic liquids, these cations can serve both as network-modifiers and to charge-balance Al3+ in fourfold oxygen coordination as described in Section 2.2. Similar compositions and structural environments can be found in glass and rock wool, E glass, and Vycor. The properties and behavior of SiO2 in metal oxide silicate melts and glasses differ somewhat from those of pure silica glass and melt. The partial molar volume of this component is slightly smaller (26.8 cm3/mol) than

3.2 Structure Structural characterization of simple and complex metal oxide silicate glasses and melts can be expressed in terms of nonbridging oxygen, NBO, per tetrahedrally coordinated cation, T (Chapter 2.4). The NBO/T-values of commercial glasses range from about 0.2–0.3 (for Pyrex glass, for example) to values greater than 3.0 for some slags (Chapter 7.4). The NBO/T of typical window glass is about 0.8, which is similar to those of rock wool. In nature, the NBO/T-values of melts from individual rock types fall within relatively broad ranges (Figure 5). In general, there is a negative correlation between the NBO/Tvalue and the SiO2 concentration. The distribution of network-modifying cations in complex systems is linked to both their alkali metal/alkaline earth ratio and the types of metal cations available for charge-balance of tetrahedrally coordinated Al3+. For the most part, the network-modifying cations in natural magma are alkaline earths because their Na + K components charge-balance tetrahedrally coordinated Al3+. Among the network-modifying cations, Mg2+ is exclusively a network-modifier, whereas Ca2+ is used both to charge-balance Al3+ and to serve as a network-modifier (Figure 6).

3 Metal Oxide–SiO2 Systems

3.3

0.2

Percent

The NBOs in glasses and melts are not equivalent energetically. Instead, the structure of metal oxide–SiO2 glass and its precursor melt is described in terms of a small number of distinct coexisting silicate structural units commonly described as Qn-species with n = 0, 1, 2, 3, and 4 where n is the number of bridging oxygen (Chapter 2.4). The overall degree of polymerization, NBO/T, is related to Qn-species abundance:

Basalt melt

0 0.0

Andesitemelt

10

Rhyolite melt

20

Glass wool

Pyrex

30

0.4

0.6

NBO = T

0.8

1.0

1.2

1.4

NBO/T of melt

Figure 5 Calculated distribution of NBO/T-values of major groups of natural magma compositions derived from the database, http:// Earthchem.org. Also shown (arrows) are approximate NBO/T-values for Pyrex glass and glass wool. Average basalt and rhyolite compositions are shown in Figure 4. Basalt melt 100

Distribution (%)

80 60 40 20 0

Mg Ca Na

0.4

0.8

1.2

1.6

NBO/T of melt Rhyolite melt 100

Distribution (%)

80 60 40 20

Mg Ca Na

0 0.0

0.2

0.4

Speciation, Cation Mixing, and Ordering

0.6

NBO/T of melt

Figure 6 Distribution of network-modifying cations (Na+, Ca2+, and Mg2+) in natural magmatic liquids of basalt and rhyolite melt compositions as a function of the NBO/T of the melts. The summary was developed from chemical data in http://Earthchem.org.

n=4

n − 4 X Qn ,

1

n=0

where X Qn is the mol fraction of the Qn-species and n is the number of bridging oxygen in the individual Qn-species. The NBO/T-parameter itself does not distinguish between different types of NBO. The abundance of individual Qn-species changes with metal oxide/SiO2 ratio of the material (Figure 7). In simple binary metal oxide–silica melts, the abundance of Q3, Q2, and Q1 species reaches maximum values at stoichiometries near NBO/Si = 1, 2, and 3, respectively, and decreases on both sides of these maxima. Orthosilicate compositions comprise both Q1 and Q0 species with free oxygen compensating for the presence of the polymerized Q1 structure. The Qn-species abundances also are affected by the ionization potential, Z/r2 (Z: formal electrical charge, r: ionic radius), of the metal cation (Figure 7) because steric hindrance near the NBO governs how individual metal cations will distribute themselves among the Qn-species. The ordering of alkalis and alkaline earths among energetically nonequivalent NBO in different Qn-species in multicomponent compositions also aids in the explanation of the mixed alkali effect. For comparison, in crystalline metal oxide–SiO2 systems, analogous steric hindrance effect instead limits the minimum metal oxide/SiO2 ratio of the crystalline materials below which crystalline compounds are not stable [9]. In the much more chemically complex natural magmatic liquids, Qn-species distributions resemble those observed for binary metal oxide glasses and melts [10]. The influence of individual network-modifying cations is difficult to establish, however, because of wide ranges of compensating effects on structure from the large number of different network-modifying cations. Whether in simple binary metal oxide silicates or more complex systems, the equilibrium constant for the principal expression that describes the equilibria among the Qn-species, 2Qn Qn − 1 + Qn + 1 (see Chapter 2.4), is positively correlated with Z/r2 at least for systems for which n = 3 in the aforementioned reaction to yield 2Q3 Q2 + Q4 (Figure 8). The enthalpy change of the latter reaction at temperatures above the glass transition is also a positive function of the Z/r2 of the metal cation and is more sensitive to Z/r2 of the more polymerized (lower bulk

201

50

Abundance (mol %)

Abundance (mol %)

2.6 Structure of Chemically Complex Silicate Systems

Q4

40

Q2

Li2O–SiO2

30 20

K2O–SiO2

10 0.6

30

0.8

1.0

Abundance (mol %)

80

1.2

NBO/Si{=(K,Li)/Si} Li2O–SiO2 K2O–SiO2

Q3

K2O–SiO2

70

1.0

Li2O–SiO2

1.2

1.4

Figure 7 Abundance evolution (mol %) of Q2, Q3, and Q4 species in alkali silicate glasses as a function of their NBO/Si-values of compositions as indicated in diagrams. For alkali silicate glasses, the metal/silicon ratio equals the NBO/Si, provided that all Si4+ is in tetrahedral coordination. The ionization potential, Z/r2, of K+ and Li+ is 0.46 and 1.49, respectively, assuming sixfold coordination of oxygen around the alkali metal. The curves for Na2O─SiO2 (Z/r2 of Na+: 0.8) fall in between those of Li2O─SiO2 and K2O─SiO2.

1.4

NBO/Si{=(K,Li)/Si}

60 50 0.6

0.8

1.0

1.2

1.4

NBO/Si{=(K,Li)/Si}

20 i=

ΔH (kJ/mol)

202

M

5 0.

M = Li

/S

0

= /Si M = Na M –20

1

M = Li

4.1 Al3+ and Qn-Species

M=K

0.50

1.00

1.50

Z/r 2

Figure 8 Enthalpy change, ΔH, for the disproportionation equilibrium, 2Qn Qn − 1 + Qn + 1, n = 3, as a function of ionization potential of alkali cation for two series of alkali metal (M) silicate compositions. In these systems, M/Si = NBO/Si assuming all Si4+ is in tetrahedral coordination in the glasses. The ΔH is derived from temperature-dependent equilibrium constant at temperatures above the glass transition and assuming that mol fraction of Qnspecies equals their activity. Note that the ΔH-value increases with increasingly polymerized melts probably as a result of increasingly nonideal mixing of the Qn-species. (Source: Modified after [8].)

NBO/Si-value) silicate melt (Figure 8). This relationship obtains because steric hindrance near NBOs diminishes with decreasing average values of n of the Qn-species.

4

properties. The role of Al3+ can vary from simple substitution for Si4+ in the network of interconnected aluminosilicate tetrahedra to more complex environments where Al, Si substitution is restricted to only some of the Qnspecies. The latter feature is important because most chemically complex compositions are depolymerized (NBO/T > 0) so that multiple Qn-species will coexist.

Aluminum and Aluminate

Characterization of the structural roles of Al3+ in aluminosilicate compositions is central to understanding their

Where there is excess alkali metal or alkaline earths over that needed for charge-balance of Al3+ in tetrahedral coordination, Al3+ may be distributed among the various Qn-species. However, this distribution is not random and Al3+ dominantly is in Q4-species. Coexisting, less polymerized Qn-species are essentially devoid of Al3+. This situation reflects the tendency of Al3+ to substitute for Si4+ in SiO4 tetrahedra with the smallest intertetrahedral angle, which is found in Q4-species. It follows that the equilibrium constant for the reaction, 2 Q3 Q2 + Q4, is positively correlated with Al/(Al + Si) of the glass and melt. For peralkaline alkali aluminosilicate melts (see Figure 1) at temperatures above their glass transition, the temperature-dependent equilibrium constant yields ΔH-values increasing from near 0 to about 40 kJ/mol in the Al/(Al + Si) = 0–0.4 range. Fewer experimental data exist for peralkaline alkaline earth aluminosilicate glasses. In chemically complex environments with both alkalis and alkaline earths present, the alkali metals associate with the Al3+ in the Q4 species, whereas alkaline earths tend to bond with NBO in depolymerized species [10]. It follows, therefore, that for systems such as natural magmatic

5 Ferric and Ferrous Iron

liquids, the Qn-distribution is controlled for the most part by the rules that govern alkaline earth compositions. This can be illustrated with the use of experimental data from ternary aluminosilicates to model the properties of chemically more complex systems. For example, the physicochemical properties of aluminosilicate glasses and melts, which vary with (Si,Al)─O bond energy, can be related qualitatively, and sometimes semi-quantitatively, to the Al/(Al + Si) ratio and to the electronic properties of charge-balancing cation because the bond energy varies with these same variables. The viscosity and activation energy of viscous flow of melts along meta-aluminosilicate joins, which are essentially fully polymerized, follow such simple evolutions within temperature intervals where the temperature-dependent viscosity is approximately Arrhenian (Figure 9). In contrast, the viscosity of peralkaline aluminosilicate melts does not show this effect of Al/(Al + Si) and actually may have a minimum at intermediate Al/(Al + Si)-values (Figure 9). This difference is because of a combination of weakening of (Si,Al)─O bonds in Q4-species with increasing Al/(Al + Si) and changing Qn-species abundance with increasing Al/(Al + Si).

The compressibility and thermal expansion of alkali aluminosilicate melts are also correlated with Al/(Al + Si) because the intertetrahedral (Si,Al)─O─(Si,Al) angle is itself more compressible and expandable with increasing Al/(Al + Si). In alkaline earth aluminosilicate systems, however, the opposite relations exist because Ca-chargebalanced Al3+ causes the (Si,Al)─O─(Si,Al) bonds to stiffen. In other words, the compressibility and thermal expansion of such aluminosilicate melts decreases with increasing Al/(Al + Si). Among the main groups of natural magmatic liquids (basalt, andesite, and rhyolite), the proportion of alkaline earths/alkali metals in charge-balancing roles decreases in the same order. This means that basaltic melts are less compressible and show smaller thermal expansion than more silica-rich melts such as rhyolite. Furthermore, the viscosity of basalt melt is less sensitive to Al/(Al + Si) than more silica-rich magma, which have a higher proportion of alkali-charge-balanced Al3+ in tetrahedral coordination.

Activation energey of viscous flow (kJ/mol)

5

500 NaAlO2–SiO2 400

300

200 0.0

Ferric and Ferrous Iron

Iron is found in three redox states, Fe , Fe2+, and Fe3+, but only the last two can enter the structure of silicate compositions in significant amounts. In this environment, the proportions of Fe2+ and Fe3+ vary with bulk chemical composition of glasses and melts, temperature, pressure, and redox conditions during equilibration of precursor melt. In magmatic liquids, the Fe3+/ Fe ranges from essentially 0 to 1 (Figure 10) in such a way that this redox ratio has been employed to estimate the activity of oxygen and, therefore, oxygen budgets during formation and evolution of earth materials and, indeed, the Earth, itself.

Na2Si2O5–Na2(NaAl)2O5

0.1

0.2

0.3

0.4

5.1 05

Al/(Al + Si)

Figure 9 Activation energy of viscous flow of aluminosilicate melts along the NaAlO2─SiO2 (nominal NBO/T = 0) (metaaluminosilicate) join (closed squares) and Na2Si2O5─Na2(NaAl)2O5 (nominal NBO/T = 0.5) (peralkaline aluminosilicate) calculated with the assumption of Arrhenian viscosity of the melts. As discussed in the text, NaAlO2─SiO2 melts and glasses do have a small fraction of a percent nonbridging oxygen, but are essentially pure Q4 with Alsubstitution for Si. Melts and glasses on the Na2Si2O5─Na2(NaAl)2O5 join, on the other hand, comprise Q2, Q3, and Q4 species with essentially all Al3+ in substitution for Si4+ in the Q4 species thus weakening the (Si,Al)─O bridging oxygen bonds in this specie. This, in turn, lowers the activation energy as for the NaAlO2─SiO2 melts and glasses. However, because of Alpreference, the proportions of Qn-species change so that Q4 abundance increases, thus countering the effect of the Al,Sisubstitution. These two mechanisms give rise to the minimum activation energy values at intermediate Al/(Al + Si) values.

Redox Relations of Iron

Equilibria between Fe3+ and Fe2+ in silicate melt and glass include interaction with oxygen in the structure. Conversely, variations in redox behavior of iron oxides affect the silicate melt structure. From the simple relationship, Fe2 + + 0 25 O2 2−

Fe3 + + 0 5 O2 − ,

2

where O is the link to the silicate structure, the relationship between redox ratio and oxygen fugacity provides a measure of the activity coefficient ratio of Fe3+ and Fe2+, gFe3+/gFe2+. This ratio often is about 1, but does depend on silicate polymerization (Figure 11). The redox ratio also varies with Al/(Al + Si) and the electronic properties of the metal cations. It increases with Al/(Al + Si) and NBO/T. The redox ratio also increases the more electropositive the network-modifying cation. This means, for example, that the Fe3+/Fe2+ of alkali silicate melts is

203

2.6 Structure of Chemically Complex Silicate Systems

1.1

Basalt

20

1.0

10

0.0

0.2

0.4

0.6

0.8

1.0

Fe3+/ΣFe

Distribution (%)

30

Fe2+/Fe3+

Distribution (%)

30

0.9 0.8 0.7

Andesite

20

0.6 1.2

10

0.0

0.2

0.4

0.6

0.8

1.0

Fe3+/ΣFe 30 Distribution (%)

204

Rhyolite

1.6 2.0 NBO/Si

2.4

Figure 11 Activity coefficient ratio of Fe2+ and Fe3+ in CaO─SiO2 glasses formed by quenching from melt after equilibration at 1600 C with different oxygen fugacity. The NBO/Si-values in this figure were calculated from the Ca/Si ratio. From the relationship to oxygen fugacity, any deviation of the concentration ratio, Fe2+/Fe3+, was ascribed to changes in the activity coefficient ratio, gFe2+/gFe3+, because (gFe2+/gFe3+)(Fe2+/Fe3+) = 0.25.

20

10

0.0

0.2

0.4

0.6

0.8

1.0

Fe3+/ΣFe

Figure 10 Distribution of redox ratio of iron (Fe3+/ Fe) among various common rock types. Database: http://Georock.org. Examples of average compositions of basalt, andesite, and rhyolite are given in Figures 5 and 6.

greater than that of alkaline earth silicate melts at the same temperature (pressure) and redox conditions.

5.2 Structural Roles of Fe3+ and Fe2+ It is sometimes assumed that Al3+ and Fe3+ occupy similar structural positions in silicate melts and glasses because of their common nominal charge and somewhat similar ionic radii. But this assumption is not necessarily warranted because Al3+ is dominantly in fourfold coordination in silicate crystals, whereas for the most part Fe3+ is in sixfold coordination with oxygen although there are exceptions to this general statement. In silicate glasses and melts oxygen coordination numbers vary with bulk chemical composition, total iron content, temperature, and redox conditions that existed

during precursor melting. The Fe3+─O bond distance of ferrisilicate glass is often used as an indicator of oxygen coordination number. For example, increasing iron content in Al-free silicates results in increasing Fe3+─O distance, which may be consistent with a transformation from fourfold to sixfold coordination. Mössbauer spectroscopy of glasses is an analytical tool with which both redox ratio of iron and coordination of Fe3+ and Fe2+ can be determined (Chapter 2.2). In alkali ferrisilicate melts equilibrated with air, Fe3+ typically is in fourfold coordination with oxygen. However, by replacing Na+ with more electronegative metals, the oxygen tetrahedra surrounding Fe3+ become increasingly distorted with an eventual changes to higher oxygen coordination numbers. As a result, in complex aluminosilicate compositions containing both alkalis and alkaline earths it is not unusual that Fe3+ exists in more than one coordination state. Most evidence suggests that Fe3+ in fourfold coordination forms oxygen tetrahedra that are isolated from those of Si4+ and Al3+. Furthermore, when both alkali and alkaline earths are potential charge-balancing cations in complex systems, alkali metals tend to associate with Al3+, whereas alkaline earths serve to charge-balance Fe3+ in tetrahedral coordination with oxygen. This means, for example, that if a rhyolite and a basalt melt equilibrated at the same oxygen fugacity, temperature, and pressure, the iron would be more oxidized in the rhyolite than in the basalt melt.

7 Perspectives

At least in FeO─SiO2 systems the Fe2+─O distances are consistent with sixfold coordination although it has also been suggested that the oxygen coordination number of Fe2+ might be closer to 4 than to 6. Results from 57Fe Mössbauer resonant absorption spectroscopy of iron-bearing glasses offer additional aid to distinguish between possible oxygen coordination numbers of ferrous iron (4, 5, and 6).

5.3

Structure–Property Relations

The physical properties of iron-bearing silicate melts and glasses are less well known than for iron-free materials. Viscosity and volume data can nonetheless be rationalized in structural terms. The partial molar volumes of FeO and Fe2O3, V FeO and V FeO1 5 , are sensitive to oxygen coordination. The V FeO in glass (between about 13 and 14 cm3/mol) resembles the molar volume of crystalline wüstite (FeO), which suggests that Fe2+ is sixfold coordinated in glasses. The V FeO1 5 -values are more variable, however, and depend on composition. For example, in SiO2─NaFeO2 glasses formed by quenching from melt equilibrated with air (and with Fe3+/SFe > 0.95), V FeO1 5 is between 20 and 21 cm3/mol (as FeO1.5), whereas for equivalent Caferrisilicate melt, V FeO1 5 = 13–15 cm3/mol [11]. These latter volumes are those expected with Fe3+ in tetrahedral and octahedral coordination, respectively. The viscosity of iron-bearing silicates depends on both redox state of iron and on the coordination state of Fe2+ and Fe3+. For example, with Fe3+ in fourfold coordination and Fe2+ in sixfold coordination with oxygen, melt viscosity increases systematically with increasing Fe3+/SFe because silicate polymerization also increases with increasing Fe3+/SFe [12]. When both Fe3+ and Fe2+ are surrounded by octahedral oxygen ligands, this relationship is reversed. Given that the redox ratio in basaltic melts normally is considerably lower and the oxygen coordination number around Fe3+ higher than in more silicate rick melts (andesite and rhyolite, for example), decreasing Fe3+/Fe2+ in the former may result in increased melt viscosity, whereas the opposite trend obtains for the latter.

6 Minor Components in Silicate Glasses and Melts Minor components such as TiO2 and P2O5 are important in natural and commercial glasses, including optical fibers and glass wool insulating materials. The structural behavior of P5+ in silicate glasses and melts is fairly well known, whereas that of Ti4+ remains more controversial, perhaps

because the oxygen coordination environment surrounding Ti4+ may be a composition-dependent variable. 6.1

Phosphorus Substitution for Silicon

In P2O5 glass, the P─O bridging bond distance (1.60 Å) is nearly identical to the Si─O distance in SiO2 glass (1.62 Å). Additionally, there is a second double-bonded and shorter (1.43 Å) P=O bond. These structural features remain for glasses in the P2O5–SiO2 system. In the latter, Si–O–P bridges can also be detected. Phosphorus in metal oxide silicate and aluminosilicate glasses and melts is dissolved by formation of phosphate (PO4) groups. Their degree of polymerization can be derived from 31P NMR spectra as a function of metal oxide/P2O5 ratio [13] in a way similar to Qn-species determinations in metal oxide–SiO2 glasses (see also Chapter 2.4 and Section 3.1). In addition, there are minor contributions from Si─O─P linkages. Mixed alumino-silico phosphate complexes are more common (Chapter 2.4). 6.2

Multiple Roles of Ti4+

The ionic radius of Ti4+ is nearly twice that of Si4+. It is not surprising, therefore, that Ti4+ in crystalline materials commonly occupies sixfold coordination, whereas Si4+ is in tetrahedral coordination. In glasses and melts, on the other hand, the structural behavior of Ti4+ is more complex. From partial molar volume of TiO2, V TiO2 -values near 30 cm3/mol in alkali silicate and V TiO2 to be ≤25 cm3/mol in alkaline earth silicate point to different structural behavior governed by the nature of the metal cations [8]. Raman and XANES spectroscopic data of SiO2─TiO2 glasses suggest Ti4+ in five- and sixfold coordination with oxygen at low concentrations ( 1 are called bridging (or network-forming). When ri is the same for all vertices, the network is called regular. Otherwise, it is irregular. For an irregular network, the average vertex coordination number, r, also called the connectivity, provides a measure of its shortrange topology. Note that, in chemically ordered networks, r is related to the two coordination numbers V and C by r=

2CV C+V

Rigid Isostatic f=0

1

The intermediate-range topology of a network is characterized by its ring-size distribution so that it, for instance, depends on whether neighboring structural units share edges or corners. By definition, noncrystalline networks have no long-range topological order. For this reason, they are termed topologically disordered (TD) networks [4].

2.3

Floppy Hypostatic f >0

Bond Constraints

The edges of a network represented by linear bonds constitute linear constraints on the coordinates of the vertices. In atomic networks, angular bonds give rise to additional constraints at the vertices. The linear and angular constraints, together, are called bond constraints. Since an angular constraint can be viewed simply as the result of an additional cross-linear bond between nextnearest neighbors, the linear and angular constraints carry equal weights. In other words, during constraint counting, one angular constraint and one linear constraint add up to two constraints. It is important to distinguish between independent and dependent (or redundant) constraints. Constraints in a network that do not change its deformation behavior are called dependent. Consider, for example, a finite planar network of four nodes situated at the corners of a square (Figure 1) for which the sides constitute four linear constraints. If these are the only constraints present, the network is floppy (i.e. it can be deformed). When a diagonal constraint is added, however, the network becomes rigid. When a second diagonal is added as the sixth constraint, no further change occurs in the deformation behavior of the network – it remains rigid. The sixth constraint, in this example, is therefore a dependent constraint. In TCT, it is important to count only the independent constraints and to exclude the dependent. To determine whether a constraint is dependent or not can be a challenging task. Owing to the presence of long-range topological order, crystalline networks contain a significant number of dependent constraints.

Stressed-rigid Hyperstatic f 0) with only four constraints originating from the edges. Middle: addition of a diagonal constraint makes the network rigid (isostatic with f = 0). Bottom: addition of a second, dependent diagonal constraint does not change the rigidity of the network.

Whereas one has to be extremely careful in applying constraint theory to crystals, this is fortunately not the case in noncrystalline TD networks.

2.4 Degrees of Freedom and the Network Deformation Modes Without constraints (as, for example, in an ideal gas), each atom has d coordinate degrees of freedom where d is the dimension of the network. As constraints are added at a vertex, its coordinate degrees of freedom decrease. If n is the average number of independent constraints per vertex, then the average degrees of freedom per vertex, f, in a network is given by f = d−n

2

If n < d, then f is positive and the network can deform without expenditure of energy. Such a network is termed “floppy” (or hypostatic) and has exactly f floppy (soft or low frequency) modes per vertex. The number of degrees of freedom decreases as n increases. When n > d, the network is over-constrained and is termed “stressed-rigid” (or hyperstatic). The excess (n − d) constraints in a stressed-rigid network are dependent if such a network exists. The transition from floppy to stressed-rigid takes place at n = d (i.e. at f = 0), which marks the disappearance of floppy modes and the onset of network rigidity. Such a network is called isostatic (Figure 1).

209

210

2.7 Topological Constraint Theory of Inorganic Glasses

In a floppy network, there may exist finite-size rigid inclusions (small group of atoms interconnected in a rigid manner) that are embedded in a floppy matrix. The average size of such rigid clusters grows as n increases till the rigid clusters begin to percolate, causing a transition from a floppy into a rigid network at n = d. Similarly, when a network is stressed-rigid (n > d), it may contain floppy clusters in a rigid matrix. The average size of these floppy clusters grows as n is reduced so that at n = d, the floppy clusters begin to percolate making the entire network floppy. Thus, a network undergoes a rigidity percolation transition at f = 0. This basic idea is at the heart of most TCT applications because n can vary with changes in both temperature and composition. In other words, since n = n(T, x), the isostatic boundary in a T–x phase diagram is described by n(T, x) = d.

3

Table 1 Degrees of freedom (f ) of d-dimensional TD networks of rigid units (δ, V ) with C units sharing a vertex (with the assumption h = θ = 0) based on Eqs. (4) and (5). Structural unit

δ

V

nu

d

C

Rod

1

2

0.5

2

3

0.5

3

4

1

3

6

0

2

2

0

3

2

1

Triangle

2

3

1

f

Square

2

4

1.25

2

2

−0.5

Tetrahedron

3

4

1.5

3

2

0

3

3

−1.5

Octahedron

3

6

2

3

2

−1

Cube

3

8

2.25

3

2

−1.5

Polyhedral Constraint Theory Therefore, the number of independent constraints per vertex (nu = Nu/V) in a rigid unit is

As mentioned before, PCT considers only chemically ordered networks which, according to Zachariasen [2], are TD networks of structural units made up of cornersharing rigid polyhedra. In such networks, it is convenient to treat the shared corners of the polyhedra as the vertices and the polyhedral structural units as links. The rigidity of a network then arises from the rigidity of the structural units as well as from the vertex-connectivity condition (i.e. the fact that all corners of polyhedral units are shared among a certain number of units). These constraints resulting from the rigidity of structural units and connectivity are termed polyhedral constraints. The deformation of a TD network is determined by the type of polyhedral structural units and by the vertexconnectivity (C) that specifies the number of polyhedral units sharing a vertex. The vertex-connectivity is related to (see Eq. 1) but is different from the average coordination number r.

A major advantage of PCT is that Eq. (3) counts correctly the number of independent constraints in a rigid unit. From Eq. (4) and the values of nu listed in Table 1 for several simple polyhedral units, one sees that nu increases with both V (for fixed δ) and δ (for fixed V > δ). When a structural unit is non-regular and rigid, other parameters, in addition to δ and V, are needed to specify the structural unit.

3.1 Rigidity of Polyhedral Structural Units

For an extended three-dimensional network (made up of a single type of structural unit) with an average C structural units sharing a vertex, the degrees of freedom, f, per vertex are

An isolated single regular polyhedral unit can be specified by two parameters: the dimension (δ) of the unit and its number of vertices (V). The dimension of the unit is the minimum dimension necessary to embed it. For example, δ = 1 for a rod, 2 for a triangular unit, and 3 for a tetrahedron. It is clear that δ ≤ d (the dimension of the network) and that V ≥ (δ + 1). When a regular polyhedral structural unit is rigid, the total number, Nu, of independent constraints in the unit satisfies the following relation: N u = δV −

δ δ+1 2

3

nu = δ −

δ δ+1 2V

4

3.2 Existence of Topologically Disordered (d = 3) Networks

f = 3 − C nu = 3 − C δ −

δ δ+1 2V

5

If f is positive, a network can exist. When f is negative, a TD network cannot exist. Thus, f = 0 provides a boundary for the existence of TD networks. If additional constraints (θ) are present at the shared corners (for example, bond angle constraints) or if there are internal degrees of freedom (h) within the structural units (for example, there is one internal degree of freedom in a unit made up of a pair of edge shared tetrahedra), then Eq. (5) can be modified as follows:

3 Polyhedral Constraint Theory

f = 3−θ −C δ−

δ δ+1 2V

−

h V

6

The degrees of freedom of TD networks are also listed in Table 1 for several rigid structural units for different values of connectivity. It should be noted that SiO2 with V = 4, C = 2, δ = d = 3 satisfies the condition of isostaticity (f = 0). Similarly, a two-dimensional TD network of corner-sharing rigid triangles (a candidate structure of B2O3 glass) is also isostatic. 3.3

Glass-forming Ability

According to PCT, a glass can be formed if and only if it can exist as a TD network (i.e. only if f ≥ 0). With increasingly positive values of f, however, the existing TD network becomes progressively more floppy and may crystallize beyond a certain value f(q) that depends on the cooling rate, q. Thus, glass formation is possible in the range for which 0 ≤ f ≤ f(q). With positive and increasing f, the potential energy of interaction (the chemical energy) increases because of unsatisfied chemical bonds. With decreasing and negative f, the strain energy in the system increases. In other words, an isostatic network represents a minimum in the total energy of the system. For this reason, the glass-forming ability is best under isostatic condition (f = 0) and becomes poor as f increases. The f = 0 boundary is termed the isostatic boundary of glass formation and the f(q) boundary the kinetic boundary of glass formation.

a function of the alkali content. Consider glass formation in an alkali silicon oxynitride system of the general composition x Na2O (1 − x)[SiO(2−y) N(2y/3)]. Note that 0 ≤ y ≤ 2 and 0 ≤ x ≤ 1. This system has three types of vertices: non-bridging oxygens with C = 1, bridging oxygens with C = 2, and bridging nitrogens with C = 3. The isostatic condition gives the limiting solubility of nitrogen, ymax = 3x/(1 − x). For y > ymax, f becomes negative. Whereas systematic investigations of nitridation of alkali-silicate glasses are not available, it is known that nitridation becomes easier upon increasing the alkali content [16]. Another example is provided by binary alkali-tellurite systems. Pure TeO2 with trigonal bipyramid structural units is over-constrained and does not form glass. Glass formation improves upon addition of alkali oxide because of formation of non-bridging oxygens, thereby increasing f and thus making it possible to form glasses when sufficient alkali oxide is added. Narayanan and Zwanziger [17] have rationalized in this way glass formation in alkalitellurite systems. 3.3.2 Glass Formation Under Hypostatic (f > 0) Conditions

This condition is best exemplified by the x Na2O (1 − x) SiO2 system where addition of Na2O leads to conversion of bridging oxygens (with C = 2) into non-bridging oxygens (with C = 1). The average value of degrees of freedom increases with increase in x: f x =

3.3.1 Glass-forming Ability and the Condition of Isostaticity (f = 0)

The isostaticity condition is satisfied in three dimensions for tetrahedral structural units (V = 4) with two units sharing every vertex (C = 2) as is the case for SiO2, GeO2, and BeF2, which are known as excellent glass formers. The isostatic condition is also satisfied for twodimensional networks made of corner-sharing triangles. This is often considered to be the reason why B2O3 is a strong glass former. An interesting application of the isostatic boundary concept is identification of limiting isostatic composition for glass formation. Consider the example of nitridation of alkali-silicate glasses. In silicon oxynitride glasses, nitrogen substitutes for oxygen forming two kinds of vertices: oxygen vertices with C = 2 and nitrogen vertices with C = 3. Adding nitrogen to silica (for which f is 0) makes f negative. This suggests that nitridation of silica will be difficult. However, addition of alkali creates non-bridging oxygens (with C = 1). Thus, nitrogen can be added to alkali-silicates while keeping f non-negative. In fact one can calculate the maximum amount of nitrogen that can be incorporated into an alkali-silicate glass as

3x 2−x

7

It is well known that glass formation in alkali-silicate systems becomes difficult for large value of x, especially when x > 0.5. 3.3.3 Glass Formation Under Hyperstatic (f < 0) Conditions

When f < 0, a TD network cannot exist. The excess strain energy can, however, be accommodated in a variety of ways that increase the value of f toward f = 0. One possibility is that the network crystallizes, thereby reducing the number of independent constraints by converting some into dependent ones. A second possibility is that new structural units form by breaking weaker constraints. When constraints are broken within structural units, the polyhedra become distorted. The existence of an extended TD network of distorted ABV polyhedral units (where the BAB angular constraint is broken at the A site but the AB length constraint remains intact) is demonstrated by the example of glass formation in the CaO–Al2O3 binary system. Since neither component is a network former, glass formation in this binary system is poor. If the presence of CaO stabilizes four-coordinated

211

212

2.7 Topological Constraint Theory of Inorganic Glasses

aluminum ions, AlIV, with two AlO4 tetrahedra sharing an oxygen vertex (as in silica), then the composition having 50% CaO should be a good glass former. However, experimental results show that glasses in this system form only in a small composition range at about 65% CaO [18]. It is possible to rationalize this observation with the constraint theory. Recently, Jahn and Madden [19] have reported from MD simulations that at 2350 K aluminum is present in Al2O3 melt in several different coordination states; about 54% AlIV, 41% AlV, 4% AlVI, and 1% AlIII. Further, it was observed that some of the oxygens are present as OIII, oxygen coordinated by three aluminums (also known as oxygen triclusters), and the remaining as normal bridging oxygens, OII. One can use this structural information and PCT to rationalize why the 65% CaO composition forms best glasses in this system. First, it can be assumed that the structures of Ca-aluminate and alumina melts are similar except for the incorporation into the network of O from CaO. Next, one can simplify the structural information by neglecting the concentrations of AlVI and AlIII. Let z be the fraction of AlIV and (1 − z) that of AlV. Then, for the composition x CaO (1 − x)Al2O3, one shows with PCT that the degrees of freedom, f, is given by f x, z =

12x + 6z − 6xz − 9 3 − 2x

8

When f = 0, Eq. (8) gives the following expression for the isostatic composition x∗ [x(f = 0)] in terms of z: x∗ z =

3 − 2z 4 − 2z

9

For z = 0.54, Eq. (9) gives x∗ = 0.65, the same value as for the best glass-forming composition [18]. 3.4 Existence of Super-Structural Units In B2O3 glass the presence of rigid, planar boroxol B3O6 units made up of three trigonal BO3 units is well established [20]. In contrast to basic polyhedral units, ABV, where a single A atom is coordinated by B atoms, super-structural units such as boroxol units contain more than one A atom. Do super-structural units then exist in other borate glasses? It is a question that has long persisted in the oxide-glass science. Super-structural units may be energetically more favorable in systems with long-range interactions. However, their larger size raises difficulties to match the density of networks with the observed density of glass. For example, the boroxol units are topologically equivalent to the basic BO3 trigonal unit (both have δ = 2 and V = 3). If all BO3 trigonal units in B2O3 glass are replaced by B3O6 boroxol units, the length scale of the structural unit is doubled (the volume thus increasing by a factor of 8)

while the mass of the unit is only tripled so that the density of a network of boroxol units is only 3/8 of that of a network of trigonal units. Further, based on topological considerations mentioned before, an extended 3-D network can incorporate only a small fraction of superstructural units with V > 4. For this reason, the dipentaborate and the di-triborate groups, two of the six super-structural units listed by Wright [20], probably do not exist in significant concentrations.

4

The Bond Constraint Theory

As originally formulated by Phillips [1] for covalent networks, structural units are not considered in BCT. Instead, the system is viewed as a network of atoms at the vertices and covalent linear bonds at the edges. These covalent linear bonds provide ri/2 linear constraints at the ith vertex of coordination number ri. In addition, there also exist [ri (d − 1) −d(d − 1)/2] covalent angular-bond constraints at the ith vertex for a d-dimensional network. The average number of constraints, n, per vertex is, therefore, n=

r + r d−1 − d d−1 2 , 2

10

where r is the average vertex coordination number. The condition of isostaticity (n = d) gives the following value for the critical coordination number r∗ (also called the rigidity percolation threshold): r∗ = d d + 1 ∗

2d − 1

11 ∗

Note that r = 2 for d = 2 and r = 2.4 for d = 3. It must be emphasized that Eqs. (10) and (11) assume that the angular constraints are intact at every vertex. This assumption does not always hold true as illustrated by silica where the angular constraints at oxygens are broken, which is generally the case for elements that do not belong to groups III, IV, and V and do not exhibit sp(n) hybridization. Application of BCT to non-covalent systems with longrange interactions such as ionic systems is approximate at best, and questionable most of the time, because these systems do not lend themselves to the count of simple nearest-neighbor constraint. For ionic systems, it is thus preferable to use PCT with structural units defined by the radius ratio of cations to anions.

4.1 Self-organization and the Intermediate Phase Self-organization designates chemical and/or topological rearrangements in a network that take place

4 The Bond Constraint Theory

spontaneously to reduce the overall energy in the system [21]. An important consequence of this process is that it allows a system to exist as an isostatic network over a range of coordination numbers or compositions. This range is sometimes known as the intermediate phase or reversibility window [22]. The range depends on the system considered and, to some extent, on its thermal history as well as on the property being measured (e.g. enthalpy release during relaxation, Raman frequency shifts in glasses, or activation energy of viscosity). For example, a coordination number range from 2.39 to about 2.52 has been reported for the intermediate phase in GexSe(1−x) system from Raman frequency shifts [22], and a range from r = 2.35 to about 2.45 in the (Na2O)x(SiO2)(1−x) system from enthalpy relaxation [23]. Interestingly, Wang et al. [24] found no evidence of any intermediate phase in the Ge–As–Se system. Also, Shatnawi et al. [25] found no discontinuities or breaks but only smooth variation with respect to composition in the structural response of GexSe(1−x) glasses in the range 0.15 < x < 0.40 implying the absence of any phase transition associated with the start and end of the intermediate phase range.

4.2 Non-bridging Vertices (or Singly Coordinated Atoms) There has been much discussion in the literature [26] about the role of dangling vertices (or non-bridging nodes) and their influence (if any) on the rigidity characteristics of a network. At least conceptually, it is clear that dangling vertices should not affect the stiffness of the network because they are not network-forming. In this respect, a confusion in the literature exists primarily because of the way constraints and degrees of freedom are counted. Clearly, if a dangling vertex is counted as being part of the network, then it is necessary to count also the length and angle constraints associated with it. A dangling vertex adds three degrees of freedom but also three constraints (one length and two angles), so that it does not make any net contribution to the degrees of freedom in a network if the counting is done correctly. However, the problem is that extra degrees of freedom often appear when the angular constraints of the dangling vertices are not included in the count [26, 27]. Because these extra degrees of freedom are associated with the floppiness of the dangling vertices themselves, they do not influence the rigidity or the flexibility of the underlying network. Thus, the opinion of this writer is that it is best to disregard the onefold coordinated atoms (i.e. dangling or nonbridging vertices) as they have no influence on the rigidity characteristics of a network.

4.3 Glass-forming Ability in Chalcogenide Systems 4.3.1 Ge–Se System

For the binary GexSe(1−x) system, the average coordination number r(x) is (2 + 2x) since r(Ge) = 4 and r(Se) = 2, and the system is isostatic at x∗ = 0.2 (corresponding to the Ge1/5 Se4/5 composition). According to Tichy and Ticha [28], however, the best glass-forming compositions lie on the Se-rich side in the range 0.06 < x < 0.15. To rationalize this apparent discrepancy, Tichy and Ticha [28] suggested to view the GexSe(1−x) system as an extended chemically ordered network of short, linearlyrigid (Se)k chains containing k seleniums that are crosslinked by Ge atoms. The ends of the Se chains are connected to Ge atoms so that four such chains share a Ge atom. Note that since x = 1/(1 + 2 k), k is 2 at x = 0.2. A network with k > 2 (corresponding to x < 0.2) should be floppy (f > 0). However, one can show that some of the degrees of freedom (let us denote these by f #) in such a network for x < 0.2 are associated with the dihedral rotation of the inner seleniums (Se#), those inside the selenium chains (–Se–Se#–Se–). A Se# atom can rotate dihedrally about the line joining its two neighboring Se without influencing the deformation pattern of the network (Figure 2). This is one example where certain internal degrees of freedom decouple from the rigidity of the overall network. In another example the extra degrees of freedom associated with a singly coordinated atom (i.e. a dangling vertex) decouple from the rigidity of the overall network. Clearly such decoupled degrees of freedom can be disregarded as far as network rigidity is concerned. The network, therefore, can satisfy the isostaticity condition in the range x < 0.2 by forming chemically ordered networks with an appropriate value of the k for the Se-chains. A value of k = 3 corresponding to x = 1/7 (or about 0.14) is close to the composition where best glass

Se

Se#

Ge

Se Ge

Se Se

Figure 2 Schematic of a Se-chain with five seleniums connecting two Ge atoms in an isostatic network (not shown). The inner Se# can rotate dihedrally about the dashed line connecting its neighboring seleniums without influencing the rigidity of the network. This dihedral motion of inner seleniums is an internal degree of freedom decoupled from the rigidity of the overall network.

213

214

2.7 Topological Constraint Theory of Inorganic Glasses

formation is observed, explaining why good glass formation takes place for x < 0.15. For x > 0.2, there is experimental evidence for edgeshared GeSe4 tetrahedra [29]. Because the presence of edge sharing does not change the value of r, the BCT results are not affected but edge sharing does cause differences in the intermediate-range topology. When one considers a pair of edge-shared tetrahedra as a single unit with four Se vertices (and two internal Ge atoms), such a bi-tetrahedral unit has an internal degree of freedom, namely rotation about the shared edge. This additional flexibility allows isostaticity to hold beyond the GeSe2 composition (x = 1/3) in the PCT formalism even though the BCT results do not change. It is also clear that the presence of Ge–Ge homopolar bonds [16] – that must exist for x > 0.33 – does not influence the short-range topology of the network. Hence, the BCT consequences do not change.

4.3.2 As–Se System

Since r(As) = 3 in the AsxSe(1−x) system, r∗ = 2.4 corresponding to x∗ = 0.4. But good glass formation has been observed in the Se-rich range from x ~ 0 to x ~ 0.23. As in the Ge–Se system, this discrepancy can be rationalized by viewing the As–Se glasses for x < 0.4 as a chemically ordered network made up of linearly-rigid (Sek) short chains, three of which being connected to every As atom. If one eliminates the internal degrees of freedom associated with the dihedral rotations of Se# in the Se chains, it follows that these chemically ordered As((Se)k)3/2 systems are isostatic for x ≤ 0.4. Note that since x = 2/(2 + 3 k), k ≥ 2 corresponds to x ≤ 0.25, which fits well the reported composition range for good glass formation [28].

4.4 Composition Variation of Properties in Glass-forming Systems Most properties of glasses exhibit rather uninteresting monotonic continuous variations even when r crosses its isostatic value. Only some configurational properties show extremum values with respect to r at the rigidity percolation threshold (i.e. at r∗ = 2.4). Tatsumisago et al. [30] reported that the configurational heat capacity and the activation energy of viscosity exhibited minima in the Ge–As–Se system at r = 2.4. Similar results were obtained by Senapati and Varshneya [31] in the Ge–Se and Ge–Sb–Se systems. It is worth noting that by investigating a range of Ge–As–Se compositions, all having the same values of r, Wang et al. [24] have reported that values of the configurational properties are not a unique function of r implying that topology alone is not sufficient to determine the variation of properties with composition, effect of chemical disorder must also be considered.

5 Temperature-Dependent Constraints 5.1 The Influence of Thermal Energy Implicit in the original PCT and BCT theories was the notion that constraints are fixed for good – either intact (= 1) or broken (= 0) – and that they do not vary with temperature (T). Thermal energy was implicitly neglected in the original theories which were thus valid only at T = 0 K. To remedy this problem, Gupta [5] introduced the concept of a T-dependent bond constraint. He argued that, if Ei is the energy of a certain class of bonds, then the value of the corresponding constraint hi(T) should be expressed by a Boltzmann expression: hi T = 1 − exp

−

Ei , kBT

12

where kB is the Boltzmann constant. Note that the value of hi always lies in the interval [0,1], being zero in the high-temperature limit, equal to 1 at sufficiently low temperatures, and decreasing monotonically with increasing T. Physically, a fractional value of a bond constraint means that only a fraction of ith type of bonds are intact at a given instant. One may associate a characteristic temperature Ti for the ith type of constraint as follows: Ti =

Ei , k b Ln2

13

so that this constraint can be considered effectively as broken (= 0) for T > Ti and intact (=1) for T < Ti. For both stretching and bending constraints, this formalism has been validated by comparisons of the standard deviations of the partial distributions calculated for glassy and crystalline alkali disilicates as a function of temperature in MD simulations [9]. The average degree of freedom per vertex, f(T), in the network thus becomes T-dependent and (for d = 3) is given by f x, T = d −

n i x hi T

14

i

Since hi is a decreasing function of T, f(T) always increases with temperature. 5.2 Extension of the Topological Constraint Theory to Supercooled Liquids In 1999, Gupta [6] extended the notion of T-dependent bond constraints to glass-forming supercooled liquids: “Since the structure of a glass formed by cooling a liquid is the same as the structure of the liquid at the glass transition (or fictive) temperature, Tg, it follows that if the glass structure is an extended TD network, then such a network

5 Temperature-Dependent Constraints

must also exist in the super-cooled liquid state at Tg.” More importantly, he argued that the configurational entropy, ΔS(T), of a supercooled liquid is approximately proportional to the average degrees of freedom per vertex, f(T). This result, later substantiated by Naumis [32], leads to several important consequences: a) At the Kauzmann temperature, TK, defined by ΔS(TK) = 0, the degrees of freedom vanish: f TK = 0

Ln η T = Ln η ∞ +

A T f T

16

Here, A is a constant independent of T. c) The fragility, m, of a liquid defined as 1 ∂ log 10 η Tg ∂ 1 T

,

17

T = Tg

is related to the temperature-dependence of f as follows: log 10

m

ηg η∞

Substituting Eqs. (12) and (14) in Eq. 16 and assuming that only one type of constraints (with n constraints per vertex) varies within the temperature range of interest, one obtains the following temperature scaling of viscosity for supercooled liquids: Ln η T = Ln η ∞ +

15

b) From the Adam–Gibbs theory of viscosity, it follows that the temperature-dependence of viscosity is simply related to that of f(T):

m

5.3 Temperature – Scaling of Viscosity (η) and the MYEGA Equation

1+

∂Ln f ∂Ln T

18

19 For deeply supercooled liquids in the vicinity of the glass transition, n is approximately equal to 3 and Eq. (16) simplifies to Ln η T = Ln η ∞ +

20

where B is a new constant. This Eq. (20) is the well-known MauroYue-Ellison-Gupta-Allan (MYEGA) expression [33] for the T-dependence of the equilibrium viscosity, which has been remarkably successful in fitting the experimental data on the T-dependence of viscosity for a large number of inorganic and organic liquids. It should be noted that, like the Vogel-Tammann-Fulcher (VFT) equation, the MYEGA has only three fitting parameters but, unlike VFT, it does not exhibit any divergence of viscosity at any finite temperature.

5.4 The Composition Variation of the Glass Transition Temperature, Tg If the value of the parameter A in Eq. (16) has a negligible composition dependence, then it follows from this equation that Tg x f Tg x

(b) f

(a) (c)

1

B E , exp T kBT

T = Tg

The value of log [ηg/η∞] is about 16. The variation of the degrees of freedom, f(T), with T, for good, poor, and nonglass-forming liquids is shown schematically in Figure 3. From Eq. (16), one then concludes that the cause of the non-Arrhenian nature of the viscosity is the temperature-dependence of bond constraints.

0

A T 3 − n + n exp − E k B T

(T/Tk)

Figure 3 Schematic variation of degrees of freedom (f ) in three supercooled liquids with increasing temperature normalized with respect to the Kauzmann temperature (TK). Curve (a) represents a strong glass former, curve (b) a fragile glass former, and curve (c) a non-glass former for which a TD network cannot exist (Source: From [6]).

= T g xref f T g xref

= const

21

Here, xref is a reference composition. The importance of Eq. (21) cannot be overstated. It provides a means of modeling the composition dependence of Tg from the knowledge of the atomic level short-range order as a function of composition. Traditionally, such information on the short-range order has been obtained from X-ray or Neutron diffraction studies. Nowadays, such information can also be obtained accurately using MD studies. Gupta and Mauro [7] used the T-dependent constraint theory to rationalize quantitatively the variation of the glass transition temperature, Tg(x), with composition in the binary GexSe(1−x) chalcogenide system. Their analysis resulted in the modified Gibbs–DiMarzio equation: Tg 0 ≤ x ≤

1 3

= Tg 0

1 , 1 − αx

22

215

2.7 Topological Constraint Theory of Inorganic Glasses

with a value of the parameter α = 5/3, which is the value observed experimentally [31]. In addition, using Eq. (18), Gupta and Mauro [7] were also able to explain the variation of the fragility, m, as a function of composition. Mauro et al. [8] later applied the T-dependent constraint theory to binary alkali–borate systems where a wealth of structural information is available as a result of years of X-ray diffraction and NMR spectroscopy

experiments. The agreement for both Tg and m between TCT and experimental results is remarkable considering that only one fitting parameter was used for all the data (see Figures 4 and 5). Using a similar approach, Smedskjaer et al. [34] have successfully extended the T-constraint theory to ternary system Na2O–CaO–B2O3 system. In 2011, they also analyzed the four component Na2O– CaO–B2O3–SiO2 system [10].

(a) 100

(a)

xNa2O-(1– x)B2O3

850

90 x Na2O-(1– x)B2O3 80

750

70 Fragility

Glass transition temperature (K)

800

700 650

60 50

600

40

550

30 Model

500

Nemilov Stolyar

Suzuki Moynihan

450 0

0.1

Model Stolyar

20 0

0.2

0.3

0.4

0.1

Nemilov Chryssikos 0.2

0.3

0.4

0.5

0.4

0.5

x

0.5

(b)

x

(b)

90

850

xLi2O-(1– x)B2O3

x Li2O-(1– x)B2O3

800

80

750

70

700

60

Fragility

Glass transition temperature (K)

216

650 600

50 40

550 30 500 450 0

0.1

Model

Kodama Moynihan

Model Chryssikos 0.2

0.3

0.4

Chryssikos

20 0 0.5

x

Figure 4 Composition dependence of the glass transition temperature for the (a) sodium borate and (b) lithium borate systems. Solid curves: predicted Tg(x) using the temperaturedependent TCT. Points: experimental data (Source: From [8]).

0.1

0.2

0.3 x

Figure 5 Variation of fragility with composition in the (a) sodium borate and (b) lithium borate systems. Curves calculated with the Tdependent TCT. The step increase in fragility around x = 0.2 is a consequence of a fragility transition in these systems (Source: From [8]).

6 Topological Constraint Theory, Thermodynamics, and the Potential Energy Landscape Formalism

5.5 Fragility (or Rigidity) Transitions and Iso-Tg Regimes A generalized T-dependent activation energy, H(T), is defined as the slope of the Arrhenius plot of viscosity: H T , x = kB

∂Ln η ∂ 1 T

23

The ratio, H(Tg, x)/(kBTg), is proportional to the fragility m. In some systems, the activation energy (or fragility) shows rounded discontinuities as a function of T or as a function of composition, X. These jumps are referred to as fragility transitions. An example of such transition in the alkali-borate systems is shown in Figure 5. Fragility transition as a function of temperature for a fixed composition is illustrated in Figure 6. In a temperature-induced fragility transition, a system always becomes more fragile at higher temperatures simply because more constraints are broken as the temperature is increased. Mauro et al. [8] made an interesting observation in the binary alkali-borate melt xM2O (1 − x)B2O3 systems where Tg appears to be a constant function of composition for a small composition range. They called this composition range the “iso-Tg regime” (Figure 4). The iso-Tg step results when a bond constraint breaks exactly at Tg. It can be shown that, within the iso-Tg regime, the fragility remains constant and equal to the low value of about 16 that is observed for strong glasses. Interestingly, the composition range of the iso-Tg regime (at least in the alkali-borate system) is nearly the same as that of the reversibility window observed by Boolchand and colleagues [22]. This coincidence raises the possibility of some connection between the two phenomena, an area that requires further investigation. 12 10 8 logη (Pa s)

6

The impressive applications of TCT demand answers to fundamental questions such as how is TCT connected to the thermodynamics of liquids and glasses and how to formulate TCT from the first-principles statistical physics of potential-energy landscapes of liquids and glasses. This is an area that has not received much attention so far except for the work of Naumis and coworkers [13, 32] that we summarize in this section. Naumis uses simple harmonic potentials to express the Hamiltonian (H) of a floppy system as follows: 3N

H= 1

p2j 2m

3N 1 − xf

+ 1

1 mω2j q2j + 2

3Nxf 1

1 mω2o q2j 2 24

Here, xf is the fraction of floppy modes (= f/3); pj and qj are, respectively, the momentum and position coordinates of oscillators representing vibrational modes of frequency ωj and floppy modes of frequency ωo. For real systems, one has to use more sophisticated interaction potentials. Nonetheless, a harmonic model gives a reasonable qualitative feel of the thermodynamics of the floppy modes. Naumis assigns a small but finite frequency ωo ( i Σk > j > i u3 r i , r j , r k + 7 The first term u1 is discarded in standard simulations because it accounts for external fields (i.e. wall, electrical field, gravity, magnetic field, and centrifugal force). The second term u2 is the most important since it represents the relevant pair potentials. When determined empirically, it actually includes three-body and many-body effects, which is why models relying on simple pair potential model reproduce reasonably well liquid or glass structures, and why it is better in this case to denote it by the term “effective” pair potential. As illustrated by Eq. (7), empirical potentials have a great flexibility since specific terms may be added if needed. When electrostatic interactions are important, a Coulomb charge–charge interaction may, for instance, be included in the form: U zz r ij

zi zj = , 4πε0 r ij

8

where zi, zj, and ε0 are the charge on atom i and j and the permittivity of free space. Because the Coulombic series converges very slowly, the Ewald, particle-mesh, or multi-pole techniques are used in periodic systems. Likewise, more complex models implement three- and fourbody terms to reproduce bond-bending and torsional forces, respectively. Alternatively, polarizable or shell models are employed to consider ions as nonrigid entities and, thus, to account for the effects of the deformation of electron clouds with suitable additional parameters. From a practical standpoint, the parameters of equations such as (4–7) can be estimated in two different ways depending on the nature of the data to which they are fitted [4]. In the most rigorous way, one relies on energy profiles determined in first-principles calculations or quantum-mechanical simulations of appropriate reference systems (cf. Chapter 2.7). Alternatively, potential energy parameters are fitted through MD or lattice dynamics calculations to some selected physical properties. Structural and elastic data are generally chosen because they are most directly related to interatomic potentials. Thermal properties may also be used, but they are sensitive to second-order effects such as anharmonicity and are in turn generally predicted less accurately.

3

Monte-Carlo Simulations

3.1 Principles of the Method First described for atomistic simulations in 1953 by Metropolis et al. [7], the MC method cannot account

for the time evolution of the system investigated. By calculating instead its physical properties from repeated samplings made on the basis of a Boltzmann energy distribution of equilibrium states, it differs from a search algorithm with which the energy of the system would occasionally increase even though a steady decrease would be sought after at every step. As already stated, the method is thus inappropriate to tackle any nonequilibrium or history-dependent phenomenon. Over MD simulations, its main advantage is to shorten the calculation time needed to arrive at the equilibrium structure if a suitable sampling method is employed. Within the framework of the canonical ensemble, the partition function Q(N,V,T) is, for example, Q N, V , T =

Λ∗∗3 N

1 dr N exp − βU p r N

, 9

where Λ =

h2 2πmk B T

is the thermal de Broglie

wavelength, β the reciprocal temperature (1/kBT), and N, r, Up, m, kB, and T are the number of atoms, atomic coordinates, potential energy of a system, atomic mass, Boltzmann’s constant, and temperature, respectively. From the partition function it follows that the probability (P) of finding a configuration rN is P rN

exp − U p r N

10

To fulfill Eq. (9), the standard Metropolis procedure in MC simulations consists of 1) setting up an initial configuration in a periodic boundary cell, 2) calculating the energy of this configuration, 3) selecting an atom at random and moving it randomly along all coordinate directions, 4) accepting the new configuration resulting from the move if it lowers the energy of the system, because the new state is more probable than the former, but keeping the former configuration otherwise only in case its Boltzmann factor is higher than a real number drawn randomly between 0 and 1. In other words, the MC method does not weight configurations selected randomly according to their Boltzmann factor to calculate the properties of the system, as was done earlier, but weight evenly instead configurations selected with the probability exp[−Up(rN)]. Its trick thus is to concentrate on the sampling in the regions of the phase space that contribute the most to the partition function. Although they will not be described here, there are several other sampling methods in the standard MC calculations to accelerate convergence to the equilibrium state [3].

4 Molecular Dynamics Simulations

3.2

Reverse Monte-Carlo Simulations

To complement standard MC simulations, the so-called reverse Monte-Carlo (RMC) method has been developed to study disordered structures [8]. It enables threedimensional structural models to be constructed in a manner consistent with experimental results. The data most commonly used are PDF and their Fourier transforms obtained from diffraction experiments (Chapter 2.2). In RMC calculations the standard procedure is to 1) set up an initial configuration in a periodic boundary cell, 2) calculate the set of quantities relevant to the experimental data considered (e.g. PDF), 3) calculate the mean square deviations χ 2 of the calculated from the observed results χ2 =

Σ yobs – ycal ρ2

2

,

11

where ρ is an appropriate measure of experimental accuracy, 4) select an atom and give it a random displacement, 5) accept the move if it leads to a χ 2 decrease, but keep the former configuration otherwise, 6) repeat from 2) to 5). To quote a single example, the structural role of “insufficient” network formers has been successfully studied by RMC in a simulation of the atomic configuration of Mg2SiO4 glass in which the measured total structural factors were well fitted [9]. The estimated bond distance of (a) 6 Si–O

Mg–O

T(r)

3 0 –3 0

1

2

3

r (Å)

(b) 6

Mg─O differs in the glass and in the crystal (Figure 3), whereas the difference in the peak position of Mg─O between the two phases reflects the structural feature the glass network is built by the corner- and edge-sharing of highly distorted Mg─O-bearing species. The advantage of the RMC method is that knowledge of interatomic potentials is not required, but its drawback is that it is not applicable to novel glass systems for which no experimental data can be compared with model values. Besides, there is a risk of arriving at an incorrect structure if the iterative procedure leads to a local, and not to the true minimum of χ 2. A simple way to avoid such a pitfall is to add a set of effective constraints on bond lengths, bond angles, or coordination numbers (CN) that will prevent spurious results from being obtained.

Si–O

4

Molecular Dynamics Simulations

The main advantage of MD simulation is to provide important structural information that complements conclusions drawn from experimental studies. One such important result was the demonstration that the structure of sodium silicate glasses fits the modified random network model because the spatial distribution of sodium ions showed a clustering tendency [10]. The result was especially significant as the extremely high fictive temperatures of glasses quenched in MD simulations strongly favor a much more random distribution. For such reasons, MD simulations have become the most popular method to study theoretically glass and liquid structures (e.g. [11, 12]). Their main advantage is to yield from the three-dimensional coordinates calculated for all atoms a variety of structural information that can often be checked against experimental data. In addition, they also provide information that escape experimental determinations and may thus point to the existence of unknown structural features. Since they deal with the instantaneous state of a system, MD simulations rest on the Lagrangian function L(r, r) of coordinates r and their time derivatives r as defined in terms of kinetic (K) and potential (Up) energies L = K − Up

Mg–O

3

12

T(r)

and on the Lagrangian equations of motion

0

d ∂L ∂r – dt

–3 0

1

2

3

r (Å)

Figure 3 As defined by Eq. (20), total correlation functions T(r) of Mg2SiO4 glass (a) and crystal (b) [9].

∂L ∂r

=0

13

This leads to m i r=f i , where m(i) is the mass of atom i and

14

225

226

2.8 Atomistic Simulations of Glass Structure and Properties

f i = ∇r i L = ∇r i U p ,

15

where f(i) is the force exerted on atom i. If the coordinates of all atoms are known at time t0, all the forces exerted and the resulting velocities are calculated with Eq. (15) and then Eq. (14). All the velocities and coordinates after a time step of Δt are updated by the time integration of the equations of motion (14). When MD methods are applied to glass or disordered systems, several important points should be noted: 1) As the proper choice of the interaction potential model is extremely important, a model with complex interaction potentials may be required if any dynamic structure or property is to be calculated after along with the static structure. 2) The particular starting configuration is not important as long as equilibration time steps are numerous enough at high temperature. Almost the same structural information should be obtained from different initial configurations. If not, the calculated results are unreliable. Advanced techniques may be used to calculate structure and properties more efficiently. To omit unimportant contributions to the dynamics, one can, for example, keep constant bond lengths such as O─H during the MD calculation. As an alternative to this dynamic constraint method, one can use nonequilibrium MD, which is especially efficient to calculate transport properties such as viscosity. Unlike with conventional MD, a continual friction force can be imposed on the system and its response be monitored.

5 Modeling: Simulation Techniques and Examples 5.1 Overall Glass Structure In atomistic simulations the positional correlation of atoms is easily investigated within a radius of half of simulation cell size (~25 Å). The most widely derived results are the PDF, the RDF, or total correlation function, T(r), which can be readily compared with those obtained in diffraction studies. In simulations, the PDF and the RDF are derived as follows. The single and pair (two-body) probability density PN(1), PN(2) are defined as PN

1

r = Σi δ r − r i

PN

2

r, r = Σi Σj

j i

16 δ r − ri δ r − rj ,

17

where N is again the number of atoms and ri is the coordinate of atom i.

The value of PN(1)(r) in homogeneous system turns out to be the number density ρ, which is defined as N/V, where V is the volume. Moreover, PN(2)(r) is expressed in terms of the PDF, g(r, r ), and number density ρ as: PN

2

r, r = ρ2 g r, r

18

As to the RDF, J(r), it is defined as the number of atoms between r and r + dr from the center of an arbitrary origin atom: J r = 4πr 2 g r, r

19

An alternative function called total distribution function, T(r), is calculated as: 20

T r = 4πρr g r, r

The information directly obtained from diffraction experiments is the intensity I(Q), which is related to J(r) by J r =1+

1 2π 2 ρ

QI Q sin Qr dQ

21

Finally, the frequently used structure factor, S(Q), is the Fourier transform of the number density ρQ first calculated in atomistic simulation: ρQ = Σi exp − iQ r i

22

Then, S(Q) is calculated from ρQ: S Q = ρQ ρ − Q

23

It is quite important to reproduce the experimental J(r) in the real space domain or I(Q) in the wave-number domain to validate the calculated three-dimensional structure. Depending on the atoms considered, X-ray and neutron diffraction experiments can yield different profiles so that both kinds of profiles should be calculated and compared with the relevant data as done in Figures 4 and 5 for MD-simulated B2O3 glass [6]. Once the total correlation and interference functions have been validated, more detailed analysis based on PDF functions can be performed, as shown in Figure 6, and important insight into structural order be obtained. Although the experimental peak positions are reproduced reasonably well by the calculated T(r) and Q I(Q), there are some discrepancies for the peak values. The position and width of the first peak represent the average length and the length distribution of B─O bonds, respectively. The second peak position and peak curve are mostly affected bond angles of O─B─O and B─O─B and size distributions. As indicated by a detailed analysis of the data, most of the discrepancy is due to a simulated fraction of only 30–50% for the so-called boroxol B3O6 rings (cf. Chapter 7.6) compared to the 60–80% range of the experimental values [13].

5 Modeling: Simulation Techniques and Examples

(a)

(a) 2000

150

Experiment Simulation

QI (Q)(e2/Å)

T (el2/Å2)

0

–1000 0.0

Experiment Simulation

100

1000

50 0 –50 –100

1.0

2.0

3.0

4.0

5.0

–150

r (Å)

0

5 Q

(b)

15

20

(b)

30 Experiment Simulation

20

9 Experiment Simulation

6 QI (Q)(barns/Å)

T (barns/Å2)

10 (Å–1)

10

0

3 0 –3

–10 0.0

1.0

2.0

3.0

4.0

5.0

r (Å)

Figure 4 Comparisons between the experimental [13] and simulated [6] X-ray (a) and neutron (b) total correlation functions of B2O3 glass.

5.2

Short-range Order

Of particular interest for characterizing short-range order are CN. In atomistic simulation, this parameter is well defined as the number of atoms falling within a given distance from an arbitrary atom. For each atomic pair this cutoff radius is typically estimated either from the corresponding bond lengths in crystal structures or from the position of minimum between the first and second peaks of the pair-distribution function. Alternatively, the CN can be estimated experimentally from the height of the first peak observed in the X-ray diffraction or neutron diffraction spectra or from the chemical and isomer shifts in NMR or Mössbauer spectra, respectively. In MD studies the oxygen CN of network-forming cations (Si, B, P, Ge, etc.) are generally calculated to be within 5% of the experimental data even for the changes with varying pressure or concentration of network-modifier alkali or alkaline earth cations. Such coordination changes from 3 to 4 for B atoms in borate glasses and from 4 to 6 for Si and Ge in silicate and germanate glasses have been well documented in this way (e.g. [12]). On the other hand, the oxygen CN is not well defined for intermediate network-forming cation (Al, Fe, Zr, etc.) or network-modifier cations when the distance

–6 0

5

10 Q

15

20

(Å–1)

Figure 5 Comparisons between the experimental [13] and simulated [6] X-ray (a) and neutron (b) interference functions of B2O3 glass.

distribution between cation and oxygen atom is broad. A slight change in the definition of cutoff radius then translates in a large change in CN. In MD simulations on sodium aluminosilicate glasses, the switch of Al from a network-forming to a network-modifying role has nonetheless been evidenced by a CN increase from six in crystal to four and five in glass (e.g. [14]) whereas the existence of fivefold coordinated aluminum and threefold coordinated oxygens has also been evidenced [15]. In silicate glasses another fundamental feature to describe variations of structure and properties is the “Qn distribution,” where the subscript n indicates the number of bridging oxygen (BO) in an SiO4 tetrahedra (Chapter 2.3). In MD simulations it is easy to identify nonbridging oxygens (NBO) on the basis of the cutoff radius. The calculated Qn distributions for sodiumsilicate glasses have been compared with that determined by MAS-NMR experiments [16]. The MD calculations reproduce the experiments reasonably, although the extremely rapid quenching rates prevailing in the MD simulation may broaden the distribution, which does depend on actual T,P conditions. The analysis of Qn is also important for phosphate glasses, because Qn

227

2.8 Atomistic Simulations of Glass Structure and Properties

(a)

0.06

50

O–B–O

40

Population

2–5 and 2–4

PDF

228

B–B

30 2–6 20 10

2–7

2–8

B–O–B

0.04

0.02

B–O 0.00 90

1–3 and 3–6 3–8 O–O

120

150

180

Bond angle (deg)

0 1

3 r (Å)

2

4

5

(b) 8 7

4

5

6

2 1

3

Figure 6 PDF functions in simulated B2O3 glass and their structural assignments [6]. The peaks labeled in (a) refer to the specific distances indicated in the elementary structural units (b).

distribution reflects their polymer-like structure that results from the existence of doubly bonded oxygen atoms. In the case of phosphate glass not many MD studies have been published and more validated potential models need to be developed. Recent MD calculations on iron phosphate glasses have demonstrated that the network connectivity is indeed dominated by the expected Qn [11]. The third useful information on short-range order is the “bond angle distribution” (BAD), because the nature of the existing polyhedral units can be ascertained from oxygen–cation–oxygen angles. For SiO2 and silicate glass, the simulated peak position is, for instance, found near 109.47 in O─Si─O angle distributions, which of course reflects the presence of Si within SiO4 tetrahedra. Likewise, the peak of O─B─O angles in B2O3 lies around 120 , in harmony with the formation of BO3 triangles (Figure 7). As for the B─O─B distribution, a significant amount of angles with 120 reveals the presence of boroxol rings (Figure 7) because, without boroxol rings, the B─O─B distribution should be around 129 as observed in B2O3 crystal [6]. In this respect, the interest of MD simulations stems from the fact that there is no direct method for determining the BAD experimentally – just a possibility to estimate roughly average values from Xray or neutron diffraction data. These simulated cation–oxygen–cation BADs are specially valuable to probe

Figure 7 Bond angle distribution in simulated B2O3 glass.

local structural changes with either temperature or pressure in single-component glasses such as SiO2, B2O3, P2O5, or GeO2. The fourth information of interest is the “torsion angle distribution” (TAD), to which particular attention is paid for polymers whose structure and properties are significantly affected by the twisted arrangement of side chains. Again, B2O3 glass illustrates the relevance of this distribution to inorganic glasses because of the steric problem raised by the interconnection of BO3 units and boroxol B3O6 rings (Figure 8). In this case, the calculated TAD suggests different connecting geometries between BO3– BO3 linkages and B3O6–B3O6 units: the former are preferentially oriented in a perpendicular direction, which means that connected BO3 units do not lie in the same plane, whereas the latter are oriented in the same direction, which means that B3O6 units do lie in the same plane [6]. For SiO2 glass, no such distinction is of course found, but MD simulations do suggest that a torsional transformation takes place between neighboring SiO4 tetrahedra at elevated temperature, in analogy with the structural changes associated with the α–β transition in cristobalite [17]. In addition, it has been suggested that the abrupt rotation of Si─O─Si equivalent to torsion movement between two SiO4 tetrahedra is the cause of anomalous thermomechanical properties in silica glass [17].

5.3 Medium-range Order Medium-range order is difficult to study either experimentally or through numerical simulations. The size distribution of rings made up of cations and oxygen atoms is in particular an important parameter when investigating geometrical features in the 5–15 Å range. Usually a ring is characterized by the number of its network-forming cations, which can be derived from the calculated atomic coordinates as shown in Figure 9 for simulated B2O3 and SiO2 glasses. Compared with cristobalite, tridymite, and quartz, whose ring sizes are 6, 6, and 6 and 8, respectively, simulated SiO2 glass shows a broad distribution around 6.

5 Modeling: Simulation Techniques and Examples

0.008

(a) 0.040

0.006 VDOS

Population

0.030 0.020

(C) (A)

(B)

0.004 0.002

0.010 0.000

0 700 0

30

60

90

0.04 0.03 Population

850

900

(cm–1)

Figure 10 Vibrational density of states in simulated B2O3 glass [6]. See text for the assignments of the peaks labeled A, B, and C.

(b)

0.02 0.01

0

30

60

90

Torsion angle (deg)

Figure 8 Torsion angle distribution in simulated B2O3 glass between BO3 and BO3 units (a) and between B3O6 and B3O6 units (b) [6]. Data sampled at 0 K to prevent peaks from being blurred by atomic vibrations.

0.4

Population

800

Wavenumber

Torsion angle (deg)

0.00

750

B2O3

SiO2

0.2

0.0 0

3

6 9 Ring size

12

15

Figure 9 Ring size distribution in simulated B2O3 and SiO2 glasses [11]. Data sampled at 0 K.

It has been speculated that the existence of sizes of oddnumbered rings are characteristic of disordered structures and might impede glass crystallization, because fivefold rotational symmetry does not exist in crystals where four-, six-, and eight-membered rings are primarily observed. In B2O3 glass, which is extremely reluctant to crystallize, the existence of B3O6 units indeed causes the presence of a peak at 3 in the ring statistics. Of more general relevance is the vibrational density of states (VDOS). One can calculate it by solving the eigenvalue problem once the curvature of the energy surface

around the stable configuration is obtained. The VDOS for simulated B2O3 glass is shown in Figure 10, where the peaks labeled A, B, and C represent the vibrations associated with independent BO3 units observed in crystalline B2O3, where B3O6 units are absent, the breathing mode of B3O6 units observed in the crystal of metaboric acid comprised of B3O6 unit, and the vibrations of B3O6 + n units with several BO4 tetrahedra comprised in rings [6], respectively. The VDOS can thus provide important structural information in terms of cooperative motion of structural units. There is another geometrical method relying on the socalled “Voronoi diagram” (e.g. [18]). It is largely employed for monatomic system for which partitioning threedimensional space is simple and easy when the calculated atomic coordinates obtained by atomistic simulations are used to delineate the portion of space assigned to every atom. These “Voronoi polyhedra” are then characterized by their numbers of faces and corners whose distributions change as positional relationships vary in the glass structure. The other geometrical method is called the analysis of “bond orientational order.” The order parameter that is rotationally invariant can be calculated with spherical harmonic functions. This order parameter has been used to investigate a local icosahedral order chiefly for monatomic system, because its value can discriminate geometrical differences between FCC, HCP, icosahedral, and BCC clusters (e.g. [18]). In summary, atomistic simulations provide a key to explaining the concept of “modified random network theory [10]” in alkaline silicate glass [10] or the existence of “super-structural units [19]” in B2O3 glass [6]. However, new analytical methods are required to understand medium-range order in more detail. 5.4

Structure-related Properties

Important thermodynamic properties can be calculated once numerical simulations have yielded atomic

229

230

2.8 Atomistic Simulations of Glass Structure and Properties

configurations and velocities. The pressure is, for example, calculated from Pij =

N 1 kT – V 3V

Σi Σj

j i

f ij r ij ,

24

where the bracket indicates an equilibrium time average and N, V, T, fij, and rij are as usual the number of atoms, cell volume, temperature, and pair force and distance between atoms i and j, respectively. The internal energy (Eint) is E int =

3 kT + Σi Σj 2

j i

f ij r ij ,

25

and the molar heat capacity at constant volume (Cv): Cv =

∂E int ∂T

26 V

Alternatively, one can derive Cv from the potential energy fluctuations through U p2 − U p

2

2 1− 3 2 k Nk 2 T 2 3 Cv

=

27

and two other interesting properties are the thermal expansion coefficient, (αp) αp =

1 V

∂V ∂T

= p

1 T

1 V

1−

∂H ∂p

, T

28 where H is enthalpy, and the thermal pressure coefficient (βV): βV =

∂p V = ∂T

1 T

∂E int ∂V

+P

29

contributions to the construction of structural models. The RDF or the PDF can indeed be readily calculated from the Fourier transform of experimental X-ray, neutron, or electron diffraction data (Chapter 2.2). Because this type of information represents averaged onedimensional structural data, however, there is always some arbitrariness when reconstructing the actual three-dimensional configuration in which one is interested. Other probes such as IR, Raman, or NMR spectroscopies can provide information only on short-range order in glass structure. In contrast, atomistic simulations do provide realistic three-dimensional configuration directly as long as an appropriate atomistic model is employed. One could confidently argue that a structural model of glass is reliable when the model matches the results of both experiments and atomistic simulations. In summary, the relation between atomistic simulation and experiment is complementary because both methodologies provide insights on different aspects of glass structure. Atomistic simulations nonetheless possess two other advantages over experimental methods. The first is that they can determine three-dimensional configurations from short- to medium-range order extending up to the size of cell length (10–100 nm). The second is that a very broad range of atomistic simulations become possible as soon as an appropriate simulation model is established. For example, it is easy to change external conditions such as temperature, pressure, or other external forces to investigate their effects on structure. And physical and chemical properties can be readily derived from the potential-energy and structural models with standard statistical mechanical methods.

T

After a model of atomistic simulation is validated so that it can reproduce static structure of glass, it can be applied to investigate transport and dynamical properties such as diffusion constants, viscosity, or the Van Hove correlation function (Chapter 4.6).

5.5 Experimental and Computational Complementarity The statically arrangement of structural units for B2O3 glass and the dynamically arrangement of structural units for SiO2 glass represent new insights on glass structure provided by MD simulations, in these cases, by the TAD, which escape any experimental determinations. These two examples thus illustrate the complementary nature of numerical simulations and experimental studies of glass structure. When the history of structural studies on glass is looked back on, it is clear that both diffraction and spectroscopic studies have made fundamental

6

Perspectives

Development of both faster computing processors and efficient simulation algorithms have expanded the range of atomistic simulations and narrowed down their discrepancies with experiments. Simulations would nonetheless benefit from improved accuracy. As becoming more common, the best way to achieve this goal is to perform first-principles MD calculation from beginning to end. Although such calculations made with standard quantum mechanical codes remain difficult when dealing with a large number of atoms, progress should result from the use of the so-called order-N and linear scaling methods, which have developed vigorously during the past decade. For oxide glasses, recent codes such as SIESTA or CONQUEST now have the potential ability to handle systems of around one thousand atoms with a supercomputer whereas calculations for systems ten times bigger should

References

become feasible in the next decade. Alternatively, better classical potentials can be derived from the energy data yielded by ab-initio methods as well illustrated by the Tuneyuki and BKS potentials used for silica glass that were based on the simple Buckingham function [4]. Whereas parameter fitting of these potential models was handmade, automatic fitting by machine learning methods is becoming popular since a huge number of data can be sampled on potential energy surfaces yielded by first-principles calculations to derive better interatomic potentials. And even if the simulation remains based on classical mechanics, the shell, polarizable, charge-equilibrium, and other models will be more widely used to reproduce better structures and properties [4]. The two other main limitations of numerical simulations currently concern the space- and timescales considered. To cope with them, combinations of two different techniques may be used as already described in Section 3 for RMC methods. Besides, MC algorithms can be integrated into MD calculations to speed up simulation of too slow structural relaxation as is the case for the formation of boroxol rings in B2O3 [11]. Of more general use, however, is a combination of classical and first-principles MD simulations [20] whereby the former yield a preliminary structure that is subsequently optimized in the latter before spectroscopic or other properties are finally derived from the firstprinciples simulations. The “coarse-graining” methods are also promising as multi-scale simulation procedures. By lumping groups of atoms into larger entities referred to as particles, which interact according to newly parametrized effective interaction potentials, they have been successfully used for polymers to describe slow dynamic modes and to investigate the cooperative motions and fluctuations observed in the intermediate- and long-range regions. For oxide glasses, however, their application is hampered by the difficulty of assigning appropriate structural fragments to coarse-grained units. Finally, it is important for glass scientists to share their know-how on simulation techniques and interatomic potentials. One of such activities takes place in the TC-3 Technical committee of the International Commission on Glass (ICG) where round-robin tests are made to compare experimental data and calculated results on standard glass samples. Such an activity will provide useful information to other glass scientists on agreement and discrepancy between experiments and atomic simulations. Another activity is conducted in TC-27 whose members discuss future directions of atomistic simulations, promote standardization of atomistic techniques, and provide information on these techniques to the glass community (e.g. [21]). In addition, ICG has published an educational

textbook, which includes one chapter on atomistic simulations [22]. In a near future, we strongly expect that any macroscopic property will be explained in terms of microscopic structure by atomistic and first-principles simulations. In addition, computational design of glass materials will advance rapidly in good harmony with experimental studies.

References 1 Zachariasen, W.H. (1932). The atomic arrangement in

glass. J. Am. Chem. Soc. 54: 3841–3851. 2 Bell, R.J. and Dean, P. (1971). The structure of vitreous

3

4 5

6

7

8

9

10

11

12

13

14

silica: Validity of the random network theory. Philos. Mag. 25: 1381–1398. Landau, D.P. and Binder, K. (2000). A Guide to MonteCarlo Simulations in Statistical Physics. Cambridge: Cambridge University Press. Allen, M.P. and Tildesley, D.J. (1987). Computer Simulation of Liquids. Oxford: Oxford University Press. Woodcock, L.V., Angell, C.A., and Cheeseman, P. (1976). Molecular dynamics studies of the vitreous state: Simple ionic systems and silica. J. Chem. Phys. 65: 1565–1577. Takada, A., Catlow, C.R.A., and Price, G.D. (1995). Computer modeling of B2O3: part II. Molecular dynamics simulation of vitreous structures. J. Phys. Condens. Matter 7: 8693–8622. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N. et al. (1953). Equation of state calculations by fast computing machines. J. Chem. Phys. 21: 1087–1092. Greevy, R.L. and Pusztai, L. (1988). Reverse Monte-Carlo simulation: a new technique for the determination of disordered structures. Mol. Simul. 1: 359–367. Kohara, S., Suzuya, K., Takeuchi, K. et al. (2004). Glass formation at the limit of insufficient network formers. Science 303: 1649–1652. Vessal, B., Greaves, G.N., Marten, P.T. et al. (1992). Cation microsegregation and ionic mobility in mixed alkali glasses. Nature 356: 504–506. Takada, A. and Cormack, A.N. (2008). Computer simulation models of glass structure. Phys. Chem. Glasses: Eur. J. Glass Sci. Technol., B 49: 127–135. Soules, T.F. (1990). Stochastic and molecular dynamic models of glass structure. In: Glass Science and Technology, vol. 4A (eds. D.R. Uhlmann and N.J. Kreidl), 267–338. San Diego: Academic Press. Johnson, P.A.V. and Wright, A.C. (1982). A neutron diffraction investigation of the structure of vitreous boron trioxide. J. Non Cryst. Solids 50: 281–311. Xiang, Y., Du, J., Smedskjaer, M.M., and Mauro, J.C. (2013). Structure and properties of sodium

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aluminosilicate glasses from molecular dynamics simulations. J. Chem. Phys. 139: 044507. 15 Stebbins, J.F. (1991). NMR evidence for five-coordinated silicon in a silicate glass at atmospheric pressure. Nature 351: 638–639. 16 Olivier, L., Yuan, X., Cormack, A.N., and Jäger, C. (2001). Combined 29Si double quantum NMR and MD simulation studies of network connectivities of binary Na2O-SiO2 glasses: new prospects and problems. J. Non Cryst. Solids 293-295: 53–66. 17 Huang, L., Duffrène, L., and Kieffer, J. (2004). Structural transition in silica glass: thermo-mechanical anomalies and polymorphism. J. Non Cryst. Solids 349: 1–9.

18 Takada, A. (2018). Voronoi tessellation analysis of SiO2

19

20

21

22

systems based on oxygen packing. J. Non Cryst. Solids 499: 309–327. Wright, A.C., Dalba, G., Rocca, F., and Vedishcheva, N. M. (2010). Borate versus silicate glasses: why are they so different? Phys. Chem. Glasses 51: 233–265. Ferlat, G., Charpentier, T., Seisonen, A.P. et al. (2008). Boroxol rings in liquid and vitreous B2O3 from firstprinciples. Phys. Rev. Lett. 101: 065504. Massobrio, C., Du, J., Bernasconi, M., and Salmon, P.S. (2015). Molecular Dynamics Simulations of Disordered Materials. Heidelberg: Springer. Takada, A., Parker, J., Durán, A., and Bange, K. (2018). Teaching Glass Better. Madrid: Cyan.

233

2.9 First-principles Simulations of Glass-formers Walter Kob and Simona Ispas Laboratoire Charles Coulomb (L2C), University of Montpellier, CNRS, Montpellier, France

1

Introduction

In their early days, i.e. in 1940–1950, computer simulations were mainly done to address questions in statistical physics, such as the properties of hard-sphere systems or the dynamics of simple crystals [1]. When a few decades later computers became more powerful and more accessible, it became possible to study the properties of real materials. For this, researchers used an approach that today is referred to as classical molecular dynamics (MD), i.e. the interactions between the particles that constitute the material are described by an effective potential with a form chosen in a rather ad hoc manner, e.g. Lennard-Jones. The parameters of the potential (e.g. the depth and the position of the well in the Lennard-Jones potential) are selected such that the density, the melting temperature for a crystal, or other macroscopic properties of the simulated system matches experimental data. Once these interactions are known, one solves numerically Newton’s equations of motion and hence obtains the trajectories of all the particles (Chapter 2.8, [1]). From these trajectories, one then can determine physical properties of the system such as the radial distribution function, diffusion coefficients, or elastic constants. Although simulation studies with effective potentials are very valuable to gain qualitative insight into the properties of liquids and solids, they usually do not allow to obtain a good quantitative description. The reason for this failure is that most properties depend in a quite sensitive manner on the potential that describes the interactions between the constituting particles of the material. Since normally these interactions depend not only on the type of atoms considered but also on the microscopic Reviewers: G. Ferlat, Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre and Marie Curie, Paris, France A. Takada, Asahi Glass Company, Yokohama, Japan

environment of the particles (e.g. the bond strength between an oxygen and a silicon will change if a hydrogen is approached to this pair), it is basically impossible to come up with a simple potential-energy expression that could describe faithfully all these different environments. This problem is particularly pronounced for glasses where, in contrast to crystals, each atomic species has multiple local environments. At present, the only method that can address this problem in a systematic manner is the ab initio formalism (also called first-principles). In this approach one does not rely on a fixed functional form for the interaction potential, but uses instead the electronic degrees of freedom of all atoms to compute the forces acting on them in the system. Once these forces are known, one solves Newton’s equation of motion to determine the trajectory of the particles and, subsequently, the properties of the system. Thus a priori the only input needed for these simulations are the species of the particles, a feature that has allowed ab initio simulations to become a highly attractive method to gain a detailed understanding of the properties of glass-forming liquids and glasses. The goal of this review is to give a brief introduction to the method, discuss its advantages but also its problems, and then to present some specific examples showing that this type of simulation is indeed very useful to improve our understanding of glasses at the microscopic scale. We will first focus on structural properties in view of the major problems caused by atomic disorder, especially in complex glasses. Vibrational properties will then be examined as the heat capacity, thermal conductivity, or transparency directly or indirectly depends on them. Because solid-state nuclear magnetic resonance (NMR) yields detailed insights into the local structure of materials (Chapters 2.2 and 2.4), especially when long-range symmetry is lacking, we will conclude this chapter with a brief description of the calculation of NMR spectra.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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2.9 First-principles Simulations of Glass-formers

2

Ab Initio Simulations

2.1 General Principles In the ab initio approach, the forces on the atoms are obtained from the electronic degrees of freedom of the system as determined from the Schrödinger equation, eΨ

= EΨ,

1

where the (complex) many-electron wavefunction Ψ({ri}; {RI}) depends on the positions of the n electrons, {ri}, as well as the positions of the N nuclei, {RI} [2], E is the energy of the electronic degrees of freedom, and the operator e is given by n

e

= −

1 2 ∇ + 2 i i=1

one-particle wavefunctions whose ground states are then searched numerically. Although at present the solution is found in a reasonable amount of time for several tens of atoms, new methods have been proposed in this field with very promising results for systems ten times bigger. The second method, which will now be described in some detail, is the density functional theory (DFT).

n i, j = 1

j> 1, i.e. that four parameters usually suffice for Eq. (7) to be fitted to practically all available experimental viscosity data [17]. Comparison with other viscosity models and numerical calculations have confirmed the excellent description of the viscosity provided by Eq. (7) for simple and complex organic and inorganic compositions (e.g. [13]). This equation can be readily approximated within narrow temperature intervals by expressions derived from the well-known Vogel-Tammann-Fulcher, Adam–Gibbs, Avramov–Milchev, or Sanditov models [14, 15, 17]. It can be used at all temperatures and gives the correct Arrhenius-type asymptotes at high and low temperatures, namely η(T) ~ exp(QH/RT) at T > Tg, where QH = Hd + Hm and QL = Hm. Obviously, the activation energy of viscosity reduces to a low value equal to Hm at high temperatures when temperature fluctuations create plenty of configurons. In contrast, some bonds need to be broken in the glassy state as temperature fluctuations do not create them effectively so that the activation energy then takes its full value QH = Hd + Hm.

5

Structural Factors

Apart from inhomogeneities and potential phase separation, glasses lack long-range order but do possess shortand medium-range ordering (Chapter 2.1). A number of models have aimed at revealing the most characteristic

253

254

3.1 Glass Formation

structural aspects of good glass formers. The most noted structural criterion for ready glass formation, i.e. at rates qc lower than 10 K/s, is based on Zachariasen theory in which the oxide glasses AmOn are assumed to be 3-D networks obeying four rules: (i) the oxygen is linked to two atoms of A; (ii) the oxygen coordination number around A is three or four; (iii) the cation polyhedra share corners; and (iv) at least three corners are shared [18]. This theory is referred to as crystallochemical, but was applicable only to oxide glasses in its original form; it led to the so-called 3-D continuous random network (CRN) model (Chapter 2.1). With respect to a glass and its isochemical crystal, the basic postulates of CRN are that: (i) interatomic forces are similar in both phases; (ii) the glass is in a slightly higher energy state; (iii) nearest-neighbor coordination polyhedra are similar; and (iv) the nature of interatomic bonds is also similar. The strong points of Zachariasen’s model are that it predicts the existence of the main oxide glass formers (SiO2, GeO2, B2O3, P2O5, etc.) and glass modifiers (Na2O, CaO, etc.) and makes room for the distinction between bridging (BO) and non-bridging oxygens (NBO). Its main limitation is that it does not consider at all modified oxides or multicomponent systems, or even non-oxide glasses. In addition, several exceptions to its rules are found as exemplified by alumina-lime glasses and chain-like glass structures (e.g. metaphosphate glasses). Smekal [19] thus developed the concept of the mixing bond nature of (good) glass formers. He noted that pure covalent bonds are incompatible with a random arrangement in view of sharply defined bond lengths and angles. Purely ionic or metallic bonds lack any directional characteristics so that the presence of mixed chemical bonding is necessary for glass formation. Indeed, known glass formers obey this concept: (i) inorganic compounds like SiO2 or B2O3 where the A─O bonds are partly covalent and partly ionic; (ii) elements (S, Se) having chain structures with covalent bonds within the chain and van der Waal’s forces between them (Chapter 6.5); and (iii) organic compounds containing large molecules with covalent internal bonds and van der Waals’ forces between the molecules (Chapter 8.8). Alternatively, Stanworth proposed a criterion for glass formation according to which the electronegativity of cations in oxide glasses falls within a certain range between 1.90 and 2.20 [20]. Although the electronegativity values of the constituent atoms can be used to predict the formation of many glasses, this criterion cannot account for systems when bond strength needs to be considered as a secondary criterion. Sun developed the bond-strength model on the assumption that, when a melt vitrifies, the stronger the metal–oxygen bond, the more difficult the structural

rearrangements necessary for crystallization become and, hence, the easier is glass formation. Glass formation is then ensured by the connectivity of bridging bonds combined with strong bonding between atoms (ions) [21]. Sun thus classified oxides according to their bond strengths so that glass formers form strong bonds with oxygen to yield a rigid network, which results in a high viscosity. He defined modifiers as weakly bonding with oxygen in such a way that they disrupt and modify the network. Without producing glasses on their own, they do form intermediate bonds with oxygen and thus aid vitrification with other oxides. In practical terms, Sun’s energy criterion establishes a correlation between the glass-forming tendency and the strength of the bond between the elements and the anion in the glass. The single bond strength Eb was defined as: Eb =

Ed , CN

8

where CN is the coordination number and Ed the dissociation energy of oxides into their gaseous elements. For B2O3, SiO2, GeO2, P2O5, or Al2O5, the single bond strength of network formers with oxygen is higher than 330 kJ/mol. Values lower than 250 kJ/mol hold for network modifiers such as Li, Na, K, Mg, or Ca whereas intermediate cations such as Ti, Zn, and Pb are characterized by values intermediate between these two figures. For both Zachariasen and Sun models Al+3 is a challenge. Although Al2O3 satisfies Zachariasen’s criteria, it does not form a glass. Likewise, with Ed = 1320–1680 kJ, alumina should be a glass former at a CN of 4 for Al3+ and a modifier at a CN of 6. Sun model was also specific to oxides. It did not account for chalcogenide glasses (Chapter 6.5) with typical bond strength of 170 kJ/mol along the chains (covalent bond) and less between the chains (van der Waals forces). An interesting intermediate class of oxide is formed by TeO2, MoO3, Bi2O3, Al2O3, Ga2O3, and V2O5, which do not vitrify by themselves but will do so when mixed with other (modifier) oxides. Rawson modified Sun’s criteria for glass formation [22] by considering the ratio of the bond strength and energy available at the melting point Tm instead of the coordination number. He noted that glass formation then correlates better with Eb/Tm, being achieved for values of this ratio higher than 0.05 kJ/mol K. The higher this value, the lower the probability for bonds to be broken at Tm, and hence the greater the vitrifiability. Glass formation is thus easier for high bond strength and low melting (liquidus) temperature, which implies that eutectic compositions do favor it. Based on Rawson and Sun approaches, a modified glass-forming criterion termed the Thermodynamic Relative Glass-Forming Ability has recently been proposed in terms of the parameter Eb/Cp Tm, where Cp is the isobaric

6 Glass-Liquid Transition

heat capacity [23], which can be regarded as an extension of Rawson’s criteria. The ordering that results from this model is not convincing, however, and its basic ideas remain to be well justified. Dietzel [24] characterized the ability of cations to enter the network structure by their field strength, which he defined as F=

Z , r2

9

where Z is its valence and r its ionic radius (Å) in the oxide. As listed in Table 2, lower field-strength cations (e.g. alkalis) are network modifiers, whereas ions with higher field strengths (such as Si, P, or B) are network formers. Interestingly, Dietzel model is appropriate for describing phase separation, either through crystallization or unmixing, in cooled binary systems such as SiO2–P2O5, SiO2–B2O3, or B2O3–P2O5. This may generally be the case when the field strengths of two cations are approximately equal since forming a single stable crystalline compound normally requires a difference ΔF greater than 0.3. The number of possible stable compounds increases with ΔF as well as the tendency to form glass. For a binary system, glass formation is likely for Δf larger than 1.33 although this theory is useful to categorize the glass-forming ability of conventional systems, but not universally [25]. Finally, the topological constraints theory introduced by Phillips [26] must also be mentioned. As reviewed in Chapter 2.7, it indicates that the glass-forming tendency is maximized when the number of constraints is equal to the number of degrees of freedom in the structure. In summary, vitrification is favored by high viscosity and configurational complexity. A more complicated chemical composition translates into a greater number of compounds that could nucleate. Owing to mutual competition between these possible crystals, nucleation and growth crystals end up being frustrated. That they do not take place upon rapid cooling thus is a consequence of a confusion principle [8].

6

Glass-Liquid Transition

Structural theories with energetic and microstructural criteria such as topological constraints describe elements that favor glass formation, i.e. the preservation of a topologically disordered distribution of basic elements in glasses. Kinetic theory shows how to avoid crystallization rather than explaining why the vitreous state really forms through the liquid–glass transition – it is at Tg that the “drama” occurs! Although kinetically controlled, the glass transition manifests itself as a second-order phase

transformation in the sense of Ehrenfest classification. Depending on the kind of measurement performed, it is thus revealed either as a continuous change of firstorder thermodynamic properties such as volume, enthalpy, entropy, or as a discontinuous variation of second-order thermodynamic properties such as heat capacity or thermal expansion coefficient across the glass transition range. As indicated by its name, the CPT treats the glass transition as a percolation-type second-order transformation [27]. It pictures it as the disappearance in the glassy state of percolating clusters of broken bonds – configurons. Above Tg, percolating clusters, which are formed by broken bonds, enable a floppier structure and hence a greater degree of freedom for atomic motion so that it results in a higher heat capacity and thermal expansion coefficient. Below Tg there are no extended clusters of broken bonds such that the material has acquired a 3-D structure with a bonding system similar to that of crystals except for lattice disorder. This disordered lattice then contains only point defects in the form of configurons. Agglomerates of fractal structures made of these broken bonds are present only above Tg, which is given by: Tg =

Hd Sd + R ln 1 − ϕc ϕc

10

In this equation Hd and Sd are the quasi-equilibrium (isostructural) enthalpy and entropy of configurons present in Eq. (7) and ϕc is the percolation threshold, i.e. the critical fraction of space occupied by spheres of bondlength diameters located within the bonding sites of the disordered lattice. For strong melts such as SiO2, the percolation threshold in Eq. (10) is given by the theoretical (universal) Scher–Zallen critical density ϕc of 0.15 ± 0.01, which results in a practical coincidence between the calculated and measured Tg values. The parameter Hm has no influence on Tg as it characterizes the mobility of atoms or molecules through the high-temperature fluidity of the melt – see Eq. (7). Because Hd is half of bond strength (Table 2), Eq. (10) shows that the higher this strength, the higher Tg. The vacancy model of the generalized lattice theory of associated solutions provides direct means to calculate thermodynamic properties as well as the relative number of bonds formed in glasses and melts when the second coordination sphere of atoms is taken into consideration [28]. In terms of chemical bonds, an amorphous material transforms to a glass on cooling when the topology of connections changes (Table 3), i.e. when the Hausdorff dimensionality of broken bonds changes from the 2.5 value of a fractal percolating cluster made of broken bonds to the zero value of a 3-D solid. In terms of bonding lattice, the

255

256

3.1 Glass Formation

Table 2 Classification of cations according to Diezel’s field strength.

Element

Valence Z

Ionic distance for oxides, Å

Coordination number

Field strength, 1/Å2

Bond strength, kJ/mol

Si

4

1.60

4

1.57

443

B

3

1.50

3

1.63

498

4

1.34

372

P

4 5

1.55

4

2.1

368–464

Ti

4

1.96

4

1.25

455

4

1.96

6

1.04

304

Al Fe

3

1.77

4

0.96

335–423

3

1.89

6

0.84

224–284

3

1.88

4

0.85

3

1.99

6

0.76

Be

2

1.53

Zr

4

Mg

4

0.86

263

6

0.84

338 255

4

2.28

8

0.77

2

2.03

4

0.53

2

2.10

6

0.45

155

6

0.34

310

2.74

8

0.27

151

2.48

8

0.33

134

2.69

8

0.28

134

2.10

6

0.23

151

1

2.30

6

0.19

84

1

2.77

8

0.13

54

12

0.10

42

Pb

2 2

Ca

2

Sr

2

Li

1

Na K Cs

1

Table 3 Hausdorff dimensionality of the bonding system at glass transition. Below Tg (glasses)

Above Tg (supercooled melts)

Broken bonds – configurons

0

2.5a

Chemical bonds backbone cluster

3

3

Chemical bonds

3

2.5a

Amorphous material

a

Experimental dimensionality – 2.4–2.8.

transition from the glass to the liquid upon heating may be explained as a reduction of the topological signature (i.e. Hausdorff dimensionality [29]) of the disordered bonding lattice from 3 for a glass (3-D bonded material) to the fractal Df of 2.4–2.8 of the melt. These are the main changes that account for the drastic variations in material properties at glass-to-liquid transition [27].

Function

Network formers: F~1.5–2.0

Intermediates: F~0.5–1.0

Network modifiers: F~0.1–0.4

Most experimental Tg data have been obtained by differential thermal analysis (DTA), differential scanning calorimetry (DSC), or dilatometry [30], where Tg is generally defined as the temperature at which the tangents to the glass and liquid curves of the relevant property intersect (Chapter 3.2). Heating (cooling) rates for DTA/DSC measurements are typically as high as 10 K/min whereas they are in 3–5 K/min range in dilatometry. As already stated, the glass transition is not abrupt but typically occurs over a few tens of degrees. For not very high cooling rates (q), its dependence on q is given by the Bartenev–Ritland equation: 1 = a1 − a2 ln q, Tg

11

where a1 and a2 are empirical constants. Although Eq. (11) also results from CPT, it should be replaced by a generalized version at high cooling rates [31]. In addition, CPT predicts that the transition takes place not as a sharp discontinuity, but over a finite temperature

6 Glass-Liquid Transition

a true phase transformation although as a nonequilibrium one. The liquid transforms in a continuous way into a glass, which behaves mechanically as a crystalline solid when the motions of atoms become very much frustrated below Tg where the extensive clusters of broken bonds of the liquid are no longer present. The degree of frustration then is actually the same as in a 3-D crystalline material so that the heat capacity does not show the same high rate of change as in the liquid. This feature is clearly seen both in experiments and as an outcome of the CPT concept (Figure 5). Importantly, CPT yields a universal law for

700

S (J/mol K)

a yst

Solid Tk

0

500

1000 T(K)

1500

2000

60

40

40

20

20

350

300

l

Cr

Figure 4 Entropy of the amorphous and crystalline phases of diopside, CaMgSi2O6. Source: After [8]. The liquid transforms into a glass below Tg, therefore the entropy of condensed phase (upper curve) does not follow the dashed line which is an extension of liquid entropy curve below Tg.

80

320

400

0

80

280 Temperature (K)

ΔSf

100

100

240

The liquid transforms to a glass s as Gl

200

100

0 200

Liquid Tg

500

120

60

CaMgSi2O6

600

120

Cp (cal/mol K)

Cp (cal/mol K)

interval where the properties of the material depend on time as well as on thermal history. Following the analysis of [8], we may ask why viscous liquids eventually vitrify instead of remaining in the supercooled liquid state when they escape crystallization. One answer to this question is purely kinetic and relies only on increasingly long relaxation times or increasing viscosities on cooling. The glass transition would result only from the limited timescale of feasible measurements so that any glass would eventually relax to the equilibrium state if experiments could last forever. In fact, a simple thermodynamic argument proposed by Kauzmann [32] indicates that this answer is incorrect. The reason originates in the existence of a configurational contribution that causes the heat capacity of a liquid to be generally higher than that of a crystal of the same composition. As a consequence, the entropy of the liquid decreases on cooling faster than that of the crystal (Figure 4). If the entropy of the supercooled liquid were extrapolated to temperatures much below Tg, it would become lower at a temperature TK than that of the crystal. Because it is unlikely that an amorphous phase could ever have a lower entropy than an isochemical crystal, the conclusion known as Kauzmann’s paradox is that an amorphous phase cannot exist below TK. The temperature of such an entropy catastrophe constitutes the lower bound to the metastability limit of the supercooled liquid. As internal equilibrium cannot be reached below TK, the liquid must undergo a phase transition before reaching this temperature. This is, of course, the glass transition, and Kauzmann’s paradox suggests that, although it is kinetic in nature, it anticipates a thermodynamic transition. In other words, CPT treats the glass transition as

0 200

240

280 Temperature (K)

320

350

Figure 5 Comparison between the heat capacities of amorphous o-terphenol measured and calculated with configuron percolation theory. Source: After [3].

257

258

3.1 Glass Formation

susceptibilities such as heat capacity or thermal expansion near Tg [3, 27]: Cp, α

1 Zarzycki, J. (1982). Glasses and the Vitreous State.

1 T − Tg

References

0 59

12

A last feature deserving to be mentioned is the “universal” dependence of the light scattering intensity on the time after a temperature jump in the glass transition range of oxide glasses, which is known as the Bokov effect [33]. The intensity displays a maximum whose height and location on the timescale depends on the previous history of the glass. The Bokov effect is associated with nonequilibrium fluctuations produced by coupling between hydrodynamic modes. Detailed investigations in the past decade have demonstrated that similarities observed in the glass transition region of oxides and polymers account for structural transformations related to the formation of spatially extensive structures, which in turn could be related to clustering effects similar to that envisaged by CPT and other similar models. The Bokov effect thus is providing additional arguments to characterize the glass transition as a second order like phase transformation rather than simply as a slowing down of dynamic processes.

Cambridge: Cambridge University Press. 2 McNaught, A.D. and Wilkinson, A. (eds.) (1997). The

3

4 5

6

7 8 9 10

7

Perspectives 11

Understanding vitrification mechanisms is of great importance either practically or theoretically. Although progress made in this respect has been very impressive, many of the questions remain unresolved. Among them, a central one is that of the glass transition itself, which has a pronounced relaxational, kinetic character in spite of its similarity with a second-order phase transition in the Ehrenfest sense with volume and entropy continuity, but discontinuities of their derivatives that are used in practice to detect Tg. Discussion about the nature of glass continues. After some lull it has gathered new momentum, especially in the second decade of the new century as the microscopic mechanisms generating the glassy state of matter are still debated. Future developments could be based on computer modeling that does also show the appearance of discontinuities in derivative thermodynamic parameters at the glass transition.

12 13 14 15 16

17

18

Acknowledgements 19

The author acknowledges help and advice from R. Doremus, V.L. Stolyarova, P. Poluektov, E. Manykin, W.E. Lee, P. James, R.J. Hand, K.P. Travis, G. Moebus, J.M. Parker, A. Varshneya, O.V. Mazurin, M. Liska, J. Marra, C.M. Jantzen, R. Tournier, C.A. Angell, and D.S. Sanditov.

20 21

IUPAC Compendium on Chemical Terminology. Cambridge: Royal Society of Chemistry. Ojovan, M.I. and Lee, W.E. (2006). Topologically disordered systems at the glass transition. J. Phys. Condens. Matter 18: 11507–11520. Schairer, J.F. and Bowen, N.L. (1956). The system Na2OAl2O3-SiO2. Am. J. Sci. 254: 129–195. Tangeman, J.A., Phillips, B.L., Navrotsky, A. et al. (2001). Vitreous forsterite (Mg2SiO4): synthesis, structure, and thermochemistry. Geophys. Res. Lett. 28: 2517–2520. Richet, P., Roskosz, M., and Roux, J. (2006). Glass formation in silicates: insights from composition. Chem. Geol. 225: 388–401. Sakka, S., Sakaino, T., and Takahashi, K. (eds.) (1975). Glass Handbook. Tokyo: Asakura Publishing Co. Mysen, B.O. and Richet, P. (2005). Silicate Glasses and Melts. Properties and Structure. Amsterdam: Elsevier. Varshneya, A.K. (2006). Fundamentals of Inorganic Glasses. Sheffield: Society of Glass Technology. Uhlmann, D.R. (1972). A kinetic treatment of glass formation. J. Non Cryst. Solids 7: 337–348. Cohen, M.H. and Turnbull, D. (1961). Composition requirements for glass formation in metallic and ionic systems. Nature 189: 131–132. Doremus, R.H. (2003). Melt viscosities of silicate glasses. Am. Ceram. Soc. Bull. 82: 59–63. Volf, M.B. (1988). Mathematical Approach to Glass. Amsterdam: Elsevier. Ojovan, M.I. (2012). Viscous flow and the viscosity of melts and glasses. Phys. Chem. Glasses 53: 143–150. Zheng, Q. and Mauro, J.C. (2017). Viscosity of glassforming systems. J. Am. Ceram. Soc. 100: 6–25. Angell, C.A. and Rao, K.J. (1972). Configurational excitations in condensed matter, and the “bond lattice” model for the liquid-glass transition. J. Chem. Phys. 57: 470–481. Ojovan, M.I., Travis, K.P., and Hand, R.J. (2007). Thermodynamic parameters of bonds in glassy materials from viscosity temperature relationships. J. Phys. Condens. Matter 19: 415107. Zachariasen, W.H. (1932). The atomic arrangement in glass. J. Am. Chem. Soc. 54: 3841–3851. Smekal, A. (1951). On the structure of glass. J. Soc. Glass Technol. 35: 411–420. Stanworth, J. (1952). Tellurite glasses. J. Soc. Glass Technol. 36: 217–241. Sun, K.-H. (1947). Fundamental condition of glass formation. J. Am. Ceram. Soc. 30: 277–281.

References

22 Rawson, H. (1967). Inorganic Glass-Forming Systems. 23

24 25 26 27 28

London: Academic Press. Boubata, N., Roula, A., and Moussaoui, I. (2013). Thermodynamic and relative approach to compute glassforming ability of oxides. Bull. Mater. Sci. 36: 457–460. Dietzel, A. (1948). Glasstruktur und Glaseigeschaften. Glastech. Ber. 22: 41–50. Vogel, W. (1994). Glass Chemistry, 2e. New York: Springer. Phillips, J.C. (1979). Topology of covalent non-crystalline solids I. J. Non Cryst. Solids 34: 153–181. Ojovan, M.I. (2013). Ordering and structural changes at the glass-liquid transition. J. Non Cryst. Solids 382: 79–86. Stolyarova, V.L. (2008). Thermodynamic properties and structure of ternary silicate glass-forming melts: experimental studies and modelling. J. Non Cryst. Solids 354: 1373–1377.

29 Mandelbrot, B.B. (1982). The Fractal Geometry of

Nature. San Francisco: W. H. Freeman and Co., 460pp. 30 Mazurin, O.V. and Gankin, Y.V. (2008). Glass transition

temperature: problems of measurement procedure. Glass Technol. 49: 229–233. 31 Sanditov, D.S. and Ojovan, M.I. (2017). On relaxation nature of glass transition in amorphous materials. Physica B 523: 96–113. 32 Kauzmann, W. (1948). The nature of the glassy state and the behaviour of liquids at low temperatures. Chem. Rev. 43: 219–256. 33 Bokov, N.A. (2008). Non-equilibrium fluctuations as a plausible reason of the light scattering intensity peak in the glass transition region. J. Non Cryst. Solids 354: 1119–1122.

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261

3.2 Thermodynamics of Glasses Jean-Luc Garden and Hervé Guillou CNRS, Institut Néel and Université de Grenoble Alpes, Grenoble, France

1

Introduction

Thermodynamics states that the properties of a system in equilibrium depend neither on time nor on past history. Glasses clearly violate this postulate. Not only do their properties depend on history but they also vary with time at temperatures at which relaxation toward internal thermodynamic equilibrium does occur, but at a rate slow enough to be observable at the timescale of the experiment performed. To deal with glasses, thermodynamics must thus consider nonequilibrium states and their actual cause, namely the irreversibility of the transition that occurs when relaxation times eventually become much longer than experimental timescales such that the material freezes in as a glass. Much attention is currently paid to the processes driving the glass transition at a microscopic scale and also to their implications for the macroscopic properties of glasses. Because this topic is extensively discussed in this chapter, we will deal here with a second fundamental issue, namely that of the phenomenological approaches followed to understand the observable macroscopic properties of glasses and, thus, to design new applications. To quote a single example, density gradients in tempered glasses are the key to thermal strengthening, which is achieved irreversibly upon cooling (Chapter 3.12). In this chapter, the basic concepts of macroscopic nonequilibrium thermodynamics will first be summarized and illustrated with experimental heat capacities for a model system, PolyVinylAcetate [PVAc, (C4H6O2)n]). The basic concepts of equilibrium and nonequilibrium will then be introduced to point out why glasses challenge Reviewers: M.A. Ramos, Laboratorio de Bajas Temperaturas, Universidad Autónoma de Madrid, Spain A. Saiter, Physics of Materials Group, University of Rouen, Saint-Etienne du Rouvray cedex, France

the laws of thermodynamics. Next, properties of the supercooled liquid state above Tg will be presented and the phenomenology of the glass transition examined in the light of calorimetric data, in particular in terms of configurational properties. The basics of nonequilibrium thermodynamics in the glass transition range will finally be reviewed along with the issue of aging below the glass transition range.

2 Basics of Nonequilibrium Thermodynamics In thermodynamics one investigates the changes occurring when a system passes from a state A to another state B. At constant chemical composition, the system is in internal equilibrium if its state is defined by only two macroscopic variables such as temperature (T), pressure (P), volume (V), enthalpy (H), internal energy (U), or Gibbs free energy (G). Their values are not only constant but independent of the pathway actually followed between any two states A and B. As stated by the First Law of thermodynamics, between A and B the internal energy varies as: ΔU A

B

= QA

B

+ WA

B,

1

where QA B and WA B are the heat and work exchanged by the system with its surroundings, respectively. Likewise, the entropy is decomposed into two parts, ΔS A

B

=

QA T

B

+ Δi S A

B,

2

where the first represents the heat exchanged with the surroundings and the second the entropy created within the system itself during the transformation.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

262

3.2 Thermodynamics of Glasses

explained by simple statistical mechanical models, the very concept of residual entropy has recently been debated [3]. On the assumption that ergodicity must hold for the entropy to be defined, the proponents of a kinetic view have claimed that the configurational entropy undergoes an abrupt jump at the glass transition in order to reach the zero value of the crystal entropy at 0 K. In contrast, the proponents of the conventional view have stressed that what matters is not time averages but spatial averages of configurational microstates [3], which is the reason why the measured residual entropies do make sense physically and correlate with the specific structural features of glasses and disordered crystals. By definition, equilibrium thermodynamics cannot alone account for fundamental questions raised when relaxation is too slow with respect to experimental timescales. Owing to the kinetic nature of the problem, use has been made of the formalism originally developed for the kinetics of chemical reactions by De Donder and his school [4]. With values increasing as the reaction proceeds, a new variable, the advancement of reaction, ξ(t) is defined to characterize the state of the system as a function of time, t, such that the reaction rate is simply dξ(t)/dt. This extensive variable, expressed in mol, accounts for the distribution of matter (local mass or density variation), or the molecular structure, within the system at any time. A new state function, the affinity, A, is then introduced to relate ξ(t) to the driving force of the reaction, its Gibbs free energy (at constant T and P):

If two equilibrium states are connected by a reversible process, then ΔiSA B = 0. If the system undergoes instead an irreversible process through which it falls out of equilibrium, then ΔiSA B > 0 since a spontaneous process is always associated with an entropy increase of the system. Upon glass formation by cooling, pressure increase, or other means, the equilibrium liquid is continuously losing internal equilibrium. As will be discussed here, the question arises as to whether there is any finite production of entropy and – if so – whether this quantity is of importance regarding the other terms involved in the process. The Third Law of thermodynamics postulates that the entropy of a perfectly ordered system is zero at 0 K. In contradiction with it, however, calorimetric measurements indicate that glasses not only possess nonzero entropies at 0 K but that this residual entropy depends on thermal history as illustrated by a simple entropy cycle calculated from measured heat-capacities and entropy of fusion (ΔSf). Beginning with a perfectly ordered crystal, whose entropy thus is 0 at 0 K, one derives the entropy of the crystal at its congruent temperature of fusion Tf, then that of the melt from this temperature down to the glass transition, and finally that of the glass down to 0 K (Figure 1). The difference S0 between this entropy and that of the crystal at 0 K is the residual entropy (Table 2), which increases with higher glass transition temperatures and, thus, with higher cooling rates, reflecting the increasingly wide distribution of configurational states obtaining with increasing temperatures. A finite residual entropy at 0 K might seem to contradict the Third Law of thermodynamics. As justified by Jones and Simon [1], however, there is no contradiction because this law applies only to crystals and other systems in internal equilibrium, which are necessarily ordered at 0 K to minimize their Gibbs free energies. This is not the case of glasses, which do obey the Nernst theorem [2] since they cannot pass from one entropy state to another at 0 K (ΔS = 0 for two neighboring glassy states at 0 K). Although such determinations also made for partially disordered crystals like ice Ih or CO have long been

A P t ,T t ,ξ t

Supercooled liquid

Liquid at equilibrium

Glass with a higher fictive temperature

Crystal at 0 K S = 0 J/K TK

Tg

− ∂G ∂ξ

3 P,T

The affinity A, expressed in J/mol, is the intensive conjugate variable of ξ. All time dependences are thus embedded into the time variations of the internal parameter ξ, or A, and of the other variables that are controlled experimentally (e.g. T, P). For a relaxing system, the instantaneous entropy production was simply written by De Donder as the product of the thermodynamic force and the corresponding flux [4],

S

Glass at 0 K ΔS0

=

Tm

T

Figure 1 Entropies of the crystal, liquid, supercooled liquid and glass phases of a substance.

3 Supercooled Liquids

Table 1 Thermodynamic states in terms of affinity and its derivatives and in terms of rate of advancement of the process. Rate of advancement dξ/dt (extensive, mol/s) Affinity A (intensive, J/mol)

A = 0 and dA = 0

dξ/dt = 0

dξ/dt

0

True equilibrium; liquid state; σ i = 0

Unphysical

Isomassic state; σ i = 0

False equilibrium; nonequilibrium state; σ i = 0

A

0 and dA = 0

Isomassic, isoaffine state; σi = 0

Isoaffine state; σ i

A

0 and dA

Nonequilibrium; glassy state; σ i = 0

Nonequilibrium; viscous state; σ i 0

A = 0 and dA

0

0

0

Liquid, glass, and relaxing liquid states are indicated by gray cells. The other cells indicate particular states that can be encountered or not during the glass transition. The value of the rate of production of entropy is indicated in each cell.

σi =

di S A dξ = × , dt T dt

4

where the thermodynamic force actually is A/T, for the sake of dimensional analysis (the entropy production being in W/K). Regarding the glass transition, the problem boils down to know A and ξ (or dξ/dt) and how they evolve with time. Depending on the values of both parameters, however, at this point several cases must be distinguished because not all of them are relevant (Table 1). The first and simplest case is that for which both A and dξ/dt are zero. It is that of the equilibrium liquid, which will thus be first considered in its metastable, supercooled extension.

3

Supercooled Liquids

Although the liquid state is generally far from simple, it can be considered as an equilibrium reference at viscosities (η) low enough that flow is easy, i.e. at high-enough temperatures at the pressure considered. In that case, the diffusion of microscopic entities, be they molecules or atoms, obeys the Stokes-Einstein relation, which relates the diffusivity D to the temperature and viscosity with: D=

kBT , Cη

5

where the coefficient C is a geometrical factor fixed by the boundary condition of the flow. From its position at time t0, a diffusing entity travels a kind of random walk over an average distance d D t − t 0 as a function of time. For low-viscosity liquids and high temperatures, D is high so that entities explore a great many different positions and configurations in a time shorter than that needed to perform a physical measurement. They do it through degrees of freedom that include not only thermal motions of translation,

rotation, and vibration but also the complex kinds of atomic motions collectively termed configurational, which are governed by strong short-range repulsions and long-range attractions in molecular liquids. The measurement then averages out all these configurations. Picturing these motions at a microscopic scale is difficult, however, especially for complex liquids or melts with various interacting entities. In various types of glass-forming liquids [5], local order can nonetheless be described in terms of degree of polymerization, formation of channels or sublattices, or formation of interpenetrating networks. Like the advancement of a chemical reaction, such structural features may be described in terms of the aforementioned parameter ξ. In internal thermodynamic equilibrium, i.e. in the liquid state, ξ is equal to ξeq(T,P), but not in the glass transition range where ξ(t) becomes a function of T(t), P(t), and A(t), revealing its nonequilibrium nature. Below the glass transition range, where the relaxation time of the configurational degrees of freedom exceeds the experimental timescale, they cease to contribute to the measured property. At temperature low enough, the structure then eventually freezes in for good in one state defined by one particular value of ξ(t), which becomes independent of the external parameters T and P. From a practical standpoint, the timescale defined by the viscosity of the material is important to determine the temperature at which the system will fall out of equilibrium when observed at the timescale of a particular experiment. There is not yet a unique model for describing relaxation phenomena in all glass-forming liquids (Chapter 3.7), whether strong or fragile with Arrhenian or non-Arrhenian viscosities, respectively [6]. In measurements of macroscopic properties, one nonetheless considers generally that experimental timescales τexp are of the order of τexp~102 – 103 seconds. The viscosity should then be of the order of 1012 Pa.s or 1013 P for structural relaxation to be complete under these conditions. To stress the usually tremendous variations of

263

3.2 Thermodynamics of Glasses

viscosity down to the glass transition, it will suffice to note that the viscosities of stable liquids (i.e. above the melting or liquidus temperature) range from 10−3 to 102 Pa.s depending on chemical composition and structural type.

4 Glass as a Nonequilibrium Substance Time-dependent effects appearing at the glass transition are clearly observed in the heat capacities measured for PVAc (Figure 2), which is a model polymeric system extensively studied because of its excellent glass-forming ability and standard Tg close to room temperature. The observed hysteresis loop between cooling and heating demonstrates that the heat capacity does not only depend on T and P but also on time. Moreover, upon heating, the heat capacity shows a typical overshoot, i.e. an endothermic event, named structural recovery process. To come back to the initial liquid state, the system needs to recover the amount of internal enthalpy that has previously been lost. From such measurements, it is possible to determine the configurational contribution to the heat capacity ΔC conf P . Here, it is defined by the difference at every temperature between the heat capacities actually measured and estimated for the glass phase: g

ΔC conf = CP − CP P

6

This type of definition also applies to other thermodynamic variables such as the thermal expansion coefficient αP, or the isothermal compressibility κT. A configurational contribution consequently represents the thermodynamic contribution that originates in configurational changes in the liquid. The glassy state then is defined as that for which the configurational movements have been frozen-in, i.e.

ΔC conf = 0 . In this state, only the vibrational motions, P i.e. the fast degrees of freedom (faster than the experimental timescale), contribute. To define this contribution over the entire temperature interval of interest, an extrapolation of the glass heat capacity from low to high temperatures is needed (Figure 2). The heat capacity of the supercooled liquid can also be extrapolated toward low temperatures (Figure 2). The difference between these values for the supercooled liquid and the glass, g

ΔC conf,eq = C lP − C P P

ΔH conf T =

T T1 T

conf ΔC conf T P dT and ΔS

ΔC conf P dT , = T T1

8

where T1 = 360 K is in Figure 2 an arbitrarily selected reference temperature. Absolute values of both state functions could be obtained from the enthalpy and entropy of an isochemical crystalline compound through the crystallization values of these functions (see Figure 1). For lack of such a compound for PVAc, only relative values are thus presented (Figure 4) in such a way that both the actual and equilibrium values are equal from 360 K to the temperature of about 315 K at which internal equilibrium is lost. Since these variations are similar for the configurational enthalpy and entropy, only the former is shown in Figure 4. Figure 2 Heat capacity of PVAc measured across the glass transition range by differential scanning calorimetry at the same rate of 1.2 C/min first upon cooling (solid circle) and then upon heating (empty circle). Dashed lines: fits made from the heat capacities measured for the glass and supercooled liquid.

0.70 0.65 0.60 0.55 0.50 0.45 0.40 280

7

then yields the equilibrium configurational contribution, which keeps increasing below Tg even though the actually observed values do vanish (Figure 3). From the equilibrium and actual configurational contributions, the variation of the configurational enthalpy ΔHconf and entropy ΔSconf, taken between two temperatures, are calculated with:

0.75

Cp (J/K)

264

290

300

310

320 T (K)

330

340

350

360

4 Glass as a Nonequilibrium Substance

Figure 3 Configurational heat capacity of PVAc across the glass transition range upon cooling: configurational contribution (solid circle) and equilibrium configurational contribution (empty circle).

0.20

ΔCpconf (J/K)

0.15

0.10

0.05

0.00

–0.05 280

290

300

310

320

330

340

350

360

T (K)

0 –2 –4 –6

–5 –6

–8 –10

ΔHconf (J)

ΔHconf (J)

Figure 4 Difference between the configurational enthalpy of PVAc and a zero reference-value taken at 360 K. Actual value (solid circle) and equilibrium value (empty circle). Inset: magnification of Figure 4 showing extrapolated values of the glass and supercooled liquid of this differential configurational enthalpy intersecting at the point M, which defines the limiting fictive temperature TM = Tf .

Aging

–12

Contrary to their equilibrium counterparts, which continue to decrease upon cooling, both the actual configurational enthalpy and configurational entropy level off in the amorphous state (Figure 4). Owing to the large width of the glass transition range, the heat capacity variations at the glass transition are much too smooth to be interpreted as reflecting the discontinuity of a second-order phase transition. Such a discontinuity can nonetheless be identified at a temperature TM defined by the intersection of the extrapolated glass and supercooled liquid (Figure 4, inset). Both configurational enthalpy and entropy are thus continuous at that temperature, which separates the glass from the supercooled liquid. The same applies to other properties such as volume. Because entropy and volume are the first derivatives of the Gibbs free energy with respect to temperature and pressure, respectively, the following relations initially derived by Ehrenfest should hold when second-order derivatives of the free energy vary discontinuously at this point M:

M

–8

–9 Tʹf –10 295 300 305 310 315 320 325 T (K)

–14 –16 280

–7

290

300

dP dT dP dT

310

330

340

350

360

=

ΔαP Δκ T

9a

=

ΔC P T M V M ΔαP

9b

M

M

320 T (K)

To express these equations in terms of discontinuities of equilibrium configurational contributions at TM, e.g. of Eq. (7), Prigogine and Defay [7] assumed that ΔC conf,eq P the supercooled liquid is in internal equilibrium down to TM (i.e. A = 0 and dA = 0) whereas the glass below TM is defined by dξ = 0. These two equalities can then be grouped to yield the so-called Prigogine–Defay (PD) ratio [7]: Π=

ΔC P ΔκT T M V M ΔαP

2

10

265

266

3.2 Thermodynamics of Glasses

Table 2 Thermodynamic parameters measured from five different glass-formers. Material

Tg (K)

ΔS0 (J/K/mol)

PD ratio

TK (K)

T0 (K)

SiO2

1480

5.1

>103

1150

CaAl2Si2O8

1109

36.2

1.5–22

815

NA Arrhenius relaxation 805

Glucose

305

1.7

3.7

241

242

PVAc

301

2.2

239

250

Glycerol

183

NA No crystal 19.4

3.7

134

123

Se

295

3.6

2.4

207

226

The values are taken from the literature.

Although considering an internal parameter ξ, this approach assumes that the glass transition occurs continuously at TM where ξg = ξl. If so, it would follow from Eq. (9) that the PD ratio should be unity. As indicated by the values listed for widely different glass-forming liquids (Table 2), however, calculated PD ratios are higher or even much higher than unity. One can explain such values by taking into account the kinetic nature of the glass transition [8]. Physically, it is making sense to assume that isobaric temperature derivatives such as ΔCP or ΔαP are not measured under the same kinetic conditions as an isothermal pressure derivative like ΔκT. Whereas this inconsistency may be removed if more than one internal order parameters ξ are involved in the thermodynamics of the glass transition [9], the problem may in contrast be compounded by the uncertainties arising from the extrapolation procedures used for deriving the relevant parameters at the temperature TM. Another puzzling fact has been long ago pointed out by Kauzmann [10] who wondered what would happen if the entropy of a supercooled liquid were extrapolated down to temperatures much lower than the experimentally observed Tg. The conclusion was that it would become lower than that of the isochemical crystal at a temperature TK, thus termed the Kauzmann temperature (Table 2), which could suggest that the liquid undergoes a continuous phase transition toward the crystalline phase at TK analogous to the critical point of fluids. One way out of the paradox implies kinetic arguments and assumes that the viscosity of the supercooled liquid diverges at a temperature close to TK. This assumption may be represented by the Vogel–Fulcher–Tammann (VFT) equation (Chapter 4.1): η = A exp

B , T − T0

11

where the temperature T0 of the viscosity divergence is actually close to the Kauzmann temperature (Table 2)

even though they may depend on the specific sample and the method of measurement. Another way out is to take with great caution the extrapolations of the heat capacity and other thermodynamic functions of the supercooled liquid. As long pointed out [e.g. 11], there is no current theory for these properties in liquid state analogous to the Einstein or Debye models that provide functional forms at all temperatures for heat capacities of crystals. As derived from strikingly old questions in glass science, these counterintuitive features indicate that glasses cannot be described by equilibrium thermodynamic states only. Nonequilibrium thermodynamics is, therefore, likely to be useful to characterize glasses and the glass transition.

5 Nonequilibrium Thermodynamics of the Glass Transition The questions raised by the Kauzmann paradox or the PD ratio clearly illustrate the need for a more fundamental thermodynamic description of the glass transition. Following the pioneering work of Tool [12, 13] and Davies and Jones [9], different approaches and phenomenological models have been developed to deal with the glass transition range itself, many within the framework of classical nonequilibrium thermodynamics [4, 11]. The starting point has been the phenomenological concept of fictive temperature (Tf) propounded by Tool [12, 13] to characterize the state of a relaxing system at any time. This temperature is similar to an order parameter ξ. It thus overcomes the limitations of the fixed limiting temperature TM, which characterizes only the point at which internal equilibrium is suddenly lost in a quenched state. On an analogous basis, a more detailed description is made in terms of two-temperature thermodynamics [14] whereby the vibrational and configurational degrees

5 Nonequilibrium Thermodynamics of the Glass Transition

of freedom are distinguished by a “classical” temperature for fast modes (phonons bath), and an effective temperature for the slow modes, respectively. The first physical models have then relied on two different approaches. In free-volume theories, one generally considers that the dynamics of the system is determined by the free space present around its atoms, which makes configurational rearrangements more or less easy. In entropy theories, among which that of Adam-Gibbs is the best known [15], the same determining role is attributed to configurational entropy. In other words, these theories assign the strong increase of relaxation times with decreasing temperatures and the eventual structural freezing in to decreases of either free volume or configurational entropy. Other more recent theories of the glass transition rely on mode coupling, random first-order transitions or energy-landscape descriptions [e.g. 16]. These different approaches have the common goal of finding the exact expression for the structural relaxation time, or its distribution, as a function of controlling parameters such as temperature or pressure, or structural order parameter. For the sake of simplicity, let us consider here conditions of constant pressure. If the additional parameter ξ is taken into account, the total differential of the enthalpy of a system can be written as the sum of two contributions (considering pressure, the generalization to three contributions would be obvious): dH

P

=

∂H ∂T

dT + P,ξ

∂H ∂ξ

dξ

12

P,T

The isobaric heat capacity is written as: Cp =

dH dT

= P

∂H ∂T

+ P,ξ

∂H ∂ξ

P,T

dξ dT

P

13 The first term on the right-hand side is the heat capacglass ity at constant ξ, i.e. C P , and the second, the configurational contribution ΔC conf as defined by Eq. (6). To P account for the kinetic nature of the glass transition, it is then necessary to rewrite Eq. (13) as: CP =

∂H ∂T

+ P,ξ

∂H ∂ξ

P,T

dξ dt dT dt

14 P

When the rate of change of ξ becomes much smaller than the rate of change of temperature, (dξ/dt)P (dT/ dt)P, the configurational contribution is negligible. Hence, it is the ratio between these two rates that is controlling the relative value of the experimentally recorded configurational heat capacity. This ratio is maximum in the supercooled liquid state, and decreases throughout the glass transition range to become

negligible in the glassy state (cf. Figure 3). There, only the first right-hand side term in Eq. (14) contributes: glass

C P,ξ = C P

< C P < C eq P

= C liquid or 0 < ΔC conf < ΔC conf,eq P P P

15

The next step thus consists in taking into account the time dependence of ξ at every temperature through the temperature dependence of the relaxation time τ. The simplest way to do this is to assume a simple exponential decay for ξ at fixed temperature and pressure: ξ − ξeq dξ = − , dt τ

16

where ξeq(P,T) is the equilibrium value of the order parameter, i.e. a variable characterizing the liquid structure that depends only on P and T. Although the relaxation time itself has been given different temperature dependences with Arrhenius, VFT, or others laws (Chapter 3.7), the important point is that they are all of an exponential nature with respect to T or P to ensure the structural freezing-in of the system. Interesting applications of these concepts have been made with the lattice-hole model of liquids, which has the advantage of lending itself to an evaluation of the order parameter ξ. Schematically, this model considers a liquid as a lattice in which disorder is represented by unoccupied sites whose fraction x depends on both temperature and pressure [17]. From the equilibrium value of the order parameter, it is thus possible to solve the linear differential Eq. (16) to find its temperature dependence and, then, to calculate the variations of the heat capacity within the glass transition range under varied conditions [18]. Likewise, the configurational Gibbs free energy may also be computed analytically as a function of temperature, pressure, and order parameter. A similar approach has been followed to incorporate the effects of pressure in the expression of the structural relaxation time for determining also how the heat capacity, thermal expansion coefficient, and isothermal compressibility vary under different conditions [19]. From the configurational Gibbs free energy calculated for the lattice-hole model, one readily simulates with the definition (3) of the affinity its variations upon vitrification (cooling) and structural recovery (heating) [19]. Thermodynamic data measured on o-terphenyl may be used to simulate the corresponding affinities during temperature ramps (Figure 5): cooling at 0.3 K/min from an initial temperature of 255 K is followed by heating at the same rate, and then by further cooling at 0.5 K/min preceding final heating at 20 K/min. That the supercooled liquid begins to lose internal equilibrium from 248 K is indicated by the departure at this temperature of the affinity curve from the zero line, which represents the

267

3.2 Thermodynamics of Glasses

Figure 5 Simulated affinities of o-terphenyl in the glass transition range upon cooling and heating as calculated from the lattice-hole model. Solid circle for −0.3 K/min and solid square for −0.5 K/min; empty circle for +0.3 K/min and empty square for +20 K/min. The horizontal line represents equilibrium (A = 0). Inset: entropy production rates calculated from the previous affinities. Solid circle upon cooling and empty circle upon heating.

0.05

0.00 3.0

1e–7

2.5

–0.05

σi (W/mol/K)

A/RT

268

–0.10

2.0 1.5 1.0 0.5 0.0

–0.15 235

240

236 238 240 242 244 246 248 250 T (K)

250

245 T (K)

maximum (equilibrium) value of the affinity during cooling. The affinity then linearly decreases with temperature below 240 K in the glassy state, with higher values for slower cooling as a result of lower glass transition temperatures. Upon heating, the affinity begins to increase linearly according to the same line pathway before crossing the equilibrium line. It then exhibits a peak whose position shifts toward higher temperatures and whose magnitude and width increase with the heating rate in ways such that the configurational heat capacity and the other thermodynamic coefficients can be simulated [19]. The entropy production can also be calculated from Eq. (4) (inset in Figure 5). In agreement with previous results [18], it shows a single peak upon cooling but two peaks upon heating. With respect to the experimental data, the advantage of the calculation is thus to distinguish clearly two contributions to the entropy produced when heat is brought to the material. The first peak is associated with a decrease of the configurational energy of the system, which is taking place because of the delay introduced by the relaxation time, even though heat is being supplied. As to the second peak, it is in contrast associated with the configurational energy necessary to recover internal equilibrium in the supercooled liquid state. Here the wording “is associated” instead of “represents” is necessary because the entropy produced and configurational entropy changes necessarily differ as a result of the irreversible nature of the glass transition. Whereas the entropy production is the product of the thermodynamic force and flux (see Eq. (4)), the variation of the configurational entropy is written as, see Eqs. (8) and (13): ∂H ∂ξ p,T dξ dt dSconf ΔC conf dT P = × = dt T T dt

P

17

255

The rate of entropy production thus reflects the spontaneous or irreversible microscopic processes that take place within the system during relaxation. As dictated by the Second Law of thermodynamics, it is always positive whether upon cooling or heating (Figure 5, inset). Physically, it can be thought of the heat irreversibly generated by friction at a microscopic scale. The resulting thermal power Pi = Tσ i, where σ i is the entropy creation in Eq. (4), is produced much too quickly to be compensated instantaneously by an exchange of heat with the surrounding heat bath. Under this circumstance, this is why an effective or fictive temperature can be defined. This surrounding heat bath is sometimes called the phonon bath since it is characterized by fast or vibrational modes. On the contrary, the change in configurational entropy is a reversible process related to the heat exchanged with the surrounding heat bath whose relevant thermal power is: Pth = T

dS conf dT = ΔC conf × P dt dt

18

Because the configurational entropy becomes constant upon vitrification, its variations have vanished (i.e. the configurational heat capacity) below the glass transition range. Above this range, in the supercooled liquid state, they of course differ from zero as indicated by dS conf,eq ΔC eq dT P = × dt T dt ∂H ∂ξ eq dT P,T dξeq dT × = T dt

19

In the transition range, the variations of the configurational entropy of the system are consequently positive or negative upon heating and cooling, respectively. As

6 Physical Aging

already evaluated long ago either theoretically [9] or experimentally [20, 21], the entropy produced is generally negligible with respect to the configurational entropy changes. The integration of the heat capacity curves measured by calorimetry is thus a pertinent way to access to the absolute value of the residual entropy at 0 K [3]. As seen from a direct comparison of Eqs. (4) and (17), arriving at this conclusion is tantamount to neglecting the affinity with respect to the enthalpy of advancement of the configurational change at every temperature: Entropy production negligible ⟺ A

∂H ∂ξ

P,T

20

6

Physical Aging

Relaxation times that depend only on temperature and pressure have been considered. Nevertheless, the complexity of microscopic structures in glasses implies the existence of a distribution of relaxation times. Relaxation processes then also depend on the instantaneous state of the system itself and, thus, on its history as, for instance, described by the Tool–Narayanaswamy–Moynihan model (Chapter 3.7, [22, 23]). A consequence is that some nontrivial relaxation processes can take place well below the glass transition range. Hence, it is interesting to study such a time-dependent process termed physical aging, which has a practical relevance through its possible effects on glass properties. The process can be illustrated with DSC scans for PVAc (Figures 2 and 6). If the sample is cooled down at some rate to 297 K, i.e. about 10 K below the calorimetric Tg, and its temperature is kept constant for a time interval ta, then its enthalpy (and entropy) relax to their lowest equilibrium values for the temperature (and pressure)

1.4 1.2 1.0 Cp (J/K)

Figure 6 Effect of aging on the heat capacities of PVAc recorded upon heating at the same rate. Heat capacity after a cooling (solid circle with line) and heat capacity after cooling and 72-hour annealing at 297 K (empty circle with line). The enthalpy released during aging estimated by the difference between the two areas included between these two curves. Heat capacities upon continuous cooling shown as solid circles.

considered. Experimentally, physical aging manifests itself as differences between the areas of DSC scans upon heating recorded for samples annealed (72 hours at 297 K) and not annealed. For the experiment without annealing, the lowest temperature of 278 K has been directly reached (see cooling curve in Figure 6). The amount of enthalpy relaxed during aging is equal to the difference between the light gray and dark gray areas in Figure 6. Of course, for a given annealing temperature, such a difference increases with the aging duration. As recently carried out on polymeric glass-formers annealed at relatively low aging temperatures for a very long time, calorimetry (DSC) can bring to light two different timescales for glass equilibration, revealing the complexity and richness of relaxation processes well below Tg [24]. Phenomenologically, however, in simple cases aging can be accounted for with the same approach as developed in previous sections. It is related to the relaxation of the order parameter ξ toward its equilibrium value ξeq(P,T) whereas the affinity A is relaxing at the same time toward zero. When applicable, the lattice-hole theory can be used to solve Eq. (16) at constant P and T to reproduce the observed process. As done for o-terphenyl [19], the order parameter is calculated at constant pressure and aging temperature T = 229.5 K with Eq. (16) and a temperature- and pressure-dependent relaxation time [19]. The affinity has been calculated upon heating at 60 K/ min, either after cooling at 6 K/min without aging, or after cooling at the same rate but with an aging process at 229.5 K (Figure 7). Upon isothermal aging, the affinity increases markedly (see the arrow in Figure 6) and then increases at the same rate as without aging. The difference is that the zero line is crossed at a lower temperature so that a much bigger peak is observed when the affinity finally recovers its zero equilibrium value at high temperatures. Since the affinity is an integrated measure of the heat capacity, the large peaks either calculated or

0.8

0.6

0.4 295

300

305

310 T (K)

315

320

325

269

3.2 Thermodynamics of Glasses

Figure 7 Effect of aging on affinities calculated with the lattice-hole model upon heating at the same rate of 60 K/min, first after a continuous cooling at 6 K/min (black line with solid circle), and second after annealing at 229.5 K (black line with empty circle). The black arrow simulating the relaxation of affinity upon aging at 229.5 K. Affinity upon continuous cooling shown as solid circles.

0.2

0.1

0.0 A/RT

270

–0.1

–0.2

–0.3 230

235

240 T (K)

245

250

observed for these properties are clear signatures of aging [19]. More complex calculations can of course be made to deal with at least two separate timescales [24], or a more realistic distribution of relaxation times.

7

Perspectives

Whether in the form of affinity, fictive temperature, or structural order parameter, additional variables must be introduced to deal with the nonequilibrium thermodynamics of glass-forming systems and, in particular, with the time dependence of their properties in relaxation regimes. Phenomenological advances now make it possible to predict these properties as a function of time and temperature or to determine accurately the entropy irreversibly produced, but the mechanisms involved at the atomic or molecular level generally remain to be deciphered. The physical nature of the glass transition is a case in point, as are the origins of Kauzmann catastrophe, of the strong variations of the PD ratio, of the diversity of relaxation timescales or of, as illustrated by the wellknown memory effects, the complex nonlinear coupling of the parameters of the differential equations with which these processes are described. Not only could highly sensitive calorimetric experiments yield valuable original data in this respect but coupling of different techniques such as dielectric spectroscopy and temperature-modulated calorimetry should bring new insights on the dynamics and thermodynamics of the glass transition. Recent experiments on ultra-stable organic glasses obtained by vapor

255

deposition techniques are, for instance, promising [25, 26]. And whereas very long aging performed well below Tg should also give new clues on the laws driving complex relaxation processes in the glassy state [24], experiments made at extremely rapid timescales (e.g. spectroscopy) are in contrast needed to investigate relaxation in supercooled liquids where equilibrium is quickly achieved. To give a single example, ultrastable organic glasses obtained by vacuum-deposition techniques should be of special interest in view of their internal stability that is equivalent of that of hyper-aged glasses (with aging time of millions of years) obtained by conventional melt cooling [25]. For this particular class of glasses, the aforedefined TM values are so much lower (by a few tens of degrees) than the standard glass transition temperatures that TM and Tg cannot be indiscriminately used in Eq. (9b) [25, 26]. Among other consequences, new insights should then be gained on the non-unity of the PD ratio. Finally, such experiments should of course be firmly complemented by fundamental work. Microscopic theories and atomistic simulations must be developed and, as stringent tests of their value, their predictions checked in terms of macroscopic physical properties.

Acknowledgments The authors thank J. Richard for data treatments and simulations carried out with the lattice-hole model, G. McKenna for PVAc samples, and the reviewers for their time, remarks, and useful corrections.

References

References

15 Adam, G. and Gibbs, J.H. (1965). On the temperature

1 Jones, G.O. and Simon, F.E. (1949). Qu’est-ce qu’un

2 3 4

5 6 7

8

9

10

11 12 13

14

verre? Endeavour 8: 175–181. (in French and in German). Nernst, W. (1969). The New Heat Theorem. New York: Dover. Takada, A., Conradt, R., and Richet, P. (2015). J. Non Cryst. Solids 429: 33–44. De Donder, T. and Van Rysselberghe, P. (1936). Thermodynamic Theory of Affinity, A Book of Principles. Stanford: Stanford University Press. Wondraczek, L., Mauro, J.C., Eckert, J. et al. (2011). Towards ultrastrong glasses. Adv. Mater. 23: 4578–4586. Angell, C.A. (1995). Formation of glasses from liquids and biopolymers. Science 267: 1924–1935. Prigogine, I. and Defay, R. (1950). Thermodynamique Chimique, Nouvelle Rédaction. Liège: Desoer; Chemical Thermodynamics (London: Longmans, 1954). Garden, J.-L., Guillou, H., Richard, J., and Wondraczek, L. (2012). Non-equilibrium configurational PrigogineDefay ratio. J. Non-Equilib. Thermodyn. 37: 143–177. Davies, R.O. and Jones, G.O. (1953). Thermodynamic and kinetic properties of glasses. Adv. Phys. (Phil. Mag. Suppl.) 2: 370–410. Kauzmann, W. (1948). The nature of the glassy state and the behavior of liquids at low temperature. Chem. Rev. 43: 219–256. Nemilov, S.V. (1995). Thermodynamic and Kinetic Aspects of the Vitreous State. Boca Raton: CRC Press. Tool, A.Q. (1945). Relaxation of stresses in annealing glass. J. Res. Natl. Bur. Stand. 34: 199–211. Tool, A.Q. (1946). Relation between inelastic deformability and thermal expansion of glass in its annealing range. J. Am. Ceram. Soc. 29: 240–253. Leuzzi, L. and Nieuwenhuizen, T. (2008). Thermodynamics of the Glassy State. New York: Taylor & Francis.

16 17

18

19

20

21

22

23 24

25

26

dependence of cooperative relaxation properties in glassforming liquids. J. Chem. Phys. 43: 139–146. Binder, K. and Kob, W. (2011). Glassy Materials and Disordered Solids. Singapore: World Scientific. Simha, R. and Somcynsky, T. (1969). On the statistical thermodynamics of spherical and chain molecule fluids. Macromolecules 2: 342–350. Möller, J., Gutzow, I., and Schmelzer, J.W.P. (2006). Freezing-in and production of entropy in vitrification. J. Chem. Phys. 125: 094505-1–094505-13. Garden, J.-L., Guillou, H., Richard, J., and Wondraczek, L. (2012). Affinity and its derivatives in the glass transition process. J. Chem. Phys. 137: 024505-1–024505-10. Bestul, A.B. and Chang, S.S. (1965). Limits on calorimetric residual entropies of glasses. J. Chem. Phys. 43: 4532–4533. Tombari, E. and Johari, G.P. (2014). Change in entropy in thermal hysteresis of liquid-glass-liquid transition and consequences of violating the Clausius theorem. J. Chem. Phys. 141: 074502-1–074502-5. Moynihan, C.T., Macedo, P.B., Montrose, C.J. et al. (1976). Structural relaxation in vitreous materials. Ann. N. Y. Acad. Sci. 279: 15–35. Narayanaswamy, O.S. (1971). A model of structural relaxation in glass. J. Am. Ceram. Soc. 54: 491–498. Cangialosi, D. (2014). Dynamics and thermodynamics of polymer glasses. J. Phys. Condens. Matter 26: 153101-1– 153101-19. Swallen, S.F., Kearns, K.L., Mapes, M.K. et al. (2007). Organic glasses with exceptional thermodynamic and kinetic stability. Science 315: 353–356. Rodríguez-Tinoco, C., González-Silveira, M., Barrio, M. et al. (2016). Ultrastable glasses portray similar behaviour to ordinary glasses at high pressure. Sci. Rep. 6: 34296–1–10.

271

273

3.3 The Glass Transition and the Entropy Crisis Purushottam D. Gujrati Department of Physics, Department of Polymer Science, The University of Akron, Akron, OH, USA

1

Introduction

Vitrification [1–3] is a prime example of an irreversible process going on at low temperatures T0 or high pressures P0 of the surrounding medium (which may be different from those of the system of interest). It is commonly believed now that almost all materials including organic and inorganic substances, man-made polymers, metals, plastics, biomaterials, drugs, etc., can be turned into a glass (or vitrified) with a suitable technique (Table 1). But our understanding of the glassy state (GS) is far from complete, mainly because they exhibit a duality in their properties, appearing either liquid- or solid-like at long or short timescales, respectively [2]. Molecular motions in liquids become progressively slower as vitrification is approached, with a characteristic time increasing from nanoseconds to beyond feasible experimental timescales time τexp (the inverse of the probed frequency ω) of the order of 102 to 105 seconds, i.e. one day (Chapter 3.7). This results in an operational definition of a range of temperatures T0g-to-T0G for the glass transition (GT). Following convention, however, we simply use T0g as the transition temperature to specify this range, which is determined by the rate of approach to the transition. The slow glassy dynamics is thought to occur because particles form cooperative groups of increasing sizes, which then define a correlated length as the ratio ζ 0 ≡ P0/T0 increases. This is the idea behind the celebrated Adam–Gibbs theory [7] of the GT. A similar time dependence is also found in spin glasses, which exhibit an exponentially large number of metastable states below

the (spin-)GT temperature due to the presence of frustration, namely, the inability of the system to minimize simultaneously the (sometimes competing) interaction energies between its constituents. This similarity has suggested frustration to be also important for a regular glass [8], although the situation is not very clear. There are many excellent recent monograph and reviews [3, 8–10] on glasses, from which the present chapter differs by its emphasis on nonequilibrium thermodynamics and its attempt to identify the communal entropy and the free volume to provide a thermodynamic unified approach to glasses [11]. We do not specifically discuss the actual form of the temporal variation except to note that the most common empirical law, valid in a limited domain, is the Kohlrausch stretched exponential q(T0, t) = q0 exp(−t/τ)β [8, 9], where the property q and some average relaxation time τ must be state-dependent quantities. In the next section, we review some important concepts and theories. It is followed by a description of glassy phenomenology in Section 3. Nonequilibrium thermodynamics used here is briefly introduced in Section 4, and its consequences for glassy relaxation are considered in Section 5. The topics of free volume and the communal entropy are taken up in Section 6. We follow this by a resulting unifying approach in Section 7. The final section contains a discussion of the results and the limitation of the approach. The present chapter partially complements the previous one.

2 2.1

Reviewers: A. Dhinojwala, Department of Polymer Science, The University of Akron, Akron, OH, USA B. Yu-Kuang Hu, Department of Physics, The University of Akron, Akron, OH, USA

Important Concepts and Theories Fast and Slow Modes

There is a hierarchy of relaxation modes [11] in a glass. Phenomenologically and for the sake of simplicity, however, we can broadly speaking divide them into at least

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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3.3 The Glass Transition and the Entropy Crisis

Table 1 Transition temperatures of some materials. Material

T0g (K)

T0K (K)

Material

T0g (K)

T0K (K)

Ref.

1-Butene

58

48

Salol

220

167

[4]

Toluene

126

96

Glucose

306

271

[4]

Selenium

307

240 ± 10

ZnCl2

380

250 ± 25

[4]

Glycerol

193

135

H2SO4.4 H2O

157

133

[4]

Diopside

1005

637

Anorthite

1160

815

[5, 6]

Figure 1 The 2-D projection of a typical 3-D trajectory for 100 min for ϕ = 0.56. Most of the time, particles are confined to their cages. Occasionally, a particle will move a long distance and get trapped in another cage. In the figure, the particle took 500 seconds to shift its position. Source: Reprinted with permission from [12].

200 nm

two distinct and widely separated timescales governing fast and slow modes in glasses. The former refers to the localized oscillations of the particles (atoms, molecules, segments, monomers, etc.) in the cells or cages formed by neighboring particles, and the latter to the translation and diffusion (translation over long distances [1]) of particles. In Figure 1, we show a two-dimensional projection of a three-dimension trajectory of a colloidal particle at high enough density, which oscillates within its cage for a long time before leaving to a new cage in which it oscillates again to leave it later on, and so on. These two distinct modes distinguish the glass from other nonequilibrium states where there is only one mode to be considered. Owing to its complexity, and its incomplete and sometimes controversial understanding, vitrification continues to attract researchers to this date.

2.2 What Is a Glass? As a physicist, we first need to ask is: What is a glass? The simple and most common answer is that glass or GS is a time-dependent nonequilibrium state of matter [2, 3, 13] found at low temperatures T0 and/or high pressures P0 of the surrounding medium. It undergoes GT from a relatively brittle solid glass into a molten state (the supercooled liquid [SCL]) as ζ 0 decreases. The striking feature of a glass, which distinguishes it from an equilibrium crystal (CR), is that it has much higher potential energies [14]. Even at absolute zero, there remains a nonzero gap between their energies. Thus, a glass can be thought of as a macrostate which has trapped a lot of frozen defects relative to the crystal that were present in the equilibrium liquid (EL) at the melting point [15]. Glass is

2 Important Concepts and Theories

V

1010

105 s

shown by a broken line is always treated as out of equilibrium and exists way below the bend. The standard formulation of entropy

10–12 s

τ

S t = − Liquid Glass transitions Glasses Crystal T0k

T0g

T0m T0

Figure 2 Schematic variation of the volume as the liquid is cooled. The freezing transition from the equilibrium liquid (line above T0m) to the crystal (shown by the green line) occurs at T0m; the latter becomes perfectly ordered at absolute zero. Bypassing crystallization leads to the supercooled liquid (shown by the line as the continuation of the equilibrium liquid). The supercooled liquid bends continuously without any discontinuity in the slope into different glasses (shown by different broken lines) at different glass transition temperatures (T0g) depending on the rate of cooling r. As r decreases, T0g also decreases (shown by arrows becoming larger), until finally it converges to its limit T0K under infinitely slow cooling rate (r 0) but now with a discontinuity in the slope. This limit is called the ideal glass transition temperature or the Kauzmann temperature, and the corresponding glass shown by the dashed curve is time-independent and is called the ideal glass (IG). A similar variation of the slopes of the density is also seen when we increase P0 at a fixed T0; we merely replace T0 in the figure by 1/P0. Thus, we can replace the horizontal axis by 1/ζ 0.

most commonly prepared in the laboratory by cooling or compressing the SCL to fall out of equilibrium (Figure 2). The genuine equilibrium state corresponds to the crystal. This does not mean that the SCL can never be treated as in equilibrium; its stationary limit, called the equilibrium supercooled liquid (ESCL) with a stretch of imagination, can be treated as an equilibrium state under the restriction that only disordered microstates are considered [15], a sensible restriction to study glasses. The simplest way to identify these microstates is to introduce an order parameter ρ. It is defined so that ρ = 0 for disordered states and ρ 0 for ordered states [15]. We denote the restricted space of disordered microstates by , and refer to the restriction as a restricted ensemble formalism in this work to distinguish it from an unrestricted ensemble in which all microstates are considered. To make a clear distinction, all possible time-dependent SCL states will be called nonequilibrium supercooled liquid (NESCL) states; they occur near but below the bends and are shown as dotted curves, whereas the continuous line refers to the ESCL. In the following, we will use the SCL to refer to both nonequilibrium and equilibrium SCLs. The GS

p k k

ln pk ≥ 0

1

in terms of microstate probability pk of the allowed kth microstate is applicable to any (equilibrium or nonequilibrium) state in both ensembles [16]; pk depends on the extensive observables (the energy E, volume V, number of particles N, etc.) in addition to the time t. In the stationary limit so that pk has no t-dependence, these entropies achieve their unique maximum value SESCL or SIG (SCR) in the restricted (unrestricted) ensemble below T0M. Above T0M, they yield SEL in both ensembles, as expected. In the stationary limit, the entropy is related to the number of microstates W in both ensembles by the famous Boltzmann formula S = ln W (we set the Boltzmann constant kB = 1 so that the entropy becomes dimensionless). 2.3

Adam–Gibbs Theory

The excess entropy defined as S SCL T 0 , t

S CR T 0 + S ex T 0 , t , T 0 < T 0M

2

has played a very pivotal role in the field of GT. Kauzmann [13] proved that it exhibits a rapid drop below T0M by for many systems. A smooth extrapolation to lower temperatures shows that it eventually vanishes at some temperature below T0M, and becomes negative if extrapolated to lower temperatures. A (kinetic) transition, i.e. a GT takes place at a higher temperature T0g to avoid this entropy crisis, known commonly as the Kauzmann paradox. In the limit of zero cooling rate r (not accessible in experiments or simulations, but accessible in a theoretical setup), the GT occurs in the ESCL at T 0ex = 0], see Figure 2, and is known T0 = T0ex [S ESCL ex as the ideal glass transition (IGT) from the ESCL liquid to an ideal glass below T0ex. It should be stressed, however, that there is no thermodynamic requirement for Sex(T0) to be non-negative. There are physical systems like He4 in which Sex(T0) can become negative at low temperatures. This means that the vanishing of Sex(T0) cannot be an argument for a GT but the vanishing of the communal entropy Scomm ESCL T 0 , to be defined later, will be as we will discuss. The thermodynamic theory due to Adam and Gibbs [3, 7–10, 15, 17] attempts to provide a justification of the entropy crisis in the ESCL by specifically considering the configurational entropy Sconf(t) S(t) − Skin(t) among the positions and interactions (which we take to be independent of momenta) among the particles [15]. Here, Skin(t) is entropy originating from the kinetic energy of the particles and its separation from S(t) is possible

275

276

3.3 The Glass Transition and the Entropy Crisis

because the internal energy E can be partitioned into two independent contributions from the positions (configurations) and momenta (kinetic energy) of the particles, respectively. In a lattice model such as in the Gibbs– DiMarzio theory [18], Sconf = S(t) as there is no kinetic energy. We must be careful not to confuse Sconf(T0, t) with SSCL(T0, t) as they are different quantities. The central idea in the Adam–Gibbs theory is that the sluggishness observed in a system is a manifestation of the smallness of the configurational entropy, i.e. the smallness of the available configurations to the system. From this theory, it follows that the viscosity η(T0) above the GT is given as follows: ln η T 0 = AAG + BAG T 0 sconf ,

3

where AAG and BAG are system-dependent constants and sconf = Sconf/N. It is commonly believed that the configurational entropy also vanishes at a positive temperature T0S (where η(T0S) diverges), which is not identical to T0ex, although they are close [17]. The derivation of Eq. (3) is based on the concept of cooperative domains of size z, which gradually increases as the temperature is lowered and diverges at T0S. At this temperature, the entire system acts like a cooperative domain. While this particular domain is disordered, its configurational entropy must vanish in this theory. As the laboratory GT temperature T0g occurs at about 50 K above T0S, the value of z at T0g is much smaller; it is of the order of 5 − 10.

2.4 Free Volume Theory The cell theory of liquids is very appealing to study the motion of individual particles [1, 3] during a GT. The localized oscillatory motion of a particle occurs around the minimum of the potential ϕ generated by its neighbors in the cell. (The set of minima from all the cells determines what is nowadays called the inherent structure [3].) Such a motion occurs at all times in the crystal unless there are interstitial vacancies. In a glass, such a motion occurs at short time and endows a glass with solid-like properties (Figure 1). But at long times, there occurs uninhibited translation and diffusion, superimposed on the oscillatory motion controlled by a continuously changing ϕ as the neighbors change [1]. This gives a glass a liquid-like property, whose central feature is the mobility of the particle. At high densities, the neighbors impede the motion in almost all directions and the motion becomes confined within the cell with little or no diffusion. At low densities, the particle can move almost freely in any direction and diffusion occurs. (The presence of chemical bonding requires the whole molecule to move together and must be eventually accounted for.) As we are interested in the

dense phase, we have both motions possible at different timescales. The ability to move long distances requires what is vaguely termed the free volume Vf, and which is communally shared by many particles. It gives rise to the fluidity. The potential ϕ felt by the particle in its cell endows the particle with what can be termed the interaction volume vi per particle: it is the volume necessary to execute its oscillatory motion in ϕ; the latter must gradually become very steep as the particle gets close to the neighbors. At low temperatures, these steep portions have almost no chance to be explored by the particle. Therefore, the interaction volume vi must be usually smaller than the cell volume Δ. Their difference Δ − vi gives the particle some elbow room for translation and must be included in Vf. The determination of Vi ≡ Nvi is somewhat technical and will be discussed later. In terms of the interaction volume Vi, we have V = Vi + Vf;

4

both components are functions of state variables. Many workers use the concept of occupied volume Vo ≡ Nvo to define Vf = V − Vo. However, the concept may be ambiguous [19]. For some, vo is just the van der Waals volume, also known as the molecular volume vm. It is just a parameter of the liquid. In contrast, the interaction volume is theoretically well defined in our approach. To inquire if they are the same is meaningless. As a van der Waals volume is merely a parameter, Vo is just a constant equal to Nvm. Such a definition will not account for the sudden change in the temperature variation (the slope) of the ideal glass volume at the kink in Figure 2. Our definition of Vi allows for such a variation. The free volume theory of Doolittle [17, 20] has attempted to describe the GT with some respectable success even though lately it has fallen out of favor. This is unfortunate as it captures the essence of the GT, which then occurs when the free volume becomes sufficiently small to impede the mobility of the molecules [20]. The Doolittle equation correctly predicts the abrupt increase in the viscosity for a large number of glass formers in a narrow range over which vf becomes very small [17]. According to this equation, the fluidity φ, which is basically the inverse of the viscosity η, is given by φ

η − 1 = ϕ0 exp − γvm vf ,

5

where γ is a fitting parameter of order unity. Phenomenologically, we identify a GT to occur normally when η ≳ 1013 poise or τ τexp; see the upper axis in Figure 2. In the Doolittle equation, the parameters γ and vm are constant. But in general, these parameters must be functions of the state variables. With this dependence, we will refer to the above equation as the generalized Doolittle equation. The free-volume picture provides a very nice way to think of the GT [1] with percolation of the free volume

3 Nonsingular Glass Phenomenology

as an important ingredient [17]. The time dependence of the free volume redistribution, determined by the energy barriers encountered during it, should provide a kinetic view of the transition, and must be properly accounted for. This approach is yet to be completed to satisfaction. One finds that a linear temperature-dependent vf = a(T0 − T0V), T0V 0, a and T0V constants, is satisfied only over a narrow range of the temperature T0 for most substances [17]. Assuming the linear dependence, we find that η(T0) diverges near T0V according to the phenomenological Vogel–Tammann–Fulcher equation ln η T 0 = AVTF + BVTF T 0 − T 0V ,

6

where AVTF and BVTF are system-dependent constants (Chapter 4.1). At T0V, Vf vanishes so that there cannot be any translational motion, i.e. any flow, which is consistent with a diverging η(T0V). The system becomes completely jammed [8]. The entropy associated with the translational motion, which we call the communal entropy Scomm, must also vanish (Section 6.2). The temperature where Scomm = 0 will be denoted by T0K in this chapter, and our attempt is to define Vf such that T0V = T0K. The vanishing of Vf is reflected in the variation of the volume; see the point on the lowest curve at temperature T0K in Figure 2, where there is a sharp kink and a discontinuity in the slope. (We have identified the temperature as T0K rather than T0V with the anticipated result obtained later that the Kauzmann temperature T0K, where the communal entropy vanishes, is the same as T0V. This is, as it should be, because the ideal glass shown by the dashed line must be a unique state.) This curve is the result of extrapolation r 0 to obtain the ESCL (solid curve) and the ideal glass (dashed curve); as a result, there is a singularity at T0K. The presence of free volume above T0K gives rise to different expansion coefficients on the two sides of T0K (Figure 3b). In contrast, the communal entropy does not vanish in Figure 3a so there is no IGT at a positive temperature in this case. The free volume and Scomm do not vanish for the laboratory glasses shown by the upper two curves in Figure 2. Similar to the Kauzmann temperature T0K for isobaric vitrification at fixed P0, a Kauzmann pressure P0K can also be identified in the ESCL where Scomm ESCL P 0 = 0 as the pressure is increased at fixed T0. We will collectively call them Kauzmann points.

S

Supercooled liquid Transition region

(b) Ideal glass TK

SR

Supercooled liquid

T0 Glass

Relaxation

(a) T0G

T0g

T0

Figure 3 Schematic variation of the communal entropy Scomm (a) of the equilibrium supercooled liquid (solid curve) and a possible time-dependent supercooled liquid, which turns into a glass (dotted curve) during vitrification. It is assumed that there is no ideal glass transition in the equilibrium supercooled liquid. The transition region between T0g and T0G has been exaggerated to highlight the point that the glass transition is not a sharp point. For all temperatures T0 < T0g, the nonequilibrium supercooled liquid undergoes isothermal (fixed temperature T0) structural relaxation in time toward the equilibrium supercooled liquid. The entropy of the equilibrium supercooled liquid is shown to extrapolate to zero, but that of the glass to a nonzero value SR > 0 at absolute zero. (b) Scomm of the equilibrium supercooled liquid for a system with an ideal glass transition at T0K, below which we obtain the ideal glass for the equilibrium supercooled liquid. In the restricted ensemble, Scomm for the equilibrium supercooled liquid becomes negative below T0K. We conjecture that for all glass-forming systems, the correct form of Scomm for the equilibrium supercooled liquid in (a) is the one shown in (b) with an ideal glass transition.

based on the one-step replica symmetry breaking in spin glasses. The one-step replica symmetry breaking is identified in a long-range spin glass model so the theory is at a mean field level. Whereas some may consider this to be a weakness of the theory, it also provides a new level of intuition about ordinary glasses. 2.6

Mode-Coupling Theory

The mode-coupling theory [8] is an example of theories based on kinetic ideas, which deals not with the GT but with the transition at the mode-coupling temperature TMC > Tg. Thus, it is not directly relevant for our review. This theory may be regarded as a theory based on firstprinciple approach, which starts from the static structure factor. In this theory, the ergodicity is lost completely, and structural arrest occurs at TMC.

3 2.5

S

Nonsingular Glass Phenomenology

Random First-Order Theory

An alternative thermodynamic theory for the impending entropy crisis based on spin-glass ideas has also been developed in which proximity to an underlying first-order transition is used to explain the GT [10]. The theory is

3.1

The Restricted Ensemble

As is well known, singularity at a phase transition emerges as the system makes a transition between two distinct equilibrium phases such as at T0M between the

277

278

3.3 The Glass Transition and the Entropy Crisis

EL (disordered) and the crystal (ordered); see the vertical dashed line at T0M in Figure 2. In equilibrium, it is customary to introduce an unrestricted partition function Z, which exhibits a singularity at T0M [14]. If the transition is somehow avoided such as during supercooling in which we continue from the equilibrium to the ESCL, then one describes such a process by considering the restricted ensemble involving [15]. The corresponding restricted partition function Z , as noted above, does not exhibit any singularity at T0M as both sides represent the same (disordered) state corresponding to ρ = 0. By considering the restricted partition function Z involving ordered microstates (ρ 0), which again does not show any singularity, and comparing the two free energies F = − T ln Z and F = − T ln Z , we identify T0M by their crossing. The singularity at T0K, the sharp kink in Figure 3b, is due to a phase transition between the ESCL and the ideal glass in the restricted ensemble involving . as the set of disordered microstates If we introduce from which we remove all microstates belonging to associated with the ideal glass, then the corresponding partition function Z can be used to describe the ESCL is inconsewithout any singularity at T0K; above T0K, quential [15] so F = F . In particular, we see from Figure 2 that the ESCL volume VESCL obtained by using will show no singularity at T0K and can be continued mathematically to lower temperatures, except that Vf will become negative under this continuation. Thus, the continuation does not give a physical state, which is reminiscent of the Kauzmann paradox. The singularity at T0K is inferred by the crossing of the free energies F = F and F . It is the absence of a singular behavior in F that is of primary interest here. This is also reflected in the absence of a singularity in the corresponding entropy S = S = − ∂F ∂T . 3.2 Absence of a Singularity in Laboratory Glasses The relaxation time τ of the system, which is independent of τexp, usually increases monotonically with ζ0; see the upper axis in Figure 2. The SCL remains in equilibrium in shown by the solid curve as long as τ < τexp, but begins to fall out of the restricted equilibrium at T0g and becomes a NESCL as soon as τexp < τ. The system is not really frozen yet, but eventually turns into a glass when τ > > τexp at a somewhat lower temperature T0G (not shown in Figure 2, but shown in Figure 3a, where we show the entropy), when the system has no discernible mobility. The loss of mobility results in “freezing” of the system without any singular changes in its thermodynamic densities in the GT region ΔTG (T0g − T0G). The state below T0G is identified as a glass. There are

no singularities at the GT temperatures of the two laboratory glasses in Figure 2 or the laboratory glass in Figure 3a. The respective curves smoothly connect with the ESCL. Thus, the experimental glass transition should be thought of as a crossover phenomenon with a gradual turnover of the ESCL through a NESCL into a glass over a temperature range. As the curves emerge out of the ESCL continuously, there is no mathematical singularity for the top two curves in Figure 2.

3.3 Ideal Glass: Analytic Continuation The continuous curve in Figure 3a shows S = S = S ESCL of the ESCL. The dotted curve shows SGS, which extrapolates to a positive value of the residual entropy SR at absolute zero [15]. In contrast, it is commonly believed that SSCL extrapolates to zero at T0 = 0, even though there are no thermodynamic requirements for this. While Figure 3a does not show any IGT, Figure 3b does at T0K > 0, where Scomm vanishes. At this point, the ESCL will undergo a phase transition into the ideal glass. We see that the ideal glass has a zero communal heat capacity (heat capacity associated with Scomm), but the ESCL has a nonzero communal heat capacity. Thus, the ideal glass and the ESCL are distinct states. As noted above, the transition will result in a singularity in the thermodynamic free energy. Despite this singularity, each state itself is nonsingular in the restricted ensemble. For example, SESCL can be mathematically extended to temperatures below T0K, although it will result in negative Scomm. This is similar to the Gibbs–DiMarzio theory, in which analytically continued S conf ESCL becomes negative below the IGT.

4 Nonequilibrium Formulation: Brief Review The nonequilibrium formulation presented here is a condensed version of our previous presentation elsewhere [11, 16]. The system that undergoes vitrification is represented by Σ. We treat it as an interacting system by embedding it in a medium Σ; their combination forms an isolated system Σ0. Quantities pertaining to Σ0 will have a suffix 0, while those for Σ will have a tilde; quantities for Σ will have no suffix. The medium is taken to be extremely large compared to Σ so that the latter does not affect the fields of Σ. Thus, its fields T , P, etc., will be denoted by T0, P0, etc., of Σ0. We will also find it convenient to use the term body to denote any one of Σ, Σ, and Σ0. The quantities pertaining to a body will not have any suffix.

4 Nonequilibrium Formulation: Brief Review

Let Σ be in a nonequilibrium state such as a glass. Its entropy S(t) must obey the second Law, i.e. the Law of increase of entropy, according to which the irreversible (denoted by a suffix i) entropy diS generated in any infinitesimal physical process within a body satisfies the inequality diS ≥ 0; the equality occurs for a reversible process. This entropy is generated within the system because of dissipative processes. Thus the suffix i can also stand for “internal.” The quantity deS with a suffix “e” will denote the entropy exchange with the medium (the “exterior”). In general, we can identify deX and diX for the change dX = deX + diX in any extensive quantity X. Therefore, dS = deS + diS. As there is no exchange entropy change (deS0 = 0) for Σ0, we have dS0 = diS0 ≥ 0 during any process. For Σ0 in equilibrium, dS0 = 0 so that S0=constant.

4.1 Concept of a Nonequilibrium State and of Internal Equilibrium 4.1.1 An Isolated Body

For Σ0 in equilibrium, S0 can be expressed as a state function S0(X0) of its extensive observables (E0, V0, N0, etc., that can be controlled by an observer) denoted by X0, from which follows the Gibbs fundamental relation for the entropy S0, dS 0 = Σp ∂S 0 ∂X 0p dX 0p ;

7

the partial derivatives are related to the constant fields of the system: ∂S 0 ∂E 0 = 1 T 0 , ∂S 0 ∂V 0 = P 0 T 0 ,

8

As X0 remains constant, S0 remains constant and has the maximum possible value given by the Boltzmann formula S0(X0) ≡ ln W0(X0), where W0(X0) is the number of microstates corresponding to the observable X0. This conclusion about the entropy when it is a state function will play an important role below. For Σ0 out of equilibrium, S0 is no longer a constant. The nonequilibrium state will continuously change, which is reflected in its entropy increase in time. This requires expressing its entropy as S0(X0, t) with an explicit time-dependence. If it happens that the changes in S0 and the state come from the variations of additional independent variables, whose set is denoted by ξ0, that keep changing with time until the body comes to equilibrium [21, 22], then S0 can be expressed as a function of X0 and ξ0 with no explicit time dependence: S0(Z0(t)), where X0 and ξ0 is collectively written as Z0. As the variables in ξ0 continue to change in time for the isolated system, they cannot be controlled by the observer; thus, they are known as the internal variables. We can identify Z0(t) as the set of nonequilibrium state variables so that the

entropy becomes a state function of Z0(t). We can extend Eq. (7) to dS 0 = Σp ∂S 0 ∂Z 0p dZ 0p ;

9

the new derivatives (∂S0/∂ξ0p) determine the affinities A0p(t), ∂S 0 ∂ξ0p = A0p t T 0 t

10

All fields and affinities continue to change in time until Σ0 reaches equilibrium. As Σ0 comes to equilibrium, all A0p(t) vanish, which requires that ξ0 are no longer independent of X0. A body for which the entropy has become a state function of Z0(t) is said to be in internal equilibrium. As there is no explicit time dependence, the entropy in internal equilibrium remains constant for the given state variables. The situation is no different than when Σ0 was in equilibrium. Thus, S0(Z0(t)) in this case has its maximum possible value for given Z0(t), and is given by the Boltzmann form S0(Z0(t)) ≡ ln W0(Z0(t)), where W0(Z0(t)) is the number of microstates corresponding to the state variable Z0(t). For a body not in internal equilibrium, the entropy must retain an explicit time-dependence so that the derivatives in Eq. (8) cannot be identified as state variables like, temperature, pressure, etc. 4.1.2 An Interacting Body

An interacting body (a body in a medium) out of equilibrium with its medium will also require internal variables. For the body in internal equilibrium, the derivatives ((∂S/ ∂E) = 1/T(t), (∂S/∂V) = P(t)/T(t), (∂S/∂ξp) = Ap(t)/T(t) ) of its entropy S give the fields T(t), P(t), Ap(t) etc. The corresponding Gibbs fundamental relation is given by dS t = Σp ∂S ∂Z p dZ p

11

4.1.3 A Simple Example for an Internal Variable

Consider an isolated body Σ0 formed by two parts Σ1, Σ2 that are initially at different temperatures T1(0) and T2(0). We imagine their volumes and particle numbers as fixed, but allow their energies E1(t), E2(t) to change with time through their mutual thermal contact. We know that eventually, they come to equilibrium at the same common temperature T0f. During this time, their temperatures keep changing. The total energy E0 = E1 + E2 is constant. The entropy S0 is the sum of the entropies S1 and S2 of the two parts. Thus, S0 is a function of two variables E1(t), E2(t). If we want to express S0 as a function of E0, we need another independent variable ξ0(t), which is evidently a function of the difference E1(t) − E2(t). We take ξ0(t) ≡ E1(t) − E2(t)]/2. This makes S0 a function of E0 and ξ0. The affinity A(t) = ∂S0/∂ξ0 is

279

280

3.3 The Glass Transition and the Entropy Crisis

A t = 1 T1 t − 1 T2 t and vanishes in equilibrium, as expected. Here, T1(t) and T2(t) are the instantaneous temperatures of the two parts and are given by 1/T1(t) = (∂S1/∂E1), 1/T2(t) = (∂S2/∂E2).

4.2 Gibbs Free Energy of an Interacting System From now on, we will only consider the system in internal equilibrium. We will further simplify our discussion by mostly considering one internal variable ξ and restrict the observables to E, V, and N for simplicity. Moreover, we will keep N fixed so that it will not be shown explicitly and allow the possibility of fluctuating E and V due to exchanges with the medium. The medium is always taken to be in equilibrium with its fields and affinity given by T0, P0 and A0 = 0; the system achieves these values when it comes to equilibrium with Σ In terms of H(t) ≡ E(t) + P0V (t), G(t) ≡ H(t) − T0S(t) = E(t) − T0S(t) + P0V(t), which are the time-dependent enthalpy and the Gibbs free energy, respectively, of the system Σ, it is easy to show that [22] S0 t − S0 = S t − H t T 0 = − G t T 0 ,

12

where S 0 S E 0 , V 0 , ξ0 is a constant, which is independent of the system. Here, S(t) and S0(t) are the entropies of Σ and Σ0. It immediately follows from this that dG/dt = − T0diS0/dt ≤ 0, as expected. We similarly have dH/dt = T0deS/dt = deQ/dt, where deQ = T0deS is the heat exchange with Σ.

5 Nonequilibrium Relaxation in Internal Equilibrium 5.1 Thermodynamic Relaxation During isobaric vitrification, the system Σ, originally in equilibrium with a medium at T 0 , P0, is suddenly brought into another medium at T0, P0 at time t = 0. As Σ is out of equilibrium, it will strive to equilibrate irreversibly (diS/ dt > 0). The resulting process is called relaxation during which various thermodynamic quantities will undergo irreversible changes dictated by the second Law, which we now investigate.

5.1.1 Heuristic Consideration

As Σ has no time to interact with the new medium at t = 0, its initial temperature T(0) is the original temperature T 0. As Σ eventually comes to equilibrium, we must have T (τeq(T0)) = T0, where τeq(T0) is the time required to come to equilibrium. Thus, T(t) continues to fall during relaxation from T 0 to T0. Accordingly, the heat exchange deQ = dH < 0. Thus, the enthalpy decreases during relaxation, which is an experimental fact [2]. Similarly, the initial entropy S(0) is the entropy S ESCL T 0 of the higher temperature. After equilibration, S(τeq(T0)) = SESCL(T0). Since the entropy increases with temperature, we conclude that the entropy also falls during relaxation from S ESCL T 0 to SESCL(T0) at t = τeq(T0).

5.1.2 Thermodynamic Support

We now support this intuitive picture by the nonequilibrium thermodynamics of the previous section. Here, we closely follow [22]. It is easy to see from Eqs. (13) and (14) that

4.3 Thermodynamic Forces for Relaxation The Gibbs fundamental relation can be written as dE t = T 0 dS t − P 0 dV t + T t − T 0 dS t − P t − P 0 dV t − A t dξ t 13

di S t = dt

Using the first Law dE(t) = T0deS(t) − P0dV(t), we find T 0 d i S t = T 0 − T t dS t + P t − P0 dV t + A t dξ t ≥ 0 14 Each of the three terms on the right must be nonnegative in accordance with the second Law T 0 − T t dS t ≥ 0, P t − P0 dV t ≥ 0, A t dξ t ≥ 0 15 The prefactor T0 − T(t), etc., in each equation represents a thermodynamic force that drives the system toward equilibrium.

1 1 dE t − + T t T0 dt dV t A t dξ t + dt T t dt

P t P0 − T0 T t

16 Each term on the right side must be nonnegative in accordance with the second Law. Let us assume that in an isobaric vitrification, P(t) = P0. In this case, we find by combining the first two terms in Eq. (16) that 1 T t − 1 T 0 dH t dt ≥ 0

17

As dH(t)/dt < 0 experimentally [2] and theoretically as noted above, T t > T0

18

6 The Free Volume and the Communal Entropy

during relaxation so that T(t) approaches T0 from above [T t T 0+ ]. It now follows from the first inequality in Eq. (15) that during vitrification dS t dt ≤ 0

19

A more refined and general argument for the validity of Eq. (19) is also available [11]. 5.2 Microstate Probabilities in Internal Equilibrium For a body in internal equilibrium, the situation is very similar to that of a body in equilibrium. Thus, the maximization of entropy results in a very similar formulation of the microstate probabilities. The equilibrium probabilities are given by pkeq = exp[−β0(Ek + P0Vk)]/Zeq, where Zeq is the equilibrium partition function, β0 = 1/T0, and Ek, Vk are the energy and volume of the kth microstate. For the body in internal equilibrium, the microstate probabilities are given by pki − eq = exp − β t E k + P t V k + A t ξk

Z i − eq , 20

where Zi − eq is the internal equilibrium partition function; β(t) = 1/T(t), and ξk is the set of internal variables for the kth microstate. The particle number N, which is held fixed in both cases, is not shown. In terms of the number of microstates W(E, V, ξ) corresponding to E, V and ξ, Zi − eq is given by W E, V , ξ exp − β t E + P t V + A t ξ ;

Z i − eq = E, V , ξ

21 it differs from Zeq due to the presence of ξ and timedependent fields/affinities.

the interactions with its neighbor. One uses the cell theory of liquids to go beyond the van der Walls theory. Here, V is divided into N cells (such as the Voronoi-type cells) of an average volume Δ per particle (Figure 4), where we show the possible cell arrangement for disordered (liquid or gas) in (a) and ordered (crystal) states in (b). Each cell has a single particle within it as shown. For molecules with connectivity such as polymers (Chapter 8.7), one must take proper care of all distinct placements of monomers that respect their connectivity. For example, if we consider a disordered conformation of a polymer with 17 monomers, then we must consider all distinct conformations of the polymer even though each conformation has a single monomer in the 17 cells in (a). Thus, there will be many more microstates for the cell pattern in (a) when connectivity has to be incorporated. There will be a single microstate if there is no connectivity to consider. This poses no conceptual problem as the average of any observable O in the cell model is given by the standard formulation O k Ok pki − eq , where Ok is the value of O for the kth microstate and the sum is over all distinct microstates. It is then clear that the entropy associated with local motion in the cell potential also contains what is commonly known as the conformational entropy due to different conformations of a molecule such as a polymer. The nonuniform model in (a) for the disordered state is a generalization of the uniform model traditionally used in cell theories. The other difference is that we allow for an internal variable. The motion of each particle within its cell is governed by ϕ due to all its neighbor, which we denote by ϕ(r|{r (t)}), where r is the position of the particle under consideration within its cell and {r } denotes the set of the continually changing positions of all its neighbors in time. The connectivity among the

(a)

6 The Free Volume and the Communal Entropy 6.1

(b) Particle

The Cell Theory

The simplest model to account for the nonzero particle size is described by the van der Waals’ equation P + N 2 a V 2 V − Nb = NT , where a accounts for the intermolecular attractive forces and the “free volume” is given by V − Nb. The parameter b is half the volume of a sphere of radius 2r0, where r0 is the “radius” of the particle [14]. It is the excluded volume for each particle and the presence of N in Nb implies its additivity. Indeed, it should be thought of as the “thermodynamic” volume of a particle, which is determined by

Figure 4 Cell representation of a small region of disordered (a) and ordered (b) configurations at full occupation: each cell contains a particle. Each cell representation uniquely defines a potential well or basin in the potential energy landscape. Each particle is surrounded by four particles in the ordered configuration, but not for the disordered configuration. In the hole theory, some of the cells remain empty.

281

282

3.3 The Glass Transition and the Entropy Crisis

neighbors and the particle must be properly accounted for in this set. The probability P(ϕ) for the potential ϕ(r|{r’(t)}) is given by the following identity P ϕ =

22

p k ki − eq

where the prime over the sum implies that the sum is restricted to those microstates in which the particle and its neighbors are restricted to be at r and r , respectively. The volume Δ must be at least as big as needed to allow for the local oscillations. The cell potential can be used to characterize the interaction volume vi: it is the minimum volume needed for the allowed local motion. One way to quantify vi is by the root-mean square of the displacement during the local motion as follows. The average over all possible cell potentials with probability P(ϕ) of the displacement squared is given by r 2rms

Σϕ P ϕ

1 2 r t dt , τϕ

23a

where r = 0 is taken to be at the minimum of the potential. The inner integral is over the time period τϕ of an oscillation controlled by ϕ. We first observe that rrms changes with the temperature. To see this most clearly, we simply consider an interparticle harmonic potential ϕ. From dimensional analysis alone, we conclude that the mean square displacement of all the particles scales as the temperature: r 2 T t k s, where ks is the spring constant of the potential. Thus, r rms T t

T t ks

1 2

,

23b

and vanishes at absolute temperature T(t) = 0. It usually happens that the oscillatory modes equilibrate rapidly with the medium. In that case, we must replace T(t) by T0. At absolute zero, particles are sitting in the potential minima, and there is an average distance dmin between particles. Half of the average distance rmin ≡ dmin/2 is taken as the “radius” of the particle, which then determines its interaction volume vm at absolute zero. This is the minimum of the interaction volume. The distance rmin should not be confused with the so-called radius r0 of a particle corresponding to the “impenetrability” of the particles. The interparticle potential begins to rise steeply for separation between particles below the “radius” r0 [14]. Thus, r0 is not strictly the radius of a particle. As the temperature increases, the linear size of the particle increases due to oscillations and so does its interaction volume, which is now given by vi = γ r min + r rms

3

in the glassy literature. Unfortunately, there is a lot of ambiguity in the definition of vo and how to obtain it theoretically [19] so we make no attempt to compare the two. The difference vf = Δ − vi is the free volume vf, that is the elbow room for the translation and rotation of the center of mass of the particle. This motion gives rise to the diffusion of the particle from the region over which the local oscillatory motion occurs. As ζ0 decreases, the elbow room, i.e. vf increases (and so do Δ and vi) but not so much so that particles are still confined within their respective cells. As the free volume increases further, the particles can escape to the neighboring cells so that sometimes a cell may have multiple occupancy of the particles. The particles will undergo local motion in the new cell before they make excursion to another neighboring cell. If the free volume increases too much, then diffusion becomes the dominant motion and the local motion is no longer possible as the particles are far apart now. A situation like this occurs in gases. The above is an average picture so that it will also occur through to fluctuations in energy, volume, and internal variables. The aforementioned scenario has been confirmed by numerical simulations that has been discussed by several authors; see, for example, Refs. [1, 22] and Figure 1. The above discussion is equally valid for the disordered and ordered macrostate. We will, however, consider the disordered macrostate in the following. An obvious refinement of the above cell theory is to allow for holes by having some empty cells. Their presence gives an additional contribution to the free volume. It also allows for a considerable variation in the number of neighboring particles due to the presence of holes, which makes this theory attractive. As the volume of a glass is considerably greater than that of the corresponding crystal or the ESCL, the glass has a significant number of holes, which decreases during relaxation. In general, the decrease in the free volume is related to the irreversible relaxation, whereas the decrease in the interaction volume is related to the equilibrium relaxation as noted above since the local motion within the cell potential occurs at the temperature T0 of the medium and not at the instantaneous temperature of the glass; see also the discussion by Matsuoka [19]. The division of volume in the interaction and free volumes results in the two volumes to be independent as they refer to independent degrees of freedom. Their existence may be related to the success of the two-parameter model of Aklonis and Kovacs [23].

24

in terms of a geometrical factor γ of order unity. The above volume may be quite different from the customarily defined occupied volume vo, which is commonly used

6.2 Communal Entropy The communal entropy Scomm plays a central role in the study of glasses [1, 15, 17]. From the fact that entropy and

7 The Unifying Approach for Glasses

volume are both extensive, we find that the entropy density σ = S/V is a homogeneous function of order zero. We can write the entropy as a sum of two terms: S = Viσ + Vfσ in which the two volumes must be extensive. This is a trivial identity but allows us to introduce two different entropy components associated with the two components of the volume. One such component is Scomm, which is associated with the translation of the particles. The free volume decreases as ζ0 increases and inhibits the translation. The particles must be fully jammed if there is no elbow room (Vf = 0). In this state, there cannot be any translation and Scomm must also vanish. This identifies the ideal glass. If we wish to identify the communal entropy associated with the free volume, then it must vanish for the ideal glass. The only possible relationship between Scomm and Vf must be linear because of their extensivity. If we write it as Scomm = Vfσ with σ σ, then the other component Sint = S − Scomm, the interaction entropy, is given by Sint = Viσ + Vf(σ − σ ). As Sint must be determined by the local motion within the cell potential ϕ, it depends on Vi but not on Vf. Hence, we take σ = σ and write S t = S int t + S comm t , S comm = V f σ, S int = V i σ; 25 each of the above two components of the entropy must be non-negative and must satisfy the second Law provided there is minimal coupling between the two kinds of motion. As said earlier, Sint includes the conformational entropy associated with different conformations of the molecules. The deep connection that we have discovered between the free volume and communal entropy shows that they vanish simultaneously in the ideal glass so that whether we vary the density (control variable P0) or the entropy (control variable T0), we obtain the unique ideal glass at the respective Kauzmann point. This, we hope, will clarify some confusion present in the field as we discuss now.

7

The Unifying Approach for Glasses

It becomes clear from the above discussion that one can consider several entropy differences (Sex, Sconf, Scomm, etc.). Some will vanish, most probably at different ζ 0, under extrapolation to higher ζ0. Similarly, various definitions of the free volume will also show that they vanish at different ζ 0 under extrapolation. Thus, unless care is taken, the vanishing of the entropy difference and the free volume will appear to be unrelated. This has created much confusion in the field. However, by a careful definition of the free volume and the relevant (communal) entropy, one ensures that they vanish simultaneously at

a point called the IGT point. At this point, they refer to the same unique macrostate; see Figures 2 and 3. In the following, we are interested in the SCL in . We will focus on the communal entropy for which we use S instead of Scomm for notational simplicity. We will exhibit E and suppress all other extensive observables below and use a single internal variable ξ for simplicity. According to the second Law SNESCL(E, ξ) < SESCL(E); see Figure 5 where various portions of entropy curves are also identified. As the slope of the curve FG determines the inverse of the internal temperature T(t) T0 of a NESCL, while that of the curve DFCK the inverse of the medium temperature T0, we conclude from the figure that TG(t) at EG is higher than TK = T0K at EK. Indeed, as TNESCL(E) = TESCL(E) at E = EF and at E = EK, where EF is the energy at F, it is evident that TNESCL(t) > T0K over FG. Here, we have used E(t) to express T(E) as T(t). As SNESCL(E, V, ξ) has no singularity over its entire range KGF, we can expand SNESCL(E, V, ξ) in the form of a Taylor series over FG around the point K. For later applicability, it is useful to consider SNESCL(E, V, ξ) as a function of T(t), P(t) and ξ(t). For the isobaric vitrification at P0 that we are considering, we set P(t) = P0. Introducing ΔT(t) ≡ T(t) − T0K and Δξ(t) ≡ ξ(t) − ξeq,K and recognizing that at K the heat capacity CPK is nonzero but finite and that the affinity A0K vanishes (as the ESCL represents equilibrium states in ), we immediately conclude that the leading terms in the expansion must be linear in ΔT(t) (no linear term in Δξ(t)) and bilinear in ΔT(t)Δξ(t). Thus, we can pull out ΔT from all the expansion terms to finally write in terms of a function ΨS whose definition is evident from the (infinite) Taylor expansion (SESCL(EK) = 0): SNESCL T t , P0 , ξ t

= ΔT t ΨS T 0K , P 0 , ΔT t , Δξ t ; 26

we have not shown any dependence on ξeq,K as it is a function of T0K, P0 so it is no longer independent. The extensive function takes the value ΨS(T0K, P0,0,0) = CPK/T0K. A similar Taylor expansion can be made for the volume VNESCL. We first recall that Vf,NESCL and the communal entropy SNESCL vanish simultaneously and that S NESCL T t , P 0 , ξ t

= σ T t , P 0 , ξ t V f,NESCL

T t , P0 , ξ t 27 (In contrast, there is no such relationship between the configurational entropy and the free volume. The simplest way to appreciate is to recognize that the configurational entropy in the Gibbs–DiMarzio theory [18] is nonzero even when the polymers cover the entire lattice, which corresponds to zero free volume.) Thus, Vf,NESCL is also non-singular and will have a Taylor expansion

283

284

3.3 The Glass Transition and the Entropy Crisis

S

K regardless of the pressure, the derivative on the right side vanishes at K. This means that (∂V/∂ξ)T,P also vanish at K, which leads to a leading bilinear combination ΔT (t)Δξ(t). Thus, the situation is as before for SNESCL so that we can write a similar form for Vf,NESCL,

D

F C

V f,NESCL T t , P 0 , ξ t

G

= ΔT t ΨV T 0K , P0 , ΔT t , Δξ t 28

We can use this form of the free volume in the Doolittle Eq. (5) to obtain

K O

EK

E

EG

Figure 5 Schematic form of communal entropies in for the equilibrium supercooled liquid and the nonequilibrium supercooled liquid in accordance with the second Law and the gap hypothesis [15]. The lowest possible energy of the equilibrium supercooled liquid is EK and the corresponding entropy is given by the curve KCFD. It vanishes at K without any singularity. The point K represents the unique ideal glass whose entropy remains zero as shown by the ideal glass entropy OK (dashed line). The lowest possible energy of the nonequilibrium supercooled liquid, which emerges continuously out of the equilibrium supercooled liquid at point F, is shown to be EG > EK at point G due to additional defects. It represents the entropy of a laboratory glass; it also has no singularity at point G so that it can be mathematically continued below EG until it vanishes. As the disordered state of zero entropy must be unique, this continuation must terminate at point K with the same slope as of the curve KCFD. It is shown by the dashed curve GK. It is in essence similar to the continuation carried out by Kauzmann but for Scomm. We do not show the axis corresponding to the independent variable ξ, which is changing along the curve FG. (At points K and F, ξ is no longer independent). The slope at point G is lower than that at point K.

around the Kauzmann point. To determine the nature of the expansion, we follow the above method to determine the leading powers of ΔT(t) and Δξ(t). The volume expansion coefficient at K due to the free volume is nonzero as we approach K from the high temperature side because of the difference in the slopes at K in Figure 2. Thus, the expansion must start with a term linear in ΔT(t). The determination of the leading power of Δξ(t) requires considering the behavior of (∂V/∂ξ)T,P. By considering the double Legendre transform G = E − T t S t + PV t , which is a systemintrinsic internal Gibbs free energy, we find that V = ∂G ∂P ξ,T so that ∂V ∂ξ

T ,P

= ∂ 2 G ∂ξ∂P = ∂A ∂P

ξ,P ;

we emphasize that G (even with P = P0 as noted above) should not be confused with the Gibbs free energy G(t) = E(t) − T0S(t) + P0V(t), which contains the temperature and pressure of the medium [14, 22]. It is the latter that decreases in a spontaneous process as discussed in Section 4.2. As the affinity A always vanishes at

η = η0 exp γvm T t − T 0K ψ V

29

in terms of the intensive function ψ V ≡ ΨV/N. We thus conclude that the phenomenological equation is a special case of the above general equation. The limited validity of the original (constant parameters) Doolittle equation also makes the VTF equation with limited validity. In addition, different concept of the free volume will also yield different temperatures where it vanishes. This explains the puzzling differences between T0V and the Kauzmann temperature noted by several workers. Using the linear relationship from Eq. (27) in Eq. (5), we obtain η = η0 exp γvm gsNESCL

30

in terms of the per particle communal entropy sNESCL ≡ SNESCL/N and g = 1/σ. This is the analog of the Adam– Gibbs Eq. (3) in terms of the communal entropy, except that the viscosity diverges at different temperatures in the two formalism. A similar argument as used above will also show that in terms of ΔTS(t) ≡ T(t) − T0S, S conf NESCL T t , P 0 , ξ t

= ΔT S t Ψconf S

T 0S , P 0 , ΔT S t , Δξ t Thus, its vanishing at T0S also shows a divergence of viscosity in Eq. (3). As all these formalisms are developed based on different approaches but with the same conclusion of diverging viscosity, it appears that the suggestion of a rapid rise in the viscosity due to a sudden drop in some form of entropy difference seems very enticing. Thus, we are driven to the conclusion that we can treat the SCL GT within a thermodynamics formalism involving some sort of entropy crisis. However, the divergences occur at different temperatures so the divergences may be devoid of any physics in terms of ideal glass. This leaves the nature of the state with a diverging viscosity quite mysterious. While the vanishing of free volume is not tied to the vanishing of sconf or sex, it occurs simultaneously with the vanishing of the communal entropy. Thus, our proposal of using the communal entropy ties the divergence of the viscosity with the vanishing of either the free

References

volume or the communal entropy at the same temperature T0K, and helps in elucidating the nature of ideal glass as a jammed state with no translational mobility and, hence, no communal entropy.

8

Perspectives

A complete understanding of viscosity divergence around GT is of technological importance. The conventional approaches to study viscosity as a function of temperature either uses ΔSex, Sconf, or Vf. Phenomenological data fitting invariably leads to a perplexing scenario in that the divergence occurs at different temperatures and does not unravel the root cause of the dynamical slowdown. This seems unsettling as the invariable conclusion is that there is no relationship between the vanishing of Vf, ΔSex, and Sconf as used in the experimental analysis. The puzzle is that the thermodynamic state of the system with a diverging viscosity must be independent of the theory used to describe the system. Such a state must be a unique state in that once the viscosity has diverged, the state cannot change in time unless disturbed. With our current understanding of nonequilibrium thermodynamics, we have begun to unravel the mystery a bit by connecting the viscosity divergence with either the vanishing of the free volume or the communal entropy. This is done by properly identifying the two concepts thermodynamically. For a system in internal equilibrium, η must be a function of the state variables: η = η(T(t), P(t), ξ(t)). For a state with diverging viscosity, there cannot be any variations in the fields. In other words, we expect a unique temperature where η diverges. At this point, which identifies the Kauzmann temperature T0K, the system mathematically turns into an ideal glass state characterized by vanishing Scomm and Vf simultaneously. This mathematical singularity appears as the sudden and rapid rise in the viscosity in laboratory glasses. Thus, the new approach provides a unified picture of the glassy behavior. While we did not discuss it here, we have shown it elsewhere [22] that our nonequilibrium thermodynamics also provides a rational for the Tool–Narayanaswamy phenomenology (Chapter 3.7). It is evident that we can never get to the ideal state in the laboratory, but this is not relevant for the mathematical expansion around the Kauzmann point. The linear relation Scomm = Vfσ associated with the free volume Vf differs from the alternate choice Sf = − ln Vf used by several authors ([19], for example). We do not consider the latter choice as it cannot only give negative communal entropy, but also does not respect the extensivity of the two quantities.

The limitation of the chapter should be mentioned. We have not discussed recent work dealing with the heterogeneity in space and time for glasses. The reason for this is that the nonequilibrium thermodynamics that we are using requires the additivity of the entropy for different parts. This requires the parts to be macroscopically large so that surface effects can be neglected. Thus, the approach is not applicable to a few particles for which we need small-size nonequilibrium thermodynamics, a field which is in infancy at present. We have also not discussed how the notion of the free volume or the communal entropy can be extended to each microstate as it evolves in time. Such a study will provide more detailed information about the resulting fluctuations going on within the system.

Acknowledgement The help from the reviewers in improving the presentation is gratefully acknowledged.

References 1 Zallen, R. (1983). The Physics of Amorphous Solids. New

York: Wiley. 2 Goldstein, M. and Simha, R. (eds.) (1976). The Glass

3 4 5

6

7

8

9

Transition and the Nature of the Glassy State, vol. 279, 1–237. New York: New York Academy of Sciences. Debenedetti, P.G. (1996). Metastable Liquids, Concepts and Principles. Princeton University: Princeton, NJ. Angell, C.A. (1997). Entropy and fragility in supercooling liquids. J. Natl. Res. Inst. Stand. Technol. 102: 171–185. Richet, P. and Bottinga, Y. (1984). Anorthite, andesine, wollastonite, diopside, cordierite and pyrope: thermodynamics of melting, glass transitions, and properties of the amorphous phases. Earth Planet. Sci. Lett. 67: 415–432. Richet, P. (1984). Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48: 471–483. Adam, G. and Gibbs, J.H. (1965). On the temperature dependence of cooperative relaxation properties in glassforming liquids. J. Chem. Phys. 43: 139–146. Berthier, L. and Biroli, G. (2011). Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83: 587–645. https://doi.org/10.1103/ RevModPhys.83.587. Ngai, K.L. (2007). All standard theories and models of the glass transition appear to be inadequate: missing some essential physics. In: Soft Matter under Exogenic Impacts (eds. S.J. Rzoska and V.A. Mazur), 91–111. Dordrecht: Springer.

285

286

3.3 The Glass Transition and the Entropy Crisis

10 Lubchenko, V. and Wolynes, P.G. (2007). The theory of

11

12

13

14 15

16

structural glasses and supercooled liquids. Annu. Rev. Phys. Chem. 58: 235–266. Gujrati, P.D. (2018). Hierarchy of relaxation times and residual entropy: a nonequilibrium approach. Entropy 20: 149. https://doi.org/10.3390/e20030149. Weeks, E.R., Crocker, J.C., Levitt, A.C. et al. (2000). Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 287: 627–631. Kauzmann, W. (1948). The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43: 219–256. Landau, L.D. and Lifshitz, E.M. (1986). Statistical Physics, Part 1, 3e. Oxford: Pergamon Press. Gujrati, P.D. (2010). Energy gap model of glass formers: lessons learned from polymers. In: Modeling and Simulation in Polymers (eds. P.D. Gujrati and A.I. Leonov), 443–496. Weinheim: Wiley-VCH. Gujrati, P.D. (2015). On equivalence of nonequilibrium thermodynamic and statistical entropies. Entropy 17: 710–754. https://doi.org/10.3390/e17020710.

17 Cohen, M.H. and Grest, G.S. (1984, 60). The nature of the

glass transition. J. Non Cryst. Solids 61 & 62: 749. 18 Gibbs, J.H. and DiMarzio, E.A. (1958). Nature of the glass

19

20

21 22

23

transition and the glassy state. J. Chem. Phys. 28: 373–383. Matsuoka, S. (1981). Free volume, excess entropy and mechanical behavior of polymeric glasses. Polym. Eng. Sci. 21: 907–921. Doolittle, A.K. (1951). Studies in Newtonian flow. II. The dependence of the viscosity of liquids on free-space. J. Appl. Phys. 22: 1471–1475. Nemilov, S.V. (1995). Thermodynamic and Kinetic Aspects of the Vitreous State. Boca Raton, FL: CRC. Gujrati, P.D. (2010). Nonequilibrium thermodynamics: structural relaxation, fictive temperature, and ToolNarayanaswamy phenomenology in glasses. Phys. Rev. E 81: 051130. Aklonis, J.J. and Kovacs, A.J. (1979). A new look at the glass transition. In: Contemporary Topics in Polymer Science, vol. 3 (ed. M. Shen), 267–295. New York: Plenum Press.

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3.4 Atomic Vibrations in Glasses Bernard Hehlen and Benoît Rufflé Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS, Université de Montpellier, Montpellier, France

1

Introduction

Atoms have by definition essentially fixed position in a solid. Their only degrees of freedom are thus vibrations around these positions with amplitudes that increase with temperature. As a thermodynamic measure of these changes, the heat capacity then determines the temperature dependence of the internal energy, entropy, and other functions. But the relevance of atomic vibrations is not restricted to thermal properties because thermal energy is involved in any process where potential energy barriers must be overcome. This is the case of not only any kind of phase transformations, including magnetic or ferroelectric transitions, but also of transport of heat, electrically charged species, or atoms. In a crystal, atoms do not vibrate independently from one another. Vibrations are instead described as a set of harmonic plane waves termed phonons whose energies are quantized, whose number and type are determined by the symmetry of the lattice, and whose frequencies vary with the wave vectors according to specific dispersion relations. Although the fundamental basis of lattice dynamics was laid down by Born and von Karman as early as 1912, the lack of spatial symmetry prevents this theory from being applied to amorphous solids. The problem of atomic vibrations in glasses has thus long been laid aside until the impressive development of new experimental techniques, computing capabilities, and theoretical advances has made it possible to tackle it fruitfully in the last past decades. The connection between the macroscopic and microscopic aspects of atomic vibrations is most readily Reviewers: P. Gujrati, Department of Physics, The University of Akron, Akron, OH, USA R. Vacher, Laboratoire Charles Coulomb, Université de Montpellier, Montpellier, France

established through the vibrational density of states, g(Ω), which is the distribution of the number of vibrational modes as a function of the frequency Ω. The vibrational isochoric heat capacity Cv(T) is directly derived from g(Ω) through Ωm

Cv T =

cv Ω, T g Ω dΩ,

1

0

where Ωm is the highest vibrational frequency. As for cv(Ω, T), it is the heat capacity of a single oscillator given by the Einstein function. cv x =

x2 ex ex − 1

2

,

2

where x = ħ Ω/kBT, and kB and ħ are Boltzmann and reduced Planck constants, respectively. In the last past decades, much progress has been made either theoretically or experimentally to determine g(Ω) as well as the various vibrational excitations existing in glasses. These advances will thus be reviewed in this chapter with a focus on low-temperature conditions under which a rich phenomenology manifests itself. When heat capacities are approaching their Dulongand-Petit limits, which is already the case for oxide glasses near room temperature, significant effects of structure and composition on vibrational properties in contrast necessarily tend to vanish. This is why such hightemperature conditions will not be considered in this chapter. The starting point will be the classical description of phonons in perfectly ordered structures with a simple one-dimensional model. The impact of disorder on the vibrational properties of the system will reveal the loss of the plane-wave character of the normal modes and the concomitant apparition of quasi-localized modes. We follow with the comparison between the low-temperature

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

3.4 Atomic Vibrations in Glasses

thermal properties of crystalline and disordered solids, underlining the relation between the well-known anomalous behavior of the latter materials and their vibrational properties. Finally, we discuss the implications for vibrational spectroscopy of sound waves and optic modes, including the boson peak.

2 Atomic Vibrations in Disordered Solids 2.1 The Diatomic Linear Chain A simple system is a chain of N atoms of mass m alternating with N atoms of mass M to which they are connected by springs of force constant K. If periodic conditions are applied, the chain forms an infinite periodic lattice of unit cells comprising one of each mass. The solution to the equation for longitudinal motions is a set of well-defined propagating plane waves with eigenfrequencies Ωj and associated wave vectors Qj, which define two dispersion curves Ωj(Qj), namely, an acoustic and an optic branch representing in- and anti-phase motion of the masses within a unit cell, respectively. Each solution j is called a normal mode or an eigenmode. For the jth normal mode, the displacement of mass l of one species reads U j,l t = uj exp i Qj r l − Ωj t

,

3

where uj is the amplitude of the mode and rl is the position of the mass in the chain. At every moment, there exists a perfect spatial oscillatory pattern of the mass displacements uj,l = uj exp(iQjrl), characterized by Qj.

(a)

One can then introduce disorder by varying the spring constants Ki along the chain, the masses, or their equilibrium positions. Here, we will assume a normal distribution of spring constants with a mean value K0 and a standard deviation δK to diagonalize the dynamical matrix and derive the eigenfrequencies and eigenmodes of the system. Owing to disorder, Uj,l can no longer be simply expressed as in Eq. (3) so that it is no longer possible to define Qj strictly. One can nevertheless expand uj,l in a Fourier series of the components Qk with amplitudes αj,k [1]. For a quasi-plane-wave normal mode j, the amplitude is significant only for αj,k for which j ≈ k. Conversely, a localized mode has a large range of nonzero αj,k. The nature of a normal mode j can thus be roughly characterized by the mean value Qj and the standard deviation of its wave vector spectral density |αj,k|2. These coefficients also control the response of the system to a plane-wave vibrational excitation [1]. As an example, eigenfrequencies Ωj have been computed for a disordered chain comprising N = 2000 masses as a function of Qj (Figure 1) with δK/K0 = 0.25 and a mass ratio M/m = 2. As noted long ago [2], the vibrational density of states of the disordered chain gd(Ω) is not much affected by disorder, especially for the acoustic modes whose density is actually similar to that of a crystalline counterpart gc(Ω). The main differences occur near termed frequencies where gc(Ω) exhibits sharp maxima, which are termed Van Hove singularities and are smeared out by disorder (Figure 1b). Although this similarity is holding particularly true for optic modes, gd(Ω) is higher than gc(Ω) by only about 3% even at low frequencies, i.e. in the acoustic regime.

(b)

(c)

2.0 Ω = 1.61 1.5

1.0

Ω = 0.24

0.5 Ω = 0.02

0.0 0.0

0.2

0.4

0.6

Fourier component Q/π

0.8

1.0

0 g (Ω)

500 1000 rI

Amplitude uj,l(t0)

Eigenmode frequency Ω

288

Figure 1 Vibrational properties of a disordered diatomic linear chain. (a) Eigenmode frequencies Ωj as a function of the mean value Qj of the wave vector spectral density αj(Q) (dots); standard deviations of αj(Q) centered on Qj characterizing the Q-spread of the jth eigenmode (very thin horizontal lines); dispersion curves of the acoustic and optic modes of the ordered chain (thick oblique curves). (b) Vibrational density of states g(Ω) of the crystalline (dashed line, gc(Ω)) and the disordered chains (dotted line, gd(Ω)). (c) Displacement snapshots for the three eigenmodes indicated.

3 Vibrations and Thermal Properties

In contrast, the nature of the vibrational modes is strongly modified by disorder (Figure 1a and b). The progressive scattering of the initial plane waves is clearly illustrated by the wide Q-spread of the eigenmodes (Figure 1a). As generally found, the higher the frequency, the larger is the deviation from a plane-wave excitation. In the long-wavelength limit, the very low-frequency acoustic modes hardly differ from those of their crystalline counterparts. Details of the force constant distribution is indeed of little concern to these long-wavelength acoustic excitations as fluctuations are averaged out. The eigenvectors (mass displacements) of these modes exhibit almost perfect oscillations in space as illustrated in Figure 1c by the lowest line corresponding to Ωj = 0.02. This is no longer true for Ωj = 0.24 for which the envelope of the mass displacements shows important spatial variations. This mode is still an extended (collective) mode as all the masses participate in the vibration, albeit with different amplitudes. The loss of the plane wave character increases dramatically for modes at higher frequency as shown for Ωj = 1.61 belonging to the optic branch in the crystalline chain. Most of the vibrational amplitude is localized on a couple of neighboring masses. All high-frequency modes show significant displacements of neighboring masses only, occurring at randomly distributed spatial positions. But these modes are not truly localized because their vibrational amplitudes are extremely small for many masses, but not exactly zero. 2.2

Real Amorphous Solids

Scattering of the vibrational modes thus increases with frequency even when elastic disorder is small enough that the vibrational density of states is similar to that of a periodic lattice. To what extent such a simple picture can be generalized has been much debated because real glasses combine positional, mass, and elastic disorder in complex 3-D structures made up of coupled structural entities. Further, disorder-induced mixing of transverse and longitudinal polarized excitations should arise at high frequency [1]. In the long-wavelength limit, sound waves propagate in glasses as they do in crystals. At that scale, amorphous solids are isotropic continuous elastic media whose low-frequency sound waves can still be reasonably described as quasi-plane-wave acoustic excitations. Phonon-like transverse acoustic excitations showing linear dispersion have been, for example, measured in vitreous silica [v-SiO2] up to ~440 GHz [3], which corresponds to a length scale of ~10 nm. This result might thus suggest that the low-temperature thermal properties of glasses should mimic those of their crystalline counterparts, at least below 2–3 K, but this does not seem to be generally the case. From the expected non-plane-wave character of the high-frequency eigenmodes, it is further anticipated

that selection rules should be relaxed in spectroscopic studies, complicating the analysis and limiting the amount of information that can be obtained from vibrational spectra.

3 3.1

Vibrations and Thermal Properties Heat Capacity

The heat capacity Cv ≈ Cp of a perfect crystal obeys Debye law Cp (T) = CDT at temperatures below ~0.01 θD, where θD is the Debye temperature and C D θD− 3 can be calculated from the sound velocities and the atomic density. At higher temperatures, Cp begins to probe the details of the atomic structure via the acoustic dispersion curves throughout the Brillouin zone and eventually the optic modes. The measured heat capacity of α-quartz nicely illustrates this point. Below 5 K, Cp/T3 almost perfectly matches the expected Debye value whereas the upturn above 10 K is fully described by the curvature of the acoustic phonon branches. In α-cristobalite, the SiO2 polymorph whose density is close to that of the glass, Cp/T3 reaches its constant Debye value only below 2 K, in agreement with its lower atomic density. Giving rise to a large bump around 13 K, the very steep increase at higher temperature is mostly related to the rapid flattening of the transverse acoustic branches in the direction [4, 5]. Because a given vibrational mode contributes to the heat capacity according to its relative weight in the vibrational density of states, the intense Raman active zone center mode of α-cristobalite around 50 cm−1 [6], for example, enhances Cp from 15 K, just above the maximum of Cp/T3. In contrast, the heat capacity of v-SiO2 does not conform to Debye model. Its larger value at 2 K indicates extra modes at low frequencies. Close to 0 K, part of this excess is due to an almost linear contribution proportional to temperature, which is associated with tunneling states [7–9], whose discussion is beyond the scope of this chapter. Subtracting this feature (Figure 2a) still leaves an excess over the Debye prediction. In agreement with their analogous local order and atomic packing, v-SiO2 and cristobalite display similar peaks in Cp(T)/T3 and reduced density of states g(Ω)/Ω2. Such common features early indicated [4] that low-energy peaks are not a peculiarity of glasses [10, 11] although they do not necessarily imply a common origin for both kinds of phases. The heat capacity of cristobalite is, for instance, completely understood in terms of phonon-branch dispersion. In contrast, the linear dispersion of sound waves up to at least 440 GHz [3] in v-SiO2 gives a constant Debye value up to ~5.5 K (dashed line in Figure 2a) which is inconsistent

289

3.4 Atomic Vibrations in Glasses

(b) 3.0 2.5

Vitreous silica α-cristobalite

103

║C

α-quartz

~T –1

~T 3

⟂C

101

2.0

100 ~T 2

1.0 0.5

103

102

100

In dielectric crystals, significant scattering of acoustic phonons is reflected in the low-temperature thermal conductivity κ. With the standard kinetic equation for gases, one approximately describes the temperature dependence of κ by 1 C v vl, 3

1

101 102 Temperature (K)

3.2 Thermal Conductivity

κ=

10–4

100

with both the position and width of the peak in Cp(T)/T3. One must assume instead a g(Ω) Ω4 relationship on top of the Debye contribution [7]. Such an Ω4 dependence of the density of states is an ubiquitous feature in disordered systems [12]. But whether the excess above the Debye expectation at temperature below the maximum in Cp/ T3 (shaded area in Figure 2a) is a manifestation of disorder and, as such, is related to a strong scattering of the acoustic phonons in glasses occurring at high frequencies is a central and still unsettled question. Only these vibrational excitations define the boson-peak modes, as will be further discussed in Section 6.

4

where Cv is the heat capacity per volume of the excitations providing the thermal transport, v their velocity of propagation, and l their mean free path [13]. This expression is obviously valid only for propagating phonons, i.e. below 1–2 THz in glasses as discussed below in the same subsection. From ambient, κ increases with decreasing temperature through the increasing lifetimes of acoustic excitations. As there are fewer and fewer phonons, l increases as T−1 at high temperatures. The mean free path is of course limited by sample dimensions so that κ goes through a maximum, the Casimir limit, and then

Figure 2 Low-temperature thermal properties of SiO2 phases. (a) Lowtemperature heat capacity of vitreous silica, α-cristobalite, and α-quartz in plots of Cp/T3 against T. Horizontal lines: Debye constants (dashed, dotted, and full line, respectively). Open circles: Cp/ T3 of vitreous silica without the twolevel system contribution. (b) Thermal conductivity of the same polymorphs. Inset: frequency dependence of the mean free path in vitreous silica in the dominant-phonon approximation.

10–3

λ

0.1 Freq. (THz)

101 Temperature (K)

10–2

ℓ ∝ Ω–4

102 101

10–1

T(K) 12.62

1.26 Mean free path (nm)

1.5

0.0 100

102

k (W/m/K)

(a)

104 Cp/T 3 (J/mol/K4)

290

2

10–5

decreases with the T3 dependence of Cv at low temperatures as illustrated by the thermal conductivity of α-quartz along the c-axis (Figure 2b). By contrast, the thermal conductivity of a dielectric glass material is much lower and has a markedly different temperature dependence. These features are illustrated by vitreous silica (Figure 2b) for which κ increases nonmonotonously with increasing temperature with a remarkable plateau beginning just below the hump in Cp/T3. At very low temperatures, κ follows an approximate T2 law instead of the T3 dependence expected from the Debye approximation. According to a widely accepted interpretation, this initial T2 rise is due to interactions between phonons and tunneling states, which reduce l in glasses [7–9]. The microscopic origin of the plateau around 3–15 K is in contrast a much more controversial issue. In early calculations, a very efficient phonon-scattering mechanism was assumed by a proportionality of l to at least Ω−4 [14], which suggested Rayleigh scattering from disorder in the glassy network. From Eq. (4), it is possible to estimate a mean value for l(T) that can be recast in l(Ω) with the dominant phonon approximation ħΩ ~ 3.8 kBT (Figure 2b). In the hypersound frequency range, i.e. below 100 GHz, l(ω) exceeds 1 μm so that it is much larger than the acoustic wavelength λ, confirming the assumption of propagation. In this range, resonant relaxation by tunneling states dominates acoustic attenuation below 1 K (Figure 2b, top x scale), yielding l(Ω) Ω−1. Above about 100 GHz, l(Ω) drops rapidly following an approximate Ω−4 trend. Near 1 THz, it becomes comparable to the acoustic wavelength λ, marking the Ioffe-Regel crossover from propagating plane-wave acoustic modes to diffuse excitations. Above the corresponding frequency ΩIR, the wave vector loses

4 Inelastic Spectroscopy in Glasses

its meaning and the notion of phonon becomes ill-defined. Sound waves do not propagate and can no longer transfer energy. The dominant phonon approximation certainly breaks down as well in this range. Only recently has this frequency region become available for coherent spectroscopy of acoustic phonons. At higher temperatures, κ rises again and eventually saturates at around 1 W/m/K. As heat transport can no longer be mediated by propagating sound waves, it is generally admitted that κ is governed here by diffusion mechanisms [15, 16]. Finally, the room-temperature conductivity of α-cristobalite of ~6 W/m/K (Figure 2b) is close to the value obtained in the direction normal to the c-axis in α-quartz and much higher than the ~1 W/m/K reported for v-SiO2. This feature suggests that the temperature dependence of the thermal conductivity of α-cristobalite is essentially governed by anharmonic processes and follows the expected crystalline increase up to the Casimir limit when the temperature is lowered. Hence, the very rapid flattening of the dispersion curves of the acoustic branches in the direction, which causes the hump in Cp/T3, is by no mean sufficient in itself to produce a plateau in κ around 10 K.

Inelastic Spectroscopy in Glasses

4.1 Dispersion Diagram and Experimental Techniques The dispersion curves of the longitudinal phonons of vitreous silica and amorphous selenium, in the region where

Wavelength (Å) 107

106

105

104

103

102

101

100 107

1018

Spectral width or Frequency (Hz)

Figure 3 Dispersion of longitudinal acoustic phonons in vitreous silica (vLA = 5960 m/s) and selenium (vLA 1800 m/s) and relevant ranges of the scattering techniques probing atomic excitations in disordered materials: ultrasonics (US), Brillouin light scattering (BLS), Raman scattering (RS), picosecond optical technique (POT), infrared absorption (IR), inelastic neutron scattering (INS), inelastic X-ray scattering (IXS), neutron spin echo (NSE), neutron backscattering (NBS), photon correlation spectroscopy (PCS), and X-ray photon correlation spectroscopy (XPCS). The frequency domain of optic vibrations in network glasses is delineated by horizontal dashed lines.

qIR

1016 Optic

1012 1010 108

US

ν-SiO 2 ν-Se

103

IXS

RS, IR

1014

105

stic

Acou

INS

(LA)

101 10–1

NBS 10–3

BLS, POT

NSE

106

&

10–5

104

TOF-NSE

10–7

102

10–9

PCS

XPCS

100

10–11

10–2

10–13 10–7

10–6

10–5

10–4

10–3

10–2

Scattering wavevector q

(Å–1)

10–1

100

101

Energy (meV)

4

they are plane waves, illustrate the variety of techniques used to study atomic excitations in disordered systems (Figure 3). The frequency range of network optic modes (typically between a few THz and ~2000 THz) is delineated by horizontal dashed lines whereas the boson peak stands on the low-frequency limit of that region (~0.5–3 THz). The longitudinal acoustic branch of vitreous silica has, for instance, been widely investigated by inelastic Xray scattering (IXS), whereas v-Se is one of the few examples where longitudinal sound velocity is sufficiently low to be accessible by inelastic neutron scattering (INS). Depending on their frequency and scattering wave vector, some of the techniques displayed in Figure 3 are sensitive to relaxation only (X-ray photon correlation spectroscopy [XPCS], photon correlation spectroscopy [PCS], and neutron spin echo [NSE]), others to both relaxation and vibrations (ultrasonics [US], Brillouin light scattering [BLS], picosecond optical technique [POT], Raman scattering [RS], IXS, INS, and neutron backscattering [NBS]) whereas the scattering vector q is not defined for infrared absorption (IR) and US, which do not involve scattering. Much of the dispersion diagram is nowadays experimentally accessible except in the domain between 10−1 and ~2 × 10−3 Å−1 located at the limit of the Ioffe-Regel crossover region, defined by qIR (Section 5.2). Owing to kinematic conditions, INS is not a technique of choice for such experiments, at least in structural glasses of rather high sound velocities. Close to q = 0, it is of course not possible to measure sound waves whose velocities are larger than those of the incident neutrons. Accordingly, the high-frequency limit of INS in Figure 3 roughly corresponds to the highest

291

292

3.4 Atomic Vibrations in Glasses

neutron velocities enabling measurements down to q ~ 0.1 Å−1. Another drawback of INS and IXS is their inability to probe transverse acoustic phonons close to q = 0.

4.2 Scattering Intensity The intensity I(q, ω) of an incident radiation scattered by a material is proportional to the space and time Fourier transform of the correlation function of the physical quantity (let us call it A), which couples to the incoming radiation [17]: I q, ω

A r, t A r + r , t + t dtdr

FT V t

5

= C A S q, ω For X-ray, neutron, and light scattering, A stands for the electronic density ρe, the coherence length b, and the dielectric susceptibility χ, respectively, and the function C(A) expresses the selection rules of the scattering experiment. It depends on the strength of the coupling of the incident radiation to a vibration and, therefore, modulates the intensity of its spectral shape given by S(q, ω). For light scattering, the susceptibility χ can be expressed in terms of the polarizability tensor α, the hyper-polarizability tensor β, or the photo-elastic tensor p , giving rise to Raman, hyper-Raman, and Brillouin processes. Neutron scattering is sensitive to all vibrations and enable measuring the phonon dispersion curves over a large (q, ω) range. The vibrational density of states is given by the normalized integral over all q-values and yields g(ω). In neutron scattering studies, however, the latter is modulated by the coherent length of the atoms so that it remains an approximate quantity. However, structural disorder prevents a general theory from being formulated to describe vibrational selection rules hidden in the expression of C(A) in glasses, analogous to the role of group theory played for crystals and molecules. This is one of the main reasons why the description of atomic vibrations is hardly accessible. Another limitation is the spatial localization of the modes described in Section 4.3.

spatial extension larger than the probed wavelength, e.g. acoustic and optic phonons in crystals Q = q = ± ki − ks

6

Only the vibrations whose wave vectors Q match those of the experiments q = ±(ki − ks) will then be active for a given scattering geometry. Hence, one observes that understanding selection rules requires to distinguish the frequency and wave vector of the vibration (Ω, Q) from that accessible by the instrument (ω, q). The other extreme situation corresponds to nonpropagating vibrations of fully localized molecular motions as observed in liquids or gases. A perfect localization in real space leads to an infinite spectral broadening of Q, ΔQ ∞, in the Fourier space. Hence, Q is not a relevant physical quantity and the vibration scatters at every q value. For the intermediate situation of quasi-localized vibrations, the coherence length of the mode – if it is sufficiently short – may induce a wave vector spectral broadening ΔQ (horizontal lines in Figure 1a). In that case, the contribution at ω in the vibrational spectrum is the sum over all modes of frequency Ω = ω having a wavevector spectral component Q matching the scattering wave-vector q of the experiment. The above conclusion holds true in glasses for optic modes as well as for short-wavelength acoustic waves since the latter progressively transform into quasi-localized vibrating entities at high frequencies (cf. Section 2). Another way to address the propagation of acoustic phonons in amorphous solids is to consider plane waves propagating in a mechanically inhomogeneous medium [18] where χ depends on position. The disorder induces a spatial modulation of the photoelastic constants, resulting in distorted acoustic waves whose coherence length is limited by local elastic inhomogeneities, as in the model developed in Section 2. A full treatment shows that the light-scattering spectrum consists of the usual Brillouin peaks and a background rising as ω2 originating from the incoherent contribution induced by these local heterogeneities.

5

Vibrational Spectra

5.1 Optic Modes in the Glass Formers SiO2 and B2O3 4.3 Coherent and Incoherent Scattering In disordered media, a very important consequence of the spatial localization of extended waves is a loss of coherence of the scattering process due to the ill-defined nature of the wave vector Q of the vibration. But the momentum keeps conserved when modes are characterized by a

Incoherent scattering process combines with structural disorder to produce broad bands in the Raman and infrared spectra. If the glass has a short-range structure similar to that of a crystalline counterpart, its vibrational spectrum will generally represent a smeared-out version of that of the crystal. For example, the similarities

5 Vibrational Spectra

between vitreous silica and its crystalline counterparts are striking (Figure 4). The lack of long-range order prevents vibrations in glasses from being described in a unique way. A first possibility is to consider the atomic displacements (eigenmodes) of an elementary structural unit such as the

Raman intensities (a.u.)

4 α-Cristobalite α-Quartz ν-SiO2

3

2

1

0 0

500

1000

Frequency ω (cm–1)

Figure 4 Raman spectra of v-SiO2, α-quartz, and polycrystalline α-cristobalite.

12

Im(ε)

10

(a) Infrared

8

TO4

6

TO2 TO3

TO1

n

F1 (HRS BP)

4 2 0

Rocking (TO4)

IHRS (Cts/s)

(b) Hyper-Raman 1

O

x6

BP

Si

0.5

Si

A1 (R) n = 3,4

0 D1

(c) Raman 3 IRS (a.u.)

Figure 5 Vibrational spectroscopy of v-SiO2 and atomic displacements for the main modes [19–21]. From top to bottom: infrared absorption, hyper-Raman scattering, Raman scattering, and vibrational density of states derived from neutron scattering [22]. N.B. F1 vibrations seen in HRS are not the only ones participating in the boson peak.

SiO4 tetrahedron of Td-symmetry or the Si–O–Si bridge of C2v-symmetry in v-SiO2, and the BO3 triangle of D3hsymmetry or the B–O–B bridge in v-B2O3. A second possibility is to define rocking, bending, and stretching motions of N–O–N units, where N=Si, B, Ge, etc. A pure bending modulates only the N–O–N bond angle whereas a pure stretching modifies the N─O bond length. Finally, numerical simulations often project displacements over three orthogonal axes also defined as bending, stretching, and rocking axes. The first one is perpendicular to the N–O–N plane, the second is parallel to the N–O–N bisector, and the third is parallel to the N–N direction. In that case, bending and stretching are not pure vibrational modes. These definitions are not unequivocal, however, so that they can foster confusion in mode assignments. Owing to network connectivity, the spectral responses generally involve several structural units, which further complicates the description. Although some of the conclusions are still discussed, atomic displacements are tentatively summarized hereafter for the main glass formers. For v-SiO2 and v-B2O3, the differences between the IR, Raman, and hyper-Raman spectra (Figures 5 and 6) indicate that selection rules do apply in glasses with sufficiently well-defined local structures. The three polar modes TO1, TO2, and TO3 in v-SiO2 are, for example,

x6

R

2

VV VH

A1 (D1, D2)

D2

1

BP F2b

g(ω) g(ω)/ω2 0

F2b 0

200

400

800 1000 600 Frequency ω (cm–1)

1200

293

3.4 Atomic Vibrations in Glasses

2

1

3

4

Figure 6 Vibrational spectroscopy of v-B2O3 and atomic displacements for the main modes [19–21]. From top to bottom: infrared absorption, hyperRaman scattering, Raman scattering, and vibrational density of states derived from neutron scattering [22]. N.B.: F1 vibrations seen in HRS are not the only ones participating in the boson peak.

5

15 Infrared

10 4*Im(–1/ε) (LO) ε″ (TO)

5

Intensity (a.u.)

2500

1

600

BP (E″)

1500

750

Hyper-Raman

A″ 2 VH VV

2

500

E′ 3

A′

1

x3 5

4

50

x 10

Raman (VV)

25

g(ω)

294

5

0 0

500

1000

1500

Frequency (cm–1)

active in IR, Raman, and hyper-Raman, in agreement with either the C2v- or Td-symmetry selection rules. Within the Td point group, F2-symmetry stretching motions of SiO4 tetrahedra (F2s) contribute preferentially to TO1 and TO2, whereas F2-symmetry bending ones (F2b) dominate in TO3 [20]. Since the Raman inactivity of TO4 cannot be accounted for by any of the internal vibrations proposed by the two structural models, this mode rather represents highly cooperative motions involving rocking of the oxygen atoms [21, 23] in the Si–O–Si bridges the weak value of the depolarization ratio (IVH/IVV) of the Raman R, D1, and D2 bands are compatible with A1bending of the Si–O–Si bridges of C2v-symmetry. The displacements are in phase in the three- and fourmembered ring (Si–O–Si)n planar structures (n = 3 and 4, respectively), and are commonly ascribed to breathing modes. Such motions induce very weak dipolar fluctuations and are, therefore, almost inactive in IR and hyper-Raman scattering (HRS). Likewise, in the vibrational spectrum of v-B2O3 (Figure 6), the atomic displacements proposed are compatible with the molecular selection rules of the D3h-symmetry group of BO3 triangles and B3O6 boroxol rings.

Although very powerful, vibrational techniques do not lend themselves to quantitative structural estimates. Even though numerical simulations are proving valuable in this respect, thanks to calculations of the coupling-to-light coefficients C(A) in Eq. (5) or to NMR calibrations, the main asset of inelastic spectroscopies remains their ability to derive information that may be difficult or even impossible to obtain with conventional structural techniques. For example, threeand four-membered rings represent only one per 670 and 550 SiO2 units, respectively [24]. These proportions are much too low to be detected in a diffraction experiment, but high enough to produce the narrow D1 and D2 Raman bands. Whereas the broad R-band probes the Si–O–Si angle distribution [22, 25], the high-frequency feature depends on the fraction of Qn-species in binary or more complex silicates. The role of modifier, charge compensator, or glass former played by other cations can also be investigated. In v-B2O3, structural information accessible by vibrational techniques concerns, for instance, the fraction of boroxol rings B3O6 and the ratio of BO3-triangles and BO4-tetrahedra in binary glasses (Chapters 2.8 and 7.6).

5 Vibrational Spectra

The combination of these mechanisms thus results in complex variations of l−1(ω, T), which strongly depend on glass composition. Finally, very short-wavelength sound waves experience a disorder-induced strong scattering regime, which dominates above 0.1–0.2 THz, depending on temperature and on the efficiency of the other damping mechanisms. The dramatic increase of l−1(ω) rapidly produces the Ioffe-Regel crossover at the frequency ωIR/2π (Figure 7a). Such a rapid decrease of the mean free path is actually the trend required to produce the aforementioned plateau in κ(T) around 10 K. With techniques ranging from Brillouin to IXS, it has become possible to study longitudinal acoustic excitations just below the IR crossover. In two favorable cases [29, 30], detailed measurements have revealed the existence of a very rapid increase of the Brillouin linewidth Γ = l−1vL, where vL is the longitudinal sound velocity as illustrated by lithium diborate glass [Li2 O 2B2O3] at 573 K (Figure 7b, inset). In the Brillouin spectrum taken at the smallest usable Q, the fitted elastic peaks have been subtracted from both the data and the fit to make the inelastic parts and their damped harmonic oscillator components apparent. At this low-q value, the Brillouin width is almost entirely instrumental, whereas it contains a real and large broadening in the bottom inset. At that point, the lineshape of the damped harmonic oscillator begins

Acoustic Excitations

At large wavelength, i.e. in the continuum limit, acoustic waves propagate in glasses as they do in crystals. Almost nondispersive sound waves have been indeed measured at low frequencies with ultrasonic (MHz) Brillouin scattering (GHz) or picosecond optical pump-and-probe (100 GHz) experiments. At these frequencies, quasi-plane waves do propagate but with higher attenuation rates than generally found in crystalline solids. The anharmonicity of thermal atomic vibrations causes the attenuation of sound waves in crystals [26] and is in addition reflected in the temperature dependence of the sound velocities or in thermal expansion. The same mechanism is also present in glasses, but it coexists with other damping processes that are mostly specific to them. At low frequencies, the energy mean free path of acoustic phonons is limited by resonant interactions with tunneling states at low temperatures and by thermally activated relaxω ation at higher temperatures, both leading to l−1 (Figure 7a). The latter mechanism is empirically described by the relaxation of group of atoms or “defects” between two or more equilibrium positions [27, 28]. At hypersonic frequencies, anharmonic processes coexist with thermally activated relaxation to drive a smooth transition from a l−1 ω law to a l−1 ω2 trend from low to high temperatures as clearly observed above GHz frequencies (Figure 7a).

(a)

(b)

Inverse mean free path (nm–1)

10–3

IXS

=

λ/

2

q = 1.1 nm–1

ℓ

1K 10 K 100 K 300 K

10–1

10–1 ω4

ω4 –15

10–5

0 ћω (meV)

ω2

10–7

15

ω1 BLS

ω2 –15

ћω (meV) 0 15

10–3

q = 2.4 nm–1

Inverse mean free path (nm–1)

5.2

10–9

10–11 105

ω1 107 109 Frequency (Hz)

Li2O–2B2O3

v–SiO2 1011

1010

1011

1012

10–5

Frequency (Hz)

Figure 7 Inverse mean free path l−1(ω, T ) of longitudinal acoustic excitations in glasses. (a) For v-SiO2: curves calculated with four damping mechanisms, namely, interactions with tunneling states, thermally activated relaxation, anharmonicity, and Rayleigh scattering at high frequency, which leads to the Ioffe-Regel crossover at ~1 THz (star). (b) For lithium diborate glass as measured at 573 K with BLS (green squares) and IXS (filled triangles). Dotted lines referred to the different damping processes: thermally activated relaxation plus lithium diffusion at GHz frequencies, anharmonicity around 0.5 THz, and Rayleigh scattering at THz frequencies. IR crossover at ~2.4 THz (star). Inset: dramatic increase of the Brillouin linewidth in IXS spectra in the IR crossover between q = 1.1 and 2.4 nm−1.

295

3.4 Atomic Vibrations in Glasses

6

The Boson Peak

The excess of vibrational modes in the reduced vibrational density of states g(ω)/ω2 translates into a broad and asymmetric band at frequencies between 0.5 and 3

THz in Raman or infrared spectra, corresponding approximately to the end of the acoustic branches. Vibrations of different origins are likely participating in that frequency region and should be separated into glassspecific vibrations (boson-peak modes) and crystallinelike vibrations (non-boson-peak modes). Many attempts have been made to relate the boson peak, e.g. to the medium-range order [31], the crystalline phases [11], or the macroscopic properties [32]. This section will focus on the origin of the vibrations underlying this excess of modes.

6.1 Oxide Glasses In quartz, a very important vibration is the soft mode associated with the structural α–β instability at 846 K whose displacements have been interpreted as librations of SiO4 tetrahedra. Its temperature dependence has been measured by neutron scattering (Figure 8b) and its frequency extrapolates to ~36 cm−1 at Tg ~ 1600 K, i.e. to the frequency of the maximum of g(ω)/ω2 measured by INS (Figure 8c). Librations of rigid units are also soft M α-Cristobalite

Wave vector

(a) Z

Γ

(b) Intensity

to deviate increasingly from the measured signal. The reciprocal of the energy mean free path corresponding to the Brillouin linewidths from all the measured IXS spectra is reported in the main graph of Figure 7b. Following a ω4 trend, the dramatic increase of l−1 is clearly evidenced over a decade. At q = qIR = 2.4 nm−1, the Brillouin linewidth reaches one-third of the Brillouin frequency, which is the Ioffe-Regel criterion. The IXS spectra measured at higher q values are inconsistent with a single damped-harmonic oscillator response, demonstrating that this approximation is no longer valid, thus marking the end of acoustic plane waves at qIR in this glass. In Brillouin light-scattering experiments made at the same temperature (Figure 7b), the l−1 values obtained also show that damping in this (ω, T) region is dominated by thermally activated relaxation processes and lithium diffusion, leading to an approximate l−1 α ω dependence, in agreement with ultrasonic experiments. From the temperature variation of the sound velocity, an estimate of the anharmonic−1 ity contribution at 573 K (lanh ω2 in Figure 7b) shows that this mechanism should dominate in a narrow frequency range around the crossover between ω1 and ω4 trends. More recently, similar IXS measurements made on v-SiO2 and glycerol [C3H8O3] have also indicated such a dramatic increase of the reciprocal of the mean free path of longitudinal acoustic excitations at THz frequencies. The results obtained for a densified v-SiO2 and then on lithium diborate glass have represented the first experimental evidence for the existence of a Rayleigh-type scattering mechanism of acoustic phonons in glasses producing an Ioffe-Regel crossover at some large acoustic wavelengths. The observation of both phenomena firmly demonstrated that the plane-wave approximation has already lost all validity at an intermediate scale, i.e. at about 1–3 nm depending on the glass. The observed crossover from propagating to diffusing sound waves has also offered a natural explanation for the anomalous low-temperature plateau in thermal conductivity. In several glasses investigated so far, ωIR is close to the boson-peak frequency ωBP, suggesting a direct relationship between both quantities. The correspondence is not one to one, however, as ωIR remains at or above ωBP. It is believed that the boson-peak frequency actually corresponds to the Ioffe-Regel crossover frequency for the transverse acoustic excitations in all glasses, but no experimental data have demonstrated the validity of this statement yet.

α-Cristobalite β-Quartz

(c)

ν-SiO2

Intensity

296

RS HRS g(ω)/ω2 0

100 Frequency (cm–1)

Figure 8 Vibrational excitations in v-SiO2. (a) Dispersion curve of acoustic modes and low-lying optic branches along the Γ M (plain lines) and Γ Z (dot dashed lines) directions of the Brillouin zone; squares Raman data. (b) Raman spectra of α-cristobalite and neutron spectra of the soft mode of β-quartz at 1250 K whose position at Tg is indicated by the dashed line at around 36 cm−1. (c) Spectroscopic signatures of the boson peak; possible vibrational contributions indicated by shadowed regions and the vertical dashed lines.

6 The Boson Peak

vibrations in β-cristobalite but are located at the zone boundary of a transverse acoustic branch. These lowfrequency excitations have been identified as rigid unit modes [33], i.e. external modes combining librations and translations of rigid elementary units. These units associate with weak interunit restoring forces in the glass and therefore vibrate at low frequency. Similarly, INS, hyper-Raman, as well as numerical simulations have highlighted the presence of librations of rigid SiO4 (F1-symmetry displacements in Figure 5) at bosonpeak frequencies in vitreous silica [34, 35]. Librations also participate at boson-peak frequencies in pure boron oxide (Figure 6) but with a lower weight than in v-SiO2. In this respect, silica is probably a peculiar system since librations are soft modes of the crystalline polymorphs, which to our knowledge is not the case for boron oxide. In connected networks, librations couple with translations of rigid units and hybridize with transverse and longitudinal acoustic phonons of similar frequency. This source of scattering combines with the strong scattering process of sound waves close to the Ioffe-Regel crossover frequency (shadowed regions in Figure 8a–c) to build up the reservoir of boson-peak modes. The loss of the Brillouin zone combined with the localization of the plane waves in the glass makes identification of these vibrations as acoustic- or optic-like useless. Owing to the different nature of these modes, the boson peak manifests itself in a way specific to the spectroscopic technique used, leading to differences in neutron, Raman, hyper-Raman, and infrared responses. What matters first and foremost is that these excitations relate to the structural disorder of the glass and to the plateau of the thermal conductivity. Crystalline-like modes may also contribute at frequencies beyond that of the boson peak such as the Raman modes at ~50 and ~120 cm−1 in α-cristobalite (Figure 8b) [36] or cation modes in soda-lime-silicate glasses [37]. Indeed, the vibrational density of states g(ω) of v-SiO2 below 300 cm−1 (as well as its Raman spectra) is very complex, pointing to numerous low-frequency optic vibrations (Figure 5). Conversely, that of B2O3 looks like Van-Hove singularities of transverse and longitudinal acoustic branches (Figure 6) emphasizing thereby a much weaker contribution from crystalline-like optic modes. 6.2

Other Glasses

The picture is even more complicated in molecular glasses (e.g. glycerol, ortho-terphenyl) where a large number of intramolecular and reorientational motions are likely to contribute at low frequency, leading to a great complexity in both vibrational responses and structural relaxation (Chapter 8.6). Hence, these systems generally do not represent good model systems for studying the boson peak.

Metallic glasses may in contrast prove useful in this respect. The simplest ones can be usually described as chemically and positionally disordered dense-packed structures without orientational interactions or intramolecular processes (Chapter 7.10). Consistent with the Lennard-Jones interacting-sphere model, the excess of low-frequency modes in Cp between ~10 and 30 K is then often composed of purely harmonic vibrations, i.e. of Einstein modes corresponding to local excitations of loose atoms in the glassy structure. Unfortunately, electronic and atomic properties often mix in metallic glasses, which may confuse the description of the boson peak and thermal properties. Electronic processes at impurity sites may, for example, contribute to localized excitations at boson-peak frequencies whereas thermal conductivity may also be dominated by electronic heat-transfer channels, which are much more efficient than atomic ones in conductors. In the large family of non-insulating glasses, amorphous silicon (a-Si) is probably one of the simplest examples. Its crystalline counterpart (c-Si) has only one triply degenerate optic mode at ω = 520 cm−1, which leads to an interesting situation where only acoustic branches contribute to the vibrational density of states below ~350 cm−1 (Figure 9a). The crystalline tetrahedral short-range order is preserved in the glassy state so that the densities of the two forms differ by 1.8% only. This structural similarity lends support to qualitative comparisons between vibrational properties. For example, the vibrational densities of states are similar below ~350 cm−1 with only a downshift of the band maxima in the glass, reflecting lower sound velocities (Figure 9b). Despite the absence of optic modes at low frequency, the Raman spectrum is not flat but displays broad structures that have been associated with both second-order processes on acoustic branches [38, 39] and disorder-induced scattering due to acoustic plane-wave destruction (Sections 2 and 5.2). The latter effect seems to be rather weak in a-Si, however, since it yields a moderate damping mechanism of the acoustic phonon branches, proportional to q2 [16, 40], as compared with the very fast q4-law observed in network glasses. This probably explains why the Raman response is very similar to the g(ω) measured by INS (Figure 9b) [41]. As in crystalline silicon, Cp/T in a-Si varies without showing evidence for two-level systems at least down to 2 K [4, 42]. The weak damping regime of the acoustic phonons goes against the formation of a plateau in the thermal conductivity as well. Unfortunately, however, existing reports are controversial and firm experimental evidence is still lacking on that question. Finally, the Ioffe-Regel crossover frequency is upshifted toward the end of the transverse acoustic branch (Figure 9b) [16], which raises some doubts about its physical meaning.

297

3.4 Atomic Vibrations in Glasses

1.0

X

(a) Trans.

0.8

Long.

q (r|u)

0.6 L 0.4

TA

LA

0.2 0.0

a-Si

Γ

TO, LO

ωIR Longitudinal LA, LO

LA

TA

ωIR Transverse

10

Boson peak modes

Plane waves

(b)

a.u.

298

Figure 9 Vibrational excitations in crystalline and amorphous silicon. (a) Dispersion curves along the X (symbols and lines) and L (dot-dashed lines) directions of the crystal [38]; dispersion curves of acoustic phonons about 25% lower in the glass than in the crystal. (b) Vibrational density of states g(ω) (thin lines) [41] and Raman scattering spectra (bold lines) of amorphous silicon [37] and c-Si. Plane wave, boson-peak mode, and ωIR transverse and longitudinal acoustic limits taken from [16].

5

c-Si 0 0

100

200

300 400 Frequency ω (cm–1)

In the current state of knowledge, the only reliable glassspecific vibrational feature of amorphous silicon is, therefore, the partial destruction of acoustic plane waves at large q (i.e. short wavelengths). Although moderate, this mechanism generates boson-peak modes at frequencies between the plane-wave regime and the Ioffe-Regel crossover at ωIR.

7

Perspectives

Inelastic scattering selection rules in glasses are relaxed by local structural and mechanical disorder, yielding broad and asymmetric spectral responses. Unlike for crystals, there exists no well-established analytical theory of the atomic displacements that underlie the spectral responses. Analyses remain mostly phenomenological, except perhaps for simple glasses for which atomistic simulations nowadays provide a firmer theoretical foundation. Indeed, the nature of the vibrations in the main oxide glass formers, up to binary and to a lesser extent ternary systems, is relatively well understood. Extracting quantitative structural information, in particular from RS, remains a challenging issue. Even more challenging is the nature of the boson peak. Its modes participate at low frequency in the vibrational

500

600

spectra of most disordered systems. These vibrating entities mostly originate from a renormalization and a redistribution of the modes of the acoustic branches due to the destruction of plane waves of nanometer wavelengths. They can eventually hybridize with low-lying optic vibrations (rigid-unit modes), such as the librations of rigid SiO4 tetrahedra in silica or loose local atomic motion in Lennard-Jones-type metallic glasses. The purely acoustic-type damping mechanism, enhanced by the second one when relevant, induces a very fast decay of the mean free path of the acoustic phonons at THz frequency, as evidenced by IXS and numerical simulations. There follows a crossover from a propagative to a diffusive character of sound waves and offers a natural explanation of the low-temperature plateau of thermal conductivity. These modes build up the boson-peak structure mostly below its maximum in g(ω)/ω2 plots in Raman and INS spectra. At higher frequencies, this spectral response mixes with those of other mechanisms, such as incoherent scattering from high-frequency acoustic branches due to the loss of wave vector selection rules, direct scattering of low-lying optic branches, second- or higher-order RS processes, and possibly others. It is tempting to define the boson peak as arising from the sum of all the excitations that construct the broad feature at THz frequency in glass, as it is often done in literature. Here, we have

References

preferred to separate the boson-peak modes from the other scattering processes since the latter are related to spectroscopic considerations whereas the former accounts for solid-state properties specific to glasses. Current advances in numerical simulations have allowed the boson-peak modes at the origin of the plateau in κ to be identified in very few cases [16, 43]. Highlighting them over the other scattering channels in a scattering experiment probably constitutes one of the most challenging issues of the coming decades.

12 Gurarie, V. and Chalker, J.T. (2002). Some generic

13

14

15

Acknowledgments 16

P. Gujrati and R. Vacher are gratefully thanked for their helpful comments on this chapter. 17

References

18

1 Taraskin, N. and Elliott, S.R. (2000). Propagation of

2 3

4

5

6

7

8 9 10

11

plane-wave vibrational excitations in disordered systems. Phys. Rev. B 61: 12017–12030. Dean, P. (1964). Vibrations of glass-like disordered chains. Proc. Phys. Soc. 84: 727–744. Rothenfusser, M., Dietsche, W., and Kinder, H. (1983). Linear dispersion of transverse high-frequency phonons in vitreous silica. Phys. Rev. B 27: 5196–5198. Bilir, N. and Phillips, W.A. (1975). Phonons in SiO2: lowtemperature heat capacity of cristobalite. Phil. Mag. 32: 113–122. Dove, M.T., Harris, M.J., Hannon, A.C. et al. (1997). Floppy modes in crystalline and amorphous silicates. Phys. Rev. Lett. 78: 1070–1073. Sigaev, V.N., Smelyanskaya, E.N., Plotnichenko, V.G. et al. (1999). Low-frequency band at 50 cm−1 in the Raman spectrum of cristobalite: identification of similar motifs in glasses and crystals of similar composition. J. Non Cryst. Solids 248: 141–145. Ramos, M.A. and Buchenau, U. (1997). Low-temperature thermal conductivity of glasses within the soft-potential model. Phys. Rev. B 55: 5749–5754. Phillips, W.A. (1972). Tunneling states in amorphous solids. J. Low Temp. Phys. 7: 351–360. Anderson, P.W., Halperin, B.I., and Varma, C.M. (1972). Properties of glasses and spin glasses. Phil. Mag 25: 1–12. Safarik, D.J., Scwartz, R.B., and Hundley, M.F. (2006). Similarities in the Cp/T3 peaks in amorphous and crystalline metals. Phys. Rev. Lett. 96: 195902. Chumakov, A.I., Monaco, G., Montana, A. et al. (2014). Role of disorder in the thermodynamics and atomic dynamics of glasses. Phys. Rev. Lett. 112: 025502.

19

20

21

22

23

24

25

26

27

aspects of bosonic excitations in disordered systems. Phys. Rev. Lett. 89: 136801. Debye, P. (1914). Zustandsgleichung und Quantenhypothese mit einem Anhang über Wärmeleitung. In: Vorträge über die kinetische Theorie der Materie und der Elektrizität, vol. VI. Leipzig: G. Teubner. Greabner, J.E., Golding, B., and Allen, L.C. (1986). Phonons localization in glasses. Phys. Rev. B 34: 5696–5701. Schirmacher, W. (2006). Thermal conductivity of glassy materials and the “boson peak”. Europhys. Lett. 73: 892–898. Beltukov, Y.M., Fusco, C., Parshin, D.A., and Tanguy, A. (2016). Boson peak and Ioffe-Regel criterion in amorphous silicon-like materials: effect of bond directionality. Phys. Rev. E 93: 023006. Hayes, W. and Loudon, R. (1978). Scattering of Light by Crystals. New York: Wiley. Martin, A.J. and Brenig, W. (1974). Model for Brillouin scattering in amorphous solids. Phys. Stat. Sol. 64: 163–172. Kirk, C.T. (1988). Quantitative analysis of the effect of disorder-induced mode coupling on infrared absorption in silica. Phys. Rev. B 38: 1255–1273. Taraskin, S.N. and Elliott, S.R. (1997). Nature of vibrational excitations in vitreous silica. Phys. Rev. B 56: 8605. Hehlen, B. and Simon, G. (2012). The vibrations of vitreous silica observed in hyper-Raman scattering. J. Raman Spectrosc. 43: 1941–1950. Galeener, F.L., Leadbetter, A.J., and Stringfellow, M.W. (1983). Comparison of the neutron, Raman, and infrared spectra of vitreous SiO2, GeO2, and BeF2. Phys. Rev. B 27: 1052–1078. Wilson, M., Madden, P.A., Hemmati, M., and Angell, C. A. (1996). Polarization effects, network dynamics, and the infrared spectrum of amorphous SiO2. Phys. Rev. Lett. 77: 4023–4026. Umari, P., Gonze, X., and Pasquarello, A. (2003). Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum. Phys. Rev. Lett. 90: 027401. Hehlen, B. (2010). Inter-tetrahedra bond angle of permanently densified silicas extracted from their Raman spectra. J. Phys. Condens. Matter 22: 025401. Maris, H.J. (1971). Interactions of sound waves with thermal phonons in dielectric crystals. In: Physical Acoustics: Principles and Methods (eds. W.P. Mason and R.N. Thurston), 279–345. New York: Academic Press. Anderson, O.L. and Bommel, H.E. (1955). Ultrasonic absorption in fused silica at low-temperature and high frequencies. J. Am. Ceram. Soc. 38: 125–131.

299

300

3.4 Atomic Vibrations in Glasses

28 Hunklinger, S. and Arnold, W. (1976). Physical Acoustics,

29

30

31

32

33

34 35

36

37

38 39

40

41

vol. XII (eds. W.P. Mason and R.N. Thurston), 155–215. New York: Academic Press. Rufflé, B., Foret, M., Courtens, E. et al. (2003). Observation of the onset of strong scattering on high frequency acoustic phonons in densified silica glass. Phys. Rev. Lett. 90: 095502. Rufflé, B., Guimbretìere, G., Courtens, E. et al. (2006). Glass specific behavior in the damping of acousticlike vibrations. Phys. Rev. Lett. 96: 045502. Malinovsky, V.K. and Sokolv, A.P. (1986). The nature of the boson peak in Raman scattering in glasses. Solid State Commun. 57: 757–761. Novikov, V.N. and Sokolov, A.P. (2004). Poisson’s ratio and the fragility of glass forming liquids. Nature 431: 161–163. Swainson, I.P., Dove, M.T., and Palmer, D.C. (2003). Infrared and Raman spectroscopy studies of the α-β phase transition in cristobalite. Phys. Chem. Miner. 30: 353–365. Buchenau, U., Prager, M., Nücker, N. et al. (1986). Lowfrequency modes in vitreous silica. Phys. Rev. B 34: 5665. Hehlen, B., Courtens, E., Vacher, R. et al. (2000). HyperRaman scattering observation of the boson peak in vitreous silica. Phys. Rev. Lett. 84: 5355–5358. Weigel, C. et al. (2016). Polarized Raman spectroscopy of v-SiO2 under rare-gas compression. Phys. Rev. B 93: 224303. Hehlen, B. and Neuville, D. (2015). Raman response of network modifier cations in alumino silicate glasses. J. Phys. Chem. B 119: 4093. Temple, P.A. and Hathaway, C.E. (1973). Multiphonon Raman spectrum of silicon. Phys. Rev. B 7: 3685–3697. Zwick, A. and Carles, R. (1993). Multiple-order Raman scattering in crystalline and amorphous silicon. Phys. Rev. B 48: 6024–6032. Christie, J.K., Taraskin, S.N., and Elliott, S.R. (2007). Vibrational behavior of a realistic amorphous-silicon model. J. Non Cryst. Solids 253: 2272–2279. Kamitakahara, W.A., Soukoulis, C.M., Shanks, H.R. et al. (1987). Vibrational spectrum of amorphous silicon: experiment and computer simulation. Phys. Rev. B 36: 6539–6542.

42 Zink, B.L., Pietri, R., and Hellman, F. (2006). Thermal

conductivity and specific heat of thin-film amorphous silicon. Phys. Rev. Lett. 96: 055902. 43 Mizuno, H., Shiba, H., and Ikeda, A. (2017). Continuum limit of the vibrational properties of amorphous solids. Proc. Natl. Acad. Sci. 114: E9767.

Additional References for Figure Captions Figure 2 Data from F. Birch and H. Clark, Am. J. Sci., 238 (1940) 529–558. U. Buchenau, M. Prager, N. Nücker, A.J. Dianoux, N. Ahmad and W.A. Phillips, Phys. Rev. b, 34 (1986) 5665–5673. D.G. Cahill and R.O. Pohl, Phys. Rev. B, 35 (1987) 4067–4073. A. Eucken. Annalen der Physik, 34 (1911) 185–221. P. Flubacher, A.J. Leadbetter, J.A. Morrison and B.P. Stoicheff, J. Phys. Chem. Solids, 12 (1959) 53–58. G.W C Kaye and W.F. Higgins, Proc. R. Soc. Lond., 113 (1926) 335–351. M. Kunugi, N. Soga, H. Sawa and A. Konishi, J. Amer. Ceram. Soc, 55 (1972) 580–580. J.C. Lasjaunias, A. Ravex, M. Vandorpe and S. Hunklinger, Solid State Commun., 17 (1975) 1045-1049. F. Simon, Ann. Phys., 68 (1922) 4–10. R.B. Sosman, p. 362 in The Properties of Silica (New York: Reinhold, 1927). R. Wietzel., Z. Anorg, Allg. Chem., 116 (1921) 71–75. R.C. Zeller and R.O. Pohl, Phys. Rev. B, 4 (1971) 2029–2041. Figure 5 Data from A.C. Hannon, R.N. Sinclair and A.C. Wright, Physica A, 201, (1993) 375–380. F. L. Galeener, G. Lucovsky and J. C. Mikkelsen, Jr., Phys. Rev. B, 22 (1980) 3983–3990. G. Simon, B. Hehlen, R. Vacher and E. Courtens, Phys. Rev. B, 76, (2007) 054210. G. Simon, B. Hehlen, R. Vacher and E. Courtens, J. Phys.: Condens. Matter, 20 (2008) 155103. Figure 8 Data from G. Dolino, B. Berge, M. Vallade and F. Moussa, J. Phys., I2 (1992) 1461–1465. V.N. Sigaev, E.N. Smelyanskaya, V.G. Plotnichanko, V.V. Kolashev, A.A. Volkov and P. Pernice, J. Non-Cryst. Solids, 248 (1999), 141–145. B. Wehinger, A. Bosak, K. Refson, A. Mirone, A. Chumakov and M. Krisch, J. Phys.: Condens. Matter, 27 (2015) 305401.

301

3.5 Density of Amorphous Oxides Michael J. Toplis Institut de Recherche en Astrophysique et Planétologie, Observatoire Midi Pyrénées, Université de Toulouse, Toulouse, France

1

Introduction

Density is a fundamental thermodynamic property, an essential characteristic of any condensed phase and one that is readily measured with great accuracy. The density of glassy and/or molten oxides is also of significant practical interest in a wide range of industrial and geological contexts. In the glassmaking and metallurgical industries, the difference in density between molten silicates and metals is the key to successful manufacture of everyday products such as float glass used in the construction and automobile industries, whereas, farther from home, the density of magmatic silicate liquids controls the timescales of movement and the spatial distribution of crystals within the interiors of the Earth, Moon, and Mars. In a little more detail, the density of amorphous oxides is a function of composition, temperature, and pressure. In the liquid state, temperature and/or compositional gradients can thus lead to density differences that are capable of driving material transport (i.e. convection), leading to mixing that may or may not be favorable for a given application. This link between large-scale material transport and liquid density highlights the critical importance of derivative properties such as thermal expansivity. Temperature-dependent changes in density are also particularly critical when cooling a liquid across the glass transition. If the need to anneal a glass before cooling it down to room temperature has been known from time immemorial, it was understood only in the nineteenth century that the internal stresses to be eliminated in this Reviewers: C. Sanloup, ISTeP, Université Pierre et Marie Curie, Paris Cédex 05, France S Webb, Geowissenschaften und Geographie, Georg-August Universität Göttingen, Göttingen, Germany

way originated from small changes in the local cooling rate throughout the glass piece (Chapter 3.7). Conversely, it was then realized that controlled generation of high local compressive stresses either by thermal or chemical means could be used to strengthen glass (Chapters 3.7 and 3.12). In the glassy state density continues to play a role, having an effect on optical properties such as refractive index and sound wave propagation. For example, chemical heterogeneities result in density differences that cause deformation of the optical path, a phenomenon generally observed in window panes produced before the float process was designed (Chapter 1.3). Further to these general considerations, it must not be forgotten that the pressure dependence of the Gibbs free energy of a phase of constant composition is simply the volume. In other words, liquid volume (and thus density) has a direct influence on free energy and thus on phase equilibria, in particular on the variation of melting temperature as a function of pressure. One obvious application of this fact is that high-pressure melting of planetary interiors is critically sensitive to liquid volume and its pressure derivative, compressibility. This brief introduction highlights a few of the implications of the density of amorphous materials. In the following, we will focus on a more detailed assessment of how volume is measured both at high and low temperature; how densities vary as a function of composition, temperature, and pressure; and how future work may lead to new breakthroughs in understanding variations in volume and/ or result in novel practical applications. In addition to volume (V), the properties of interest here are the thermal expansivity (∂V/∂T)P and the isobaric thermal expansion coefficient α = 1/V(∂V/∂T)P along with the isothermal and adiabatic compressibilities, ßT = −1/V(∂V/∂P)T and ßs = −1/V(∂V/∂P)S, respectively.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

3.5 Density of Amorphous Oxides

2 Measuring the Density of Amorphous Oxides

2.2 Density of Amorphous Solids

2.1 Theoretical Considerations

liq

ui

d

For a homogeneous liquid in internal thermodynamic equilibrium, the volume is uniquely defined at a given pressure and temperature (Figure 1). This also applies to the supercooled liquid state in the absence of crystals as long as the experimental timescale is longer than the structural relaxation time (Chapter 3.12). Because structural relaxation is a thermally activated process, with a more or less exponential temperature dependence, the transition from a fully relaxed liquid in internal equilibrium to an amorphous material whose structure is fixed (i.e. a glass) typically occurs over a restricted temperature range upon cooling. This kinetic origin of the liquid-to-glass transition has the consequence that the temperature at which internal equilibrium of the liquid can no longer be maintained depends on cooling rate. Because the thermal expansion coefficient markedly decreases from the liquid to the glass state, the volume/density of a glass cannot be calculated from pressure, temperature, and composition alone, but also requires knowledge of the temperature–time path during cooling. Put another way, glass chips of the same composition can have different densities if they have been cooled at different rates (Chapters 3.8 and 10.11).

Fu lly

re l

ax ed

Fictive temperature (rapid quench)

Volume

302

nched glass

e Rapidly qu

s ched glas

ρs =

ρl wa , wa − wl

1

where wa and wl are the weights of the sample in air and in the immersing liquid, respectively. Such measurements present no particular difficulties, requiring only a high precision balance and a good control and measurement of temperature, because the density of the fluid bath depends on this parameter. It is good practice to check the density of a well-known standard such as sapphire before measuring the density of several glass chips. Under these conditions, errors lower than ±0.0003 g/cm3 can readily be obtained for glass chips of a few tens of milligrams.

Time-dependent changes

2.3 Measurements in the Glass Transition Range

en

Slowly qu

Some of the earliest attempts to measure the density of amorphous oxides systematically were developed by the glassmaking industry well over 100 years ago with a simple but efficient technique with which a glass bead is immersed in a liquid whose temperature is varied until its point of neutral buoyancy is reached. If the density of the liquid is known as a function of temperature, then that of glass may be determined to better than 0.05%. Whereas this technique is well suited for extremely precise measurements of a sample whose density is approximately known, it is far less practical for an unknown sample since a given reference liquid only covers a small range of density. For this reason, alternative methods have been developed, also typically based on Archimedes’ principle, which states that a solid body immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body. One may apply this principle to measure the density of amorphous solids (ρs) by weighing a glass chip in air and in a fluid of known density (ρl), such as toluene. The weight in air provides a measurement of the mass of the chip, whereas the difference between the weight in air and in the fluid is used to calculate the volume of the chip with

Fictive temperature (slow quench) Temperature

Figure 1 Volume variations in the glass transition range: contrast between the uniquely defined value of the supercooled liquid and the cooling-rate-dependent values of the glass. Limiting fictive temperature defined by the intersection of the extrapolated glass and liquid curves. Volume changes toward the equilibrium value associated with structural relaxation indicated by the thin dashed lines (after [1]).

In the glass transition range, it is possible to study the properties of fully relaxed supercooled liquids that do not crystallize [1, 2]. However, the high temperatures and high viscosities of the liquids then prevent Archimedean-based techniques from being used. One simple approach is to measure glass density as a function of temperature and extrapolate to the fictive temperature where the density of the glass and liquid are identical. In this way, a single volume (density)–temperature coordinate of the liquid can be defined, a data point that can be

2 Measuring the Density of Amorphous Oxides

combined with measurements made at superliquidus temperatures. A more detailed knowledge of volume in this temperature range is also possible if one simply measures temperature-dependent length changes of fully relaxed liquids in the glass transition range. However, the temperature must be low enough for the viscosity of the sample to be sufficiently high that the sample does not collapse under its own weight, nor deform under the weight of the system used to measure length change. This constraint requires viscosities higher than ~1011 Pa s. Given such high viscosities, care must be taken to ensure that the time spent at a given temperature is sufficiently long for the liquid to reach a fully relaxed state. Such measurements require excellent temperature stability and can last up to several days for a single measurement, but they provide direct and precise insight into volume changes over a temperature range of typically 50 C [1, 2]. Furthermore, such measurements strikingly highlight the difference between the instantaneous elastic response of the sample to temperature change and the longer temperature-dependent viscous response that scales with structural relaxation time (Figure 2). An alternative method for measuring the volume of a fully relaxed liquid at low temperature uses the equivalence of enthalpy and volume relaxation in the glass transition range that has been demonstrated for silicate, aluminosilicate, and borosilicate liquids [2]. In this case, when heating a glass to the fully relaxed liquid state,

2.4

Measurements at Superliquidus Conditions

Superliquidus melts are typically of low viscosity, so Archimedes’ principle can be used again to measure liquid density. In this case, the melt is held in an inert crucible (typically Pt or Pt/Rh) and an inert “bob” of known mass and density (and thus volume) is introduced into the molten oxide at high temperature [4]. The difference in weight of the bob measured in air and in the molten oxide provides a measure of the mass of molten oxide displaced. Knowing the volume of the bob, the density of the melt can thus be determined from Eq. (1). The difficulty associated with this sort of experiment resides in making stable measurements at the necessary high temperatures, typically in the range of 1200–1600 C for molten silicates. Potential edge effects between the bob and the crucible and surface tension effects at the melt–air interface require the use of two bobs of different mass in order to provide robust determinations of liquid density. For this

985

T (K)

980 975 970

32 31 30 Length change (μm)

Figure 2 Imposed variation of temperature (upper panel) and associated effect on length of a cylinder of supercooled CaMgSi2O6 liquid (lower panel). The variation in length of the sample clearly distinguishes the instantaneous (vibrational) and delayed (configurational) contributions to volume relaxation in response to a temperature change, in addition to illustrating the temperature dependence of relaxation time (after [1]). The total length change as a function of temperature may be used to quantify expansivity, this method providing a highly precise estimate of this parameter.

the variation of the derivative property heat capacity (∂H/∂T) as a function of temperature should show the same normalized variations as expansivity (∂V/∂T). Given that heat capacity may be readily measured at all temperatures across the glass-to-liquid transition and that expansivity may be measured to temperatures at least as high as the peak associated with hysteresis, the expansivity of the relaxed liquid just above the glass transition can be inferred [3].

29 28 27

ΔL2

ΔL1

26 25 24 23 1600

1800

2000

2200

2400

2600

Time (minutes)

2800

3000

3200

303

304

3.5 Density of Amorphous Oxides

reason this technique is generally referred to as the double-bob Archimedean method. Under optimal conditions, inaccuracies as small as 0.2–0.3% in density are possible. Other techniques such as the maximum bubble-pressure method or use of falling spheres have uncertainties that are up to 10 times larger, so data acquired in those ways are not generally considered today. For liquids melting at temperatures high enough that Pt equipment may no longer be used, crucibles and bobs can be made of other noble metals such as Ir, extending the possible temperature range to ~1800 C. Above such temperatures it becomes difficult to find materials that are rigid enough to contain the melt while remaining inert. In this case containerless levitation techniques can now be employed. For example, a laser-heated sphere of known mass can be suspended on a jet of inert gas imaged in 3-D and its volume measured as a function of temperature. However, in light of the experimental difficulties associated with temperature control and measurement on the one hand and variations in the shape of the sample on the other, the inaccuracies of such measurements are at this moment three or four times higher than for the Archimedean techniques [5].

2.5 Compressibility and the Pressure Dependence of Density The variations of volume with pressure are typically determined in one of two complementary ways. First of all, use may be made of the fact that the velocity of wave propagation in a liquid (v) is a function of density (ρ) and the adiabatic bulk modulus (Ks) according to the equation Ks =

1 = ρv2 ßs

2

It should be appreciated, however, that if the characteristic timescale of the wave (i.e. the inverse of its frequency) is shorter than the structural relaxation time of the liquid, then some fraction of energy may be transported by shear waves. In this case, the bulk modulus has contributions from both longitudinal modulus and shear modulus. It is thus essential to measure the speed of wave propagation over a wide range of frequencies to ensure that a constant value is determined, indicating that the bulk modulus is that of a fully relaxed liquid. For the case of sound waves in the kHz to MHz range, this constraint typically means studying liquids whose shear viscosity is less than 10 Pa s. Use of ultrasound techniques to measure the compressibility of liquids dates back to the nineteenth century, but such techniques were dramatically improved by the advent of interferometry in the early twentieth century and then subsequently adapted in the mid-twentieth

century to the high-temperature measurements of molten oxides [6]. More recently the Brillouin scattering technique has been used to measure the compressibility of molten silicates up to temperatures exceeding 2300 K [7]. Because this technique employs hypersonic frequencies (a few tens of GHz), structural relaxation is negligible, and only the vibrational (glassy) contribution to compressibility is measured in this case. The difference between fully relaxed compressibilities measured using ultrasonic frequencies and the fully unrelaxed value determined using hypersonic frequencies can be used to derive the configurational contribution to compressibility [7]. Despite the constraints of high temperature, adiabatic moduli may be determined with these techniques to within 1%, allowing reasonable extrapolation of density around the chosen reference pressure (most conveniently 1 bar). On the other hand, when pressure is much greater than 1 bar, a direct measurement of density is to be preferred to provide a well-constrained equation of state, including the pressure dependence of compressibility. In this respect, the most commonly employed experimental technique consists of bracketing the density of a highpressure liquid relative to the known densities of minerals or metals such as boron nitride, platinum, graphite/diamond, or refractory olivine. In this case, a capsule containing the liquid of interest is placed within a pistoncylinder or multi-anvil device in which pressure may reach up to ~25 GPa. Two spheres of the solid whose equation of state is well known are added to the capsule, one at each extremity (i.e. top and bottom). After a sufficient time spent at high temperature and pressure, one determines whether the spheres sink or float in the liquid (thus the name sink/float technique). This assessment may be made based on ex situ techniques, that is to say, after quenching the sample and then determining if the spheres end up at the top or the bottom of the capsule [8]. Alternatively, with the advent of synchrotron facilities, it is now possible to observe the movement of a sphere within the liquid in situ at high pressure and temperature. Again, sinking and floating spheres indicate whether or not markers are denser than the melt. With these techniques, the result of a given experiment does not provide a direct measurement of the density of the liquid, but rather an open-ended bracket. Precise determination of liquid density thus ideally requires a neutral buoyancy experiment bracketed by a sink and a float at slightly lower and higher pressures. Further complications include uncertainties in the equation of state of the density markers and potential chemical reaction between the markers and the liquid of interest. For all these reasons, high-pressure densities measured in this way typically have inaccuracies of several percent, which is minor relative to the 25–50% change in density that

3 Measured Density Variations

typically occurs over pressure ranges of ~10 GPa [8]. In this pressure range, more refined in situ X-ray techniques with synchrotron radiation have recently been used to measure density from the absorption coefficients of the liquids and the compressibility from the structure factor q (cf. Chapter 2.2) [9]. At pressures higher than those accessible to the sink/ float technique, liquid densities may be measured from shock-wave compression. In this technique a projectile is launched at variable velocity against a liquid sample held in an inert metallic capsule. From determination of the shock Hugoniot, that is to say, the covariation of shock and particle velocities in the sample, the pressure–volume coordinates of the sample during isentropic compression can be derived. The extreme conditions and elevated cost of the experiment, the short timescales involved (potentially leading to incompletely relaxed states), and the necessary presence of capsule materials in front of and behind the liquid sample make such measurements challenging, but densities can be measured with an imprecision on the order of 1% for pressures up to at least 250 GPa [10].

3

Measured Density Variations

3.1 Superliquidus Densities at 1 bar: Variations as a Function of Composition The superliquidus volumes of the common networkforming oxides such as SiO2, B2O3, P2O5, and GeO2 have all been determined, but these are not necessarily the easiest materials to investigate owing to their high liquidus temperatures and viscosities (e.g. SiO2), their volatility (e.g. B2O3), or their corrosive nature (e.g. P2O5). Indeed, the direct measurement of the molar volume of pure liquid SiO2 is so challenging that indirect measurements such as extrapolation of densities to pure SiO2 from binary systems, use of the melting curve of cristobalite, and measurements on quenched glasses are preferred measures of the molar volume and expansivity for this oxide [11]. Since the 1950s, early systematic interest in the density of molten oxides was largely driven by the field of metallurgy, with the acquisition of data in many binary and ternary systems containing silica as the principal oxide, diluted by various network-modifying oxides, such as SiO2–Na2O or SiO2–CaO (e.g. [4]). The densities measured in these simple systems demonstrate that for mole fractions of SiO2 ranging from 0.35 to 0.85, molar volume is approximately a linear function of composition at fixed temperature. This observation indicates that in terms of volume, silicate liquids can be considered as ideal solutions (i.e. there is no excess molar volume associated with

mixing of different components), offering the possibility to construct simple predictive models for superliquidus density (e.g. [4, 12]). If the same is true at all temperatures and pressures, then to a first approximation the bulk density of complex liquids can be reconstructed from a set of partial molar volumes at reference conditions (V i ), partial molar expansivities (dVi/dT) and partial molar compressibilites (dVi/dP), one for each oxide component. V liq T , P, X i =

Xi V i +

dV i dV i T − 1673 + P−1 , dT dP

3

where Vliq(T, P, Xi) is the molar volume of the liquid at temperature T (in K) and pressure P (in bars), and V i are the partial molar volumes at reference conditions of 1673 K and 1 bar. In subsequent years, the earth science community spearheaded the acquisition of new data across a broad compositional range in multicomponent systems containing up to 10 different oxides, albeit still concentrated on liquids dominated by silica. This wealth of new highquality data made it possible to refine the predictive models for superliquidus density, confirming that simple temperature-dependent partial molar volumes that are constant across wide compositional ranges are generally an excellent first-order approximation, both for aluminosilicate and borosilicate melts [13, 14]; Table 1). In detail, certain authors have highlighted deviations from ideality that are typically assumed to originate in one of two ways. First of all such nonidealities may represent an excess volume resulting from the interaction of two or more oxide components. Alternatively, a given oxide component may have more than one possible structural environment in the melt, each one having a different partial molar volume. For the first case, pushing compositions to extremes can reveal the limits of the ideal mixing approximation. This is illustrated by measurements across the CaO– Al2O3–SiO2 ternary that include data for CaO-free, Al2O3-free, and SiO2-free liquids [20]. However, even in this extreme case, a single excess volume term between CaO and SiO2 is sufficient to rationalize all the data. An illustration of the second case is provided by TiO2, an oxide component that has a partial molar volume in silicate melts that increases with the addition of alkalis (e.g. Figure 3a). This increase can be understood by the associated increase in the mean coordination number of Ti in the liquid (Figure 3b). Similar effects can also be found for expansivities, the thermal expansion of the TiO2 component decreasing as alkali content increases [19]. The case of B2O3 is also of interest in this respect as boron occurs in both threefold and fourfold coordination in silicate and alumina-silicate melts, the relative

305

306

3.5 Density of Amorphous Oxides

Table 1 Partial molar volumes, thermal expansions, and compressibilities of oxide components of silicate liquids. Vi

(dVi/dT)1bar

(dVi/dP)1673K

[(dVi/dP)]/dT

(10−3cm3/mol-K)

(10−4cm3/mol-bar)

(10−7cm3/mol-bar-K)

1673K

(cm3/mol)

26.90

0

−1.89

a,b

23.16

7.24

−2.31

Al2O3a

37.11

2.62

−2.26

B2O3c

41.10

7.64

—

Fe2O3d

41.52

0

−2.53

3.1

12.68

3.69

−0.6

−1.8

11.45

2.62

SiO2a TiO2

FeO

e

MgOa CaO

a

1.3 — 2.7 —

0.27

−1.3

0.34

−2.9

16.57

2.92

SrOf

20.45

3.1

—

—

f

26.20

4.6

—

—

ZnOf

13.46

5.8

—

—

BaO

14.13

2.1

—

—

NiOf

12.48

3.1

—

—

f

25.71

4.1

—

—

16.85

5.25

−1.02

MnO PbO

f

Li2Oa

−4.6

Na2O

28.78

7.41

−2.4

−6.6

K2Oa

45.84

11.91

−6.75

−14.5

Rb2Of

54.22

33.2

—

—

Cs2Of

68.33

48.8

—

—

P2O5g

64.50

—

—

—

a

a

Values from [13]. For TiO2, the values shown are those typical of geological liquids [13]. In detail, the partial molar volume of this component is a function of coordination number, as illustrated in Figure 3. c Values from [14], applicable for B2O3 < 15 wt %. d For Fe2O3, the values shown here are taken from [15] and correspond to liquids rich in alkalis for which the coordination number of Fe3+ is close to 5. e For FeO, the values shown here are taken from [16] and correspond to liquids poor or devoid of alkalis. f Values from [17], for a SiO2 partial molar volume of 26.75 cm3/mol at 1400 C. g Value from [18]. b

proportion of these structural roles being a sensitive function of alkali content (Chapter 7.6). Detailed investigation of the density of boron-containing liquids indicates that distinguishing threefold and fourfold boron can lead to a better reproduction of the experimental data and that the partial molar volume of a B2O3 component with only trigonal B3+ is close to the value measured in pure liquid B2O3 [14]. Because the speciation of B3+ is not generally known in the liquid at high temperature, however, it has been concluded that a single partial molar volume for the B2O3 component is sufficient for practical purposes, at least for liquids containing less than ~15 wt % B2O3 [14]. A third situation of note is that of multivalent cations, for which each oxidation state may be expected to be associated with a different partial molar volume. The case of iron (as FeO and Fe2O3) is of particular importance

given the large concentrations of this element in melts of geological and metallurgical interest. When investigating these liquids, the first difficulty is thus controlling and/or measuring the relative proportions of FeO and Fe2O3, which depend on temperature, oxygen fugacity, and melt composition (Chapter 5.6). Of note is the fact that the temperature dependence of redox ratio may thus lead to volume changes that are not simply the effect of expansivity. Furthermore, both Fe2+ and Fe3+ exist in several coordination states, ranging from 4 to 6 (Chapter 2.6), complicating the interpretation of available volume data. The most recent considerations of this issue have thus endeavored to study liquids containing only one valence state of iron. Data from a wide range of simple alkali-bearing and alkali-free systems indicate that the partial molar volume

3 Measured Density Variations

33

interior, these volatiles may have a significant and critical effect on liquid density. Making detailed measurements in situ at high temperature and pressure is particularly challenging. Alternatively, fully relaxed volatile-bearing liquids may be studied in the glass transition range at one bar using glasses quenched from high pressure. In this way the partial molar volume of H2O has been quantified and found to be generally independent of the silicate melt composition, the total water concentration, and the speciation of water [21]. The partial molar volume of H2O derived at 1000 C is greater than that typical of bulk anhydrous silicates, such that the effect of 1 wt % dissolved H2O on the density of a basaltic melt is equivalent to increasing the temperature of the melt by ~400 C or decreasing the pressure by ~0.5 GPa.

(a)

32 VTiO2 (cm3/mol)

31 30 29 28 27 26 6.0

(b)

Average Ti coordination

5.6 5.2

3.2 Variations in Density over Large Temperature Ranges

4.8 4.4 4.0 3.6 0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Mole fraction of K2O

Figure 3 Effects of structural changes on the volume properties of TiO2-bearing potassium silicate liquids [19]. (a) Increase of the partial molar volume of the TiO2 component with K2O content at 1373 K. (b) Average coordination number of Ti in the quenched glasses.

of Fe2O3 may show significant variations, consistent with changes in average coordination state. However, the partial molar volume of Fe2O3 is independent of both composition and temperature in alkali-rich liquids, with a value consistent with a coordination number of Fe3+ of approximately five [15], which may be used for practical purposes. For FeO, measurements in a wide range of alkali-poor liquids indicate that a single temperaturedependent partial molar volume is sufficient to describe the data [16]. However, it should be appreciated that this partial molar volume is consistent with a coordination number of Fe2+ of almost six, leading to the possibility that for liquids in which Fe2+ occurs in a lower coordination state (e.g. upon addition of significant alkalis), the relevant partial molar volume could be lower. A final case of interest is the influence of volatile species such as water or CO2. On the one hand, the equilibrium solubility of such species is very low at atmospheric pressure, making their influence on density minor at best at these conditions. On the other hand, at the higher pressures associated with partial melting of the Earth’s

In general, data from superliquidus temperatures are obtained over an interval on the order of 500 C. In this range, a constant thermal expansivity is sufficient to describe the data, with a few rare exceptions such as molten B2O3 [22], the latter possibly indicating major temperature-dependent structural changes. Given that superliquidus volume generally shows ideal mixing, the same is to be expected for expansivity (that is to say, ∂V/∂T, not to be confused with the thermal expansion coefficient α). This is indeed found to be the case ([6]; Table 1). For silicate melts, the strong covalent nature of the Si–O bond is such that there is little change in the Si–O length, thermal expansion being driven by expansion of the Si–O–Si angle. For this reason, the partial molar thermal expansion of SiO2 is smaller than those of other oxides, whereas among the network-modifying oxides such as K2O or CaO, the partial molar thermal expansion coefficients are inversely correlated with cation field strength, a trend also observed for partial molar heat capacities. Given that relaxed liquid volumes and expansivities can also be defined just above the glass transition, combining all available data provides access to variations in volume over a temperature interval that is typically in excess of 1000 C. If a single V–T coordinate at the fictive temperature is used, within nominal experimental error, a case might be made for expansivities that are constant over this entire temperature range. However, if all available measurements in the glass transition range are used, including multiple V–T coordinates and expansivities derived from the equivalence of volume and enthalpy relaxation, it becomes clear that expansivity typically decreases with increasing temperature (Figure 4). This decrease in expansivity appears most pronounced in depolymerized melts of low silica and alumina content,

307

3.5 Density of Amorphous Oxides 21.0 Molar volume (cm3/gfw)

308

20.5

20.0

19.5

19.0 800

1000

1200

1400

1600

1800

2000

Temperature (K)

Figure 4 Temperature-dependent nature of the thermal expansion coefficient of CaMgSi2O6 liquid [1]. Thick line at ~1000 K: direct volume measurements [1]. Other line in the glass transition range: values derived from the assumed equivalence of structural and enthalpy relaxation [3]. Thin dashed line: extrapolation with a constant thermal expansion coefficient of the volumes measured in the glass transition range, not matching the individual measurements made at superliquidus temperature with a doublebob Archimedes technique.

such as diopside (CaMgSi2O6) melt (Figure 4), but less prominent in more polymerized liquids [1]. These data therefore argue for caution when extrapolating predictive models outside of the range where experimental data were collected. Below the glass transition, density continues to be a function of temperature, but then expansivity values become those typical of solids, i.e. much lower than those of fully relaxed liquids. From a theoretical point of view, calculation of room-temperature density requires knowledge of the fictive temperature, the density of the liquid at that temperature, and the expansivity of the glass. In practice, glass densities can be calculated to a reasonable approximation with the partial molar values derived from extensive databases obtained on usual samples, typically obtained by the glassmaking industry (e.g. [23]). 3.3 Variations in Density with Pressure As indicated above, the compressibility of superliquidus melts can be measured by ultrasound techniques if the density is known. Since the 1980s liquids covering a wide enough range of composition have been studied at one bar to quantify the compressibility of individual oxide components within the framework of Eq. (1) (e.g. [6, 13]). Indeed, once elements with multiple valence states and/or coordination numbers are taken account of, it is found that a set of partial molar compressibilities (expressed as ∂V/∂P, not ß) is sufficient to describe the pressure dependence of complex liquids (Table 1). For silicate melts, the open structure and strongly covalent

nature of the Si–O bond are such that low-pressure compression takes place through changes in the Si–O–Si angle, leading to a partial molar compressibility for SiO2 that is high compared with those of networkmodifying oxides. Among the network modifiers, there is again a negative correlation between compressibility and cation field strength. In detail, the compressibility in ternary aluminosilicate liquids appears to have nonideal contributions, with excess terms between Al2O3 and both CaO and Na2O in the CaO–Al2O3–SiO2 and Na2O–Al2O3–SiO2 systems, indicating complexities and differences in compression mechanisms [24]. One can highlight such complexities by combining 1bar data, low-pressure compressibility, sink/float data, and shock-wave data for a given composition to follow the variation of volume over a wide range of pressure. Where this is possible, volume changes are typically described by empirical equations of state (EOS) inspired by those used for crystalline materials, for example, the Birch–Murnaghan equation: 3 P = K0 2

V0 V

7 3

−

V0 V

5 3

1+

3 35 + K0 K0 + K0 − 4 K0 −3 + 8 9

3 K −4 4 0 V0 V

2 3

V0 V 2 3

−1 2

−1 + … ,

4 where K0, K 0, and K 0 are the bulk modulus and its firstand second-order pressure derivatives, all for P = 1 bar. For molten silicates the bulk modulus increases with increasing pressure, and for a given liquid, a single equation may typically be fitted to all available volume– pressure data across the widest pressure range possible. For example, a single third-order Birch–Murnaghan isentrope centered at 1 bar and 1573 K plus a Mie–Grüneisen thermal pressure approximation reproduces the measured volumes of fayalite melt (Fe2SiO4) from room pressure to 161 GPa [25]. However, in situ quantification of the compressibility of fayalite liquid at pressures near 5 GPa is not in agreement with the value derived from the previously proposed EOS over the relevant pressure range [9]. This example illustrates that equations of state used successfully for crystalline solids may not necessarily be applicable to molten oxides over large pressure ranges. The reason for this is that, in contrast to crystalline materials, melts may experience gradual changes in the coordination number of one or more cations over certain pressure intervals. For example, in fayalite liquid, the coordination state of Fe increases from ~5 to ~7 between room pressure and 7.5 GPa, explaining the “anomalous” variation of compressibility. A similar transition, albeit

5 Perspectives

at higher pressure, has also been proposed for Mg in liquid forsterite (Mg2SiO4). Likewise, B, Ge, Al, and Si undergo transitions to higher coordination number over a different pressure ranges, B3+ and Al3+ at pressures lower than 5 GPa, whereas conversion of Ge and Si from fourfold through fivefold to sixfold coordination takes place at pressures of 5–10 and 20–40 GPa for pure GeO and SiO2 respectively [9], although some interesting amorphous–amorphous transitions may also occur in these latter two systems (Chapter 3.9). Similar transitions are also found for static compression of amorphous solids and even for crystalline materials that are observed to undergo amorphization when subjected to GPa pressures (Chapter 3.10). All of these structural changes are expected to influence bulk density. In the liquid state they should in principle be taken into account when defining and fitting a volume–pressure– temperature equation of state. On the other hand, given the unrelaxed nature of glasses, care must be taken when interpreting density variations of amorphous solids. This care involves both quantifying the fictive pressure of the glass if it is formed by cooling of a liquid at high pressure and identifying permanent vs. reversible changes in density upon compression/decompression.

4

Practical Applications

One of the most obvious practical consequences of density changes concerns the variations in volume associated with cooling through the glass transition, which is commonly used in physical tempering (Chapter 3.12). In the glassy state, volume changes are also important if the glass is in contact with a substrate, as a difference in expansivity can result in the generation of stresses at the interface during heating/cooling cycles. The same is also true for materials that contain an intimate mixture of glass and crystals, for example, glass ceramics used as kitchen hotplates. Independently of the interfaces between a glass and other materials, the thermal expansivity of amorphous oxides may be of importance in itself for certain applications, in particular those where stringent constraints on the geometry of optical path are required. The mirrors and lenses used for astronomical telescopes, including the Hubble space telescope, are a particularly good example of such an application where ultralow expansivity is required. Such glasses are typically a mixture of SiO2 and TiO2, particularly refractory compositions that require innovative fabrication processes such as flame hydrolysis. In addition to their relevance to industrial applications, the volumes of molten oxides are also of considerable importance in geological systems. Notwithstanding the question of convection alluded to in the Introduction,

the solubility and partitioning behavior of minor elements in silicate melts are directly influenced by liquid density. For example, the solubility limit of noble gases (He, Ar, etc.) in silicate melts is a function of the “ionic porosity” of the liquid, that is to say, a measure of the free volume that it not occupied by the atoms. One consequence of this fact is that dramatic decreases in solubility may occur at high pressure as the density of the liquid increases as a result of structural modifications such as changes in the coordination states of network-forming cations (e.g. [26]). Furthermore, from a thermodynamic standpoint, partial molar volumes also influence how oxide components will partition between liquid and solid phases, as illustrated for metal–silicate partitioning of the oxides GeO2 and Ga2O3 [27]. Finally, as a fundamental contribution to the pressure dependence of free energy, volume has a critical influence on high-pressure phase equilibria. This is most readily illustrated by the well-known Clausius–Clapeyron relation stating that the pressure dependence of the fusion temperature of a congruently melting phase is dP dT

=

ΔS , ΔV

5

where ΔS and ΔV are the entropy and volume of fusion. Because the entropy of a liquid is always greater than that of a solid of the same composition, this relation implies that the sign of the slope of the liquidus is determined by the density difference between the solid and liquid. Given that the compressibility of liquids is generally greater than that of solids, volumes of fusion qualitatively decrease with increasing pressure and may even become negative (i.e. liquids are denser than crystals). In this case the Clapeyron slope may vary from positive to negative, the melting temperature being independent of pressure where crystal and liquid have the same density. In more complex multicomponent systems, the situation is not so simple, and neutral buoyancy is not necessarily related to a change in sign of the liquidus slope (e.g. [28]). On the other hand, the question of neutral buoyancy during melting of planetary mantles is a question of some significant interest given that such a “density trap” could have significant geochemical and geophysical consequences, so even today this possibility raises significant interest in the geological community [29].

5

Perspectives

Over the coming years, a better understanding the density of amorphous oxides will ultimately be driven by new experimental data that constrain the details of volume changes as a function of composition, temperature, and pressure. In this respect, direct determination of derivative

309

310

3.5 Density of Amorphous Oxides

properties such as expansivity and compressibility, in particular at high pressure, will be particularly important. New and innovative techniques involving synchrotron radiation may help make significant progress (e.g. [9]), although solid–liquid partitioning behavior at high pressure remains an approach that may have more to offer (e.g. [30]). In any case, it is becoming increasingly clear that detailed interpretation of volume data cannot be made without quantification of the structure of the melt and any changes in structure that may occur upon heating and/or compression. The possibility to study liquids in situ at high pressures and temperatures will be of critical importance given that quenched glasses represent the structure of the liquid at a single P–T coordinate and that retrieval of the relevant fictive temperatures and pressures is not a trivial issue (e.g. [31]). Here again synchrotron-based techniques, including new approaches such as X-ray Raman scattering, may help make significant breakthroughs. Finally, the dramatic increases in computing power are revolutionizing techniques based upon numerical modeling such as molecular dynamics and ab initio calculations (Chapters 2.9 and 2.10). The temperature domain accessible with these techniques is now comparable to that of laboratory experiments, and the number of particles used is sufficiently large to be representative of a bulk liquids. For these reasons, such modeling efforts will undoubtedly lead to new insight concerning how volume and structure are related (e.g. [32]).

5 Langstaff, D., Gunn, M., Greaves, G.N. et al. (2013).

6 7

8

9 10

11

12

13

Acknowledgments

14

Thanks are due to M.-H. Chopinet for many helpful discussions on this topic.

15

References 16 1 Toplis, M.J. and Richet, P. (2000). Equilibrium density

and expansivity of silicate melts in the glass transition range. Contrib. Mineral. Petrol. 139: 672–683. 2 Sipp, A. and Richet, P. (2002). Kinetics of volume, enthalpy and viscosity relaxation in glass forming liquids. J. Non-Cryst. Solids 298: 202–212. 3 Knoche, R., Dingwell, D.B., and Webb, S.L. (1995). Leucogranitic and pegmatitic melt densities: partial molar volumes for SiO2, Al2O3, Na2O, K2O, Rb2O, Cs2O, Li2O, BaO, SrO, CaO, MgO, TiO2, B2O3, P2O5, F2O−1, Ta2O5, Nb2O5, and WO3. Geochim. Cosmochim. Acta 59: 4645–4652. 4 Bockris, J.O.’.M., Tomlinson, J.W., and White, J.L. (1956). The structure of the liquid silicates: partial molar volumes and expansivities. Trans. Faraday Soc. 52: 299–210.

17

18

19

Aerodynamic levitator furnace for measuring thermophysical properties of refractory liquids. Rev. Sci. Instrum. 84: 124901. Rivers, M.L. and Carmichael, I.S.E. (1987). Ultrasonic studies of silicate melts. J. Geophys. Res. 92: 9247–9270. Vo-Thanh, D., Polian, A., and Richet, P. (1996). Elastic properties of silicate melts up to 2350K from Brillouin scattering. Geophys. Res. Lett. 23: 423–426. Vander Kaaden, K.E., Agree, C.B., and McCubbin, F.M. (2015). Density and compressibility of the molten lunar picritic glasses: implications for the roles of Ti and Fe in the structures of silicate melts. Geochim. Cosmochim. Acta 149: 1–20. Sanloup, C. (2016). Density of magmas at depth. Chem. Geol. 429: 51–59. Rigden, S.M., Ahrens, T.J., and Stolper, E.M. (1989). Shock compression of molten silicate: results for a model basaltic composition. J. Geophys. Res. 94: 9508–9522. Mysen, B. and Richet, P. (2005). Silicate Glasses and Melts: Properties and Structure, 131–168. Amsterdam: Elsevier. Bottinga, Y. and Weill, D.F. (1970). Densities of liquid silicate systems calculated from partial molar volumes of oxide components. Am. J. Sci. 269: 169–182. Lange, R.A. and Carmichael, I.S.E. (1987). Densities of Na2O–K2O–CaO–MgO–FeO–Fe2O3–Al2O3–TiO2– SiO2 liquids: new measurements and derived partial molar properties. Geochim. Cosmochim. Acta 51: 2931–2946. Linard, Y., Nonnet, H., and Advocat, T. (2008). Physicochemical model for predicting molten glass density. J. Non-Cryst. Solids 354: 4917–4926. Liu, Q. and Lange, R.A. (2006). The partial molar volume of Fe2O3 in alkali silicate melts: evidence for an average Fe3+ coordination number near five. Am. Mineral. 91: 385–393. Guo, X., Lange, R.A., and Ai, Y. (2014). Density and sound speed measurements on model basalt (An–Di– Hd) liquids at one bar: new constraints on the partial molar volume and compressibility of the FeO component. Earth Planet. Sci. Lett. 388: 283–292. Bottinga, Y., Richet, P., and Weill, D.F. (1983). Calculation of the density and thermal expansion coefficient of silicate liquids. Bull. Minéral. 106: 129–138. Toplis, M.J., Dingwell, D.B., and Libourel, G. (1994). The effect of phosphorus on the iron redox ratio, viscosity, and density of an evolved ferro-basalt. Contrib. Mineral. Petrol. 117: 293–304. Liu, Q. and Lange, R.A. (2001). The partial molar volume and thermal expansivity of TiO2 in alkali silicate melts: systematic variation with Ti coordination. Geochim. Cosmochim. Acta 65: 2379–2393.

References

20 Courtial, P. and Dingwell, D.B. (1995). Non-linear

21

22

23

24

25

26

composition dependence of molar volume of melts in the CaO–Al2O3–SiO2 system. Geochim. Cosmochim. Acta 59: 3685–3695. Richet, P., Whittington, A., Holtz, F. et al. (2000). Water and the density of silicate glasses. Contrib. Mineral. Petrol. 138: 337–347. Napolitano, A., Macedo, P.B., and Hawkins, E.G. (1965). Viscosity and density of boron trioxide. J. Am. Ceram. Soc. 48: 613–616. Mazurin, O.V., Streltsina, M.V., and ShvaikoShvaikovskaya, T.P. (1993). Handbook of Glass Data. Amsterdam: Elsevier. Webb, S. and Courtial, P. (1996). Compressibility of melts in the CaO-Al2O3–SiO2 system. Geochim. Cosmochim. Acta 60: 75–86. Thomas, C.W., Liu, Q., Agee, C. et al. (2012). Multitechnique equation of state for Fe2SiO4 melt and the density of Fe-bearing silicate melts from 0–161 GPa. J. Geophys. Res. 117: B10206. Chamorro-Perez, E., Gillet, P., Jambon, A. et al. (1998). Low argon solubility in silicates melts at high pressure. Nature 393: 352–355.

27 Holzapfel, C., Courtial, P., Dingwell, D.B. et al. (2001).

28

29

30

31

32

Experimental determination of partial molar volumes of Ga2O3 and GeO2 in silicate melts: implications for the pressure dependence of metal–silicate partition coefficients. Chem. Geol. 174: 33–49. Walker, D., Agee, C.B., and Zhang, Y. (1988). Fusion curve slope and crystal/liquid buoyancy. J. Geophys. Res. 93: 313–323. Lee, C.-T.A., Luffi, P., Höink, T. et al. (2010). Upsidedown differentiation and generation of a primordial lower mantle. Nature 463: 930–935. Gaetani, G.A., Asimow, P.D., and Stolper, E.M. (1998). Determination of the partial molar volume of SiO2 in silicate liquids at elevated pressures and temperatures: a new experimental approach. Geochim. Cosmochim. Acta 62: 2499–2508. Gaudio, S.J., Lesher, C.E., Maekawa, H., and Sen, S. (2015). Linking high-pressure structure and density of albite liquid near the glass transition. Geochim. Cosmochim. Acta 157: 28–38. Guillot, B. and Sator, N. (2007). A computer simulation study of natural silicate melts. Part II: high-pressure properties. Geochim. Cosmochim. Acta 71: 4538–4556.

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313

3.6 Thermodynamic Properties of Oxide Glasses and Liquids Pascal Richet1 and Dominique de Ligny2 1 2

Institut de Physique du Globe de Paris, Paris, France Department of Materials Science and Engineering, Friedrich Alexander Universität Erlangen-Nürnberg, Erlangen, Germany

1

Introduction

In Molière’s famous seventeenth-century play The Middle-Class Gentleman, the main character Mr. Jourdain is a nouveau riche who is delighted to learn from his Master of philosophy that he had been speaking in prose for 40 years without knowing it. Would ancient glassmakers have been proud to learn that they had been likewise unknowingly practicing thermodynamics ever since the beginnings of their craft millennia earlier? Along with their fellow ceramists and metallurgists, they did it empirically to make the best out of their limited fuel and material resources. When the new science of thermodynamics eventually emerged at the beginning of the nineteenth century, fundamental insights were at last gained to improve the energy efficiency of high-temperature processes (Chapter 10.9). Leaving aside the glass itself, interest was first paid to the combustion reactions and heat storage by refractory materials. Since then, however, glass has entered the scene with approaches that have progressively become fairly complex as exemplified in widely different fields such as energy-efficiency assessments (Chapter 9.8), fluid-dynamics simulations of the whole melting and forming processes (Chapter 1.7), and melting reactions (Chapter 1.3) to which the present chapter is most relevant. In glassmaking, the main thermal properties required for thermodynamic calculations are the hightemperature heat capacities (Cp) and enthalpies of formation (ΔHf) of the melts from the raw materials. Interestingly, such measurements were pioneered in the late nineteenth century by geophysicists at the request of Reviewers: A. Takada, Research Center, Asahi Glass Co. Ltd., Yokohama, Japan A. Whittington, Geological Sciences, University of Missouri, Columbia, MO, USA

William Thomson (1824–1907), better known as Lord Kelvin, within the context of the controversy over the age of the Earth ([1] and ref. therein). Since then, interest in the thermodynamic properties of glasses and melts has been strongly enhanced by the development of phaseequilibria calculations (Chapter 5.3), which are now extensively performed to predict liquidus temperatures under most varied conditions in industry as well as in geology. These models are only as good as their input data are. In this respect, an important practical difficulty stems from the wide composition ranges to be dealt with. This constraint makes it necessary to establish additional models for predicting reliably these input data as a function of not only composition but also temperature and, in geophysics, of pressure. Such models can be purely empirical, but it is preferable to give them a physical basis and to relate them to well-defined structural features for interpolations and, still more, for extrapolations made outside the composition ranges from which they have been established. In addition, one should not overlook the fact that the glassy state raises by itself interesting thermodynamic problems, especially at low temperatures (Chapter 3.4), which are related to the fundamental problem of the glass transition (Chapter 3.3). In the present chapter, the operational applicability of the concept of entropy (S) to glasses in relation to their nonequilibrium nature must be justified before the experimental methods used to determine thermodynamic properties from the vicinity of 0 K to superliquidus temperatures are briefly summarized. The effects of chemical composition on thermodynamic properties can then be reviewed. Including such issues as the boson peak and residual entropy, the heat capacity and entropy are examined in four distinct temperature ranges: (i) below 50 K, where medium-range order is mainly involved; (ii) up to 300 K,

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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3.6 Thermodynamic Properties of Oxide Glasses and Liquids

where the influence of short-range order prevails; (iii) between room temperature and the glass transition, where compositional effects tend to vanish; (iv) above the glass transition, where much complexity is introduced by configurational degrees of freedom. Finally, the problems raised by determinations of enthalpies of mixing and of formation are briefly addressed. Because these topics are treated elsewhere, the physics of low-temperature heat capacity anomalies (Chapter 3.4) as well as thermal conductivities and diffusivities (Chapter 4.5) are not dealt with.

2

Thermodynamic Functions

2.1 The Entropy Problem Determining the entropy change between two thermodynamic states requires the existence of a reversible pathway between them. The fact that glasses are nonequilibrium substances may thus seem to be problematic in this respect. Below the glass transition range, however, the structure of a glass is fixed so that any irreversible relaxation can be neglected during a calorimetric measurement. It is through the glass transition that difficulties arise since heat capacities measured upon heating and cooling differ, and so do entropy variations between two temperatures calculated along these distinct pathways (cf. Chapter 10.11). But the entropy created irreversibly across the glass transition is small enough to be operationally neglected and to allow the residual entropy of the glass at 0 K to be determined from calorimetric cycles involving the crystalline, liquid, and glass forms of substance [2]. The procedure has also been followed for other nonequilibrium systems such as ice, CO, and other orientationally disordered crystals with the appropriate thermochemical cycles (e.g. [3]). Although long accepted [4], the notion of residual entropies at 0 K for amorphous or disordered substances has recently been rejected as inconsistent with the fact that the loss of ergodicity at the actual glass transition would imply the simultaneous loss of any configurational entropy because the system would become unable to explore all its configurational states [5, 6]. Against this kinetic picture, simple theoretical considerations [7] and detailed analyses of calorimetric measurements [8] have supported the conventional view. The origin of the divergence between the two pictures is the manner in which microstates are counted in statistical-mechanical models depending on whether Gibbs or Boltzmann entropy is considered [9]. The “entropy-loss” view of the kinetic picture considers only the number of states actually visited by the system at the observational time

scale. The approach of the conventional standpoint is in contrast concerned with the probability of occurrence of the relevant states, be they actually explored or not by the system. Its important point is that energy, volume, entropy, and other extensive properties remain state variables for a system that is not in internal equilibrium. Even though more than two of these variables are needed to specify the state of the system, their values remain uniquely defined [9]. Such a picture is in particular consistent with the equivalence of the kinetics of structural, enthalpy, and volume relaxation observed for silicate melts [9], with the “additivity” of extensive variables over different macroscopic parts of a system [10] and with fundamental considerations of nonequilibrium thermodynamics [11].

2.2 Gibbs Free Energy and Stability At constant temperature and pressure, the equilibrium state of a system is determined by the minimum of its Gibbs free energy (G). From a practical standpoint, the validity of the entropy concept for glasses has thus the important consequence to make determinations of their Gibbs free energies (G) possible, as long done for phases in internal equilibrium for which available data are assessed in thermodynamic tables and databases (e.g. [12]). If the standard pressure state of 0.1 MPa (1 bar) is denoted by and the subscript f refers to formation properties from elements or oxides, these data sets include CP (T), S (T), ΔHf (T), and ΔGf (T). The Gibbs free energy of formation of a phase from its constituting elements or oxides is ΔGf T 0 = ΔH f T 0 − T 0 ΔSf T 0 ,

1

whereas the enthalpy (H) and entropy (S) are related to the heat capacity by dH = C p dT ,

2

Cp dT dS = T

3

The Gibbs free energy can then be calculated at every temperature with ΔGf T = ΔH f T 0 +

T T0

ΔC p f dT − T ΔS f T 0 +

ΔC p f dT , T0 T T

4 where T0

S T0 = S 0 + 0

Cp dT T

5

2 Thermodynamic Functions

If a reversible phase transition takes place in the system at a temperature Tt between T0 and T, it is taken into account via its enthalpy of transition ΔHt (Tt), viz. ΔGf T = ΔHf T0 + T

+ Tt

Tt T0

ΔCp f dT + Δt H Tt

ΔCp f dT −T ΔSf T0 +

Tt

Δ Cp f

T0

T

dT +

Δ t H Tt + Tt

T Tt

Δ Cp f dT T

6 Application of Eq. (6) to phase-equilibria calculations may be simply illustrated at high temperatures with SiO2 glass, liquid, and polymorphs. In plots made against temperature, the intersections of the calculated ΔGf T delineate the respective stability limits of quartz, cristobalite, and SiO2 glass and liquid. These limits are clearly seen if one takes one of these phases as a reference – say, cristobalite – and plot instead the differences between its ΔGf T and those of cristobalite (Figure 1). Quartz appears to be the phase stable below 1100 K and to melt metastably at 1700 K whereas cristobalite melts itself at 2000 K. In practice, however, quartz can be kept for a while above 1100 K because the kinetics of its transformation into cristobalite, which depends on many other factors than the ΔGf of the transition, becomes rapid only above 1400 K [13]. Because Cp differences between the solid phases are small, however, the ΔGf curves have very similar slopes and their intersection temperatures usually have rather large uncertainties. If known independently from phase-equilibria experiments, such temperatures

2000

G

la

ss

Tg 1000 Tq–I

500 0

Cristobalite Tc–I

Tq–c z Qu art

–1500 600

Tα–β

800

uid

–1000

Liq

∆Gf°x – ∆Gf°crist. (kJ/mol)

1500

–500

in turn represent important information to ensure the internal consistency of thermodynamic data sets through appropriate adjustments of the calorimetric results to within their error margins.

1000

1200

1400

1600

1800

2000

2200

T (K)

Figure 1 Stability of SiO2 forms as indicated by the dashed line where they have the lowest Gibbs free energies of formation (Source: Data from [13]). Slope changes in the quartz and amorphous SiO2 curves due to the α–β and glass transitions, respectively.

2.3

Experimental Approaches

2.3.1 General Remarks

The apparent complexity of Eqs. (4) and (6) should not conceal a basic simplicity since all thermodynamic properties of a substance are determined if one knows only its heat capacity as a function of temperature along with ΔHf at a single temperature and the entropy at 0 K, which is by convention taken to be zero for perfect crystals. At room pressure, calorimetric experiments are thus of two kinds (Table 1) depending on whether one measures enthalpy differences between two temperatures for the same phase or between different phases at the same temperature. In the former case, one measures enthalpy differences (ΔH) for a given temperature interval ΔT = T – T0. In the latter case, one is faced with the general problem raised by the sluggishness of the reactions of interest, which makes direct heat measurements impossible. One must then devise alternate routes leading from the initial to the final state considered, along which enthalpies can be measured. 2.3.2 Heat Capacity and Enthalpy

If ΔT is large in the calorimetry experiment, then one determines Cp by differentiating analytical expressions fitted to the H(T) – H(T0) measured as a function of T [13]. A major advantage of this drop-calorimetry method is that heat exchange does not need to be controlled at high temperatures where radiative transfer is predominant. Only the high temperature of the sample has to be measured precisely along with the heat released upon cooling at T0, which can be done very accurately if T0 is close to room temperature. With transposed drop calorimetry, the sample is in contrast dropped from room temperature in a calorimeter kept at temperatures of up to 1000 K where the enthalpy absorbed is measured; the precision is not as high as in usual drop calorimetry, but the advantage is in some cases to ensure a final reproducible state for the sample. If the ΔT and ΔH of the calorimetry experiment are in contrast small, as is the case of the heat brought to the sample in adiabatic calorimetry [14], then one assumes that Cp = ΔH/ΔT with appropriate curvature corrections to account for the actual temperature dependence of the heat capacity of the sample between T0 and T. Inaccuracies as low as of 0.1% can be achieved with adiabatic calorimetry but heat exchange between the sample and its

315

316

3.6 Thermodynamic Properties of Oxide Glasses and Liquids

Table 1 Experimental calorimetric methods. Method and property measured

Sample size

Drop calorimetry with ice or other kinds of calorimeters HT – HT0

Example of companies

Inaccuracies

Effective measurement

1–10 g

400–1900 K 0.2% On derived Cp: 0.5%

Sample dropped from high (T) to low (T0) temperature; HT – HT0 proportional to the amount of ice melting as determined from the volume decrease of the transition (constant temperature at 273 K).

Self-made

Adiabatic calorimetry Cp

1–10 g

4–15 K : 5% 15–25 K : 1% 25–50 K : 0. 5% 50–350 K : 0.1%

Measurement of the increase of temperature ΔT after a known input heat Q.

Self-made

Relaxation calorimetry (isoperibol) Cp Differential scanning calorimetry (isoperibol) Cp

1–500 mg

0.1–300 K: around Relaxation time to reach the final temperature after an increase PPMS by 1 and 2% of temperature can be related to the global heat capacity of the quantum design sample and sample holder after calibration.

0.1–3 g

90–1500 K: 1–3%

Sample and reference heated under the same conditions at the Netzsch, same rate between temperatures T1 and T2. Difference between PerkinElmer Setaram, etc. the heat fluxes measured by power compensation or with a thermopile, integrated from T1 to T2 and divided by T2 − T1 to derive Cp. Calibration needed from known standards. Nonequilibrium measurement.

Calvet-type calorimetry (isothermal) Cp

10–500 mg

300–1000 K ΔH : 1%

Heat flow caused by the phase change integrated as measured Self-made, Setaram with a calibrated thermopile made up of a 3-D network of thermocouples; sample usually dropped into the calorimeter from room temperature.

surroundings becomes increasingly difficult to control when temperature increases, and blackbody radiation becomes significant, so that the measurements are usually restricted to temperatures lower than 400 K. This restriction also applies to the newer but slightly less accurate physical property measurement system (PPMS) with the heat capacity option [15] whose major advantage is to require samples of a few tens of mg, which are hundred times smaller than those needed for adiabatic calorimetry. The other technique of differential scanning calorimetry (DSC) has become extensively used because it is rapid, commercially available, requires small samples of a few tens of mg, and lends itself to dynamic measurements made at heating rates of up to a few hundreds of degrees per minute. This is a modern form of differential thermal analysis in that it relies on comparisons made with a standard, generally corundum, whose heat capacity is accurately known, which is heated under conditions as similar as possible as those of the sample. Measurements with inaccuracies of 1% can be made if the heat fluxes to both sample and standard are measured with Calvet-type calibrated thermopiles made up of hundreds of thermocouples in series. The precision is less good, but the sensitivity may be higher, when only the differences in the power delivered to the sample and standard are measured with less expensive equipment. But the main limitation of

the technique is its upper temperature limit of about 1000 K for precise enough results, which severely restricts its uses for glass-forming liquids to compositions with low Tg’s. Interesting observations can nonetheless be made with some setups working up to 1650 K, but with errors of about 3% that are inappropriate for Cp measurements. 2.3.3 Enthalpies of Transformation

To determine enthalpy differences between different phases that do not react rapidly, the trick consists in measuring the enthalpy of solution into the same solvent of all the phases of interest (e.g. a glass and a crystal of the same composition). Conditions approaching those of infinite dilution are maintained so that the enthalpy of the transformation is simply given by the sum of the enthalpies of solution weighted by the stoichiometric coefficients of the reaction. With Calvet-type calorimeters, these solution-calorimetry measurements are also performed with thermopiles. They are made either close to room temperature with hydrofluoric acid, HF, which work well for alkali- and SiO2-rich materials [14], or near 1000 K with molten lead borates for more refractory samples that would leave undissolved fluoride residues in HF solutions [16]. If the heat capacities of the phases considered are known, the measured enthalpies of transition can then be referred to any other temperature.

2 Thermodynamic Functions

220 Liquid

200

Cm (J/mol K)

160

Na2SiO3

s Glas l Crysta

140 Li2SiO3

120 100 500

uid

Liq

700

900

1100 1300

1500

∆Hm

1700 1900

T (K)

H

Figure 2 Enthalpies of fusion of Na2SiO3 and Li2SiO3 directly measured by drop calorimetry as discontinuities in the Cm = (HT – H273)/(T – 273) curves at the melting temperatures of 1362 and 1474 K, respectively (Data from [17]). Premelting effects apparent in anomalous enthalpy increases beginning 150 and 10 K below the congruent melting points of Na2SiO3 and Li2SiO3, respectively.

The complementary nature of the two general calorimetric methods is obvious in determinations of enthalpies of fusion. Contrary to most metals and salts, which crystallize readily upon melt cooling, oxide compounds generally vitrify at least partially. Direct measurements of the enthalpy of crystallization are thus restricted to very few cases where no glass at all is present in the sample after rapid cooling in the calorimeter (Figure 2). A more complicated procedure must in general be followed. It consists in combining the enthalpy of vitrification of the crystal measured by solution calorimetry at a convenient temperature Tv with the relevant enthalpy or Cp data to derive the enthalpy of fusion at the higher melting temperature Tm (Figure 3). This procedure has thus been followed to determine most of the data available for about 30 oxides and silicates [18, 19]. Because it increases with the interval Tm–Tv and the Cp difference between the liquid and crystal phases, the enthalpy of fusion can actually be twice as great as the enthalpy of vitrification so that the latter generally does not represent a good approximation for the former. 2.4

∆Cp(Tm)

∆Cp(Tg)

CP

∆Hm

180

The Influence of Thermal History

In view of the Cp decrease observed upon cooling at the glass transition, glasses quenched at different rates have necessarily different enthalpies (Figure 3). The enthalpy difference between two glasses having fictive temperatures Tf2 and Tf1 is then given by ΔH v2 − ΔH v1 = C pl T g − C pg T g T f2 − T f1 = ΔC p T g T f2 − T f1 ,

7

s

Glas

∆Hv1

∆Hv2 l

sta

Cry

Tg Tf2 Tf1

Tm

Figure 3 Heat capacity and enthalpy above room temperature of the crystal, glass, and liquid phases of a substance melting congruently at Tm. Enthalpy of fusion at Tm determined from the enthalpy of vitrification measured by solution calorimetry at Tv and the heat capacities of the amorphous and crystalline phases between Tv and Tm. Glass enthalpy and Cp decreases at the glass transition represented for slowly and rapidly cooled glasses of fictive temperatures Tf1 and Tf2, respectively.

where the subscripts l and g refer to the supercooled liquid and glass, respectively (Figure 3). Except for hyperquenched glasses (Chapter 3.8), these effects can often be neglected because very large differences in quenching rates are needed to produce variations of fictive temperatures greater than a few tens of degrees [20]. An additional simplifying feature is that the influence of the fictive temperature on the heat capacity of the glass can be neglected as long as temperatures are not lower than about 50 K [20]. There is, however, another instance where fictive-temperature effects must be considered. It is the determination of enthalpies of mixing between melts from solution-calorimetry measurements made on glasses with widely different fictive temperatures. Because enthalpies of mixing are typically 10 times smaller than enthalpies of fusion, corrections made with Eq. (7) are no longer negligible. Meaningful results are thus obtained only if the measurements are referred with this equation either to the same fictive temperature or to a common equilibrium temperature [21] as clearly illustrated by the enthalpies of mixing in the Na2O–SiO2 system for which differences in fictive temperatures between SiO2 and the Na-bearing glasses investigated could reach 800 K [22].

317

3.6 Thermodynamic Properties of Oxide Glasses and Liquids

3 Low-temperature Heat Capacity and Entropy

S 298 − S 0 =

Like that of any solids, the heat capacity of glasses is a measure of the progressive excitation of atomic vibrations when thermal energy is brought to the substance and increases its temperature. In this respect, the fundamental feature is the vibrational density of states g(ν), i.e. the distribution of the number of vibrational modes as a function of frequency (Figure 4). For each vibration mode of frequency ν, the heat capacity is given by an Einstein function x2 ex , ex − 1 2

cν T =

8

where x stands for hν/kT, and h and k for Planck and Boltzmann constants. The heat capacity of the glass is the integral of Eq. (7) over g(ν) from 0 to the maximum vibrational frequency νm: νm

CV T =

cv T g ν dν

9

0

Neglecting the very small differences existing below 300 K between the isobaric (Cp) and isochoric (CV) heat capacities, one then calculates the vibrational entropy from 1

0.8

0.6

0.4 g(ѵ) 0.2 300 50 0

0

100 300

200 600 ѵ

900

1200

298 0

3.1 From the Vibrational Density of States to the Heat Capacity

g(ѵ) Cv (T) (a.u.)

318

1500

(cm–1)

Figure 4 Relationship between the vibrational density of states, g (ν), of SiO2 glass and the heat capacity as given by the areas below the g(ν)cv(T) functions plotted at the indicated temperatures. Data from [23].

Cp dT , T

10

where the residual entropy S0 cannot be omitted because it is not zero for glasses and other disordered substances. With increasing temperatures, modes of progressively increasing frequency (and energy) contribute to the heat capacity. For SiO2 glass, only modes of frequencies lower than 200, 400, and 600 cm−1 contribute significantly to Cp below about 50, 100, and 200 K, respectively (Figure 4). Of course, these regimes do not have sharp boundaries but such simple considerations are useful to discuss the composition dependence of low-temperature heat capacities and entropies for which there is now a wealth of experimental data. These low-frequency modes involve either weak bonds or the motion of a large number of atoms and, as such, can be considered as probes of mediumrange order. Indeed, it is only in this temperature range that a dependence of Cp on the thermal history of the glass is detected, the heat capacity being higher for samples with higher fictive temperatures and lower density (e.g. [20]). But Cp values below 50 K are so small that they barely contribute to the room-temperature entropy as given by Eq. (10). High-frequency modes in contrast are a direct reflection of short-range order, which involves the strongest atomic interactions and dominate the room-temperature entropy.

3.2 Oxygen Coordination of Network-modifying Cations In a first approximation, atomic vibrations in solids may be considered to be harmonic oscillations whose frequencies decrease as the mass of the atoms involved increases and increase with the strength of their bonding (cf. ν = 1/[2π (μ/k)1/2] of the diatomic molecule, where μ is the reduced mass and k the force constant). For disilicate glasses (Figure 5), the heat capacities thus decrease from K to Na and Li as a result of increasing cation mass and of the increase in average bond strength caused by the decrease of the ionic radius of the alkali. In addition, they are higher for glasses than for their isochemical crystals as a result of a larger volume, which affects acoustic modes through a decrease of the bulk modulus, and of a bond-strength disordering in the network at constant volume [25]. A third factor is the presence at low frequency of the excess of vibrational modes to be described below in Section 3.5. Nevertheless, the overall similarity of the data for glasses and crystals excludes markedly different shortrange order not only in disilicate glasses and crystals but also, more generally, in binary SiO2–M2O systems for which vibrational entropies vary linearly up to the metasilicate compositions (Figure 6). Hence, especially for potassium silicates, the average oxygen coordination

3 Low-temperature Heat Capacity and Entropy

60

20

GeO2GI h-GeO2

Na Cp/R

TiO2

50

Li S298 – S0 (J/mol K)

15

10 K

SnO2 Tr

40

Qu

t-GeO2 Co

Cr

GI

SiO2

30

5

St 0

0

50

100

150

200

250

20 10

300

15

20

25

30

V (cm3/mol)

T (K)

Figure 5 Low-temperature heat capacities of alkali disilicate M2Si2O5 glasses (solid curves) and crystals (dashed curves). Data from [24]. 90 SiO2–M2O

Figure 7 Vibrational entropy of SiO2 and GeO2 glasses and polymorphs against the molar volume of the phases. SiO2: Gl (glass), Qu (quartz), Cr (cristobalite), Tr (tridymite), St (stishovite), and Co (coesite). GeO2: Gl (glass), t- (tetragonal form), and h(hexagonal form). Data for SnO2 (cassiterite) and TiO2 (rutile) added to complement the trend for tetragonal crystals. Data from [26, 27].

S298 – S0 (J/mol K)

80 K 70 Na 60 50 Li 40 30

0

10

20

30

40

50

60

70

mol % M2O

Figure 6 Vibrational entropy of alkali silicate glasses (solid symbols) and crystals (open symbols). Source: Data from [33] and de Ligny (unpublished results).

number should be close to the value of about 5 that holds in crystals. 3.3 Oxygen Coordination of Network-Forming Cations That the effects of oxygen coordination, or atomic packing, are much more important than those of volume (at constant coordination) is clearly illustrated by the

network-forming cations Si4+ and Ge4+. For the isostructural forms of SiO2 and GeO2 (Figure 7), the vibrational entropy is much higher for tetrahedral than for octahedral coordination. Because Si─O and Ge─O bond distances are shorter for the former coordination than for the latter, the internal vibrational modes have lower frequencies in SiO4 and GeO4 tetrahedra than in SiO6 and GeO6 octahedra, but the ensuing lower contributions to the heat capacities are more than compensated by the effects of the Cp decreases of the lattice modes that are due to the shorter Si─Si and Ge─Ge distances between second-nearest neighbors in the dense, highpressure phases. A similar effect of the change of four- to sixfold coordination of aluminum is apparent in the S298 – S0 data of sodium and calcium aluminosilicates (Figure 8). In both series, the vibrational entropies vary linearly from pure SiO2 to the meta-aluminous compositions for glasses and low-pressure crystals, in accordance with the tetrahedral coordination reported for both Si4+ and Al3+ [19]. In contrast, the high-pressure phases of crystalline jadeite (Jd, NaAlSi2O6) and Ca-Tschermak pyroxene (CaTs, CaAl2SiO6) have entropies departing negatively from these trends because all or some of their Al is sixfold coordinated.

319

3.6 Thermodynamic Properties of Oxide Glasses and Liquids

Table 2 Partial molar relative entropies of oxides in silicate glasses, and entropy coefficients of oxides in crystals for the coordination numbers indicated by Roman numbers.

70 SiO2–MnAIO2 65 S298 – S0 (J/mol K)

320

NaAIO2

60 55

Ca0.5AIO2 50

Oxide

Glasses

SiO2

43.37

40.3 (IV)–24.0 (VI)a

GeO2

59.33

55.3 (IV)–39.7 (VI)

IV

Al2O3b

72.8

72.1–43.8c

Al2O3

48.5

59

45

42

V

VI

45

CaTs

Jd 40 0

Al2O3

IIIB IIIF

20

40

60

80

IV

mol % MnAIO2

B2O3c

63.7

B2O3c

70.2

B2O3

MgO

Figure 8 Vibrational entropy of crystals (open squares) and glasses (solid circles) along the joins SiO2–NaAlO2 and SiO2–Ca0.5AlO2. Minerals with six-coordinated Al: Jd (NaAlSi2O6 and Ca–Ts (CaAl2SiO6). Data from [26].

The determining influence of short-range order on vibrational properties is also demonstrated by the fact that the entropy of silicate crystals may be calculated as a sum of entropy coefficients pertaining to oxide components characterized by the coordination number of the cation [28]. In view of the continuous nature of glass solutions, the same procedure can be applied to derive partial molar heat capacities and vibrational entropies for oxides in glasses (Table 2). The generally additive nature of S298 – S0 (Figures 6 and 8) is confirmed by the fact that data available for about 50 different compositions can be reproduced to better than 1% with a set of composition-independent partial molar entropies. As expected, the influence of Al speciation in aluminosilicates is clear since partial molar heat capacities (Figure 9) and entropies decrease from four- to fiveand then sixfold coordination [30]. Another noteworthy feature is that two different Na2O and K2O components must be distinguished depending on whether the alkali element is “free” or is associated as a charge compensator with tetrahedral Al [26]. The higher entropies calculated in the latter cases indicate that association with Al causes the coordination number of the alkali to increase from the aforementioned number of about 5 to a much higher value similar to those determined for tectosilicates. But a single entropy is derived for Ca and for Mg when transforming from network modifier to a charge compensator, indicating that in contrast the environment of alkali earth

54

33.5 30.7

26.7 (VI)–27.7 (VII)

CaO

42.8

39.6 (VI)–38.7 (VIII)

Li2O

49.0

38.5 (IV–V)

Na2O

85d

76 (IV–V)

96.7a

97.3 (IX)

K2 O

3.4 Partial Molar Entropy of Oxides in Silicate Glasses

Crystals

FeO Fe2O3

d

108

101 (V–VI)

119.1a

114.3–120.4

56.1 116

43.2 (IV–VIII) 85 (VIII)

a

For Al charge-compensating alkali. Average value of 69.1 to be used if Al speciation is unknown. c Three-coordinate boron belonging either to boroxol rings (IIIBB2O3) or “free” (IIIFB2O3) [Richet, unpublished]. Average value of 37.36 J/mol K for pure B2O3 glass. d In Al-free silicates. Source: Data (J/mol K) from [23, 26, 29–31] for glasses and [28] for crystals. b

cations does not change much upon a less strong association with two tetrahedral Al3+ ions. As for boron, one must not only assign widely different values to threeand fourfold coordination but distinguish in the former between borons that belong to the so-called boroxol rings (Chapter 7.6) and the others (Table 2).

3.5 Calorimetric Boson Peak For some glasses [23], additivity of the heat capacity can break down below about 50 K where there exist strong positive deviations with respect to the Debye T3 laws commonly observed near 0 K by crystals. This calorimetric anomaly originates in an excess of modes found between 30 and 150 cm−1 in the vibrational density of states, known as the boson peak (Chapter 3.4), with respect to Debye model that considers a solid as an

3 Low-temperature Heat Capacity and Entropy

10

Cristobalite Glass

70

10 105 Cp/T 3max

80

8

VIAI

Cp (J/mol K)

50 VAI

2O3

2O3

IVAI

40

2O3

CaO

30

SiO2

105 Cp/T 3 (J/g atom K4)

60

20

5

0 10

20 30 V (cm3/mol)

6

4 Quartz

2 Coesite

10

Stishovite 0

0

0

50

100

150

200

250

0

20

40

200

T (K)

Figure 9 Influence of the coordination state of aluminum on the partial molar heat capacities of Al2O3 in aluminosilicate glasses, compared with those of CaO and SiO2. [30].

60

80

100

T (K)

Figure 10 Calorimetric boson peak of SiO2 glass and polymorphs. Data sources in [19, 27]. Inset: maximum of the boson peak against the molar volume of the polymorphs (open square: SiO2 glass).

14 KS

12

KS2

KS4

105Cp /T3 (J/g atom K4)

isotropic continuum in which longitudinal and transversal acoustic waves propagate with constant velocities. Owing to this common reference to Debye model, the calorimetric anomaly will also be referred to as a boson peak. It is in fact not peculiar to glasses and other disordered solids (Chapter 3.4). As indicated by peaks in plots of Cp/T3 against T, the calorimetric anomaly is even greater for cristobalite than for SiO2 glass although it markedly decreases to quartz and coesite and vanishes for stishovite, which does follow Debye law (Figure 10). For SiO2 glass, the boson peak is assigned to coupled librations of the corner-shared SiO4 tetrahedra (at 0.3–4 THz frequencies) coexisting with sound waves [32]. Its marked decrease can also be assigned first to an increasingly compact arrangement of SiO4 tetrahedra, which hinders librational motion, and then to the change from fourto sixfold Si coordination, which makes it impossible [19]. In binary alkali silicate glasses, the calorimetric boson peak increases in intensity and decreases in temperature from Li to Na and K (Figure 11) as replacement of large and heavy K+ ions by smaller, more tightly bonded Li+ ions shifts vibrational modes to lower frequencies. Additional insights can be gained in this respect from the inversions of Eq. (8) made to derive the low-frequency

10 S

8 6

NS3

NS2 NS

4 LS3

2 0

LS2

0

10

20

30

40

50

60

70

80

T (K)

Figure 11 Calorimetric boson peak of SiO2 (S) and alkali silicate glasses. Data from [33].

part of the vibrational density of states from Cp data. Well-defined first peaks representing the excess modes are obtained in this way [33]. As expected from the linear trends of the input Cp data, their positions and intensities

321

3.6 Thermodynamic Properties of Oxide Glasses and Liquids

(a)

(b) 150 Na

140

Li

14

12

130

1014 Intensity

ωmax (cm–1)

K

120 110

10 Na 8

K 6

100 90

Li 40

50

60

70

80

90

4 40

100

50

60

mol % SiO2

70

80

90

100

mol % SiO2

Figure 12 First peak of the vibrational density of states of alkali silicate glasses as determined by inversion of low-temperature heat capacities [33]. (a) Position of the peak. (b) Intensity.

also vary linearly with M2O content in alkali silicates (Figure 12) and point to a combination of librational modes from the SiO2 component and localized vibrational modes for network-modifying cations [33, 34]. The intensity decrease caused by network depolymerization, which restricts librational motion, is more than compensated by increasing the intensity of localized vibrations. Despite the wide variations found in the position and magnitude of the boson peak, another strikingly simple feature is the collapse of all data on a single master curve when the temperature and maximum of the peaks are used as normalizing parameters for plotting the experimental data (Figure 13). But this universal representation remains to be accounted theoretically.

4

High-temperature Properties

4.1 Glasses Above room temperature (Figure 14), an important feature is that the glass transition takes place when the heat capacity becomes close to the Dulong and Petit harmonic limit of 3 R/g atom where R is the gas constant [35]. It follows that any composition dependence tends to vanish at the glass transition where only the number of atoms in the formula unit eventually matters. Hence, the Cp 40 Na2TiSi2O7

1.2

35

CaMgSi2O6 CaAI2Si2O8

Cp (J/g atom K)

1

Cp /T 3/(Cp/T 3)PB

322

0.8 0.6

WG

30

NaAISi3O8 25

SiO2

3R/g atom

0.4 20 0.2 Glasses 0 0

2

4

6

8

10

T/TPB

Figure 13 Universal representation of the calorimetric boson peak with the reduced variables T/Tmax and Cp/Cpmax. Data for 20 silicate, aluminosilicate, and oxynitride glasses from [33, 34] and ref. therein.

15 300

600

Liquids 900

1200

1500

1800

T (K)

Figure 14 The highly contrasting changes in the heat capacities of some silicate at the glass transition. WG: window glass. Data sources in [19].

4 High-temperature Properties

Table 3 Partial molar heat capacities of oxides in glasses, Cpi = ai + biT + ci/T2 + di/T1/2 (J/mol K). 103 bi

SiO2

127.200

−10.777

4.3127

Na2O

70.884

26.110

−3.5820

K2O

84.323

0.731

−8.2980

CaO

39.159

18.650

−1.5230

MgO

46.704

11.220

−13.280

Al2O3

175.491

−5.839

−13.470

TiO2

64.111

22.590

−23.020

FeO

31.770

38.515

−0.012

Fe2O3

135.250

12.311

−39.098

B2O3

215.151

−3.435

15.836

H2O

82.804

di

80

−1463.9

Di

70

−1370 50 800

1000

1200

1400

1600

1800

2000

T (K)

−2920

Source: Data from [36] and from [37] for H2O.

additivity observed below 300 K also obtains at higher temperatures with the simplifying feature that the speciation of Al and alkalis no longer needs to be considered. This feature is illustrated by the convergence of the partial molar heat capacities of the Al2O3 species already under way below 300 K (Figure 9), but does not hold for boron for which there remains a large Cp difference between IIIB2O3 and IVB2O3. To within their error margins, available heat-capacity and relative-enthalpy data can thus be reproduced from room temperature up to the glass transition with composition-independent partial molar heat capacities of the form (Table 3), 2

,

11

where xi is the mol fraction of oxide i and the coefficients for SiO2 and B2O3 are simply those of the Cp expression of the pure oxide glass [36]. If additional oxides need to be considered at not too high contents, then use can be made of the heat capacities of their crystalline forms in view of the generally small differences observed between glasses and crystals. 4.2

Wo

60

−48.274

C p = Σ xi ai + bi T + ci T 2 + d i T 1

Cm (J/gfw K)

ai

An Py

10−5 ci

Oxide

90

Liquids

As long as crystallization does not take place, there is not any change in the physical properties of melts when the liquidus is crossed. This feature applies in particular to the heat capacity, which varies smoothly from the supercooled to the stable liquid domain. In practice, experimental difficulties generally stem from incipient crystallization above the glass transition and very high liquidus temperatures. In other words, only short temperature intervals can very often be investigated in either

Figure 15 Mean heat capacity, Cm = (HT − H273)/(T − 273), of some aluminosilicate glasses and melts on both sides of the glass transition: An (CaAl2Si2O8), Py (Mg3Al2Si3O12), Wo (CaSiO3), and Di (CaMgSi2O6). Liquidus and glass transition temperatures indicated by arrows; data referred to 1 mol of oxide components; for clarity reasons, data for Py and Wo displaced upward by 3 and 5 J/gfw K, respectively. Data from [21].

domain. Not to introduce any bias, the most reliable measurements must rely on a single technique working from Tg to superliquidus temperatures. Even though quite a few valuable DSC measurements are now available, they are limited to restricted temperature intervals for low-Tg compositions for which high-temperature extrapolations are not warranted. In the following, only drop-calorimetry results obtained up to 1850 K will thus be mentioned (Figure 15). If precise measurements are made both near Tg and at superliquidus temperatures, the crystallization curtain is not a great impediment, thanks to the reliable interpolations that can be made and make it, for instance, possible to ascertain whether or not the heat capacity of the liquid varies with temperature. In addition, the results yield the Cp changes at the glass transition (ΔCp), which vary from about 10 to 50% and display extremely strong dependences on composition (Figure 14). This variety is exemplified by (i) window glass and sodium silicate melts whose heat capacities are constant over the whole temperature intervals investigated, which can reach 1000 K; (ii) titanosilicate melts, which show record high ΔCp’s reaching 50%, followed by markedly negative values of dCp/dT; (iii) aluminosilicate melts, with ΔCp values ranging from 10 to 30% and positive dCp/dT values increasing in the order Mg, Ca, and Na in ternary systems [19]; (iv) other complexities found in borosilicates for which dCp/dT is also variable without being correlated with B2O3 content [38]. It is beyond the scope of this chapter to discuss such differences. But it is worth noticing that some are reminiscent of those observed at low temperatures, which

323

3.6 Thermodynamic Properties of Oxide Glasses and Liquids

Table 4 Partial molar heat capacities of oxides in melts, Cpi = ai + biT + ci/T2 (J/mol K) [39]. Oxide

SiO2

a

ai

103 bi

10−5 ci

81.37

Li2O

107.7

Na2O

100.6

K2Oa

50.13

Rb2O

97.36

BeO

46.65

CaO

86.05

SrO

86.12

BaO

79.96

ZnO

92.57

MnO

82.73

MgO

85.78

PbO

55.98

Al2O3

27.21

TiO2

75.21

FeO

78.94

Fe2O3

199.7

Y2O3

233.7

Sb2O3

204.8

Bi2O3

257.7

La2O3

241.8

aluminosilicates [19]. A model with “average” partial molar heat capacities is nonetheless useful especially for chemically complex compositions for which errors usually made with simple models compensate to a large extent (Table 4).

4.3 Residual Entropies

15.78

The residual entropy of a glass, S0, represents the entropy frozen in at the glass transition. It increases with increasing cooling rates. It can be determined by calorimetric methods from the entropy of melting of the crystal and the appropriate integrations of heat capacities measured between 0 K and Tm for the crystal, liquid, and glass phases (Figure 16), namely Tm

Sg 0 = Sc 0 +

0

C Pc ΔH m dT + + T Tm

Tg

C Pl dT + Tm T

0

C Pg

Tg

T

dT

13 94.28 875.3

When melting temperatures are not too high (i.e. 1900 K at most), these measurements are possible if there exists an isochemical crystal that (i) melts congruently, so as to have ΔSm = ΔHm/Tm and (ii) can be considered perfect at 0 K, so as to have a zero entropy at 0 K. These practical and thermodynamic constraints are the reason

Excess Cp = 151.7 xSiO2 xK2 O (J/mol K) to be included [39].

B2O3

200

are assigned to the dual structural role of cations that are either network modifiers or charge compensators for tetrahedrally coordinated cations. Likewise, it is tempting to assign the unusual heat capacities of titanosilicate melts to a decreasing extent of (Ti, Si) mixing on tetrahedral sites with decreasing temperatures, which would result in the coexistence of silicate and titanate species without unmixing at the lower temperatures [19]. From a practical standpoint, the occurrence of the glass transition when the Dulong-and-Petit limit is approached makes it possible to approximate the configurational heat capacity by the simple relation [18]

Liquid

Tg 150 S (J/mol K)

324

ΔSm

100 Tm Glass 50

Crystal

C p conf T = C pl T − C pg T g = C pl T – 3 nR, 12 where n is the number of atoms in the unit formula, which provides values as accurate as those one would determine experimentally. Although Cp additivity is clearly observed in simple systems such as Li2O– and Na2O–SiO2 or MgO–Al2O3–SiO2, it breaks down in Ca and Na

S conf 0

0

200

400

600

800

1000

T (K)

Figure 16 Calorimetric determination of the residual and configurational entropies of B2O3 glass and liquid. Data from [31].

4 High-temperature Properties

Table 5 Residual entropies of oxide glasses determined from calorimetric measurements performed between 0 K and the melting point of the stable crystal.

Oxide

Sg(0) J/mol K

Sg(0) J/g atom K

B2O3

11.2

2.2

GeO2

6.6

2.2

SiO2

5.1

1.7

Na2SiO3a

5.11

0.8

18.0

2.0

K2SiO3a

12.6

2.1

CaSiO3

8.8 23

MgSiO3

11.2

2.2

7

1.0

Mg2SiO4a

2.3

NaAlSiO4

9.7

1.4

NaAlSi3O8

36.7

2.8

KAISi3O8

28.3

2.2

CaAl2Si2O8

36.8

2.8

Mg3Al2Si3O12

56.3

2.8

Mg2Al4Si5O18

94

3.2

Sg 0 2 − Sg 0

a

Unpublished, less accurate derivation. Source: Data from per mol or reported to the number of atom (g atom) [19].

15

1

T f2

C Pl − C P g

T f1

T

=

dT ≈ C Pl − C Pg

ln

T f2 T f1

16

why available data are rather scarce (Table 5). Of particular interest is the result obtained for NaAlSiO4 whose residual entropy is smaller than that of SiO2, on a g atom basis (i.e. per atom). Both glasses are made up of a continuous, open network of TO4 tetrahedra whose purely topological entropies should not be widely different. The lower entropy of NaAlSiO4 was, therefore, indicating a highly ordered Al─Si distribution, which has later been confirmed by NMR measurements [19]. That residual entropies determined from calorimetric experiments are thus making physical sense is also confirmed, among other examples, by the very low value calculated for Mg2SiO4 whose extremely poor vitrifiability may be assigned to the very rapid rate at which configurational entropy is lost [40]. More generally, the validity of the concept of residual entropy for glasses is also illustrated by a different approach based on Adam–Gibbs theory of relaxation processes. From the postulated proportionality between relaxation times and configurational entropy, Sconf, one finds that the viscosity is given by [41] log η = Ae + Be TS conf ,

C conf P dT , Tg T

these expressions represent a three-parameter equation for viscosity. From fits made with Eqs. (13) and (14) to data spanning wide intervals from the glass transition range to superliquidus temperatures, one then derives the Ae and Be parameters and the residual entropy at the relevant glass transition temperature. The strikingly good agreement of these values with the values determined by calorimetric experiments thus validates the whole approach (Figure 17), which is especially useful as there is no other experimental method available for determining configurational entropies. For hyperquenched glasses, however, very high fictive temperatures can affect entropy significantly. Provided that the fictive temperatures and relevant heat capacities are known, the entropy difference between glasses with different thermal histories is readily accounted with

1.8

CaMgSi2O6

T

S conf T = S conf T g +

14

As recently discussed [42], this effect could be the reason why glass fibers dissolve much more rapidly than bulk glass pieces in aqueous solutions. 60 Mg3AI2Si3O12

50 CaAI2Si2O8

40 Svis (J/mol K)

K2Si2O5a

where Ae is a pre-exponential term and Be a parameter proportional to the Gibbs-free energy barriers opposing viscous flow. Because the temperature dependence of Sconf can be calculated with Eq. (11) and

NaAISi3O8

30 CaMgSi2O6

KAISi3O8

20

10 CaSiO3

0

0

MgSiO3

10

20

30

40

50

60

Scal (J/mol K)

Figure 17 Comparison between residual entropies derived from calorimetric and viscosity measurements. Data sources in [19].

325

3.6 Thermodynamic Properties of Oxide Glasses and Liquids

5

Reaction Thermodynamics

5.1 Enthalpies of Mixing In a solution, the Gibbs free energy is the weighted sum of the chemical potentials μi of the components G=

x i μi =

where xi is the mole fraction of component i and ΔHmix and ΔSmix are the enthalpies and entropies of mixing, respectively. As already alluded to, ΔHmix can be determined by solution calorimetry from the measurements made on the end-members and other compositions of the system of interest. Even when if one considers only binary or pseudo-binary joins, the number of relevant glass-forming systems is so large that the data available for some tens of joins [18] represent but a small fraction of those that would be worth investigating. Hence, the important Al─Si substitution for a number of alkali and alkaline earth cations will serve here to illustrate a few salient points [43]. These results are plotted as negatives of enthalpies of solution to reflect directly the enthalpy scale (Figure 18). Enthalpies of mixing between SiO2 and Mx/2AlO2 SiO2 are negative in all systems, which attest to strong affinity between these components. The enthalpy minimum lies near 50 mol % with a depth that increases with the field strength of the M-cation from +10 to below −20 kJ/mol from Mg- to K-aluminosilicates and the relative extent of freezing-point depressions at eutectic points. Although they are directly relevant to phase equilibria, these data require the aforementioned fictive-temperature corrections for use in Eq. (17). For samples whose glass transition temperatures are higher

Mg 10 Ca Sr

0

Cs Rb

Ba Li

–10

Na –20

K 0

20

than 700 C, the temperature of solution calorimetry, the adjustments can amount to 5 kJ/mol or more [21] to determine accurately enthalpies of mixing between SiO2 and the most SiO2-poor composition investigated for a given system.

xi μi + ΔH mix – T ΔS mix , 17

– ΔHs (kJ/mol)

326

40

60

80

100

Mol % SiO2

Figure 18 Enthalpies of solution of aluminosilicate glasses along binary joins. Data from [43].

5.2 Gibbs Free Energies of Formation As a rule, mixing of individual oxides in glass-forming systems is highly nonideal in terms of both enthalpy and entropy factors (Chapter 5.3). Because atomic interactions are essentially of a binary nature (Chapter 2.8), however, mixing of two binary systems is much less nonideal, and so on when the chemical complexity keeps increasing. In thermodynamic modeling, it is thus advantageous to select as components not the relevant oxides but more complex entities in which the main interactions are already embodied [44]. In a given system, a natural choice then is to select for a particular composition the phases constituting the stable crystalline assemblage indicated by the phase diagram, between which the mixing enthalpies and entropies are negligibly small compared with those of the constituting oxides. In this way, a given property Y of a glass or its melt is simply approximated by the sum Y = Σ xi Y i ,

18

where xi is the mol fraction of constitutional phase i and Yi is its partial molar property, which is assumed to be independent of composition. Taking the enthalpy of a glass at room temperature as an example, one obtains the Hi values from the available enthalpies of formation of ΔHfi of the ith crystalline phase and its enthalpy of vitrification ΔHvi, i.e. Hi = ΔHfi + ΔHvi. If ΔHvi data are lacking, then the approximation ΔHvi ≈ ΔHmi/2 may be used. For entropies, the other rule of thumb ΔSv ≈ ΔSmi/3 applies. If a glass melt above liquidus temperature is considered, the procedure is the same except that the Hi values refer to the liquid state. To select the right set of components, use is made of the fact that in most systems of natural or industrial interest four oxides make up at least 85% of the composition and that stoichiometric compounds rarely bear more than three different oxides. Thus, the major four oxides are allotted according to existing phase diagrams while the rest is determined by normative geochemical calculations. On this basis, the composition of a complex system can be expressed unambiguously [45]. The major advantage of the method thus is that no structural information at all is needed as long as multicomponent systems (ternary and beyond in terms of oxides) are dealt with. Its usefulness is apparent in Table 6 where excellent agreement is found between the experimental and model

6 Perspectives

Table 6 Determination of the Gibbs free energies of formation from the oxides for a few glasses from calorimetric and viscosity measurements. Data in wt % and kJ/mola. Oxide

V1

SiO2

V2

42.10

V3

42.8

V4

42.4

44.7

Fe2O3

6.20

8.0

7.4

Al2O3

20.02

24.0

21.3

21.0

CaO

13.2

12.25

15.25

9.11

4.02

10.2

5.0

MgO

5.03

Na2O Tg

5.25

13.5

11.7

892.6

924.3

2.83 958.9

12.85 902.4

Cpg(Tg)

25.46

25.43

25.37

25.36

Ae

−1.4755

−1.02

−2.68

−1.09

Be

90.379

79.283

138.670

84.704

7.00

6.11

9.22

6.66

Sconf(Tg) ΔS0

5.06

5.11

4.41

4.99

36.80

32.76

44.43

52.56

f

−40.69

−33.86

−9.76

−32.29

ΔG f(exp)

−44.14

−33.98

−35.43

−12.94

−41.4

−35.0

−37.0

−10.6

S(Tg) − S0 ΔH

ΔG f (calc)

b

a

Experimental data from an unpublished report prepared at IPGP by D. Brisart; solution calorimetry at 973 K in lead borate done with J. Rogez at the TECSEN laboratory (CNRS, Marseilles). b [45].

values of the Gibbs free energies of formation of four glasses.

6

Perspectives

That physical properties can represent a valuable source of structural information is often overlooked. Structures are determined by thermodynamics, and not the other way around. Despite any structural complexities of the amorphous state, an important simplifying feature is that properties of glasses generally vary smoothly with composition, without all the irregularities displayed by those of crystals caused by the constraints imposed by the specificities of discrete crystal structures. In other words, structural conclusions drawn from a few amorphous compositions can in general be extended readily to a much wider composition range than can be done for crystalline materials. The conclusions are the most straightforward for solids when properties are vibrational in origin. Difficulties are much greater for liquids whose variety of mechanisms involved in temperature-induced structural changes remain elusive in spite of the enormous amount of

structural information that is being gathered with a variety of techniques [19]. The contrast with the scarcity of thermodynamic data at temperatures much higher than 1000 K is striking. Additional measurements are thus needed but the lack of commercially available highprecision equipment is a real impediment that could last and affect progress to be made either for tailoring new materials or for understanding igneous processes at all relevant scales. A really fundamental goal will be to integrate into a consistent framework the structural and thermodynamic aspects in a way consistent with the fact that decreasing energy scales correlate with increasing interaction length scales. Recent work on melting mechanisms illustrates this kind of approach [46]. The starting point is the correlation observed between the calorimetric premelting effects displayed by Na2SiO3 and Li2SiO3 (Figure 2) and changes in the Raman spectra pointing, without significant enthalpy effects, to the production of mobile Na+ ions and Si─O− moieties that remain part of the crystalline silicate chains as negatively charged Q2 species; these species then react with “normal” Q2 units to cross-link the chains with Q3 species, liberating along the way “free” oxygen O2− ions. Actual melting finally takes place with a sharp enthalpy change through depolymerization of silicate chains by free O2− ions to form Q1 species also observed spectroscopically, whereas the same reactions proceed in the reverse order upon crystallization. Another field where much remains to be done is highpressure experiments or, at least, measurements on permanently densified glasses, which are of fundamental interest in geophysics and are also catching the physicists’ attention. The few available data for the pressure dependence of the enthalpy (Table 7) indeed suggest that strong composition-structure effects are also to be revealed. For completeness, one must also recall that thermodynamic and volume (Chapter 3.5) properties are closely related through the pressure derivative of the Gibbs free energy, (∂G/∂P)T = V. Any progress made on the equations of state of melts will thus be of immediate relevance to high-pressure thermodynamic properties. Table 7 Variations of the enthalpy (kJ/mol) of oxide glasses with the density (g/cm3). Glass

GeO2 SiO2

(∂H/∂ρ)T

−32.3 (14.1) −44 (20)

K2Si4O9

−105.2 (10.7)

Na2Si4O9

−52.1 (13.6)

NaAlSi3O8

−9.1 (10.4)

Source: Data from [47].

327

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3.6 Thermodynamic Properties of Oxide Glasses and Liquids

Acknowledgments Warm thanks are due to R. Conradt, A. Takada, and A. Whittington for their critical review of this chapter.

14

15

References 1 Bouhifd, M.A., Courtial, P., Besson, P. et al. (2007).

2 3

4

5

6 7

8

9

10

11

12

13

Thermochemistry and melting properties of basalt. Contrib. Mineral. Petrol. 153: 689–698. Bestul, A.B. and Chang, S.S. (1965). Calorimetric residual entropy of a glass. J. Chem. Phys. 40: 3731–3733. Conradt, R. (2009). On the entropy difference between the vitreous and the crystalline state. J. Non-Cryst. Solids 355: 636–641. Gibson, G.E. and Giauque, W.F. (1923). The third law of thermodynamics. Evidence from the specific heats of glycerol that the entropy of a glass exceeds that of a crystal at the absolute zero. J. Am. Chem. Soc. 45: 93–104. Mauro, J., Gupta, P.K., and Loucks, R.J. (2007). Continuously broken ergodicity. J. Chem. Phys. 126: 224504. Gupta, P.K. and Mauro, J. (2008). The laboratory glass transition. J. Chem. Phys. 126: 224504. Goldstein, M. (2008). On the reality of residual entropies of glasses and disordered crystals. J. Chem. Phys. 128: 154510. Johari, G.P. (2011). Specific heat relaxation-based critique of isothermal glass transition, residual entropy and time-average formalism for ergodicity loss. Thermochim. Acta 523: 97–104. Takada, A., Conradt, R., and Richet, P. (2015). Residual entropy and structural disorder in glass: a review of history and an attempt to resolve two apparently conflicting views. J. Non-Cryst. Solids 429: 33–44. Gujrati, P.D. (2010). Loss of temporal homogeneity and symmetry in statistical systems: deterministic versus stochastic dynamics. Symmetry 2: 1201–1249. Gujrati, P.D. (2018). Hierarchy of relaxation times and residual entropy: a nonequilibrium approach. Entropy 20: 149. https://doi.org/10.3390/ed0030149. Robie, R.A., Hemingway, B.S., and Fisher, J.R. (1995). Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 Bar (105 Pascals) Pressure and at Higher Temperatures, U.S. Geological Survey Bulletin, vol. 2131. Washington, DC: U.S. Goverment Printing Office. Richet, P., Bottinga, Y., Deniélou, L. et al. (1982). Thermodynamic properties of quartz, cristobalite and amorphous SiO2: drop calorimetry measurements

16

17

18

19 20

21

22

23

24

25

26

27

between 1000 and 1800 K and a review from 0 to 2000 K. Geochim. Cosmochim. Acta 46: 2639–2658. Robie, R.A. and Hemingway, B.S. (1972). Calorimeters for heat of solution and low-temperature heat capacity measurements. U.S. Geological Survey Professional Paper, 755. Hwang, J.S., Lin, K.J., and Tien, C. (1997). Measurement of heat capacity by fitting the whole temperature response of a heat-pulse calorimeter. Rev. Sci. Instrum. 68: 94–101. Navrotsky, A. (1997). Progress and new directions in high-temperature calorimetry revisited. Phys Chem. Miner. 24: 222–241. Téqui, C., Grinspan, P., and Richet, P. (1992). Thermodynamic properties of alkali silicates: heat capacity of Li2SiO3 and lithium silicate melts. J. Am. Ceram. Soc. 75: 2601–2604. Richet, P. and Bottinga, Y. (1986). Thermochemical properties of silicate glasses and melts: a review. Rev. Geophys. 24: 1–25. Mysen, B.O. and Richet, P. (2005). Silicate Glasses and Melts. Properties and Structure. Amsterdam: Elsevier. Richet, P., Robie, R.A., and Hemingway, B.S. (1986). Lowtemperature heat capacity of diopside glass (CaMgSi2O6): a calorimetric test of the configurationalentropy theory applied to the viscosity of liquid silicates. Geochim. Cosmochim. Acta 50: 1521–1533. Richet, P. and Bottinga, Y. (1984). Anorthite, andesine, wollastonite, diopside, cordierite and pyrope: thermodynamics of melting, glass transitions and thermodynamic properties of the amorphous phases. Earth Planet. Sci. Lett. 67: 415–432. Hovis, G.L., Toplis, M.J., and Richet, P. (2004). Thermodynamic mixing properties of sodium silicate liquids and implications for liquid-liquid immiscibility. Chem. Geol. 213: 173–186. de Ligny, D., Westrum, E.F. Jr., and Richet, P. (1996). Entropy of calcium and magnesium aluminosilicate glasses. Chem. Geol. 128: 113–128. and 140 (1997) 151. Labban, A., Berg, R., Zhou, J. et al. (2007). Heat capacities and derived thermodynamic properties of lithium, sodium, and potassium disilicates from T = (5 to 350) K in both vitreous and crystalline states. J. Chem. Therm. 39: 991–1000. Guttman, C. (1972). Low-temperature heat capacity difference between glasses and their crystals. J. Chem. Phys. 56: 627–630. Richet, P., Robie, R.A., and Hemingway, B.S. (1993). Entropy and structure of silicate glasses and melts. Geochim. Cosmochim. Acta 57: 2751–2766. Akaogi, M., Oohata, M., Kojitani, H., and Kawaji, H. (2011). Thermodynamic properties of stishovite by lowtemperature heat capacity measurements and the

References

28

29

30

31

32

33

34

35

36 37

coesite-stishovite transition boundary. Am. Mineral. 96: 1325–1330. Holland, T.J.B. (1989). Dependence of entropy on volume for silicate and oxide minerals: a review and a predictive model. Am. Mineral. 74: 5–13. Sipowska, J.T., Atake, T., Mysen, B.O., and Richet, P. (2009). Entropy and structure of oxidized and reduced iron-bearing silicate glasses. Geochim. Cosmochim. Acta 73: 3905–3913. Richet, P., Nidaira, A., Neuville, R.R., and Atake, T. (2009). Aluminum speciation, vibrational entropy and short-range order in calcium aluminosilicate glasses. Geochim. Cosmochim. Acta 73: 3894–3804. Richet, P., de Ligny, D., and Westrum, E.F. Jr. (2003). Low-temperature heat capacity of vitreous GeO2 and B2O3: thermophysical and structural implications. J. Non-Cryst. Solids 315: 20–30. Buchenau, U., Prager, M., Nücker, N. et al. (1986). Lowfrequency modes in vitreous silica. Phys. Rev. B 34: 5665–5673. Richet, N.F. (2009). Boson peak of silica and alkali disilicate glasses: inferences from low-temperature heat capacity. Physica B404: 3799–3806. Richet, N.F. (2012). Boson peak of alkali and alkaline earth silicate glasses: influence of the nature and size of the network-modifying cation. J. Chem. Phys. 136: 034703. Haggerty, J.S., Cooper, A.R., and Heasley, J.H. (1968). Heat capacity of three inorganic glasses and liquids and supercooled liquids. Phys. Chem. Glasses 9: 47–51. Richet, P. (1987). Heat capacity of silicate glasses. Chem. Geol. 62: 111–124. Robert, G., Whittington, A.G., Stechern, A., and Behrens, H. (2014). Heat capacity of hydrous basaltic glasses and liquids. J. Non-Cryst. Solids 390: 19–30.

38 Richet, P., Bouhifd, M.A., Courtial, P., and Téqui, C.

39

40

41

42

43

44

45

46

47

(1997). Configurational heat capacity and entropy of borosilicate melts. J. Non-Cryst. Solids 211 (3): 271–280. Richet, P. and Bottinga, Y. (1985). Heat capacity of aluminum-free liquid silicates. Geochim. Cosmochim. Acta 49: 471–486. Richet, P., Benoist, L., and Leclerc, F. (1993). Melting of forsterite and spinel, with implications for the glass transition of Mg2SiO4 liquid. Geophys. Res. Lett. 20: 1675–1678. Richet, P. (1984). Viscosity and configurational entropy of silicate melts. Geochim. Cosmochim. Acta 48: 471–483. Angeli, F., Charpentier, T., Jollivet, P. et al. (2018). Effect of thermally induced structural disorder on the chemical durability of international simple glass. Mater. Degradation 2: 31. https://doi.org/10.1038/s41529-0180052-3. Roy, B.N. and Navrotsky, A. (1984). Thermochemistry of charge-coupled substitutions in silicate glasses: the systems M1/nn+AlO2-SiO2 (M = li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Pb). J. Am. Ceram. Soc. 67: 606–610. Conradt, R. (2004). Chemical structure, medium range order, and crystalline reference state of multicomponent oxide liquids and glasses. J. Non-Cryst. Solids 345–346: 16–23. Conradt, R. (2008). The industrial glass-melting process. In: The SGTE Casebook. Thermodynamics at Work, 2nde (ed. H. Kack), 282–303. Boca Raton: CRC Press. Nesbitt, W., Bancroft, G.M., Henderson, G. et al. (2017). Melting, crystallization and the glass transition: toward a unified description for silicate phase transitions. Am. Mineral. 102: 412–420. Richet, P., Hovis, G., and Poe, B. (2004). Energetics of pressure-induced densification of GeO2 glass. Chem. Geol. 213: 41–47.

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3.7 Structural and Stress Relaxation in Glass-Forming Liquids Ulrich Fotheringham Research and Technology Development, Schott AG, Mainz, Germany

1

Introduction

An essential feature of the glassy state is the existence of configurational degrees of freedom. Both the number and the occupational state of these configurational degrees of freedom have an enormous impact on macroscopic properties such as the refractive index or the specific enthalpy and volume. Most of the configurational degrees of freedom may be considered as frozen-in below the glass transition range on any realistic timescale. If reheated into this temperature range, however, glass will undergo structural relaxation, i.e. the occupational state of these degrees of freedom will change which is equivalent to changes of the atomic structure. These changes will tend to minimize Gibbs free energy at the environmental temperature and they will have the impact on macroscopic properties mentioned above. A good example of structural relaxation is the thermal shrinkage observed when glass is reheated to temperatures just below the glass transition. Said change of the specific volume is of particular importance for, e.g. high-temperature coating processes. Similarly, structural relaxation leads to what is called refractive index drop in precision molding of lens elements. A straightforward way to observe the glass transition range is by differential scanning calorimetry – calorimetric glass transition, see Section 3.5). In addition, glass will use this reconfiguration capability to undergo stress relaxation, i.e. timedependent yielding to an imposed stress by viscous flow. In this chapter, the above examples will be presented in detail to illustrate the practical relevance of structural relaxation. Then, the concept of fictive temperatures will

Reviewers: Paul Joseph, Department of Mechanical Engineering, Clemson University, Clemson, SC, USA Markus Kuhr, Research and Technology Development, Schott AG, Mainz, Germany

be introduced. At constant temperature and pressure, the time-dependence of the physical properties of a relaxing material indicates that other variables have to be defined to describe its state. This is done with fictive temperatures, which are the basis of the various models that account for the kinetics of structural relaxation. Stress relaxation is the other topic. In the transition range, the mechanical high-temperature response of glass – like a viscous liquid – and the mechanical low-temperature response – like an elastic solid – coexist. Their combined effect is called viscoelasticity: when glass is exposed to strain, stress will occur as an initial response, and this stress will subsequently decrease over time due to the above reconfiguration mechanism. There are two fundamental viscoelastic cases, the constant volume one (shear) and the constant shape one (pressure), which will both be discussed at the end of the chapter.

2 Structural Relaxation: A Few Examples As it has already been said, the classical example of structural relaxation is the linear dependence of the refractive index on the logarithm of the cooling rate [1]. The slope is proportional to the number of configurational degrees of freedom, the occupational state of which is determined by the cooling rate. This issue will be discussed in more detail. A second example is prestressing or toughening of glass plates (Figure 1), which hinges on viscous flow upon processing but is also influenced by the differing occupational states of the configurational degrees of freedom at the glass surface and in the glass core [2–4]. When heated above the glass transition range and then rapidly cooled, a glass plate develops a temperature gradient such that the temperature is highest in its core and

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

332

3.7 Structural and Stress Relaxation in Glass-Forming Liquids

Figure 1 Prestressing/toughening of a glass plate. T

T

T ΔT

TG

z Cooling of hot glass plate: surface contracts relative to the core ⇒ tension at the surface, compression in the core.

z

z Above glass transition temperature TG: all stresses relax. At glass transition temperature: glass passes stress-free, but with temperature gradient ΔT.

At room temperature: ΔT vanishes, core contracts relative to the surface ⇒ tension in the core, compression at the surface, not relaxing!

lowest at its surface. As a consequence, the surface contracts relative to the core, which results in compressive stress in the core and tensile stress at and near the surface. At temperatures above the glass transition range, these stresses relax by viscous flow. Therefore, the glass plate passes this range stress-free during further cooling, but with a (high) internal temperature gradient that gradually diminishes and finally disappears at room temperature. As a consequence, the core contracts relative to the surface, which results in tensile stress in the core and desirable compressive stress at the surface. These stresses are permanent and increase fracture toughness – as long as the glass plate is not reheated to the glass transition range. Most of the contraction of the surface relative to the core and, then, of the core relative to the surface is due to thermal expansion. There is, however, a secondary effect due to said differing occupational states of the configurational degrees of freedom at the surface and in the core. As already stated, the occupational state of the latter depends on the cooling rate. The higher the cooling rate, the more high-energy states are occupied and vice versa. As the high-energy states are more space consuming than the low-energy ones, said secondary effect due to thermal expansion results. Owing to the comparatively low thermal conduction in glass, the cooling rate is much faster at the surface than in the core during prestressing. This results in an inhomogeneous distribution of occupational states over the plate cross-section, and in return in an additional contribution to the final contraction of the core relative to the surface. The third example is the peak of the absorption curve of silicate glasses [5] in the Gigahertz/Terahertz range, which is a typical feature of all glass-forming systems, the so-called Boson peak. Its intensity is sensitive on the cooling rate and, thus, on the occupational state of the configurational degrees of freedom [6]. Hence, it is the relaxational state that eventually determines the course of the absorption curve in this frequency regime.

3

Structural Relaxation

3.1 Description of the Configurational State by at Least One Fictive Temperature Usually one or more order parameters or one or more fictive temperatures (Sections 3.2–3.4) are selected to quantitatively describe the configurational state of a glass and, thus, the response of the macroscopic properties to its changes [7, 8a]. The basic idea is to take temperature as what it is in terms of thermodynamics, i.e. a distribution parameter indicating the average excitation level of every degree of freedom belonging to the thermal reservoir considered. If one makes a Gedankenexperiment (thought experiment) distinguishing between two thermal reservoirs consisting of degrees of freedom that are either all vibrational or all configurational (Figure 2), then one must also distinguish between two temperatures [9–11]. The first is the common temperature; the second is the distribution parameter describing the average excitation level of the configurational degrees of freedom, which is called fictive temperature. If enough thermal energy is exchanged with the environment at a high enough rate, the vibrational and environmental temperatures are equal. If, in addition, there is also sufficient energy exchange between the vibrational and configurational degrees of freedom, complete thermal equilibrium is achieved and the temperature is uniform. Regarding kinetics, the equilibration of vibrational and configurational degrees of freedom is a thermally activated process. What is called glass transition range is the temperature interval where, upon cooling, thermal activation is no longer large enough for ensuring equilibration and instead becomes too small for making equilibration possible on any realistic timescale. For the fictive temperature, this means that it remains equal to the environmental temperature above the glass transition but is frozen in at a constant value below it. This value is

3 Structural Relaxation

Figure 2 Imaginary separation of glass into two thermal reservoirs containing either the vibrational degrees of freedom (occupation number exp(−i hν/kT)/Z, i = 1, … ,∞, ν vibrational frequencie, h Planck’s constant, Z = Σ exp(−i hν/ kT) partition function for one vibrational degree of freedom) or the configurational degrees of freedom (for the two state examples shown here: occupation number ground level 1/Z , occupation number upper level exp(−Δ/kT)/Z , Z = 1 + exp(−Δ/kT) partition function).

Glass

Ground level, enthalpy = 0 Vibrational degrees of freedom

determined by the actual equilibration kinetics and the applied cooling rate. A shortcoming affects the description of the configurational state of a glass with a single fictive temperature, however, because this picture implicitly assumes strong coupling, i.e. an intense exchange of energy, between all configurational degrees of freedom to ensure that their average excitation levels follow a single distribution parameter. Coupling between configurational degrees of freedom is only indirect, however, because there is no direct energy transfer path between them. Rather, this energy transfer involves the vibrational degrees of freedom as mediator and runs this way: one configurational degree of freedom – vibrational degrees of freedom – other configurational degree of freedom. Thus, the coupling between the configurational degrees of freedom depends on the excitation level of the vibrational degrees of freedom so that it is subject to thermal activation itself. Therefore, a set of fictive temperatures is required for the description of the configurational state of a glass. In other words, the thermal reservoir containing the configurational degrees of freedom must be split into a number of sub-reservoirs, each having a fictive sub-temperature as a distribution parameter. From a theoretical standpoint, this change makes the concept less satisfactory than expected, but it has the major advantage of leading to very useful quantitative predictions of certain glass properties.

Configurational degrees of freedom

The second assumption is that any macroscopic property responds linearly to infinitesimal changes in both the environmental and the fictive temperatures: dH M = cvib dT + cconf dT f p p dV V = 3αvib dT + 3αconf dT f … or dT + cconf dT f,1 + dH M = cvib p p,1

3 where cp is the specific heat at constant pressure and α the linear coefficient of thermal expansion (3α = volume coefficient of thermal expansion) [8a]. For convenience, one writes in the case of n fictive subtemperatures: dT + cconf dH M = cvib p p

dV V = 3α

dV = dV

…

+ dV

conf

v1 dT f,1 +

cconf p,i

, cconf p

dT + 3α vi =

conf

αconf i , αconf

+ vn dT f,n , n

cconf = p

cconf p,i i=1

v1 dT f,1 +

+ vn dT f,n ,

n

αconf = …

αconf i i=1

4 and may also define a weighted mean value of the fictive sub-temperatures by

dH = dH vib + dH conf vib

+ cconf dT f,n p,n

dV V = 3αvib dT + 3αconf dT f,1 + + 3αconf dT f,n 1 n n fictive sub − temperatures …

vib

Such quantitative models first rely on the assumption that vibrational state and configurational states may be separated, i.e. that changes in macroscopic properties such as the enthalpy H or the volume V of a glass sample of mass M may be split into a vibrational and a configurational part and thus be written:

2

one fictive temperature

vi = 3.2 Prediction of Glass Properties from Temperature and Fictive Temperature(s)

Excited level, enthalpy = ∆

n

1

Tf≔

vi T f,i i=1

5

333

334

3.7 Structural and Stress Relaxation in Glass-Forming Liquids

where the vi coefficients are assumed to be the same. In this manner, one obtains [8a]: dT + cconf dT f dH M = cvib p p dV V = 3αvib dT + 3αconf dT f …

6

Note that a change dTf of this weighted mean (and any resulting change dH, dV, or anything else) may be caused by different sets of dTf,i leading to the same dTf = Σ vi dTf,i. Together with a kinetic model for the fictive temperature(s), Eqs. (2), (3) and the following ones allow macroscopic properties like enthalpy and volume to be calculated from the thermal history of the glass. At this point, one should inquire why the vi coefficients are the same for H, V, and other macroscopic properties. As a matter of fact, whether the kinetics of H, V, or other macroscopic properties (e.g. refractive index) is related to one fictive temperature or to one set of fictive sub-temperatures has been debated extensively. With respect to all types of glass-forming systems, including polymers, the former alternative does not seem to be correct (as pointed out by, e.g. [12]), although the differences between the two are small (e.g. [13]). For silicate glasses, however, this universality seems to exist [14]. All examples given below do support this view that the kinetics of all macroscopic properties are related to a single fictive temperature or a single set of fictive sub-temperatures. To ensure a fair comparison of differently obtained kinetic data, an appropriate deconvolution of, e.g. DSC data has to be carried out (see Section 3.5). Note that, the timescales of the vibrational and configurational responses to a jump in a state variable are essentially different. For an instantaneous temperature jump ΔT (at t = 0 for simplicity), there will first be an almost instantaneous change in vibrational states causing an enthalpy change cvib p ΔT, followed by a time-dependent variation of the configurational state. The resulting enthalpy change is given by cconf T f t − T f 0 at any p time t > 0. The actual value of Tf(t) − Tf(0) depends on kinetics. At some temperature below the glass transition range, the time to equilibrate vibrational and configurational degrees of freedom will become immeasurably long and Tf(t) − Tf(0) = 0 will hold on any realistic timescale. Only for t ∞ the system will eventually equilibrate and Tf(∞) − Tf(0) = ΔT will hold. Accordingly, the fictive temperature of a glass sample cooled from temperatures in or above the glass transition range to temperatures significantly below will reach an effectively final value that will not experience appreciable change on any realistic timescale (i.e. for t < ∞!). This value is called the glass transition temperature TG. As TG depends on the cooling rate, or more generally, the

thermal history, one may also define of TG in a unique sense referring to the value obtained from glass linearly cooled at 2 K/min. It is determined by dilatometry according to ISO 7884-8 [15].

3.3 Tool’s Original Model The concept of fictive temperature as well as the first step toward a model of glass relaxation were proposed by Tool in 1946 [7] in terms of a structural relaxation time τ. The rate equation describing the kinetics of a single fictive temperature Tf was expressed with an Arrhenius-type Ansatz (approach) dT f T − Tf = , dt τ

τ = τ 0 eH

R T

7

where R is the gas constant. The basic ideas of this Ansatz are that: 1) the system tends to equilibrate, i.e. Tf = T, with a driving force given by the difference T − Tf. 2) the system is configurationally trapped in a potential cage where it vibrates at a frequency ν = 1/τ0; a move toward another configuration then requires a jump over an enthalpy barrier H. With these assumptions, H should be of the order of magnitude of the dissociation energy of a network, for example, that required to break all oxygen bridges. Since configurational rearrangements involve cooperative motion of numerous atoms rather than hopping of individual ones only, H is usually considerably higher than the enthalpy required for overcoming a microscopic barrier. For polymer glasses, H may actually exceed the dissociation energy of the C─C bond by half an order of magnitude [16]. Concerning ν, one is tempted to identify it with the Einstein frequency or another typical frequency of atomic vibrations. One finds, however, that the high values found for H have to be associated with either very high ν or very low τ0 values to make, with Tool’s formalism, the glass transition occur in the experimentally observed range, i.e. at several hundred rather than at several thousand degrees. To assess the applicability of Eq. (7), one may have a glass equilibrate at a temperature T0 first and then make a temperature jump from T0 to T at t = 0. In that case, the fictive temperature for t > 0 is given by the differential Eq. (7) for constant temperature and for the initial condition Tf(0) = T0. The solution is the well-known singleexponential relaxation function: Tf = T + T0 − T

e−t

τ

8

3 Structural Relaxation

However, more sophisticated approaches have had to be developed, since neither enthalpy nor volume relaxation conforms to such a simple solution. ρ(g/cm3)

3.4 The Tool–Narayanaswamy– Moynihan Model This model is commonly known as Tool– Narayanaswamy or Tool–Narayanaswamy–Moynihan since its nonlinear character was dealt with by Narayanaswamy [17] and Moynihan [18]. As Mazurin, Rekhson, and Startsev had independently come to the same results [19] and as Kohlrausch-type kinetics had been introduced by Mazurin and Rekhson [20], it is appropriate to follow Hodge’s [21] suggestion and term it Tool–Narayanaswamy–Moynihan(−Mazurin–Rekhson–Startsev), or TNM(MRS) model for short. Two main facts have motivated its introduction: 1) The configurational response of enthalpy or volume (or any other macroscopic property) to a temperature jump after equilibration is not by a single but by a stretched exponential, i.e. H or V (or another property) approximately follow a so-called Kohlrausch(– Williams–Watts)-function exp[−(t/τ)b), 0 < b < 1 [22, 23] as also does a calculated fictive temperature (Figure 3). 2) Particularly for large temperature jumps, one observes an asymmetry between the upward and downward temperature jumps to the same final temperature. If prior equilibration was at a higher temperature, relaxation is faster and vice versa. The famous density relaxation experiments by Hara and Suetoshi [24] illustrate this behavior (Figure 4). H (t) – H (∞) H (t ↓ 0) – H (∞)

,

V (t) – V (∞) V (t ↓ 0) – V (∞)

,

Samples pre-annealed at 500 °C 2.502

Tf (t) – V (∞) Tf (0) – V (∞)

1 0.8 0.6

t b

2.50 2.498 100

50

150

200

t (min)

2.496

Samples pre-annealed at 560 °C

2.494

Figure 4 Density measurements of Hara and Suetoshi on sodalime-glass during annealing at 530 C.

These two facts are allowed for by the TNM(MRS) model in the following way: 1) The configurational state of a glass is described by a distribution of fictive sub-temperatures rather than by a single fictive temperature. By fictive temperature, without any further index, a weighted mean of the fictive sub-temperatures as defined in (5) is implied: n

Tf t =

n

vi T f,i t , i=1

vi = 1

9

i=1

2) All fictive sub-temperatures follow from the same type of differential equation as Tool’s original one: dT f,i T − T f,i = dt τi

10

3) As a consequence, the isothermal relaxation of every fictive sub-temperature upon a temperature jump can be represented by a single-exponential (approximately, if ΔT is not too large, see below). 4) The coefficients vi, relaxation times τi, and number n of fictive sub-temperatures are chosen such that the Kohlrausch-type response of the fictive temperature is best reproduced by the corresponding series of fictive sub-temperatures with single-exponential relaxation (“Prony-series”; with n given, the vi and τi are found by an appropriate optimization routine):

e−( τ )

0.4

Tf t = T + Tf 0 − T

0.2 0

= T + Tf 0 − T

e

0.5

1

t τ

n

t −( τ )

0

e−

1.5

2

2.5

vi e −

t τi

i=1

3

n

t/τ

Figure 3 Single exponential exp(−t/τ) versus stretched exponential exp(−(t/τ)b), b = 0.3. H(t 0), V(t 0) denote the values H, V take after the instantaneous vibrational response to the temperature jump, i.e. only the time-dependent configurational response is shown.

b

vi

T + Tf 0 − T

e−

t τi

i=1 n

=

vi T f,i t i=1

11

335

3.7 Structural and Stress Relaxation in Glass-Forming Liquids

On the assumption of thermorheologic simplicity, b and, as a consequence, all vi and quotients τi/τ are assumed independent of temperature. 5) The asymmetry of upward and downward temperature jumps is allowed for by the following modification of the thermal activation term: τi = τ0,i e H

R

x T + 1 − x Tf

12

where x is the so-called nonlinearity parameter that ranges from 0 to 1. If x = 1, Arrhenius behavior is obtained whereas x < 1 means that thermal activation is faster than with Arrhenius for Tf > T and slower for Tf < T. In Eq. (12), Tf is the weighted mean from (9). The deviation from Arrhenius-type thermal activation causes the differing forms of relaxation functions for small and large temperature jumps for which there is, or there is no, significant difference between Eq. (12) and exp(H/RT), respectively. As a consequence, the solutions to Eq. (10) are not single exponentials for large temperature jumps.

3.5 Calorimetric Determination of the TNM(MRS) Model Parameters Differential scanning calorimetry [25] is a convenient technique to determine relaxation parameters (Figure 5). One measures the heat flux dH into a sample heated at ambient pressure and at constant rate dT/dt, which is commonly identified with capp p dT. Here, “apparent” means that any possible glass transition or crystallization is deliberately ignored. With respect to Eq. (6), one obtains: capp p

dT dH dT dT f ≔ = cvib + cconf p p dt dt dt dt

13

Below the glass transition, the measured cp values are purely vibrational whereas above it, they are also configurational. To distinguish between both contributions,

one may extrapolate cp from below to above the glass transition with, for instance, the Einstein model and the Dulong–Petit-value as a high-temperature limit of cvib p . In the glass transition range, the rapid variations of capp p reflect the fictive temperature(s) kinetics upon heating at a constant rate. From an analysis of this peak, the parameters of the TNM(MRS) model may be determined [26]. The procedure is as follows. From Eq. (13), one obtains: vib capp dT f dT p − cp = dt cconf dt p

Calorimetric glass transition

2.5

Figure 5 Typical DSC of an “optically” (i.e. slowly) cooled BK7 sample. Heating rate 12 K/min. Data as measured (no deconvolution). Measurement by SETARAM Multi-HTC 96® at the accredited laboratories of SCHOTT AG.

Measurement

2 1.5 1 0.5 Einstein model 0

0

200

400

600

800

Temperature (°C)

1000

14

In an optimization routine, one calculates the left side of Eq. (14) from Eqs. (9), (10), and (12) and equates it to the right side by varying the parameters H, τ0, b, and x. In the first step of every optimization loop, a set of vi and τi is calculated according to the optimization procedure already described with Eq. (11). The number n indicating the length of the “Prony Series” is individually picked and should be “sufficiently high.” In the example below, a value n = 10 is used. To make sure that the parameters obtained from DSC are real and not adversely affected by unavoidable noise in the data, it is recommended to identify features like peak width, peak-to-peak distance, etc., that are very sensitive to a single parameter. One scan does not provide enough different features but two at different heating rates are in principle fine. These features are the position of the versus T curve, inflection point of the simulated capp p the width of the calorimetric glass transition, the shift of said inflection point with the heating rate, and the asymmetry of the glass transition, which are most sensitive to the parameters τ0, b, H/R, and x, respectively (Figure 6). Of course, an appropriate deconvolution of the DSC data is a prerequisite for achieving an excellent agreement between the calculated and experimental thermogram [27, 28].

3

cpapp (J/(gK))

336

1200

1400

3 Structural Relaxation

(e)

(a) 2.5 dTf /dT

2 1.5

Heating rate1 K/min, start values: H/k = 86 639 K (from enthalpy per mole to break all oxygen bridges), x = 1, b = 0.5, τ 0 = 4.87·10–46s (τ =τ 0·10H/(kT) =1 at inflection point)

dTf /dT

3

1 0.5 0 480

500

520

540

560

580

3 Heating rate 1 K/min, H/k = 54 164 K, x at start value, 2.5 b = 0.99, τ = 5.49·10–26 s: 0 distance of 1K/min peak and 2 4K/min peak o.k., position of 1.5 inflection point o.k. (despite mutual shift of curves), slope 1 of high-T shoulder of simulated peak not o.k., 0.5 ⇒ reduce x 0 480

600

500

520

Temperature (°C)

2.5 2

3.5 Heating rate 1 K/min, H, x at start values, τ0 adjusted, b not yet adjusted ⇒ calculated peak too broad

3 2.5 dTf /dT

3

dTf /dT

560

580

600

(f)

(b)

1.5

2 1.5 1

1

0.5 0.5 0 480

500

520

540

560

580

2 1.5

Heating rate 1 K/min, H, x at start values, b = 0.96, τ0 = 4.07·10–43 s: position and width of peak o.k., shape not satisfactory

2.5 2

570

590

610

Heating rate 1 K/min, H/k =70 584.6, x = 0.709, b = 0.719, τ0 = 3.907·10–35 s, almost perfect fit

1.5 1

1

0.5

0.5 0 480

550

(g)

dTf /dT

2.5

530

Temperature (°C) 3

3

510

600

(c) 3.5

Heating rate 4 K/min, H/k = 54 164 K, x at start value, b = 0.99, τ0 = 5.49·10–26 s: distance of 1K/min peak and 4K/min peak o.k., position of inflection point o.k. (despite mutual shift of curves), slope of high-T shoulder of simulated peak not o.k., ⇒ reduce x

0 490 Temperature (°C)

dTf /dT

540

Temperature (°C)

0 480 500

520

540

560

580

500

600

520

540

560

580

600

590

610

Temperature (°C)

Temperature (°C)

(h)

(d) 3.5

dTf /dT

3 2.5 2

3.5

Heating rate 4 K/min, H, x at start values, b = 0.96, τ0 = 4.07·10–43 s: 4 K/min-peak too close to 1 K/min-peak ⇒ H too big

3 2.5 dTf /dT

4

1.5

2 1.5 1

1

0.5

0.5 0 490

Heating rate 4 K/min, H/k = 70 584.6, x = 0.709, b = 0.719, τ0 = 3.907·10–35 s, almost perfect fit

510

530

550

570

Temperature (°C)

590

610

0 490

510

530

550

570

Temperature (°C)

Figure 6 (a–h) Subsequent adjustment of the TNM(MRS) model parameters τ0, b, H/k, and x (adjustment of the latter not shown here) in order to make the simulated dTf/dT curves (dashed lines) overlap with those obtained from measurement on BK7 (solid lines).

337

3.7 Structural and Stress Relaxation in Glass-Forming Liquids

3.6 Prediction of Thermal Shrinkage with the TNM(MRS) Model Once the parameters of the TNM(MRS) model are known, their predictive power can be ascertained from comparisons made between observed and calculated thermal shrinkage (Figure 7). In other words, the calorimetric TNM(MRS) parameters will be applied here to volume measurements. In these experiments, a temperature jump is simply realized through the transfer of a sample equilibrated in an oven at a given temperature to another oven at a different temperature. The glass can then be repeatedly removed from the latter at different times for length measurements at room temperature without any spurious influence of a dilatometer push rod. Provided that αconf is known from a density measurement in the molten state, comparison of the measured values with TNM(MRS)-based calculations may be made without any fit parameter from l t −l t 0 l t 0

Δl = αconf l

Tf t − Tf 0 15

Here on the left side is the relative shrinkage of the sample (as calculated from the measured sample length after a temperature jump at t = 0, the immediate response of the sample at t = 0 being discarded); and on the right side is the difference of the fictive temperatures at times t and 0. Note that whereas these paragraphs deal with BK7®, similar recent investigations at Clemson University [29, 30] have dealt with the new glass N-BK7®.

The predictive power of the “calorimetric” TNM(MRS) model can again be demonstrated for an “optical”

0

50

100

n λ, q = n λ

150

ref

+

∂n λ T f q − T f,ref ∂T f

16

where λ is the wavelength, ∂n/∂Tf is assumed to be a constant, and “ref” refers to a reference state defined, for instance, by a standard cooling rate. With the parameters of the TNM(MRS) model known from DSC and ∂n/∂Tf from an additional temperaturejump experiment, one may calculate n(λ,q) from the reference value n(λ)ref. For sake of simplicity, one may use an empirical linear relation from Moynihan and coworkers, which links the final fictive temperature and the logarithm of the cooling rate [18]: H H q − = ln 2 q1 RT f,1 RT f,2

17

where Tf1,2 is the fictive temperature upon linear cooling at a rate q2,1. Although (17) has not yet been rigorously derived, it is widely applied because it condenses the essential result of the TNM(MRS) model in the case of linear cooling. Inserting (17) into (16) leads to: n λ, q = n λ

ref

+

∂n λ T f q T f,ref q ln ∂T f qref H R

For an approximation and further simplification, one may replace Tf(q) and Tf,ref with the TG value according to [15]: n λ, q = n λ

Time (h) 0

property, namely the refractive index with its dependence on a linear cooling rate [31]. Provided that the eigenfrequencies of the electron oscillators do not depend on thermal history, the refractive index is a function of density only, which in turn is a function of the fictive temperature. The room-temperature value of the latter depends on the cooling rate q = dT/dt. Therefore, one may write:

18

3.7 Prediction of Refractive Index with the TNM (MRS) Model

200

–200 ∆l/l (ppm)

338

–400 –600 –800 –1000

Figure 7 Comparison of a thermal shrinkage experiment on BK7 (solid line) with values calculated by the TNM(MRS) model (dashed line) with the parameters τ0, b, H/k, and x determined above and αconf = 37 ppm/K determined from a density versus temperature measurement in the molten stage. Measurement at the accredited laboratories of SCHOTT AG.

ref

+

∂n λ T 2G q ln ∂T f H R qref

19

Thus, the above-mentioned logarithmic relationship between the refractive index and the cooling rate may be derived from relaxation dynamics. To calculate numbers, ∂n/∂Tf, TG, and H/R have to be known from the above-mentioned experiments (∂n/∂Tf, by V block refractometer measurement after annealing at different temperatures, i.e. by a temperature jump experiment; TG, by dilatometry; H/R, by DSC plus data reduction according to the TNM(MRS) model). An overview of glass characterization methods is provided by [32]. The refractive index considered is nd, i.e. the one at the helium d-line, 587.6 nm. For the crown glass P-SK57® and the flint glass P-LaSF47®, the values are given in Table 1 [31]. (N.B. For crown and flint glasses, see [33] and chapters 6.1 and 10.9).

4 Shear Viscoelasticity

Table 1 Properties of glasses P-SK57® and P-LaSF47®. Glass

P-SK57® ®

P-LaSF47

TG/ C

(∂nd/∂Tf)/(1/K)

493

0.000 067 2

530

0.000 117

F1 F2

(H/R)/K

z1

84 396.5

z2

F z

103 154 Figure 8 Maxwell model for viscoelasticity: spring in series with a dashpot (piston moving in a hollow cylinder filled with a viscous fluid). z1 and z2, dislocations of spring/piston; z, total dislocation; F1 = F2 = F, force measured along the setup.

Table 2 Calculated versus measured refractive index values for glasses P-SK57® and P-LaSF47®. Cooling rate/ (K/h)

Glass

P-SK57®

P-LaSF47®

nd (measured)

nd (calculated)

2 (reference)

1.587 00

—

9.5

1.586 26

1.586 27

47

1.585 56

1.585 52

236

1.584 85

1.584 77

2 (reference)

1.806 10

—

9.6

1.805 03

1.804 95

47

1.803 98

1.803 79

230

1.802 89

1.802 63

With the values from Table 1, one may calculate the refractive indices for different cooling rates and compare them with the measured ones, as provided in Table 2. Between the measured and the calculated values, one finds a maximum difference 0 and corresponds to the Voigt model above. See [34] or [35] for the mathematical derivation.

≕K t

ε0 ,

vi

1 − e−t

τi

ε0

i

vi = 1 i

63 Concerning the temperature dependence, the assumptions are the same as made above for shear viscoelasticity in that K0 and K∞ are considered constant. Likewise, b is considered not to depend on temperature (assumption of thermorheologic simplicity). It is further assumed that the activation enthalpy of bulk relaxation is the same as for shear stress [8h] as well as for structural relaxation and that the same holds for the nonlinearity parameter x so that the relaxation time is given by: τ = τ0 e H

R

x T + 1 − x Tf

64

where the fictive temperature Tf is the same as defined as in Eq. (9). For nonequilibrium calculations (varying temperature, varying fictive temperature), one must again convert

345

346

3.7 Structural and Stress Relaxation in Glass-Forming Liquids

these expressions into differential equations by calculating the time derivative of both sides. Once more, one preferably chooses Prony-series representations as starting points. 5.2 Bulk Viscoelasticity for Large Pressure Changes – Fictive Pressure As described by Eq. (60), the response of a glass to a constant pressure p0 is both immediate (p0/3K0) and delayed, with a final value p0 (1/3K∞ − 1/3K0). The latter can be interpreted as the impact of a second, fictive pressure Pf, with an initially zero value, a final value p0, and an intermediate behavior described by unity minus a Kohlrausch function. One then rewrites Eq. (60) as: ε=

1 1 1 1 p + − 3K 0 0 3 K ∞ K 0

pf = p0 1 − e

− t τ

pf ,

65

b

Owing to the temperature dependence of the retardation time τ, the fictive pressure is maintained when p0 is removed after cooling to room temperature. The term pf (1/3K∞ − 1/3K0) may then be used as a measure of permanent densification. At pressures high enough that the energy pVm is similar to or higher than RT (Vm, molar volume), the pressure and fictive pressure dependences of the retardation time must also be taken into account. With the TNM(MRS) Ansatz, one obtains for the isothermal case [43]: τ = τ 0 eH

RT

e

p x' V ∗ RT + pf

1 − x' V ∗ RT

66 i.e. a modified version of the original expression in [43] formulated to ensure that the equilibrium value of τ from the original TNM model follows for p = 0. As an analog of the activation enthalpy, V∗ is called the activation volume [44] whereas x is the analog of the nonlinearity parameter x.

6

Perspectives

The linear thermo-viscoelastic theory of relaxation [8, 34], see also as presented here has been extremely successful in applied glass science, see, e.g. [45]. There are shortcomings, however, which demand further research not only from a scientific but also from a glass practitioner’s point of view. Three of them shall be shortly discussed here. The first issue is the essentially non-Arrhenian temperature dependence of relaxation times, which is a characteristic feature of systems with configurational degrees of

freedom and, therefore, one key issue of relaxation theory. The most common explanation has been given by Adam and Gibbs [46]. Originally, it had been developed to explain structural relaxation but has since been generally applied to all relaxation phenomena including the underlying mechanism of viscous flow [47]. Thus, it has been possible to find a theoretical derivation of the widely used empirical (and essentially non-Arrhenian) Vogel–Fulcher–Tamann law of viscosity [48]. The basic assumption of this derivation, however, is that cp,configurational = constant/T holds, which is incompatible with the theory presented here. So the applicability of the latter is limited to a small temperature range, e.g. a small temperature range around the glass transition over which a constant value for cp,configurational and an Arrhenian temperature dependence of the relaxation times can be assumed. The second issue is the assumption of thermorheologic simplicity that has been challenged by, e.g. Ducroux, Rekhson and Merat [49], who pointed out that thermal shrinkage effects and stress relaxation at temperatures much below the glass transition are poorly predicted by the linear thermo-viscoelastic theory as presented here. Their idea was to replace the constant Kohlrausch parameter b with a temperature-dependent one, i.e. b(T), which takes the value “1” at some temperature between the glass transition and the melting point and decreases with decreasing temperature. Below the glass transition temperature, b(T) will take so low values that the corresponding Kohlrausch function will comprehend comparatively fast relaxation processes, which in return will explain low-temperature relaxation effects. Again, these findings indicate that the applicability of the linear thermoviscoelastic model as presented here is limited. The third issue refers to fictive temperature and fictive pressure. An extension of Eq. (66) to the non-isothermal case has to take into account the equivalence of the effects of different parameters. Both a decrease of the fictive temperature and an increase of the fictive pressure lead to a density increase and, in turn, an increase of the relaxation time. This issue is addressed by current research (“density temperature scaling” [50]). Reviewing the above three points, one comes to the conclusion that there is a definite need, both in glass science and glass industry, for a comprehensive and consistent relaxation model, which allows for all features mentioned.

References 1 Lillie, H.R. and Ritland, H.N. (1954). Fine annealing of

optical glass. J. Am. Ceram. Soc. 37: 466–473. 2 Nursey, P.F. (1875). Toughened glass. J. Soc. Arts 23: 631–666.

References

3 Rekhson, S.M. (1993). Thermal stresses, relaxation, and 4

5

6

7

8

9 10

11

12

13

14 15

16

17 18

19

hysteresis in glass. J. Am. Ceram. Soc. 76: 1113–1123. Mauch, F. and Jäckle, J. (1994). Thermoviscoelastic theory of freezing of stress and strain in a symmetrically cooled infinite glass plate. J. Non Cryst. Solids 170: 73–86. Naftaly, M. and Miles, R.E. (2005). Terahertz timedomain spectroscopy: a new tool for the study of glasses in the far infrared. J. Non Cryst. Solids 351: 3341–3346. Angell, C.A., Yue, Y., Wang, L.M. et al. (2003). Potential energy, relaxation, vibrational dynamics and the boson peak, of hyperquenched glasses. J. Phys. Condens. Matter 15: 1051–1068. Tool, A.Q. and Saunders, J.B. (1945). Expansion effects of annealing borosilicate thermometer glasses. J. Res. NBS 34: 199–211. G.W. Scherer, Relaxation in Glass and Composites (Malabar, FL: Krieger Pub. Co, 1992) pp. 113–174 (a), p. 31 (b), p. 3 (c), p. 24 (d), p. 190 (e), p. 27 (f ), p. 49 (g), p. 61 (h). Prigogine, I. and Defay, R. (1954). Chemical Thermodynamics. London: Longman. Fotheringham, U., Baltes, A., Müller, R., and Conradt, R. (2009). The residual configurational entropy below the glass transition: determination for two commercial optical glasses. J. Non Cryst. Solids 355: 642–652. Takada, A., Conradt, R., and Richet, P. (2013). Residual entropy and structural disorder in glass: a two-level model and a review of spatial and ensemble vs. temporal sampling. J. Non Cryst. Solids 360: 13–20. Guo, Y. and Priestley, R.D. (2015). Non-Equilibrium Phenomena in Confined Soft Matter (ed. S. Napolitano), 47–88. Heidelberg: Springer. Simon, S.L., Sobieski, J.W., and Plazek, D.J. (2001). Volume and enthalpy recovery of polystyrene. Polymer 42: 2555–2567. Webb, S. (1997). Silicate melts’ relaxation, rheology, and the glass transition. Rev. Geophys. 35: 191–218. ISO 7884-8 (1987). International Organization for Standardization ISO Central Secretariat, Geneva, Switzerland: International Organization for Standardization. Hutchinson, J.M. (1997). Relaxation processes and physical aging. In: The Physics of Glassy Polymers (ed. R. N. Haward), 85–153. Dordrecht: Springer. Narayanaswamy, O.S. (1971). A model of structural relaxation in glass. J. Am. Ceram. Soc. 54: 491–498. Moynihan, C.T., Easteal, A.J., DeBolt, M.A., and Tucker, J. (1976). Dependence of the fictive temperature of glass on cooling rate. J. Am. Ceram. Soc. 59: 12–16. Mazurin, O.V., Rekhson, S.M., and Startsev, Y.K. (1975). The role of viscosity in the calculation of the properties of glass in the glass-transition region. Fiz. Khim. Stekla 1: 412–416. (English translation).

20 Rekhson, S.M. and Mazurin, O.V. (1974). Stress and

21

22

23

24

25

26

27

28

29

30

31

32

33

34

structural relaxation in Na2O-CaO-SiO2 glass. J. Am. Ceram. Soc. 57: 327–328. Hodge, I.M. (2008). A personal account of developments in enthalpy relaxation: a tribute to C. T. Moynihan. J. Am. Ceram. Soc. 91: 766–772. Kohlrausch, R. (1854). Theorie des elektrischen Rückstandes in der Leidener Flasche. Ann. Phys. Chem. 91: 56–82. and 179–214. Williams, G. and Watts, D.C. (1970). Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function. Trans. Faraday Soc. 66: 80–85. Hara, M. and Suetoshi, S. (1955). Density change of glass in the transformation range. Rep. Res. Lab. Asahi Glass Co. 5: 126–135. Höhne, G., Hemminger, W., and Flammersheim, H.-J. (1996). Differential Scanning Calorimetry, 21–24. Berlin: Springer. DeBolt, M.A., Easteal, A.J., Macedo, P.B., and Moynihan, C.T. (1976). Analysis of structural relaxation in glass using rate heating data. J. Am. Ceram. Soc. 59: 16–21. Fotheringham, U. (1999). Applying the dynamics of the structure to tailor the glass properties. In: Analysis of the Composition and Structure of Glass and Glass Ceramics, 313–343. Berlin: Springer. Fotheringham, U., Müller, R., Erb, K. et al. (2007). Evaluation of the calorimetric glass transition of glasses and glass ceramics with respect to structural relaxation and dimensional stability. Thermochim. Acta 461: 72–81. Gaylord, S., Ananthasayanam, B., Tincher, B. et al. (2010). Thermal and structural property characterization of commercially moldable glasses. J. Am. Ceram. Soc. 98: 2207–2214. Koontz, E., Blouin, V., Wachtel, P. et al. (2012). Prony series spectra of structural relaxation in N-BK7 for finite element modeling. J. Phys. Chem. A 116: 12198–12205. Fotheringham, U., Baltes, A., Fischer, P. et al. (2008). Refractive index drop observed after precision molding of optical elements: a quantitative understanding based on the Tool–Narayanaswamy–Moynihan model. J. Am. Ceram. Soc. 91: 780–783. Kuhr, M. (2015). Analytische Methoden zur Untersuchung von Schmelzaggregaten. In: Chemische, Physikalische und Emissionsrelevante Analytik für die Glasindustrie, HVG-Fortbildungskurs. Offenbach: Verlag der Deutschen Glastechnischen Gesellschaft. Bach, H. and Neuroth, N. (1998). The Properties of Optical Glass, Schott Series on Glass and Glass Ceramics, 1e. Berlin, Heidelberg, New York: Springer. J. de Bast and P. Gilard, p. 23 (a), p. 24 (b), p. 26 and pp. 166–167(c), p. 30 (d), pp. 132–161 (e), in Rhéologie du verre sous constrainte dans l’intervalle de transformation, Institut pour l’Encouragement de la Recherche

347

348

3.7 Structural and Stress Relaxation in Glass-Forming Liquids

35

36

37

38

39

40

41

42

Scientifique dans l’Industrie et l’Agriculture “I.R.S.I.A.”, No. 32 (1965). Fotheringham, U. (2019). Viscosity of glass and glassforming melts. In: Springer Handbook of Glass (eds. J.D. Musgraves, J. Hu and L. Calvet), 79–111. Cham: Springer International Publishing. Fotheringham, U., Wurth, R., and Rüssel, C. (2011). Thermal analyses to assess diffusion kinetics in the nanosized interspaces between the growing crystals of a glass ceramics. Thermochim. Acta 522: 144–150. Beitz, W. (1998). Dubbel: Taschenbuch für den Maschinenbau, 18e (ed. K.-H. Küttner), C8–C26. Berlin: Springer. SCHOTT North America, Inc.. (2009). BOROFLOAT® 33 – Mechanical Properties Home Tech, SCHOTT North America, Inc. www.us.schott.com/borofloat. https://www.us.schott.com/borofloat/english/ download/index.html” (accessed 4 June 2020) Serizawa, H., Lewinsohn, C.A., and Murakawa, H. (2001). FEM evaluation of asymmetrical four-point bending test of SiC/SiC composite joints. Trans. JWRI 30: 119–125. Fotheringham, U. (2006). Dynamic mechanical analysis with an asymmetric 4-point bending mode, Abstract Book, 6. In: American Ceramic Society GOMD Spring Meeting. Greenville, SC: ACerS. Kadali, H. (2009). Experimental characterization of stress relaxation in glass. PhD thesis. Clemson University, Clemson. Joshi, D. and Joseph, P.F. (2014). Parallel plate viscometry for glass at high viscosity. J. Amer. Ceram. Soc. 97: 354–357.

43 Alba-Simionesco, C. (1994). Isothermal glass transitions

44

45

46

47

48

49

50

in supercooled and overcompressed liquids. J. Chem. Phys. 100: 2250–2257. International Union of Pure and Applied Chemistry, Compendium of Chemical Terminology – The Gold Book, Version 2.3.3, 2014-02-24C, IUPAC, Zürich, Switzerland (2014) 1598. http://goldbook.iupac.org/files/pdf/ goldbook.pdf (accessed 4 June 2020) Loch, H. and Krause, D. (eds.) (2002). Mathematical Simulation in Glass Technology, Schott Series on Glass and Glass Ceramics. Berlin, Heidelberg, New York: Springer. Adam, G. and Gibbs, J. (1965). On the temperature dependence of cooperative relaxation properties in glassforming liquids. J. Chem. Phys. 43: 139–146. Angell, C.A. (1991). Relaxation in liquids, polymers and plastic crystals - strong/fragile patterns and problems. J. Non Cryst. Solids 131–133: 13–31. Hodge, I.M. (1987). Effects of annealing and prior history on enthalpy relaxation in glassy polymers. 6. AdamGibbs formulation of nonlinearity. Macromolecules 20: 2897–2908. Ducroux, J.-P., Rekhson, S.M., and Merat, F.L. (1994). Structural relaxation in thermorheologically complex materials. J. Non Cryst. Solids 172–174: 541–553. Alba-Simionesco, C., Kivelson, D., and Tarjus, G. (2002). Temperature, density, and pressure dependence of relaxation times in supercooled liquids. J. Chem. Phys. 112: 5033–5038.

349

3.8 Hyperquenched Glasses: Relaxation and Properties Yuanzheng Yue Department of Chemistry and Bioscience, Aalborg University, Aalborg, Denmark

1

Introduction

Besides melt-quenching, various different routes may be applied to obtain a glass [1]. For instance, vitreous silica can be prepared via vapor condensation, sol–gel techniques, and argon plasma or heavy-particle bombardment of crystalline silica. The most common route remains melt-quenching, however, which is why much work has been done on melt-quenched glasses to understand the glass transition and relaxation, along with their impact on glass properties (Chapter 3.7). Various experimental and theoretical approaches have been used for this purpose. One of the most effective is hyperquenchingannealing-calorimetric (HAC) scanning whereby a glass-forming liquid is first hyperquenched at a rate higher than 105 K/s, subsequently annealed below Tg, and then scanned by differential scanning calorimetry (DSC) [2]. Upon hyperquenching, the liquid structure is arrested in a highly “excited” configurational state owing to the extreme slowing down of the relaxation process with a sudden drop of temperature. Through sudden energetic and structural trapping at high temperatures, a liquid becomes a hyperquenched (HQ) glass far from equilibrium, which has a significantly higher fictive temperature (Tf) than a slowly cooled bulk glass. The energy evolution in the HQ glass during the sub-Tg annealing can be followed and quantified through a DSC upscan. Upon sub-Tg annealing and DSC upscanning, the highly excited configurational state is gradually relaxing so that Tf decreases. This feature makes it possible to observe the energetic development of a HQ glass well below Tg, from

Reviewers: Joachim Deubener, Institute of Non-Metallic Materials, Clausthal University of Technology, Clausthal-Zellerfeld, Germany Pierre Lucas, Department of Materials Science and Engineering, University of Arizona, Tucson, AZ, USA

which information is gained about the structural heterogeneity of the corresponding liquid at T = Tf. From enthalpy relaxation, one can then infer how the potential energy and structure of the glass evolve upon annealing or dynamic heating and how both depend on the chemical composition of the material. In addition, the atomic vibrational dynamics in HQ glasses upon annealing can be observed with neutron, inelastic X-ray, or nuclear inelastic scattering techniques. The present chapter reviews advances made in understanding relaxation of HQ glasses. The methods for determining Tf and cooling rate are presented. The relaxation features are correlated with the energetic and structural heterogeneities in glass. Striking differences in relaxation modes between strong and fragile HQ glasses are shown and discussed. As an effective method, the HAC approach is used to identify the so-called Johari– Goldstein relaxation and to reveal the thermodynamic change accompanied by the fragile-to-strong liquid transition. The potential-energy dependence of the vibrational properties of HQ glasses is illustrated. Finally, some perspectives in this research are briefly described.

2 Fictive Temperature and Cooling Rates The fictive temperature (Tf) of a glass is the temperature at which the structure of its equilibrium liquid has been frozen-in (Chapter 3.7, [3–5]). It is determined by the cooling rate and the pressure applied to the liquid and represents the average level of the glass on the potential energy landscape. One of the reasons why it is important to quantify the thermal history of the glass in terms of both Tf and the cooling rate of glass is that these parameters exert a strong impact on mechanical and optical properties so that they are crucial for glass production

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

3.8 Hyperquenched Glasses: Relaxation and Properties

process. The problem is indeed of great practical interest because it concerns in particular mineral and stone wool, which are very rapidly drawn and cooled down as fibers (Chapter 9.3), as well as metallic glasses produced as ribbons (Chapter 7.10). In preamble, it must be stressed that the relaxation and physical properties substantially differ for HQ and slowly cooled glasses of the same chemical composition [6–8]. To picture the basics of enthalpy relaxation in HQ glasses, a stone-wool sample will be selected here. As produced with a cascade process (Chapter 9.3) and hyperquenching at a disc rotation speed of about 6000 rpm [2], the fibers have a mean diameter of about 3.5 μm and a standard Tg of 944 K (Figure 1). Their composition is (wt %) 41.5 SiO2, 21.3 Al2O3, 1.6 TiO2, 7.3 Fe2O3, 13.9 CaO, 11.7 MgO, 1.6 Na2O, and 0.8 K2O. In DSC upscans (Figure 1), there is a large difference between the measurements performed on the HQ sample (Cp1) and on the same sample reheated after cooling at 10 K/min (Cp2), which will be termed the standard glass sample [5]. In other words, the excess Cp of the HQ with respect to the standard glass originates in a potential energy gradually recoveres upon dynamic heating, which of course depends on both glass composition and fictive temperature. Since the mechanical work done upon fiber stretching is small enough to be neglected, the excess enthalpy can itself be assumed to be the excess internal energy stored during hyperquenching. To proceed further, it useful to define Tc as the onset temperature (=0.52 Tg) of the enthalpy release, above which the fictive temperature gradually drops with increasing temperatures; Te as the equilibrium temperature (=1.06 Tg) at which the quenched-in energy is completely released; Ts as the shoulder temperature (=0.72 Tg)

This excess enthalpy can alternatively be characterized by the fictive temperature Tf of the HQ glass. This parameter is determined with the enthalpy-matching method [5], which assumes that ΔH represents the excess enthalpy of the liquid with respect to the glass over the interval Tg – Tf (Figure 2): T eq

C p2 − C p1 dT =

Tc

Tf

C pl − C pg dT ,

2

T g,ref

where Cpl and Cpg are the isobaric liquid and glass heat capacities, respectively. For the HQ stone wool, one finds in this way a Tf of 1155 K (=1.23 Tg) if the Cpg curve is extrapolated to the liquid region with an equation of the form C pg = a + bT + c T 2 + d T 0 5 ,

3

where a, b, c, and d are constants. If the viscosity–temperature relationship of the glassforming liquid is known, one can in addition calculate the cooling rate qc of the HQ glass with [5]: log qc = 11 35 – log η T f

4

In Eq. (4), η(Tf) is the viscosity at temperature Tf, which is 5.05 Pa.s, so that the cooling rate of the stone-wool fibers is about 2 × 106 K/s.

Tg = 941

1.6

0.10

Teq

Tc

0.05

=

0.00 400

600 800 T (K)

1000

Tc

Teq Cp2

Cp1

0.8

Tg

1.4

A

600

800

Tf = 1155 Cpl

B B

1.2

Cpg

Cp2 1.0

A Cp1

0.8 400

1

Ts

0.15

1.0

C p2 − C p1 dT

Tc

1.8

0.20

1.2

T eq

ΔH =

Cp (Jg–1K–1)

1.4

at which Cp1 = Cp2 and the liquid returns to internal equilibrium; and Teq as any temperature above the glass transition range [5]. The enthalpy (ΔH) released upon heating is then given by:

0.25 ΔCp (Jg–1K–1)

1.6

Cp (Jg–1K–1)

350

1000

T (K)

Figure 1 Excess enthalpy of a stone wool as given by the difference between the DSC of the HQ (Cp1) and standard (Cp2) samples at the same rate of 10 K/min. Inset: excess capacity, ΔCp = Cp2 − Cp1, as a function of temperature (characteristic temperatures defined in text).

400

600

800

1000

1200

T (K)

Figure 2 Determination of the fictive temperature Tf of the HQ stone wool with the energy-matching method. Same Cp data as in Figure 1, Cpl and Cpg being the liquid and glass heat capacities, respectively, and Tg the standard glass transition temperature.

3 Sub-Tg Relaxation

3

Sub-Tg Relaxation

Determinations of excess enthalpies are just a first step in the characterization of HQ glasses as it is also important to know how enthalpy relaxes, i.e. to evaluate the rates at which the fictive temperature change and the excess enthalpy is released upon either static annealing or dynamic heating. Although enthalpy relaxation is a nonlinear, non-exponential process, it has been extensively studied owing to its importance for understanding the nature of glass and the glass transition and for optimizing physical properties of glass products [4]. Most studies have dealt with slowly cooled glasses but scientists have recently realized that the enhanced nonequilibrium features of HQ glass fibers and ribbons make these materials particularly interesting for studying the glass transition and relaxation phenomena [2]. This is why sub-Tg annealing is a key approach to obtain dynamic and thermodynamic information on the glass transition. Two parameters are independently acted upon in this respect, namely, the annealing temperature for a given time and the annealing time at a given temperature. Taking as a DSC reference the standard stone wool, one observes in the first case that, for HQ samples cooled at a rate of 2 × 106 K/s [2], the left cutoff of the enthalpy release peak (i.e. the exotherm below Tg) gradually shifts to higher temperatures until the peak completely disappears when the temperature Ta of eight-day annealing increases (Figure 3). Upon annealing, the configurational states of higher potential energy (or weaker bonding) are transformed into states of lower potential energy. When Ta is sufficiently high (but still lower than Tg), a preendotherm occurs below the onset temperature of the

exotherm (Figure 3). This pre-endotherm becomes larger with increasing Ta, but its onset remains constant. At the same time, the exotherm becomes smaller with Ta so that the exotherm and endotherm coexist in a certain range of Ta. The annealing time ta has a similar effect on the calorimetric response of the HQ stone wool at Ta = 723 K (Figure 4). When the annealed sample is heated from room temperature to Te, a pre-endotherm again appears, followed by an exotherm [2]. The pre-endotherm becomes more pronounced with ta and shifts to higher temperatures until the exotherm disappears. This feature implies that, upon sufficient annealing, the potential energy of weakly bonded structural units in the HQ glass drops to a level below that of the standard glass, and finally to that corresponding to the given Ta, whereas that of strongly bonded structural species remains higher than that of the standard glass. Besides, a simple way to determine the relaxation kinetics is to consider the time dependence of the fraction ΔHrem/ΔHtot of the excess enthalpy that has not been released during the DSC upscan (Figure 4, inset). One can then make a fit made to the experimental data with a Kohlrausch function ΔHrem/ΔHtot = exp.[−(t/τ)β], where τ is the characteristic, temperature-dependent relaxation time, and β (0, 1) is the stretching exponent describing the broadness of the relaxation time distribution (Chapter 3.7). The value β = 0.16 obtained for Ta/Tg = 0.66 is much lower than that those found in the energylandscape influenced regime (0.45 < T/Tg < 1). The small

1.8 1.0

ta

1.4

1.2

1.0

b

a

ta = 8 days Cp (Jg–1K–1)

Cp (Jg–1K–1)

1.6

Ta (K) a: non-annealed b: 573 c: 623 d: 673 e: 723 f: 773 g: 823 h: standard

h

1.4

1.2

g

ΔHrem/ΔHtot

1.6

1.8

A: non-annealed B: 1min C: 4 min D: 15 min E: 50 min

d

e

0.6 0.4 101

F: 3.5 h G: 12 h H: 2 days I: 8 days

102

B

1.0

c

0.8

C D

103 104 ta (s)

105

106

H I E FG

A

Ta = 723 K

f 0.8 400

500

600

700

800

900

1000

T (K)

0.8 600

700

800

900

1000

T (K) Figure 3 Effect of the annealing temperature (Ta) on the enthalpy relaxation of stone-wool fibers annealed for eight days. Thick, dark curve: DSC upscan curve of the standard sample. Up- and downscan rates of 20 K/min.

Figure 4 Effect of the annealing time (ta) on the enthalpy relaxation of stone-wool fibers annealed at 723 K. Thick, dark curve: DSC upscan curve of the standard sample; up- and downscan rates of 20 K/min. Inset: ΔHrem/ΔHtot as a function of ta, where ΔHrem is the enthalpy remaining in the sample after annealing and ΔHtot is the total energy stored by HQ; solid line: Kohlrausch fit to the experimental data.

351

3.8 Hyperquenched Glasses: Relaxation and Properties

β value derived thus indicates that the distribution of relaxation times of the HQ glass upon annealing at 723 K becomes broader compared to that of the standard glass. Additional information on energetic and structural heterogeneities in glass near Tg may be obtained through stepwise annealing studies [2]. Upon annealing, the relaxing parts of microstructures become less disordered and more stable in comparison with those of the standard glass. When the annealed HQ glass is upscanned in DSC, the degree of disorder in the relaxing part of the structure increases and gradually approaches that of the standard sample. This process leads to an endothermic event, i.e. to a pre-endotherm whose extent increases with both Ta and ta. The pre-endotherm occurs only when the glass is hyperquenched and then annealed. It is more pronounced for glasses with higher Tf than for those with lower Tf under the same annealing conditions [2, 6]. Additional features of the pre-endotherm of the annealed stone-wool samples are noteworthy (Figure 5). The sample annealed for eight days at 773 K exhibits a pronounced pre-endotherm (Curve 1 of Figure 5), which completely disappears when the annealed sample is reheated in DSC to the crossover temperature (Tcross = 897 K), then cooled down to room temperature, and finally reheated to the maximum temperature (Curve 2 of Figure 5). At the same time, the exotherm remains unaffected. The pre-endotherm of the annealed HQ glass and the Tg endotherm of the standard sample have different physical origins. One can eliminate the former and then 1.8 Tg endotherm 1.6 Cp (Jg–1K–1)

352

1.4

Pre-endotherm Tcross

1.2

3

1.0

2 1 Exotherm

0.8 600

700

800

900

1000

T (K)

Figure 5 Isobaric heat capacity (Cp) as a function of temperature (T) showing the influence of heating condition on the pre-endotherm of the stone-wool sample subjected to a sufficient degree of the annealing. Curve 1: the sample annealed at 773 K for eight days; Curve 2: the sample annealed at 773 K for eight days, and then heated from 298 K to the crossover temperature (Tcross) of 897 K; Curve 3: the standard sample.

recover it by properly choosing heating and reannealing procedures. In contrast, the Tg endotherm is not removable by heating and annealing processes as it always occurs in up- and downscan as long as crystallization is avoided. The Tg endotherm is of course caused by the glass transition, which is accompanied by an abrupt increase in configurational entropy whereas the preendotherm is a signature of the strong non-exponential relaxation of the HQ glass upon annealing. As a matter of fact, all types of glasses have a spectrum of relaxation times, which implies the existence of many micro domains of different Tg values [2].

4

Anomalous Relaxation

The stone wool considered in previous sections is a relatively fragile liquid, whose viscosity–temperature relation is thus strongly non-Arrhenian (Chapter 4.1). Since relaxation is closely related to liquid fragility (Chapter 3.7), it is useful to turn now to germania (GeO2), a strong liquid [9] whose HQ glass will be compared with that of calcium metaphosphate (CaP2O6), another fragile melt [10]. Even when plotting the DSC ΔCp curves against the normalized temperatures T/Tg to account for Tg differences, there is a striking difference between both materials in terms of the Ta dependence of enthalpy relaxation. For HQ CaP2O6 (Figure 6a), the left cutoff of the ΔCp peak gradually shifts to higher temperature with increasing Ta ( Rc). Thus, viable (supercritical) crystal clusters capable of deterministic growth must exceed a critical size. It is this criticality that determines the crucial impact of these embryos of the newly evolving phase on the nucleation processes. Taking the chemical potential difference and the specific interfacial energy as constants (i.e. employing the so-called “capillarity” approximation), one can derive the critical cluster size and the value of ΔGc at the critical size from the extremum condition d(ΔG)/dT = 0. These parameters are given by Rc =

2σ 1 16π σ 3 , ΔGc = σAc = , Ac = 4πRc 2 cα Δμ 3 3 cα Δμ 2 2

These relations remain valid if more accurate expressions for Δμ are employed and the curvature dependence of the interfacial energy is accounted for. The concepts discussed above are illustrated in Figure 1a within the framework of the classical model of nucleation, whereby the change in the Gibbs free energy of cluster formation reaches a maximum ΔG = ΔGc for the critical cluster size, R = Rc. In this model, the clusters grow or decay while preserving their properties, so size is the only parameter specifying the state of the cluster. A more realistic picture of cluster formation is presented in Figure 1b, where not only the size but also the composition (described by the number of particles, ni, of two components) of the cluster may change. In this case, the critical cluster corresponds to a saddle point of the Gibbs free energy surface. The evolution to the new phase via the saddle is shown by the dark (red in the colored version) curve. In Figure 1c, we show an alternative

2 Crystal Nucleation and Classical Nucleation Theory

(b)

(a) 1.4

∆G/∆Gc

1.2 ∆G

1.0 0.8 0.6 n2

0.4 0.2 0

0

0.5

1

1.5

2 0

Reduced radius, R/Rc

Cluster composition, xα

(c) 1.0 0.8 n1

0.6 0.4 0.2 0

0

0.5

1

1.5

2

2.5

Reduced radius, R/Rc

Figure 1 The classical model of nucleation and possible generalizations. (a) With only one parameter employed to describe the state of the cluster. (b) Change of Gibbs free energy in cluster formation when more than one parameter is used. (c) Alternative to the classical scenario of crystallization in multicomponent liquids (See electronic version for color figures).

to the classical picture of phase evolution, which is similar to spinodal decomposition (cf. [3]). In this case, the composition of the critical crystal cluster changes retaining a nearly constant size and only after completion of this process the kinetics are governed by the growth of clusters with a roughly constant composition. In a variety of cases in multicomponent systems [3], the latter path of evolution (Figure 1c) – and not the classical picture (Figure 1a) – dominates phase formation. Critical clusters do not form according to the predictions (the evolution criteria) of macroscopic thermodynamics, but instead by stochastic thermal fluctuations. According to underlying assumptions of statistical physics, the probability of such fluctuations can be expressed as a function of the minimum work for a reversible thermodynamic process. The minimum work to form a critical cluster is Wc = ΔGc, where ΔGc is given by Eq. (2). This quantity, Wc, the work of critical cluster formation, plays a decisive role in nucleation theory. Initially, the nucleation rate is small. Then, after a certain time interval, τ, the so-called time lag for nucleation,

the rate of nucleation, J (i.e. the number of supercritical clusters formed per unit time in a unit volume of the liquid), approaches a constant value, the steady-state nucleation rate, Js. In an early description of this initial period of nucleation by Zeldovich (cf. [3]), the nucleation rate as a function of time, t, was expressed by the relation J t = J s exp −

τ t

3

The initial stage of nucleation observed in experiments is often described by the Collins–Kashchiev relation (cf. [3]): N t = J sτ

∞ t π2 −1 m t −2 − exp − m2 2 m τ 6 τ m=1

4 This mathematical equation gives a relation for the number, N(t), of supercritical crystallites as a function on time, t. For longer times than some induction time (t tind), Eq. (4) can be approximated by

561

5.4 Nucleation, Growth, and Crystallization in Inorganic Glasses

1015 12

(a) J/Js

10

0

2

4

8

6

Js,(m3s)

0

10

t/τ

4 tind

103

2Na2O·1CaO·3SiO2 (470°C)

0 0

2

4

6

8

10

12

2

107

Li2O·2SiO2(465°C) 2Na2O·1CaO·3SiO2 (465°C)

1- 3MgO·Al2O3·3SiO2 2- Li2O·2SiO2 3- Na2O·2CaO·3SiO2 4- 2Na2O·1CaO·3SiO2

101 0.45

14

3

109

105

Li2O·2SiO2 (430°C)

2

4

1011

0.4

8 6

(c)

1013

(b)

0.8

N/Jsτ

562

0.5

1 0.6

0.55

0.65

T/Tm

t/τ

Figure 2 Experimental nucleation rate data for several silicate glasses. (a) Reduced crystal number density, (N(t)/Jsτ), versus reduced nucleation time, (t/τ). The solid line is the master curve calculated from Eq. (4). (b) Reduced nucleation rate versus reduced nucleation time calculated from Eq. (4). (c) Experimental steady-state nucleation rate, Js, versus reduced temperature, T/Tm, for four stoichiometric glasses. Tm is the melting temperature (see [6] for details).

J s t − t ind , t ind =

N t

π2 τ 6

5

where τ is the nucleation time lag. Over a sufficiently large timescale, Eqs. (3)–(5) approach steady-state nucleation conditions, i.e. (dN/dt) = Js = constant. With Wc = ΔGc, the steady-state nucleation rate, Js, can be written as [3] J s = J 0 exp

−

ΔGc kBT

= J 0 exp

−

Wc , J0 = kBT

σ D , k B T d 40

6 where D is an appropriately chosen diffusion coefficient and d0 is a size parameter explained in greater detail below. Experimental results that illustrate the establishment of a steady-state nucleation rate and its dependence on temperature are shown in Figure 2. For the case shown in Figure 1a (congruent crystallization, assuming that the state of the cluster does not change with size and is the same as that of the newly evolving macroscopic phase), D in Eq. (6) is the diffusion coefficient of the structural building units in the liquid, and d0 is their diameter. If several components of the liquid diffuse independently, D must be replaced by an effective diffusion coefficient, which is a combination of the partial diffusion coefficients and the concentrations of the different components in the liquid, and d0 must be replaced by the average size of these independently moving species [3]. In the application of the theory, it is also often assumed that the effective diffusion coefficient can be replaced by

the Newtonian shear viscosity, η, via the Stokes– Einstein–Eyring (SEE) equation [3]: D

kBT d0 η

7

However, its applicability to states near and below the glass transition temperature (where homogeneous crystal nucleation is commonly observable) has been questioned even for “one-component” congruent systems, where decoupling of relaxation (expressed by viscosity) and atomic transport (represented by the diffusion coefficient) is frequently reported (e.g. [7]). Application of this expression is even more questionable for multicomponent systems. Another issue is related to the case of highly viscous glass-forming melts, for which a non-Newtonian viscosity should be employed to describe viscous flow [3]. Leaving aside the reservations above, by applying the SEE relationship, one arrives at the following expression for the steady-state nucleation rate: Js =

σk B T exp d 50 η

−

ΔGc kBT

8

To apply Eq. (8) to the interpretation of experimental data, one has to determine the work of critical cluster formation, Wc = ΔGc, i.e. to specify the thermodynamic driving force of phase formation, Δμ, and the specific interfacial energy, σ in Eq. (2). Assuming that the bulk properties of the crystal clusters are the same as those of the macroscopic crystals, one arrives at the simplest

2 Crystal Nucleation and Classical Nucleation Theory

approximation by a Taylor expansion of Δμ(T) in the vicinity of the melting temperature: Δμ T = Δhm 1 −

T , Tm

9

where Δhm is the enthalpy of melting per structural unit of the crystal and Tm is the melting temperature (generalizations of this relation can be found in [3]). Since the interfacial energy of the critical nucleus is not directly measurable, it is normally evaluated using the Stefan–Skapski–Turnbull rule [3]: σ=ς

qm 1 3 2 3 N A vm

, qm = N A Δhm ,

10

via the molar enthalpy of melting, qm. In Eq. (10), NA is Avogadro’s number, ς is a factor varying from 0.4 to 0.6, and νm is the molar volume. This relation has been widely employed (see [3] and Baidakov et al. [8]). By substituting these relations into the expression for the steady-state nucleation rate, its temperature dependence can be interpreted straightforwardly. The steady-state nucleation rate Js is equal to zero at T = Tm, where Δμ = 0, cf. Eq. (9). This rate increases with decreasing temperature because of the decrease in the work of critical cluster formation borne out by Eq. (2), until this trend is overcompensated by the exponential increase in viscosity with decreasing temperature. When these classical concepts are employed to interpret experimental data, a qualitative and partly quantitative agreement is sometimes found (cf. Figure 2). In most cases, however, the classical approach underestimates the steady-state nucleation rates by 20–55 orders of magnitude, e.g. [6]. In the classical approach, the deviations between experiment and theory can be (artificially) resolved by the introduction of a size dependence of the specific interfacial energy, as discussed by Gibbs [5] and later by others, particularly by Tolman (cf. [3]). But this type of solution gives rise to other problems [6]. Another possible solution, in agreement with results of computer simulations and density functional computations, consists in accounting for the size dependence not only of the surface but also of the bulk properties of the clusters of the newly evolving phases. The bulk properties of the clusters generally depend on their sizes. Hence, the surface properties, including the surface tension, must also be size dependent. Thus, this approach also leads to a size dependence of the surface energy, but the primary variation of the properties of the clusters lies in the size dependence of their bulk properties. Thermodynamically, one can treat these problems by generalizing the classical Gibbs approach (cf. [3]), which allows for a description of the cluster properties as a

function of size and degree of supercooling. With this new thermodynamic (generalized Gibbs) approach, one concludes that the classical theory – assuming macroscopic bulk properties of the clusters and employing the capillarity approximation for the specific interfacial energy – overestimates the work of critical cluster formation, and hence, underestimates the values of steady-state nucleation rates [3]. Therefore, the classical theory with the “capillarity” approximation may serve as a tool for roughly estimating the nucleation rate curve (i.e. its dependence on temperature and/or pressure), but it must be improved to account for the above-specified effects for a detailed and quantitatively accurate description of the phenomenon. So far, we have considered the case of crystal nuclei that form evenly within a pure liquid. This mechanism is known as homogeneous nucleation. However, nucleation can be readily catalyzed by impurities, such as solid particles embedded in the volume or present on the external surface of glasses. Nucleation originating at such preferential sites is denoted as heterogeneous (e.g. [3, 9]) and can be described by the theoretical concepts outlined above if the work of critical cluster formation for homogeneous nucleation, Wc, is replaced by WcΦ. Here, Φ ≤ 1 is the nucleating activity of the heterogeneous nucleation core, and its value depends on the mechanism of nucleation catalysis. As a rule, heterogeneous nucleation dominates at small supercooling because of the lower work of critical cluster formation than that of homogeneous nucleation. At high supercooling, homogeneous nucleation dominates due to the much larger number of sites (all “molecules” of the system) where homogeneous nucleation may proceed. The reader should note that, in certain cases, the evolution of the new phase may not proceed via the saddle shown as a dark curve in Figure 1b (in red in the colored version) but via a ridge trajectory indicated by a light curve in Figure 1b (in yellow in the colored version), if such a trajectory is kinetically favored. This type of behavior may be expected to occur in crystallization occurring at large degrees of supercooling because of the disordered and nonstoichiometric nature of the crystals that precipitate in the early stages. Frequently, several different stable or metastable phases may be formed at some given initial state of the supercooled liquid. As Ostwald suggested (cf. [3]), in such cases the most favorable stable phase is not formed immediately. Instead, the final stable phase is reached via several stages in which different metastable phases are formed until the most stable phase is developed: this is the so-called Ostwald’s rule of stages or Ostwald’s step rule. As first proposed by Stranski and Totomanov (cf. [3]), this evolution path can also be explained by kinetic considerations.

563

5.4 Nucleation, Growth, and Crystallization in Inorganic Glasses

3 Basic Models of Crystal Growth in Supercooled Liquids It is now generally accepted that the properties of the crystal–liquid interface have a decisive influence on the kinetics of crystallization. Theoretical treatments of crystal growth have therefore focused closely on the interfacial structure and its effect on crystallization. With the assumption of congruent crystallization, three standard models have been developed for treating crystal growth theoretically (e.g. [10, 11]). These models are described briefly below: i) Normal growth: The interface is pictured as rough at an atomic scale. Growth takes place at step sites, which represent a sizable fraction (0.5–1.0) of the interface. Assuming that this fraction does not change appreciably with temperature, the growth rate, u(T), can be expressed as u=f

D 1 − exp 4d 0

−

Δμ kBT

,

11

where f is close to unity and Δμ is treated as a positive quantity. ii) Screw dislocation growth: This model assumes the interface is smooth but imperfect at an atomic scale. Growth takes place at a few step sites provided by screw dislocations that intersect the interface. The growth rate is still given by Eq. (11), where f is now the fraction of preferred growth sites (on the dislocation ledges) at the interface. In this case, f is given approximately by f (Tm − T)/(2πTm) [7]. More generally, according to Jackson [10], f = (Δsm/kB)ξ holds, where Δsm is the entropy of fusion per particle and ξ is the number of nearest-neighbor sites in a layer parallel to the surface divided by the total number of nearest-neighbor sites. Factor ξ is the largest for the most closely packed planes of the crystal, for which it is approximately equal to 0.5. For ƒ < 2, the minimum free energy configuration corresponds to half the available sites being filled and represents an atomically rough surface. In contrast, for ƒ > 2, the lowest free energy configuration corresponds to a surface where few sites are filled and a few units are missing from the completed layer, which represents an atomically smooth interface. Hence, for materials with Δsm < 2kB, the most closely packed interface planes should be rough. For materials with Δsm > 4kB, the most closely packed surfaces should be smooth, the less tightly packed surfaces rough, and the growth anisotropy rate large. iii) Surface nucleation or two-dimensional growth: According to this model, the interface is smooth

and perfect at an atomic scale and thus free of intersecting screw dislocations and growth sites. Growth then takes place by the formation and growth of new twodimensional nuclei at the interface. In this case, the growth rate is expressed by u = C3

D exp 4d 20

−

C2 , T ΔT

12

where C2 and C3 are parameters that determine the time required for the formation of the two-dimensional nucleus relative to that required for its propagation across the interface, respectively. Possible growth modes are illustrated in Figure 3. Similarly to nucleation, the interplay between increasing driving force for crystallization, Δμ, and decreasing diffusion coefficient (or increase in viscosity) with decreasing temperature results in a maximum of the crystal growth rates. This maximum is located at higher temperatures than that of the maximum of the steady-state nucleation rate shown in Figure 2c. There are also other growth modes, which are rate limited not by processes at the liquid–crystal interface but by mass transport toward the interface. A specific example is a diffusion-limited segregation, which is of particular importance in multicomponent systems. Accounting for size effects on the growth kinetics, one can express the rate for such a growth mode as (e.g. [11, 12]) dR B 1 1 = , − dt R Rc R

13

T (°C) 10–3

400

500

600

700

800

900

Tg

10–4

1000

Tm

10–5 10–6 U (m/s)

564

10–7 10–8 10–9 10–10 10–11 10–12 10–13 700

800

900

1000

1100

1200

1300

T (K)

Figure 3 Crystal growth rates for Li2O∙2SiO2 glasses obtained by different authors. The lines correspond to the screw dislocation mechanism (full curve) and two-dimensional surface nucleated growth (dashed curve) [7].

4 Overall Crystallization and Glass-forming Ability: The Johnson–Mehl–Avrami–Kolmogorov Approach

Figure 4 Crystal morphologies formed by nucleation and growth in glass-forming liquids as observed by optical microscopy (crystal sizes from 5 to 100 μm). From top left to bottom right: (i, ii, iv) LS crystals nucleated on defects of a CaO∙Li2O∙SiO2 glass surface during its preparation via melting–cooling. (iii) Crystallization propagating from the surface toward the center of a CaO∙Li2O∙SiO2 glass specimen; lithium metasilicate crystals nucleated on two perpendicular surfaces and grew toward the sample center. (v) Surface of a CaO∙Li2O∙SiO2 glass sample after cooling a melt in a DSC furnace; the large-faceted and needle-like crystals are calcium and lithium metasilicates, respectively. (vi) Internal crystallization in a Ti-cordierite glass; pure stoichiometric cordierite (2MgO∙2Al2O∙5SiO2) glass underwent only surface nucleation, but the same glass doped with more than 6 mol % TiO2 shows internal crystallization of μ-cordierite. (vii) Needle-like crystals in CaO∙Li2O∙SiO2 eutectic glass formed by internal crystallization in the temperature range between the solidus and the liquidus; these wollastonite crystals appear on the cooling path. (viii) Starlike NaF crystals inside a PTR glass (treatment at a high temperature near the solubility limit).

where B is a combination of parameters describing the liquid under consideration, being proportional to the effective diffusion coefficient governing the rate of supply of the different components to the growing or dissolving cluster. Equation (13) and its modifications for other growth modes serve as a basis for the theoretical description of the competitive growth of clusters denoted as coarsening or Ostwald ripening. In these late stages of phase formation, larger clusters may grow further only when subcritical crystals are dissolved. The theoretical description of this process was first developed by Lifshitz and Slezov (cf. [11]). Today it is often referred to as the Lifshitz–Slezov–Wagner theory. This theory provides expressions for the average size, R , and the number, N, of supercritical clusters in the system as a function of time. For diffusionlimited growth (Eq. (13)), one obtains R

3

t, N

1 t

14

An account of the effect of elastic stresses on coarsening, which leads to qualitative modifications of the coarsening behavior, is reviewed in [3, 12]. The above relationships allow one to describe the growth of crystals with smooth planar or spherical interfaces advancing in the liquid. However, more complex growth patterns do exist, and more complex models of growth are required to properly take into account

possible interfacial instabilities, surface roughening, or other growth modes such as diffusion-limited aggregation [11]. With such complex growth modes, a variety of intricate and beautiful crystal shapes may evolve, some of which are illustrated in Figure 4.

4 Overall Crystallization and Glassforming Ability: The Johnson–Mehl– Avrami–Kolmogorov Approach The overall crystallization of supercooled liquids occurs by a combination of crystal nucleation and growth. The kinetics of such processes is usually described by a theory independently derived between 1937 and 1941 by Johnson, Mehl, Avrami, and Kolmogorov [13–17] (JMAK theory). In this approach, the evolution of the total amount of crystalline phase is described as a function of time, accounting simultaneously for nucleation and growth. The basic equations of this approach can be developed as follows. Let us assume that, in a time interval dt (t , t + dt ), a number dN(t ) = J(t )[V − Vn(t )] of clusters of critical size is formed in the volume [V − Vn(t )]. Here, V is the initial volume of the glass-forming melt and Vn(t ) the volume already crystallized at time t . These clusters grow and, at time t, occupy a volume

565

566

5.4 Nucleation, Growth, and Crystallization in Inorganic Glasses

dV n t, t = ωn J t

n

t

V −Vn t

dt

u t dt

,

t

15 where ωn is a shape factor and the integral term describes the growth of the dN(t ) clusters formed at t until time t, i.e. in the time interval (t–t ), the exponent n is the number of independent spatial directions of growth. Introducing the ratio, αn(t) = (Vn(t)/V), between the current volume of the crystalline phase versus the initial volume of the glass-forming melt, one has dαn t, t = ωn J t

1 − αn t

n

t

dt

u t dt t

16 Integration, i.e. taking the sum over all the time intervals dt in the range of (0, t), yields t

αn t = 1 − exp ωn J t dt 0

n

t

u t dt t

17 Provided the nucleation and growth rates are both constant, one reaches as a special case αn t = 1 − exp

−

ωn Jun t n+1

n+1

18

Conversely, if a number N0 of supercritical clusters is formed immediately at time t = 0, growing in n independent spatial directions, one arrives instead at αn t = 1 − exp − gN 0 un t n

19

The analysis of the time dependence of the αn(t)-curves thus leads one to the specification of nucleation and growth kinetics. The JMAK theory has been employed in numerous studies to analyze experimental data and determine the degree of crystallinity as a function of time in both isothermal and non-isothermal heat treatments of glass systems. Emphasis has usually been given to the determination of the so-called Avrami coefficient m = n + 1 obtained from the slopes of experimental ln[ln(1 − α)−1] versus ln(t) plots. An overview of various nucleation and growth mechanisms and the resulting values of the Avrami coefficient are given in [3]. However, there is some uncertainty in such analyses, because different combinations of nucleation and growth laws may lead to the same Avrami coefficient. For this reason, a separate investigation of the growth kinetics may be required to reach definite conclusions [14].

It is important to underline that the JMAK theory, as given by Eqs. (18) and (19), does not apply to non-isothermal processes. These two equations are derived from the assumption of constant nucleation and growth rates, which are not achieved in nonisothermal processes. Therefore, in non-isothermal cases, the general relationships, Eqs. (16) and (17), must be employed to describe overall crystallization. This requires taking into consideration not only thermal nucleation (formation of supercritical clusters due to thermal fluctuations at given values of critical cluster size and thermodynamic barrier) but also athermal nucleation (i.e. the change in the number of supercritical clusters due to the variation of the critical cluster size resulting from the change in temperature). Such considerations must also be taken into account when the JMAK formalism is employed to determine whether a liquid will transform into a glass upon cooling or whether it will crystallize. Following Uhlmann (cf. [10]), one can consider a supercooled frozen in liquid as a glass if, after vitrification, the volume fraction of the crystal phase does not exceed a certain value of, say, 10−6 (the detection limit by microscopy). Using appropriate expressions for nucleation and growth rates, one can then compute (through Eq. (18) for isothermal conditions) the time required to reach the volume fractions thus defined. In this way, one arrives at the socalled T(ime)T(emperature)T(ransformation) curves (TTT curves) exemplified in Figure 5 (cf. also [18] and figure 10.8 in [3]). These curves give some insight into the characteristic timescales required to prevent measurable crystallization effects. One should keep in mind, however, that these curves overestimate the critical cooling rates for glass formation by about one order of magnitude because, as mentioned earlier, crystallization upon cooling proceeds under non-isothermal conditions. Using experimental nucleation and growth rate data, Rodrigues and Zanotto [19] calculated TTT curves for different isothermal and non-isothermal crystallization situations. They also accounted for the breakdown of the SEE equation at a temperature Tb (somewhat higher than Tg) where the effective diffusion coefficient that controls crystal growth decouples from the value of diffusivity calculated by the SEE equation (Eq. (7)). In Figure 5 we show an example of such a curve for a stoichiometric BaO∙2TiO2∙2SiO2 glass, which undergoes copious internal homogenous crystal nucleation. The agreement with experimental data (which, in this case, were also obtained in isothermal conditions) is quite impressive, indicating that the JMAK equation is accurate if all the assumptions involved in its derivation are met.

5 Perspectives

Figure 5 Simulated TTT curves for a BaO∙2TiO2∙2SiO2 glass with crystallized volume fraction α = 0.05 using, in one approach, the screw dislocation growth model both above and below Tb (tsd – dashed line), and in the other the Arrhenius equation below Tb (tbreakdown – solid line). Experimental data points (black stars) obtained at 993, 1003, 1013, and 1023 K [15].

1350 tbreakdown(T) = (3·0.05/π·I(T)·u(T )3)1/4 1300

t (T) = (3·0.05/π·I(T)·usd(T)3)1/4

1250

T (K)

1200 Tb = 1155 K

1150

α = 7.8 × 10–2

1100

α = 4.7 × 10–2 α = 3.9 × 10–2

1050

α = 4.9 × 10–2 1000 Tg = 983 K 950 102

103

104

105

106

107

108

109

1010

t (s)

5

Perspectives

Significant advances in the understanding and control of crystal nucleation and growth processes in glass-forming liquids have been achieved in the last five decades. It is now well-established that almost all materials can vitrify when subjected to sufficiently fast cooling from the liquid state. Thus, novel materials, such as metallic and chalcogenide glasses with unusual properties, have been obtained successfully by very fast quenching. Also, controlled, catalyzed internal crystallization of specific glasses has led to a variety of advanced glass ceramics that are now manufactured commercially. More profound insights into glass crystallization processes, such as precise predictions of nucleation and growth rates and critical cooling rates for glass formation, based solely on materials properties, will depend critically on new developments in nucleation and growth theories and computer simulations. Despite the many advances achieved in understanding crystallization processes in glasses, some problems remain open. Among the most important, we remark the following: (i) specification of the bulk (structure, composition, density) and surface properties of the critical nuclei and sub- and supercritical crystals as a function of their sizes; (ii) description of the temperature dependence of the crystal nucleus–liquid interfacial energy and the degree of validity of the Stefan–Skapski–Turnbull equation; (iii) applicability of the SEE (viscosity) relationship in calculating the effective diffusion coefficients that control crystal nucleation and crystal growth; (vi) a clear

understanding of the causes of the breakdown of the SEE equation reported for crystal growth somewhat above Tg; (v) unveiling the cause of the reported breakdown of the CNT in describing the temperature dependence of experimental nucleation rates below Tg; (vi) a deeper understanding of the relationship, if any, between the molecular structure of glass-forming melts and the nucleation and growth mechanisms [20]; (vii) the relation between the sizes of supercritical nuclei vis-à-vis the sizes of cooperatively rearranging regions (CRR) of the configurational entropy theory and the domains of heterogeneous dynamics (DHD) envisaged in the structure of viscous liquids [21]; and (viii) comparison of the estimated (by extrapolation) structural relaxation time and the characteristic time for crystallization of glass-forming liquids at the (predicted) Kauzmann temperature, TK [22, 23]. Such a comparison could resolve the paradox, following Kauzmann’s suggestion of the possibility that the putative state of negative entropy may never be reached because crystallization would always intervene before structural relaxation. A detailed analysis of the Kauzmann paradox and his hypothesis about the existence of a kinetic spinodal has been performed recently [24]. In addition, the ratio of the mentioned times scales is of considerable importance concerning the problem whether some basic assumptions of CNT concerning the methods of determination of the thermodynamic driving force and the surface tension hold or not for crystallization under time-dependent temperature and/or pressure [25]. All these problems, in addition to several others not

567

568

5.4 Nucleation, Growth, and Crystallization in Inorganic Glasses

mentioned here, such as the development of novel glasses and glass ceramics, having exotic, unusual compositions and combination of properties, serve as great incitement for glass crystallization being a very active research topic!

dt kB D d0 Tm Δhm

Acknowledgments The authors are indebted to their numerous co-workers and students for enjoyable and educative joint research in the past 40 years and to Profs. E. B. Ferreira and F. C. Serbena for their critical comments. Generous and continuous funding by the Brazilian agencies CAPES, CNPq, and São Paulo Research Foundation, FAPESP (CEPID grant # 13/07793-6), is much appreciated.

Table of Symbols ΔG R A N Δμ μl μcr σ cα P T G Rc ΔGc ni Wc τ J Js t nc τR η tind dN

Gibbs free energy difference cluster radius nucleus surface area number density of supercritical crystallites chemical potential difference the chemical potentials per particle in the liquid the chemical potentials per particle in the crystal surface free energy particle number density in the crystal cluster pressure temperature Gibbs free energy critical radius change in the Gibbs free energy for a critical cluster number of particles of the different components in the cluster work of critical cluster formation time-lag in nucleation rate of formation of supercritical clusters steady-state nucleation rate time number of particles in a cluster of critical size Maxwellian relaxation time Newtonian viscosity induction time change of number of clusters of critical size

qm NA ς f Δsm C2, C3

B

R dt V Vn ωn αn(t) = (Vn(t)/V) N0 n Tb Tg TK Φ

time interval Boltzmann’s constant diffusion coefficient diameter melting temperature heat of melting of one crystal phase particle heat of melting Avogadro’s number correction factor fraction of preferred growth sites entropy of melting parameters determining the time required for the formation of the two-dimensional nucleus and for its propagation across the interface, respectively. combination of parameters proportional to the effective diffusion coefficient average size of the nuclei time interval volume volume crystallized shape factor time-dependent crystallized fraction number of supercritical clusters number of independent spatial directions Stokes–Einstein breakdown temperature glass transition temperature Kauzmann temperature catalytic activity factor of a heterogeneous nucleation core

References 1 Morey, G.W. (1938). The Properties of Glass, 1954. New

York: Reinhold Publishers. 2 Höland, W. and Beall, G.H. (2013). Glass-Ceramic

Technology, 2nd ed. Hoboken, NJ: Wiley. 3 Gutzow, I.S. and Schmelzer, J.W.P. (1995). The Vitreous

State: Thermodynamics, Structure, Rheology, and Crystallization. Berlin: Springer; Heidelberg: Springer, 2nd enlarged ed., 2013. 4 Zanotto, E.D. (2013). Crystals in Glass: A Hidden Beauty. Hoboken, N.J: Wiley. 5 Gibbs, J.W. (1926). Collected works. In: Thermodynamics, vol. 1. New York: Longmans.

References

6 Fokin, V.M., Zanotto, E.D., Yuritsyn, N.S., and

7

8

9 10

11 12 13 14

15 16

Schmelzer, J.W.P. (2006). Homogeneous crystal nucleation in silicate glasses: a 40 years perspective. J. Non-Cryst. Solids 352: 2681–2714. Nascimento, M.L.F., Fokin, V.M., Zanotto, E.D., and Abyzov, A.S. (2011). Dynamic processes in a silicate liquid from above to below the glass transition. J. Chem. Phys. 135: 194703. Baidakov, V.G., Protsenko, S.P., and Tipeev, A.O. (2013). Temperature dependence of the crystal-liquid interfacial free energy and the endpoint of the melting line. J. Chem. Phys. 139: 224703/1–224703/12. Volmer, M. (1939). Kinetik der Phasenbildung. Th. Steinkopff: Dresden. Uhlmann, D.R. (1982). Crystal growth in glass-forming liquids: a ten-year perspective. In: Advances in Ceramics, vol. 4 (eds. J.H. Simmons, D.R. Uhlmann and G.H. Beall), 80–124. Columbus: American Ceramic Society. Jackson, K.A. (2004). Kinetic Processes. Weinheim: Wiley-VCH. Slezov, V.V. (1999). Kinetics of First-Order Phase Transitions. Weinheim: Wiley-VCH. Kolmogorov, A.N. (1937). On the statistical theory of crystallization of metals. Izv. Akad. Nauk SSSR 3: 355–359. Johnson, W.A. and Mehl, R. (1939). Reaction kinetics in processes of nucleation and growth. Trans. AIME 135: 416–458. Avrami, M. (1939). Kinetics of phase change. I. General theory. J. Chem. Phys. 7: 1103–1112. Avrami, M. (1940). Kinetics of phase change. II. Transformation time relations for random distribution of nuclei. J. Chem. Phys. 8: 212–224.

17 Avrami, M. (1941). Kinetics of phase change. III.

18

19

20

21

22

23

24

25

Granulation, phase change, and microstructure kinetics of phase change. J. Chem. Phys. 9: 177–184. Kelton, K.F. and Greer, A.L. (2010). Nucleation in Condensed Matter: Applications in Materials and Biology. Amsterdam: Elsevier. Rodrigues, B.P. and Zanotto, E.D. (2012). Evaluation of the guided random parametrization method for critical cooling rate calculations. J. Non-Cryst. Solids 358: 2626–2634. Zanotto, E.D., Tsuchida, J.E., Schneider, J.F., and Eckert, H. (2015). Thirty-year quest for structure-nucleation relationships in oxide glasses. Int. Mater. Rev. 60: 376–391. Johari, G.P. and Schmelzer, J.W.P. (2014). Crystal nucleation and growth in glass-forming systems: some new results and open problems. In: Glass: Selected Properties and Crystallization (ed. J.W.P. Schmelzer), 531–590. Berlin: de Gruyter. Kauzmann, W. (1948). The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43: 219–256. Zanotto, E.D. and Cassar, D.R. (2018). The race within supercooled liquids – Relaxation versus crystallization. J. Chem. Phys. 149: 024503. Schmelzer, J.W.P., Abyzov, A.S., Fokin, V.M. and Schick, C. (2018). Kauzmann paradox and the crystallization of glass-forming melts. J. Non-Cryst. Solids 501: 21–35. Schmelzer, J.W.P. and Schick, C. (2012). Dependence of Crystallization Processes of Glass-forming Melts on Prehistory: A Theoretical Approach to a Quantitative Treatment. Phys. Chem. Glasses B 53: 99–106.

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5.5 Solubility of Volatiles Bjorn Mysen Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC, USA

1

Introduction

Even though a few hundred ppm of dissolved water may affect to a measurable extent physical properties of SiO2 glass [1], volatile concentrations higher than 1% usually are required to exert significant effects in oxide glasses and melts. Because pressures of the order of 100 Pa are typically needed to achieve a solubility of 1 wt %, dissolution of volatiles remains a difficult and expensive task, which is hampering any practical application of the materials produced. As a result, volatile solubilities and their effects on physical properties have been mostly studied to understand the fundamental role they play in geological processes. The relevant systems are then made up of silicates along with the halogens F2 and Cl2, the He–Xe series of noble gases, and a number of species in the system C–O–H–N–S, namely, H2O, H2, CO2, CO, CH4, N2, NH3, SO2, S, and H2S. To illustrate in this chapter the manner in which the structure and physical and chemical properties of silicate glasses and melts change upon volatile dissolution, we will review experimental data from systems that are comparatively simple (unary to quaternary) with extrapolation to more complex chemical environments when appropriate.

2 2.1

Principles and Concepts Reactive and Nonreactive Solubility

The solubility of volatiles in a silicate structure and its effects on it depend on gas and silicate compositions Reviewers: K.-U. Hess, Earth and Environmental Sciences, LudwigMaximillians-Universität, Munich, Germany A. Whittington, Geological Sciences, University of Missouri, Columbia, MO, USA

together with temperature, pressure, and redox conditions (as generally specified by oxygen or hydrogen fugacity). The sensitivity to the interplay of these conditions is illustrated by the fact that, under reducing conditions, species such as CH4 and NH3 may form in the presence of hydrogen, whereas formation of carbides and nitrides takes place instead if hydrogen is lacking in the melt. These examples also illustrate the generally reactive nature of volatile dissolution, where the volatile species forms chemical bonding with the silicate structure and in the process affect the properties of the material. Examples include H2O, which forms OH groups. The CO2 and SO2 form forms CO3 and SO4 groups, respectively, by sharing oxygen with the silicate. In other structural interactions, oxygen in the silicate structure can be replaced with functional groups such as CH3 from methane and NH2 from ammonia and S-bearing groups from H2S. Exchange of oxygen in the silicate tetrahedra with C, N, or S can also occur. In addition, water, carbon dioxide, ammonia, and methane can dissolve either as molecular or nonreactive molecular species together with a reactive portion (e.g. OH groups and H2O) whose proportions also depend on all intensive thermodynamic variables. Species that dissolve only in molecular and nonreactive form at noble gases and N2. Although it is possible to dissolve volatiles in glasses, most experimental studies have been performed on melts, which were then temperature-quenched to glass to ascertain that an equilibrium state was actually reached and to give sound basis to thermodynamic modeling of the solution process. In this chapter we will thus restrict ourselves to these conditions. It is implied, therefore, that the volatile species have equilibrated with the silicate structure under specific temperature, pressure, and redox conditions before the melt is quenched to a glass. Two kinds of experiments must be further distinguished depending on whether the melt is undersaturated or saturated with

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

5.5 Solubility of Volatiles

the volatile of interest. In the latter case, equilibration between the volatile in the melt and in a coexisting gas phase is of course necessary. 2.2 Glass Versus Quenched Melt The physics of the glass transition is discussed elsewhere (Chapter 3.3). Here, we will address only how, or the extent to which, volatiles dissolved in melts may be quenched in the glass structure and whether, or the extent to which, the structure of volatile components in glass is a viable representation of the structural environment of volatile-containing silicate melts. The solubility in melts of the individual volatile species considered in this chapter differs significantly, is slightly temperature dependent, and is often a pronounced function of pressure (Table 1). As a result, a melt must be decompressed and cooled down from the equilibrium conditions either to synthesize a glass with a desired volatile content or in order to examine a volatile-bearing glass as a proxy for its melt. In order to retain the volatile content in the quenched glass of the high-temperature/ pressure melt, the quenching rate must exceed the rate at which volatiles may exsolve. The exsolution rate depends primarily on the diffusivities of volatiles and the nucleation rate of gas bubbles in the cooling melt. Furthermore, equilibria between different functional groups of volatile species in principle depend on both temperature and pressure. Therefore, when studying volatiles in glass, it must be kept in mind that volatile contents and their solution mechanism may have been affected by the glass-forming process.

understanding relationships between composition, temperature, and pressure (Figure 1). At a given pressure, there exists a temperature range from the solidus (a eutectic point is used for this illustration in Figure 1) to a critical point (c. p.), where a melt is saturated with respect to the volatile component of interest. In this temperature range, a solvus separates the stability field of volatile-saturated melt+volatile-rich fluid and the boundary between volatile-rich fluid and volatile-saturated melt. The former boundary defines the solubility of the volatile component(s) in the melt. At temperatures above the critical point, there is no distinction between melt and fluid. The width and height of the solvus (in the temperature–composition space illustrated in Figure 1) diminish with increasing pressure. The solubility of volatiles in silicate melts is sensitive to pressure. As already stated, it often can increase from only a few hundred ppm at ambient pressure to several mol % at several hundred MPa. Water is an example of such a component. The effects of temperature are generally smaller, but remain significant, and can also be dependent on pressure. As for redox conditions, they also affect the silicate–volatile phase relations through their influence on volatile speciation. For example, the solubility of CH4 is less than half of that of CO2 for a given silicate composition, temperature, and pressure. Ammonia (NH3) solubility, on the other hand, can be several times higher than that of N2.

Supercritical fluid c.p.

2.3 Intensive Variables (Pressure, Temperature, Redox Conditions)

Fluid

Melt

A description of the principles that govern silicate–volatile equilibria at temperatures above the liquidus is useful for

Melt + fluid m

f

(s) tal ys lt Cr +me

Table 1 Solubility (mol %) of H2O, CO2, and SO2 in NaAlSi3O8 composition melt near 1500 C as a function of pressure (GPa).

Temperature

572

e.p.

Pressure (GPa)

H2O

CO2

SO2

0.5

59

4.2

1.6

Silicate

1.0

78

6.1

2.1

1.5

82

7.6

2.5

2.0

84

Figure 1 With water as an example, schematic representations of phase relations in silicate + volatile systems. Only a simple eutectic defines the minimum temperature of melting and a simple solvus separating volatile-bearing melt from silicate-bearing fluid, which determines the solubility of volatile component as a function of temperature at given pressure. The width of the solvus depends on pressure and silicate composition and can also vary with redox conditions.

8.2

2.8

2.5

9.0

3.1

3.0

9.6

3.3

Source: data summary from [2].

Crystal(s) + fluid Volatile

3 Reactive Volatiles in Silicate Glass and Melt

Composition

Silicate and gas composition affect solubility and solubility mechanisms of volatiles in melts. When a multicomponent gas coexists with a melt with which it is completely miscible, the gas composition is enriched in the component that is least soluble in the melt. Examples are silicate–H2O–CO2 mixtures because the solubility of CO2 in silicate melts is only a small fraction of that of H2O (see Table 1). When gas speciation is redox dependent, the fractionation of the components between the melt and coexisting gas will also vary with redox conditions. The activity–composition relations in the gas phase also can play an important role. As defined above, volatile solution is nonreactive when it is governed by the availability and dimensions of the cavities (structural locations) in the structure that are occupied by the volatile molecules. Then the degree of melt polymerization (NBO/Si; see Chapter 2.6) is the most important variable affecting this solubility because the more polymerized a silicate melt and glass, the greater the availability of cavities thanks to the larger proportion of rings made up of SiO4 tetrahedra. An example is silica-rich compositions where Q4 species are the dominant structural components (threedimensionally interconnected network of silicate tetrahedra). Moreover, for a given silicate melt, temperature, and pressure, the solubility increases as the atomic or molecular radius of the nonreactive element or compound decreases. Examples are noble gases (He–Xe) and N2. When the dissolved volatile component interacts chemically with the silicate, its solubility depends on the availability of bridging and nonbridging oxygen and on the electronic properties of network-forming and network-modifying cations. When cations serve to charge-balance tetrahedrally coordinated Al3+, the nature of the charge-balancing cations also affects solubility and solution mechanisms. In addition, silicate composition affects the temperature- and pressuredependent solubility of the volatile components such as OH−, CO32−, SO32−, NH2−, and CH3.

3 Reactive Volatiles in Silicate Glass and Melt Except noble gases and molecular nitrogen, all the tiles considered in this chapter are reactive. Other tiles may dissolve in a manner that includes reactive and nonreactive species (e.g. molecular vs. OH groups and CO2 vs. CO3 groups). 3.1

structure and properties. Its solubility in silicate melts is also greater than that of any of the other volatiles except, perhaps, fluorine. 3.1.1 Solubility and Solution Mechanisms

When quenched from a hydrous melt, glasses have water contents varying from a few hundred to a few thousand ppm at ambient pressure to several tens of mol % at pressures in the MPa–GPa range. In silicate–H2O systems, there exists a maximum pressure and temperature above which complete water miscibility obtains, which defines the critical point (c.p., shown schematically in Figure 1). The pressure/temperature coordinates of the critical point are sensitive functions of silicate composition and range from about 1 GPa/600 C for Na silicates to >5 GPa/>1100 C for Mg silicates. The electronic properties (ionization potential) of the metal cation appear the most important variable affecting the pressure/temperature coordinates of the critical point. Below the critical point (c.p. in Figure 1), the solubility of H2O is a strongly nonlinear and positive function of total pressure and a positive or negative function of temperature depending on pressure and silicate composition (Figure 2). In addition, water solubility strongly depends on silicate composition, being a negative function of Al/ (Al+Si) and of the ionization potential, Z/r2, of the metal cation (Z: formal electrical charge, r: ionic radius). In

14

AOQ SiO2

12 Solubility of H2O in melt (wt %)

2.4

10 8

Trachyte

6 4 2

volavolaboth H2 O

Hydrous Glass and Melt

Among the volatiles discussed in this chapter, dissolved water has the most profound influence on glass and melt

0 0

200

400

600

800

Pressure (MPa)

Figure 2 Isothermal solubility of pure water in various silicate melts as a function water pressure, PH2 O. Trachyte (data from [3]) a natural magma composition (SiO2 = 61.71 wt %, Al2O3 = 18.56, FeO = 3.17, MnO = 0.27, MgO = 0.23, CaO = 1.64, Na2O = 6.11, K2O = 7.09), AOB (data from [4]) are for a model composition (SiO2 = 76.14 wt %, Al2O3 = 13.53, Na2O = 4.65, K2O = 5.68). Solubility data for SiO2 melt are from [5].

573

5.5 Solubility of Volatiles

contrast, water solubility in aluminosilicate melts increases with the electronegativity of the cation that charges compensate Al3+ in tetrahedral coordination (see Chapter 2.6). Under equilibrium conditions the high-pressure and temperature solution mechanisms of water vapor in silicate melts have been described by the expression H2 O + O2 −

2 OH − ,

1

where the abundance ratio of molecular water, H2O , to structurally bound OH groups, H2O /OH, varies because the proportion of molecular H2O increases with increasing total water content (Figure 3). For glasses, the H2O / OH ratio is insensitive to temperature, but above the glass transition, equilibrium (1) shifts to the right with a ΔH around 30 kJ/mol. The O2− in Eq. (1) is the structural link between the water speciation and silicate structure. In its simplest form, such as in the system SiO2–H2O, the OH groups are formed by breaking the oxygen bridges in the threedimensional network structure of silica glass and melt: 2Q4 + H2 O

2Q3 H ,

2 4

where SiO2 is represented as Q and Q (H) denotes a Q3 species with protons serving as network-modifying cation (see Chapter 2.4 for discussion of Qn species in silicate glasses). In chemically more complex silicate glasses, OH groups also bond with Al3+, alkali metals, and alkaline

3

earths, thus creating more complex relations between the structure, composition, and solubility and solution mechanisms of water in silicate melts and glasses (Figure 2).

3.1.2 Structure–Property Relations

Transport, volume, and thermodynamic properties of silicate glasses and melts significantly depend on water content because of the alteration of the silicate structure caused by formation of OH groups. Viscosity, electrical conductivity, and diffusion are quite sensitive, so about 1 wt % water, for example, can lower melt viscosity by several orders of magnitude. Increasing water content also results in increasing configurational entropy, lower glass transition temperature, and lower melting temperatures (see data review in [1], Chapter 14). These variations are partly due to formation of depolymerized Qn species upon water dissolution. Similar reasoning explains increased diffusivity of water at higher water contents.

3.2 Oxidized Carbon (CO2) Carbon is the second most abundant element of the C–O–H–N–S system in Earth. In the C–O–H subsystem, CO2 at the temperature of molten silicates is stable down to oxygen fugacities about three to four orders of magnitude lower than that of air.

3.2.1 Solubility and Solution Mechanisms

3O 8

6

lSi

O9 Si 4

aA :N 2O

4

H

OH or H2O concentration calculated as wt % H2O

574

a2

:N

O H2

Si O 9 OH: Na 2 4

OH: NaAlSi3O8 2

0

0

2

4 6 8 Bulk H2O concentration (wt %)

10

Figure 3 Speciation of water as molecular H2O and OH groups in melts of compositions indicated as a function of bulk (total) water content. Data for Na2Si4O9 glasses quenched from 1100 C at 200 MPa (data from [6]) and for NaAlSi3O8 glass quenched from 1400 C and 1.5–2.0 GPa (data from [7]).

The solubility of CO2 in silicate melts at ambient pressure is lower than 0.1 wt %, but it increases rapidly with pressure and also varies with the water content of the melt sometimes with a maximum CO2 solubility at intermediate CO2/H2O abundance ratios. The solubility of CO2 is less than 10 % of that of water under otherwise identical silicate composition, temperature, and pressure, and it depends more strongly on melt composition. Of particular importance are polymerization (NBO/T) and the electronic properties of the network-modifying cations (alkali metals and alkaline earths) (Figure 4). There is a positive correlation of CO2 solubility with NBO/T whether in chemically simple or more complex silicate compositions [9]. The Al/(Al+Si) ratio and metal cation types and proportions also affect the solubility. From vibrational (Raman and FTIR) and carbon-13 NMR spectroscopy of quenched, CO2-saturated melt (glass), carbon dioxide is found to dissolve in the form of CO32− complexes and molecular CO2. The expression, which is analogous to that describing the H2O/OH relationships in silicate glasses and melts (Eq. (1)), is CO2 + O2 −

CO3 2 −

3

3 Reactive Volatiles in Silicate Glass and Melt

3.2.2 Structure–Property Relations Solubility of CO2 in melt (wt %)

14

10

6

2

1.5 GPa/1275–1600 °C

0.0

1.0 NBO/T of melt

2.0

Figure 4 Solubility of carbon dioxide in CaO–MgO–Al2O3–SiO2 melts determined in glass quenched from 1275 to 1600 C at 1.5 GPa as a function of the degree of polymerization of the melt (NBO/ T, where T = Al3++Si4+) (data from [8]).

Here, as for water, the O2− is the link to the silicate structure. This link can be replaced by Qn-species equilibria to yield 2Qn + 1 + CO3 2 −

CO2 + 2Qn

4

This equilibrium is sensitive to bulk composition and shifts to the right with increasing metal oxide/SiO2 and Al/(Al+Si) ratio ([1], Chapter 16). In mixed CO2/H2O environments, decreasing CO2/H2O in coexisting gas also shifts this equilibrium to the right. Available information indicates that at temperatures above the glass transition, equilibrium (3) shifts to the left with increasing temperature and decreasing pressure (Figure 5).

Mol fraction, CO2/(CO2 + CO3)

1.0

0.8 2 GPa 0.6 5 GPa 0.4 10 GPa 0.2

0.0 1400

1600

1800

2000

2200

2400

Temperature (K)

Figure 5 Calculated proportion of molecular CO2 and carbonate groups, CO3, in melt of basalt composition as a function of temperature and pressure (calculations by [10]). See also Chapter 2.6 for further discussion of basalt composition.

Solution of carbon dioxide in glasses and melts results in increased Qn+1/Qn abundance ratio in the silicate, i.e. the network becomes increasingly polymerized (Eq. (4)). This is the opposite of the effect of dissolved water, which causes the silicate network to depolymerize (Eq. (2)). Therefore, melt and glass properties that vary with melt polymerization will also vary with the concentration of dissolved carbon dioxide. This change will, for example, cause expansion of more polymerized liquidus phases compared with CO2-free systems. Moreover, configurational heat capacity and entropy would tend to decrease because the partial molar heat capacity of the more polymerized Qn species is smaller than that of depolymerized Qn species. It follows that transport properties will also change with proportion of dissolved carbon dioxide. Experimental data relevant to these important properties are, however, scarce, so many of these predictions cannot as yet be benchmarked against experimental data. 3.3

Reduced Carbon

The reduced carbon species of interest in the C–O–H subsystem of volatiles are CO, C, and hydrocarbons. Among possible hydrocarbons, only CH4 is found stable under the temperature/pressure conditions of melt precursors of silicate glass. 3.3.1 Solubility, Solution Mechanisms, and Properties

Solubility and solution mechanisms for elemental C in silicate melts and glasses are not well established. By analogy with C solubility in crystalline silicates, it is likely of the order of tens of ppm. This oxidation state, therefore, will not need to be considered further. Likewise, little can be said about carbide solubility and solution mechanisms in silicate–C–O melts, which would obtain in highly reducing, H-free environments but have not been examined to any significant extent. Carbon monoxide, CO, predominates in the C–O system at the temperatures of molten silicates within comparatively narrow oxygen fugacity range of about 2 log units. The solubility ranges from f H2 (MW) > f H2 (NNO) > f H2 (MH) at the same temperature and pressure.

and S2 + 3O2 + 4Qn Mm +

Sulfur can exist in at least four different oxidations states (S6+, S4+, S∘, and S2−). Among these, the solubility of elemental sulfur in silicate melts and glasses is likely so small that it will not be considered further. For the other oxidation states, the solubility may reach thousands of ppm while depending on bulk silicate composition, temperature, pressure, and sulfur fugacity, f s2 , and oxygen fugacity, f O2 . Whether under reducing or oxidizing conditions, sulfur solubility is a positive function of the metal oxide/SiO2 ratio of the glass (Figure 9). At constant silicate composition, it first decreases with increasing f O2 and then increases because different solution mechanisms operate for the different redox states. On the oxidizing side of the minimum, one has S2 + 3O2 + 2O2 −

2SO4 2 − ,

7a

where decreasing f O2 results in decreasing sulfur solubility (as SO42− groups). On the reducing side of the minimum, the sulfur solubility, now as S2− groups, increases with decreasing f O2 : 2−

2S

2−

+ O2

7b

These relations can be expanded to describe sulfur speciation with the silicate Qn species: S2 + 4Qn Mm +

–16

Figure 9 Sulfur solubility in Na2O–SiO2 melts as a function of redox conditions in glasses quenched from 1200 C and at ambient pressure (data from [11]).

Sulfur

S2 + 2O

–11 log fO2 (MPa)

Pressure (GPa)

3.5

–6

4Qn + 1 + 2S2 − Mm + + O2 , 8a

4Qn + 1 + SO4 2 − Mm + 8b

m+

In these expressions, M denotes network-modifying cations that also serve to charge compensate the Sbearing functional group. Expressions (8a) and (8b) illustrate how the redox state of sulfur species is linked to the degree of silicate melt polymerization (here expressed as the abundance ratio, Qn+1/Qn). In both cases, decreasing melt polymerization, Qn/Qn+1, drives the equilibrium toward the higher solubility, which is as observed. These same two expressions point to how properties of the Mm+ cation(s) govern sulfur solubility. This feature is often expressed as sulfur capacity, Cs, which is defined as Cs = Wti (f O2 /f s2 ) and embodies the fact the relative stability relations of Qn (Mm+) and the sulfur species exert strong control on sulfur solubility. This feature has important metallurgical implications that are discussed in Chapter 7.4.

3.6

Halogens

Fluorine and chlorine are the two halogens that have received most attention. Structural and property data are much more extensive for F-bearing than for Clbearing glasses and melts in part because fluorine has a quite high solubility even at ambient pressure and because it exerts major effects on glass properties. It is

577

5.5 Solubility of Volatiles

often assumed that these features are due to the fact that F− can substitute for O2− in the silicate network in simple systems such as SiO2–F, having in this sense a role similar to that of OH− upon water dissolution. For physical properties such as viscosity and liquidus phase relations, however, addition of fluorides to silicate glasses and melts often has substantially different impact on properties compared with that of equimolar proportions of dissolved water. The solubility of chlorine generally is lower than that of fluorine. Effects of bulk composition on solubility also differ because variations in metal cation type and Al/(Al+Si) ratio, for example, have significantly greater effects on fluorine than on chlorine solubility. Furthermore, the functional relationships between melt composition and solubility differ for the two halogens whose effects on melt and glass properties are quite different. Chlorine barely causes viscosity changes, whereas the effects of fluorine are often of the same magnitude as those of dissolved water. Melting temperatures and melting phase relations are also affected in different ways where, on an equimolar basis, fluorine causes greater freezing point depression than H2O and is more effective than Cl by several hundred percent. There are important differences in the solution mechanisms of fluorine in SiO2, in metal oxide/SiO2, and in metal oxide/Al2O3/SiO2 melt and glass systems. The simple SiO2–F system comprises Si–F bonds, whereas, as determined from 19F MAS NMR data, the dominant solution mechanism in metal oxide/SiO2 systems is simple metal fluoride complexing. In aluminosilicate melts, the solution mechanism involves chargebalanced Al3+ and Si4+, where the relative import of Si4+ and Al3+ in the F-bearing complexes correlates with the original Si/Al ratio. In comparison with hydrous metal oxide/SiO2 glasses and melts, the metal fluoride complex plays a more important role in the structure than metal oxide–OH complexes [12]. For chlorine, the dominant solution mechanism is interaction between Cl− and alkali metals or alkaline earths. If there is direct interaction with the rest of the silicate structure, these effects are of subordinate importance.

temperature and pressure, the H2 solubility is proportional to the square root of pressure, which points to chemical interaction between the dissolved hydrogen and the silicate structure. The freezing point depression of silicate caused by H2-rich fluids also suggests that hydrogen interacts chemically with the silicate melt structure [13].

4 Nonreactive Volatiles in Silicate Glass and Melt The nonreactive volatiles in silicate glasses and melts are the noble gases and molecular N2. As already stated, solution of hydrogen, water, carbon dioxide, and methane partly takes place in the form of nonreactive species. In melts and glasses containing several percent or more water, more than 50 % of this water is dissolved in the molecular form H2O. However, as noted above [Section (3.1)], the proportion of molecular H2O decreases with increasing temperature above the glass transition. Molecular CO2 and CH4 likely also vary with temperature, but few experimental data are available. The proportion of the molecular form is also quite sensitive to bulk composition, so for both the methane and carbon dioxide systems, the more important the molecular and nonreactive forms, the more silica-rich (more polymerized) a melt. For volatiles that exist exclusively in molecular form in silicate melts and glasses (inert gases and N2), there is a simple relationship between solubility and atomic or molecular dimensions (Figure 10). Near ambient

10–6

Solubility (mol/g MPa)

578

He

Ne

Ar N2 Kr

Xe

10–7

10–8

3.7 Hydrogen Hydrogen solubility data exist for only a few melt and glass compositions, namely, SiO2 glass, NaAlSi3O8 melt, and CaMgSi2O6 melt. In SiO2 glass, hydrogen solubility is a linear function of pressure and is comparable to those of the noble gases in silicate melts. These data are consistent with solution of H2 in molecular form. However, at higher

10–9 1.5

2.0

2.5

3.0

3.5

4.0

Diameter (Å)

Figure 10 Solubility of nonreactive gases in tholeiite basalt melts at ambient pressure and 1350 C as a function of atomic/molecular diameter (data from [14, 15]).

References

pressure, the noble gas solubility, Xi, is proportional to its concentration in the gas phase, Pi, via a proportionality constant, Ki: Xi = Ki Pi

9

So the Ki value (Henry’s law constant) for a given silicate composition is negatively correlated with the atomic radius of the noble gas. This constant increases with silica content of the melt. The temperature dependence of noble gas solubility is slight and can be either positive or negative, whereas the Ki value decreases nonlinearly with pressure. The deviation from linearity increases with pressure and with noble gas atomic radius. In natural silicate melts, the enthalpy of solution, ΔHs, ranges from near 5 to about 20 kJ/mol and decreases with increasing atomic radius. This enthalpy becomes increasingly sensitive to melt polymerization (equivalent to metal/silicon ratio) as the atomic radius of the noble gas increases. The solubility mechanism or mechanisms of noble gases in silicate melts and glasses have been modeled with the assumption that the gas occupies holes in the structure. For example, the partial molar volumes obtained from solubility measurements estimate the porosity of SiO2 glass. The partial molar volumes in silica glass are 16.4 ± 1.4, 10.3 ± 2.3, and 5.5–10.8 cm3/mol for Ar, Ne, and He, respectively.

examination that combines simulation with in situ experiments will add further to the development. Technology has slowly becoming available with which at least structural characterization at high temperature and pressure can be carried out. Solubility data may also be obtained in this manner, provided that the temperature and pressure effects necessary to translate instrumental information into solubility are known. For example, infrared absorption can be conducted with melts, but temperature and pressure effects on molar absorption coefficients are poorly known. The principles are beginning to emerge and will give a sounder basis to thermodynamic modeling of volatile–melt equilibria (Chapter 5.3).

References 1 Mysen, B.O. and Richet, P. (2018). Silicate Glasses and

Melts, 2e. New York: Elsevier. 2 B. O. Mysen, Solubility of volatiles in silicate melts under

3

4

5

Perspectives

Many volatile components commonly dissolve in the form of simple anionic complexes (e.g. OH groups, CO3 groups, etc.). To develop an understanding of how volatiles affect structure and properties of glasses and melts, however, it is necessary to establish how these reactive functional groups interact with the silicate structure. This goal may now be attainable with the aid of modern spectroscopic methods. Ideally, such characterization should be conducted while the samples are at the temperatures and pressures of interest because temperature quenching and decompression of a melt can lead to changes in both concentration of the volatile component(s) and their structural interaction. Numerical simulations of solution mechanisms also show promise and likely will become more important in the future as computational capacities and speed advance. For nonreactive solution, such approaches will, for instance, picture how “inert” gases contribute themselves to the formation of the cavities in which they are accommodated. Integrated

5

6

7

8

9

the pressure and temperature conditions of partial melting in the upper mantle, p. 1–14 in H.J.B. Dick, Magma Genesis, Proceedings of the AGU Chapman Conference on Partial Melting in the Mantle (Portland: Oregon Bureau of Mines, 1977). Di Matteo, V., Carroll, M.R., Behrens, H. et al. (2004). Water solubility in trachytic melts. Chem. Geol. 213: 187–196. Holtz, F., Behrens, H., Dingwell, D.B., and Johannes, W. (1995). H2O solubility in haplogranitic melts: Compositional, pressure, and temperature dependence. Am. Mineral. 80: 94–108. Kennedy, G.C., Wasserburgh, G.J., Heard, H.C., and Newton, R.C. (1962). The upper three-phase region in the system SiO2-H2O. Am. J. Sci. 260: 501–521. Zotov, N. and Keppler, H. (1998). The influence of water on the structure of hydrous sodium tetrasilicate glasses. Am. Mineral. 83: 823–834. Silver, L., Ihinger, P.D., and Stolper, E. (1990). The influence of bulk composition on the speciation of water in silicate glasses. Contrib. Mineral. Petrol. 104: 142–162. Brooker, R.A., Kohn, S.C., Holloway, J.R., and McMillan, P.F. (2001). Structural controls on the solubility of CO2 in silicate melts Part II: IR characteristics of carbonate groups in silicate glasses. Chem. Geol. 174: 241–254. Brooker, R.A., Kohn, S.C., Holloway, J.R., and McMillan, P.F. (2001). Structural controls on the solubility of CO2 in silicate melts. Part I: bulk solubility data. Chem. Geol. 174: 225–239.

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10 Guillot, B. and Sator, N. (2011). Carbon dioxide in silicate

13 Luth, R.W., Mysen, B.O., and Virgo, D. (1987). Raman

melts: A molecular dynamics simulation study. Geochim. Cosmochim. Acta 75: 1829–1857. 11 Nagashima, S. and Katsura, T. (1973). The solubility of sulfur in Na2O-SiO2 melts under various oxygen partial pressures at 1100 C, 1250 C, and 1300 C. Bull. Chem. Soc. Jpn 46: 3099–3103. 12 Mysen, B.O., Cody, G.D., and Smith, A. (2004). Solubility mechanisms of fluorine in peralkaline and metaaluminous silicate glasses and melts to magmatic temperatures. Geochim. Cosmochim. Acta 68: 2745–2769.

spectroscopic study of the behavior of H2 in the system Na2O-Al2O3-SiO2-H2. Am. Mineral. 72: 481–486. 14 Lux, G. (1987). The behavior of noble gases in silicate liquids: Solution, diffusion, bubbles and surface effects, with application to natural samples. Gechim. Cosmochim. Acta 51: 1549–1560. 15 Libourel, G., Marty, B., and Humbert, F. (2003). Nitrogen solubility in basaltic melt. Part I. Effect of oxygen fugacity. Geochim. Cosmochim. Acta 67: 4123–4136.

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5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses Reid F. Cooper Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI, USA

1

Introduction

Size and charge are first-order considerations of the cation role in the structure of ionic melts and glasses. But many cations, particularly of transition metals, are heterovalent, that is, the cation charge and size are affected by the chemical potential of the oxidizing elements. Consequently, redox potential becomes not only (i) a tool in engineering the properties of synthetic melts and glasses but also (ii) a variable in the service properties of formed glasses, both synthetic and natural. The thermodynamics involved in the study of redox are reasonably straightforward, the caveat being the standard one for multicomponent solutions, i.e. the need to know the relationship between component activity and component concentration. Redox dynamics, i.e. the coupling of thermodynamics with kinetics, are more complicated. Here, dynamics are considered from two end-member perspectives: closed systems, where the redox potentials of various component cations interact on a short timescale such that reactions are local (nominally at atomic scale), and open systems, in which the structural state of the melt or glass is being modified dynamically by an external redox potential. The establishment and control of color in glass or the use of redox reactions in glassmelt fining are examples of the former, while the float-glass process and the ambient-environment “weathering” of synthetic and natural glasses are examples of the latter. The heterovalency of ions (both of cations and some anions, e.g. those of sulfur) effects semiconductor properties in the melts/glasses, which is important in both closed- and open-system contexts.

Reviewers: D.L. Kohlstedt, Department of Earth Sciences, University of Minnesota, Minneapolis, MN, USA A. Pommier, IGPP, Scripps Institution of Oceanography, La Jolla, CA, USA

In what follows, redox thermodynamics are considered from the perspective of the chemical potentials/ activities of oxides and not of ions. As learned from Hermann Schmalzried [1], this is distinctly practical: one can control straightforwardly the activities of oxides (and of other neutral elements or compounds) in experimental and production settings; the same is not true for the activities of ions. Nevertheless, one can consider redox based on an ion-activity perspective (e.g. Chapter 5.9). Additionally, for simplicity, this chapter emphasizes silicate glassmelts and glasses. The extrapolation of the ideas and approach presented here to SiO2-free oxide and halide melts and glasses is straightforward. The challenge is almost always in having good, useful solution models for these complex multicomponent systems.

2 Oxidation/Reduction Thermodynamics 2.1 Reference Reactions: Pure Metal to Pure Metal Oxide; Pure Oxide to Pure Oxide of Different Valence The relative oxidation potentials of the various elements are the natural starting point for treating redox reactions in multicomponent melts and glasses. One can discern them by examining the reference reactions in which a pure metal reacts with pure molecular oxygen. Because we are interested in relative potentials, the reactions should each be written in terms of one mole of O2(g), i.e. x M + O2 y

Keq

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

1 Mx O2y , y

1

582

5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

where, applying the law of mass action, one expresses the equilibrium constant Keq as K eq =

aMx O2y aM

x y

1 y

aO 2

= exp

− Δr Go1 RT

2

In Eq. (2), ai is the activity of species i, RT has the usual meaning, and Δr Go1 is the standard Gibbs free energy of reaction (1), “standard” because reaction (1) involves “pure” reactants creating “pure” products, i.e. no solutions are involved. At equilibrium, the metal M and the metal oxide are both present: aM = aMx O2y = 1; consequently, Eq. (2) can be rewritten as Δr Go1 T = − RT ln K eq = RT ln aO2

3

At low pressures, the activity of oxygen is equivalent to the partial pressure, pO2 (in atmospheres). As stated by the Gibbs phase rule, for a pure metal–pure metal oxide in equilibrium, two phases coexist in a two-component system, so Eq. (3) is directly employed to define the metal–metal oxide buffer for oxygen.1 At elevated pressures the formalism remains the same, but one must use instead G.N. Lewis’ fugacity function, i.e. Δr Go1 T = RT ln f O2 , if the relationship between fugacity and activity is known. In Eqs. (2)–(3), Δr Go1 has enthalpic and entropic components, i.e. Δr Go1 = Δr H o1 − T Δr S o1 , where H and S of each reactant and of the product in reaction (1) are both functions of temperature: at any specified T, then, Δr H o1 and Δr S o1 can be calculated via integration of ΔrCP(T) and ΔrCP(T)/T, respectively, where CP is the isobaric heat capacity, which is, in general, a nonlinear function of T. To the Δr Go1 T so calculated, a function can then be adjusted, typically of the form Δr Go1 T = A + BT log T + CT , where A, B, and C are constant fit parameters. Tables of such data for standard oxidation reactions are readily available in the literature (e.g. [2, 3]). A graph of Δr Go1 T = RT ln aO2 = RT ln pO2 , atm vs. T is presented as Figure 1 (after [4] and the references therein). This type of plot is known as an Ellingham

1 Keq is defined for isobaric conditions; hence pressure is ignored in Eqs. (2) and (3). Δr Go1 , of course, is a function of both temperature and pressure, but as Gibbs free energy is a state variable, it can be evaluated along any arbitrary path. This presentation, thus, will concentrate on (isobaric) temperature sensitivity; the analysis is extrapolated to other pressures nominally straightforwardly through evaluation of the pressure effects on enthalpy and entropy. The “nominal” caveat is related to the requirement of having good data and models for the equations of state of the phases involved.

diagram; the additional axis for the oxygen activity (partial pressure in atm) is explained below.2 Because the reactions follow the form of reaction (1), i.e. each in terms of 1 mol of O2(g) reactant, the relative oxidation potentials of metals and of transition metal oxides are revealed, with more negative values of Δr Go1 representing a greater oxidation potential (i.e. a more stable oxide). Immediately obvious is that the data for each reaction plot essentially as a straight line (or a continuous series of straight lines with slope changes corresponding to phase changes of the reactants and/or products): the temperature sensitivity of ΔrG is the blatant one associated with the relationship ΔrG = ΔrH – TΔrS , that is, the temperature sensitivities of ΔrH and ΔrS are revealed as second-order effects. As such, the slopes of the solid metal-to-solid metal oxide “curves,” for example, indicate that the entropy decrease associated with incorporation of a mole of O2 gas into a crystalline solid is approximately –185 J/ mol/K. In passing, note that a reaction in which 1 mol of O2(g) reacts with a solid to produce 1 mol of a gaseous oxide, e.g. C + O2(g) = CO2(g), has approximately a zero slope, whereas one in which 2 mol of product gas are formed, e.g. 2 C + O2(g) = 2 CO(g), has a negative slope. The highest values on this Ellingham diagram correspond to elements such as Cu, Fe, Ni, Co, and also Au, Ag, and the platinum-group elements considered by geochemists to be siderophile (literally, iron loving); the lowest values are, in contrast, for elements such as Ca, Al, Li, Ti, and Si that are considered as lithophile (rock loving). One ramification of plotting RT ln pO2 , atm vs. T is that any straight line that goes through the origin of the graph, Δr Go1 = 0 and T = 0 K (the point labeled as O in the upper left-hand corner of the diagram), has a slope of R ln pO2 , i.e. it is a line of constant oxygen activity: this is the foundation of the farthest-out external scale (along the graph’s right-hand side and bottom) labeled pO2 . The straightforward way to use the graph is to evaluate the slope of a line emanating from the origin through the point where a specific Δr Go1 reaction curve intersects a specified temperature. For example, to determine at 1400 C the oxygen activity at which nickel and nickelous oxide are in equilibrium, the so-called Ni : NiO (“NNO”) buffer for oxygen, one extends a line from the point 0 through the point Δr GoNi NiO; 1400 C and reads the appropriate pO2 off the far-right axis: at this temperature, NNO is pO2 2 × 10–6 atm (aO2 2 × 10–6).

2 There are also axes corresponding to gas mixing ratios for H2:H2O and for CO : CO2, which can be used to design a controlled-oxygenactivity atmosphere – via gas-phase reaction/equilibrium – at a specified temperature; see Ref. [4].

2 Oxidation/Reduction Thermodynamics

Figure 1 Ellingham diagram as modified by Richardson and Jeffes [4]: ΔrG (=RT ln pO2) vs. T at ambient pressure. All reference reactions are written in terms of 1 mol of oxygen; thus plotted, the relative oxidation potentials of metals and of transition metal oxides are revealed, with more negative values of ΔrG representing a greater oxidation potential (i.e. a more stable oxide) (1 kcal = 4.184 kJ).

583

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5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

Another use of the Ellingham plot is determinations of phase equilibria. Consider, for example, two specimens, one of pure Ni and the other of pure Ti, both placed in a closed system along with some pure oxygen gas, but not enough to convert fully the Ti to TiO2 or the Ni to NiO. After a long reaction time, one predicts that the thermodynamically stable state would be a rind of TiO2 on the Ti specimen and unoxidized Ni, with the oxygen activity of the system lowered to the Ti : TiO2 buffer. But this experiment only “works” if the two metal specimens are not touching and if the temperature is low enough that the vapor pressures for Ti and Ni are minimal. In other words, pure Ti has a significantly greater oxidation potential than pure Ni. This analysis is consistent with describing the reference Ti–Ni–O displacement reaction: Ti + 2 NiO = TiO2 + 2 Ni; Δr Go4

4

where oxygen is “displaced” from bonding with Ni to bonding with Ti. In Eq. (4) Δr Go4 is a function of T; it can be determined directly on the Ellingham diagram: at a fixed temperature, Δr Go4 is the (vertical) distance between the Ni : NiO and Ti : TiO2 buffer lines (e.g. at 1400 C, Δr G oTi TiO2 ≈ –600 kJ/[mol O2] and Δr GoNi NiO ≈ –180 kJ/[mol O2]; thus, Δr Go4 ≈ –420 kJ/[mol O2]). It is significant to note that the Ni : NiO and Ti : TiO2 buffer lines do not cross: consistent with the Gibbs phase rule, there is no oxygen activity at which phase-pure Ti, TiO2, Ni, and NiO are simultaneously stable at any given temperature. Further, it would be incorrect to interpret the Ellingham diagram or reaction (4) as suggesting that rutile (α-TiO2) precipitating in a Ni matrix is a thermodynamically stable assemblage: in such a hypothetical system, neither aNiO or aTi is unity, which is the prerequisite for such a simple interpretation. The Ellingham diagram (Figure 1) includes, too, reactions for heterovalent cation oxides, specifically 6 FeO + O2(g) = 2 Fe3O4 (the wüstite–magnetite [WM] buffer) and 4 Fe3O4 + O2(g) = 6 Fe2O3 (the magnetite–hematite [MH] buffer); other versions of the diagram might include similar reactions, e.g. for the various valence oxides of Mn (critical for dry cell battery chemistry) or Sn (critical for the float-glass process, as seen below). As evidenced by the line-like topology of their respective ΔrG curves, the thermodynamics of these oxide–oxide reactions is identical to that of the metal–metal oxide reactions. 2.2 General Redox Reactions: The Case of Solutions The comment concerning the non-stability of an Ni– TiO2 composite and the parenthetical caveat about the Ni–Ti–O2(g) thought experiment, both presented above,

are an admonition: care must be exercised in applying the Ellingham diagram to redox problems when one is considering solutions, e.g. oxidation of metal alloys and/or redox conditions in multicomponent oxides like glasses or glassmelts. As the activities of either products or reactants shift away from unity, the Gibbs free energy driving potential is changed. This is accounted for through use of the activity quotient: Δr G 1 T = Δr Go1 T + RT ln

ni i ai, products ni i ai, reactants

, 5

where i ani i are the products of the relevant activities, each raised to its respective stoichiometric coefficient (ni). The correction term in Eq. (5) is a linear function of temperature and additionally is equal to zero at T = 0 K. Given that Δr Go1 T is effectively a straight line, one recognizes that, on the Ellingham diagram, the activity-quotient term simply rotates the standard-reaction free energy function about its intercept on the ordinate (i.e. about Δr H o1 at 0 K). As different metal–metal oxide buffer lines rotate because of the activity effect, one discovers redox couples that are “unexpected,” i.e. electron exchanges reducing what are considered more stable oxides and oxidizing what are considered more noble metals. A useful example is the redox reaction occurring in the float process for soda-lime-silica flat glass (“NCS,” which includes small amounts of Al2O3 and/or MgO). The original invention by Pilkington, Ltd., seemed straightforward enough: float glassmelt as a continuous ribbon on a bath of liquid metal ([5], Chapter 1.4). The metal for the float bath had six technical prerequisites: (i) an appropriate temperature range of liquid stability (Tm < 600 C; Tb > 1050 C), (ii) a low vapor pressure at the high-T condition (pi ~ 10–7 atm at 1050 C), (iii) a density much exceeding that of NCS (ρNCS;1050 C ~ 2.5 g/cm3), (iv) distinct nobility relative to the metals composing the oxides of the NCS glassmelt (i.e. a siderophile element), (v) ease of environmental oxidation control, and (vi) low toxicity. Molten tin was the obvious choice, particularly when economic considerations were added to the technical ones. The process development was challenging because of the reaction between the liquid NCS and the liquid Sn. Pilkington [5] did not consider the reaction problem from the perspective of redox thermodynamics, but the redox understanding is actually crucial [6]. At its original contact with the liquid-Sn bath at T ≈ 1050 C, the NCS glassmelt contains very little – to first order, none – of the tin oxides SnO and SnO2; similarly, the high-purity Sn float bath contains very little Na, Ca, or Si metal. But consider the reaction of Sn to stannous oxide in the context of the float reaction,

2 Oxidation/Reduction Thermodynamics

Δr GoNa Na2 O T . A similar analysis can be done for 0 in the liquid Sn, and so the reference– Si:SiO2: aSi reaction curve rotates counterclockwise. As illustrated in Figure 2, the ΔrG(1)(T) lines thus cross: the result is a large driving potential for Sn from the float bath to be oxidized (and added to the glassmelt ribbon) in a coupled reaction with SiO2 and Na2O from the glassmelt, which are reduced (and added to the liquid-metal float bath). The magnitude of the ΔrG driving potentials for these redox couples is that of an isothermal vector from the ΔrG(Sn:SnO)(T) line to either of the Δr G Na Na2 O T or Δr G Si SiO2 T lines. The activity effect illustrated in Figure 2 is important to understand, too, for any metal crucible–glassmelt reaction, including the incorporation of ionic platinum into a glassmelt through a redox couple of Pt with silica (± less stable oxide components of the glassmelt) (e.g. [7]). The kinetics of such a reaction will be discussed below, including its implications for the chemical morphology and performance of float-processed flat glass. A clear ramification of the thermodynamics presented here is that design of any melting and delivery process in glass manufacturing strongly depends on understanding the activity–composition relationships both in glassmelts and in the metal or ceramic materials with which they come in contact. Unfortunately, this is not straightforward: silicate melts are distinctly complex solutions (Chapter 5.3); metallic melts can be similarly complex, particularly those involving alloying with the group 14 metalloid elements, which include Sn and Si and are prominent in the float process. Silicate melt solutions

i.e. 2 Sn(l) + O2(g) = 2 SnO(l). Not shown in Figure 1, the reference-reaction Δr GoSn SnO T line is very close to the one for Fe : FeO (Figure 2). Application of Eq. (5) gives Δr G Sn SnO T = Δr GoSn SnO T + RT ln

a2SnO a2Sn pO2

6

At the glassmelt/liquid–Sn interface, at the initial contact of the glassmelt with the float medium, aSn 1 and pO2 is set by the forming-gas (H2 : N2) atmosphere that is sustained in the float-bath chamber (~10–14 atm at 1050 C; this is also the activity of oxygen in the liquid tin). As noted above, however, aSnO in the glassmelt is essentially zero. As a consequence, the activity-quotient term in Eq. (6) is negative, and strongly so, ΔrG(Sn:SnO)(T) is a line strongly rotated clockwise from that characterizing Δr GoSn SnO T (Figure 2). Continuing, one can consider the Na : Na2O equilibrium for the float situation (4 Na(l) + O2(g) = 2 Na2O(l)): Δr G Na

Na2 O

T = Δr GoNa ln

Na2 O a2Na2 O a4Na pO2

T + RT

7 At the glassmelt/liquid–Sn interface, aNa2 O is initially that of the glassmelt (~10–1), pO2 is again that of the forming-gas atmosphere, but aNa in the liquid Sn is vanishingly small. As a consequence, Δr G Na Na2 O T is a line strongly rotated counterclockwise from the reference –300

4Na + O2 = 2Na2O; ΔrG 2Sn+ O2 = 2SnO; ΔrG°

Si + O2 = SiO2; ΔrG

–400

ΔrG°; ΔrG (kJ [mol O2]–1)

Figure 2 Ellingham diagram (after [6]) for several oxides in the float-glass reaction, for reference conditions (ΔrG ; solid lines), and for the (non-reference) conditions characteristic of the liquid-Sn/glassmelt interface (ΔrG; broken lines). The curved arrows indicate the direction of rotation of the ΔrG lines according to Eqs. (5)–(7). Because of the thermodynamics of solution formation, there is an extremely large driving potential for the reduction of components in the glassmelt (e.g. Na+ and Si4+) and the related oxidation of the liquidSn float medium.

–500

–600

4Na + O2 = 2Na2O; ΔrG°

–700 Si + O2 = SiO2; ΔrG° –800

–900 2Sn + O2 = 2SnO; ΔrG –1000 0

200

400

600

800

Temperature (K)

1000

1200

1400

585

586

5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

are often described via polymerization (e.g. [8]) or quasichemical models (e.g. [9], Chapter 5.3). The latter consider silicate melts as solutions of discrete, distinctly ordered multi-ion units and are the basis for automated calculation of relatively simple systems with two or three oxide components, as, for instance, made by the calculator FactSageTM (Facility for the Analysis of Chemical Thermodynamics, Center for Research in Computational Thermodynamics, École Polytechnique de Montréal, Canada, and GTT-Technologies, Herzogenrath, Germany; http://www.factsage.com.) Intriguingly, complex multicomponent natural silicate melts are well modeled as regular solutions (i.e. with an ideal entropy of solution and usually a nonzero enthalpy of solution) if the appropriate units are selected as components, e.g. Fe2SiO4 and Mg2SiO4 entities instead of FeO and MgO, CaSiO3 instead of CaO, etc. This is the approach of the quasichemical thermodynamic calculator MELTS and its derivatives ([10], OFM Research, Inc., Seattle, WA, USA; http://melts.ofm-research.org/index.html).

3

Oxidation/Reduction Kinetics

The kinetics of redox reactions in silicate melts and glasses is complicated by two physical factors. (i) The “equilibrium” structure of a glass or glassmelt depends on the valence states of the component ions (e.g. [11], Chapter 2.4); as such, redox reactions are accompanied by structural relaxations that have a direct effect on ion mobility. (ii) For transition metal cations, particularly, but also ionized metalloids such as S and Si, the incorporation of heterovalent ions affects the electronic transference number such that, for a broad range of temperatures, the electrical conductivity of a glass or glassmelt, although decidedly modest (Chapter 4.2), is effected almost exclusively by electronic species, namely, electrons in the conduction band and/or electron holes in the valence band. In condensed matter kinetics, this feature is described as the “semiconductor condition” (e.g. [1], p. 81): for electronic species, the product of concentration and mobility, that is, the transport coefficient, outstrips that of any of the ions; the result is that the fluxes of ions are all decoupled, one from another. The combination of the two effects allows for curious, sometimes surprising reaction morphologies or textures. When a system is subjected to a differential in thermodynamic potentials that moves it out of equilibrium, the only “rule” in kinetics is that it must evolve in a manner that lowers its Gibbs free energy. There is no requirement that the system achieves a new stable equilibrium; metastable states are possible – and likely – as are discrete transient morphologies for systems continuing to evolve

as a differential potential persists. Applied to the ionic systems considered here, an additional caveat is that near-atomic-scale charge neutrality must be preserved. The situation would be more complex if glass-ceramic materials were considered because the metastability of the crystalline phase(s) would require an additional constraint on ionic flux. The kinetics of redox reactions will be considered from two end-member perspectives. (i) Open systems are where a glass or glassmelt reacts with the external environment in the process of reaching equilibrium with it through far-beyond-atomic-scale electrochemical diffusion; these situations cover both manufacturing (e.g. in the float-glass process, the continuing reaction between the liquid-metal float bath and the glassmelt ribbon) and application (e.g. oxidation of glasses originally manufactured in reducing situations but subjected to persistent use at ambient conditions characterized by a high chemical potential of oxygen). (ii) Closed systems are where redox potentials are created within the glassmelt solely by the quenching process. The reactions are then local: electronic transfer associated with redox and the related structural relaxation occurs at the near-atomic scale. Closed-system understanding is important in the control of color, is put to use in glassmelt fining, and addresses manufacturing problems caused by glassmelt–crucible reactions.

4

Open-System Redox Dynamics

Consider an FeO-bearing aluminosilicate melt subjected to an environment in which the majority of Fe2+ is not stable. This situation happens frequently in nature with basaltic magma, an aluminosilicate melt whose nine main oxide components include the transition metal oxides FeO, MnO, and TiO2. In the partially molten upper mantle of Earth, redox equilibrium is originally achieved at conditions that can be taken as T ~ 1250 C and pO2 ≈ 10–8 atm, giving a Fe3+/(Fe2+ + Fe3+) of ~0.1. Upon eruption, the basalt is very quickly brought to ambient conditions with a pO2 = 0.21 atm that of course persists; consequently, the basaltic glass formed in the eruption oxidizes with time, i.e. with continued exposure to the ambient environment. Ignoring convection, this oxidation must proceed by chemical diffusion, but the issue then is to determine which species are migrating. 4.1 The Phenomenology of Open-System Oxidation The open-system oxidation problem, specifically where the valence of iron and its impact on structure of the glass

4 Open-System Redox Dynamics

time) crystalline thin films of SiO2-free, single-cation oxides or multiple-cation oxide solid solutions or compounds such as spinel. The outward flux of cations is charge-compensated by a counterflux of electron holes, jh•. As for h•, it is an electronic defect having a single positive charge, which is denoted by the superscript dot; the creation of the electron holes near the free surface is the source of the electrons necessary for the ionization of oxygen that is required to form the crystalline surface oxides.3 The glass or glassmelt is oxidized internally, at the internal reaction front not by the addition of oxygen but rather by the removal of cations, i.e. the O2–-to-cation ratio does increase, but by the removal of cations. The kinetics overall are rate limited by the diffusion of divalent network-modifying cations: the distance to the redox front from the free surface, Δξ, follows parabolic kinetics, i.e.

Fe-bearing glass

jO2

Air

jO2–

I

II

jh•

jh•

III

jM

2+

Δξ

Internal oxidation front

Δξ 2+

Figure 3 Kinetic modes for the oxidation of a Fe -rich aluminosilicate glass or melt, drawn as having the external environment being that of air (pO2 = 0.21 atm) [12]. Three independent “modes” – I, II, and III – are illustrated.

or melt are the redox response, is presented phenomenologically in Figure 3 [12]. Three distinct dynamic responses – “modes” – to the oxidation potential are distinguished: one involving the chemical-diffusion flux of molecular O2 (jO2; mode I) and two others involving ionic diffusion, mode II for anion diffusion/flux, jO2 − , and mode III for cation diffusion/flux, jM2 +. The three modes occur simultaneously at mutually independent rates: the mode that dominates the redox kinetics is the one with the fastest initial response, i.e. that allows the internal reaction front to migrate from the free surface most rapidly. The dominant mode does not necessarily lead to the lowest Gibbs free energy state for the glass or glassmelt. This feature moves the drawing a bit away from simple phenomenology: Fe2+ has its primary role in a silicate glass or glassmelt as a network modifier; as the Fe3+/Fe2+ ratio increases with oxidation, Fe3+ more and more fills a network-former role ([11], p. 351). The internal reaction front, then, is that location where the oxygen activity becomes sufficiently high that the structural change occurs. With the molecular change, the mobility of atoms and of ions changes also. For broad ranges of temperature and iron content (temperature as low as 800 C with a total Fe2+ + Fe3+ content ~10–2 at %), mode III dominates the oxidation dynamics of aluminosilicate melts and glasses [12]. Divalent network-modifying cations stream to the free surface where they react with environmental oxygen to produce (with sufficient concentration and thermal energy and/or

2

= 2k p t;

kp

X M2 + DM2 +

Δr G , RT

8

where k p is the parabolic reaction-rate constant, X M2 + is the mole fraction (concentration) of the mobile divalent network-modifying cations in the region between the free surface and the internal oxidation front (i.e. across Δξ), and DM2 + is the average diffusion coefficient for the divalent cations in the oxidized region (cf. [1], p. 172). As emphasized by Eq. (8), the kinetics of a diffusion-ratelimited reaction is a product of (i) the mobile-species concentration with (ii) the species mobility and with (iii) the normalized (to RT) driving potential of the reaction. An average diffusion coefficient is cited because the mobility of an ion should generally be affected by the oxygen activity (see below), which, of course, varies across thickness Δξ. Mode III oxidation dynamics in aluminosilicate glasses and glassmelts have a direct parallel in the dynamics of oxidation of crystalline oxides and silicates. In the crystalline state, decoupled cation fluxes occur against an immobile O2– sublattice since the transport coefficient for oxygen anions is orders of magnitude smaller than that of many of the cation species, Si4+ being one of the obvious exceptions ([1], p. 171). Oxidation of glasses and glassmelts suggests that cation diffusion, specifically that of network-modifying cations, occurs against the relative immobility of the ionic species involved in the network. 3 Mode III kinetic response is prima facie evidence that the semiconductor condition holds for iron-oxide-bearing glasses and glassmelts. FeO-bearing, multicomponent crystalline oxides/silicates or glassmelts/glasses are broadly demonstrated to be p-type (i.e. h•; the p stands for positive) semiconductors: over a broad range of temperature and of FeO composition, the conductivity of the material occurs via electron transfer from Fe2+ to Fe3+ within the valence band of the material, that is, charge transfer occurs by the motion of vacant electron states (“holes”) within the otherwise filled valence band.

587

588

5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

Because the dynamics in the crystalline state are effected by the motions of point defects, the similar dynamics in glassmelts and glasses suggests a parallel to point defects that are operative in the amorphous state. As consequence, one can couple a phenomenological description of the kinetics with a qualitative understanding of the dynamics that identifies defects and their reactionimpelled motion in the amorphous state. Kinetically, phenomenologically, mode III can be understood by evaluating the two active compensating fluxes, jM2 + and jh• , using Fick’s first law, i.e. − cM2 + DM2 + dηM2 + RT dξ − cM2 + DM2 + dμM2 + dφ + 2F = RT dξ dξ

jM 2 + =

9

and jh• =

− ch• Dh• dηh• − c h• D h• = RT dξ RT

dμh• dφ +F dξ dξ 10

With Eqs. (9) and (10), Fick’s first law is depicted as modified by Einstein, i.e. the driving force for chemical diffusion is not a gradient in concentration, but rather the gradient in chemical potential or, for ionic solids and liquids, the gradient in electrochemical potential ([1], p. 63). In these equations, ci is the concentration, ηi the electrochemical potential, and μi the chemical potential each of the species i, whereas φ is the electrical potential and F is Faraday’s constant (96 485 J/mol/V). The continuity condition is the requirement for charge neutrality: zi ji = 0 = 2jM2 + + jh•

or 2jM2 + = − jh• ,

11

i

where zi is valence. For mode III to be operational, ch• Dh• is much greater than cM2 + DM2 + ; on this basis, one finds that dηh• = 0 when substituting Eqs. (9) and (10) into Eq. (11): hence, one cannot sustain an electrochemical potential gradient for the electron holes, which is the definition of the semiconductor condition introduced earlier. Concentrating on the divalent-cation flux (Eq. 9), one sees that the chemical potential gradient of an ion species is expressed, specifically dμM2 + dξ, which is difficult to control in experiments or in production, as was noted in the Introduction. Knowing how neutral species are formed by reaction of ions with electrons (e.g. M2+ = M + 2h•) and oxide components by the reaction of metal with oxygen (M + ½O2(g) = MO), one can transform Eq. (9) into a description of mode III oxidation [12]: jM2 + =

+ cM2 + DM2 + dμO2 2RT dξ

12

This equation is of fundamental importance in understanding mode III oxidation: it proclaims that a chemical potential gradient of oxygen can have, as its primary response, a flux of cations; oxidation needs not require a flux of atomic, molecular, or ionic oxygen. The operation of mode III oxidation has been demonstrated with ion (Rutherford) backscattering spectroscopy (RBS) (e.g. [12]). These experiments revealed the existence of surface oxide films, which are not represented in Figure 3, whose thickness increases with reaction time, and also the rather sharp boundary of the oxidation front that moves inward. Both the growth of the crystalline surface film (or of divalent-cation concentration in its absence) and that of the divalent-cationdepleted oxidized glass zone follows parabolic kinetics. Further, the rate of growth of Δξ matches well the tracer-diffusion rate for divalent network-modifying cations for the composition/structure of the oxidized glass, which is orders of magnitude faster than that of oxygen tracer diffusion whether by atoms, molecules, or ions [12, 13]. Whereas mode III response is robust, the morphology/ texture of the reaction is sensitive to the thermodynamic conditions. A FeO-bearing CaO–MgO aluminosilicate glass (“Fe-CMAS”; no alkali oxides) oxidized in air near its glass transition temperature, for example, results in nm-scale crystalline ferrite (MgFe2O4) being precipitated at the internal oxidation front; these precipitates exist in a substantially iron-depleted, oxidized glass. In contrast, a basaltic glass (prepared from remelted basalt rock), similar in polymerization to the Fe-CMAS glass but containing ~4.1 mol % of total alkali oxides (Na2O + K2O), experiences no internal precipitation of ferrite. “Stabilization” of Fe3+ as a network former in the oxidized glass occurs instead through incorporation of alkali ions, particularly Na+, which had diffused from significant depth in the specimen to the internal oxidation front [12]. For a basaltic liquid subjected to an air environment, however, mode III oxidation still occurs, but the internal interface is the place where the oxygen activity is such that ferrite (Fe3O4) becomes a liquidus phase for the temperature of the experiment: the structural changes in the melt wrought by the loss of divalent cations to the free surface changes the liquidus equilibrium (the phase diagram “evolves”): the liquid thus gets supercooled isothermally [13]. There are variations on the theme of reaction modes presented in Figure 3; these depend on the overall chemistry of the glassmelt or glass and/or temperature. As the alkali oxide content of a glassmelt increases, particularly relative to the content of transition metal oxides, the transport coefficient of the alkali ions (particularly Na+ ± K+) can, for example, exceed that of the electronic species. Mode III can remain the dominant mechanism, but

4 Open-System Redox Dynamics

the compensating flux becomes that of alkali ions: the oxidized glassmelt changes from an electronic to an ionic or a mixed conductor (e.g. [14]). Again with a sufficient content of network-modifying alkali or alkaline earth oxides, the dynamics can evolve to mode II as temperature increases, with a compensating flux provided by cations instead of by h• (e.g. [15]). The shift to mode II with increasing temperature is straightforwardly understood: the activation energy for mobility of O2– is greater than that of the network-modifying cations. One consequence is that at high enough temperature the mobility of O2– will exceed that of the network-modifying cations, and thus the O2– transport coefficient becomes dominant. Molecular O2 also sees its mobility increase rapidly with temperature [15]. A change of redox dynamics to mode I is unlikely for most multicomponent silicates, however, due to the limited solubility of the gas keeping the O2 transport coefficient relatively small.

4.2 A Structural Perspective on Open-System Oxidation Dynamics As noted above, mode III oxidation of glassmelts and glasses is similar to that observed in crystalline oxide or silicate solid solutions. In (Fe,Mg)O (magnesiowüstite) and (Fe,Mg)2SiO4 (ferromagnesian olivine), as examples, the physical manifestation of the oxygen activity is the coupled concentrations of negatively charged vacancies on the divalent-cation sublattice, which are denoted by VM2 + (NB. the subscript denotes the sublattice and the superscript charge – a prime is a negative charge; here there are two of them), and electron holes, which physically are Fe3+ present on the divalent-cation sublattice (h• ≡ Fe•M2 + ). The concentrations are coupled by the requirement of charge neutrality, specifically [h•] 2 [VM2 + ], where the brackets denote the number of defects per molecule on the lattice, a unitless concentration. As the oxygen activity increases, the concentration of both defects increases: [h•], [VM2 +] pm O2 where m ~ ⅙ ([1], p. 171). In the oxidation of these (and similar) Fe2+-bearing crystalline compounds, then the hole and vacancy concentrations are higher at the free surface and lower in the interior. Holes and vacancies thus flux inward, whereas the geometric requirement that a vacancy exchange with an ion on its sublattice imposes a divalent-cation flux outward: mode III. It is important to note that the motion of h• does not require the diffusion of Fe3+ ions; rather only the electron is moved from one iron ion to another, which is a much faster and lowerenergy process. Nevertheless, the defect Fe•M2 + causes a local distortion in the crystal structure, a “small polaron,” which tracks with the motion of the electron hole; the diffusion process is described as polaron

hopping and is characterized by a Boltzmann statistics that is similar to that of ionic diffusion. Of course glassmelts and glasses have neither a lattice nor sublattices. But they do have an atomic structure, and mode III oxidation response of network-modifying cation motion against a relatively immobile aluminosilicate network evokes parallels to point-defect phenomena. The structure of amorphous silicates is described statistically: bond lengths and bond angles have distributions. Defects, then, can be viewed as extraordinary bond lengths and angles, a perspective originally championed by Schaeffer [16]. Based on dynamical similarities between the amorphous and crystalline states, one may anticipate the creation of such defects at equilibrium concentrations of a part per thousand, atomic, or less. The defect concentrations, being functions of both temperature and chemical potential(s), can be characterized through chemical equilibria. One effective approach to this end is an application of the polymerization model of Hess [8]. The Hess model evaluates polymerization of amorphous silicates by paying particular attention to the bonding environments of oxygen anions: structural elements in reactions are described by having the bonds to each O2– characterized by a summed Pauling bond strength (electrostatic valence) of two; these elements are then used to write reactions that are balanced both in matter and in charge. For example, in the case of the oxidation of a glass or glassmelt at its free surface, network-modifier Fe2+ reacts with atmospheric oxygen to create networkmodifier Fe3+; in Hess notation, 4 SiOFe0 5 + SiOSi + ½ O2 g = 6 SiOFe0 33

13

In reaction (13), SiOSi represents a bridging oxygen, 2 SiOFe0.5 represents a network-modifier Fe2+, which provides one positive charge to each of two O2–, and 3 SiOFe0.33 represents a network-modifier Fe3+, which is the manifestation of an electron hole, or small polaron, in the amorphous structure. By inspection, one sees that reaction (13) is atomically balanced. The reaction is charge-balanced as well: two Fe2+ cations have provided one electron each to ionize the neutral oxygen atom, which is then bonded to the amorphous silicate. The reaction is depicted schematically in Figure 4a, whose part (1) represents the left side of the equilibrium and part (2) the right, Fe2+ being represented by the generic M. One easily imagines that the bonding of the oxidized iron (Fe3+ ≡ M–h• in the figure) to three O2– anions instead of Fe2+ to two anions distorts locally the structure of the glassmelt/glass; in Figure 4, this feature is depicted as a polyhedral void. Nevertheless, one understands that as the electron holes migrate inward, the distortion travels with them and divalent cations are displaced in the opposite direction (Figure 4b): in the kinetic response, the

589

5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

(a) (1) Si

Si

½O2

O

O

M

M

Free surface

O Si

Si

Si

(2)

Si

Si O

O

O

h•

Free surface

M

M h• O Si

Si

O

O

Si

O

O Si

Si

distortion acts effectively as a “vacancy” in the amorphous structure. As suggested by Greaves [17], Figure 4b additionally assumes a percolative nature for the spatial distribution of network-modifying oxide components in the amorphous state; such an interpretation is consistent with the redox reaction textures of sufficiently depolymerized melts/glasses [11, p. 317]. One can infer from reaction (13) that the oxidation reaction is depolymerizing because the bridging oxygen unit Si–O–Si is consumed. This is counter to experience according to which oxidized glassmelts increase in polymerization and so in viscosity. But it must be emphasized that reaction (13) is actually a “half reaction,” that is, the overall oxidation reaction is the sum of two half reactions, one at/near the free surface (depicted in Figure 4a) and the other at the internal reaction front, the two half reactions mediated and rate limited by chemical diffusion ([1], p. 104). As described above for some non-alkali oxide-bearing glasses, the reaction at a temperature near the glass transition causes precipitation of nm-scale ferrite at the internal interface. The simplified version of this half reaction, in Hess notation, is

(b)

6 SiOFe0 33 + 2 SiOM0 5 = MFe2 O4 Sp + 4 SiOSi, 14a

Si–O tetrahedra 2+

O

O

O

O h•

M

M

M h•

O

O

O

O

Si–O tetrahedra

where M here is either Mg or Fe (i.e. the magnesioferrite–magnetite solid solution; the subscript “Sp” standing for crystalline spinel). Here one sees the formation of four bridging oxygens as three network-modifying cations are extracted from the solution (plus the requisite amount of O2–) to form the crystalline ferrite. In glasses with alkali oxides, Fe3+ tends to have a network-former status, charge-compensated by a localized alkali ion that no longer fulfills a network-modifier role. Taking Na+ as the alkali species, one simplifies in Hess notation this half reaction as 6 SiOFe0 33 + 2 SiONa = 2 NaFeO2 + 4 SiOSi, 14b

Polaron Cation

where NaFeO2 represents the network-forming Fe3+ [8]; six bridging oxygens are formed in the consumption of eight nonbridging oxygens. A summation of reaction

Si–O tetrahedra O

O

O

O

M

M

O

O

h•

M h• O

O Si–O tetrahedra

2+

➤

590

Figure 4 Schematic illustration of small polaron dynamics in silicate glassmelts and glasses [13], with structural units based on the melt polymerization model of Hess [8]. M is a divalent networkmodifying cation; M–h• is a trivalent network-modifying cation. (a) Formation of a small polaron via oxidation (cf. reaction (13)): (1) unreacted glass/glassmelt and (2) formation of a polaron as two divalent network modifiers become trivalent network modifiers as atmospheric oxygen accepts two electrons and bonds into the glass/glassmelt as O2–. The structural distortion so created follows the migration of the h•. Note also the consumption of a bridging oxygen (Si–O–Si): this near-surface (half ) reaction is depolymerizing. (b) Migration of a small polaron, and the associated (counter) motion of the network-modifying cation, in a transition metal-bearing silicate glass/glassmelt.

4 Open-System Redox Dynamics

(13) with either reaction (14a) or (14b) illustrates a definite net increase in polymerization for the oxidized glass/ glassmelt. The simplification in reactions (13) and (14) is that each half reaction must have as a product the mobile species that “communicate” the oxidation potential between the external and internal interfaces. The free-surface reaction, reaction (13), clearly produces 2h• (≡ 6 SiOFe0.33), which diffuse inward; a more complete description of reaction (14a and b) at the internal interface must include the fact that the structural relaxation that results in precipitation of ferrite or in incorporation of Fe3+ as an alkali-ion-compensated network former must also “release” divalent network modifiers to diffuse toward the free surface. These more complete reactions are described in [12] and in the references cited there. 4.3 Open-System Reduction and the Float-Glass Reaction Under some circumstances, dynamic reduction can be understood as the mirror image of the oxidation process. Specifically, O2− is chemically ablated (i.e. by reaction with neutral species in the atmosphere) from the free (a)

Sn2+ Sn redox levels

Sn4+ Sn oxide-rich layer ∼10 nm

Sn Fe

10–40 μm Sn “hump” (Sn4+ max.)

Steep decline in Sn conc. to ∼500 nm

Nominal semiinfinite diffusion profile

Concentration

Figure 5 Open-system redox dynamics in the NCS-on-Sn float-glass process [6]. (a) Schematic summary of chemical observations of ionic Sn and Fe in the near-float-surface region (~50–100 μm) of the glassmelt ribbon. Ionic Sn is concentrated in the first 500 nm and then assumes a Fickian compositional profile, but one punctuated with an anomalous buried hump. Ionic Fe is depleted in the region of Sn diffusion, but shows an anomalous maximum near the depth limit of Sn penetration. Sn2+ is the dominant Sn oxidation state at/near the surface, giving way to Sn4+ at the position of the Sn hump (see top of schematic). The concentration humps for Sn and for Fe are evidence of two internal redox couples effecting local structural change in the glassmelt. (b) Schematic of fluxes (with senses shown) and internal reaction fronts (ξ and ξ ) active in the glassmelt/float-metal reaction, consistent both with the chemical profile presented in (a) and with an understanding of dynamic reduction effected by cation diffusion.

surface in a half reaction that consumes h•; the reaction both decreases the activity of h• and increases the activity of divalent-cation oxides at the free surface, impelling outward diffusion of h• and inward diffusion of M2+ network-modifying cations. These dynamics are essentially the reverse of reaction (13) and of Figure 4a, i.e. consider the compound figure in the order (2) (1). Structural relaxation of the glassmelt/glass occurs at an internal interface, one that shifts ever deeper, following parabolic kinetics. Depending upon the thermodynamic conditions, the internal reaction can yield, too, precipitation of nm-scale precipitates of metal ([11], p. 326). The foundation of the float-glass reaction, from the perspective of the glassmelt ribbon, is dynamic reduction that is accompanied by solution formation; the metallic float medium experiences oxidation and solution formation, but this side of the reaction is not rate limiting and so is ignored here. The thermodynamics was articulated in Section 2.2 and illustrated in Figure 2. At the molten tin/glassmelt interface, tin is oxidized through electron donation to cations in the silicate, which are reduced: Sn2+ then is incorporated into the glassmelt, and metallic Na (particularly), Si, Fe (a minor component of NCS glass), and Ca are added in various amounts to the tin bath. The reaction texture is telling (Figure 5a).

ξ=0

Fe maximum

ξ

Depth

(b) Float metal

Glassmelt j Na+

j Mo

j Mn+

j Sno

j Sn2+

j h•

j Mn+

j Fe2+

j Fe2+

j Sn4+ ξ=0

ξʹ

ξʺ

ξ

591

5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

(a) 0

fO

2

=

6.

4×

–100

10 – 1

5

at

m

Q)

–200

–300

ΔrG°= RT In fO2 (kJ [mol O2]–1)

+O 4 SiO

:2

–400

G° Δr

2

+

O3 Fe 2 =2

Fe 2

°: 2

CO

iO 2 2S

2 +O

=2

CO

ΔrG: FHQ

–500

O:CO 2

Δ rG: 2

–600

(FH

2

IW-4.5 1400 °C reaction conditions

G Δr

CO + O 2

;C = 2 CO 2

:1

= 750

O2

)+

O2

=

(s

G Δr

:2

:2

–800

Δ

Si

s) O(

+O

2

Si

iO 2

O

–700

2

=

2S

Si

° rG

–900

–1000 –200

0

200 400 600 800 1000 1200 1400 1600

Absolute zero

Temperature (°C)

(b) –300

Closed-system cooling redox potential

2C

O+

RT In fO2 * (kJ [mol O2]–1)

592

–400

O2 =

2C

IW-4.5 1400 °C reaction conditions

O2 (

ΔrG potential drops for reduction of C4+ via oxidation of Fe2+ and/or Si2+ on cooling

fixed

C 2+

: C 4+ )

2 Fe2SiO4 + O2 = 2 Fe2O3 + 2 SiO2 –500

(fixed Fe2+:Fe3+) 2+

iO 2S

–600 1200

1250

(s)

+

=2

SiO

2

ed (fix

Si

+ i4 )

:S

O2

1300 Temperature (°C)

1350

1400

5 Closed-System (or Internal) Redox Dynamics

Employing a variety of analytical techniques, surfacescience studies of the float-bath side of the glassmelt ribbon reveal Fick’s second law diffusion profile for ionic Sn extending into the silicate. This profile, however, is punctuated by an anomalous Sn-concentration hump, which is distinctly inconsistent with simple diffusion-effected solution formation [6]. Near the end of ionic Sn penetration, one also finds an anomalous hump of the ionic Fe concentration. These humps are unequivocal evidence of reaction-effected changes in the internal atomic structure of the glassmelt, both of which are related to redox dynamics. Referring to the schematic geometry depicted in Figure 5b, one sees that the Sn hump corresponds to a location where Sn2+, a reasonably mobile network modifier, is oxidized to Sn4+, which, if still too large a cation to be a network former, will have a notably diminished mobility compared with Sn2+ in the glassmelt. The location of this internal interface (ξ = ξ in Figure 5b) corresponds to the position where the activity of SnO is sufficiently high to drive a redox couple where 2h• are consumed in the creation of Sn4+. This reaction creates a “sink” for h• at ξ , which is dealt with by a flux of h• emanating from the deeper interface ξ , the site of the internal reduction reaction. At ξ , reaction (14b) is driven from the right to the left, i.e. Na+-compensated networkformer Fe3+ is reduced to a combination of networkmodifier Fe3+ (≡ h•), network-modifier Fe2+, and network-modifier Na+. The physics of the reactions and the nature of the fluxes depicted in Figure 5b are justified in Ref. [6]. As evidence in its favor, we have employed this analysis to demonstrate distinct control of the kinetics of the float reaction by (i) doping the glassmelt with additional electron acceptors (Fe3+), (ii) alloying strongly the float medium (i.e. to lower the activity of Sn), and (iii) replacing Sn altogether in the float medium with an alloy whose oxidizable component, when fully ionized, assumes a definite network-former role within the glassmelt (e.g. Ge).

5 Closed-System (or Internal) Redox Dynamics The other end-member dynamics are where diffusion beyond the molecular scale is not anticipated because of either (i) sluggish kinetics at low temperature or (ii) little time spent at an elevated temperature. The extreme situation of this type is thermal quenching, where the thermal diffusivity and heat flux outstrip the transport coefficient of any atomic/ionic component of the system. In such situations, the composition of the glassmelt/glass cannot change, but the redox potentials can because of the relative temperature effects on the activity coefficients of the components. This evolution of the redox potentials is illustrated with an Ellingham-diagram analysis in Figure 6, which compares open- and closed-system thermodynamics for an iron-oxide-bearing calcium–magnesium aluminosilicate melt that has been driven to equilibrium with a very low oxygen activity [18]. The condition where T = 1400 C and the oxygen activity is controlled and sustained at 6.4 × 10–15 (i.e. an ambient-pressure fugacity of f O2 = pO2 = 6.4 × 10–15 atm) is noted in Figure 6a as the center of the small circle, nominally at the right center of the diagram, whose ordinate is –460 kJ/(mol O2). This condition is highly reducing: the oxygen activity is four and a half order of magnitude below that for the reaction between metallic iron and the mineral wüstite (“IW–4.5”) for this temperature. In this example, the oxygen activity is created and sustained by dynamic mixing and reaction of CO(g) and CO2(g) at a ratio of 750 : 1; thus, beyond setting the oxygen activity, the glassmelt at equilibrium must incorporate carbon oxides in forms that include physically dissolved molecular species (i.e. present in the free volume of the melt) as well as chemically dissolved ionic/covalent species (i.e. incorporated into the structure of the glassmelt as, e.g. carbonate, carbonyl, or even

➤

Figure 6 Thermodynamic analysis associated with open-system reduction and closed-system (internal-redox-couple) quenching [18]. (a) Ellingham diagram drawn to demonstrate equilibration of an iron-oxide-bearing calcium–magnesium aluminosilicate glassmelt held at 1400 C and maintained at an oxygen activity (fugacity, f O2 ) of 6.4 × 10–15 atm. In this example, the low-oxygen-fugacity environment was set by dynamic mixing of carbon monoxide and carbon dioxide at a ratio of CO : CO2 = 750 : 1; at 1400 C, this produces an f O2 that is four and a half order of magnitude lower than the iron–wüstite buffer, i.e. “IW–4.5.” Equilibrium requires that each and all of the ΔrG curves (solid lines) must rotate – that is, all activities are adjusted (cf. Eq. (4)) – such that all ΔrG curves (dashed lines) converge at the thermodynamic conditions. In the figure, the only ΔrG and ΔrG lines presented are those involving heterovalent cations – C2+,4+, Si2+,4+, and Fe2+,3+. The reaction depicted as fayalite–hematite–quartz (FHQ) is used for the Fe2+–Fe3+ equilibrium, consistent with the solution model MELTS [10]. (b) A close-up of Ellingham “space” for quenching. From the equilibrium condition, one evaluates an effective oxygen potential (fugacity, f ∗O2 ) by holding the mole fractions constant – the definition of quenching – but allowing the activity coefficients to change with temperature. The solid curve is the effective oxygen potential calculated for the FHQ reaction directly from MELTS. The dash-dot-dot curves are logical postulates based upon limited solution data for Si2+,4+ and C2+,4+. The divergence of the curves demonstrates that there develops a potential upon cooling to reduce C4+ to C2+ through a redox couple that oxidizes Fe2+ and/or Si2+. The extent of these reactions in reality (in this case, causing bubbles of CO(g) to form, C2+ being especially insoluble in aluminosilicate melts) depends on the thermal history, particularly the cooling rate.

593

594

5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

carbide species). Equilibrium with the open system requires all of the component oxide ΔrG(T) curves (lines) to converge at the aforementioned condition. Some of the Ellingham ΔrG (T) lines rotate clockwise, some counterclockwise. Most of the rotation is based on the activity effects of forming the glassmelt solution, although the impact of oxygen activity on curve rotation is significant. In the analysis of quenching, one determines an “effective” oxygen activity, presented in Figure 6b as an effective fugacity, f ∗O2 , by holding mole fractions fixed but evaluating the potential based on the temperature sensitivities of the various activity coefficients ([3], p. 240). Consider the Fe2+–Fe3+ equilibrium. Because fayalite and hematite are the components representing ferrous and ferric iron, respectively, in the MELTS solution model [10], the reaction of interest is fayalite (Fa) being oxidized to hematite (Hm) plus quartz (Q): 2Fe2SiO4 + O2(g) = 2Fe2O3 + 2SiO2 (“FHQ”). The mass-action relationship for the glassmelt is Δr G1400

C

= − 460 kJ mol O2

−1

= Δr GoT ,FHQ + RT ln γ 2Hm X 2Hm γ 2Fa X 2Fa

γ 2Q X 2Q f ∗O2

15 ,

where Xi is the mole fraction and γ i (=γ i(T)) is the activity coefficient, both of species i in the glassmelt solution, and f ∗O2 is in units of atm (i.e. the oxygen term becomes unitless by its normalization to 1 atm). The calculation is “pinned” to the condition where equilibrium was established at 1400 C. As temperature is lowered, Δr GoFHQ evolves as do the γ i; holding the Xi fixed at their values of the original 1400 C equilibrium allows calculation of f ∗O2 ,FHQ T , which is shown as the FHQ∗ solid line in Figure 6b. The slope of FHQ∗ is steeper than the FHQ curve in Figure 6a. Given good solution models, similar calculations might be done for the CO/CO2 and SiO/SiO2 equilibria, which, unfortunately, have not been calibrated. The dash-dot-dot curves in Figure 6b are thus drawn based on inferences from the literature concerning the solubilities of the various species in an alkaline earth aluminosilicate melt. One sees that, with increased cooling, a greater and greater potential develops for the reduction of C4+ to C2+ by acceptance of electrons from Fe2+ and Si2+. Whether the redox-exchange reaction is realized, of course, depends on the kinetics of cooling and on any subsequent thermal treatment. Since the redox exchange is accompanied by structural relaxation of the glassmelt or glass, the kinetics will be phonon assisted, again following Boltzmann statistics.

The thermodynamics described in Figure 6b can be applied to decipher a variety of phenomena encountered in glassmaking and also to understand the structure and chemistry of melts from studies of quench specimens. Brightly colored “ruby” glasses are created by the precipitation of noble (e.g. Au) or relatively noble (e.g. Ag, Cu) colloidal metal via “striking,” i.e. driving a closedsystem redox exchange by reheating a formed, often colorless glass (Chapter 6.2). In gold ruby glasses, the gold in the high-temperature glassmelt exists in ionized form (Au+ ± Au3+). To produce colloidal metal, a reducing agent is added, a typical one being SnO, although oxides of Se and Te have been used historically as well [19]. The thermodynamics of striking are directly analogous to the closed-system C–Si–Fe redox couples presented in Figure 6b. Reheating and holding the glass at a temperature below its original melting/solution temperature, usually between the annealing and softening points, provokes the redox exchange Au2O + SnO = 2 Au + SnO2; the magnitude of the ΔrG exchange potential allows the barrier to crystal nucleation to be overcome. The “soak” time of anneal is selected to effect growth of the colloidal metal crystals so as to achieve the desired color and saturation. The growth process is an Ostwald ripening. Its slowness is due to the insolubility of metal atoms in the silicate solution, since diffusion through the silicate is accomplished by ions and not by atoms ([20], p. 723). These very same physics effect the precipitation of Pt metal inside quenched melts that are initially prepared in platinum crucibles or in Pt-lined production furnaces [7]. Platinum, too, dissolves into glassmelts as an ionic species ([20], p. 723); as a consequence, melts with as high a polymerization as practicable that are melted in a reducing atmosphere minimize the incorporation of Pt2+ and Pt4+ and so the potential for its internal reduction into metal precipitates [7]. In contrast, the solubility of platinum-group elements (PGE: Ru, Rh, Pd, Os, Ir, and Pt) in highly depolymerized, high-temperature aluminosilicate melts is of particular interest with regard to understanding the chemistry and physics of terrestrial planetary differentiation and core formation. For years, this solubility was underestimated because of the formation of PGE metal “micronuggets” within the quenched experimental charges: this metal was not understood to have precipitated as a result of a closed-system redox reaction such as described here. The correct explanation has been arrived at through clever experiments under extreme conditions (2500 C; 2.2 GPa), whereby a highly MgO- and FeO-rich aluminosilicate melt was reacted with platinum metal in the context of containment within a graphite capsule. When the melt experienced sufficiently rapid cooling and a

References

sufficient cooling-rate gradient, the redox-effected precipitation of metal and of CO(g) in the more slowly cooled regions of the charge could be observed along with the high solubility of ionic Pt and C corresponding to the experimental conditions [21]. The carbonate (or carbonyl) reduction to CO(g) follows exactly the physics depicted in Figure 6b. The removal of gas bubbles or “seed” by fining of glassmelts has long involved application of redox agents, particularly As3+,5+ and Sb3+,5+, a practice that is now less frequent owing to environmental and worker-health concerns and also, in the case of glass used as substrates for electronic displays, because of chemical incompatibilities between these group 15 metalloids and silicon- or germanium-based circuitry. The pentavalent oxides added to the glass batch are reduced to the trivalent state during melting. For many years, the release of oxygen gas by the reaction, e.g. As2O5 = As2O3 + O2(g), was thought to facilitate the gravity-driven migration of bubbles to the free surface. Given the small amount of pentavalent oxide added to the batch, however, calculations of Stokes’ flow dynamics of bubbles so produced suggest that this reaction represents a minor contribution to fining. Rather, the re-oxidation to the pentavalent state at a lower temperature can absorb oxygen from the bubbles and thus cause them to shrink [22, 23]. Overall, the physics of fining are a convolution of the open- and closed-system cases presented above. Again, one can understand the driving potential for the trivalent-to-pentavalent oxidation reaction in a way consistent with the closed-system description of Figure 6b, but at issue is the amount of physically dissolved O2(g) in the glassmelt. As the glassmelt cools, thermal contraction reduces the free volume of the melt; consequently, the chemical potential of the physically dissolved O2(g) increases. Re-oxidation of the fining agent consumes some of this physically dissolved oxygen through its incorporation into the melt structure as O2– and so affects locally the structure of the glassmelt. The modified glassmelt can thus accept more O2(g) molecules from the bubble, shrinking it. This situation is similar, of course, to the surface reactions associated with an open system. Kinetic models for bubble shrinkage in the reaction so described employ a simple Fick’s second law approach but are only partially successful: despite being rate limited by diffusion of molecular oxygen, the dynamics probably has more in common with the open system as depicted as mode I in Figure 3, where the internal interface is the place where the trivalent-to-pentavalent reaction and structural relaxation occur. Particularly in NCS glassmelts, an additional aspect of the fining process is that the Na2O and CaO components are frequently introduced as carbonates in the batch.

Breakdown of these carbonates produces CO2(g), which makes up a significant component of the gas bubbles to be removed in fining. Again, consistent thermodynamically with Figure 6b, redox couples between the CO2 and the trivalent metalloid oxide component in the glassmelt oxidize the metalloid to the pentavalent state while producing CO(g), whose transport coefficient through the glassmelt to its free surface is much, much greater than that of CO2(g) ([24], p. 210).

6

Perspectives

The bulk properties of glasses such as color, electronic and ionic conductivity, viscosity, etc. are directly related to atomic-level structure and, thus, to ion valence. Endowing a bulk glass with specific properties via internal (closed-system) redox couples is a thermochemical design problem of broad flexibility because it makes available control of chemical activities via composition and of cooling-effected driving potentials in both post-melting and post-forming processing; optimal protocols can be identified via multivariable experimental design. More intriguing, however, are the possibilities of open-system redox in affecting/effecting electro-optical response in glass at or near the free surface. Consider, for example, a processing approach whereby the float bath is alloyed with transition element or rare earth metals so as to incorporate these in the near surface of the glassmelt via redox exchange. Depending on the initial composition of the glassmelt, the combination of redox exchange and solution formation can produce not just one specific location of a controlled local structure (like the Sn hump in conventional NCS float glass; Figure 5a) but multiple layers of such structure, i.e. redox-effected Liesegang banding. Optical interference and amplification are potential responses that can be so controlled.

References 1 Schmalzried, H. (1981). Solid State Reactions, 2e.

Weinheim, FRG: Verlag Chemie. 2 Kubaschewski, O., Evans, E.L.L., and Alcock, C.B. (1967).

Metallurgical Thermochemistry, 4e. Oxford: Pergamon. 3 Paul, A. (1990). Chemistry of Glasses, 2e. London:

Chapman and Hall. 4 Darken, L.S. and Gurry, R.W. (1953). Physical Chemistry

of Metals. New York: McGraw-Hill. 5 Pilkington, L.A.B. (1969). The float glass process. Proc.

Roy. Soc. London A314: 1–25.

595

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5.6 Redox Thermodynamics and Kinetics in Silicate Melts and Glasses

6 Cook, G.B. and Cooper, R.F. (1999). Redox dynamics in

7 8

9

10

11 12

13

14

the high-temperature float processing of glasses. I. Reaction between undoped and iron-doped borosilicate glassmelts and a gold–tin alloy. J. Non-Cryst. Solids 249: 210–227. Ginther, R.J. (1971). The contamination of glass by platinum. J. Non-Crys. Solids 6: 294–306. Hess, P.C. (1980). Polymerization model for silicate melts. In: Physics of Magmatic Processes (ed. R.B. Hargraves), 3–48. Princeton, NJ: Princeton University Press. Blander, M. and Pelton, A.D. (1987). Thermodynamic analysis of binary liquid silicates and prediction of ternary solution properties by modified quasichemical equations. Geochim. Cosmochim. Acta 51: 85–95. Ghiorso, M.S. and Sack, R.O. (1995). Chemical masstransfer in magmatic processes 4. A revised and internally consistent thermodynamic model for the interpolation and extrapolation of liquid-solid equilibria in magmatic systems at elevated-temperatures and pressures. Contrib. Mineral. Petrol. 119: 197–212. Mysen, B.O. and Richet, P. (2005). Silicate Glasses and Melts: Properties and Structure. Amsterdam: Elsevier. Cook, G.B. and Cooper, R.F. (2000). Iron concentration and the physical processes of dynamic oxidation in an alkaline earth aluminosilicate glass. Am. Mineral. 85: 397–406. Cooper, R.F., Fanselow, J.B., Weber, J.K.R. et al. (1996). Dynamics of oxidation of a Fe2+-bearing aluminosilicate (basaltic) melt. Science 274: 1173–1176. Pommier, A., Gaillard, F., and Pichavant, M. (2010). Time-dependent changes of the electrical conductivity of

15

16 17 18

19 20

21

22

23

24

basaltic melts with redox state. Geochim. Cosmochim. Acta 74: 1653–1671. Magnien, V. et al. (2008). Kinetics and mechanisms of iron redox reactions in silicate melts: the effects of temperature and alkali cations. Geochim. Cosmochim. Acta 72: 2157–2168. Schaeffer, H.A. (1984). Diffusion-controlled processes in glass-forming melts. J. Non-Cryst. Solids 67: 19–33. Greaves, G.N. (1985). EXAFS and the structure of glass. J. Non-Crys. Solids 71: 203–217. Cooper, R.F., Everman, R.L.A., Hustoft, J.W., and Shim, S.-H.D. (2010). Mechanism and kinetics of reduction of a FeO-Fe2O3-CaO-MgO aluminosilicate melt in a high-CO-activity environment. Am. Mineral. 95: 810–824. Stookey, S.D. (1949). Coloration of glass by gold, silver, and copper. J. Am. Ceram. Soc. 32: 246–249. Nernst, W. (1904). Theoretical Chemistry, transl. from the 4th German ed. by R.A. Lehfeldt and C.S. Palmer. London: Macmillan. Cottrell, E. and Walker, D. (2006). Constraints on core formation from Pt partitioning in mafic silicate liquids at high temperatures. Geochim. Cosmochim. Acta 70: 1565–1580. Greene, C.H. and Lee, H.A. Jr. (1965). Effect of As2O3 and NaNO3 on the solution of O2 in soda-lime glass. J. Amer. Ceram. Soc. 48: 528–533. Doremus, R.H. (1960). Diffusion of oxygen from contracting bubbles in molten glass. J. Am. Ceram. Soc. 43: 655–661. Doremus, R.H. (1994). Glass Science, 2e. New York: Wiley.

597

5.7 Optical Basicity: Theory and Application John A. Duffy University of Aberdeen, Old Aberdeen, Scotland, UK

S iron + O2 – slag = S2 – slag + O2

1 Introduction: The Need for a Suitable Basicity Scale for Oxide Melts Ordinary glass is made by heating a mixture of basic oxides, Na2O, CaO, etc. with SiO2. The vast range of possible compositions allows much scope for optimizing properties such as refractive index or color, mechanical strength, or high-temperature chemical reactivity. Extensive correlation studies have shown convincingly that properties of the glass or melt rely heavily on chemical composition in terms of basicity (basicity rather than acidity, because usually bases are the focused variable). For many years, however, the quantifying of basicity was a frustrating problem. Probably the most serious limitation to progress was to disregard the fundamental difference of the O2– ion compared with other monatomic anions that are usually encountered in solution chemistry. These are singly charged, but for oxygen, addition of a second electron to the already charged O– ion is thermodynamically unfavorable. In the present context, this questions the viability of the O2– species. The seriousness of this problem is illustrated by the questionable adoption of the Lux-Flood theory (a discussion of which is in [1]) together with its analogy of p(oxide) with pH and also by the improbable anionic counterions suggested for redox equilibria. As illustrated by many examples, redox reactions impinge greatly on molten salt chemistry. Thus, for the Fe2+/Fe3+ ion couple in the manufacture of glass, the equilibrium might be written as 4Fe3 + + 2O2 – = 4Fe2 + + O2 air

1

Likewise, the refining action of metallurgical slags can be described by Reviewers: M.D. Ingram, University of Aberdeen, Old Aberdeen, Scotland, UK E.I. Kamitsos, National Hellenic Research Foundation, Athens, Greece

2

Thermodynamic approaches to such equilibria are not straightforward. Indeed, Eq. (1) suggests that increasing melt basicity favors the lower oxidation state cation, whereas experimentally one usually observes the reverse. There was much research effort attempting to deal with the problems, especially in view of their technological importance. Overall, the literature of the time (up to the 1970s), and meetings of professional groups, reflected notable conflict. What was needed was a chemically convincing theory with a numerical scale that would facilitate meaningful comparisons between, say, a sodium silicate, a potassium silicate, and a sodium borate melt. Trends in physical and chemical properties would then be linked directly to this common scale rather than to chemical constitution. Such a scale was eventually provided in 1971 with the introduction of the optical basicity theory [2].

2 Theoretical Foundation of Optical Basicity With the concept of optical basicity, one considers an oxide glass or crystal in artificial terms as an array of its constituent cations, Na+, Ca2+, Si4+, … and O2– ions. Chemical bonding between these species, which can be described as Lewis acid–base neutralization, uses much of the negative charge on the oxygen. It is the remaining charge that chiefly causes those properties of the glass that are recognized as its basicity. Because this residual charge varies markedly with cation composition, it is the measuring of these changes in electronic charge that is at the heart of optical basicity. To achieve this goal, probe cations are dissolved in the molten glass. They were specially chosen, so when they are coordinated by the oxygen atoms of the glass, they

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

598

5.7 Optical Basicity: Theory and Application

would signal fundamental features of the chemical bonding. Transition metal ions can be seen as an obvious choice because their bonding is understood in terms of molecular orbital theory (which, as the ligand field theory, had been purposefully developed for inorganic coordination chemistry during the years leading up to ~1950). Their d–d spectra, obtained using conventional UV/visible/near-infrared (optical) spectroscopy, reveal a decrease in repulsion energy between the electrons in their d-level. It is this effect that concerns the optical basicity model because, vitally, it provides a simple description of the chemical bonding between the probe ion and the oxygen atoms of the glass. For transition metal complexes, chemical bonding generally results in the d electrons experiencing greater shielding from the positive nucleus, extra to that provided by the core electrons. Consequently the d orbitals expand and the d–d repulsion decreases. It was C.K. Jørgensen who referred to this expansion as the nephelauxetic effect [3]. The repulsion between the d electrons is expressed as the Racah B parameter. For the free uncombined metal ion, this important energy (frequency, Bf) is known from its atomic spectrum, which is published in standard tables. When the metal ion is complexed by the ligands and the orbitals expand, Bf falls to Bcomplex. Since Bf represents 100 % ionicity, decreasing B can be taken as the introduction and increase of covalency within the bond between the ligand and metal ion. Jørgensen assigned the proportional reduction of the Racah parameter, i.e. the ratio (Bf – Bcomplex)/Bf, to the contributions of ligand and metal ion (parameters h and k) such that Bf – Bcomplex = hk Bf

3

The h parameter was set at unity for the H2O ligand in crystalline aqua complexes such as [Ni(H2O)6]2+, [Cr(H2O)6]3+, etc. The d–d absorption spectra of these complexes allow the parameter k to be derived for each metal ion. With these parameters to hand, one can then determine the values of h for Cl–, NH3, … from the spectra of chloro, ammine, and other complexes. The set of h and k values shows good consistency on going from one complexed metal ion to another. For what would be the optical basicity model, the strategy adopted is to restrict the donor atom to oxygen (always in the oxidation state of −2 and denoted oxide(-II)), and therefore to regard the coordination by the aqua ligand as a particular case for oxide(-II) ligands. In short, this scheme has the great interest in allowing the complexation of metal cations by silicate, borate, etc. to be considered in terms of molecular orbital theory, that is, in terms of the nephelauxetic effect. In practical terms, however, obtaining Bcomplex from d–d absorption spectra is complicated. Fortunately, past

investigations have shown that one can avoid much difficulty by using instead the s–p spectra of (n − 1)d10ns2 metal ions such as Pb2+ and Tl+ [4]. Their UV absorption bands, which arise from transitions to the (n − 1) d10ns1np1 configuration, are Laporte allowed and very intense, even for the nominally spin-forbidden 1S0 3P1 band. This band has the lowest energy and usually presents itself with a clearly defined frequency maximum, which we label ν. Significantly, this frequency has features in common with Bcomplex so that it can be used for estimating covalency changes in the oxide(-II) bonding with the metal ion. For example, the frequency ν is linearly proportional to the h parameters of Cl−, Br−, NH3, etc. However, since the frequency shifts for the variation of Bcomplex on the one hand and the 1S0 3P1 (6s 6p) on the other arise from very different mechanisms, the extrapolated frequency values of νf for the Pb2+ and Tl+ ions in the free gaseous state (that is when h is zero) will not necessarily be exactly the experimental values. Indeed, this was found to be the case, with νf equal to 60 700 cm−1 for Pb2+ and 55 300 cm−1 for Tl+ (experimental values for the free ions being, respectively, 64 391 and 52 393 cm−1). These optical-spectroscopy results and others [4] were regarded as promising for constructing an acid–base scale suitable for measuring the basicity of melts and glasses. Already there is a defined zero, which is the free ion value of the 1S0 3P1 frequency, νf, for (n − 1)d10ns2 ions – admittedly an “adjusted” free ion value. Initially, attention was directed mainly toward the Pb2+ ion on which to construct the basicity scale (although the Tl+ and other ions were also used). In order to avoid the many problems associated with the idea of “100 % covalency,” pragmatically crystalline calcium oxide was chosen for unit optical basicity. The Pb2+ ion in the highly basic CaO environment has its 1S0 3P1 band frequency, νCaO, at 29 700 cm−1, and hence the frequency range from 100 % ionicity to the CaO environment, (νf − νCaO), is 60 700–29 700 cm–1, i.e. 31 000 cm−1. Writing νmedium for the probe-ion frequency in the medium under investigation, for example, a glass, one defines the optical basicity, Λ, by analogy with the Racah B parameter as the proportional energy change, (νf – νmedium)/(νf – νCaO) [2]: Λ=

60 700 – νmedium , 31 000

4

or, for when Tl+ is used, Λ=

55 300 – νmedium 18 300

5

When the probe ion is added to the melt (e.g. as a 10−3 molar nitrate), the salt readily decomposes, and the metal ions occupy the sites presented by the network medium (we can usually ignore the small quantity of oxide(-II) that

2 Theoretical Foundation of Optical Basicity

is generated). An example of the use of Eq. (4) is for Pb2+ dissolved in a sodium borate (20 mol % Na2O) glass (Figure 1), where νmedium is 45 000 cm−1 and therefore Λ = 0.51. Usually although not always, optical basicity is quoted to two decimal places, but for comparative purposes it can be useful to have three places. Of course, it is necessary that the glass has good UV transparency, although fluorescence spectroscopy can also be used for lower-quality samples. With the accumulation of optical basicity data for a variety of glasses, the next step is to consider how Λ is related to chemical constitution. In addressing this question, we return to the artificial model, which is the starting point of optical basicity, and consider how the array of oxide(-II) ions becomes neutralized by the constituent cations. For example, in the glass CaO–SiO2 (40 : 60, mol ratio), taking the formula as Ca2Si3O8, it is seen that neutralization would be one quarter by the Ca2+ and three quarters by the Si4+. In the general case, these are the equivalent fractions of the oxides X(oxide A), X(oxide B), etc. Additionally, however, the tendency for covalency causes the electron donor power of the oxide(-II) ions (atoms) to be further decreased, being affected more by the silicon than by the calcium. With this simple picture, a new factor is introduced, the basicity moderating parameter, symbol: γ A, γ B, …, such that

Λ=

X oxide A X oxide B + + γA γB

This equation is the fundamental expression of optical basicity. For a binary oxide, X(oxide) is unity and Λ is simply 1/γ M, so Eq. (6) becomes Λ = X oxide A Λ oxide A + X oxide B Λ oxide B + 7 Following this, use is often made of relationships of the type γA =

X oxide A Λ – X oxide B γ B

8

It is important to use Eq. (7) with caution because an isolated binary oxide might behave with a different γ value when present in glass. This happens for P4O10 in the Na2O–P2O5 glass system when, initially, its Λ value, 0.48, appears to decrease with addition of Na2O, so the 1 : 1 glass unexpectedly has the same optical basicity as that of the original phosphorus(V) oxide. Lithium borate glasses behave similarly when the stereochemistry of boron changes from trigonal planar to tetrahedral. For silicate systems, however, this complication seldom arises, so it has been consistently found that γ is 2.100 ± 0.001 for silicon. By Eq. (8), it thus becomes possible to obtain the γ M values for other metal ions using the spectroscopically obtained Λ values that are available (Table 1). These are substituted into Eq. (6) to calculate Λ of the medium,

1

Table 1 Original (pre-2002) values of γ M for cationsa and Λ for binary oxides.

Absorbance

0.8 Cation

Basicity moderating parameter, γ M

Optical basicity, Λ(oxide)

Lithium

1.00

1.00

Sodium

0.87

1.15

Potassium

0.73

1.4

Cesium

0.60

1.7

Calcium

1.00

1.00

0.6

0.4

0.2

30 000

33 000

40 000

Wavenumbers

45 000

50 000

(cm–1)

Figure 1 Optical absorption spectrum (in the UV region) of Pb2+ probe ion dissolved in sodium borate glass (20 mol % Na2O). Pathlength: 1.5 mm; Pb2+ concentration (nominal): 1.1 × 10−3 M. Note: Increasing wavenumber corresponds to decreasing wavelength, e.g. 30 000 cm−1 ≡ 333 nm and 50 000 cm−1 ≡ 200 nm.

6

a

Strontium

0.9

1.1

Barium

0.87

1.15

Magnesium

1.28

0.78

Aluminum

1.65

0.60

Silicon

2.10

0.48

Boron

2.35

0.42

Phosphorus

2.5

0.40

See Table 3 for post-2002 values.

599

600

5.7 Optical Basicity: Theory and Application

thereby allowing one to correlate the chemical formula of the glass or slag with its physical and chemical properties [4]. Thus it is possible to predict changes in physical/chemical properties from changes in the chemical formula of the melt. Sometimes it is necessary to consider two important questions: (i) whether the probe ion occupies already existing sites or whether it “misbehaves” and generates its own site and (ii) whether or not the optical basicity changes when the melt transforms to a glass, and vice versa. These two questions are intermingled and have been given careful consideration. As described below, it has gradually become apparent how Pb2+, Tl+, and various other probes play a valuable role for investigating glass, especially the chemical bonding and structure.

3

Redox Equilibria in Network Melts

Molten silicates, borates, and others are excellent solvents for redox equilibria many of which have technological application (Chapter 5.6). In extraction metallurgy, for example, it is vital to understand how chemical composition affects the ability of the slag to remove troublesome impurities from the molten metal ([5] and Chapter 7.4). In the case of sulfur that is present in molten iron, this property is measured as the sulfide capacity, CS, (defined as S × PO2 P S2 , where % S is the weight % of sulfur in the slag and P O2 and PS2 are the equilibrium partial pressures of O2 and S2). Experimental data for silicate and aluminosilicate blast-furnace slags at 1500 C show that the overall reaction expressed by Eq. (2) is related to the slag optical basicity by log C S = 12 0Λ – 11 9

9

As a more basic oxide is added, the increase in melt basicity results in the production of further nonbridging oxide(-II). For example, expressing this process as Ca2 + O2 – + Si – O – Si = Ca2 + + Si – O – + – O – Si,

increases with increasing optical basicity, which can be thought of in terms of the tendency for the anionic network to provide oxide(-II) “ions” for participation in Eq. (2). Many slag studies have been undertaken by extraction metallurgists for dealing with a wide range of impurities, such as sulfur, phosphorus, water, and so on [5]. Turning now to glassmaking, we note that the presence of redox ion pairs such as the Fe3+/Fe2+ couple often requires careful control of melt composition to stabilize the desired oxidation state [6]. Because of experimental difficulties, investigations have been limited to just a few ion pairs. It has been found that in contrast to the observation made above for sulfur, increasing optical basicity favors the upper oxidation state. To account for this feature, the metal ions are considered initially as being in the isolated, free state, a condition for which Λ is by definition zero. Both ions are unstable to the extent of their ionization energies, that is, the sum of the first + second for Fe2+ and the first + second and third for Fe3+. Increasing Λ of the melt corresponds to an increasingly negative environment, and this effects stabilization for both metal ions through chemical bonding in the formation of the [FeO6] or some other chromophore. Because of the larger cationic charge for the trivalent ion, however, a greater optical basicity is required for Fe3+. This extra charge can be pictured as being fed through electron delocalization (mainly by π-bonding) from the nonbridging oxide(-II)s generated in Eq. (10). The stabilization of upper oxidation state ions by increasing optical basicity is probably general (except for Cu2+/Cu+) and is satisfactorily expressed in terms of two empirical parameters, a and b: log

lower state upper state

= a – bΛ

11

Results for silicate melts at 1400 C and in an air atmosphere are summarized in Table 2.

10

one represents the transfer of the oxide(-II), initially in an electrovalent environment of CaO, to the silicate melt where it reacts with bridging Si–O–Si, thereby producing charged Si–O– units. The bonding between the Ca2+ ions and the anionic framework is essentially ionic since a charge of around +1.2 has been estimated to “reside” on the calcium. The balancing negative charge is spread over the oxide(-II) atoms, being more concentrated for the nonbridging oxide(-II)s than for the bridging. The optical basicity idea does not envisage unit negative charge on the nonbridging oxide(-II)s nor a zero charge for bridging oxide(-II)s. The overall charge

Table 2 Relationship of redox ratio, R, for ion couples with optical basicity; R = [lower state]/[upper state] in silicate melts at 1400 C in air atmosphere. Ion couple

Equilibrium

Fe3+

Fe2+

4Fe3+ + 2O2− = 4Fe2+ + O2

6+

3+

Cr

Cr

Ce4+

Ce3+

4+

2+

Sn

As5+

6+

4Cr

2−

+ 6O

log R

= 4Cr

3+

+ 3O2

4Ce4+ + 2O2− = 4Ce3+ + O2 4+

2−

+ 2O

2+

= 2Sn

3.2–6.5Λ 8.2–13.7Λ 5.5–8.3Λ

Sn

2Sn

+ O2

0.6–3.6Λ

As3+

2As5+ + 2O2− = 2As3+ + O2

5.2–8.9Λ

5 Chemical Reactions: Changes in Structure and Bonding

The optical basicity model is not restricted to glasses and melts but applies equally well to aqueous solutions [7]. Electrode potential data in acidic and basic aqueous solution at 25 C have provided a means for predicting a and b for several ion pairs for which no directly obtained results (at 1400 C) are available. By similar means, Λ has been correlated with the tendency for precipitation of the element out of the molten glass, for example, platinum, silver, and lead. It is of interest that early attempts to create a scale for basicity involved many studies of glasses containing redox ion pairs and correlating their equilibria with glass composition. UV/visible spectrophotometry was often used. With color changes occurring for decreasing basicity, commonly chosen ion pairs and their chromophores were Cr6+/Cr3+ (yellow owing to [CrO42−])/(green, owing to 3d3 [CrO6]); Mn3+/Mn2+ (red owing to 3d4 [MnO6])/ very pale pink (owing to spin-forbidden d5 [MnO6]); Ce4+/Ce3+ (orange owing to charge transfer)/colorless 5d band in the UV]); and the (owing to [Ce3+ 4f1 stereochemical change of Co2+ deep blue [tetrahedral CoO4/]pale pink [octahedral CoO6].

4 Optical Basicity and Electronic Polarizability To explore the possibility of a more “fundamental” optical basicity scale, investigation can be made into the relationship between Λ and the oxide(-II) electronic polarizability. The real part, n, of refractive index of glass is a measure of the reduction in the velocity of the photons as they induce oscillating distortions of the electron charge clouds when they pass through (Chapter 6.1). The electronic polarizability, α, expresses the ease of exercising this distortion for the particular cations and anions of the glass. These values are more or less fixed, except for oxide(-II) where αoxide(-II) varies over a wide range. In a glass the value of αoxide(-II) is part of the total electronic polarizability, αmol: one obtains it, therefore, by subtracting the total cationic polarizabilities, αi, and dividing by the number of oxide(-II) atoms assumed in the formula of the glass: αoxide -II =

αmol – αi total oxide -II

12

(formula weight/density) and N is Avogadro’s number. As an example, we take the glass of mole percentage composition 0.33 Na2O 0.095 CaO 572 SiO2, which has a refractive index of 1.529 and density of 2.652 g/cm3. Its arbitrary formula weight in grams is (33.3 × 61.98 + 9.5 × 56.08 + 57.2 × 60.08), and Vm is 6033/2.652 = 2275 cm3. From Eq. (13), αmol, the polarizability of the glass, is 278.25 Å3. We subtract the cationic polarizability of Na+, Ca2+, and Si4+, i.e. αi = 17.33 Å3 (using values of αM in Table 3), and divide by the number of oxide(-II) atoms assumed in the formula of the glass, i.e. 157.2. polarizability is therefore The αoxide(-II) (278.25 – 17.33)/157.2, i.e. 1.660 Å3. To derive now the sought-after “fundamental” optical basicity scale, the substitution into Eq. (6) is made using the most reliable basicity moderating parameters, namely, of calcium(II) and silicon(IV). Their γ M values are 1.00 (by definition) and 2.00 (cf. Section 2), respectively. In 2002, published refractivity data (n and ρ) were available for 15 calcium silicate glasses from 39.0 to 57.5 mol % CaO. From these data, values of αoxide are obtained as indicated above, and Eq. (6) gives Λglass values for each of the glasses. When plotted together with the same data for crystalline SiO2 and CaO (Figure 2), these data reveal the relationship very close to [8]: Λglass =

3 133αoxide -II – 2 868

1 2

1 567

– 0 362 14

Significantly, unlike the probe-ion method for measuring Λ, this new one is noninvasive and avoids the possible probe-ion misbehavior noted in Section 2. For many glasses the optical basicity ranges from approximately 0.3 to 0.65, an interval for which Eq. (14) can be simplified to: Λglass = 0 699αoxide -II – 0 547

15

In principle, Eqs. (13) and (12) then (14) or (15) allow the optical basicity of a (binary) silicate glass to be calculated from its density and refractive index and the γ M value to be obtained from Eq. (8). The values derived in this way are listed in Table 3. Mostly they differ only slightly from the earlier probe-ion method; lithium seems the single exception.

Use of the Lorentz–Lorenz relationship αmol =

3V m × 4π N

n2 – 1 , n2 + 2

13

allows αmol (in Å3) for the glass to be calculated (assuming isotropy) from the refractive index, n (usually the sodium D line), and density, ρ. In Eq. (13) Vm is the molar volume

5 Chemical Reactions: Changes in Structure and Bonding For technological reasons, the interaction of SiO2 with CaO, Na2O, etc. usually takes place in the lower-melting cullet. The optical basicity of SiO2 is 0.48, corresponding

601

5.7 Optical Basicity: Theory and Application

Table 3 Electronegativity, xM, polarizability, αM, and αoxide(-II) in binary oxides; basicity moderating parameter, γ M, also in glasses. Oxide

xM

xO–xM

xO

% ionicity

αM (Å3)

αoxide(-II) (Å3)

γM

Cs2O

0.79

1.49

2.28

80

2.42

0.66

Rb2O

0.82

1.51

2.33

73

1.40

0.70

K2 O

0.82

1.56

2.38

66

0.83

0.76

Na2O

0.93

1.65

2.58

54

0.179

0.905

Li2O

0.98

1.91

2.89

45

0.029

1.58

1.23

BaO

0.89

1.86

2.75

74

1.55

3.7

0.75

SrO

0.95

1.91

2.86

59

0.86

3.07

0.95

CaO

1.00

1.97

2.97

58

0.47

2.49

1.000

MgO

1.31

1.92

3.23

34

0.094

1.71

1.10a

La2O3

1.10

1.97

3.07

67

1.32

Y2O3

1.22

1.90

3.12

56

0.55

2.47

0.96

Sc2O3

1.36

1.88

3.24

50

0.286

2.14

1.11

Al2O3

1.61

1.86

3.47

21

0.052

1.46

1.65a

SiO2

1.90

1.67

3.57

22

0.0165

1.41

2.10a

B2O3

2.04

1.66

3.70

18

0.003

1.39

2.47b

P2O5

2.19

1.45

3.64

17

0.00

1.33

2.1c

0.85

For fourfold coordination; for sixfold, γ Mg = 1.65, γ Al = 2.48, γ Si = 3.15. For threefold coordination; for fourfold, in borate glasses, γ B = 4.2. c Varies in phosphate glasses. a b

2.4 Oxide (-II) polarizability

602

CaO

2.2

2.0 1.8 1.6 SiO2 1.4 0.4

0.6 0.8 Optical basicity, Λ

1.0

Figure 2 Plot of oxide(-II) polarizability, αoxide(-II), versus optical basicity of calcium silicate glasses, 39–57.5 mol % CaO (Λ range, 0.60–0.69). Data for SiO2 and CaO at the extremes (Λ = 0.476 and 1.000, respectively). Ignoring the data point for CaO, the line fits Eq. (14).

to a Λ-difference between SiO2 and these bases usually of well over 0.5. Similar differences are evident for borate, phosphate, and the glasses of certain other oxides. For many of these glass systems (though not for silicates),

however, the increase in the experimental Λ varies irregularly with glass composition. This occurs for borate glasses where γ B, which is 2.47 for both vitreous and crystalline B2O3, deviates markedly from Eqs. (6) and (7) upon addition of alkali to the glass. This is observed in the UV spectra of Pb2+ and Tl+ probe ions and also with the farinfrared frequencies of “rattling” Na+ ions [9]. The most obvious cause of this effect is the well-known structural change of boron from trigonal planar to tetrahedral coordination ([1], Chapter 7.6). One of the most important results of this change is the elimination of the π-component from the bonding of oxide(-II)s that are attached to the four-coordinated boron atoms. The π-bonding in glass is normally important for the delocalization of electronic charge and for the benefit that this undoubtedly has for reactions occurring in the glass or melt. Thus, the newly formed tetrahedral BO4– units become “stops” embedded in the overall electron delocalization associated with the glass structure. An interesting feature of chemical bonding in inorganic compounds is that the σ-component serves to transfer negative charge from the donor to the acceptor atom. Normally this is supplemented by some degree of π-bonding, which allows further donation of negative charge. In addition, π-bonding can provide “back-coordination” where some of the negative charge spills back to

5 Chemical Reactions: Changes in Structure and Bonding

the donor atom. This scheme of bonding is recognized as a means for preventing the buildup of positive or negative charge in a molecule and is known as the (Pauling) electroneutrality principle. In the case of the BO4– units, we have been discussing that the absence of π-bonding means that any back-coordination cannot occur; there is the possibility that in the BO4– unit the negative charge resides mainly on the boron atom. Accordingly the basicity moderating parameter, γ B, of the boron atom is appreciably higher than for trigonal planar boron. This idea of an increase in γ B is supported by an analysis of the refractivity data for alkali borate glass systems where calculated values of αoxide(-II) are substituted into Eq. (14). The results show how Λ for each glass increases only very slowly for initial additions of alkali oxide, whereas for lithium oxide there is a decrease in Λ up to a Li2O content of approximately 25 mol %. It appears that the γ B value for tetrahedral boron is counter-effective to the increasing basicity of the relatively feeble alkali oxide. When Eq. (8) is adapted to accommodate also the (unknown) γ B value for tetrahedral boron, calculations reveal that the γ B value for tetrahedral boron is 4.7 [10] on the slightly false assumption that exactly two are generated by each added oxide(-II) atom. At this point, there is an important question. Does the chemical behavior of a series of glasses, such as the stabilization of upper/lower oxidation states of metal ions (Section 3), follow the same trend as the calculated optical basicity, for example, in the case of borate glasses when the calculation assumes γ B equal to 2.47 for threefold coordinated boron and 4.7 for fourfold. Experimental data for the redox ion pairs Cr6+/Cr3+ and Ce4+/Ce3+ indicate that such a parallel does indeed exist. For these ion pairs there is the usual trend of the upper oxidation state being favored by increasing alkali oxide content, but this trend is very slight for initial additions of oxide to boric oxide, and, dramatically, for Li2O, the trend is the reverse for both ion pairs. It is only after approximately 25 mol % Li2O that the more usual effect of upper oxidation state stabilization occurs. This startling trend almost exactly parallels the trend in the calculated optical basicity, making the result highly significant. It illustrates how deviations in predicted optical basicity are paralleled by corresponding deviations in chemical behavior. Looked at in another way, deviations in the properties of a glass system with composition, often described as “anomalous behavior,” can be understood, at least partially, in terms of a chemical bonding analysis of the type described here. It also emphasizes the importance of π-bonding in the glass network and the consequences if it is lost. Another aspect concerning the combination of optical basicity and chemical bonding is the success for identifying the ionic/covalent nature of the sites

provided by a glass as metal ions travel through. Studies of phosphate glasses and melts and especially of borate glasses indicate that sites of higher rather than of lower optical basicity are favored by mobile metal ions (and vice versa) [9]. For example, subjecting a 35 mol% Na2O sodium borate glass, coated with a thallium–Hg amalgam and floating on mercury, to an electric field results in driving Tl+ ions into the glass [6]. After subsurface cleaning with an ion beam, the UV spectrum of the Tl+ ions indicates the existence of sites of optical basicity equal to 0.66–0.67, which is much greater than expected for this glass. The assistance to ionic mobility might be anticipated for sites where the interaction with oxide(-II) is more covalent, as signaled by the large Λ, since the influence of large lattice energies is bound to be less important. Similar experiments using lead rather than thallium show little movement of Pb2+ ions into the glass. Instead, O2− ions migrate to the lead electrode, with formation of PbO, while Na+ ions are converted to sodium at the mercury electrode. This leaves a volume of the original sodium borate glass that is devoid of Na2O: it has become a volume of vitreous boric oxide. The mechanism proposed for this reversible reaction involves a “handing over” of oxide(-II) ions between threefold and fourfold coordinated boron atoms [11]. For the interaction of silicates with phosphates, borates, etc., or even with other silicates, there is sometimes the problem of deciding which “salt” is the acid and which is the base. For example, when considering the equilibrium K2 Si2 O5 + Na2 SiO3 = K2 SiO3 + Na2 Si2 O5 ,

16

does twice the amount of alkali oxide in Na2SiO3 on the left-hand side compensate for the stronger basicity of K2O in K2Si2O5? Calculations with Eq. (6) show that Λ is 0.65 for K2Si2O5 and 0.69 for Na2SiO3, indicating that Na2SiO3 is the base. Furthermore, on the right-hand side, Λ is 0.76 for K2SiO3 and 0.61 for Na2Si2O5, so the optical basicity differences are 0.04 and 0.15 for the left- and right-hand sides, respectively. It follows that Eq. (16) represents an acid–base neutralization and should proceed from right to left, which indeed is found to be the case. This consideration of Eq. (16) illustrates how, within a material, chemical bonding results in an uneven distribution of electrical charge and how optical basicity reflects the extent of the negative charge borne by the anionic moiety, presumably on its surface. Thus, when two materials of different Λ are in contact, there exists a chemical driving force that, ideally, is proportional to the optical basicity difference [12]. There are of course many factors influencing reactions of this type, for example, high lattice energy. Nevertheless, examination of subsolidus compatibility diagrams (as summarized in the

603

604

5.7 Optical Basicity: Theory and Application

American Ceramic Society’s Phase diagrams for ceramists) does indicate many instances supporting the idea that optical basicity is an important factor. The involvement of Λ in the acid–base neutralization for solids discussed above suggests that there might be a similar situation for aqueous conditions through the existence of a relationship with Brønsted acidity. This idea has been tested with suitable sets of pK values for appropriate parent acids, for example, phosphoric acids. In addition to orthophosphoric acid, H3PO4, phosphorus(V) forms several condensed oxyacids containing both bridging and nonbridging oxide(-II)s. Equation (6) gives Λ for each conjugate base (γ M is set arbitrarily at unity), and one can plot these values against the pK (conjugate acid) values of the various phosphate (and other) species. A roughly linear relationship is obtained, which, moreover, includes the points for water, namely, the bases H2O and OH– [4].

6 High and Low Optical–Basicity Materials It is seen from the periodic table that the nearest neighbor to oxide(-II), with its outer 2s2 2p6 configuration, are fluoride(-I) with the same configuration and sulfide(-II) with the configuration 3s2 3p6. To what extent does the optical basicity model extend to the chemistry of these adjacent elements? In view of the extra unit nuclear charge, fluoride systems (with no other anion) might be imagined to have optical basicities that are one half of the corresponding oxide systems. It is possible that this situation is equivalent to “one electron worth” of screening in the case of oxide(-II). Probe-ion studies made with Pb2+ for molten alkali fluorides remarkably support this idea. Further support comes from polarizability results for crystalline binary fluorides and also complex compounds such as alkali fluoroborates, fluorosilicates, and fluoroaluminates. These results mean that it is possible to use Eq. (6) for calculating the optical basicity of a fluoride glass, but with the condition that the γM values are double those for the corresponding oxides, alternatively, by using Eq. (7), but with the oxide Λ halved. It is apparent that with Λ(fluoride) = ½Λ(oxide), some fluoride materials have very low optical basicities, for example, Λ is 0.23 for crystalline Na[BF4] and is 0.35 for the glass 0.100 MgF2 0.283 CaF2 0.231 SrF2 0.386 AlF3. Mixed fluoride–oxide melts and glasses have been prepared and their refractivity Λ values discussed comparatively with all-oxide glasses [13, 14]. In these media the Pb2+ probe ion shows that it is responding to a single, mixed oxide–fluoride environment rather than to two distinct environments.

Sulfide(-II) systems are at the other extreme of optical basicity. From the point of view of chemical bonding, some are semiconductors and are close to electron itineracy, for example, mercury(II) sulfide with a band gap Eg = 2.10 eV. Studies of optical basicity for semiconductors present difficulties, but in recent years various investigations have been undertaken on sulfur, selenium, and tellurium semiconductor-type materials (e.g. [15]). For crystalline ZnS, a more amenable semiconductor, Pb2+, has its 1S0 3P1 frequency at 20 400 cm−1 in zinc blende and at 19 700 cm−1 in wurtzite. These yield Λ = 1.30 and 1.32 respectively, that is, a significantly greater basicity compared with Λ = 0.91 for ZnO. Trends for MgS, CaS, SrS, and BaS in electronegativity and polarizability fit into the same pattern as for fluorides and oxides. Perhaps it is surprising that the optical basicity of water itself has been subjected to so little study. It will be recalled that in the development of the nephelauxetic effect (Section 2), Jørgensen set h for H2O as unity. One of the reasons for this assignment was the consistency of d–d spectral data for [M(H2O)n]z+ chromophores (n, normally six), and with h = 1.00 and Λ = 0.39 for H2O. However, it appears that when the constricted conditions of the coordination sphere are removed, Λ for the free H2O molecule rises to 0.51. Further work in this area is called for. It is of interest that “less related” anionic systems have been investigated, for example, molten chlorides, where probe ions indicate the possibility of establishing a chloride optical basicity scale [2]. Acid–base titrations, for example, have been performed with molten AlCl3.

7 Optical Basicity and Electronegativity It is not surprising that there should be a link between electronegativity, x, and optical basicity since both schemes are concerned with unequal sharing of electronic charge in chemical bonding. In terms of the basicity moderating parameter, γ M, and the Pauling-type electronegativity, xM, it has long been established [1] that γM =

4xM – 1 3

17

with the condition that this relationship is restricted mainly to the M cations having the outer s2p6 configuration, thereby excluding most transition metal ions. This condition also applies for Eq. (18). Although for binary oxides xO is usually assigned a value of around 3.5, closer inspection shows that this value refers only to the “covalent” oxides (see Table 3). However, with increasing ionicity in the metal–oxide

7 Optical Basicity and Electronegativity

(-II) bonding, there is a marked decrease in xO. The effect is shown in Figure 3 where the points (unlabeled for clarity) are for the oxides shown in Table 3. Most lie close to the relationship [12] xO =

4 1 – 0 86 xM – 0 25

18

The reason for this decrease in xO is that the increasingly negative charge on the covalently bound oxide (-II) atom renders it reluctant to acquire further negative charge. It becomes unstable with a tendency to lose an electron and to form the peroxide, (O–O)2–, or superoxide, (O–O)–, ion. Generally, the electronegativities that are assigned to the elements, in a particular oxidation state, are taken as “fixed,” but the oxide(-II) species stands out as a gross exception. Indeed, the trend shown by Figure 3 is an abnormality compared with the other elements in the periodic table. It might be argued that it is this feature that allows optical basicity to operate in a significant way. The non-fixed character of xO has a profound effect on the use of electronegativity as an indicator for trends in ionicity or covalency. In general, it is the electronegativity difference that denotes such a trend, as in the series from iodide to bromide to chloride. However, this scheme has limited application for oxides. As seen in Table 3, the electronegativity difference between Na2O and SiO2 hardly exists, xO – xNa = 1.65 and xO – xSi = 1.67, even though Na2O is ionic, whereas SiO2 is covalent; similar cases are ionic BaO and amphoteric Al2O3 where for both, xO – xM is 1.86. Among others, these considerations show that for binary oxides of general formula MaOb, it is

Electronegativity, xO

4.0

3.5

3.0

2.5

2.0 0.5

1.0

1.5

2.0

2.5

Electronegativity, xM

Figure 3 Plot of oxide(-II) electronegativity, xO, in binary oxides MaOb, against electronegativity, xM (see Table 3). Points at bottom left-hand area are for “ionic” oxides; those at the top are for “covalent” oxides.

the decreasing value of xO that signals increasing ionicity in the metal–oxide(-II) bonding. The value of xO – xM for each binary oxide in Table 3 is obtained from its enthalpy of formation, Q (in electron volts, that is, –ΔH f /96.48, with ΔH f in kJ/mol) divided by the “number of bonds,” b (two for CaO, four for SiO2, etc.), where Q requires the addition of 1.13 eV per oxygen because of the double bond in the O2 molecule. On the Pauling scale, the electronegativity difference, xO – xM, is given as xO – xM =

Q + 1 13b 2b

1 2

19

Assuming xM to be invariant, then one obtains xO by addition (Table 3). The relationship of for example (17–19) leads to the following expression linking the heat of formation of a binary oxide, MaOb, with its optical basicity [16]: Q 2 85 – 1 16Λ Ma Ob – 0 75 =2 b Λ Ma Ob

2

20

This relationship has been applied to silicates and aluminosilicates. For example, CaO Al2O3 2 SiO2 requires use of Eq. (20) for each of the three constituent oxides, followed by addition of the relevant Q values to obtain the total Q for the compound. Results have shown that with some refinements to Na2O and K2O (see Figure 3), there is a convincing correlation of Q with the optical basicity of the compound. Since Λ is related to chemical constitution through Eq. (6), it is apparent that optical basicity offers a method for calculating the heat of formation of a silicate or an aluminosilicates from its chemical constitution [16]. It is surprising that in the past, with some exceptions, the chemical bonding aspects of glass have tended to be ignored or considered only at a fairly elementary level. Usually the approach is in terms of valence-bond theory with the depiction of electron pairs. Alternatively it is in terms of band theory where electrons are “accommodated” in energy bands. How does the concept of optical basicity connect with these approaches? As explained in Section 2, it is already apparent that optical basicity itself is derived from a molecular orbital approach in exploiting orbital expansion parameters. This connection has allowed calculations for binary oxides (using ionization energies for isoelectronic sets of free ions) that provide estimates of charge-cloud sharing and hence of the ionicity of MZ+ (see Table 3). Although they incorporate arbitrary assumptions (as do other atomic/ionic parameters, e.g. ionic radii), nevertheless, these data are useful for comparative purposes. In effect, optical basicity serves to indicate ranking in the ionic/covalent character of the chemical bonding in a similar way that electronegativity difference does for simple non-oxide(-II) compounds.

605

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5.7 Optical Basicity: Theory and Application

For a glass or melt, it is the uneven spread of electron density over the electronic surface of the “molecules” (for want of a better word) that is responsible for many of its properties, for example, as a reaction medium for redox equilibria. Historically, a related point of interest concerns the Lorentz–Lorenz relationship, Eq. (13), and how the molecular polarizability, αmol, replaced the molar refractivity Rm (in cm3) in the Clausius–Mossotti expression: Vm κ – 1 , Rm = κ+2

21

where Vm remained the molar volume, in cm3, but, κ, the dielectric constant, became n2 (Maxwell, strictly at infinite wavelength). When Eq. (21) is written as Rm 1–3 , = Vm κ+2

22

it is seen that as the value of Vm decreases and approaches Rm (effected by compression or chemical substitution of a metal oxide “bronze,” for example), κ approaches infinity. This condition corresponds to a polarization catastrophe and the onset of metallic bonding. In terms of simple band theory, the energy gap (or band gap), Eg, becomes zero as the valence band and conduction band merge into each other. Indeed, the plot of Eg for oxides reveals a close proximity to the empirical expression [17]: E g = 20

1 – Rm Vm

2

,

23

which implies again that Eg is zero when Vm = Rm. It should be noted that the quantities of both Rm and αoxide(-II), together with Eq. (23), have, all three, optical basicity as their common link. There are many occasions when chemical bonding is regarded in terms of a sliding scale from covalent to ionic (for example, see Table 3). However, this description is often inadequate, especially when so many materials are viewed in terms of dielectrics, semiconductors, and metals (or insulators, semiconductors, and conductors). Such inadequacies confront glass science. As far as oxide glasses are concerned, Figure 4 is relevant in providing a small selection of binary oxides in an attempt to illustrate these aspects of bonding. The horizontal scale denotes covalent to ionic (through Pauling-type electronegativity, xO), and in addition, progressing upward from that scale, there is increasing tendency for electron itineracy. The latter feature might be described as the “metallic component” of bonding, increasing with decreasing Eg and with the upper limit (the metallic regime) at Eg equal to zero. To indicate

Metallicity 0.0 [1– Rm/Vm}

TiO V2O3

0.1 0.2 Ag2O Fe2O3

0.3

CuO Cu2O TiO2 In2O3 MoO3 Sb2O3 Sb2O3 FeO NiO ZrO TeO2 2 ZnO SnO2

0.4 0.5

Cs2O

BaO SrO CaO

0.6

MgO B2O3

Al2O3 Li2O

SiO2 P2O5

0.7 Covalent X0 = 3.8

Ionic 3.4

3.0

2.6

2.2

Figure 4 Schematic bonding chart for binary oxides (abbreviated for clarity): covalency to the left-hand side and ionicity to the right; height indicates closeness to nonmetal-to-metal transition.

the unifying approach provided by optical basicity for these types of chemical bonding, the alternative to Eg, namely, (1 – Rm/Vm), is taken as the vertical scale (see above). The diagram implies that increasing electron itineracy can be a feature regardless of the ionic/covalent nature of the bonding of the oxide. A more complete diagram is discussed by Edwards et al. who also considered the onset of metallicity generally [17].

8

Perspectives

The Lewis idea of chemical bonding, where a base is a donor of electronic charge and an acid an acceptor, is well suited for many inorganic oxide(-II) materials and has been implicit in the present revue. Under chemical conditions, the electronic state of oxide(-II) has a flexibility that is greater than for any other element. This accounts for its wide range of electronegativity, xO, of its electronic polarizability, αoxide(-II), and of its ability to donate charge when acting as a Lewis base. All of these features are incorporated into the optical basicity model. At the heart of optical basicity is the existence of a hypothetical array of oxide(-II), O2–, ions. These are influenced by the constituent cations, Ca2+, Si4+ …, according to the extent that they balance the overall negative charge, that is, according to their equivalent fractions, XCa, XSi, …. In addition, there is unequal sharing

References

of the charge density in the chemical bonding. The combination of the two effects determines the electronic state of the oxide(-II) in terms of its power to react as a Lewis base (for example, in breaking up the silicate network; see Eq. 10) and in terms of its electron donor power (for example, in its coordination with probe cations). The overall effect is expressed, for the cation, as its basicity moderating parameter, γ Ca, γ Si …, and for the compound as the optical basicity, Λ, according to Eq. (6). This model is set in the context of well-established chemical theory and incorporates a background of molecular orbital theory and orbital expansion phenomena. The effective functioning of optical basicity and its universal application, which also includes catalysis and geochemistry, are because of this “pedigree.” Inorganic oxidic materials, from network glasses and melts on the one hand to aqueous solutions on the other, are amenable to the optical basicity approach [6, 7, 18]. Practically, optical basicity started with probe ions (Pb2+, Tl+) and the quantitative treatment of the orbital expansion effect in their electronic spectra, mainly in the UV/visible (optical) region of the spectrum. The optical basicity scale derived from these data correlates well with the chemistry and physics of the media. This provides a means for predicting the trends in properties for a series of glasses using Λ values calculated from chemical constitution with Eq. (6). Noninvasive methods for measuring optical basicity, such as the use of oxide(-II)-1s energies [19], oxide(-II) polarizabilities (αoxide(-II); see Section 4), or cation rattling frequencies in the far-infrared region [9], have extended the usefulness of optical basicity. They help to provide much needed insights into the nature of chemical bonding in glass and for the interaction with hosted cations, whether static or field driven. Generally, the optical basicity model implies two important facts about the structure and bonding of glass that, at the present, are often overlooked. First is the existence of electron delocalization (analogous with aromaticity in organic chemistry, though perhaps to a lesser degree), and second is the absence of whole electron charges, for example, on nonbridging oxygen atoms. By implication, the overall existence of some degree of π-bonding must be assumed. For borate systems, partial loss of this feature, accompanying the switch from threefold to fourfold coordination, accounts for some anomalous behavior. Deeper study into these features, not only for borate but for phosphate, germanate, and other glasses, will lead to a better understanding of the mechanism for field-driven ion transport, including movement of O2− ions through the glass [6, 11]. Acquiring a better understanding of chemical bonding, especially the onset of metallization, is vital for the development of glass science, so glass continues to expand its role as a future material [17].

Acknowledgment The author is grateful to Dr. E.I. Kamitsos and Professor M.D. Ingram for helpful comments.

References 1 Duffy, J.A. and Ingram, M.D. (1976). An interpretation of

2

3 4

5

6

7

8

9

10

11

12

13

glass chemistry in terms of the optical basicity concept. J. Non Cryst. Solids 21: 373–410. Duffy, J.A. and Ingram, M.D. (1971). Establishment of an optical scale for Lewis basicity in inorganic oxyacids, molten salts and glasses. J. Am. Chem. Soc. 93: 6448–6454. Jørgensen, C.K. (1969). Oxidation Numbers and Oxidation States, Chapter 4. Berlin: Springer-Verlag. Duffy, J.A. and Ingram, M.D. (1971). A new correlation between s-p spectra and the nephelauxetic ratio β: applications in molten salt and glass chemistry. J. Chem. Phys. 54: 443–444. Yang, Y.D. and Sommerville, I.D. (2002). Relationship between optical basicity and various capacities in metallurgical slags. Phys. Chem. Glasses 43C: 362–371. Baucke, F.G.K. (2000). Electrochemistry of Glasses and Glass Melts, Including Glass Electrodes, Chapter 2 and 3 (eds. H. Bach, F.G.K. Baucke and D. Krause). New York: Springer-Verlag. Duffy, J.A. and Baucke, F.G.K. (1995). Corrosion of metals in molten silicates: relationship with electrode potentials in aqueous solution. J. Phys. Chem. 99: 9189–9193. Duffy, J.A. (2002). The electronic polarisability of oxygen in glass and the effect of composition. J. Non-Cryst. Solids 297: 275–284. Duffy, J.A., Harris, B., Kamitsos, E.I. et al. (1997). Basicity variation in network oxides: Distribution of metal ion sites in borate glass systems. J. Phys. Chem. B 101: 4188–4192. Duffy, J.A. (2008). The importance of π-bonding in glass chemistry: Borate glasses. Phys. Chem. Glasses Eur. J. Glass Sci., Part B 49: 317–325. Baucke, F.G.K. and Duffy, J.A. (1980). Ion migration study in a sodium borate glass: proposal of a new oxide transport. J. Electrochem. Soc. 127: 2230–2233. Duffy, J.A. (1990). Bonding, Energy Levels and Bands in Inorganic Solids, Chapters 6 and 8. Harlow: Longman Group. Velli, L.L., Varsamis, C.P.E., Kamitsos, E.I. et al. (2008). Optical basicity and refractivity in mixed oxyfluoride glasses. Phys. Chem. Glasses Eur. J. Glass Sci. B49: 182–187.

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14 Duffy, J.A. (2011). Optical basicity of fluorides and mixed

oxide-fluoride glasses and melts. Phys. Chem. Glasses: Eur. J. Glass Sci. B 52: 107–114. 15 Dimitriov, V. and Komatsu, T. (2014). Optical basicity and chemical bonding of ternary tellurite glasses. Phys. Chem. Glasses Eur. J. Glass Sci., Part B 55: 13–17. 16 Duffy, J.A. (2004). Relationship between optical basicity and thermochemistry of silicates. J. Phys. Chem. B 108: 7641–7645. 17 Edwards, P., Kuznetov, V., Slocombe, D., and Vijayaraghaven, R. (2013). The electronic structure and

properties of solids. In: Comprehensive Inorganic Chemistry II, vol. vol. 4 (eds. J. Reedijk and K. Poeppelmeier), 153–176. Oxford: Elsevier. 18 Salanne, M., Simon, C., and Madden, P.A. (2011). Optical basicity scales in protic solvents: water, hydrogen fluoride, ammonia and their mixtures. Phys. Chem. Chem. Phys. 13: 6305–6308. 19 Dimitrov, V. and Komatsu, T. (2003). Correlation of optical basicity and O1s chemical shift in XPS spectra of oxide glasses. Phys. Chem. Glasses Eur. J. Glass Sci. 44: 357–364.

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5.8 The Glass Electrode and Electrode Properties of Glasses Anatolii A. Belyustin1 and Irina S. Ivanovskaya2 1 2

Saint Petersburg State University, Universitetskaya quay 7. Saint Petersburg, Russia Physical Chemistry Department, Saint Petersburg State University, Universitetskii prospect, 26, Petrodvorets, Saint Petersburg, Russia

Nothing tends to the advancement of knowledge as the application of a new instrument Sir Humphry Davy (1778-1829)

1

Introduction

As indicated by the Latin term acidus (from aceo, to be sour, deriving from acer, sharp, piercing), the notion of acidity has very long been familiar even though it was understood poorly. As a reminiscence of the atomic theory of Democritus (ca 470–380), the chemist Nicolas Lémery (1645–1715) [1] still assigned acidity to tiny particles when he wrote that “the acidity of a liquor consists in sharp salt particles, which keep moving.” As evidences, he explained, were the tingling on the tongue caused by acids or the fact that “not only all acid salts crystallize as spikes but all dissolutions of different matters caused by acid liquors are taking the same figure upon crystallization.” Differences in acidity then simply resulted from differences in the size and sharpness of these particles. The concept of base is much more recent. Because of the close association traditionally made between acids and salts, it was heuristically propounded by another famed chemist, Guillaume-François Rouelle (1703–1770), to describe “the substance that serves as a basis” (base, in French) to an acid for the precipitation of a salt [2]. In spite of the tremendous progress that followed Lavoisier’s chemical revolution at the end of the eighteenth century, however, a precise definition of relative acidity–basicity along with ways to measure it remained lacking. It was Reviewers: A. Bratov, Instituto de Microelectronica de Barcelona, IMBCNM, Bellaterra, Spain E. Bychkov, Université du Littoral Côte d’Opale, Dunkerque cédex, France

in 1909 that work made in Copenhagen at the Carlsberg Laboratory on the effect of acidity on proteins led S.P.L. Sørensen (1868–1939) to define pH, for pondus hydrogenii (hydrogen weight), as the cologarithm of the hydrogen ion concentration in an aqueous solution [3]. Thanks to progress made in the thermodynamics of solutions, Sørensen redefined in 1924 his fundamental concept of pH in terms of the activity of the hydrogen ion [4]. From the equilibrium dissociation of water into H+ and OH− ions, it then followed that a solution is acidic or basic depending on whether its pH is lower or higher than 7, respectively. The usefulness of these definitions would have been very limited, however, had not means to measure hydrogen activity been devised. It is in this respect that glass had a considerable impact by having made measurements possible as soon as the pH concept was defined. The glass electrode, whose centenary was commemorated in 2009 [5], was in effect a fundamental invention. Its working principle is rather simple: it is the electromotive force (emf ) produced when cations are exchanged between the glass surface and the investigated solution. But the phenomena actually involved are much more complicated than long thought, so a theoretical understanding of the glass electrode has long been lagging behind its various applications. Actually, the possibility to vary at will the composition of glass electrodes was a critical factor in their successful design. These could thus be customized to work over specific pH and temperature ranges and, in addition, used to measure the activity of other singly charged cations such as the alkalis, Ag+, or even NH4+, illustrating how a successful concept can then be applied to unsuspected fields. To describe these features, the various kinds of glass electrodes and their uses will be first presented. We will then show how the determining influence of chemical composition on the properties of the glass

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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5.8 The Glass Electrode and Electrode Properties of Glasses

electrode may be in turn used to investigate the structural role of cations in glass. As made in particular by the School of Nikolskii–Schultz at Leningrad/St. Petersburg (SPb) University, the successive steps to understand theoretically the glass electrode will be reviewed finally.

(b)

(a)

(c)

Insulating glass

2 Types and Properties of Glass Electrodes 2.1 The Glass Electrode At the origin of the glass electrode were the bioelectric experiments made by the physiologist Max Cremer (1865–1935). Knowing that glass possesses electroconductivity, he investigated the emf of a cell made up of a glass membrane connecting two aqueous solutions and found that it varies with the difference in their acidity/ basicity [6]. But it was the electrochemist F. Haber (1868–1934), of ammonia synthesis fame, and his PhD student Z. Klemensiewicz who shortly afterward took advantage of the phenomenon to design the glass electrode as an instrument for determining acid–base titration curves that had the great advantage over the Pt|H2 electrode in that it was insensitive to redox potential and devoid of the possible catalytic action of Pt on the solution [7]. Both Сremer and Haber worked with an industrial glass whose electrical resistivity was quite high. To reduce the resistance of electrode, glass membranes were thus made very thin, even after Mac-Innes and Dole had optimized their sensitivity with a 22% Na2O 6% CaO 72% SiO2 glass [8]. Such fragile and not very sensitive glass electrodes remained used only for laboratory research until they found in the late 1930s the innumerable applications still known today as a result of further glass optimization to make the bulb sturdier, of electronic amplification of the weak emf signal, and of the design of portable instruments fully incorporating the electronics along with both glass and reference electrodes as made by the then UCLA faculty George Beckman (1900–2004) with his instrument, which he named pH meter. A glass electrode is made of two different glasses, one for the insulating tube and the other for a thin membrane that is most often blown as a bulb (Figure 1a). To restrict the pH measurement to the bulb area, the former has a resistivity from five to seven orders of magnitude higher than that of the bulb, with typical values of 1016 and 1010 Ω m, respectively [9]. Thanks to the limitless shapability of glass, the membranes may be easily formed to the requirements of particular applications, e.g. flat sensors for surface measurements (on skin or paper) or in small volumes of solutions or as a spear for measurements in soil, meat, etc. To perform the

Inner reference electrode

External reference electrode

Vacuum-tight joint

Electrolyte

Vacuum

Porous diaphragm

Inner buffer solution

Electronic conductor

Alloy

Glass membrane

Figure 1 Three kinds of glass electrode design for pH and pM measurements. (a) “Classic.” (b) Combined. (c) With a reversible alloy-based solid internal contact.

measurements a glass electrode requires an external reference electrode. A typical modern pH probe thus is a combination electrode where the HCl solution filling the tube ensures the electrical contact with the glass membrane and encloses an Ag/AgCl reference electrode (Figure 1b).

2.2 pH Measurements In aqueous solutions all ions have a water solvation shell, so the H+ ion is just a convenient fiction with which a variety of more complex species, such as the hydroxonium ions (Н3О+), are accounted for thanks to the fact that the chemical potential of H+ is by definition identical in all such species for systems in internal thermodynamic equilibrium (e.g. [10]). In pH determinations, the H+ concentration is expressed in moles of solute per volume of solution (mol/dm3). Following IUPAC recommendations (2000–2002), we will then define pH as pH = − paH = − log

mH γ H , m0

1

where m is the concentration expressed in molalities (mol/kg), γ H is the activity coefficient of Н+ ions and m = 1 mol/kg.

2 Types and Properties of Glass Electrodes

For measurements with a glass electrode, a commonly used galvanic cell is Cu Pt Ag, AgCl HCl solution glass Mb test solution KCl; AgCl Ag

Pt Cu,

2

where || indicates a diffusive barrier. The symmetry of the cell aims at canceling out any potential created at interfaces and, thus, at ensuring that the measured emf only results from the contrast between the test and HCl reference solutions. Operationally, an important parameter is the рН interval where the Nernst equation is valid, namely, E = E0 +

2 3RT 2 3RT , = E0 − F log aH F pH

3

where E is the emf of the cell (2) minus the potential of the reference electrode (usually immersed in a 3.5 mol/dm3 KCl solution), E0 is the standard potential at aH = 1 (or pH = 0), R is the gas constant, T is the absolute temperature, and F is Faraday’s number. The value of E0 includes the diffusion potential at the boundary of the two solutions (which may be eliminated by appropriate means) and the potential at the inner side of the glass membrane, which is not constant but depends on temperature, on the inner solution composition, and on changes in the glass surface induced by the solution. In view of this complexity, a glass electrode cell is calibrated by means of standard pH buffer solutions before measurements are made. Graphically its pH response in a Nernstian E–pH plot is a straight line whose slope can be considered constant over a definite рН range (Figure 2). The width of this Nernstian range depends on temperature, composition of the electrode glass, and nature and concentration of the acid and singly charged

cations in solution. At high pH, the observed positive deviations from linearity (i.e. the so-called alkaline errors) are caused by interferences between H+ and alkali cations. At low pH, acid errors represent deviations from linearity toward negative E values that are due not only to the electrode response itself but also to interferences caused by high anion concentrations. The membranes of modern pH glass electrodes are produced from lithium silicate glasses to which other oxides are added. As a result of complex optimization, their compositions typically fall in the ranges (in mol %) 21–33 Li2O 1–4 Cs2O 3–5 La2O3 [or Nd2O3, Er2O3] 1–4 CaO [or BaO], where the complement to 100% is SiO2. Lithium silicates constitute the base glass because of their high chemically durability and relatively wide region of pH response. Addition of alkaline earth oxides CaO (or BaO) somewhat extends this region toward high pH values, whereas rare earth oxides do so toward low pHs and in addition increase the chemical durability of electrodes with respect to acidic and alkaline solutions. The average values of these oxide concentrations characterize the so-called universal glass electrode. These electrodes may be used for general applications at temperatures near ambient showing the Nernstian linear response in a 0–13 рН range in electrolyte solutions with M+ concentration of 0.1 mol/ dm3. Glasses with lower Li2O concentrations can work at higher рН and higher concentration of interfering alkali ions in solution. Although they are working well at higher temperatures, their high resistance prevents them from being used near ambient. On the contrary, lower working temperatures can be achieved with higher Li2O concentrations, but the range of linear response then becomes shorter.

2.3

pM Measurements

As made for the H+ ion, it was early observed that glass electrodes of appropriate compositions are also reacting to concentration changes of other singly charged cations. In analogy with pH, pM scales for the activities of these cations have thus been defined as

E (mV) –500 –400 –300

pM = − log aM

–200 –100 0 —1 —2

+100 0

2

4

6

8

10

12

14

pH

Figure 2 Extent of linearity of the E–pH relationship of a 22 mol % Na2O silicate glass electrode in solutions: 1 – cNa = 0.1 mol/dm3; 2 – cNa = 3 mol/dm3.

4

As made of sodium or lithium silicate glasses containing considerable concentration of Al2O3 and some B2O3 [5], these electrodes show a reversible response to various cations, mainly Na+ but also K+, NH4+, Li+, Ag+. In the subacid, neutral, and alkaline solutions containing only one of the specified cations, they show almost Nernstian M+ response for concentrations ranging from saturation to about 10−4 mol/dm3. In the presence of other cations, this interval is shorter. They are less common used than pH glass electrode but are nonetheless rather widespread.

611

612

5.8 The Glass Electrode and Electrode Properties of Glasses

2.4 High-Temperature Glass Electrodes Glass electrodes with a solid internal contact have been developed to extend the temperature range of measurements up to 200 C. The difficulty to be overcome was that when Pt, Au, Ag, Cr, Al, or even Hg is used for connections with the glass membrane, the transition from the ionic conductivity of the glass membrane to the electronic conductivity of the contact metal is not reversible. This results in troublesome potentials that may originate from impurities in the contacting metals and fast potential drift. The principles to be fulfilled for overcoming the problem were formulated by Nikolskii [11]: (i) the electrode process occurring at the boundary between an ionic conducting membrane and an electronically conducting contact must of course be itself reversible; (ii) the exchange current of the process must be sufficiently large compared with the current flowing through the system under measurement; (iii) any side process must be prevented at the boundary. These requirements are satisfied with the metal solid contact invented at Leningrad/St. Petersburg University [5, 12], which consists of a thin layer of an alkali metal alloy evenly spread over the inner surface of a glass membrane. Alloys such as LiIn, LiSn, NaSn, or KPb are formed with the same alkali as present in the glass and the electrode is sealed under vacuum to prevent the alkali from reacting with water vapor. These alloys are electronic conductors in which metal ions are diffusing. Exchange of alkali M+ ions on the alloy/glass interface takes place according to the reaction M + glass + e- alloy ⇄M alloy ,

5

which establishes electrochemical equilibrium and governs the electrical potential at this interface. Because of mutual saturation of the phases, the electrode potential does not depend on the volume of the phases and, thus, to within large limit, on the gross composition of the alloy. In this way potentials are highly reproducible, and E0 values can be so stable as permitting in some instances to use factory calibrations. An additional advantage is a wide working temperature range, which, for instance, allows these glass electrodes to be sterilized at 150 C with water steam.

under an argon atmosphere), their electronic conductivity is four orders of magnitude higher than those of their ionic components. To ensure a reversible contact with the glass membrane, a chemical coating of silver or copper is deposited on the inner surface of the glass electrode in contact with the metal wire. These glass electrodes can be simply prepared with a glassblower torch. Their chemical inertness and sufficient exchange currents cause them to behave like noble metal electrodes in reversible redox systems such as Fe3+’2+, Fe[CN]64+,3+, quinone/hydroquinone, etc. In addition, they are insensitive to the gaseous components of redox systems such as (1/2) Cl2(g)/Cl−, H+/(1/2)H2(g), or O2(g)/ H2O. Not only are these electrodes well suited to measure redox potentials in various systems under aerobic conditions, but they can also be selected for systems where other electrodes commonly used for redox measurements faces difficulties. In the study of the system Ce4+/Ce,3+ (redox potential ЕH = 1.44 V), the use of Pt electrodes, for instance, suffers from two side processes, namely, oxidation of the electrode material along with decomposition of cerium solutions on the Pt surface with evolution of oxygen from water, whereas a glass electrode is free of such limitations. These glasses are actually semiconductors because their conductivity is electronic in nature. When used to prepare electrodes, they result in a special sensitivity to the level of the redox potential of the solution. By selectivity we mean here that the electrode can partially equilibrate with a system i regardless of the presence of a competing system j [13]. The effect is due to special features of the energy distribution among the charge carriers in the surface layers such that n-type semiconductors are selective to redox systems with a low EH, e.g. −0.38 V for the Eu3+/Eu2+ system, whereas p-type semiconductors are selective to high EH systems, e.g. 1.44 V for the Ce4+/Ce,3+ system. In both cases the EH values are outside the thermodynamic stability limits of water [14]. Glass electrodes are thus valuable for these applications because they are indifferent in a wide range of redox potentials and pH solutions, thanks to their high chemical stability, as illustrated by kinetic parameter study of the reaction Ti3+ + O2 (for the system Ti4+/Ti3+, EH = −0.11 V) in the presence of molecular oxygen in the solution [15].

2.5 Glass Electrodes for Redox Measurements For performing redox measurements other important glass electrodes were elaborated by Pisarevskii et al. in the 1960s [5, 12] on a different basis since the electronic conductivity and activity of electrons relies here on the variable valence states of Fe3+,2+ and Ti4+,3+. With the compositions (mol %) 10 Li2O 5 Na2O 18 Fe2O3 67 SiO2 (type I glass, synthesis under reducing conditions) and 10 Na2O 5 K2O 29 TiO2 5 Ti2O3 3 Nb2O5 50.5 SiO2 (type II glass, synthesis

3 Glass Structure as Viewed by the Glass Electrode 3.1 The Electrode Method From the middle of the 1950s, the Nikolskii–Schultz School carried out systematic research on electrode properties of glasses of M2O–RxOy–SiO2 systems [16], where

3 Glass Structure as Viewed by the Glass Electrode

a′ –E 1′ 1 1″

4 3

0 1′ 1

2

4

6

10

12

5 14 pH 2

a

Figure 3 Structural role of elements as determined from electrode properties of alkali silicate glasses. Solid lines: experimental Е–рН curves; dashed lines: calculated values with Nikolskii’s Eq. (9). Glasses: M2O–SiO2. M2O is the first modifier, SiO2 is the first network former (1); М2О–RxOy–SiO2. RxOy role: 1 , 1 is the second modifier; 2, 3, 5 are the second network formers; and 4 is the intermediator. The straight line аа is the hypothetical Н+ function csol M + = const

M = Na or Li was the initial network modifier, Si the initial network former, and R any other element incorporated. The electrode method to study glass structure is based on the fact that, when part of SiO2 is replaced by RxOy, differences in the pH response (E–pH curves) with respect to that of a binary M2O–SiO2 glass depend on whether the element R is another network former or another network modifier or is playing an intermediate role. Ions in glass mutually polarize each other. Here binary alkali silicate glasses M2O–SiO2 (15–33 mol % M2O; M = Li, Na) will be used as references for subsequent comparison. One can consider that their electrode potential is determined only by H+ ions up to pH 8–10, whereas M+ metal ions begin to influence the potential at higher pH values (Figure 3, curve 1). The reason is that a binary glass has weak acidic ionogenic groups [SiO3/2]OH. The bond strength of hydrogen in these groups is mainly covalent and very strong.

3.2

Effect of a Second Network Modifier

If a network modifier is added as a third oxide RxOy to the glass, the ion Rz+ placed in the environment of an [SiO3/2] OM group polarizes the O–M (O–H) bond. This effect is either weaker or stronger than that of the initial M+

cation. The former case for instance applies to Cs, Ca, or Ba: the O–H bond then becomes stronger, and the linear H+ response of the glass electrode extends into the higher pH region (Figure 3, curve 1 ). For Mg or Be, the opposite holds true: the O–H bond weakens, and the H+ response linear region narrows down (Figure 3, curve 1 ). These phenomena are named the electrode effect of the second modifier [16].

3.3

Effect of a Second Network Former

Addition of network-forming ions Rz+ has dramatic effects as their incorporations into the silicate network induce changes in the coordination number k or in the interatomic distances R–O inherent to the RxOy oxide. These cations Rz+ have so strong polarizing effects that they form their own element silicate ionogenic groups [SiO4/2] − [ROk/2](k − z)− (k − z) M+ (for simplicity, reference to [SiO4/2] in such groups will be omitted hereinafter). This case is in particular that of Al, B, Ga, and Fe (z = 3, k = 4) (Figure 3, curves 2 and, 3), Sn and Zr (z = 4, k = 6) (Figure 3, curve 5). The subsequent exchange of M+ for H+ or M+ from the solution results in the formation of the [ROk/2](k − z)−(k − z)H+ (or M+ ) groups, which are strongly acidic in H+ form. The O–H and O–M bonds in these groups do not differ significantly either in their character (they are mostly ionic) or in their energy. This feature results in an early disruption of the H+ response (at pH = 1–3). If a fairly small quantity (1–4 mol %) of the network-forming oxide RxOy is added, then the appearance of [ROk/2](k − z)−(k − z)H+ groups manifests itself as a “step” in the E–pH curve at pH values from 1–3 to 5–6, followed by a decrease of E caused by the predominance of silicate groups (Figure 3, curve 3). This response is akin to the titration curve of a mixture of strong and weak acids. At higher concentrations of the network formers, the glass electrode responds to pH changes only in the region of the strong acidic solutions, and it shows response to the M+ ion at pH higher than 3 or 4. In Figure 3 this behavior corresponds to the horizontal parts of curves 2 and 5 at csol M + = const. Introduction of oxides of Y, La, and Ti and of some rare earth elements into the glass composition eliminates the acid error and gradually reduces limits of H+ response. This is the intermediator effect (Figure 3, curve 4). In such studies of E–pH curves for M2O–RxOy–SiO2 glasses, it was thus possible to determine successfully the structural role of the network-modifying, intermediator, and network-forming ions for about 30 different elements of the periodic system [16]. This method was thus applied to elucidate the structural role of a variety of oxides much earlier than made with direct, structuresensitive methods (Section II).

613

614

5.8 The Glass Electrode and Electrode Properties of Glasses

4

Theories of the Glass Electrode

4.1 Nikolskii’s Thermodynamic Ion-Exchange Theory Experimental data accumulated in the 1920s gave a sound basis to the first theory of glass electrodes. As formulated in 1937 by Nikolskii [17], the idea that the primary phenomenon at work in both glass electrodes and other ionselective electrodes is ion exchange has gained general recognition. The ion-exchange equilibrium + + + + MMb + Lsol ⇄Msol + LMb

6

is thus established between the glass membrane and the solution, so L+ cations (H+) also appear in the membrane. Identical cations also exchange between the membrane and solution + + ⇄Lsol , LMb

7

+ + MMb ⇄Msol ,

8

in reactions that are faster than ion exchange. The potential-determining equilibrium will be thus the reactions + + HMb ⇄Hsol (7) and (8) in the regions of H+ and M+ response, respectively. It is within the framework of this thermodynamic ionexchange theory that Nikolskii derived the following equation for the glass electrode potential: E = E0 + 2 3

RT + , log aH+ + K exch H + ,M + aM F

9

where E is the emf of a galvanic cell (2), the parameters E0, R, T, F are as defined in Eq. (3), and aH + and aM + are the ion activities in the solution. The exchange constant then is K exch H + ,M + =

Mb asol H + aNa + Mb asol Na + aH +

0,sol 0,sol μ0,Mb − μ0,Mb + Na + − μH + − μNa + , = exp H RT

10

where the difference between the standard chemical potentials of the ions in the glass membrane and in the 0,sol solution μ0,Mb i + , μi + reflects the bond-strength differences in these phases. This constant characterizes the sorption selectivity of the ions by the membrane from the solution as well as the position of the transition region [17]. It is the “influence factor” of the M+ ion on the H+ response of the glass electrode that has actually different meanings in different theories.

pH response. These limitations stimulated further development of the theory through the rejection of two important assumptions made by Nikolskii to derive Eq. (9). The first was the unity activity coefficients of both H+ and M+ ions in glass, which meant that the activity coefficients γ i ’s were assumed independent of the degree of substitution of one kind of ion by another. The second was the assumption that the sum of the ions concentration in glass (or in the membrane) is constant: Mb Mb 0 cMb H + + cM + = cR − = c ,

where cMb R − is the concentration of the fixed anionic sites in the membrane. Two approaches may be distinguished in the subsequent evolution of the theory. On the one hand, the assumption made by G. Eisenman et al. [18, 19] about the nonideality of a glass membrane, i.e. ai,Mb = cni,Mb , where the parameter n relates the activity of the ion to its concentration, allowed a smooth transition from H+ to M+ response to be described successfully. With another approach, the same result was obtained by Nikolskii et al. [16] on the basis of the concept of various ionogenic groups in glass and their dissociation constants. Moreover, this theory successfully explained the stepwise pH response illustrated by curve 3 in Figure 3. The concept of the potential of a glass electrode as a phase boundary potential was replaced by the idea of a membrane potential, i.e. a potential drop accounting for those occurring at phase boundaries as well as for diffusion potentials in surface layers on both sides of the glass membrane. Equilibrium at the boundary, which determines the phase boundary potential, then specifies the boundary conditions for the diffusion potential [20]. Experimental evidence for these two phase boundaries has come from studies of the glass electrode potential dynamics and the actual composition of surface layers of some alkali aluminosilicate glasses after the transfer of the glass electrode from HNO3 or MNO3 solutions into an AgNO3 solution, and vice versa [21]. 4.3 Nikolskii–Eisenman Equation In many respects the electrode properties of glasses such as the extension and slope of the electrode response or its selectivity depend on the mobilities of ions and on the mechanism of their transport in glass. The Nikolskii– Eisenman equation [16, 19] describes the glass electrode potential as a membrane one: E = E0 + 2 3

4.2 Evolution of the Theory An equation such as (9) cannot describe the whole experimental E–pH curves, in particular, the extended transition from one response to another as well as the stepwise

RT uM + 1 n + log aL + + K exch L,M aM uL + F

1 n

n

11 Unlike Eq. (9), this expression takes into consideration the nonideality of the glass membrane (through the factor

4 Theories of the Glass Electrode

n), and it also includes the ratio of the ions mobilities in the membrane changing the significance of the “influence factor.” In Eq. (11), E, E 0 , R, T , F, aL + , and aM + are defined as above, whereas uM + , uL + are the ion mobilities at the glass surface layers, their ratio being assumed to be constant. The product uM + uL + n K exch determined from potentiometric measurements is named the potentiometric pot sel selectivity coefficient K pot L M (or K L M ), whereas K L M and n are empirical parameters, which are characteristic for a particular glass for any given pair of cations. If L+ designates H+, then n > 1 and Eq. (11) may be fit to experimental curve. If L+ is Na+ and M+ is K+, then as a rule n = 1. This equation describes well the glass electrode behav+ K pot ior in the regions of pure H+ (at aH + H M aM ) + K pot It also or pure M+ responses (at aH + H M aM describes well a smooth transition from H+ to M+ responses, hence challenging Nikolskii’s equation in [17], which did not consider a factor n and predicted a sharp transition from one response to another.

4.4 Processes in the Surface Layers of Glass and the Glass Electrode Potential A deeper insight into the operation of the glass electrode was achieved through observations of the concentration profiles of ions in glass layers that were altered by interaction with the solution (Figure 4). Along with studies of chemical and electrochemical processes at the glass–solution boundary, these observations have led to Cm

1

lʺ I

V

II

III

IV

l 0.5

Si – O – Si

x (μm)

Figure 4 Typical profiles of ion concentrations in the surface layers of glass. I: Steep gradient of Me+ characteristic of durable lithium silicate glasses, reflecting a “simple” ion interdiffusion. II, III, IV, and V: S-shaped profiles characteristic of sodium silicate and aluminum sodium silicate glasses, indicating ion interdiffusion accompanied by other processes such as dissolution of the glass network or its hydrolysis. The thicknesses of the surface layers involved can be defined as l, l’, l”.

+ H2 O⇄

SiOH + HOSi

12

and processes such as microphase separation accompany the interdiffusion process in the surface layers that cause their structural transformations and changes in site numbers R−, so the glass electrode potential changes with time. For this reason, Doremus [22] proposed an equation for the potential of glass membranes consisting of two parts differing in their composition and/or in structure and, accordingly, by their values uM + , uL + and K exch L M, i.e. K pot L M. Changes within the interfacial boundary region may cause E change to with t. A multilayer model of an inhomogeneous altered surface layer with m (1…k…m) sublayers has been proposed [21] to account for this dependence. Experiments have indeed shown that the dynamics of glass electrode potential correlates with the temporal changes in the ionic composition of the glass surface layers.

4.5

Nernst–Planck–Poisson Model

Another modern potentiometric model [23] regarded as promising uses the Nernst–Planck–Poisson (NPP) system of equations to simulate the nonequilibrium response. Unlike in the phase boundary model, electroneutrality and steady-state/equilibrium assumptions are abandoned so that the space and time domains are accessed. The NPP model describes a system consisting of m layers (phases) within which the concentration changes of r components – ions or uncharged chemical species (as it is done in multilevel model) – and a change of the electrical field in space and time take place. The NP equation describes the transport of ions by diffusion and migration, whereas the P equation governs the electrical interaction of the species. The model predicts well an ionsensor response and also the selectivity and the variability of the lower detection limit over time.

4.6

lʹ 0

a better understanding of the dynamics of the glass electrode potential and other properties of the glass surface. It has in particular been established that hydrolysis/condensation reactions of the form

Baucke’s Dissociation Mechanism

Using high-resolution techniques of ion bombardment for spectrochemical analysis (IBSCA) and nuclear reaction analysis (NRA) to study glass surfaces, Baucke [24] gave a most detailed description of the surface layers for lithium silicate glass. He described the state at the glass– solution interface as a dynamic equilibrium both in terms of thermodynamics and electrochemical kinetics. He pointed out that the electrochemical mechanism of the glass electrode potential formation is a consequence

615

616

5.8 The Glass Electrode and Electrode Properties of Glasses

of a process termed charge division at the boundary (the dissociation mechanism). Uncharged surface groups RH and RM are formed because of glass interaction with the solution. Their dissociation results in the appearance on the glass surface of a minute concentration of negatively charged groups R−, e.g. SiO− or SiOAl−, depending on the compositions of the glass and of the solution (and in particular of its ion concentrations). These anionic groups provide a density of negative charges on the surface and, therefore, give rise to a negative potential of the glass membrane with respect to that of the solution. Both the concentration of the charged groups and the glass electrode potential are functions of the solution composition E = f (pH, pM). The reactions of dissociation (and association) of the glass surface groups are in cumulative equilibrium: RH s + H2 O sol ⇄R −

s

+ H3 O +

sol

,

KD,H ,

13

and R−

s

+ M+

sol

⇄RM s ,

KA,M

14

From the respective equilibrium constants of these reactions, KD,H and KA,M, Baucke defined a “selectivity product,” namely, (KD,H KA,M). This product plays a role similar to that of Kexch in Nikolskii’s Eq. (9), i.e. it determines whether or not a glass electrode exhibits a pH or pM response and it characterizes the position of the transition region. According to Ref. [24] this “selectivity product” is constant and its magnitude is equal to 10−12. A thermodynamic treatment of the acid dissociation equilibrium, Eq. (13), yields the equation s

E = E 0H +

RT a − aH O + ln R s 3 = E 0H F aRH aH2 O s

15

RT a − log s R +23 − pH, F aRH aH2 O which thus describes the linear pH dependence of the glass membrane potential as it is usually known. This equation also indicates that the potential of the glass is determined by the minute concentration of the dissociated groups, R−, which are bound to the glass surface and are thus in contact with the solution. Among the significant features of this approach is the theoretical proof of the fact that the experimental slopes of the E–pH (pM) curves are slightly lower than “ideal” ones (namely, 59.16 mV/pH at 25 C) by lying in the range 58–59.1. This difference exists because the change in the activity of ions Н+ and М+ is connected with the activity change in the other members of the equilibrium.

5

Perspectives

Elaboration of new glass compositions along with progress in electronics and instrument manufacturing has produced glass electrodes with more robust membranes that could be operated outside the laboratory in a such different contexts as chemical industry, environmental and pollution control, medicine, oceanography, biology, or life sciences. Hence, only temperature probably is a fundamental parameter now measured more frequently than pH! Development of new special glasses for electrodes with a reversible solid contact will expand further applications in wider temperature ranges with the same excellent reproducibility. The stability of these glass electrodes at high temperature makes it possible to sterilize them with steam under pressure (150 C) and, therefore, to apply them in biotechnical pH monitoring. They will, for instance, be commonly used all over the world to monitor pH and pM for evaluation of the health level in animals and humans (for example, in their aggressive intestinal tract). Thanks to their insensitivity to gaseous components, redox glass electrode will in addition be utilized for measuring redox potentials in microbiological systems under aerobic conditions where interferences with the system O2/H2O will be avoided. Likewise, these electrodes will be fit for measuring pH in Antarctic waters below 0 C as well as up to 3000 atm in deep ocean depths down to the Marianas Trench (11 km)! Baucke studies have actually represented a significant advance in understanding the operational mechanism of glass electrode. From a theoretical standpoint, however, the current framework does not account yet consistently for the dependence of the glass electrode properties on the composition and structure of the glass (especially those properties governed by the ionic mobility), for the extended interval of glass electrode potential in the transition region, or for the dynamics of the potential at transition from one response of glass electrode to another. One can thus surmise that a unified theory of the glass electrode will be created on the basis of Nikolskii– Eisenman theory, Baucke’s approach, and multilayer and Nernst–Planck–Poisson models.

References 1 Lémery, N. (1701). Cours de chymie, 9e, 23–24. Paris:

Estienne Mischallet. 2 Rouelle, G.F. (1754). Mémoire sur les sels neutres, dans lequel on fait connoître deux nouvelles classes de sels neutres, & l’on développe le phénomène singulier de l’excès d’acide dans ces sels. Mém. Acad. Roy. Sci.: 572–588.

References

3 Sørensen, S.P.L. (1909). Enzym Studien, II. Mitteilung

4

5

6

7

8

9

10

11

12

13

ueber die Messung und die Bedeutung der Wasserstoffen koncentration bei enzymatische Prozessen. Biochem. Z. 21: 131–304. Sørensen, S.P.L. and Linderstrøm-Lang, K. (1924). On the determination and value of pH in electrometric measurements of hydrogen ion concentration. Compt. Rend. Lab. Carlsberg 15: 1–40. Belyustin, A.A. (2011). The centenary of glass electrode: from Max Cremer to F. G. K. Baucke. J. Solid State Electrochem. 15: 47–65. Cremer, M. (1906). Über die Ursache der elektromotorischen Eigenschaften der Gewebe, zugleich ein Beitrag zur Lehre von den polyphasischen Elektrolytketten. Z. Biol. 47: 562–608. Haber, F. and Klemensiewicz, Z. (1909). Über electrische Phasengrenzekräfte. Z. Phys. Chem. 67: 385–431. MacInnes, D.A. and Dole, M. (1930). The behavior of glass electrodes of different compositions. J. Am. Chem. Soc. 52: 29–36. Mazurin, O.V., Leko, V.K., Streltzina, M.V. and Shvaiko-Shvaikovskaya, T.P. SCIGLASS. Professional. 7.12 Tables 31420, 31421. Richet, P. (2001). The Physical Basis of Thermodynamics: With Applications to Chemistry, 31. New York: Plenum Press. Nikolskii, B.P. and Materova, E.A. (1985). Solid contact in membrane ion-selective electrodes. Ion-Selective Electrode Rev. 7: 3–39. Belyustin, A.A., Pisarevsky, A.M., Lepnev, G.P. et al. (1992). Glass electrodes: a new generation. Sens. Actuators B 10: 61–66. Pisarevskii, A.M., Schultz, M.M., Nikolskii, B.P., and Belyustin, A.A. (1969). Glass electrode with electronic response. Dokl. Akad. Nauk USSR 187: 364–367.

14 Pisarevsky, A.M. and Polozova, I.P. (2000). Indicator

15

16

17 18

19

20 21

22

23 24

electrode in redox measurement. Vestnik SPbSU Series 4, Phys., Chem. 20: 92–102. Pisarevsky, A.M. and Polozova, I.P. (2010). Redox measurements in solutions with low values EH. Vestnik SPbSU Series 4, Phys., Chem.: 100–108. Nikolsky, B.P., Shultz, M.M., Belyustin, A.A., and Lev, A. A. (1967). Recent developments in the ion-exchange theory of the glass electrode and its application in the chemistry of glass. In: Glass Electrodes for Hydrogen and Other Cations. Principles and Practice (ed. G. Eisenman), 174–222. New York: Marcel Dekker. Nikolsky, B.P. (1937). Theory of the glass electrode 1. Acta Phys.-Chim. URSS. 7: 597–610. Eisenman, G., Rudin, D.O., and Casby, J.U. (1957). Glass electrode for measuring sodium ion. Science 126: 831–834. Eisenman, G. (1967). The origin of the glass electrode potential. In: Glass Electrodes for Hydrogen and Other Cations. Principles and Practice (ed. G. Eisenman), 133–173. New York: Marcel Dekker. Helfferich, F. (1962). Ion exchange. New-York: McGraw-Hill. Belyustin, A.A. (1999). Silver ion response as a test for the multilayer model of glass electrodes. Electroanalysis 11: 799–803. Doremus, R.H. (1967). Diffusion potentials in glass. In: Glass Electrodes for Hydrogen and Other Cations. Principles and Practice (ed. G. Eisenman), 101–132. New York: Marcel Dekker, Inc. Lewenstam, A. (2011). Non-equilibrium potentiometry – the very essence. J. Solid State Electrochem. 15: 15–22. Baucke, F.G.K. (2000). Electrochemistry of solid glasses. In: Electrochemistry of Glasses and Glass Melts, Including Glass Electrodes (eds. H. Bach, F. Baucke and D. Krause), 35–268. Berlin: Springer.

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5.9 Electrochemistry of Oxide Melts Christian Rüssel Otto-Schott-Institut, Jena University, Jena, Germany

1

Introduction

Synthetic as well as natural glasses generally contain more or less high fractions of polyvalent elements, which may thus occur in at least two different oxidation states even if only under extremely oxidizing or reducing conditions. In industry, these elements are either impurities in the raw materials or added on purpose to the glass batch, for example, as fining or coloring agents (Chapter 1.2). The main physical property of a glass influenced by the redox state is the color, i.e. the transmissivity of light in certain wavelength ranges. To a high extent, this feature determines product quality and may in particular reflect the temperature distribution within the melting tank. Other important properties of glasses that depend upon polyvalent elements are fluorescence and solarization. Whether for fundamental or industrial reasons, polyvalent elements and their redox properties must be accurately characterized. If electrochemical methods are particularly valuable in these respects, it is because they are well suited for determining not only the thermodynamics of redox equilibria but also the diffusion coefficients of redox couples or the concentrations of polyvalent species even in glasses contained in melting tanks. A significant advantage of these methods is that they are in principle much faster than those involving redox equilibration experiments. As originally developed to study aqueous or organic solutions, electrochemical methods require good ionic conductors, that is, melts containing alkali oxides at concentrations higher than 10 mol % whose conductivity thus is purely cationic ([1], Chapter 4.2). Reviewers: R. Conradt, RWTH Aachen University, Aachen, Germany P.-J. Panteix, Institut Jean Lamour, Université de Lorraine, Nancy Cedex, France

To review these methods in this chapter, it will be useful to summarize first the basics of redox thermodynamics, referring the reader to Chapter 5.6 for a more complete account. After a brief summary of experimental methods, the thermodynamic determination of redox standard potentials and equilibrium constants will be described. Diffusion coefficients will then be dealt with, followed by voltammetric chemical analyses. Finally, the principle of impedance spectroscopy will be discussed. Because ionic conductivity strongly depends on temperature, the temperature range for which a specific method can be applied is restricted. As a general rule, the larger the ionic conductivity, the smaller the minimum temperature at which a certain electrochemical method can be applied. An upper limit for an electrochemical measurement is only imposed by the chemical and mechanical stability of the used materials. Since electrodes are generally made out of platinum, the upper limit should be about 1650 C. The minimum possible temperature also depends on the method used. For example, simple potentiometric experiments, such as oxygen activity measurements, are possible at lower temperatures than voltammetric measurements where current voltage curves are recorded.

2 Thermodynamics of Redox Equilibria At high temperatures, polyvalent elements in reduced and oxidized forms build equilibria with the oxygen physically dissolved in the melt (O2−): An +

z 2− O 2

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

An − z +

z O2 , 4

1

620

5.9 Electrochemistry of Oxide Melts

where n is the number of transferred electrons and An and An − z are the redox species in its oxidized and reduced state, respectively. The constant of this equilibrium depends on both temperature and melt composition: z 4

K T =

aAn − z aO2 z 2

aAn aO2 −

,

2

where ai is the activity of species i. Except for silver in certain systems (see Section 5), the equilibrium described by Eq. (1) shifts to the right with increasing temperature. In other words, the reduced state is favored with increasing temperature since production of gaseous oxygen causes the large entropy increase associated with the stable high-temperature state by Le Chatelier’s moderation principle. Because the O2− species do not occur in noticeable quantities in most glass compositions, and its activity is in addition unknown, it is more suitable to describe the redox equilibrium by another equilibrium constant K (T) defined as z 4

K T =K T

z 2 aO 2 −

aAn − z aO2 = , aAn

3

which also depends upon melt composition. In most glass melts, the concentration of physically dissolved oxygen is much smaller than those of polyvalent ions, so the equilibrium described by Eq. (1) does not shift noticeably upon quenching if no other redox pair is present in the melt [2]. This is the reason why one can determine redox equilibrium constants by equilibrating a melt with an atmosphere of known oxygen partial pressure, quenching the sample and analyzing the An/An − z ratio by appropriate physical or chemical means. But this procedure is time consuming because the needed diffusion of oxygen into or out of the sample tends to be slow under conditions where speeding up of the equilibration process by convection is not possible because of a high melt viscosity. Although the quantity of melt equilibrated with the atmosphere in these experiments is usually as small as a few grams, one should always ensure that equilibrium with the atmosphere is actually reached. An alternative procedure is to measure the oxygen activity of the melt with a ZrO2-based sensor. In the literature, numerous studies on redox equilibria relying on such equilibration methods have been reported (e.g. [3]). In the last two decades, however, redox equilibria have frequently been studied electrochemically [4, 5]. Although the most common method is square-wave voltammetry, impedance spectroscopy is also used. To perform these measurements, electrodes are inserted into the melt, and measurements are directly carried out, typically in the 1000–1600 C range. In addition to the

redox equilibrium data, diffusion coefficients are also derived from the recorded voltammograms. According to Eq. (1), the ratio An/An − z depends on the gas atmosphere, temperature, and, furthermore, melt composition. From the equilibrium constant K (T), the standard Gibbs free energy, ΔG (T), can be obtained. If its temperature dependence is also determined, then the standard enthalpy, ΔH , and entropy, ΔS , can also be derived from ΔG T = ΔH – T ΔS = – RT ln K T ,

4

where R is the gas constant. In addition, the standard potential E0 of the redox pair and its temperature dependence can be determined because it is related to the standard Gibbs free energy, ΔG (T), by ΔGo T = − nFE 0 T ,

5

where F is Faraday constant and n is the number of transferred electrons. Empirically, available experimental data have been used to account for the dependence of redox equilibria on melt composition in terms of formulae that account for the contribution of each component by an incremental system, generally with the assumption of a linear effect for each of them. Actually, however, this approach is highly questionable at least for elements such as alumina or boron whose oxygen coordination numbers and structural role vary with the overall glass composition (Chapters 2.4, 7.6) as also mentioned below.

3

Experimental Aspects

In usual laboratory electrochemical measurements, from 50 to 250 g of glass is melted between 1000 and 1600 C, depending on composition, in a platinum crucible in a high-temperature furnace (for instance, with MoSi2 heating elements). The highest signal-to-noise ratios are obtained if the power supply of the furnace delivers a d. c. voltage. For oxygen activity measurements, the potential between a zirconia probe and a platinum electrode may, for instance, be measured (Figure 1). Whereas the zirconia electrode must be as large as possible, the wire forming the three-phase boundary melt/Pt/air must be as thin as possible to minimize oxygen transport. If air is used as a reference gas, the oxygen activity, aO2 , of the melt can be calculated with E = RT 4F ln aO2 0 21 bar

6

It follows that measurements of aO2 at varied temperatures also enable ΔHo to be calculated. For voltammetric measurements (Figure 2), three electrodes are inserted into the melt from the top: a platinum

4 Standard Potentials and Equilibrium Constants

Air

1600 °C

4 Potential Alumina tubes

3 I in mA

Platinum wire

1400 °C

1

Large platinum electrode

0

Figure 1 Experimental set up for measurements of oxygen activities in a glass melt.

1200 °C –600 –500 –400 –300 –200 –100 E in mV

0

100

Figure 3 Effects of temperature on peak potentials in voltammograms recorded for a 10 Na2O 10 MgO 10 Al2O3 70 SiO2 (wt %) melt doped with 0.25 mol % Fe2O3 [7].

Air

Working electrode Platinum wire

Platinum wire

2

1300 °C

ZrO2 solid electrolyte

Potentiostat

1500 °C

Alumina tubes Reference electrode ZrO2 solid electrolyte

Counter electrode Platinum plate

Figure 2 Experimental set up for voltammetric measurements in glass melts.

present with overlapping current–potential curves or in any other nonideal case, for instance, if adsorption at the electrode takes place [8]. As described in detail in the literature [9], it is best to deconvolute the curve in terms of experimentally recorded matrix currents and theoretically calculated current–potential curves [6] of the particular electron transfers. Equilibration with the surrounding atmosphere is in fact not necessary because the working electrode has a starting potential – usually 0 mV vs. the zirconia-air electrode – which yields the same redox ratios as achieved upon equilibration with air. From the peak current densities, ip, diffusion coefficients can in addition be obtained with ip = const D1

wire (1 mm in diameter) as the working electrode, a platinum plate as a counter electrode (size: 2 cm2), and a ZrO2-based reference electrode flushed with air. These three electrodes are connected to a potentiostat, which is the main part of the electronic equipment because it ensures that the potential between the working and reference electrodes is always equal to the required value. The potentiostat is further connected to a computer, which also controls the desired time dependence of the potential and records the current. The fundamentals of this method are well documented in literature (e.g. [6]). In square-wave voltammetry, the most frequently used technique, the potential–time dependence is a staircase ramp upon which a rectangular wave (τ = 10–400 ms, potential amplitude ΔE = 100 mV) is superimposed. One measures the current after each half-wave and then calculates the difference between two consecutive values to derive the standard potential of the redox pair considered. In simple cases, this potential is given by the maximum observed in the current–potential curve (Figure 3). The situation is more complicated if two redox pairs are

2

C o ΔE τ − 1 2 ,

7

where Co is the total concentration of the polyvalent ion, D is the mean diffusion coefficient of its oxidized and reduced species, ΔE is the pulse potential, τ is the step time of the square wave, and const is equal to 0.31 π −1/2 F2 n2/(RT). In summary, a simple potential measurement enables first the oxygen activity of the melt to be determined and then the redox ratio to be calculated if the thermodynamics of the redox pair considered is known.

4 Standard Potentials and Equilibrium Constants To verify the validity of the determined dependence of a redox ratio on oxygen activity, one dopes the melt investigated with the polyvalent element of interest and equilibrates it under different oxygen fugacities at the same temperatures. The redox ratios are then determined independently, for instance, by spectroscopic methods. In a

621

5.9 Electrochemistry of Oxide Melts

Fe3 + + e − = Fe2 +

8

With decreasing temperatures, the peak potential becomes increasingly negative, varying from about – 145 mV at 1600 C to –225 mV at 1200 C, thus indicating a shift of the iron redox equilibrium toward the oxidized Fe3+ state. In parallel, the strong decrease observed for the peak currents is caused by decreasing diffusion coefficients. As for the final increases of the current at potentials more negative than −500 or −600 mV (depending on temperature), they are due to partial decomposition of the melt into platinum silicide. More comprehensive results illustrate the effects of changes of either composition or temperature on iron redox equilibrium. The effects on potentials of the substitution of MgO for SiO2 at 1600 C (Figure 4) [7] are in fact similar to those of decreasing temperatures (Figure 3): increasing MgO concentrations yield more negative potentials through shifts toward the Fe3+ state, whereas diffusion coefficients increase notably. This similarity is borne out by comparisons made between the effects of temperature and MgO concentrations on peak potentials whose variations are approximately linear in both cases (Figure 5). The effect of glass composition on the peak potentials also enables conclusions to be derived on the melt structure at the respective temperature, for example,

on the way in which an increasing Al2O3 concentration causes Al to be no longer solely incorporated in tetrahedral coordination. Copper raises more difficulties than iron because the initial reduction of Cu2+ into Cu+ is followed by reduction of Cu+ into metallic Cu, which can alloy with the Pt electrode. Because the second of the two peaks of voltammograms (not shown) thus has to be discarded, only the peak potentials of the first reaction are displayed in Figure 6 [10] against temperature for Cu-doped sodium aluminosilicate melts with varying Al/(Al + Si) ratios. In these instances, the measurements become increasingly inaccurate above 1000 C because of signal superimposition with matrix currents at positive potentials caused by the decomposition of the glass matrix and the resulting formation of gaseous oxygen. At all temperatures, the peak potentials increase with increasing Al2O3 –50 –100 1600 °C –150 1500 °C E in MV

plot of log ([An]/[An+z]) against log (aO2 ), aO2 = oxygen activity, the results define a straight line with an n/4 slope. As a matter of fact, all redox pairs studied in this way conform to Eq. (1), so this relationship is experimentally well proved [5]. As a first example, the square-wave voltammograms recorded at different temperatures from a potential of 0 mV for an iron-doped (Na,Mg) aluminosilicate are shown in Figure 3. All curves display a distinct maximum caused by the reduction of Fe3+ to Fe2+:

–200 1400 °C 1300 °C

–250 –300 –350

5

0

10 15 20 MgO concentration in mol %

25

Figure 5 Voltammetric peak potentials as a function of the MgO concentration in glass melts with the basic compositions composition 10Na2O x MgO 10 Al2O3 (80 − x) SiO2 doped with 0.25 mol % Fe2O3 [7]. 200

20 MgO

150 Peak potential in mV

7 6 5 I in mA

622

4

15 MgO 10 MgO

3 5 MgO 2

x=15

50 x=10 0 x=5

–50 –100

1 0

100

x=20

–150 800 –600 –500 –400 –300 –200 –100 E in mV

0

100

Figure 4 Effects of (MgO, SiO2) substitution on peak potentials in voltammograms recorded at 1600 C for 10 Na2O x MgO 10 Al2O3 (80 − x) SiO2 melts doped with 0.25 mol % Fe2O3 [7].

850

900

950 1000 1050 Temperature in °C

1100

1150

Figure 6 Voltammetric peak potentials of the Cu+/Cu2+ peak as a function of the temperature in melts with the basic mol% compositions 26 Na2O x Al2O3 (74 − x) SiO2 doped with 1 mol % CuO [10]. Solid lines: regression lines.

5 Diffusion Coefficients

concentration from 5 to 15 mol % and then drop off so abruptly at higher contents that below 1000 C the most negative peak potential is that of the sample with 20 mol % Al2O3, because then Al2O3 is no longer incorporated solely in tetrahedral coordination. Within experimental errors, the potentials again depend linearly on temperature for all studied compositions. The slopes and intercepts of these lines thus directly yield the standard entropies, ΔS , and enthalpies, ΔH , of the redox reaction, whose highest absolute values are thus found for the 20 mol % Al2O3 sample. Not surprisingly, a great many voltammetric measurements have been made on soda-lime-silica melts in view of their considerable industrial importance. A selection of data obtained for a variety of redox couples shows that, with the single exception of Ag /Ag+, all peak potentials increase in absolute values with increasing temperatures with distinct but not so different slopes (Figure 7) [11]. As a result, the order of these redox couples remains basically the same at different temperatures. Of course, the values for a given redox couple reflect the particular manner in which both valences are incorporated in the melt structure. Hence, they depend on melt composition as already shown by Figures 4–6. For polyvalent elements

200 Sb3+/5+

As3+/5+

such as iron, tin, and copper, this effect has been studied in detail, so structural models for their incorporation have been proposed [1, 9]. From the broad variety of glass compositions investigated for the Fe3+/Fe2+ couple, a model of prediction of the peak potential, for instance, has relied on sodium and aluminum speciation to yield E p 1300 C = a + b Na2 O NBO + c Na2 O Al + d MgO + e CaO + f Al2 O3 t + g Al2 O3 o + h SiO2 , 9 where [Na2O]NBO and [Na2O]Al are the Na2O concentrations of network-modifying and Al charge-compensating sodium, respectively, and [Al2O3]t and [Al2O3]o are the Al2O3 concentrations of tetrahedral and octahedral aluminum, respectively. The fit parameters are a = 20 mV and b = 8.76, c = 3.42, d = 7.84, e = 11.19, f = 2.7, g = 7.34, and h = 2.72 mV/mol % [1]. Other empirical formulae have been proposed in narrower composition ranges, from which the redox ratios can also be calculated from the glass composition and the oxygen activity. [7, 9]. The Ag /Ag+ redox potential is a special case because its decreases with increasing temperature in Al-free melts (Figure 7), as already noted, and also below 1100 or 1200 C in aluminosilicate melts before increasing “normally” at higher temperatures [12]. The Ag+ ion can be a network-modifying or a charge-compensating cation for tetrahedral Al3+, like alkali and alkaline earth cations with which it competes for bonding with either nonbridging or bridging oxygens. The complex voltammetric results thus point to complex structural interactions as function of both temperature and composition, which remain to be investigated specifically.

–200 As0/3+

Sb0/3+ E in mV

Cu0/+

5

Diffusion Coefficients

–400 Ag0/+ Mo3+/5+ –600

Fe2+/3+

Zn0/2+ Pb0/2+

Ni0/2+

V3+/4+

–800

Mo0/3+ –1000

D = Do ∙ exp E a RT ,

Cd0/2+

800

In addition to peak potentials, square-wave voltammetric experiments have yielded a wealth of diffusivities for polyvalent elements. Some of them are represented in an Arrhenius plot for a standard soda-lime-silica glass in the rather wide 750–1300 C range (Figure 8) [13]. As determined from fits made with Arrhenius equation to the experimental data, they range from 3×10−17 to 2×10−10 m2/s:

900

1000 1100 1200 Temperature in °C

1300

Figure 7 Effect of temperature on the electrochemical series for a glass with the composition 16 Na2O 10 CaO 74 SiO2, doped with various types of polyvalent elements [11].

10

where Ea is the activation energy and Do a preexponential factor. At a temperature of 850 C, the diffusion coefficients vary from 3×10−17 to 10−11 m2/s, i.e. by more than six orders of magnitude. The largest are those of silver, known to be very mobile in a glass network, which, for example, makes this element highly suitable for ion

623

5.9 Electrochemistry of Oxide Melts

1300 1200 1100

900

1000

–6.5

800

20 Na2O 80 SiO2

–10

–11

Ago

Log D (D in cm2/s)

–7.0 15 Na2O 85 SiO2 –7.5 26 Na2O 74 SiO2

–8.0 33 Na2O 67 SiO2 –8.5

Log D (D in m2/s)

624

Cd2+

–12

–9.0 7.0

Te4+ Fe2+

–13

Bi3+ As3+

Cr3+

Ni2+

Pb2+ Co2+

–14 Ta5+

Sn4+

Sb3+

–15

–16

Cr6+

7

8 1/Temperature in

9 10–4

K–1

Figure 8 Arrhenius plot of the diffusion coefficients of various polyvalent elements determined in a glass with the basic composition 16 Na2O 10 CaO 74 SiO2 [13].

exchange. These diffusion coefficients are in the same order as those of other network modifiers such as alkalis. The smallest values are those of Cr6+, which possesses a high charge and seems to be tightly bonded to the glass network. These diffusion coefficients are in the same range as those of silicon. The coefficients of ions with valences from 2 to 4 lie in between the values of Ag+ and Cr6+. As usual, diffusivities conform to a compensation law whereby the activation energies of faster diffusing species are lower and, conversely, those of slowly diffusing species are higher (Figure 8). But the large variations of the data plotted illustrate that Stokes–Einstein law is not generally valid because these diffusion coefficients should otherwise vary with the reciprocal of ionic radii, i.e. under no circumstances by more than one order of magnitude at the same temperature. Obviously, the way in which the respective redox species are incorporated in the melt structure plays an important part, and it is of course not simply determined by the ionic radius and the charge of the ion.

7.5 8.0 1/Temperature in 10–4 K–1

8.5

Figure 9 Arrhenius plot for the mean diffusion coefficients of Cu+/Cu2+ for different sodium silicate melts [14].

The strong effects of composition are illustrated by Arrhenius plots of the mean diffusion coefficients of Cu+/Cu2+ for different sodium silicate melts (Figure 9) [14]. In all cases, the temperature dependence is actually Arrhenian. Although similar values are found for Na2O concentrations in the 15–26 mol % range, the diffusion coefficients are the smallest for the 15 mol % Na2O melt, pass through a maximum at 20 mol % Na2O, and then markedly decrease at higher contents. The surprising result is that copper diffusion coefficients are smaller than in the melt with the highest Na2O concentration, i.e. with the lowest viscosity [14]. There are thus two competing regimes, namely, the first where Stokes–Einstein equation obtains and the second where copper becomes more strongly incorporated with increasing Na2O concentration.

6 Voltammetric Sensors: Quantitative Determinations of Polyvalent Elements Yet another application of voltammetry deals with the quantification of polyvalent elements, which can be performed directly, even in technical glass-melting furnaces where glasses such as green and amber are produced. These materials contain iron, chromium, and sulfur. Chromium occurs in three different valence states, namely, Cr2+, Cr3+, and Cr6+ and thus shows the two peaks of the redox pairs Cr2+/3+ and Cr3+/6+. Altogether four voltammetric peaks are expected (two for chromium and one for both iron and sulfur) and are actually observed (Figure 10) [15]. The attributed peak potentials are known from laboratory studies of melts that contain only one of these polyvalent elements. If the attributions of peaks to the redox steps Cr6+/3+, Cr2+/3+, and Fe2+/3+ are clear, that of the sulfur peak is not. The shape of

7 Impedance Spectroscopy

1: Green glass 2: Glass matrix

6 ΔI in mA

7: Fe3+/2+

4 Dashed

8: Cr3+/2+

5: Cr6+/3+

5+6+ 7+8

2 Dotted 1–2

6: Sulfur

0 –1000

–800

–600

–400

–200

0

E in mV

Figure 10 Voltammogram recorded for a green glass melt (curve 1) and a melt without any polyvalent element [15]. Difference curve (1–2) decomposed into contributions of Cr6+/3+ (curve 5), sulfur (curve 6), Fe3+/2+ (curve 7), and Cr3+/2+ (curve 8). Curve 4, sum of the simulated curves 5–8.

the voltammogram is always the same, but the origin of the peak, i.e. the attributed redox pair, is not definitely known, possibly because electrode adsorption plays an important part. But this limitation does not prevent sulfur from being quantitatively determined in the melt (Figure 10). First, a voltammogram is obtained for the melt under study and another for a melt with the same basic composition, but without any polyvalent elements. After subtracting the latter curve from the former, one decomposes with a least squares method the resulting difference into four bands whose peak potentials and full widths at half maximum yield the sought after contents of chromium, iron, and sulfur [15]. In the same base glass composition and at the same temperature, the peak potentials and halfwidths do not depend on the respective concentrations.

By contrast, only a few studies have been performed with impedance spectroscopy on the thermodynamics and diffusion of polyvalent ions in glass melts (e.g. [16]). Here the same three-electrode equipment as used for voltammetric studies is suitable, and a large variety of methods is in principle possible. The method most frequently applied consists in superimposing on a given d.c. potential and a.c. potential with an amplitude of 5–50 mV and a frequency in the 10−2–106 s−1 range. Then one simply studies the effect of the d.c. potential by repeating the experiment at different values. To obtain impedance spectra, the absolute value of the impedance and the phase angle or the real and the imaginary parts are measured and plotted for illustration. The next step involves setting up first a physical model of the processes at the working electrode and then an equivalent circuit composed of resistors, capacitors, and some other impedance elements. A suitable software is finally used to optimize the values of each impedance elements. If the simulated spectrum agrees with the measured values within the limits of the experimental error, the equivalent circuit is assumed to give an appropriate description of the electrode reactions. Experiments done with three different d.c. potentials on a 16 Na2O 15 Al2O3 69 SiO2 sample doped with 0.25 mol % Fe2O3 illustrate the procedure (Figures 11–13). 60 50 Phase angle in °

8

40 c

30

b

a

20 10 0 1000

7

Impedance Spectroscopy

The last technique to be presented is impedance spectroscopy, a fairly versatile tool to investigate glasses and melts. It is, for instance, extensively used in studies of corrosion processes (Chapter 5.10). Examples are corrosion of molybdenum electrodes in contact with glass melts or of ion conductive glass in contact with molten salts. Impedance spectroscopy is also commonly applied to investigate electrical relaxation phenomena, mostly at temperatures below the glass transition, and also phase separation when changes in ionic conductivity allow the temperatures of the transitions, or even their kinetics, to be determined.

Impedance in W

a

100

b c

10

1

0.1

1

10 100 1000

100 000

Frequency in s–1

Figure 11 Impedance spectra in a melt with the basic composition 16 Na2O 15 Al2O3 69 SiO2, doped with 0.5 mol % Fe2O3 recorded at 1500 C at different superimposed d.c. potentials of −400 mV (a), −150 mV (b), and 0 mV (c) [16]. Solid lines: simulated curves. Please note that the absolute values of impedance and phase angle are drawn.

625

5.9 Electrochemistry of Oxide Melts

RΩ

W

RE

L

CD

Figure 12 Equivalent circuit used to simulate the obtained impedance spectra [16]. L, inductivity; RE, ohmic resistivity of the melt between the working and reference electrodes; RΩ, resistivity due to the electron transfer reaction; CD, double layer capacitance; and W, Warburg parameter.

700 Warburg parameter in Ws–1/2

626

1550 °C 1500 °C 1450 °C 1400 °C 1350 °C

600 500 400 300 200

processes), a resistor RE (accounting for the limited ionic conductivity of the melt and increasing with decreasing electric conductivity), and an inductance L predominantly attributed to the wiring. For the melt compositions studied, the resistor RΩ is negligibly small because the temperature is high enough that the electrode reaction is not kinetically hindered during the measurements. That this equivalent circuit is appropriate is shown by the good agreement found between the simulated and experimental values (Figure 11). Interestingly, most elements of the equivalent circuit do not depend on the d. c. potential. Only the Warburg parameter W does so. It should possess a minimum at the standard potential of the electrode reaction, as borne out by the minima observed at five different temperatures between 1350 and 1550 C (Figure 13) where all points were extracted from individual simulations of the impedance spectra. Actually the Warburg parameter is the largest at 1550 C, where the diffusion coefficient of iron is highest, and decreases with decreasing temperatures. In all cases, a minimum is observed at potentials between −200 and −150 mV. The respective potential is identical with the respective standard potential.

100 0 –600

–500

–400 –300 –200 DC potential in mV

–100

0

Figure 13 Dependence of the Warburg parameter on the superimposed d.c. potential at various temperatures for a 16Na2O 15Al2O3 69SiO2 base melt [16].

In spectra recorded at 1500 C in the 10−2–106 s−1 frequency range (Figure 11), the absolute value of the impedance is approximately constant and in addition does not depend on the d.c. potential at frequencies higher than 2 × 103 s−1. At lower frequencies, however, the differences become significant, the impedance increasing with the voltage applied. As for the phase angles, they are all negative up to a frequency of 2 × 104 s−1 above which they become positive (NB in Figure 11, the absolute values of impedance and phase angle are drawn). At the lowest frequency (0.1 s−1), the absolute value of the phase angle is the largest and then decreases continuously until the minimum is reached. The curve obtained for −150 mV is clearly different from those recorded at the other potentials. In a second step, the impedance spectra are simulated with an equivalent circuit (Figure 12), which is the simplest possible suitable to describe the electrochemical experiment. It is composed of the capacitance of an electrochemical double layer CD, a resistor RΩ (which is >0 Ω if the electrode reaction is kinetically hindered), a socalled Warburg impedance W (accounting for diffusion

8

Perspectives

Although the majority of electrochemical studies of glass melts have dealt with alkali or alkaline earth silicates and alumosilicates, some have been carried out on phosphates or borosilicates. In the latter, voltammetric measurements are similar to those made on silicates because the potential range accessible is approximately the same and limited by the same processes, namely, the formation of gaseous oxygen and platinum silicide at positive and negative potentials, respectively. Studies in borosilicate melts have concentrated on a composition suggested for the vitrification of nuclear waste (57 SiO2 12.2 B2O3 16.8 Na2O 11.1 Li2O 2.9 MgO 0.2 ZrO2 0.1 La2O3) [17]. Thanks to high alkali concentrations and, thus, to high ionic conductivities, measurements have been readily made as a function of temperature for a variety of polyvalent elements, transition metals included. The electrochemical series of elements is similar to that in a soda-lime-silicate glass melt, although the absolute values are somewhat different (compare [11, 17]). By contrast, electrochemical measurements are difficult to perform in phosphate melts, probably because of high water concentrations. These lead to an increase in current at potentials more negative than 700 C, which is supposedly due to the formation of PH3 or P2H6. In a glass melt with the composition NaPO3 2 Sr(PO3)2, an electrochemical series of elements has nonetheless been

References

determined. With respect to silicates, the main difference is that the redox pair Sb3+/Sb5+ has a standard potential that is more negative than that of the As3+/As5+ redox pair. Future studies should also focus on polyvalent rare earth elements such as Ce3+/4+, Eu2+/3+, and Yb2+/3+ relevant to luminescent materials (Chapter 6.3), which up to now have not been studied electrochemically. Here, the luminescence should widely be affected by the redox state. Knowledge of thermodynamic data of redox equilibria is valuable to understand the redox reactions that are taking place when the temperature is changed. Although these reactions are frozen in below Tg, thermodynamics has indeed a stronger effect on these reactions than kinetics.

7 Wiedenroth, A. and Rüssel, C. (2003). The Effect of MgO

8

9

10

11

References

12

1 Rüssel, C. and Wiedenroth, A. (2004). The effect of glass

2

3 4

5

6

composition on the thermodynamics of the Fe2+/Fe3+ equilibrium and the iron diffusivity of Na2O/MgO/CaO/ Al2O3/SiO2-Melts. Chem. Geol. 213: 125–135. Rüssel, C., Kohl, R., and Schaeffer, H.A. (1988). Interaction between oxygen activity of Fe2O3 doped soda-lime-silica glass melts and physically dissolved oxygen. Glastech. Ber. 61: 209–213. Johnston, W.D. (1964). Oxidation-reduction equilibria in iron containing glass. J. Am. Ceram. Soc. 47: 198–201. Müller-Simon, H. and Mergler, K.W. (1988). Electrochemical measurements of oxygen activity of glass melts in glass melting furnaces. Glastech. Ber. 61: 293–299. Takahashi, K. and Miura, Y. (1987). Electrochemical behavior of glass melts. J. Non Cryst. Solids 95 & 96: 119–130. Osteryoung, J.G. and Osteryoung, R.A. (1985). Squarewave voltammetry. Anal. Chem. 57: 101A–110A.

13

14

15

16

17

on the thermodynamics of the Fe2+/Fe3+ - redox equilibrium and the incorporation of iron in sodamagnesia-alumosilicate melts. J. Non Cryst. Solids 320: 238–245. Benne, D., Keding, R., and Rüssel, C. (2005). Redox processes in a tin doped melt with the basic composition 20 Na2O ∙ 80 SiO2 studied by square-wave voltammetry and impedance spectroscopy. J. Non Cryst. Solids 351: 2987–2994. Wiedenroth, A. and Rüssel, C. (2001). The Fe2+/Fe3+-Redox equilibrium in 5 Na2O 15 CaO x Al2O3 (80 - x) SiO2 (x= 525) liquids. J. Non Cryst. Solids 290: 41–48. Kaufmann, J. and Rüssel, C. (2010). Thermodynamics of the Cu+/Cu2+-redox equilibrium in alumosilicate melts. J. Non Cryst. Solids 356: 1615–1619. Rüssel, C. and Freude, E. (1989). Voltammetric studies of the redox behaviour of various multivalent ions in soda lime silica glass melts. Phys. Chem. Glasses 30: 62–68. Claußen, O. and Rüssel, C. (1999). A Voltammetric Study of the Ag+/Ago equilibrium in soda-alumina-silicate melts. J. Mol. Liq. 83: 295–302. Rüssel, C. (1991). Self diffusion of polyvalent ions in a soda lime silica glass melt. J. Non Cryst. Solids 134: 169–175. Kaufmann, J. and Rüssel, C. (2010). Diffusion of copper in soda-silicate and soda-lime-silicate glasses. J. Non Cryst. Solids 356: 1158–1162. Claußen, O. and Rüssel, C. (1996). Quantitative in-situ determination of iron in a soda-lime-silica glass melt with the aid of square-wave-voltammetry. Glastech. Ber. Glass Sci. Technol. 69: 95–100. Schirmer, H. and Rüssel, C. (2010). Square wave voltammetry and impedance spectroscopy in iron doped melts with the compositions xNa2O ∙ 15Al2O3 ∙ (85-x) SiO2. Eur. J. Glass Sci. Technol. B, Phys. Chem. Glasses 51: 189–194. Claußen, O. and Rüssel, C. (1997). Thermodynamics of various polyvalent main group elements in a borosilicate glass melt. J. Non Cryst. Solids 209: 292–298.

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5.10 Glass/Metal Interactions Carine Petitjean1, Pierre-Jean Panteix1, Christophe Rapin1, Michel Vilasi1, Eric Schmucker2, and Renaud Podor3 1

Université de Lorraine, CNRS, IJL, F-54000 Nancy, France CEA, Université Paris-Saclay, Gif-sur-Yvette, France 3 ICSM, Univ Montpellier, CEA, CNRS, ENSCM, Bagnols sur Cèze, France 2

1

Introduction

Contact between metals and molten oxides takes place in a large variety of industrial processes. The resulting sticking and adhesion phenomena are either an integral component of the process or a drawback to be avoided. For example, preoxidation of a metal part ensures tight sealing with glass in fields as diverse as jewelry, decorative furniture, or electrical and electronic technologies. On the contrary, in glassmaking or glass forming (e.g. Chapter 1.5), sticking between the glass and the mold, crucible or stirrer must be avoided as it may induce defects on the product and corrosion of the tools. The purpose of this chapter is thus to give an overview of the physicochemical interactions between glasses or melts and metallic materials. Complexity is actually a general feature of these chemical interactions because of the fundamentally different natures of metals and oxide melts. As metals and metallic alloys exhibit a high electropositivity, i.e. an ability to be oxidized to a cationic state, molten oxides are electrolytic solvents that may dissolve ionic species and in addition may act as oxidizing agents. Redox reactions involving dissolved metal and nonmetal species may thus occur in molten silicates and lead in fine to the dissolution of metallic solids if the metal and molten glass are in close contact over a wide interfacial area. To deal with these interactions, the fundamentals of wettability and sticking will first be considered. Then the chemical interactions between glass and metallic alloys will be detailed as they rule the corroded or Reviewers: G. Libourel, Géoazur UMR7329, Sophia-Antipolis, Valbonne, France A.A. Rahim, School of Chemical Sciences, Universiti Sains Malaysia, USM, Pulau Pinang, Malaysia

passivated state of the metal. This done, the next three sections will be successively dedicated to the key parameters controlling the chemical reactivity of glass/metal interfaces, the methods and techniques used to study them, and finally typical cases of metallic materials corrosion.

2 Wetting, Sticking, and Adhesion Phenomena Any study of glass/metal interactions must begin with wetting as it is the first step toward either the unwanted corrosion of the metal or the desired sticking and adhesion between the two phases [1]. Referring to recent contributions [2, 3] for a more detailed treatment and other examples, we will first state that the concept of wetting is based on the contact angle (Figure 1) measured between a glass droplet and the relevant substrate. In a first approximation, this angle is evaluated by the classical Young–Dupré equation, namely, γ sv − γ sl = γ lv cos θ ,

1

where γ sv is the solid surface energy, γ sl the solid–liquid interfacial energy, and γ lv the surface tension of the liquid in contact with the vapor phase. Complete wetting consists in the total spread of the liquid onto the substrate, i.e. θ = 0, whereas partial wetting is obtained for values of θ comprised between 0 and 90 . When wetting occurs it means, therefore, that γ sl is lower than γ sv, the difference (γ sv − γ sl) being its driving force. Many parameters influence the wetting of a molten glass onto a metallic substrate: (i) temperature; (ii) the chemical composition of the surrounding atmosphere, notably its oxygen fugacity; (iii) the roughness and composition of the solid surface, which can be oxidized or not; and

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

630

5.10 Glass/Metal Interactions γlv

Vapor θ

Liquid

γsv

γsl

Solid Equilibrium: γsv – γsl = γlv ∙ cos(θ)

Figure 1 Scheme of a liquid sessile drop in equilibrium with a solid substrate: γ sv is the solid’s surface energy, γ sl the solid–liquid interfacial energy, and γ lv the surface tension of the liquid in contact with the vapor phase.

(iv) the composition of the glass, which determines both the rate of spreading and the potential extent of chemical reactions upon reactive wetting. The wetting experiments made by the “transferred drop” version of the sessile drop technique proposed by Pech et al. [3] takes into account all these parameters (Figure 2). They are performed in a metallic furnace in an atmosphere of purified helium with an oxygen partial pressure lower than 10−9 Pa. The device must be equipped with windows so that the drop morphology can be video recorded at high temperature. The contact angle θ and the drop base radius R are then measured directly from the recorded images. The glass must first be introduced into the furnace on an auxiliary substrate. A dynamic vacuum is established (Ptotal = 10−5 Pa), and the temperature is then increased up to 1200 C. This step allows gas bubbles to be removed and fining of the glass specimen to be achieved, typically in two hours. Then, the temperature is decreased down to the chosen wetting temperature (Tw) [3]. At this stage, the drop is raised until it touches the studied substrate to form (a)

gradually a pendular bridge through which the melt is transferred to the substrate by capillary forces. Upon cooling, the last step consists in measuring the temperature at which the glass spontaneously separates from the substrate. This detachment temperature (Td) is typically lower than the glass transition temperature (Tg) by several hundred degrees. As an example, the wetting of a soda-lime glass – with 13.4 wt % Na2O, 10.9 CaO, 1.4 MgO and 1.6 Al2O3 and Tg = 560 C – on a standard stainless steel substrate will be considered. The following observations are made [2]:

• •• • •

The contact angle θ ranges from 60 to 70 between 965 C and 1200 C. The spreading rate increases with the test temperature. The substrate roughness increases the actual contact area and, therefore, causes a decrease of both the contact angle and spreading rate. The detachment temperature lies between 100 C and 150 C. The metal surface is not oxidized.

Interestingly, these results are not sensitive to changes in the contents of more (Cr, Si) or less (Ni, Co, Fe, Mo) oxidizable elements in the stainless steel. For a platinum substrate, a typical noble metal, the results are similar except for the detachment temperature Td, which is just 20 C lower. Partial wetting is observed when metals are investigated in a neutral atmosphere. When electropositive atoms are linked by metallic bonds, wetting is nonreactive and relatively insensitive to the nature of the metal. Adhesion is thus ensured by physical Figure 2 Successive temperature–time steps of the “transferred drop” variant of the sessile drop technique. (a) Deposition of the glass onto an auxiliary substrate, (b) glass after fining on the auxiliary substrate, (c) drop raised to the test substrate for transfer by capillary contact and formation of a pendular bridge, and (d) hanging glass drop. Source: Reprinted with permission from [3].

(b)

T

1200 °C

(d)

Glass refining Tw

Wetting Study substrate

500 °C

(c)

Cooling

Cv Glass transfer

Td Detachment High vacuum (10–5 Pa)

He 50 kPa

t

3 Control of High-Temperature Chemical Interactions at the Metal/Molten Glass Interface

interactions. These results are consistent with those of Zackay et al. [4]. In contrast, for a vitreous carbon substrate, the contact angle θ and detachment temperature Td are 135 and 300 C, respectively. In such a nonelectropositive compound characterized by covalent bonds, nonwetting is partial, and adhesion is rather due to van der Waals interactions and is thus relatively weak. One can improve wetting and sticking by oxidizing the surface of the metal. The cohesion of the formed oxide is due to ionic (or ionocovalent) bonds. The same kind of bond can exist between the oxide and the glass, as the latter is also an ionocovalent compound. Under such conditions, low contact angles are actually measured with the transferred drop technique as a result of a reactive wetting process. In addition, good adhesion is achieved since no detachment is observed (Td < 20 C), especially when the mismatch between the thermal expansion coefficients of the metal substrate and of the glass is well accommodated by the interfacial oxide layer. The oxide layer can be formed either at high temperatures in atmospheres with high oxygen contents or by in situ oxidation of the immersed metal surface by the oxidizing species initially present or added to the glass [3]. In such cases, the oxide layer is permanently stable if its constituting elements have reached their solubility limit in the molten glass (see Section 3). Clearly, these concentrations are determined by the overall composition of the considered glass matrix. In many cases, however, oxide dissolution in the glass is quicker than its formation at the metal surface [3] inducing corrosion of the metallic solid [5]. A preoxidation treatment of the substrate is then necessary. These various features have been taken into account for developing optimized glass/metal interfaces with noble metals like Pt or Au and, more frequently, with oxidizable metals such as Cu, Ag, Fe, Cr, Fe–Ni–Co (Kovar), Mo, W, Zr, and Ti and their respective oxides [6]. Of course, these are widely used in many applications like sealants for vacuum tubes, incandescent light bulbs, or tight channeling of fuel and oxygen in solid oxide fuel cells [7]. Other promising applications are self-healing materials such as glass–vanadium–boron composites as their oxidation leads to the formation of a V2O5 B2O3 glass (Tmelting = 700 C), which can wet, fill, and heal cracks during service.

3 Control of High-Temperature Chemical Interactions at the Metal/ Molten Glass Interface The chemical reactions occurring at the glass/metal interface are controlled by the chemistry of the melt and the reactivity of the metal with the melt species. Three parameters must be considered. These are (i) the oxygen pressure (pO2) at the metal/glass melt interface,

which controls redox reactions; (ii) the glass basicity (aO2−), which controls oxo-complexation; and (iii) the temperature, which controls kinetic effects and reactivity through the Gibbs free energy driving forces. These three parameters are not strictly independent. Most elements present in melts can, for instance, react with free O2− ions to form oxo-complexes in a way that also depends on pO2, as indicated by the general equation that describes redox equilibrium between two different oxidation states of the same element [8, Chapter 5.6)]: MOy2y − m

−

+

n n O2 + x − y − O2 − 4 2

MOx2x − m − n

−

2 Besides, the potential E is related to the Gibbs free energy ΔG through the relationship: ΔG = −nFE, where F is the Faraday constant (i.e. 96 500 C/mol) and E is determined from E = E0 +

MOx2x − m − n − RT ln n 4 nF MOy2y − m − O2 O2 −

,

x−y−n 2

3 where E0 is the potential at the appropriate standard state, R the gas constant, T the temperature, and n the number of electrons exchanged in the reaction. For a fixed melt composition, the stability domain of the redox species is summarized on a redox potential scale [5]. The electroactivity domain of the solvent is defined by the upper and lower redox couples, which are generally O2/O−II and SiIV/Si0 for silicate melts (Figure 3). But the width of this window does in principle depend on melt composition. For example, a high concentration of lead oxide PbO (such as in crystal glass) narrows it on its cathodic side because of the reduction of PbO into metallic Pb (Figure 3). The solubility of oxides in melts also strongly depends on the melt potential, as illustrated by the chromium solubility or the residual sulfur content [9, 10] curves determined for soda-lime-silicate melts (Figure 4). The variations of oxide solubilities with the redox state of the melt can also strongly influence (and control) the formation (or not) of solid species at the metal/glass interface. The formation of a layer at the metal/glass interface is summarized by the flowchart of Figure 5. At the onset of the metal/glass contact, the chemical potentials of the relevant components differ in the two phases, which means that the interfacial zone is not in an equilibrium state. Redox reactions are a way to lower these chemical potential differences: either an element of the alloy is oxidized by another of the melt, which is reduced (Figure 5a), or an element of the melt is reduced at the metal/glass interface, followed by subsequent oxidation of an element of the alloy (Figure 5b), resulting in the formation at the

631

5.10 Glass/Metal Interactions

Figure 3 Scale of formal potential (Ef) at 1050 C of the main redox couples present in glass or constituting alloys with reference to the yttria-stabilized zirconia (YSZ) electrode.

Electroactivity domain of a silica-based glass

FeII/Fe0 CrIII/CrII NiII/Ni0 CrII/Cr0

CoII/Co0

–1.0

NiIII/NiII CrVI/CrIII

CoIII/CoII FeIII/FeII

–0.8

–0.6

MoVI/MoIII II/Pb0 IV 0 III 0 Pb Si /Si Mo /Mo ZnII/Zn0

–0.4

–0.2

0.0

+0.2

0.7

E(V)

O2/O–II

TeIV/Te0

Figure 4 Chromium solubility (at %) and residual sulfur content (wt %) in a soda-lime-silicate melt versus oxygen partial pressure.

1.2

0.8 at % (Cr) T = 1473 K, Na2O–CaO–3 SiO2

1.0

wt % (SO3) T = 1673 K, 16 wt %Na2O 0.6

0.6

0.4 0.3

wt % (SO3)

0.8

0.5 at % (Cr)

632

0.4

0.2 0.2 0.1 0.0 –14

0.0 –12

–10

–8 –6 log (pO2)

–4

–2

interface of an oxide layer and a metallic compound layer, respectively. Depending on the species that form and on their reactivity with the elements of the melt, several reaction pathways must be considered:

• •

If an oxide layer forms, the oxide is stabilized at the interface when its solubility in the melt is low (Figure 5e), which limits the progress of the reaction. Alternatively, this oxide can react with elements of the melt to form another compound (Figure 5d). If the solubility of the oxide is high, it dissolves into the melt, which is then locally enriched with an element initially present in the alloy (Figure 5c). If a metallic layer forms, the metal can react with the alloy to yield intermetallic compounds through the solid-state (sometimes liquid-state) reactions determined by the phase diagrams (Figure 5f ).

For the (c), (d), and (f ) pathways, both composition (i.e. aO2−) and melt potential are locally modified at the interface, and so do the chemical properties of the melt. The rate of these local modifications is directly related to the

0

temperature of the system. If it is very fast, the solvent properties at the interface can markedly change [11] and modify the initial reaction pathway, especially because the diffusion rate of O2 in the melt strongly depends on the temperature. In addition, the equilibration of the chemical potentials at the metal/glass interface depends on the initial redox state of the glass and on the thickness of the melt layer between the metal and the surrounding atmosphere. Finally, the composition and physical state (solid, liquid, or gaseous) of the phase formed at the interface depend on temperature, so attention should also be paid to the pertinent phase diagrams.

4 Characterization of the Glass/Metal Interaction Several experimental techniques and methods have been developed to study the formation of layers at the metal/ glass interface either from post mortem analyses (i.e. qualitative and quantitative metallographic observations) or from in situ measurements (electrochemical studies)

4 Characterization of the Glass/Metal Interaction

Initial conditions Eglass > Eint > Emet

th wi er tal y t e e la E m de e m → noxi in th ss a nt la f E g n o rese io at nt p rm me o F le → ee th

(a)

Eglass Glassmelt Eint Metal Emet

(d)

Mixed oxide phases

ide ox e th ion of rros n tio co olu → ss yer i D la

M oxide layer

Reaction of the oxide layer with the elements St → abil present in the melt Pr ity ot of ec th tio e Eint = Eglass n ox of id th e l M oxide layer e ay m e (e) etal r Metal

E

→ me la F t

(c)

Glass melt enriched in M oxide element

→

(b)

ye or r w ma Ein i ti t th th g on e la of gl ss a as p m sm re et el se alli t nt c in

(f) G metallic elements

Reaction of the metalic elements with the metal

Morphology of the layers formed at the metal/glass interface

Development of a layer at the metal/glass interface

→ Formation of intermetallic compounts

Complex layer

→ Corrosion

Eint = Emet

Figure 5 Pathway for the formation of layers at the metal/molten glass interface.

[8]. A combination of both methods obviously provides complementary information on the interaction mechanisms.

corrosion rates can be determined from measurements of the thickness variations of the sample. 4.2

4.1

“Raw Immersion” Technique

An easy way to observe directly the influence of parameters such as glass composition, temperature, time of interaction, and surface state of an alloy (raw, preoxidized, roughness, etc.) on the reactivity of the alloy is provided by the “raw immersion” technique. With it, corrosion by a molten glass is carried out at a laboratory scale. A metallic sample is totally or partially immersed at high temperatures in a crucible filled with an appropriate amount of glass, the second configuration involving the presence of a triple point. After a given period of time, the sample is removed from the melt and quenched in air. A heat-shrinkable tube can be applied around the sample in order to preserve the glass surrounding the metal/alloy, which may crack upon quenching. All characterization methods of solids (scanning electron microscopy, electron probe microanalysis, etc.) can then be used to determine the morphology of the layers formed at the metal/glass interface and to investigate various features such as dissolution, reaction with the elements present in the melt, stability of the oxide layer, or reaction of the metallic elements with the metal. In addition,

Electrochemical Methods

4.2.1 General Principles

As molten glasses exhibit a significant ionic conductivity, they are considered as good electrolytes. The use of electrochemical techniques is thus appropriate to characterize the various redox reactions involved in the corrosion of materials by these media. Because many such techniques may be used, only the most common in corrosion studies will be reviewed. Electrochemical measurements in molten glass are made in the same way as in aqueous media. The potential is controlled between working and reference electrodes, whereas the current density is measured between the working electrode and a counter electrode. Electrochemical measurements in molten glass require the use of specific materials that can withstand the harsh conditions imposed by high temperatures and contact with the molten silicate. Refractory ceramic materials (e.g. alumina, mullite, refractory cements) are recommended for constructing the electrodes, and noble metals such as platinum and Pt–Rh alloys are favored for the wires providing the electrical contacts. The reference electrode must have a constant electrochemical potential in a given glass. Yttria-stabilized

633

634

5.10 Glass/Metal Interactions

zirconia (YSZ) is preferably used for this purpose thanks to its stability at high temperatures and to its high conductivity for O2− ions that is at the root of the use of the redox couple O2/O2− as a reference. The counter electrode must be inert and present a maximum surface area to optimize current collection. Depending on the nature of the study, two types of working electrodes are used. For characterization of glass properties, the working electrode also has to be chemically inert: noble metals are mostly used. For characterization of the metal/glass interaction, the electrode is made up of the studied metal in the form of a rod [5] or embedded in a ceramic tube letting a cross section serving as a surface electrode (Figure 6). The nature of the crucible containing the glass is another important issue. A ceramic crucible is a low-cost solution. Its main disadvantages are brittleness, possible pollution by reaction with the glass sample, and the use for only one glass sample. A metallic (nonnoble) crucible is thus a better choice providing it is first subjected to polarization at a potential low enough to allow reduction of silicon, which will then be reoxidized into a protecting silica layer. As to noble metals, they suffer from their cost but have the dual advantage of high chemical stability and possible use as a reference and/or a counter electrode [11]. In this case, the existence of a triple point must be taken into account as it will cause a perturbation of cathode curves if gaseous oxygen is reduced into oxide ions in the melt. When positioning the electrodes, the solution resistance must be minimized by keeping the tips of the electrodes as close as possible, especially for the reference and the working electrodes. The electrolyte resistance between these electrodes causes an ohmic drop that leads to an error in the measured potential differences. Molten glasses are most often highly conductive. It has been shown that an electrical resistivity lower than 4 Ω has no influence on the measured potential differences.

the interaction of a metal with the same glass, the only difference being that the working electrode has then to be made from the metal in question. The existence of three domains can be demonstrated: active, passive, and transpassive (i.e. domain presenting corrosion phenomena at potentials higher than for the passive domain). Linear voltammetry is destructive since a large potential domain scanning modifies the surface state of the material. 4.2.3 Corrosion Potential and Polarization Resistance

The most basic electrochemical measurement is the corrosion potential (Ecorr), which characterizes the active or passive state of the alloy and determines the reactions that may occur at the metal surface by comparison with the formal potentials of the redox couples (identified here with the standard potentials of the redox couples) present in the metal and in the glass. Experimentally, it is the open-circuit potential taken by a metal (i.e. the working electrode) under given conditions of temperature, glass and atmosphere compositions, etc. The polarization resistance Rp is another important parameter, which can lead to the evaluation of the corrosion rate thanks to Stern–Geary method. Its measurement requires an additional counter electrode. A potential difference is applied between the working electrode (analyzed material) and the reference, as the counter electrode is used for current measurement. The working electrode is polarized around the corrosion potential (for example, from Ecorr – 10 mV to Ecorr + 10 mV). The calculation of the slope of the current vs. potential plot leads to the determination of Rp according to 1 di = Rp dE

2 3RT , αa nF 2 3RT , βc = αc nF

βa =

With an inert working electrode, linear voltammetry is conveniently used to determine the electroactivity window of a glass. The same method can be used to study

2

3

4

1: Studied material 2: Silico-aluminous cement 3: Outer mullite tube

5 6

Figure 6 Sketch of a working electrode for corrosion characterization of metals and alloys.

Top view 1

1

4

where i is the current. By taking into account the number of electrons involved in the anodic and cathodic reactions, the kinetic parameters βa and βc are derived from

4.2.2 Linear Voltammetry

Side view

at E = E corr ,

5 4: Inner mullite tube 5: Platinum wire (ø = 0.5 mm)

5 Corrosion of Metals and Alloys by Molten Glass

Here n is the number of electrons involved and αa and αc are the charge transfer coefficients of the anodic and cathodic reactions, respectively (with values ranging from 0 to 1, which is generally taken equal to 0.5 in a first approximation). The corrosion current (which is directly proportional to the corrosion rate) is then obtained from the Stern–Geary relation I corr =

βa βc 1 B × = 2 3 βa + βc Rp Rp

7

Finally an order of magnitude of the corrosion rate is given by Faraday’s law vcorr =

I corr tM , nρF

5 Corrosion of Metals and Alloys by Molten Glass

8 5.1

where Icorr is the corrosion current (A/cm2), t is time (s), M is the average molecular weight of the alloy (g/mol), and ρ is the average density (g/cm3). The measurement of both corrosion potential and polarization resistance as a function of time is an indicator of the evolution of the system. This technique is commonly used for the corrosion of superalloys by molten glasses. It allows the choice of adapted materials to be optimized under defined conditions according to their chemical composition, morphological properties, surface condition, etc. 4.2.4 Electrochemical Impedance Spectroscopy

Understanding the corrosion mechanisms and interpreting them in terms of diffusion, oxide layer formation, and charge transfer processes is another important goal. The electrochemical impedance spectroscopy (EIS) technique is well suited for this purpose, although few studies have yet been performed with it for molten glasses. The impedance measurement can be performed under different conditions. The potential can be the natural potential of the alloy in the melt. Under these conditions, the alloy can be in active or passive state. As a consequence, interpretation of the impedance measurements must take into account the initial condition of the alloy surface. It is also possible to impose a potential, for example, to reach phenomena occurring when the alloy is in the transpassive state, at high potentials. Figure 7 Effects of tellurium reduction on platinum stability in argon atmosphere as seen on backscattered electrons micrography. (a) Pt sample immersed in a waste glass containing TeO2. (b) Higher magnification of the micrograph of Pt–Te eutectic grain boundary.

Much information can also be gained from Nyquist and Bode representations [12], i.e. plots of –Im(Z) vs. Re(Z) and of modulus and phase vs. log f, respectively, on parameters such as the resistance of the electrolyte (Re) or the charge transfer resistance (Rct). The impedance loops (Nyquist representation) are attributed to charge transfer reactions in the alloy or in the formed layers, depending on their frequency range.

5.1.1 Noble Metals

To date, platinum and platinum alloys are extensively used in the glass industry thanks to their very high resistance to corrosion and erosion. Platinum is, for instance, used for melting pots, coating of melting vats, stirrers, and other ancillary equipment. Its hightemperature mechanical properties become limited above 1200 C, however, because of low creep resistance and recrystallization, which makes the penetration of the molten glass possible along the boundaries of the growing grains and, thus, causes degradation of the material. Furthermore, Pt alloys can react in reducing atmospheres with metallic or semimetallic elements to form low melting point compounds [13]. Under reducing conditions, species such as TeIV can be reduced to metallic state because the potential of the molten glass (−0.5 V) becomes lower than the formal potential of the TeIV/Te0 couple, namely, Ef(TeIV/Te) = −0.35 V (Figure 3). By reaction with platinum, tellurium then forms an alloy with a eutectic temperature lower than 900 C, thereby causing fast degradation of the material (Figure 7). Platinum also undergoes catastrophic corrosion in a molten glass when it is coupled with other metallic substances such as nickel-based superalloys. Galvanic coupling not only increases the corrosion/oxidation of metallic alloys but also induces more damages in

Glass

(a)

Corrosion of Pure Metals

100 μm

10 μm

(b)

Voids Pt

Pt–Te eutectics

635

5.10 Glass/Metal Interactions

platinum. The reason is that, as described for reducing conditions, reduction of oxidized species of the glass (Si4+, Mo6+, P5+, etc.) to a zero degree of oxidation takes place on the platinum surface where compounds with low melting points form.

5.2 Corrosion of Alloys In a hot corrosion context, Ni-based superalloys with a high Cr content and Al as an alloying element are a priori the best candidates for high-temperature applications (e.g. heating elements, gas turbine engines, etc.). The reason is that both metals have long been known to form at their surface the thermodynamically stable oxides Cr2O3 and Al2O3.

5.1.2 Common Metals

Particular attention has been paid to Fe, Co, Ni, and Cr [5, 11] because of their presence in the cobalt or nickel-based superalloys mainly used in the glass industry. Their corrosion in a soda-lime-silicate glass has been studied with thickness-loss measurements and electrochemical methods. For Cr, the existence of a wide passivation plateau with very low current densities (~ 0.4 mA/cm2) has been observed (Figure 8). The ability of Cr to build a protective chromia (Cr2O3) layer when imposing a potential lying in the passivation domain (from −900 to 0 mV according to Figure 8) demonstrates the possibility of using Cr as a protective component of superalloys in molten glasses. By contrast, the oxide layers that can form at the metal/glass interface with Fe, Co, and Ni are not protective. When compared with thickness-loss measurements, electrochemical methods offer the possibility of identifying the corrosion mechanisms. This feature is of great importance since it opens the way to improving the corrosion resistance of metallic materials. In addition, the corrosion rates calculated from polarization curves are close to those determined from thicknessloss measurements [5]. Data obtained by electrochemical methods, therefore, can be used as semiquantitative indicators to classify metals and alloys according to their resistance against corrosion in molten glasses.

5.2.1 Alumina-Forming Alloys

Corrosion of alumina-forming alloys in molten glasses is poorly documented in the literature. A recent study [14] has shown that upon raw immersion in molten glass, these alloys remain in the active state. An important Al loss is also observed. A preoxidation treatment does not improve the corrosion resistance. Indeed, according to the potential measurements, the alumina layer dissolves in the melt in a few minutes. This result is in accordance with the well-known high solubility of Al2O3 in oxide melts [15], which thus prevent aluminaforming alloys from being used as a high-temperature glass contact material (Figure 5c). 5.2.2 Chromia-Forming Alloys

In contrast, chromia-forming alloys are often used in the glass industry. As examples, they serve as construction materials for processing pots and susceptors in metallic melter pot furnaces, as well as electrodes in Joule-heated ceramic melter pots used for the elaboration of radioactive waste-containing glasses. Considering that the passive state can be obtained for pure chromium, similar studies have been devoted to chromia-forming alloys. For example, the corrosion of Nix–Cr(1 − x) alloys, with 0 < x < 1, in a soda-lime-silicate glass (with low MgO, Al2O3, and Fe2O3 contents) is characterized at 1100 C

Figure 8 Passivation plateau of chromium seen in anode polarization measurements at 1050 C in an industrial soda-lime-silicate glass, contrasting with the sharp variation observed for iron, cobalt, and nickel. Inset: photomicrograph of the chromia protecting layer formed.

Cr2O3

Glass

Cr Co I (mA/cm2)

636

Fe 8 6 Cr

4 Ni

2 0

–1400 –1200 –1000

–800

–600

–400 E (mV)

–200

–2

0

200

400

600

5 Corrosion of Metals and Alloys by Molten Glass

by important corrosion currents higher than 3 mA/cm2. A low Cr content in the alloy is not sufficient to build a protective oxide layer. On the contrary, a high Cr content induces spallation of the layer caused by the development of compressive stresses that result from the significant thickness of the forming chromia layer. Di Martino et al. [5] have extensively studied the corrosion of Ni-based and Co-based commercial superalloys with chromium content as high as ~30 wt % in borosilicate glass melts at 1050 C. Their results for a superalloy preoxidized or not immersed in the molten glass are compared in Figure 9. Direct immersion of the alloy spontaneously causes a corrosion that is characterized by a low potential (Ecorr). When the alloy is in active state, the initial potential is low (≈−1.2 V, the oxidant being Si4+; Figure 3), and an anodic peak (here I = 2.9 mA/cm2) is followed by a wide passivation plateau with relatively low current densities (I ≈ 0.5 mA/cm2). In the active state, the measured Rp values are close to 10 Ω cm2, which represents corrosion rates ranging between 15 and 35 mm/yr [5]. One can protect the Cr-containing alloys against active corrosion by performing a preoxidation treatment in air prior to the immersion of the alloy in molten glass (Figure 5e). This treatment “helps” the alloy to build a compact and adhesive chromia layer at the metal–melt interface that prevents direct contact between both phases. As a consequence, the alloy is directly in the passivation region characterized by a high corrosion potential (−0.4 V < Ecorr < −0.1 V) and a high polarization resistance (200 < Rp < 800 Ω cm2). These values point to

Active state

Glass

a corrosion rate of about 2 mm/yr, that is to say, one order of magnitude lower than that determined for an alloy in the active state. After several hours of immersion of a Ni– 30Cr alloy in a silicate melt at 1050 C, a 3–5 μm thick chromia layer remains present at the metal/glass interface. This oxide layer is at the origin of the alloy passivation, preventing glass penetration and lowering the corrosion rate. A 20–30 wt % Cr content in the alloy is thus required to develop a protective chromia layer. Nevertheless, depending on physicochemical conditions (temperature, melt composition, etc.), this chromia layer would not develop spontaneously in a molten glass, so a preoxidation step would be necessary to favor its formation at the metal/glass interface. Even though chromia-forming alloys show great potential since the solubility limit of chromia is one of the lowest among oxides [9, 14, 15], one must keep in mind that oxide growth always competes with dissolution in a molten glass: if the latter prevails over the former, the alloy will of course not be protected against glass corrosion. 5.3

These relative roles of oxide growth and dissolution depend on temperature. A transition from the passive to the active state of a Cr2O3-forming alloy is shown by measurements of the electrochemical parameters Ecorr and Rp as a function of the molten glass temperature [11]. At low temperatures, a chromia layer first develops at the metal/glass interface and ensures passivation of the

Passive state

Glass

Alloy

Temperature Effects

Alloy

50 μm

50 μm

Active state

6

Passive state

Transpassivation

I (mA/cm2)

5 4 3 2

Passive state Depending on the alloy Ecorr = –800 mV to –300 mV Rp = 200 to 800 ohms.cm2

1

Active state

Ecorr = –1200 mV Rp = 10–20 ohms cm2

0 –1.4

–1.2

–1

–0.8 –0.6 –0.4 –0.2 E (V)

–1

0

0.2

0.4

Scan rate: 600 mV/h

Figure 9 Anodic polarization curves of Co-based alloy in borosilicate glass for active and passive states at 1050 C. The interpretation of the curves is supported by the SEM micrographs for both conditions.

637

638

5.10 Glass/Metal Interactions

superalloy indicated by high Ecorr and Rp values. With increasing temperatures, the alloy then proceeds to the active state upon drastic decreases of both Rp and Ecorr. Whereas formation of the Cr2O3 layer is rate limited by diffusion of chromium from the metallic substrate and of dissolved oxygen from the molten glass, its dissolution is controlled by the solubility of Cr2O3 and the diffusion of Cr species in molten glass.

3 Pech, J., Braccini, M., Mortensen, A., and

4

5

6

Perspectives

In any application, glass/metal interactions involve many individual processes. Studies of simplified systems will allow the effects of many physicochemical parameters (e.g. viscosity, basicity, etc.) to be determined individually. Likewise, the different elemental processes involved in corrosion mechanisms should be taken into account, and their kinetic contribution to the overall process should be estimated. Predicting the growth and dissolution of chromia layers as a function of temperature and alloy and melt compositions is, for instance, one of the main challenges for future developments. A predictive lifetime model could then be set up and applied to many applications, for example, the corrosion by CMAS-like glasses in aeronautical applications, the production of float glass, the sealing of solid oxide fuel cells stacks, etc. For this purpose, specific experimental and characterization methodologies need to be designed for each application. For corrosion by molten glass, electrochemical techniques are particularly adapted. They should be developed.

References 1 Zhong, D., Mateeva, E., Dahan, I. et al. (2000). Wettability

of NiAl, Ni-Al-N, Ti-B-C, and Ti-B-C-N films by glass at high temperatures. Surf. Coat. Technol. 133–134: 8–14. 2 Kaplan, W.D., Chatain, D., Wynblatt, P., and Carter, W. C. (2013). A review of wetting versus adsorption, complexions, and related phenomena: the Rosetta stone of wetting. J. Mater. Sci. 45: 5681–5717.

6 7

8

9

10

11

12

13 14

15

Eustathopoulos, N. (2004). Wetting, interfacial interactions and sticking in glass/steel systems. Mat. Sci. Eng. A. 384: 117–128. Zackay, V.F., Mitchell, D.W., Mitoff, S.P., and Pask, J.A. (1953). Fundamentals of glass-to-metal bonding: I, wettability of some group I and group VIII metals by sodium silicate glass. J. Am. Ceram. Soc. 36: 84–89. Di Martino, J., Rapin, C., Berthod, P. et al. (2004). Corrosion of metals and alloys in molten glasses – part 1: glass electrochemical properties and pure metal (Fe, Co, Ni, Cr) behaviours. Corros. Sci. 46: 1849–1864. Roth, A. (1994). Vacuum Sealing Techniques. New York: American Institute of Physics. Sharma, K., Kothiyal, G.P., Montagne, L. et al. (2012). A new formulation of barium-strontium silicate glasses and glass-ceramics for high-temperature sealant. Int. J. Hydrogen Energy 37: 11360–11369. Tilquin, J.Y., Glibert, J., and Claes, P. (1995). In situ electrochemical investigation of copper in binary sodium silicate melts at 1000 C. Electrochim. Acta 40: 1933–1938. Khedim, H., Podor, R., Panteix, P.J. et al. (2010). Solubility of chromium oxide in binary soda-silicate melts. J. Non Cryst. Solids 356: 2734–2741. Beerkens, R.G.C. (2003). Sulfate decomposition and sodium oxide activity in soda–lime–silica glass melts. J. Am. Ceram. Soc. 86: 1893–1899. Abdelouhab, S., Rapin, C., Podor, R. et al. (2007). Electrochemical study of chromium corrosion in Na2O – xSiO2 melts. J. Electrochem. Soc. 154: C500–C507. Macdonald, J.R. (1987). Impedance Spectroscopy: Emphasizing Solid Materials and Systems. New York: John Wiley & Sons. Fischer, B. (1992). Reduction of platinum corrosion in molten glass. Platin. Met. Rev. 36: 14–25. Abdullah, T.K. et al. (2016). Electrochemical characterization of chromia- and alumina-forming nickel-based superalloys in molten silicates. Appl. Surf. Sci. 360: 510–518. Manfredo, L.J. and McNally, R.N. (1984). Solubility of refractory oxides in soda-lime glass. J. Am. Ceram. Soc. 67: 155–158.

639

5.11 Durability of Commercial-type Glasses Marie-Hélène Chopinet1, Hervé Montigaud1, Patrice Lehuédé1, and Sylvie Abensour2 1 2

Saint-Gobain Recherche, Aubervilliers Cedex, France UMR 125 CNRS/Saint-Gobain Surface du Verre et Interface, Aubervilliers Cedex, France

1

Introduction

Chemical inertness is one of the key properties that has rendered glass so valuable two millennia ago when the invention of blowing made glass vessels of any size and shape commodity products in the Roman world (Chapter 10.3). As clearly shown by the marked iridescence commonly seen on ancient glass pieces, however, inertness was not absolute. Of course, one could rightly invoke the very long periods of time elapsed since their production to account for their superficial alteration. Under a variety of circumstances, it nonetheless happens that even modern products can suffer from an alteration strong enough as to make them valueless. Problems caused by the reactivity of glass in wet environments are thus as old as glassmaking. They have long been rather well known, so industrial glass compositions have been optimized to satisfy many requirements, among them, the hydrolytic resistance needed for the intended use as exemplified by glasses used as containers in pharmacy (Chapter 7.7). As a rule, the problems stemming from glass alteration mainly occur instead under “unusual” storage or transportation conditions. Other corrosion occurrences are related to extreme conditions. Cases in point are those found in dishwashing machines where aqueous corrosion at relatively high temperatures may be favored by the detergents used together with rinsing and brightening agents. In this chapter the basic alteration mechanisms in acidic and basic media will be first described. The specific problems raised by soda–lime, lead-crystal, or borosilicate glasses under their conditions of use will then be briefly mentioned. Next, attention will be paid to the

Reviewers: Ph. Barboux, Institut de Recherche de Chimie, Paris, France E. Vernaz, CEA DEN/DTCD Marcoule, Bagnols sur Cèze, France

problems affecting flat and container glass during storage and transportation under confined conditions. Finally, solutions to this problem will be presented. By focusing on practical problems, this chapter may be considered as an introduction to the following one where corrosion mechanisms are reviewed in detail at the atomic scale.

2

Chemical Processes and Parameters

For all types of glasses, two chemical processes cause the initial modification of the material surface in contact with the aqueous solution. Their relative importance strongly depends on the pH of the medium [1–3]. 2.1

Neutral or Acidic Media

In an acidic or neutral environment, a cation-exchange reaction takes place between network-modifying cations – sodium and calcium in soda-lime silicates – from the glass surface and the hydrated H+ ions of the solution according to the reaction Si – O − Na + glass + H + aq ➔Si – OH + Na + aq 1 With the exception of very pure vitreous silica, which lacks network-modifier cations, any glass exchanges ions as described by Eq. (1). This first reaction produces a hydrated dealkalized layer on the surface (Figure 1), usually called a leached layer, whose thickness is usually too small to affect the properties of the product. As an example, the dealkalized layer is about 100 nm thick in champagne bottles having been filled with wine for many years [4]. This thickness is nearly constant in the whole area in contact with the wine and indeed too small to compromise the properties of the bottles.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

5.11 Durability of Commercial-type Glasses

2.2 Basic Media

100 000

In a basic environment, the alteration reactions are a little more complex because they involve the fragmentation of the silicate network and not a simple exchange of network-modifier cations:

Si

Intensity (cps)

10 000 Na

Ca

– Si – O – Si − + OH − ➔ – Si – O − + HO – Si – ,

1000 AI

2 −

– Si – O + H2 O➔ – Si – OH + OH

100

SiOH

10 0

200

400 Depth (nm)

600

−

3

Adding these two reactions, one describes the hydrolysis as – Si – O – Si − + H2 O➔2 – Si – OH

800

Figure 1 Cation exchange described by reaction (1) at the surface of a soda-lime silica glass as revealed by the contrast between the concentration profiles of SiOH and Na and Ca observed after water attack and rinsing.

The leached layer passivates in some way the glass surface as its presence decreases the rate of penetration of H+aq ions. Its growth kinetics (Figure 2) is typical of a diffusion-controlled mechanism because its thickness increases as the square root of time [5]. It is often described as a “gel layer” because its main component is SiO2-containing silanol groups SiOH. On the other hand, the high solubility of alkali cations in aqueous solutions makes them easy to be “missed” if the sample is rinsed before examination. Without rinsing either by the surrounding solution or by rain or any other external action, however, the alkali cations extracted from the glass are in general adsorbed or simply remain in the leached layer. As described below, this observation is consistent with reactions of the glass surface with atmospheric CO2 or SO2. 0.6

4

Reaction (4) takes place only when the pH is higher than 9 or 10 (Figure 3). It indicates that the OH− ions are not consumed, but act as a catalyst causing the reaction to proceed linearly with time in the absence of the passivation layer that forms under acidic conditions (Figure 4). Then, the collapse of the silicate network can cause an irreversible alteration of the glass surface. Especially if it is spatially heterogeneous, this collapse modifies glass properties – optical, in particular – but sometimes mechanical as well. Owing to its intrinsically basic nature, cement, for instance, gives rise to an interaction with glass that is described in this manner [6]. 2.3 Evolution of Water Attack: From Reactions (1) to (4) The “basic” reaction (4) may also be considered as a continuation of the acidic reaction (1) because consumption of the H+ ions of the initially neutral or slightly acidic solutions causes the pH increase required to trigger it. For this evolution to occur, however, the ratio between the area of reacting glass and the volume of the solution must of course be high. This condition excludes not only open systems but also glass immersed in a solution whose pH will very rarely become basic. Hence, it mainly applies

HCI 1.1M

0.4

μg SiO2/(g SiO2 min)

Thickness (μm)

640

HCI 1M

0.2

0

5

10

15

20

1/2

Time (minutes)

Figure 2 Diffusion-controlled nature of the alteration reaction (1) demonstrated by the linear relationship between the thickness of the leached layer and the square root of time (Source: From [5]).

6.0 4.0 2.0 0 0

3

6

9

12

pH

Figure 3 The very strong sensitivity to pH of the solubility of silica glass in an aqueous solution at 80 C [1].

3 Alteration as Related to Glass Composition

6 600

N

Dissolved glass (mg)

4 400

1

2 2

0

3

200

0

2

40

60

80

100

Relative humidity (%)

0

0

1

5

3

7

pH

Figure 4 Effect of solution renewal on the dissolution kinetics of a soda-lime glass in a basic N/2 NaOH solution [3]: (1) 90 ml every 30 minutes; (2) 10 ml every four hours; (3) no renewal base line.

to products submitted to a confined, moist atmosphere such that the volume of water is actually small compared with the glass surface area. As a matter of fact, after processing, the reaction can begin as soon as industrial products are submitted to a naturally wet atmosphere because the surface of alkali or alkaline earth aluminosilicates gets covered at room temperature by a very thin water layer at relative humidities as low as 30 % [7]. The process originates in the polar nature of the water molecule, which makes van der Waals bonding possible with a variety of high-energy surface defects such as low-coordinated charged silicons or isolated nonbridging oxygens. As a result of Eq. (1), the process yields OH groups on the surface, which are themselves covered with water molecules linked by van de Waals bonds. The water layer thickness depends on the partial pressure of water vapor (Figure 5). Even if water condensation is not visible on the glass surface, it follows that reactions between glass and water are nearly always possible. Museum rooms kept under controlled atmospheres are no exceptions.

3 Alteration as Related to Glass Composition 3.1

Soda-Lime Glass

Whether as flat, container, or even insulating fibers, glasses of the soda-lime family are by far the most commonly produced. Fundamentally their alteration originate in the relatively weak bonding of Na+ ions to the silicate network as made obvious by the fact sodium-rich binary silicate glasses are highly hydroscopic: they would

Figure 5 Average number of layers of molecular water on the surface of various glassy or crystalline oxide substances as a function of relative humidity [7].

simply disappear over rather short periods of time without the addition of calcium. But CaO is a poor flux compared with Na2O, so increasing further the content of the less mobile Ca2+ ion to improve chemical durability [8] would end up in an enhanced devitrification tendency upon melt cooling. Without this problem, in contrast, the introduction of 0.5–3 wt % Al2O3 in the composition notably increases glass durability [9]. Possibly a modification of the structure of the leached layer is involved, as suggested by Al2O3 contents that can reach 15 wt % in this surface layer. A second factor is the decrease of the content of network-modifier sodium ions resulting from their charge-compensating role for Al3+ in tetrahedral coordination (Chapter 2.4). At first sight such a decrease might seem too small to translate into significantly improved durability, but it is unlikely fortuitous that similarly small amounts of Al2O3 cause metastable immiscibility in the Na2O–SiO2 system to disappear [10]. One may thus surmise that introduction of small amounts of Al3+ results in a more homogeneous distribution of sodium in the overall structure, which makes H+ ions less readily exchangeable for Na+.

3.2

Lead-Crystal Glass

At PbO contents higher than 24 wt %, lead-crystal glass presents a correct resistance to water hydrolysis, but it is more sensitive to corrosion in an acidic environment. Some lead can then be released in solution when drinking glasses and decanters contain liquids such as wine [11]. Regulating authorities have thus imposed leaching tests with a 4 % acetic acid solution for 24 hours at 22 C [12] during which the amount of lead released must be lower than 5 and 2.5 mg/l for containers with a capacity of less and more than 600 ml, respectively. If the amount of lead released is greater than these values, either the composition of the glass must be modified to improve

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5.11 Durability of Commercial-type Glasses

its durability or the inner surface of the container must be treated to decrease the lead concentration in the first atomic layers so as to minimize further release upon use. The former procedure involves increases in SiO2, reduction of alkalis or addition of trace amounts of MgO or ZnO, and the latter acid polishing, ammonium sulfate fuming, or deposition of coatings [13]. That acid aging prior to use is an efficient manner to reduce subsequent lead leaching agrees with analyses performed on 24 % PbO lead glass decanters after 10 or 20 years of continuous use, which have confirmed that the process is self-limiting exponentially as a function of the distance from the glass–liquid interface [14]. This is the reason why crystal-glass manufacturers usually recommend to fill before use a new crystal-glass container with vinegar for 24 hours and then to rinse it thoroughly.

less sodium oxide (Chapter 9.3). Nevertheless, their specific surface area is very similar, so potential problems related to the pH increase are only delayed.

3.3 Borosilicate Glasses

4 Post-Production Corrosion of Flat and Container Glass

®

Commercial alkaline borosilicate glasses (Pyrex type) are well known for their high durability [15], which results from stabilization of alkali cations through charge compensation of tetrahedral boron (Chapter 7.6) and, in phase separated glasses, by the stable silica-rich matrix within which the phase rich in alkali borate is dispersed. The absence of alkali cations free to migrate into water from the surface yields a glass nearly as stable as silica glass, except in basic environments, which makes them in pharmacy the best containers for drugs (Chapter 7.7). Other compositions of this type of glass are commonly used for vitrification of nuclear waste for very long-term storage (Chapter 9.10). In this particular case, the dissolution of the glass matrix nearly stops when the maximum solubility of silica in the surrounding medium is reached and a condensed protective layer forms. But this step is never encountered in common uses of ordinary commercial glasses. 3.4 Insulating Glass Fibers With basically soda-lime compositions, to which a few wt% B2O3 are added, glass wool is closely related chemically to soda-lime silicate glass (Chapter 9.3). Its alteration thus conforms to the above description. The major difference concerns the extremely high specific surface area of glass wool. If these fibers are immersed into water, the pH immediately increases to values higher than 10.5 because of the very fast leaching of alkali cations made possible by the extremely high ratio between glass surface area and the volume of the solution. The attack may thus be very rapid if the product is not protected against water vapor condensation. Insulating glass fibers called rock wool are more resistant because they contain large amounts of alumina and

3.5 Reinforcement Fiberglass The typical E-glass used for those applications is a calcium aluminosilicate containing less than 1 wt % of Na2O (Chapter 1.6). The sizing covering the fibers is in principle efficient against water penetration. Corrosion nonetheless can take place through interaction with acidic species that would be present in the immediate vicinity of the fibers. Calcium, aluminum, and boron are then extracted, potentially inducing a loss of mechanical properties.

4.1 Flat Glass The composition of soda-lime glass has only changed marginally ever since it was produced at a really industrial scale two millennia ago in furnaces of up to 20-ton capacity (Chapter 10.3). Empirically, it had already been found that what we now term the eutectic region of the Na2O– CaO–SiO2 system was ensuring not only the lowest temperatures for melting and chemical homogenization but also the appropriate long-term durability with respect to rain and other atmospheric agents. Under usual climatic conditions, the thickness of leached-glass layer is smaller than 100 nm [16] because the corroding solution in contact with the glass surface keeps renewed, so the pH remains neutral. In the modern world, however, this condition is not necessarily satisfied upon glass storage or transportation where efforts are made to save as much space (and air) as possible. For flat glass, the surfaces of the panels are, for instance, kept apart with spacers, usually polymer powders having a grain size of a few tens of microns. If water penetrates in between the panels, most frequently through condensation, then the ratio between the glass surface area and the volume of the aqueous solution can become very large, so the pH increases until reaction (4) begins. The leached layer has a different composition and, thus, a different refractive index. If its thickness reaches a fraction of 1 μm to become commensurable with the range of wavelengths of visible light, then iridescence will manifest itself as optical interferences. In addition, the attack cannot be homogeneous because water is trapped by the polymer spheres. The eye being very sensitive to optical differences, this inhomogeneous corrosion also becomes visible very rapidly through slight

4 Post-Production Corrosion of Flat and Container Glass

light scattering. In this case, an acidic polymer may thus improve the situation. In usual storage alteration, the chemical profile is characterized by a 100 nm-surface layer enriched in silica. Reprecipitation of silica extracted from the glass may yield a thin, very heterogeneous, and fragile, lightscattering layer on the surface. This type of defect appears faster when water condensation is coupled with high temperatures, for instance, upon shipping in tropical or equatorial areas. At a much smaller scale, the effect is similar to that observed on artifacts found in archeological excavations. This phenomenon also occurred in the early double-glazing windows within which air could circulate, but not fast enough to ensure a sufficiently low humidity content. The result was occasionally the formation of a whitish or even, in some extreme cases, crizzling layer. When the surface modification is visible, the glass is usually rejected: Only polishing with cerium oxide could restore a satisfying surface, but the process is much too expensive to be applied to usual flat glass. Even if the modification has not yet become visible, the glass can still be useless for applications requiring treatments such as thin-layer deposition, a process commonly used today, because adhesion difficulties or problems caused by a heterogeneous aspect could occur. The precipitation of large crystals such as sodium and calcium carbonates or sulfates is less problematic when the species extracted from the surface (e.g. Na+, Ca2+) and adsorbed in the “gel layer” react with gases present in trace amounts in the atmosphere such as CO2 and SO2. For carbonates, these reactions are, for instance, 2 NaOH + CO2 ➔Na2 CO3 + H2 O, Ca OH

2

+ CO2 ➔CaCO3 + H2 O

5 6

Usually those crystalline salts are simply washed out, with acidic water for calcium salts, before using the glass. Finally, a peculiarity of float glass (Chapter 1.4) should be Figure 6 Effect of rinsing on the inner surface of a soda–lime bottle after a one-year outdoor storage as seen in SEM micrographs (2000× magnification). (a) Before rinsing: presence of both Na2CO3 and CaCO3. (b) After rinsing: only CaCO3 left.

noted with respect to the asymmetry existing between the “tin” and “atmosphere” sides. The existence in the former of a sharp SnO2 gradient beginning with contents of a few wt % right at the surface makes this side more durable than the latter, which in practice is the only one affected by corrosion. 4.2

Container Glass

After manufacturing, containers are gathered on pallets closed by polyethylene sheets and stored for periods typically ranging from a few days to a few months. Depending on storage conditions, water condensation can take place and cause alteration of the inner sides of containers according to reaction (1). Again, the extracted alkali and alkaline earth ions (in practice, Na and Ca) can react with atmospheric CO2 to precipitate carbonates. Although SO2 has a greater reactivity in this respect than CO2, the SO2 partial pressure in the pallet is usually too low for sulfites or sulfates to precipitate. Sodium carbonate crystals form as needles whose size reaches a few hundred microns, often well crystallized in a crow’s feet pattern (Figure 6). They may be difficult to observe because a high hygroscopicity cause them to absorb so much water under a wet atmosphere that they dissolve in the form of a droplet, from which crystals can then reprecipitate under drier conditions. Owing to its small solubility of about 0.001 g/100 ml in water, calcium carbonate does not experience similar cycles of precipitation–dissolution. It forms instead small hexagonally shaped prisms that are initially about 1 μm long and become much larger when alteration proceeds (Figure 7). Analyses of the glass underneath the altered zone or after light-acid washing shows that the glass surface is indeed depleted in Na and Ca. The optical aspect is slightly modified by a thin light-scattering layer that is not easily observed when the glass is colored. After

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5.11 Durability of Commercial-type Glasses

Figure 7 Optical micrography of large CaCO3 crystal present on the inner side of a bottle stored one year without rinsing (magnification 200).

filling of the container, sodium and calcium salts dissolve because of the slight acidity of the content, and the veil thus completely disappears. But carbonate crystals can act as nucleation sites for bubble formation in the case of carbonated beverages, which then causes filling problems. Under the adverse conditions, for instance, found in warm climates, one can observe below the CaCO3 crystal holes of a similar dimension that signal a localized attack of the glass surface. As these crystals are especially insoluble, their presence as solid deposits on the surface can induce condensation of water if the relative humidity is high enough. The very basic pH locally induced by the process [17] generates defects that cannot be removed by an acidic treatment. This kind of extreme alteration was also observed when the first dishwashing machines used high-pH salts at high temperatures during long washing cycles. The attack was often nonuniform as a result of variations of chemical composition in the glass surface. As resulting from contact of the glass with the forehearth refractories, local Al enrichment leading to a reduced alteration could then be observed.

This type of chemical alteration can be found within containers but not on flat glass despite its lower hydrolytic resistance. This could be explained by the formation of sulfates on flat glass, instead of carbonates in bottle glass. In the specific case of pharmaceutical bottles, besides the cations released, the porosity of the surface layer resulting of the attack can induce adsorption of molecules from the content on the internal wall of the container, thus the necessity of the treatment for this type of use (cf. Section 6). The external side can also present such phenomena, but the problem is less severe for two reasons. The first is that it does not have any consequence on the content of the container. The second is that this external side is usually covered with a thin protective tin (or titanium) oxide + polymer (PMMA) film (Chapter 1.5).

5

Characterization Methods

A brief summary of the various normalized tests devised to determine commercial glass durability is presented in Table 1. Apart from those normalized methods, other tests can be applied, especially to flat glass, in environmental climate chambers reproducing alternating humidity and temperature conditions. For practical purposes, a temperature increase of 10 C is considered to yield roughly a twofold increase of the alteration rate as a whole. This rule of thumb is of course approximate as reactions (1) and (4) have different activation energies, which should not be forgotten when corrosion tests are performed at temperatures higher than those of use to determine the durability of a glass. One must also keep in mind that the ratio between the surface area of the glass and the volume of the solution is the fundamental variable for the switch from reactions (1) to (4). In addition to chemical analysis, it is essential to determine the species leached out of the glass surface after the test and to study the chemical modifications induced by the alteration. Various methods exist for such surface characterization, such as scanning electron microscopy,

Table 1 Summary of some tests made to determine glass durability.

a

Reference

Medium

Type of glass

Surface or bulka

ISO 4802-1/2

Water

Any

Surface

121 (autoclave)

1

Acid/base, Na

ISO 720

Water

Any

Bulk

121 (autoclave)

1

Acid/base, Na

Temperature ( C)

ISO719/DIN12111

Water

Any

Bulk

98

ISO 7086

Acetic acid 4 %

Lead crystal

Surface

22

Time (hours)

Measurement

Acid/base, Na 24

Pb, Cd, Cr

Bulk usually means that the glass sample is ground to a definite grain size so as to know accurately the surface area before testing.

References

but mainly secondary ion mass spectrometry that allows concentration profiles to be measured with a resolution of a few nanometers (Chapter 2.3). When the attack is severe enough, the scattering of light observed in optical measurement can yield a good qualitative idea of the glass alterability.

6

Protection Methods

The most obvious way to protect flat or container glass against water corrosion is to keep it from variations of temperature and humidity during storage before use. But this is not always possible, especially for flat glass, which is subjected to longer travel times than containers whose rather low value makes long-distance transportation uneconomical. Two solutions have thus been adopted by flat glassmakers, namely, deposition of a thin layer of a weak acid like adipic acid [(CH2)4(COOH)2]; the precursor in nylon synthesis, which keeps the pH of the medium at low values; or pulverization at the surface of a Zn2+-bearing solution. Although the actual mechanism by which the glass surface is protected by Zn2+ is not well understood, the effect results in a three- to fivefold time increase of safe storage. For either pharmaceutical containers in contact with drugs or lead-crystal glass in potential contact with food or beverages, the hydrolytic resistance of the glass can be increased by up to 10 times if a dealkalization treatment is applied at high temperature. Referring to Chapter 7.7 for the former case, it will suffice here to state that several methods can be used [18]: dealkalization by ammonium sulfate, difluoroethane, or simply SO3. At high temperature (550–600 C), sodium is extracted from glass and combines with the gas to give

exchange with protons coming from aqueous solutions. This modified layer is sufficient to make thin-film deposition difficult on flat glass, which has induced glass manufacturers to store newly produced pieces in controlled temperature shops and/or to reduce the storage time before coating, for instance, or making protection treatments, without completely eliminating the problem. Modifications of the chemical composition of the glass through alumina addition has quite a large effect although this influence has not yet been completely explained. The probable reason is that Al2O3 accumulates at the surface in a hydrated form along with SiO2 and so plays a role on the reorganization of the surface layer and on the diffusion processes through it. This layer being very rich in water, its examination under vacuum with usual analytical tools is not really adequate. As described in the following chapter, new methods are thus required to gain new insights on the chemical stability of glass.

References 1 Douglas, R.W. and El-Shamy, T.M. (1967). Reactions of

2 3

4

5

2 Si – O – Na + + SO3 ➔Si – O – Si + Na2 SO4 7 On the surface of the glass, this reaction forms a few hundred-nanometer-thick layer, having a composition close to SiO2, which acts as barrier to sodium migration and block the advancement of reaction (1) at a negligible level.

7

Perspectives

Although modern industrial products do not often present visible alteration, glass is far from being chemically inert. It is not rare to observe modifications of its chemical composition within a surface layer of about 0.1 μm driven by the mobility of alkaline cations and their

6

7

8

9

10

glasses with aqueous solutions. J. Am. Ceram. Soc. 50: 1–8. Scholze, H. (1991). Glass, Nature, Structure and Properties, 329–339. New York: Springer. Berger, E. (1936). Fundamental principles underlying the chemical corrosion of glass. J. Soc. Glass Technol. 20: 257–278. Jupille, J. (2001). Les surfaces du verre: structure et physico-chimie. C. R. Acad. Sci. Paris, Série IV 2: 303–320. Ahmed, A.A. and Youssof, I.M. (1997). Attack on soda lime silica glass bottles by acetic, citric and oxalic acids. Glastech. Ber. 70: 76–85. Larner, L.J., Speakman, K., and Majumdar, A.J. (1976). Chemical interactions between glass fibres and cement. J. Non-Cryst. Solids 20: 43–74. Hagymassy, J., Brunauer, S., and Mickhail, R.S. (1969). Pore structure analysis by water vapor adsorption: I. tcurves for water vapor. J. Coll. Interface Sci. 29: 485–491. Clark, D.E., Dilmore, M.F., Ethridge, E.C., and Hench, L. L. (1976). Aqueous corrosion of soda-silica and sodalime-silica glass. J. Am. Ceram. Soc. 59: 62–65. Wassick, T.A., Doremus, R.H., Lanford, W.A., and Burman, C. (1983). Hydration of soda-lime silicate glass, effect of alumina. J. Non-Cryst. Solids 54: 139–151. Topping, J.A. and Murthy, M.K. (1973). Effect of small additions of Al2O3 and Ga2O3 on the immiscibility temperature of Na2O-SiO2 glasses. J. Am. Ceram. Soc. 56: 270–275.

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11 Grazian, J.H. and Blum, C. (1991). Lead exposure from

15 Taylor, P., Ashmore, S.D., and Owen, D.G. (1987).

lead crystals. The Lancet 337: 141–142. 12 ISO 7086/1 (September 2019). Glass hollowware in contact with food – release of lead and cadmium – part 1: test method; and ISO 7086/2 (November 1982). Glassware and glass ceramic ware in contact with food – release of lead and cadmium – part 2: permissible limits. 13 Hynes, M.J. and Jonson, B. (1997). Lead, glass and the environment. Chem. Soc. Rev. 26: 133–146. 14 Barbee, S.J. and Constantine, L.A. (1993). Release of lead from crystal decanters under conditions of normal use. Food Chem. Toxicol. 32: 285–288.

Chemical durability of some sodium borosilicate glasses improved by phase separation. J. Am. Ceram. Soc. 70: 333–338. 16 Lombardo, T., Chabas, A., Lefevre, R. et al. (2005). Weathering of a float glass exposed outdoor in urban area. Glass Technol. 46: 271–276. 17 Verità, M., Falcone, R., Sommariva, G. et al. (2009). Weathering of the inner surface of soda-lime-silica glass containers exposed to the atmosphere. Verre 15: 49–53. 18 Ahmed, A.A. and Youssof, I.M. (1995). Corrosion of dealkalised soda-lime-silica glass bottles by different aqueous solutions. Glass Technol. 36: 171–179.

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5.12 Mechanisms of Glass Corrosion by Aqueous Solutions Roland Hellmann ISTerre, CNRS, Université Grenoble Alpes, 38058 Grenoble Cedex 9, France

1

Introduction

Chemical alteration by aqueous solutions is one of the most important processes undergone by glasses, either in industrial and environmental applications (Chapter 5.11) or naturally at the Earth’s surface (Chapter 7.3). Induced by the intrinsic chemical instability of glass, aqueous alteration is referred to as corrosion in a laboratory setting, or chemical weathering in nature. Chemical weathering is due to the action of abiotic or biotic agents, or both, and plays a major role in controlling seawater chemistry and aqueous CO2 uptake during dissolution [1], for example. Industrial and environmental applications of glass corrosion include the development of durable corrosionresistant packaging (Chapter 7.7), in situ remediation of polluted water, carbon (CO2) capture and storage, or secure, long-term isolation of industrial and nuclear waste (Chapters 9.9 and 9.10), [2]). Archaeometry is another important field associated with glass weathering and can be used for dating of archeological glass objects and paleoclimate reconstructions [3]. Knowledge of the molecular-scale mechanisms of alteration is a prerequisite for understanding how glasses react with aqueous solutions, thereby permitting more accurate modeling of corrosion and long-term durability. Corrosion is characterized by a combination of physical and chemical processes leading to the formation of one or more surface altered layers at the expense of the pristine glass. These layers not only are primarily composed of elements derived from the dissolution of the glass, but Reviewers: J.P. Icenhower, Sandia National Laboratories, Carlsbad Program Group, Carlsbad, NM, USA T. Geisler, Steinmann-Institut für Geologie, Universität Bonn, Bonn, Germany

also typically incorporate chemical species from the surrounding bulk solution. Separating the fresh glass from the solution, this near-surface zone has a varied terminology in the literature: leached layer, gel, surface altered layer, interfacial reprecipitate, palagonite. Because the phases making up this zone are intimately associated with the chemical alteration of the glass, understanding the details of their formation is crucial to elucidating corrosion mechanisms. Two approaches are necessary to achieve this goal: the first aims at determining the chemical composition, structure, and physical properties (e.g. porosity, pore size distribution, permeability) of the surface altered layer(s), and the second at studying the interfacial region that delimits the boundary between the pristine glass and the adjacent surface altered layer. Critical to the development of a mechanistic model are accurate measurements of the chemical and structural gradients between these two phases. For this purpose, advanced analytical techniques having very high spatial resolution, elevated mass resolution, or both, should be used. In this chapter, the discussion of corrosion mechanisms is largely based on a historical–chronological presentation. Two early models that characterized the state of knowledge up to the mid-1980s are first described [4], followed by the traditional model based on preferential cation leaching and interdiffusion. Frequently called the leached-layer model, it combines many of the elements found in the two early models. It has held sway over the past three decades and is still the predominant mechanism in the literature. The last model treated is relatively new and is based on CIDR. Acceptance of this mechanism, initially developed in mineralogy and geochemistry, has been quite contentious but has nevertheless been gaining attention in the glass community.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

5.12 Mechanisms of Glass Corrosion by Aqueous Solutions

List of Acronyms (cf. Chapters 2.3 and 5.1) APT EDX CIDR

atom probe tomography energy-dispersive X-ray spectroscopy coupled interfacial dissolution-reprecipitation EFTEM energy filtered TEM EPMA electron-probe microanalysis FIB focused ion-beam milling HAADF high-angle annular dark field HRTEM high-resolution TEM RBS Rutherford backscattering spectrometry RNRA resonant nuclear reaction analysis SIMS secondary-ion mass spectrometry, including nano- and time-of-flight-SIMS STEM scanning TEM XPS X-ray photoelectron spectroscopy

Early Models

Dran and colleagues [4] summarized the two prevailing models regarding the aqueous dissolution of silicate glasses that held sway in the mid-1980s. The first was thought to apply to chemically complex or natural glasses. Its proponents postulated an overall congruent dissolution process, characterized by the stoichiometric release of both framework and network-modifying elements. As dissolution proceeds, the concentrations of silica and other elements build up in the bulk solution, so that upon reaching saturation, one or more secondary crystalline phases (generally silicates) precipitate onto the glass surface (Figure 1a). The alternate model was relevant to chemically simple, laboratory-produced glasses. It is based on the in situ preferential release of mobile,

3

Leached-layer Model

3.1 The Standard Model The current generalized approach to glass corrosion has many similarities with the two early models. The altered zone, or leached layer, is composed of three separate entities (Figure 2). Adjacent to the pristine glass is an interdiffusion zone or layer, which is characterized by preferential removal of cations and sigmoidal chemical profiles, and is sometimes referred to as a hydrated glass layer [6]. Following this layer is a gel layer composed primarily of hydrated silica, where all the elemental concentrations are relatively constant. In the first stages of corrosion, the glass structure at the surface is progressively transformed by the selective leaching of certain cations (alkali and alkaline earth network modifiers, as well as network formers such as B) [2, 7–14]. For the interdiffusion zone to remain electroneutral, the preferentially released cations are replaced by H ions (i.e. H3O+) from the bulk solution. Each H3O+-cation couple (e.g. H3O+–Na+, H3O+–Ca2+, H3O+–B4+) can be characterized by a single interdiffusion coefficient that depends (b)

Altered layer

Stoich. release cations,Si

Unaltered glass

Si,O

Bulk fluid 1.0

Altered layer

0.5

H+

Cations

Unaltered glass

Inner interface diffusion front

Bulk fluid

Outer interface

(a)

network-modifying cations (e.g. Na+, Li+, K+) into the bulk solution. Keeping the relict, leached glass structure electrically neutral requires replacement of the leached cations by H ions (most likely H3O+) from the bulk solution; this process may also be accompanied by the influx of molecular H2O into the leached layer. The outer edge of the silica-rich leached layer releases Si and O to the bulk solution through chemical hydrolysis reactions (Figure 1b). Interestingly, one or the other mechanism has been used to account for the alteration of volcanic glasses, depending on their age [5].

Concentration (normalized)

2

Inner interface dissolution front

648

Si,O

Silica-rich 2° phases

0 0

Depth into solid

0

Depth into solid

Figure 1 Cross-sectional diagrams of early models of an altered glass layer. (a) Congruent glass dissolution, followed by precipitation of secondary crystalline phases on the glass surface from a saturated solution. (b) In situ transformation of the glass structure via selective cation removal by interdiffusion, characterized by sigmoidal and anti-correlated H and cation depth profiles.

3 Leached-layer Model

Surface altered layers (not to scale)

Bulk fluid

2° crystalline precipitates

Gel (hydrated silica)

Interdiffusion zone (preferential release of cations)

Unaltered glass

0

H+ Cations

0

H+

Cations

Inner interface diffusion front

Relative concentration

1

Depth into solid

Figure 2 The distinct chemistry and structure of the three layers of the leached-layer mechanism: anti-correlated chemical profiles in the interdiffusion zone, relatively constant concentrations in the amorphous gel phase, and specific compositions of crystalline precipitates at the interface between the gel and the corroding aqueous solution.

on the individual diffusion coefficients of both components. In other words, the outward diffusion rates of cations are coupled to the rate-determining (slower) inward diffusion rates of H ions. For simplicity, only two profiles representing a single interdiffusion couple are shown in Figure 2, whereas in reality there will be multiple interdiffusion profiles with different gradients and depths, depending on the charge of the cation (i.e. interdiffusion of H3O+–B4+ will be significantly slower, and thus shallower, than H3O+–Na+). Throughout the process, the inner interface of the diffusive layer (the diffusion front in Figure 2) continuously advances into the glass at a rate characteristic of solidstate volume interdiffusion. This process is the same as in the early model (Figure 1b), in particular because the leached relict zone remains covalently bonded to the pristine glass via Si–O linkages [7]. The outer interface of the diffusion layer is where silica is released to solution. Because of its relict nature and the sigmoidal shape of its diffusion profiles, the leached layer should not have a sharp structural and chemical interface with the pristine glass. At a significantly higher reaction progress (ξ), a separate porous gel layer composed primarily of hydrated silica begins to form on top of the diffusive layer, mainly by hydrolysis and condensation reactions. Hence, the diffusive zone advances by interdiffusion into the pristine glass at its inner interface and is consumed by gel formation at its external interface [2, 7–9, 14, 15]. Once the gel layer has formed and continues to grow, silica is released both at the outer interface of the interdiffusion layer, as well as at the external boundary of

the gel in contact with the bulk solution. However, silica resorption can occur throughout the gel layer when aqueous silica becomes saturated in the bulk solution and within the gel pores [2]. These processes are sketched in Figure 2 as (i) inward H ion diffusion, (ii) counterbalanced outward diffusion of preferentially released cations, (iii) silica release (straight dark arrows), and (iv) silica resorption (curved dark arrows). A net balance of all these rates governs the overall thicknesses of the interdiffusion and gel layers over time. The pronounced porosity of the gel layer allows for the unimpeded inward and outward flux of reactants and products between the bulk solution and the diffusive zone–pristine glass interface. In some cases, however, eventual pore closure in the gel layer may retard the overall corrosion process [16]. Moreover, depending on the composition of the glass, alteration conditions, and composition of the bulk solution, aggregates of secondary crystalline phases (zeolites, phyllosilicates, metal oxyhydroxides, hydrosilicates) may precipitate (Figure 2) on top of the gel as a third layer [2, 7–9, 15, 17]. The attributes of this model are well illustrated in a study [9] of the three-month aqueous alteration of SON68 borosilicate at pH 8 and 90 C (Figure 3), a chemically complex analog of the glass produced at La Hague, France, for storing nuclear waste [7]. The three different layers illustrated in Figure 2 are apparent in the chemical depth profiles (Figure 3) determined by SIMS. The leached layer consists of an inner interdiffusion zone (where sigmoidal B and Li profiles are anti-correlated with a roughly sigmoidal H profile) and an outer gel (where

649

5.12 Mechanisms of Glass Corrosion by Aqueous Solutions

1.00 Outer interface

Inner interface

4.0

Gel layer

0.10

3.0

B 2.0 Interdiffusion zone

Li

0.01

Pristine glass

0

2

4

Figure 3 The interdiffusion zone, gel, and surficial crystalline phases of the leached-layer model illustrated by chemical profiles measured after a three-month corrosion of SON68 borosilicate glass at 90 C and pH 8. SIMS O− ion beam rastered over 250 × 250 μm2 area, positive ions collected from window covering 60% of this area. Source: Adapted from figure 6, [9].

1.0

H 0.00

C/Co (H)

Phyllosilicates

C/Co (Li and B)

650

6

8

10

Depth (μm)

depleted B and Li and enriched H concentrations are relatively constant), on top of which phyllosilicates have crystallized as a porous layer. Currently, the leached layer model of glass corrosion, as exemplified by Figure 3, is the most widely accepted, in particular within the established glass community. It is the basis for nearly all codes modeling the macroscale chemical alteration of glasses in aqueous solutions (e.g. GRAAL [7]). 3.2 A Complex Hybrid Model A major concern with most studies supporting the leached-layer mechanism is that the depths and gradients of the measured chemical profiles strongly depend on the analytical techniques used. This is illustrated by the results of a 25.75-year laboratory experiment [6], whose authors were among the first to study glass corrosion with atom probe tomography (APT), a very powerful technique that can provide three-dimensional reconstructions of the chemical and isotopic composition of a sample with subnanometer depth and lateral spatial resolution, as well as very high mass resolution (m/ Δm = 1000, FWHM). In this study, SON68 glass was altered at 90 C and pH 7.0–7.2 in a slowly renewed granitic groundwater solution. From SEM observations, the sample consisted of the pristine glass, a hydrated (diffusive) glass layer (1000 nm), a gel layer (7500 nm), and surficial crystalline phases (a few hundreds of nanometer), yielding a total alteration thickness of approximately 9000 nm. Highresolution chemical profiles at the pristine glass-hydrated glass interface, determined by APT (Figure 4), reveal smooth decreases of Li, Na, B, and Al concentrations with increasing depth from the pristine glass interface, with gradient widths of ≈ 50 nm, and up to ≈100 nm for Na (Figure 4a). On the other hand, Si and H show smooth enrichment trends from the pristine glass interface, with gradient widths of 40–50 nm, whereas K (originating mainly from the granitic solution) and Ca increase over

distances of 10–20 nm and 100 nm. Much sharper gradient widths for Na and B (3–4 nm), K (5 nm), Li (17 nm), and H (20 nm) were also observed in this study (Figure 4b). Taken together, these results were interpreted in terms of a two-stage mechanism. First, an initial preferential loss of Li by interdiffusion with H occurred, which led to sigmoidal, anti-correlated Li and H profiles that became relatively constant after 15–20 nm. Subsequently, Na and B were preferentially released by dissolution, creating very sharp dissolution front profiles (Figure 4b), with strong depletion >15 nm depth. In this hybrid model, an interdiffusion process has been combined with preferential dissolution, resulting in a steep interdiffusion front that is partially coincident in space with an even sharper dissolution front within the hydrated glass layer (Figure 5). The entire hydrated layer is by their definition a product of interdiffusion [6], but the results indicate that the diffusion profiles only extend to a depth of 20 nm from the interface with the pristine glass (Figure 4b). Diffusion modeling of leached layers [18, 19] shows that a 1000-nm thick diffusion zone characterized by a thin and steep diffusion front occupying only 20 nm at the inner extremity is physically not reasonable. In other words, the leached-layer model cannot explain how the remaining 980 nm of the hydrated layer forms, and in particular, why over the course of 25.75 years the Li and H profiles remained so sharp and so close to the interface with the pristine glass, although at the same time silica dissolution should have been occurring at the expense of the outer interface of the hydrated glass layer. Moreover, the K profile is anticorrelated with those of Na and B and mimics them in terms of sharpness and position with respect to the dissolution front. However, K had presumably diffused into the diffusive zone from the solution, a scenario that should have led to a K profile mimicking those of H and Li. The suggestion of a hybrid diffusion–dissolution process occurring near the pristine glass interface is interesting, but whether this is physically realistic can be

3 Leached-layer Model

(a) 20 Concentration (at. %)

Figure 4 Chemical profiles of pristine glass–hydrated glass interface obtained by APT of a borosilicate SON68 sample corroded 25.75 years at 90 C and pH 7. (a) Profiles extending from the pristine glass to a depth of 500 nm into the hydrated glass. (b) Close up of the first 30 nm of the hydrated glass, based on original profiles (a) that were replotted with a “proximity histogram method”, producing significantly sharper elemental gradient widths. The true [B] may be lower than shown – see [6]. Source: Adapted from figure 3, [6].

Si

15

H

10 3 Ca AI B*

2 1 0

Na K Li 100

0

200

500

10

Nominal hydrated

14

Nominal pristine

(b) Concentration (at. %)

400

300

Distance (nm)

6

2 0

5

10

15 20 Distance (nm)

25

30

(a) Hydrated glass (interdiffusion) layer 1000 nm

Inner interface

Outer interface

Glass

Gel (b)

Li–H interdiffusion K diffusion front 5 nm width

20 nm width

K

Li

H

Na, B

Li

H

Na, B dissolution front 3–4 nm width

Inner interface

Figure 5 Hybrid leached-layer preferential dissolution model [6] illustrated by a schematic partial cross section of the hydrated layer and its two interfaces (refer to previous Figure 4). (a) The 1000nm thick hydrated glass (interdiffusion) layer is shown in its entirety. The sharp interdiffusion profiles and preferential dissolution front occupy only the extremity of the hydrated glass layer, at the inner interface with the pristine glass (20-nm thick light vertical band, drawn to scale). (b) Close up of inner interfacial region, showing partially overlapping profiles representing interdiffusion (H and Li), preferential dissolution (Na, B), and diffusive uptake (K) from the bulk solution.

0

651

652

5.12 Mechanisms of Glass Corrosion by Aqueous Solutions

questioned. In particular, this process assumes that solidstate volume interdiffusion in a glass at 90 C is faster than competing chemical hydrolysis reactions (e.g. [20]). If true, one could ask why the diffusion and dissolution fronts would still be nearly spatially commensurate after nearly 26 years in spite of their significantly different rates. The Li ion is small and carries a +1 charge, whereas the inward diffusing, charge-compensating H species (most likely H3O+) is significantly larger so that it will be much slower than Li and, thus, be rate determining in the Li–H diffusion couple [18, 19]. The ultimate question is, therefore, whether the Li and H profiles represent true interdiffusion, or an entirely different process. An alternative and physically more realistic explanation of the sharp chemical gradients measured, in particular for Li, Na, B, and K, is the coupled interfacial dissolution–reprecipitation mechanism.

4 Coupled Interfacial DissolutionReprecipitation (CIDR) 4.1 High-resolution Analyses Regardless of the particular manner in which chemical profiles are theoretically interpreted, a fundamental point is that the need for high-resolution data is primordial. Two types of recent experimental and analytical advances fulfill this necessity. The first involves sample preparation techniques, initially ultramicrotomy [5, 15, 21, 22] and more recently, focused ion-beam (FIB) milling [23]. Not only have these techniques allowed altered mineral and glass specimens to be prepared in cross section, but the resultant ultrathin sections (lamellae) are electron transparent and, therefore, analyzable by TEM techniques. These advances have eliminated the need to use SIMS, XPS, RNRA, RBS, or EPMA to measure chemical depth profiles. These techniques are based on successive measurements starting from the top of the surface altered layer, proceeding downward through the layer, and finally finishing in the pristine mineral or glass. More importantly, their beam footprints range from tens of μm to several mm; when applied to samples with rough surfaces and irregular internal interfaces, the ensuing chemical profiles are artificially enlarged (i.e. smeared out), making them considerably wider than they really are. The second important advance has been the use of analytical techniques having extremely high spatial resolution (Table 1), with beam footprints in the nanometer to sub-nanometer range, to measure surface altered layers directly in ultrathin electron transparent cross sections. These techniques, primarily TEM combined with electron-energy filtering (EFTEM) and electron-energy loss spectroscopy (EELS), or STEM-EDX (scanning

Table 1 Chemical-gradient widths (nm) of boron profiles in surface altered layers formed on SON68 borosilicate glass measured with different techniques [6]. ToF-SIMS

>1000

NanoSIMS (O− beam) +

350 ± 150

NanoSIMS (Cs beam)

170 ± 30

EFTEM

≤30

APT

3–4

TEM-energy dispersive X-ray spectroscopy), have yielded novel nanometer-scale resolved chemical maps of the interfacial region encompassing the unaltered primary phase and the secondary surface altered layer(s). Moreover, high-resolution chemistry measurements of glass corrosion by TEM have recently been complemented by the application of APT, whereas isotope tracer experiments have provided unique insights into the dynamic nature of the corrosion process. The power of these new approaches has been demonstrated by the nm-sharp chemical and structural interfaces evidenced in altered minerals (e.g. [19, 22, 24]) and glasses (e.g. [6, 16, 21, 25–27]). Spatially commensurate chemical and structural interfaces, which are very sharp at the nanometer to sub-nanometer scale, bear none of the hallmarks of diffusion, namely, smooth and broad sigmoidal chemical profiles spanning the region between the pristine glass interface and the outer boundary of the gel [18–20]. Likewise, the formation of rhythmic and patterned alteration layers with sharp chemical and isotopic boundaries reflect chemical self-organization processes that are difficult to reconcile with a preferential cation leaching–interdiffusion mechanism. In summary, techniques such as APT, EFTEM, and STEM-HAADF have allowed researchers to gain unprecedented chemical and structural data on interfaces needed to improve corrosion models, which have in fact contradicted the majority of previous studies on both mineral and glass alteration mechanisms.

4.2 Dissolution/Reprecipitation Even though CIDR is a relatively recent theory as applied to glass corrosion, it traces its roots back to at least 1967, when it was proposed to explain the replacement of Na feldspar by K feldspar under hydrothermal conditions. Rather than invoking the standard idea of interdiffusional + + ⟷ Ksolution to explain the formation coupling of Nafeldspar of authigenic K feldspar, O’Neil and Taylor [28] instead postulated that “the mechanism of oxygen and cation exchange in these experiments involves the fine-scale solution and redeposition in a fluid film at the interface

4 Coupled Interfacial Dissolution-Reprecipitation (CIDR)

between the exchanged and unexchanged feldspar.” Hay and Iijima [29] perhaps alluded to a similar process, “The sharp interface between unaltered sideromelane [a basaltic glass, see Chapter 7.2] and palagonite suggests that palagonite was formed by a microsolution-precipitation mechanism rather than by simple hydration and devitrification.” In the following years, however, this new idea was to receive scant attention in the geosciences, or other related fields, for that matter. Further development of the theory has been marked by an intertwined history between mineral and glass studies. At least 20 years ago, researchers primarily from the geochemical–mineralogical community began to question the fundamental tenets of the traditional leached-layer model when novel experimental/analytical approaches were developed and applied to altered samples. These led to new interfacial measurements that ultimately made this change in status quo thinking possible. Thus, it took about 30 years after the publication of the pioneering O’Neil and Taylor study [28] for CIDR to be resurrected and further developed into a more complete theory for both mineral alteration [22, 30] and glass corrosion [21, 25, 27]. According to the CIDR mechanism, the surface altered layer (i.e. equivalent to the interdiffusion zone and gel in Figure 2) is essentially a precipitate of amorphous hydrated silica. In a superficial sense, this model resembles that of Figure 1a, which is based on precipitation of crystalline (silicate) phases from an oversaturated bulk solution. The major difference is that the coupled interfacial dissolution–reprecipitation mechanism is based on an interfacial process involving tight spatial and temporal coupling between stoichiometric dissolution at a sharp chemical reaction front at the pristine glass surface, and quasi-simultaneous reprecipitation within an ultrathin fluid film in contact with the same interface. In cross section, this interfacial fluid film is composed of two to three layers of ordered water molecules (thickness RCs > RSi ≈ RMo) was attributed to solubility control (i.e. CIDR) within thin fluid film at pristine glass dissolution front. These data complement solid-state results for the one-month sample shown in Figures 7 and 8. Source: Adapted from figure S4, Supp. Information, [27].

500

Mol fraction released (× 106)

658

Mol fraction Li B Cs Mo Si

400

300

200

100

0

0

50

150

100

200

250

Days

release rates as evidence for preferential release of certain labile elements coupled to incorporation of hydronium ions from the bulk solution. This is manifested by higher apparent release rates compared with that of Si, which ultimately results in the creation of a relict Si-rich leached layer (Figures 1–3). However, the aqueous data purportedly showing preferential release can alternatively be explained in terms of CIDR. In this case the intrinsic dissolution process at the pristine glass surface is congruent, but subsequent retention (i.e. reprecipitation) of released elements is controlled by each cation’s relative solubility in the interfacial fluid film. Thus, soluble cations (Li, B) are preferentially released to the bulk solution, elements such as Cs with intermediate solubility are partially retained, and finally, minimally soluble elements (Si, Mo) are preferentially retained by the precipitation of an amorphous silica phase. Thus, the composition of the altered layer can be estimated by thermodynamics. The strong correlation between relative elemental solubility [34] and degree of retention within the altered layer (Figure 10) is strong evidence in favor of CIDR and not an interdiffusion-controlled leached-layer process. This example also illustrates an important point: aqueous data alone, although useful, can be ambiguous and therefore do not lend themselves to precise mechanistic interpretations. Thus, obtaining nanometer-scale solid-state data is primordial for the determination of any corrosion mechanism at the molecular scale. As a final note, the aqueous data shown in Figure 10 were used to calculate the Gibbs free energies (ΔG) of common low-temperature polymorphs of silica (Supp. Information [27]). All ΔG values were highly negative, thereby indicating that the observed amorphous Si-rich surface altered layers (Figures 7 and 8) did not precipitate

from an oversaturated bulk fluid, but more likely represent an interfacial reprecipitation phenomenon dependent on the special properties of thin fluid films. 5.3 Dissolution Rates as a Function of Composition Chemical composition is major factor in the corrosion of glasses. A classification of corrosion resistance of a broad range of compositions and types [35, 36] shows the following generalized glass order (with some overlap between types): soda–lime (e.g. medieval and antique glasses) < nuclear high-level waste (e.g. SON68) < natural (e.g. obsidian) < commercial (e.g. Duran, Pyrex brands) < pure silica. A general rule of thumb is that corrosion durability increases with the proportion of networkforming elements (e.g. Si, Al, B) coupled to a concomitant decrease in the abundance of network-modifying elements (e.g. Ca, Na, Li, Mg, K). The former group of elements polymerizes the glass structure, whereas the latter depolymerizes it (Chapter 2.4). To quantify these observations in terms of thermodynamics, many studies have used an approach based on a linear free energy relation (LFER). As developed in pioneering studies [37, 38], the LFER approach allows the susceptibility of glass to hydration (i.e. aqueous corrosion) to be estimated from the weighted sum of the Gibbs free energies of hydration (ΔGhydr(i)) of its individual orthosilicate or oxide constituents (i). Although based on some restrictions and simplifying assumptions [35], this approach offers a good starting point for qualitatively estimating the durability of a glass. Thus, species such as SiO2, Al2O3, CaO, Fe2O3, and MnO2 are predicted to stabilize the glass structure (positive ΔGhydr values), whereas

5 Rates of Dissolution and Element Release

CaSiO3, Na2SiO3, and K2SiO3 destabilize it (negative ΔGhydr values) [35]. There is, in fact, an inverse linear relation between log[Si] released and ΔGhydr of the glass; in other words, the more negative ΔGhydr, the less durable the glass and the higher the degree of Si release to solution. As a further refinement, ΔGhydr can be adjusted for the solution pH to account for the dissociation of silicic and boric acids at high pH [36]. Glass composition is related to structure in terms of nonbonding oxygen (NBO) bonds, since ΔGhydr correlates well with the number of NBO [37]. Hence, glass structure is usually not considered as a separate mesoscopic parameter distinct from composition. At the molecular scale it nonetheless plays a key role in glass corrosion, seemingly contradicting the preceding statement. As an example [16], it was found that the initial corrosion rate of a borosilicate glass was slowed down by substitution of zirconia (0–8 mol % ZrO2) for silica. In the long term, however, the overall degree of corrosion increased with zirconia concentration because ZrO2 hindered restructuring of the gel layer and, thereby, prevented pore closure. This phenomenon was deduced to be ultimately responsible for stopping corrosion by drastically decreasing the rates of diffusion of aqueous species within the gel.

5.4 Dissolution Rates as a Function of pH and Temperature The effect of pH and temperature on glass dissolution is also quite strong and just as important as chemical composition of the glass. As has been developed and described in numerous geochemical studies for mineral dissolution kinetics, the following type of generalized rate equation for heterogeneous surface reactions [39] has also been widely applied to glass corrosion in aqueous solutions: Rate = k 0 Ae − Ea

RT

anHH++

ani i f ΔGr

1

i

In Eq. (1), k0 is the forward rate constant, A the reactive surface area, Ea the thermal activation energy of the overall reaction, R the gas constant, and anHH++ the activity of H+ raised to a power n; the product operator term expresses the influence of the activities of other aqueous species that either catalyze or hinder the dissolution reaction; finally, f(ΔGr) is a Gibbs free energy (or chemical affinity) term expressing the effect of deviation from chemical equilibrium on the rate, written here in a manner not based on any specific mechanism (e.g. transition state theory). By definition, f(ΔGr) = 0 at equilibrium. Many of the parameters in Eq. (1), such as k0, n, Ea, and f(ΔGr), can vary as a function of temperature, pressure, pH, and other variables.

If corrosion takes place far from equilibrium and catalysis/inhibition due to other species in solution is unimportant, then Eq. (1) can be simplified and rewritten in terms of two equivalent expressions [39]: Rate = k 0 Ae − Ea Rate = k 0 Ae

RT

− E a RT

anHH++

2a

n +,ads X HH+,ads

2b

Whereas Eq. (2a) expresses the pH dependence of corrosion in terms of the activity of H+, Eq. (2b) expresses it in terms of the mole fraction of H+ adsorbed on surface sites. Both approaches are valid, but do not necessarily predict identical rates. At any given temperature glass dissolution rates show the U- or V-shaped dependence on pH commonly observed for silicate minerals, which is not necessarily symmetric with respect to pH. As determined from regression of rate–pH data or adsorption isotherms of H+ or OH−, the values for n in Eqs. (1) and (2) generally range from 0 to 1 at acid pH and 0 to −1 at basic pH, where corrosion is catalyzed by H+ and OH−, respectively. At 4 < pH < 8, the pH dependence is weak at most, so that corrosion rates are more or less constant (over a pH range that may be more restricted). Activation energies, derived from regression of ln R vs 1/T (K) data, are typically around 80 kJ/mol [34]. They are representative of hydrolysis reactions of 3-D networks of cation–oxygen framework bonds. With respect to both the leached-layer model and CIDR, an Ea = 80 kJ/mol increases the (Si) release rate by a factor of 20 between 25 and 55 C. However, advance of the diffusion front into the pristine glass (Figure 2) is characterized by a significantly higher Ea, which reflects the extremely slow nature of solid-state diffusion at low to moderate temperatures [20].

5.5 Decrease of Dissolution Rates by Chemical Affinity (ΔGr) and Pore Closure Effects A smooth exponential decrease of release rates is observed in virtually all glass corrosion studies (Figure 10). In terms of leached-layer theory, this evolution has been split into five regimes [7] that have no precise boundaries: (i) initial diffusion (interdiffusion), (ii) initial rate, (iii) rate drop, (iv) residual rate, and (v) alteration resumption (only under certain conditions). The chemical and physical causes of the rate decrease have long been debated. In closed systems, a decrease of the f(ΔGr) term in Eq. (1) has been commonly invoked as a result of the increasing concentration of dissolved glass species (i.e. Si) in solution. With the assumption of a rate-controlling activated-surface complex, Aagaard and Helgeson [40] calculated from transition state theory that:

659

660

5.12 Mechanisms of Glass Corrosion by Aqueous Solutions

f ΔGr = 1 − exp n

ΔGr RT

3

with n = 1 [39], Eq. (3) can then be expressed in a simpler form: f ΔGr = 1 − Q K

4

Alternative relations have also been suggested, for instance f ΔGr = 1 − Q K

1 n

5

with n = 10 [41]. In both Eqs. (4) and (5), Q refers to the ion activity product (IAP) of a given dissolution reaction, and K refers to the IAP at chemical equilibrium (i.e. solubility product). Application of such relations to glass corrosion is problematic because a glass and a solution cannot be in chemical equilibrium since the reverse reaction will not lead to glass precipitation. Defining the Q/K ratio with respect to glass corrosion has thus been very controversial. According to Grambow [42], dissolution of borosilicate glasses can be represented by the reaction SiO2 + H4SiO4. This approach relies on the assumption H2O Aglass ≈ ASiO2 (A denotes affinity), such that the parameter Q in Eq. (4) represents the aqueous silica concentration in the bulk solution and porous gel, and K refers to the solubility of amorphous SiO2. At advanced reaction progress, the buildup of aqueous silica in the bulk solution and within the pores of the gel will progressively slow down the release of Si from the external interface of the diffusion layer (Figure 2). The original hypothesis of ASiO2 -controlled dissolution was subsequently modified to include the effect of water diffusion through the hydrated diffusion layer [11]: if the layer is thin and water diffusion is unhindered, corrosion can continue at elevated rates, even for chemical affinity conditions of the bulk solution close to silica saturation. The same study [11] also suggested that soluble elements (e.g. Na and B) have a “collective response” with respect to silica concentrations, meaning that their release rates decrease significantly when the bulk solution attains silica saturation. Nonetheless, the silica-affinity model [42] has been criticized for not being compatible with many experimental observations [8]. Recent experiments on SON68 glass based on progressive addition of aqueous silica (0–150 ppm Si) have also cast doubt on its validity [43]. Even though rates decreased by a factor of 150 upon addition of Si, their pronounced nonlinear nature stands at odds with the linear decrease predicted by Eq. (4). In part because of such observations, a similar affinity model depending on the dissolution affinity of the gel layer was proposed [44]. Rather than just considering silica, it postulates that all elements in the solution and in the

gel layer determine the dissolution affinity. This approach therefore predicts that long-term corrosion is controlled by the chemistry of the bulk solution, and in particular, by secondary phases, which precipitate and thereby control ion concentrations. Another viable mechanism accounting for decreasing reaction rates is based on the transport properties of surface altered layers. These layers have the potential to decrease the bidirectional fluxes of aqueous reactant and product species between the bulk solution and the pristine glass. Alteration layers that form upon corrosion may be intrinsically dense, or may morphologically evolve with time so as to progressively decrease rates of diffusion of aqueous species within their porous structure. It has been argued that progressive densification of the outer parts of gel layers leads to pore closure [16], which in turn significantly decreases diffusion rates within the gel layer and thereby the intrinsic rate of glass dissolution. Another study used 29Si isotope tracer profiles measured on two different sample faces after 86-day corrosion experiments [45]: from the outer gel edge to the gel– pristine glass interface, 29Si diffused a total distance of 950 nm (bulk solution side); on the other side of the monolith in contact with a glass powder, the gel thickness was much thinner (≈ 150 nm), and most importantly, the gel acted as a diffusion barrier to 29Si, allowing penetration only over the outermost 30 nm. For closure of gel porosity to occur, and by implication a corrosion rate that becomes negligible (R ≈ 0), the authors [45] postulated that two conditions must be met: (i) the gel must have a high Si concentration, and (ii) the bulk solution must be silica saturated. Complementary Monte Carlo simulations supported these results and showed that clogging of the porous gel occurred at the external gel–bulk solution interface.

6

Perspectives

A systematic approach is needed to study in detail the molecular-scale mechanisms that control chemical alteration of glasses in aqueous solutions. This goal can only be achieved with a methodology that goes beyond standard analytical methods that have been widely used in the past. The choice of how altered glass samples are prepared, and which analytical techniques are used, is of critical importance for obtaining data useful in deciphering the molecular-scale mechanism of alteration, as well as modeling the glass corrosion process and its kinetics. Based on published data, the decrease in long-term rates of dissolution most likely are due to chemical and physical processes working in tandem. More in-depth work will have to be done to ascertain the partitioning between

References

chemical and physical rate-decreasing processes as a function of time during glass corrosion. The cornerstone for the long-term prediction of glass corrosion is an accurate understanding of the underlying mechanism(s). Therefore, employing high spatial and high mass resolution techniques to analyze surface altered phases and their interfaces with unaltered glass should be strongly encouraged for future glass studies. Moreover, corrosion experiments using isotopically labeled bulk fluids, and in some cases even labeled glasses, have already shown their enormous potential to provide complementary information on the dynamics of glass corrosion. When taken together, the combined use of all of these advanced techniques may allow for a longterm goal to be realized: establishing whether or not all glasses are ultimately controlled by the same mechanism of dissolution. Going even further, it may perhaps even lead to a universal mechanism that links mineral and glass alteration processes at the nanometer scale.

7 Frugier, P., Gin, S., Minet, Y. et al. (2008). SON68 nuclear

8

9

10

11

12

Acknowledgments The author thanks the reviewers J.P. Icenhower, T. Geisler, and E. Ruiz-Agudo (Dept. Mineralogy and Petrology, Univ. Granada, Spain) for their useful comments and suggestions.

13

14

References 15 1 Staudigel, H. (2013). Chemical fluxes from hydrothermal

2 3

4

5

6

alteration of the oceanic crust. In: Treatise on Geochemistry, 2 ed. (eds. H.D. Holland and K.K. Turekian), 583–606. Amsterdam: Elsevier. Grambow, B. (2006). Nuclear waste glasses – how durable? Elements 2: 357–364. Anovitz, L.M., Elam, J.M., Riciputi, L.R., and Cole, D.R. (1999). The failure of obsidian hydration dating: sources, implications, and new directions. J. Archeol. Sci. 26: 735–752. Dran, J.-C., Petit, J.-C., and Brouse, C. (1986). Mechanism of aqueous dissolution of silicate glasses yielded by fission tracks. Nature 319: 485–487. Crovisier, J.-L., Advocat, T., and Dussossoy, J.-L. (2003). Nature and role of natural alteration gels formed on the surface of ancient volcanic glasses (Natural analogs of waste containment glasses). J. Nucl. Mater. 321: 91–109. Gin, S., Ryan, J.V., Schreiber, D.K. et al. (2013). Contribution of atom-probe tomography to a better understanding of glass alteration mechanisms: application to a nuclear glass specimen altered 25 years in a granitic environment. Chem. Geol. 349–350: 99–109.

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glass dissolution kinetics: current state of knowledge and basis of the new GRAAL model. J. Nucl. Mater. 380: 8–21. Jégou, C., Gin, S., and Larché, F. (2000). Alteration kinetics of a simplified nuclear glass in an aqueous medium: effects of solution chemistry and of protective gel properties on diminishing the alteration rate. J. Nucl. Mater. 280: 216–229. Valle, N., Verney-Carron, A., Sterpenich, J. et al. (2010). Elemental and isotopic (29Si and 18O) tracing of glass alteration mechanisms. Geochim. Cosmochim. Acta. 74: 3412–3431. Doremus, R.H. (1975). Interdiffusion of hydrogen and alkali ions in a glass surface. J. Non-Cryst. Solids 19: 137–144. Grambow, B. and Müller, R. (2001). First-order dissolution rate law and the role of surface layers in glass performance assessment. J. Nucl. Mater. 298: 112–124. Dran, J.-C., Della Mea, G., Paccagnella, A. et al. (1988). The aqueous dissolution of alkali silicate glasses: reappraisal of mechanisms by H and Na depth profiling with high energy ion beams. Phys. Chem. Glasses 29: 249–255. Petit, J.-C., Della Mea, G., Dran, J.-C. et al. (1990). Hydrated layer formation during dissolution of complex silicate glasses and minerals. Geochim. Cosmochim. Acta 54: 1941–1955. Bunker, B.C. (1994). Molecular mechanisms for corrosion of silica and silicate glasses. J. Non-Cryst. Solids 179: 300–308. Thomassin, J.-H., Boutonnat, F., Touray, J.-C., and Baillif, P. (1989). Geochemical role of the water/rock ratio during the experimental alteration of a synthetic basaltic glass at 50 C. An XPS and STEM investigation. Eur. J. Mineral. 1: 261–274. Cailleteau, C., Angeli, F., Devreux, F. et al. (2008). Insight into silicate-glass corrosion mechanisms. Nat. Mater. 7: 978–983. Staudigel, H., Furnes, H., McLoughlin, N. et al. (2008). 3.5 billion years of glass bioalteration: volcanic rocks as a basis for microbial life? Earth-Sci. Rev. 89: 156–176. Hellmann, R. (1997). The albite-water system part IV. Diffusion modeling of leached and hydrogen-enriched layers. Geochim. Cosmochim. Acta 61: 1595–1611. Hellmann, R., Wirth, R., Daval, D. et al. (2012). Unifying natural and laboratory chemical weathering with interfacial dissolution–reprecipitation: a study based on the nanometer-scale chemistry of fluid–silicate interfaces. Chem. Geol. 294–295: 203–216. Vila, I.M. (2016). Diffusion in mineral geochronometers: present and absent. Chem. Geol. 420: 1–10. Buck, E.C., Smith, K.L., and Blackford, M.G. (2000). The behavior of silicon and boron in the surface of corroded

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nuclear waste glasses: an EFTEM study. Mater. Res. Soc. Symp. Proc. 608: 727–732. Hellmann, R., Penisson, J.-M., Hervig, R.L. et al. (2003). An EFTEM/HRTEM high-resolution study of the near surface of labradorite feldspar altered at acid pH: evidence for interfacial dissolution-reprecipitation. Phys. Chem. Miner. 30: 192–197. Wirth, R. (2004). Focused ion beam (FIB): a novel technology for advanced application of micro- and nanoanalysis in geosciences and applied mineralogy. Eur. J. Mineral. 16: 863–876. Daval, D., Sissmann, O., Menguy, N. et al. (2011). Influence of amorphous silica layer formation on the dissolution rate of olivine at 90 C and high pCO2. Chem. Geol. 284: 193–209. Geisler, T., Janssen, A., Scheiter, D. et al. (2010). Aqueous corrosion of borosilicate glass under acidic conditions: a new corrosion mechanism. J. Non-Cryst. Solids 356: 1458–1465. Geisler, T., Nagel, T., Kilburn, M.R. et al. (2015). The mechanism of borosilicate glass corrosion revisited. Geochim. Cosmochim. Acta 158: 112–129. Hellmann, R., Cotte, S., Cadel, E. et al. (2015). Nanometre-scale evidence for interfacial dissolution– reprecipitation control of silicate glass corrosion. Nat. Mater. 14: 307–311. O’Neil, J.R. and Taylor, H.P.J. (1967). The oxygen isotope and cation exchange chemistry of feldspars. Am. Mineral. 52: 1414–1437. Hay, R.L. and Iijima, A. (1968). Nature and origin of palagonite tuffs of the Honolulu Group, on Oahu, Hawaii. In: Studies in Volcanology: A Memoir in Honor of Howell Williams, Memoir, vol. 116, 331–376. Geological Society of America. Putnis, A. (2002). Mineral replacement reactions: from macroscopic observations to microscopic mechanisms. Mineral. Mag. 66: 689–708. Fenter, P. and Sturchio, N.C. (2004). Mineral-water interfacial structures revealed by synchrotron X-ray scattering. Prog. Surf. Sci. 77: 171–258. Marry, V., Rotenberg, B., and Turq, P. (2008). Structure and dynamics of water at a clay surface from molecular dynamics simulation. Phys. Chem. Chem. Phys. 10: 4802–4813.

33 Leonard, D. and Hellmann, R. (2017). Exploring dynamic

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surface processes during silicate mineral dissolution with liquid cell TEM. J. Micros. 265: 358–371. Conradt, R. (2008). Chemical durability of oxide glasses in aqueous solutions: a review. J. Am. Ceram. Soc. 91: 728–735. Perret, D., Crovisier, J.L., Stille, P. et al. (2003). Thermodynamic stability of waste glasses compared to leaching behaviour. Appl. Geochem. 18: 1165–1184. Jantzen, C.M. (1988). Prediction of glass durability as a function of glass composition and test conditions: thermodynamics and kinetics. In: Proceedings of the 1st International Conference on Advances in the Fusion of Glass (eds. D.F. Bickford, W.E. Hosfall and F.E. Wholley), 24.1–24.17. Westerville, OH: American Ceramic Society. Paul, A. (1982). Chemistry of Glasses. London: Chapman & Hall. Jantzen, C.M. and Plodinec, M.J. (1984). Thermodynamic model of natural, medieval and nuclear waste glass durability. J. Non-Cryst. Solids 67: 207–223. Lasaga, A.C., Soler, J.M., Ganor, J. et al. (1994). Chemical weathering rate laws and global geochemical cycles. Geochim. Cosmochim. Acta 58: 2361–2386. Aagaard, P. and Helgeson, H.C. (1982). Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. I. Theoretical considerations. Am. J. Sci. 282: 237–285. Bourcier, W.H., Carroll, S.A., and Phillips, B.L. (1994). Constraints on the affinity term for modeling long-term glass dissolution rates. Mater. Res. Soc. Symp. Proc. 333: 507–512. Grambow, B. (1985). A general rate equation for nuclear waste glass corrosion. Mater. Res. Soc. Symp. Proc. 44: 15–27. Icenhower, J.P. and Steefel, C.I. (2013). Experimentally determined dissolution kinetics of SON68 glass at 90 C over a silica saturation interval: evidence against a linear rate law. J. Nucl. Mater. 439: 137–147. Bourcier, W.L., Pfeiffer, D.W., Knauss, K.G. et al. (1990). A kinetic model for borosilicate glass dissolution based on the dissolution affinity of a surface alteration layer. Mater. Res. Soc. Symp. Proc. 176: 209–216. Jollivet, P., Angeli, F., Cailleteau, C. et al. (2008). Investigation of gel porosity clogging during glass leaching. J. Non-Cryst. Solids 354: 4952–4958.

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Section VI. Glass and Light

Figure 1 Coloration in a thirteenth-century stained glass of Chartres cathedral. Deep blue, tetrahedral Co2+; purple, octahedral Mn3+ (oxidizing conditions); light blue, octahedral Cu2+ (oxidizing conditions); green, mix of Cu2+ and Fe2+ (mildly oxidizing); red, ruby glass, nano Cu0 metal (reducing conditions) (cf. Chapter 6.2). Lower right part of a window depicting the life of St. James the Greater, whose donation by the Furrier and Draper guilds is acknowledged by this scene where a client is checking fabric quality. Source: © Robert Malnoury; Martin, Inventaire général, ADAGP. (See electronic version for color figures.) Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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From a dual practical and scientific standpoint, no other material has been so intimately associated with light than glass because of its translucency (or transparency), of the isotropy of its optical properties, and of its limitless shapability. One can even wonder how the laws of optics and the fundamental properties of light could have been determined without glass (Chapter 10.10). Not only has this close association between glass and light not weakened in the modern world, but it has actually been strengthened to a point that could not have been guessed even in a narrow past. This section of the Encyclopedia will make it very clear. This first chapter is a reminder of the fundamental concepts of optics provided by A. Clare who begins with light as an electromagnetic radiation to introduce the concepts of refraction, reflection, dispersion, absorption, and reemission and the manner in which these phenomena are put to use in basic optical devices (Chapter 6.1). The earliest man-made glasses were colored. It took a great many centuries before the transparency so closely associated with glass was eventually achieved. Purposely colored glass nonetheless never lost its great aesthetic appeal as so clearly illustrated by stained glass (Figure 1, Chapter 10.8). As reported by G. Calas, L. Cormier, and L. Galoisy, the quantum mechanical framework of solid-state physics makes it possible (i) to explain that coloration results from interactions of light with nanoparticles or with ions dissolved in well-defined sites of the glass network and (ii) to tailor rigorously light absorption for specific purposes in definite frequency ranges (Chapter 6.2). Luminescence is another kind of light–matter interaction whereby an absorbed incident photon undergoes inelastic scattering to be reemitted at a lower frequency or, occasionally, at a higher frequency when another photon is, for example, involved. In the case of glasses discussed by L. Wondraczek, it is with rare earth and transition metal doping elements that luminescence has been optimized to give rise to special and visual effects or to technical applications such as laser gain media (Chapter 6.3). Certainly, the most important modern glass device in optics is the fiber for remote vision and especially for telecommunications without which the Internet would not exist. The challenges to make longdistance applications successful were immense, but J. Ballato shows how they have been solved at a rapid pace in terms of glass composition, purity, industrial synthesis, and drawing as well as in terms of the optical design itself and of the mono- or multimode nature of the signal transmitted (Chapter 6.4). Without coloring elements, silicate glasses are transparent in the visible range. In contrast, they strongly

absorb light beyond 750 nm through the excitation of atomic vibrational modes. For infrared transmission, glasses with heavier and less strongly bonded atoms are thus needed to lower vibrational frequencies. The fluoride and chalcogenide systems whose structures and properties are examined by B. Bureau and J. Lucas are especially interesting in this respect as they present glass-forming compositions that lend themselves to the drawing and molding operations required to make use of their original optical properties in applications such as passive light guides or active fiber lasers and amplifiers (Chapter 6.5). Thanks to their photoluminescence, as then explained by J. Heo and K. Xu, rare earths in chalcogenide glasses are becoming significant elements in new active optoelectronic devices such as amplifiers and midinfrared gain media either as doping ions or as quantum dots, i.e. nanocrystals whose optical properties become not only atomic-like (through quantum confinement effects) but tunable when their sizes reduce to a few tens of nm (Chapter 6.6). The last chapters deal with the engineering of glass in up-to-date applications involving mainly – but not exclusively – light. Because light first interacts with the surface of a material, the variety of surface modifications reviewed by I. Sökmen, S. Oktik, and K. Bange, ranging from polishing and ion exchange to texturing and structuring, may enhance not only mechanical properties but also light transmission and absorption (Chapter 6.7). Various kinds of thin films deposited on glass surfaces are other means extensively used to modify glass surfaces. They are described by S. Oktik, I. Sökmen, and K. Bange, the best-known example being that of low-emissivity coating on window panes to improve thermal insulation (Chapter 6.8). From the time of oil lamps, glass has been a major component of light appliances thanks to its transparency and rigidity. As reviewed by H. Yamazaki and S. Yamamoto, the changes from fire to electrical lighting in the late nineteenth century with the arc and then the incandescent, fluorescent, discharge, and xenon lamps and now LEDs and OLEDs have been made possible because each time the right glasses and forming processes have been made available (Chapter 6.9). The history of displays told by K. Maeda is similar: just as highly absorbant lead-bearing glasses had to be designed for the traditional cathode-ray tubes of TV sets, new alkali-free compositions with very high strain temperatures had to be developed to produce the now ubiquitous LCD, LED, and OLED flat-panel displays for which an outstanding mechanical stability is required at the high temperatures at which electronically active devices are deposited (Chapter 6.10).

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6.1 Optical Glasses Alix Clare Kazuo Inamori School of Engineering, Alfred University, Alfred, NY, USA

1

Introduction

From the first refraction measurements made in the second century (Chapter 10.10) to the current ubiquity of optical devices exemplified by communication fibers (Chapter 6.4), optics has clearly been the scientific discipline with which glass has had the tightest ties. Today, optics in fact depends so heavily on glass that specific compositions tailored for particular applications are much too numerous to be counted. In these applications, glass plays either a passive role with respect to light, changing its path, or separating different wavelengths as done by lenses or prisms, or an active role in producing light itself as in lasers and other optoelectronic devices (Chapter 6.6). The question, then, is to know why glass – predominantly oxide glass – is the archetypical material used for propagating light and interacting with light in optical devices. To answer this question in this chapter, the basics of light–matter interactions, the properties relevant to traditional optics, and the material aspects of the glass that influence them will thus be reviewed briefly. More detailed accounts are given in standard textbooks (e.g. [1, 2]) whereas a comprehensive compilation of the physical properties of glasses and other materials relevant to optics is also available [3]. Traditional optics basically relies on the laws of reflection and refraction. The former was already known in Antiquity and the latter has long been derived from Fermat’s principle of least-action. According to this principle, light takes the quickest path to propagate between any two points, which is thus determined by the relative velocities at which the media are traveled as expressed by

Reviewers: J. Ballato, Materials Science and Engineering, Clemson University, Clemson, SC, USA L. Wondraczek, Otto Schott Institute of Materials Research, University of Jena, Jena, Germany

their indices of refraction. This phenomenological approach has been extremely important to design traditional optical components and it has the advantage of being also applicable to the refraction of acoustic waves. But a much deeper understanding of optical phenomena has resulted from the discovery made by J. Clerk Maxwell (1831–1879) that light of any wavelength is an electromagnetic wave, and then from the development of quantum electrodynamics. Since then, tailoring of glass compositions for specific applications has ceased to be an empirical exercise to take instead advantage of the new fundamental physical insights gained. In preamble, it is thus useful to present a few theoretical considerations. As an electromagnetic wave, light is made up of perpendicular electric and magnetic fields oscillating at the same frequency. It interacts with matter in ways that are controlled by the electrical and magnetic properties of the material of interest. Both are largely determined by electrical charges and the manner in which their motion and energy depend on the oscillating fields within the material. In view of their low mass, electrons are controlling many optical properties through both their number density and the relative ease with which they can move in the material to polarize it as measured by the permittivity. Depending on whether they are bound or free, electrons, for instance, cause refraction by slowing down the speed of light or undergo more complex interactions through absorption and reflection. Be they free or bound, electrons are usually governed by band structures, which themselves strongly depend on the type of bonding within the glass and, thus, on chemical composition. Through compositional changes, this is the reason why one can vary to a large extent the electron density and the optical properties of glasses. Traditionally, however, most of these materials are electrical insulators at room temperature so that they have a wide

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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bandgap and very few free electrons. Direct interaction of the oscillating electric field with electrons then is dominant. For some optical components, however, other kinds of materials are used in combination with traditional glasses to obtain a particular optical effect. If a high reflectivity is, for instance, required, metallic coatings are used because the free electrons of the metal can absorb and emit as well visible light at any frequency through their available free states. Depending upon the quality of the surface, metals can thus be very efficient reflectors of visible light.

2

Basic Features

2.1 Reflection Versus Refraction When light hits an air–glass interface (Figure 1), it is either reflected (R) or transmitted (Tin) through refraction into the glass. At the second interface between glass and air, the beam Tin is partly reflected to be refracted again at the first interface, reinforcing R, whereas its other part (Tout) is transmitted and refracted into the air. Through refraction to Tin and inverse refraction to Tout, distortion is not apparent unless the glass is very thick and/or is very refractive. In the latter case, multiple reflections may occur, especially in thick glass, because reflection in an electrically insulating material depends on the refractivity difference with air, its intensity increasing with it. In short, the more refractive is the glass with respect to air, the larger the proportion of light reflected compared with that transmitted at that interface.

2.2 Angle of Incidence A light beam traveling in vacuum consists of parallel straight lines or rays despite the fact that many sources undergo divergence. For a perfectly flat air/material interface, the angle of incidence is measured with respect to the normal (Figure 2). If its surface is scratched, however, then the material is hit by a light beam at many different angles so that light reflection and scattering are diffuse

Tout

R

I

Tin

Figure 1 Reflection and refraction of a light hitting a glass surface from the left.

θ

θ

Figure 2 Light reflected by a glass surface.

because they take place at a variety of angles. A very clear specular reflection (from the Latin speculum, mirror) of an image, keeping all its details, is not possible. If the beam is reflected internally, i.e. from a glass–air interface, it may be so totally depending on its angle of incidence. It is this fundamental property that allows optical fibers to guide light (Chapter 6.4) whereas many traditional optical components rely in contrast on the fact that the extent of bending of a light traversing an interface also depends on refractive index. In traditional optics, silicate glasses prevail because of their high transparency in the visible region. If high transparency is required, then an optically smooth surface is also needed so that one may control the light rays. And since the interfacial refractive index also controls the direction of the light beam, in traditional optics often the surface and the ultimate thickness of the component are modified so as to alter the direction of the light beam at a given position on the lateral air–glass interface. 2.3 Beam Light Characteristics The properties of the beam light of interest must also be considered to account for the extent to which a glass causes the light to be reflected, scattered, transmitted, or altered. The wavelength distribution is a first important parameter even if one deals with only the visible region, which represents the very small fraction of the total electromagnetic spectrum where the eye has a fairly high resolution; depending on a number of factors, the lower and upper limits of this region lie at some fixed values in the ranges 380–400 and 700–780 nm. Many traditional optics experiments were originally carried out with white light, which is a superposition of all the visible spectral colors (Chapter 10.10). The energy, and thus frequency and wavelength, is specific to each source so that light interacts with a material in a way that strongly depends on its wavelength distribution. White lights can have different shades depending on their color distribution and intensities. Until recently, most of those used in traditional optics were emitted by heated filament or gas-discharge lamps (Chapter 6.9). To limit spatial divergence, however, the light had to be collimated between its source and the optics. With the

3 Transmitted Light Tin

invention of lasers and, more recently, of solid-state light sources, spatial divergence has been much reduced but at the price of emissions restricted to specific wavelengths. Attempts have thus been made to make white solid-state emitters but they tend to favor the shorter, and not the longer wavelength end of the visible spectrum so that their shade is blue instead of yellow as in filament sources [4]. In traditional optics, the lights of filament bulbs and discharge lamps are the least and most intense, respectively (Chapter 6.9). Much higher intensities are obtained with single-wavelength laser sources whose light is amplified and does not spatially diverge but remains collimated. Although a high intensity might seem very favorable for optical experiments, it can result in unexpected effects even at wavelengths at which the material is not absorbing because impurities or weak interactions can cause the higher intensity of electric-field oscillation to give rise to higher order, nonlinear responses to the light [5].

3 3.1

Transmitted Light Tin Light Refraction

As an oscillating electromagnetic wave, light does not need a medium to propagate. When it does travel through matter, the electrons present respond more directly by a reduced wave velocity to oscillations for the electric than for the magnetic field. At a given wavelength, this slowdown is measured by the refractive index, n = velocity of light in a vacuum velocity of light in the medium

1

As described by Snell’s law (Chapter 10.10), the difference between the angles of incidence i and of refraction r on both sides of an interface (Figure 3) thus reflects a difference between the relevant indices of refraction: n=

sin i sin r

2

On exiting from the higher-index material on the right to the same lower-index material (Figure 3), the light is refracted away from the normal where it becomes parallel to the incident ray from the other surface. In practice, the speed in air is often considered instead of that in vacuum. Not only was refraction generally studied at interfaces involving air but, with its index of refraction of 1.003, air is similar to vacuum in its retardation of electromagnetic radiation. In contrast, retardation is particularly important in electrically insulating solid media in which, especially at high electronic densities, bound electrons respond slowly to propagate the wave.

Figure 3 Light passing through interfaces where the index of refraction is changing.

3.2

Dispersion

Although lights of all wavelengths travel at the same speed in a vacuum, they do not do so in a transparent material whose response for a given wavelength depends on its number density of bound electrons. Specifically, the speed at which the electrons can respond to move the wave through the material depends on the frequency of the oscillating field (how often it increase/decreases and changes direction) and how close to one another are the electrons. Because the frequency of the field oscillation controls the velocity reduction of the wave, it causes the refractive index of the medium to depend on frequency, even in the narrow visible range and, thus, on color. This is why each color of an initially white light is refracted at a slightly different angle at an interface. This dependence of the refractive index of a medium on wavelength is known as the dispersion of the material. For pure silica glass, n, for instance, decreases from 1.53 to 1.4 from 0.3 to 3.6 μm wavelengths (Figure 4). If dispersion allows the different wavelengths of a light to be separated with a prism or gratings, it also results in the chromatic aberration that severely limits the resolution of a single magnifying lens since for a given incident beam the different wavelengths are focused at different distances (Chapter 10.10). As a simple way to account for dispersion in the visible range, it is customary to measure the index of refraction at three well-defined wavelengths toward the end and in the middle of the visible range. The blue F-line of hydrogen at 486.13 nm (nF), the yellow d-line of helium at 587.56 nm (nd), and the red C-line of hydrogen at 656.28 nm (nC) are often selected for this purpose. When no indication is given, the reported index of refraction is nd, which is the one referring to the middle of the visible region. The index difference between the F and C lines is the average or principal dispersion. More

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6.1 Optical Glasses

1.55

(a)

n

1.50

1.45

UV

i

IR

1.40 0

1

2

3

4

λ (μm)

r

(b)

Figure 4 Index of refraction of SiO2 glass (Corning code 7940) from the ultraviolet to the far infrared. Source: Input data from [6].

i

conveniently, the dispersion may be simply characterized by a parameter V defined by Ernst Abbe (1840–1905) in terms of the indices of refraction for red (nr), yellow (ny), and blue (nb) colors, namely V = ny – 1

nb – nr ,

r

3

whose reciprocal is termed the relative dispersion. Along with the index of refraction, the Abbe number is useful for summarizing the optical properties of glasses as a function of composition (Figure 5; see also Figure 6 of Chapter 7.9). The long-standing opposition between flint and crown glasses is in particular readily rationalized in terms of V values lower and higher than 50, respectively. An ideal optical glass would combine a high refractivity with a low dispersion. As obvious in the Abbe diagram,

Figure 6 External refraction and total internal reflection in glass. (a) Refractive index of air to glass, n = sin i/sin r. (b) Total internally reflection at the interface between a higher- and a lower-index medium.

Figure 5 Abbe diagram for inorganic glasses and organic polymers. WG, soda-lime silica window glass. Source: After [7].

2.00 Crown

Flint

1.80

-beari

Lanthanum

Lead

Inorganic glasses

1.70

ng gla

sses

1.90

Refractive index n

668

Lanthanum Barium

1.60 Phosphate

Fluorine

1.50

WG

CMMA PMMA

DPSC

PC PS SMA SAN SMMA FMS SCMA Organic polymers

Borosilicates

1.40 90

80

70

60

50

Abbe number Ѵ

40

30

20

10

3 Transmitted Light Tin

such a combination would actually run counter the observed trend according to which a high refractive index tends to correlate with a high dispersion. The reason is that the higher electron density that can respond to the oscillating electric field, the more the electromagnetic wave slows down whereas the electric field of the light wave is similarly slowed down by the field causing charged particles – typically the electrons – to oscillate (in the same way that a moving body is more slowed down by a denser medium). The type of material, its composition, and structure thus control the number density and types of electrons (free or bound) with which the wave interacts and, hence, the oscillations caused by the field. For an analytical description of dispersion, one usually fits a Cauchy or Sellmeier equation to the observed wavelength–refractive index relationship. The latter equation is preferred for optical glasses [8]. If λ designates the vacuum wavelength, in micrometers, its general form is n2 λ = 1 +

Bi λ2 , λ2 − C i

4

where the summation is made over the absorption resonance peaks and the fit parameters Bi and Ci represent the

strengths of these resonances and the squares of their frequencies, respectively. Particularly in the visible range, the dispersion of optical glass becomes specially strong close to an absorption frequency where the refractive index becomes very sensitive to the wavelength because it is a function of the first derivative of the absorbance (Figure 7). This index goes through zero at the absorption peak, and then steeply increases with the wavelength until reaching a sharp maximum and decreasing. As discussed below, the origin of such a dispersion in traditional optical glasses is the ultraviolet absorption edge from electrons excited across the electronic bandgap.

3.3

Light Absorption and Re-emission

The propagation of light is also affected by absorption or scatter by the medium. The wave-particle duality requires to consider light as isolated packets of waves, known as photons, for which de Broglie relation states that E = hν,

where h is Planck’s constant and E and ν are energy and frequency. If E exactly matches the energy interval between two states of charged particles within the material (usually electrons, for visible light), then the photon may be absorbed. By inducing a change from a lower to a higher energy state in the material, the photon then finds itself eliminated from the transmitted light. Through a sample of thickness d, the intensity I transmitted is given by Beer–Lambert law, I = I 0 exp − αd ,

Figure 7 Relationship between absorption peak and refractive index.

5

6

where I0 is the intensity of the incident light and α the absorption coefficient at the wavelength considered. As already stated, absorption can take place if the energy of the wave oscillation exactly matches an energy interval to bring an electron from a lower to a higher level in the electronic structure of the material. If there are free electrons, like in metals, these intervals are very numerous so that many photons are absorbed and often immediately re-emitted because higher-energy states have short lifetimes. For electrically insulating materials, like traditional optical glasses, any photon whose energy exceeds an analogous interval transfers part of it to an electron so that its frequency is diminished instead in the transmitted light. For solid materials, the energy intervals depend on the electronic structure of the individual atoms, on how these are bonded, and on the overall atomic structure of the glass. In general, the band structure of the material has to be considered. As electrical insulators, most traditional

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6.1 Optical Glasses

4

Glass Properties

6

4.1 Bonding 4 Log α (cm–1)

670

2

0

–2

–4 –2

–1

0

1

2

Log energy (eV)

Figure 8 Absorption spectrum of window glass. Source: After [9].

optical glasses have a full valence band, a wide bandgap, and an empty conduction band. As a result, they typically absorb light only at energies higher than those of the violet end of the spectrum, which causes electrons to be excited from the valence into the conduction band over the wide gap. But many of these glasses have polar bonds, which give rise to vibrations and, thus, to absorption at infrared frequencies. By a happy coincidence, the eye is sensitive in the range where silicate glasses absorb very little between the UV and IR ranges (Figure 8). This is the very simple reason why these materials look transparent and why they have been traditionally used in optics. But transparency may be modified, for example, by addition of colorant ions acting as filters for specific wavelengths. Typically, the absorbing ion has a low enough concentration such that it is incorporated in the network as an isolated species that keeps its distinct electronic energy levels without participating in the band structure of the glass (Chapter 6.2). As a result, color filters transmit the light that is not absorbed by the isolated ions, whose absorption coefficients vary considerably; for example, small quantities (fractions of a weight %) of cobalt oxide in glass give a deep blue color whereas similar quantities of a rare earth like neodymium oxide would give a very pale (almost invisible violet color). When promoted to higher energy levels, however, these ions tend to return to their ground state but they often do it not immediately and not directly. It the de-excitation takes place through intermediate electronic levels, i.e. at smaller energy intervals, the light emitted has a longer wavelength (lower energy). For certain ions such as some rare earths and transition metals, such a photoluminescence can be quite strong (Chapter 6.3).

In general, there are three types of primary bonding in traditional materials, namely metallic, covalent, and ionic. Most materials combine two of them, often in conjunction with secondary weaker bonding such as van der Waals. In metals, light predominantly interacts with free electrons because, regardless of the band structure, very little energy is needed to let them oscillate. With partially filled or overlapping bands, the electronic structure of metals causes all wavelengths to be absorbed – albeit not with the same intensity – and re-emitted immediately. In traditional optics, metals have thus been used to enhance reflectivity in the form of thin polycrystalline films deposited on a glass surface. Although metallic glasses have been known for some time as ribbons or other kinds of thin samples, they are more recent in the bulk (Chapter 7.10). As a result, they have yet to make an influence in traditional optics although, if they could be made optically smooth, their enhanced corrosion resistance should be an asset to make highly reflective surfaces. In traditional oxide optical glasses, bonding is either ionic or covalent and more typically represents a combination of the two (Chapter 2.1). The degree of covalency depends on the relative tendencies of the metallic species to give up electrons and of the nonmetal species to accept them as determined by their relative electronegativities. Two bonded species with a small or zero difference in electronegativity form a largely or completely covalent bond, respectively. If the electronegativity difference is large, the bond has an ionic character that is strong but cannot be complete. When many atoms are present in the solid, the electron energy levels combine to form bands. In contrast to those of metallic bonds, the new atomic energy levels are usually full so that the electrons tend to be bound up in bonding. With covalent and ionic bonding, free electrons are available if the highest filled (valence) band is separated from the next highest empty (conduction) band by a gap so as to allow conduction to take place. Typically, those bandgaps are very large for solids with a predominantly ionic character. In more covalently bonded solids, they can be in contrast small enough to promote electrons to the conduction band either at room temperature or with low-energy photons. Bonding is on average a 50 : 50 covalent ionic mix in silicate glasses, which have thus generally a large bandgap. The polarizing interactions that control the speed of light through are thus typically due to bound electrons in the material. On the short wavelength/high energy end of the spectrum, transparency is limited by the bandgap of the

5 Glass Responses

material – a wider bandgap shifting transmission toward higher energies, at shorter wavelength typically in the ultraviolet spectrum. On the long wavelength end, transparency is in contrast limited by vibrational transitions of the bonds, provided their polarities make their excitation possible by the electromagnetic radiation. For most inorganic glasses, the limit to the transmission of infrared light actually depends on the strengths and masses of the bonded species, weaker bonds, and heavier bonded species allowing for longer transmission at infrared wavelengths (Chapter 6.5). 4.2

Homogeneity

Another good reason for making glass the standard transparent medium in traditional optics relates to its homogeneous, stress-free structure that can be achieved with adequate melting and annealing procedures at least at a scale larger than or equal to the wavelength of light. There is, therefore, a striking contrast with polycrystalline materials in which not only different crystallographic directions often have different light-wave velocities and refractive indices, but in which transparency is limited by reflection and refraction at grain boundaries. Wavelength-dependent processes such as Rayleigh and Mie scattering can nonetheless occur in glasses because of unavoidable structural inhomogeneity at the atomic scale. Although such processes have to be considered for optical fibers (Chapter 6.4), they do not constitute a problem for the relatively conservative path lengths of light in traditional optical components.

5 5.1

Glass Responses Reflection

Independently of Snell’s law, which rules prisms, lenses, and other optical components, changes in refractive index at an interface can also control the reflecting properties of the glass. At an interface between a low- and a high-index material, the intensity of the reflected light is greater in the latter. In a highly polarizable material, the reason is that the light is more slowed down through more interactions with oscillating electrons so that it is less transmitted and more reflected. Application of Fermat’s principle to reflection then implies that the angles of incidence and reflection are the same. But whether or not one can see a reflected image depends on the aforementioned optical smoothness of the interface since roughness would result in variations of the incident and reflected angles. In internal reflection (Figure 6), there is also an interface between the high- and low-index materials through which

refraction would take place if the angle between the transmitted light and the interface normal is larger than the angle to the same normal in the material. Since the refractive index is greater within the material than outside it, significant reflection of the light back into the glass would seem unlikely according to our previous discussion of the phenomenon. By virtue of Fermat’s principle, this may nevertheless occur for a reflection angle equal to the angle of incidence to that interface. Internal reflection actually becomes significant when the angle of refraction into the low-index medium becomes 90 or higher with respect to the normal, in which case the light is wholly reflected internally. Known as total internal reflection, the phenomenon is used occasionally in traditional optics, mostly in prisms, but by far its most significant impact is its use in light transmission along optical fibers (Chapter 6.4). 5.2

Absorption

If the energy of the photons of the wave exactly equals the interval between two states of a charged particle, then the particle can transition from a low- to a high-energy state. As an obvious consequence, the number of photons of that particular energy is reduced in the light beam in a way that depends on their availability. Unless purposely doped for filtering specific visible wavelengths of light, most oxide or silicate optical glasses typically have two major fundamental absorptions to contend with that are dependent on composition. Apart from a few specialty exceptions, traditional optical glasses are not electron conductors; they have large electronic bandgaps between the upper filled valence bands and empty conduction bands. Owing to structures more disordered than those of their crystalline counterparts, glasses have less clearly defined band edges. Because of insufficient energy, however, visible light cannot enable electronic conduction through promotion of electrons across the bandgap. Only photons in the ultraviolet can do it. In this case, once the minimum energy gap is exceeded, the conduction band is wide enough to accept multiple electrons so that this energy represents more an absorption edge than an absorption peak. Hence, fewer potentially electronically conducting bonds – typically more ionic – are required for extended transparency in the ultraviolet. At the low-energy end of the visible, it is also the oscillating electric field that interacts with the material. But in this infrared region, the energies typically couple with the vibrations of polarized bonds, which result from some ionic character associated with electronegativity differences. The frequency of the absorbed light depends upon the frequency change of bond vibrations in the glass. If bonds terminate by light elements and have a low force constant, they couple with IR radiations of lower frequencies, or longer wavelengths, which are likely transmitted

671

6.1 Optical Glasses

further into the infrared. Alternatively, transmission can also be achieved with a 100% covalently (nonpolar) bonded element whose vibrations do not involve polar species so that they do not couple with the electric field oscillation of the electromagnetic wave.

2

1.9

1.8 PbO

5.3 Glass Types for Traditional Optics Optical glasses transparent in the visible have traditionally been made from oxides, SiO2 being predominant. Although silica is a single-compound glass former, it tends to be used only when high purity or extended transmission into the ultraviolet is needed. The main reason is that its vitrification either requires very high melting temperatures or methods such as chemical vapor deposition (Chapter 6.4), which are both expensive. Multicomponent silicate glasses are thus usually preferred because of lower melting temperatures, easier chemical homogenization, lower viscosities, and, thus, ready casting to obtain an optically homogeneous material after careful annealing (Chapter 3.7). Specific oxides can be added to ease both melting and glass formation (typically modifiers such as alkali or alkaline earth metal oxides) and to tailor the refractive index (typically high polarizability ions such as lead), absorption (such as transition metal oxides) or photoluminescence (such as rare earth oxides) bands and other optical properties. 5.4 Engineered Glass for Specific Optical Properties An important distinction was made in the eighteenth century between the soda-lime crown and the lead-bearing flint glasses (Chapter 10.10). Although hundreds of new compositions have been designed since the beginning of the twentieth century, this distinction remains useful to characterize the refractivity and dispersion of optical glasses, which can now be varied over large domains (Figure 5). Systematic measurements of the index of refraction made for binary metal-oxide silica systems have been especially useful in this respect (Figure 9). Replacement of SiO2 or network-forming Al2O3 by heavier metal oxides, for instance, results in a higher refractivity because the polarizability is higher for nonbridging than for bridging oxygens. But that structural factors play a significant role is actually indicated by some unexpected differences or similarities. For instance, sodium and potassium silicates have the same indices, which are lower than those of lithium silicates because of structural collapse around the small Li+ ions. As expected, in contrast, indices are higher in alkaline earth than in alkali systems, and still more so for lead silicates. From a practical standpoint, a more important feature is the almost linear

nd

672

1.7 BaO 1.6

1.5

SrO CaO Li2O Na2O

K2O

B2O3 1.4

0

10

20

30

40

50

60

X (MxOy)

Figure 9 Effect of composition on room-temperature refractive indices at 589 nm in binary metal-oxide silicate glasses. Source: Input data from [6].

variations of nd with composition (Figure 9). These simple trends have been the basis of empirical models of prediction of the refractive index as a function of chemical composition, which are thus extensively used as starting points in the design of new compositions. A simple approach is based on Lorentz–Lorenz relationship between the polarizability and refractive index, which had long proven successful when applied to organic compounds. For inorganic glasses, the molar refractivity is then related to the molar volume Vm and the index of refraction at the wavelength considered by: Rm = V m n2 − 1

n2 + 2

7

And the molar refractivity of the glass is then assumed to be the sum of the ionic refractivities of its constituting oxides: Rmi =

xi Rmi ,

8

where xi is the mol fraction of oxide i and Rmi, for instance, varies (in cm3) from 0.05 (B3+) and 0.07 (P5+) to 0.1 (Si4+), 0.17 (Al3+) 0.2 (Li+), 1.33 (Ca2+), 3.1 (Pb2+), and 4.3 (Ba2+) [10]. But a limitation of the constant values of this model is that, in turn, the molar refractivity of oxygen (O2−) cannot be considered constant as it must, for instance, varies from 3.55 (in quartz) to 4.53 (in Ca2SiO4) or 4.97 (in Ba2SiO4) to agree with the experimental data [10]. More complex models of prediction of the refractive index have thus been devised (e.g. [11]), which are beyond the scope of this chapter.

6 Interaction of Optical Components with Light

Although optical glasses were traditionally transparent only in the visible, transmission in both the ultraviolet and infrared is needed for many applications (Chapter 6.5). A higher electronic bandgap is needed to increase transparency in the UV, which one achieves easily by introducing strong ionic bonds to lower the covalent character of the glass. With about 50% covalent bonding, silica itself is quite UV transmitting but its aforementioned processing difficulties offset the advantage of not needing addition of weakly bonded modifier cations. As done with chalcogenides and fluoride glasses (Chapter 6.5), the strategy for increasing the transparency in the infrared consists in decreasing the polarity of the bonds, making the bonded species heavier and weakening bonds such that the fundamental vibrational absorption edge shifts to lower energies and, therefore, to longer wavelengths. Many optical components require a high index to reduce the volume and, thus, the weight of the glass required. Since the refractive index is raised by a higher electron density along the light ray, it would seem logical to add to the composition heavier elements with many electrons such as lead. Whereas lead was earlier used to raise the refractive index, it also makes the glass more dispersive (Chapter 10.10). In prisms, for example, this feature was an advantage but the increased optical aberration is problematic in lenses (Chapter 10.10). Other dopants such as barium and some lanthanides are thus better suited to raise the refractive index, thanks to their high electron density, because they do not significantly raise the dispersion at the same time (Chapter 10.11). The effect is probably due to the higher ionic character of the bonding of these ions with oxygen, which increases the absorption bandgap and, thus, shifts the dispersion tail to shorter wavelengths. Although it is not itself a glass former and cannot be incorporated at contents higher than 40%, La2O3 has proven especially effective to raise nd up to nearly 1.73 while keeping an Abbe number lower than 1.55 [12].

6 Interaction of Optical Components with Light 6.1

Lenses

For a thin lens whose constant radii of curvature are R1 and R2, the focal length (f) in air is given by the relation 1 f = n – 1 1 R1 – 1 R2

9

In addition to the refractive index, two other factors are at play to change the propagation of light, namely the angle of incidence angle and the optical path length of the glass. Curved surfaces, for instance, mean that the

Focal points

Figure 10 Refraction of a light beam coming from the left and traveling parallel to the principal axis of lenses: convergence to the focal point for a convex lens, and divergence for a concave lens. Chromatic aberration resulting from focal lengths increasing with increasing wavelength from blue to red. Spherical aberration avoided if the radius of curvature of is not constant but vary such that the lens has the shape of a rotational hyperboloid.

rays from a parallel beam of light enter the glass at different angles, therefore getting refracted at different angles both in and out of the glass as illustrated by the simple convergent and divergent lenses (Figure 10). As already understood in the Middle Ages (Chapter 10.10), thanks to these two refractions, a lens constitutes a means of focusing and defocusing the rays, thus magnifying or reducing an image or changing the light to or from a parallel beam. In all cases, further control of the effects can be made through adjustments of the refractive index and/ or the physical thickness profile (the two surfaces) of the glass. Originally, the lenses used for early optical experiments were made from crown or flint glasses which were polished and ground to acquire a shape that would allow the rays of the light to be redirected as needed in the particular application. More modern optical glasses use barium as a compositional additive to raise the refractive index as it reduces the hazards associated with manufacturing components. In principle, with more modern techniques for fabrication such as chemical vapor deposition (cf. Chapter 6.4), it is even possible to produce a

673

674

6.1 Optical Glasses

functional gradient in the refractive index of a parallelepipedic piece of glass to achieve the same lens effects.

6.2 Mirrors Like analogous lenses, a convergent mirror focuses the light whereas a divergent mirror spreads it. The fraction of light reflected is given by the reflectivity (R), which depends on the indices of refraction of the two media involved, on the angle of incidence, and on light polarization. For normal incidence, polarization is not relevant and the reflectivity reduces to R = n1 – n2

n1 + n2

2

as uranium or other actinides. In the early days of optical filters, transition metal ions were used because for many of them the d-block absorptions gave an intense color in the visible for only a modest dopant level. The main problem with these outer d-block orbitals is that the ions can have different oxidation states, whose energies are impacted by the surrounding anions, their number, their geometry, and their bond length. Known as the ligandfield effect, this feature is the principal reason why a particular transition metal such as chromium can produce different colors in different oxide environments (Chapter 6.2).

10

For a crown glass (n = 1.5) in air, the reflectivity thus is 4%. As reflective optical components, mirrors are made by application of a thin layer of metal to a pristine glass surface. Many mirrors for optical experiments and instrumentation require the metallic film to be deposited on a shaped substrate such as spherical, or even parabolic, again to allow control over the direction of the light rays. Glass was typically used because it is easy to mold and subsequently machine/polish to a desired shape. For a low precision (e.g. decorative) mirror, the metal can be applied to the rear of the glass so as to be protected from mechanical damage. But the accuracy of the image reflected by the metal layer can be impacted by the optical transmission within the glass plate. For high-precision optics, therefore, the metal is applied to the atomically flat front surface of the glass. The glass substrate for the metallic surface can be molded, machined, and polished to be anything from plane to spherical or parabolic surface depending on the intended function of the mirror. The metal used for optics in the visible region was originally a tin/mercury amalgam before the much less hazardous silver could be deposited in the nineteenth century. Today, a good reflectivity is achieved with either silver or aluminum to which a little copper is added. With modern techniques, a large variety of coatings are in fact commonly deposited in several layers to ensure good bonding and protection against oxidation (Chapter 8). For infrared light, gold may be used as the reflective metal.

6.3 Filters Filtering out a single or a range of wavelengths to ensure that only specific frequencies are allowed to pass usually requires the band structure of the glass to have dopant quantities of colorant species (Chapter 6.2). Many of these ions are either transition metals or rare earths. There are some limited glasses with other dopants such

6.4 Prisms and Gratings Highly refractive glasses were often used for prism to disperse white light into its individual colors. Thanks to their higher dispersion, the original flint glasses were thus preferred in these applications. In more modern experiments, diffraction gratings are often favored because they can be work both in reflection or in transmission. In a grating, slits or grooves with a spacing d wider than the wavelength of the light of interest act as individual point sources interfering with one another constructively or destructively depending on the incident angle: d sin θmax = mλ

11

The order m of the diffraction strongly depends on the shape of the grooves. In view of the difficulties met when machining them on the original glass substrates, however, grooves are now generally ruled on polymer substrates with holographic rather than mechanical techniques.

7

Perspectives

From optical benches in research laboratories to modern telescopes, microscopes, and cameras, inorganic glasses have no competitors for high-quality optics owing to an unmatched capability to tailor their refractive and dispersive properties in wide domains through compositional adjustments (Figure 5). The prospects for widening further these domains are weak, however, because the effects of all economically affordable elements have already been investigated. Actually, some of them like thorium, beryllium, or cadmium would be of interest but their use is ruled out for obvious environmental reasons. In parallel, the quality of the glass itself has been much improved. Some of the defects that plagued early opticians remain present, but at extremely low levels. Improvements in melting procedures and batch homogenization combined with a better understanding of relaxation processes (Chapter 3.5) makes it, for instance, possible to achieve

References

indices of refraction constant to within 5 10−7 and to reduce bubbles to levels so low that their total cross sections can be only 0.006 cm2 in a volume of 100 cm3 [12]. At the same time, mechanical and physical properties and chemical resistance to the atmosphere, stain, acids, alkalis, or phosphates have also been optimized for the intended conditions of use. A review of only the most important current applications of optical glasses is clearly beyond the scope of this chapter. Homogeneous glass is the basic component of the tens of lenses, mirrors, and beam splitters assembled on optical benches to propagate or condition light, in particular for a wide variety of spectroscopy experiments (Chapter 2.2) that can be made on samples as small as a few microns directly observed under extreme conditions of temperature or pressure. Likewise, the simple design of the original microscopes and telescopes has been replaced with very complex setups (e.g. [13, 14]). In a modern microscope, a single objective may, for instance, consist of a set of up to 15 lenses to correct all kinds of aberrations, reduce background noise, and yield sharp images even at large fields of view. For obvious reasons, thinner and more lightweight lenses are preferred, which implies higher refractive indices. In the design of such instruments, computer modeling has largely taken over traditional optical-table experiments to determine the shape and type of glass needed for a particular component and to test and verify their intended combinations. But inorganic glasses can be very good at producing some unexpected results at the physical modeling stages of the making the components so that some compositional iteration may still be required at this stage. Concerning the resources, one should note that traditional inorganic glasses requires much energy to be synthesized but also that the raw materials used are quite plentiful and relatively inexpensive. We might thus see a resurgence of inorganic glasses for traditional optical applications, especially where large volumes are required, as a way toward a greener environment. In at least two important applications, inorganic glasses have nonetheless been replaced by organic polymers (Chapter 8.8) whose lightness, resistance to mechanical shock, and easy forming have been major assets. These are eyeglasses and lenses for cell phones, tablet computers, or personal assistants with market sizes of the order of billions of units in each instance. The quality achieved in the latter case by lenses with a focal length of 4.5 mm yielding a resolution ranging from 0.3 to 12 MP is a real technological feat, especially when one considers that these lenses are produced by injection molding at a very low price – from 3 to 5 US$ in the early 2010s – and that a mechanical zoom is not common for cost and size

reasons [7]. As impressive as they are, polymers nonetheless suffer from intrinsic limitations. These are clearly revealed by a comparison of their Abbe diagram with that of oxide glasses (Figure 5), which points to a rather narrow range of refractive indices so that inorganic glass thus remains without rival for high-precision optics. As for their lesser sensitivity to temperature and the improvements currently made in terms of scratch resistance, they are important practical advantages that give them another edge over polymers.

References 1 Brooker, G. (2003). Modern Classical Optics. Oxford:

Oxford University Press. 2 Guenther, B.D. (2015). Modern Optics, 2e. Oxford:

Oxford University Press. 3 Weber, M.J. (2003). Handbook of Optical Materials. Boca

Raton, FL: CRC Press. 4 Anonymous (2012). LED Color Characteristics.

5 6

7 8

9

10 11

12 13 14

Washington, DC: U.S. Department of Energy Factsheet PNNL-SA-84900. Simmons, J.H. and Potter, K.S. (2000). Section 7.1.2. In: Optical Materials. San Diego, CA: Academic Press. Mazurin, O.V., Streltsina, M.V., and SchvaikoShvaikovskaya, T.P. (1983). Handbook of Glass Data. Part A. Silica Glass and Binary Silicate Glasses. Amsterdam: Elsevier. Steinich, T. and Blahnik, V. (2012). Optical design of camera optics. Adv. Opt. Technol. 1: 51–58. Ghosh, G. (1997). Sellmeier coefficients and dispersion of thermo-optic coefficients for some optical glasses. Appl. Opt. 36: 1540–1546. Bagley, B.G., Vogel, E.M., French, W.G. et al. (1976). The optical properties of a soda-lime-silica glass in the region from 0.006 to 22 eV. J. Non Cryst. Solids 22: 423–436. Vogel, W. (1994). Glass Chemistry, 2e. New York: Springer. Scholze, H. (2013). Glass Natur, Struktur und Eigenschaften, new e. Berlin: Springer, trans. Lakin, M.J. (1991). Glass: Nature Structure and Properties, 3e. New York: Springer. Anonymous (2011). Optical Glass. Description and Properties. Mainz: Schott. Martin, L.C. (1966). The Theory of the Microscope. London: Blackie. Wilson, R.N. (2004). Reflecting Telescope Optics, I. Basic Design Theory and its Historical Development. II. Manufacture, Testing, Alignment, Modern Techniques. Berlin: Springer.

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6.2 The Color of Glass Georges Calas, Laurence Galoisy, and Laurent Cormier Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Sorbonne Université - CNRS - IRD - MNHN, Paris, France

1

Introduction

Color has been a most attractive feature of glass for millenia, from the glazes and pearls of the Suse period (4000 BCE) to the elaborated Roman houseware at the beginning of our era and to the stained glasses that blossomed during the European Middle-Ages. The kaleidoscope represented by medieval stained glasses (Figures VI and 1) illustrates the wide range of coloration of these glasses. The analysis of the coloration mechanisms gives information on the elaboration conditions, redox, and fining conditions. The control of color throughout the synthesis process is a key component of glassmaking. This importance was underlined by Weyl’s founding book, “Colored glasses,” where much of the knowledge on this topic available in the 1950s was summarized [1]. In present-day technology, functional glasses are often developed because absorption bands within UV and IR regions give rise to specific applications. This is, for instance, the case of iron-bearing glasses for which the main absorption band of Fe2+ in the 1000–1200 nm region makes efficient absorption of solar energy possible, while keeping light transmission in the visible range sufficient to ensure adequate visibility through car windshields. On a more general basis, the limited energy range in which oxide glasses are absorbing, because of the presence of (un)wanted impurities, does not preclude these glasses to be commonly transparent in the near-IR (Chapter 6.1), which is an important parameter for modeling the diffusive radiative transport. The color of a glass depends on light absorption, scattering, or reflection at wavelengths in the Reviewers: P. Bingham, Sheffield Hallam University, Sheffield, UK M.-H. Chopinet, Saint-Gobain Recherche, Aubervilliers, France

immediate vicinity of the visible spectral region. As other coloration processes, it depends also on the incident light source used and on the observer’s eye sensitivity. In the absence of coloring agents such as chemical impurities, defects, clusters, and nanophases, most oxide glasses are colorless because they do not absorb visible light. This is the very reason for their extensive use as components for optical instruments or communications, e.g. silica glass for light transmission down to 160 nm, beyond the transmission domain of the Earth’s atmosphere. In the presence of impurities or structural defects, glasses are colored by selective absorption in specific regions of the visible spectrum. Optical absorption then gives indications on the nature and structural environment of coloring species and, in turn, on glassmaking parameters such as batch composition, furnace atmosphere, melting temperature, or duration of the melting process. Glass color is an exemplary illustration of structure–property relationships in glasses [2] through the connection between the atomic-scale structure of the glass and the nature and the intensity of the absorption bands that cause glass coloration. As will now be shown, the physical mechanisms behind coloration can be ligand-field effects, charge-transfer processes, or quantum-confinement effects in metal or semiconductor nanoparticles.

2 2.1

Background on Color Processes Light Transmission by Glasses

The color of glass arises from variations in the light transmission efficiency throughout the visible spectrum, which lies between about 400 and 800 nm (Chapter 6.1). At the origin of coloration are absorption bands or

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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6.2 The Color of Glass

absorption edges whose effects are measured in terms of light transmission T through a glass plate T = I I 0,

1

(a)

where I0 and I represent the intensities of the incident and transmitted light, respectively. Reflection losses occur at glass–air interfaces, however, but they are readily accounted for because the intensity of the incident (Iin) and reflected (IReflected) beams are related by I Reflected = I in n − 1

2

n + 1 2,

2

where n is the index of refraction of the glass. For a sodalime-silica glass (n = 1.523), Eq. (2) indicates that a fraction f of approximately 0.04 of the incident beam is reflected at each interface, regardless of the wavelength in the visible region where n varies by about 0.01. Because light absorption depends on both glass thickness (l) and concentration of coloring elements (c), a more fruitful assessment of the process relies on Beer– Lambert law, which relates for a given wavenumber the absorbance A to these parameters and to the molar absorption coefficient ε (also known as molar extinction coefficient, or molar absorptivity) A = log I 0 I = log 1 T = εcl

(b)

The ratio A/l is referred to as the linear absorbance, allowing comparison between samples with different thicknesses. As indicated by Eq. (3), the transmission as a function of wavelength and absorbance as a function of wavenumber are easily interconverted. For a soda-lime glass, however, the two representations do not carry the same information in the visible and near-infrared spectral regions (Figure 2). Whereas transmission is the property of interest in practical applications, the absorption spectrum has to be considered instead in order to understand the coloration mechanisms because its bands can be assigned to definite structural components. Transmission to absorbance interconversion is probably one among the most spectacular structure–property relationships in materials. At short wavelengths (or high wavenumbers), one observes the onset of UV absorption, which is due to electronic transitions between the valence and conduction band tails across the bandgap. This absorption edge can be described by another absorption coefficient, α, which follows an exponential Urbach-type law as a function of the wavenumber ν, α

Figure 1 French stained glass from the thirteenth century (cf. Figure VI). (a) Notre-Dame of Chartres cathedral (1215–1240), Bay 5, James and Josuas, detail of The life of St. James the Greater (cf. Figure VI), Chartres. © Malnoury, Robert; Martin, J., Inventaire général, ADAGP. (b) Sainte Chapelle, Paris (1245–1250). © RMN (Musée de Cluny, Paris). (See electronic version for color figures)

3

exp hν E u ,

4

where Eu is the Urbach energy that accounts for the energy distribution of the localized states in the valence band tail. On this absorption edge are superimposed intense charge-transfer bands, also located in the near UV, which have a Gaussian lineshape (see Section 5).

2 Background on Color Processes

(a)

Fe3+

1820 nm

Fe2+

485 nm

415 nm

0.2

440 nm

380 nm

Charge transfer

0.4

OH vibrations

Absorbance

0.6

1050 nm

0.8

Background absorption

0 28 000

23 000

13 000

18 000

8000

3000

Wavenumber (cm–1)

(b) 100

0 300

1050

5400 cm–1

20

cm–1

40

20 500 cm–1

60 26 400 cm–1 24 000 and 22 800 cm–1

% Transmission

80

800

1300

1800

2300

2800

Wavelength (nm)

Figure 2 Glass coloration as examined from the standpoints of absorption and transmission for a soda-lime silicate glass containing 0.87 wt % Fe2O3 (sample thickness 4 mm). In the absorbance spectrum (a), the electronic transitions of Fe2+ and Fe3+ are clearly apparent in the near IR and visible-near UV, respectively. As to the transmission spectrum (b), it is used to represent coloration and provides colorimetric parameters. Source: After [3]. (See electronic version for color figures)

2.2 The Role of Transition Elements as Coloring Agents The color of glass is generally due to electronic transitions in transition elements between localized electronic energy levels that are split by the ligand field. Transition elements are characterized by the presence of unpaired electrons in partially filled d- or f-orbitals. Electronic transitions within these orbitals are at the origin of selective light absorption at characteristic energies, usually within or in the vicinity of the visible spectrum [4]. The energy and intensity of these transitions vary as a function of the transition metal ion present, its oxidation state, and its immediate surrounding (site symmetry, nature of the ligands). As d–d transitions are parity forbidden according to the selection rules for electric dipole transitions (Laporte

rule), transition elements in principle should not have a high coloring efficiency. This feature holds particularly true for 4f-elements, in which the electronic levels retain an atomic character because 4f-orbitals are shielded by the outer electronic shells and not admixed with other electronic states. Hence, the molar absorption coefficient of lanthanides is 5–10 times smaller than that of 3d elements, yielding only faint colors even at concentration levels of several wt %. For d-transition elements, the d-orbitals are not shielded by outer orbitals so that there is some admixture with other states when there is no inversion center at the site occupied by the transition element (distorted sites, tetrahedral or 5-coordinated sites). This admixing partially relaxes the Laporte selection rules, making 3delements such as Fe, Cu, Cr, V, Mn, Co, and Ni the major

679

6.2 The Color of Glass

coloring agents in glasses. Two main mechanisms are involved: (i) electronic transitions between crystal-field split 3d-electronic levels; (ii) charge-transfer processes, i.e. a transfer of the electronic density between the transition element ion and its ligands or other neighboring transition elements. As compared with the former, the latter is allowed and then results in an intense coloration. In both cases, optical transitions depend on the speciation of the transition element, namely its oxidation state, coordination number, site distortion, and on the nature of the chemical bond with its ligands (Table 1).

2.3 The Sites Occupied by Transition Elements in Glasses: A Limited Disorder The fact that glass coloration can be assigned to one or several species of transition elements indicates the presence of well-defined cation sites. It is thus an obvious inadequacy of the Zachariasen model of oxide glasses not to describe the local environment of cations. During the last decades, many experimental studies and numerical simulations have demonstrated that the structure of oxide glasses and melts is more organized than assumed with a continuous random network. They have shown that cations are not restricted to fill holes within the polymeric network but tend to define their own environment according to the well-known crystal-chemical rules that exist in crystals. A major advance has thus been this conclusion that cations have a heterogeneous structural distribution, which contributes to an original medium-range order of oxide glasses and makes it possible to explain charge-transfer processes involving transition elements.

Because of a usually lower density caused by atomic disorder, the coordination number of cations is generally lower in glasses than in crystals of similar composition. Some cations mimic network formers by occurring in tetrahedra connected to the polymeric network within a well-defined topology: such are the cases of tetrahedral Ni2+, Zn2+, and Fe3+. Network modifiers are cations such as alkalis or alkaline earths that are 6- or higher-coordinated. Contrary to what is observed in crystals, however, few transition metal ions are octahedrally coordinated in glasses and there is no evidence for higher coordination of 3d ions. The most important ions adopting an octahedral coordination are trivalent and highly charged cations such as Cr3+, V3+, or Zr4+, as well as Co2+ and Ni2+ in the special case of alkali-poor borate glasses where they occur as CoO- and NiO-derived 2-D-nanodomains. Other transition metal ions such as Fe2+, Ni2+, and Fe3+ are frequently distributed among various site geometries whose proportions and resulting effects on color depend on chemical composition. They are often 5-coordinated – a coordination seldom observed in crystals – which gives rise to original colorations. This structural evidence points to the presence of small sites where cations have a structural role intermediate between those of network formers and modifiers. But the fact that transition metal ions cause well-defined optical absorption spectra in glasses indicates that their site distribution is limited despite the amorphous structure of these materials. The need for satisfying the charge neutrality of ligands implies a connection to the glassy polymeric network and indicates that a concept of quasi-molecular complexes does not describe the actual structural location of these ions.

Figure 3 Successive splittings of dorbitals of transition elements in different coordination numbers and site geometry. The dashed lines represent the electronic transitions that can be observed in a one-electron system.

Energy

680

Free ion

Tetrahedral coordination

Octahedral coordination

Distorted octahedral coordination

Five-coordination (Square pyramid)

3 Crystal-Field-Driven Glass Color

3

Crystal-Field-Driven Glass Color

3.1

Crystal-Field Effects

The relative energy of d-orbitals varies as a function of the coordination number and distortion of the site occupied by the transition element, and by the bond covalency with the ligands. All these factors give rise to characteristic splittings (Figure 3) that make transitions between these electronic levels possible with a selective absorption of light that causes glass coloration. The position of these electronic levels gives indications on the local symmetry and magnitude of the ligand field splitting. The intensity of these transitions is determined by selection rules for which the spin state of the transition

metal ions plays an important role since absorption bands are less intense when the transition implies a change of the electron spin. For instance, Mn2+ and Fe3+ are not efficient coloring agents because both ions have five electrons occupying the five d-orbitals (Figure 4a), which leaves room for only spin-forbidden transitions of low intensity. Although less abundant than Fe3+ in glasses melted in air, Fe2+ gives them their characteristic green coloration caused by the presence of an intense absorption band in the near-infrared because a sixth 3d-electron (Figure 4a) produces spin-allowed electronic transitions. This contrast is reflected in the molar absorption coefficient of these ions, which is an order of magnitude lower for Fe3+ relative to Fe2+ (Figure 4b). Molar extinction

(a)

Fe3+

Fe2+

Molar absorption coeff. (cm–1.wt % Fe2O3)

(b) 9

9

8

8

7 6

7

Fe2+

6

5

5

4

4

3

3

Fe3+

2

2

1

1

0 4000

0 9000

14 000

19 000

24 000

29 000

Wavenumber (cm–1)

Figure 4 Influence of the electronic configuration on the optical absorption efficiency of Fe2+ and Fe3+. (a) Schematic representation of the population of 3d orbitals. For Fe3+, five electrons occupy the five d-orbitals so that d–d transitions are forbidden. For Fe2+, the sixth electron gives rise to an electronic transition. (b) Spectral dependence of the molar absorption coefficient of Fe3+ and Fe2+ in a soda-lime-silica glass. Source: After [3]. The large difference in coloring power between these oxidation states results from the different electronic configuration shown in (a).

681

682

6.2 The Color of Glass

coefficients are important to model optical absorption spectra in glasses, provided the chemical composition of the glasses be similar: as optical properties are additive, it is possible to compute optical absorption spectrum expected from the presence of various coloring elements (Table 2). Finally, another factor to be taken into account is the electrostatic repulsion between 3d-electrons because it influences the optical absorption spectra by shifting the free-ion electron energy levels prior to the action of crystal field. This interelectronic repulsion can be expressed in terms of three parameters A, B, and C known as the Racah parameters (after Giulio Racah, who first described them). Racah parameters are ion-specific and for a given ion vary with the electron localization (i.e. with cationligand bond covalency). The reduction of interelectronic repulsion between the 3d-electrons corresponds to a more covalent character of the transition metal ion oxygen bond. 3.2 Peculiar Sites, Peculiar Colors: The Example of Ni2+ Nickel yields colors ranging from brown and yellow in Na-, Li-, or Ca-bearing glasses to purple or blue in K-,

Rb-, or Cs-bearing glasses or, less commonly, green or even orange in some alkali-deficient borate and borosilicate glasses (Figure 5). This broad palette of hues in oxide glasses is directly related to the varying coordination of Ni2+ [6]. Probably one of the most commonly observed colors, the brown arises from continuously decreasing absorption from the purple to the red parts of the visible domain along with the absence of an absorption maximum in the visible domain. That color is indeed very sensitive to local structure as shown by a comparison between the optical absorption spectra of crystalline and glassy CaO NiO 2SiO2 (Figure 6). The former has the light green color characteristic of [6]Ni2+. In the latter, Ni2+ occupies a small proportion of tetrahedral sites but it is mostly present in triangular bipyramids that give rise to the brown color through a broad, asymmetric absorption band around 22 500 cm−1 (444 nm). Weak and broad absorption bands in the visible and near-infrared correspond to the other electric transitions expected for [5] Ni. The existence of these [5]Ni sites has been confirmed by complementary Ni K-edge extended X-ray absorption fine structure (EXAFS) and X-ray absorption near edge structure (XANES) spectroscopy and neutron diffraction coupled with isotopic substitution. As underlined below for Fe2+, however, most methods do not

O(2) Ni

O(1)

26%K2O εapp (l/mol/cm) 70 [4]Ni

60 50 40

purple

14%Na2O

[5]Ni

30 20 10 0

brown

Ni

15 000

20 000

O(1)

O(2)

25 000

Wavenumber (cm–1) 7%K2O Ni [6]Ni

green

Figure 5 Optical spectra and structural models explaining the color of purple, brown, and green borosilicate glasses containing Ni2+ in four-, five-, and sixfold coordination, respectively. Source: After [5]. (See electronic version for color figures.)

3 Crystal-Field-Driven Glass Color

provide indication on the actual site geometry of the [5]Ni site, which has been mostly derived from optical absorption spectroscopy. Optical transitions from tetrahedral Ni2+ are present as a minority contribution in most optical absorption spectra of Ni-bearing silicate, aluminosilicate, and borosilicate glasses, with the noticeable exception of low-alkali borate or borosilicate compositions. In glasses containing large alkalis (K, Rb, Cs), [4]Ni2+ causes a blue/purple coloration through the presence of an intense absorption band located near 16 000 cm−1, in the red region of the visible spectrum, and a transmission window at short wavelengths (Figure 5). This chemical dependence of glass coloration will be discussed in Sections 4.1 and 6.1.

of Fe2+ shows two absorption bands, the most intense near 9000 cm−1 with an extension to higher wavenumbers in the red region that also affects glass coloration. A significant absorption down to 16 000 cm−1, i.e. outside the absorption domain of octahedral Fe2+ in crystals, indicates the presence of [5]Fe. A detailed magnetic circular dichroism study has confirmed that the Fe2+ absorption band is mostly caused by four- and fivefold coordinated species [7]. This result agrees with Mössbauer and Fe K-edge XANES and EXAFS data, which indicate that Fe2+ coordination varies continuously from four- to Table 1 Glass coloring mechanisms.

3.3 Peculiar Sites with a Continuous Site Distribution: Fe2+ and Fe3+ Although iron is the most common coloring element in glasses, the geometry of the sites occupied by Fe2+ and Fe3+ is still a matter of debate in spite of numerous studies made with a broad range of structural and spectroscopic methods that includes X-ray and neutron diffraction, Mössbauer spectroscopy, electron paramagnetic resonance, XANES and EXAFS, optical absorption, and luminescence (Tables 1 and 2). Like for Ni2+, there is no evidence for octahedral coordination of Fe2+ in silicate glasses, but the picture is less clear-cut for Fe3+. The optical absorption spectrum 0.5 P O 0.6 P

0.3

0.2

P

P

T

0.4

0.1 0.2 0 5000

10000

20000 25000 15000 Wavenumber (cm–1)

Examples

Efficient concentration

Crystal-field transitions

d-Elements

0.1–10 wt %a

Atomic-like transitions

4f-Elements

1–10 wt %

Ligand to metal charge transfer

O–Fe3+, O–Ce4+, S2−– Fe3+, O2−–U(VI)

10–1000 ppm

Intervalence charge transfer

Fe2+–Fe3+, Fe2+–Ti4+

1–10 wt %

Nanoparticles

Au0, AgCl, Cd(S, Se)

10–100 ppm

Lower efficient concentrations for [4]Co2+ (some 10–100 ppm) and 4dand 5d-elements (e.g. Pt4+: a few 100 ppm).

Table 2 Color yielded by various transition metal ions in glasses.

0.8

O

O

0.4

Glass

Absorbance (crystal) (a.u)

Absorbance (crystal) (a.u)

Crystal

a

Cause of coloration

30000

Figure 6 Effect of nickel coordination on the absorbance spectra (derived from diffuse reflectance) of CaNiSi2O6 crystal and glass which are green and brown, respectively. The position of the three similarly intense peaks of octahedral Ni2+ in the crystal (O) contrast with the two weak peaks and the large high-energy band produced by Ni2+ in the trigonal bipyramids of the glass (P), to which tetrahedral Ni2+ contributes a shoulder (T). Source: After [6]. (See electronic version for color figures.)

Oxidation state

Coordination number

Color

Ti3+

6 (distorted)

Lilac

V4+ (VO2+)

6 (distorted)

Blue

6

Green

4

Yellow

4+

Cr

4

Blue

Cr3+

6

Green

Cr

6 (distorted)

Blue

Mn3+

6 (distorted)

Purple

Mn

4, 5

Light yellow/orange

Fe3+

4, 5

Light yellow

V

3+

CrVI (CrO42−)

2+

2+

2+

4, 5 (6?)

Green

Co2+

4

Violet blue

Ni2+

6

Apple green, yellow

Ni2+

5

Brown

2+

4

Blue, purple

6 (distorted)

Blue

6

Yellow

Fe

Ni

Cu2+ 4+

Pt

683

6.2 The Color of Glass

fivefold. These complementary techniques do not provide further information on the actual site geometry of [5]Fe sites, however, which may range from a square pyramid to a trigonal bipyramid geometry. Optical absorption spectra are very sensitive to this variation in the local symmetry that gives rise to distinct electronic transitions. A modification of the geometry of the [5]Fe site as a function of glass composition may explain the variations observed in the position of the broad Fe2+ absorption band near 10 000 cm−1 in glasses. This continuous distribution thus contrasts with the bimodal distribution between discrete site geometries observed for Ni2+, each one being characterized by well-defined spectroscopic parameters. Owing to experimental difficulties, the interpretation of the Fe3+ optical absorption bands in glasses has also been much discussed. It nonetheless appears that (i) the most intense bands arise from field-independent transitions that do not depend on site geometry; (ii) the other crystal-field transitions are superimposed on and can be obscured by the tail of the intense O–Fe charge-transfer transitions that occur in the near UV; (iii) as underlined in Section 3.1, Fe3+ transitions are spin-forbidden and hence of lower intensities than those of Fe2+ by more than one order of magnitude. In a recent investigation of glasses in which iron was fully oxidized, however, Fe3+ speciation could be unambiguously determined by EXAFS [8]. Providing information on the origin of the transitions observed in the optical absorption spectra, this study clearly showed that Fe3+ coordination is changing from 4 to 6 as a function of the nature and concentration of the alkali and alkaline earth cations present, the coordination number of Fe3+ increasing with decreasing cation ionic radius ratio. Alkali–alkaline earth glasses show evidence of a stabilization of [4]Fe3+, illustrating a preferential link between [4]Fe and the alkalis [8] and indicating that transition metal ions are not probing the average glass structure, but favor some local surroundings. 3.4 Presence of One Site Geometry: Cr3 Like in most crystalline compounds, Cr3+ occurs in glasses only in octahedral coordination because of the high crystal-field stabilization energy of the d3 configuration. The crystal-field spectrum of Cr3+ exhibits two broad, intense bands at 15 000 and 22 000 cm−1, which occur in the visible range and have characteristic Gaussian line shapes with bandwidths close to that observed in crystals (Figure 7). This is consistent with the observed Cr–O interatomic distances and their small radial disorder determined by Cr K-edge EXAFS. These absorption bands define transmission windows near 10 000, 18 000, and 27 000 cm−1: only the second one is responsible for the characteristic green color observed in Cr-bearing

30 Molar extinction coeff.(l/mol/cm)

684

KS3 20

NS3

10

LS3 0

12 000

16 000

20 000

24 000

28 000

Wavenumber (cm–1)

Figure 7 Molar extinction coefficients of Cr3+ in K-, Na-, and Litrisilicate glasses (referred to as KS3, NS3, and LS3, respectively); experimental spectra (solid curves) and fits made with Gaussian bands (dashed curves), which are also plotted as dotted curves for LS3. For clarity, the data for NS3 and KS3 have been shifted upward by 2.7 and 12 L/mol/cm, respectively. Source: After [9] (See electronic version for color figures.).

glasses since the others are outside the visible spectrum. Additional weak features near the maximum of the bands are linked to field-independent spin-forbidden transitions, resulting in characteristic interference dips. Other transition-element cations exhibiting only one site geometry in glasses include Ti3+, V3+ and V(IV) (actually the vanadyl group, VO2+), Cr2+ and Cr4+, etc. Special mention must be made of Mn3+ and Cu2+ for which the main absorptions band undergo Jahn–Teller splitting of the excited eg level through spontaneous distortion of the octahedral coordination, which increases the crystal-field stabilization energy. As a result, Mn3+ allows light transmission in the red and violet part of the visible spectrum, resulting in the characteristic pink/magenta color of Mn-bearing glasses, whereas Cu2+ exhibits a unique, large transmission window in the blue-green part of the spectrum.

3.5 The Case of Silent Species: Co2+-Bearing Glasses The typical blue color of Co-bearing glasses is due to an intense absorption band located in the orange and red parts of the visible spectrum that is characteristic of [4] Co2+ (Figure 8). This assignment from optical absorption spectroscopy is in agreement with XANES and EXAFS data. Even though the hue of Co-bearing glasses

4 Variation of Glass Coloration

230 100

50

CFSE (kJ/g.ion)

Molar extinction coefficient (l/mol/cm)

235 150

NaCa

KCa

10 000

15 000

Wavenumber

225 O Di

20 000

NS3

NBS O

O

does not vary much with glass composition, the intensity of the coloration (and hence of the absorption bands) does change. As an example, replacement of K by Na in R2O CaO 4SiO2 (R = K, Na) glasses decreases the optical transition intensity by 35% whereas the molar extension coefficient of [4]Co2+ complexes is only half of the values reported for potassium and sodium silicate glasses. This is an indication that Co2+ converts to less absorbing, silent species when replacing a given alkali by either a smaller alkali or alkaline earths. As indicated by EXAFS data, the smaller molar extension coefficient cannot be attributed to a distortion of the Co tetrahedral site, as observed in crystals. These observations suggest the presence of higher coordinated, weakly absorbing species, that are difficult to quantify because the optical absorption bands of [4]Co2+ overlap the transitions expected for [5]Co2+ and [6] Co2+. Although the low intensity of these spectroscopically silent species does not help in recognizing them in optical absorption spectra, they directly affect the intensity of light absorption and hence the efficiency of Co2+ as a coloring agent.

Variation of Glass Coloration Dependence of Color on Glass Composition

Changing glass composition affects the effective charge of the oxygen ligands, and hence crystal-field splitting magnitude as well as cation‑oxygen covalence. Transition elements are indeed interesting structural probes of glass

215 0.45

NS2 O

25 000

KS2 O

KBS O

(cm–1)

Figure 8 Influence of the nature of the alkali cation on the intensity but not on the lineshape of the optical absorption bands of Co2 + -bearing K2O CaO 4SiO2 (blue) and Na2O CaO 4SiO2 (red) glasses. Absorbance is represented as represented by the molar extinction coefficients, allowing quantitative comparison between the two glasses. Source: After [10]. (See electronic version for color figures.)

4.1

LS2

220 0 5000

4

O

0.5

0.55

0.6

0.65

0.7

Optical basicity, (Λglass)

Figure 9 Variation of Cr3+ crystal-field splitting, represented as the crystal field stabilization energy (CFSE), as a function of optical basicity in glasses. Filled squares: multicomponent silicate and aluminosilicate glasses, which mimic chemical variations during magmatic differentiation; open circles: alkali silicate glasses (NS, KS, and LS refer to sodic, potassic, and lithic silicate glasses, respectively, NBS and KBS stand for sodium and potassium borosilicate glasses) and Di for diopside (CaMgSi2O6) glass; filled triangles: alkali borate glasses. Source: After [11].

structure. Two different cases can be distinguished in this respect. When only one site geometry exists (e.g. Ti3+, Mn3+, Cr3+, V4+, and V3+), the chemical dependence of the optical spectra manifests itself mostly through a shift of the main absorption bands. When two sites (e.g. Ni2+, Ti4+) or more (e.g. [4]Fe2+ and [5]Fe2+, [8]Nd3+ and [9]Nd3+) are present, their relative proportions vary with glass composition without much shifting of the electronic transitions. An abundant bibliography exists in this domain, but is mostly restricted to some specific glass systems. We will illustrate this section with Cr3+ and Ni2+. 4.2 Variation of Site Geometry: Presence of a Single Type of Site The case of Cr3+ has been studied extensively. This cation retains a regular octahedral coordination in most oxide glasses [11] in spite of some variations in the magnitude of crystal-field splitting and of disorder effects induced by glass composition mostly as a function of the nature of the modifier cation (but not of its concentration). In multicomponent glasses (Figure 9), the crystal-field intensity increases with optical basicity (cf. Chapter 5.7). In alkali silicate glasses, however, it varies only with the nature of the alkali and not with its concentration. In mixed

685

6.2 The Color of Glass

alkali–alkaline earth glasses, optical absorption parameters in addition remain close to the values found in binary silicate glasses with the same type of alkalis, which reveals that Cr3+ shows a strong preference for alkalis in its immediate environment. These observations indicate that Cr3+ is insensitive to the overall glass structure. It builds instead its own environment, which is also demonstrated by its heterogeneous distribution in the glass structure [11]. 4.3 Variation of Site Geometry: Presence of Two Sites When a glass bears an ion such as nickel that distributes between two sites, its color vary with glass composition [6] as the fractions of [5]Ni2+ and [4]Ni2+ sites. In silicate glasses, alkalis and alkaline earths are either network modifiers when they coexist with [5]Ni or chargecompensators for [4]Ni. The mean Ni speciation thus depends only on the nature of the alkali or alkaline earth. As observed in Section 4.2 for 3d-ions in a single type of site, however, the concentration of the alkali or alkaline earth does not influence glass color in silicate glasses. By contrast, in borate and borosilicate glasses, the Ni-site geometry and color progressively change with increasing alkali or alkaline earth content from octahedral (green) to distorted octahedral (yellow), trigonal bipyramid (brown), and finally tetrahedral (purple). This trend likely arises from the interaction of alkali and alkaline earths with boron when its coordination changes from [3]B to [4]B with increasing alkali/alkaline earth concentration. As a consequence, some borosilicate glasses show a peculiar orange color that is otherwise rarely encountered. In this case, Ni has the three coordination numbers 6, 5, and 4: [6]Ni is probably associated with the borate sublattice, and [5]Ni and [4]Ni with the silicate sublattice. 4.4 Redox Equilibria and Glass Coloration The influence of the redox state on glass color has been much investigated [12]. For instance, Cr-bearing glasses show a change in glass color from green to yellow when melting conditions vary from reducing to oxidizing. This trend is due to the formation of a chromate complex (CrO4)2− that gives rise to a charge-transfer transition from oxygen to chromium located near 28 000 cm−1 in oxidized glasses (Figure 10). The tail of this intense band extends from the UV to the visible and is superimposed on the Cr3+ absorption bands because there exists a considerable difference between the molar extinction coefficients of Cr3+ and Cr6+, which are 18–20 and 4200 l/(cm/ mol), respectively. As a result, optical spectroscopy measurements of the chromium redox state cannot be made

14 SCN SBN SBNox

12 Linear absorbance (cm–1)

686

10 8 Cr(VI)

6 4

Cr(III)

2

0 10 000

15 000

20 000 Wavenumber

25 000

30 000

(cm–1)

Figure 10 Linear absorbance spectra of Cr3+ and (CrO4)2− in sodalime-silica (SCN) and sodium borosilicate (SBN and SBNox) glasses. The position of the absorption bands characteristic of the two oxidation states of chromium in the glasses is indicated. Source: After [14].

on glasses in the presence of relatively high concentrations of Cr6+ in the form of chromate groups. Wet chemical analysis or other spectroscopic methods have to be performed instead. The interaction between redox pairs is widely used during glass fining. For instance, manganese has traditionally been known as the glassmaker’s soap because, if added to soda-lime-silica glass in the form of an oxide such as MnO2, it makes the green color arising from iron impurities less intense by oxidizing Fe2+ into Fe3+ Mn4 + + 2 Fe2 +

Mn2 + + 2 Fe3 +

And because only spin-forbidden transitions are associated with the d5 configuration of both Mn2+ and Fe3+ (Figure 4a), their low intensities result in weakly colored glasses. The effect is not permanent, however, as the interaction with sunlight (solarization) favors the reverse reactions: Mn2 + + hν Fe3 + + e −

Mn3 + + e − , Fe2 +

As illustrated by old windows and doorknobs, this phenomenon is at the origin of the well-known purple glass of which desert amethyst glass is a natural variety.

5 Temperature Dependence of the Optical Absorption Spectra of Glasses: Thermochromism

5 Temperature Dependence of the Optical Absorption Spectra of Glasses: Thermochromism Color changes are often spectacular upon heating: brown Ni-bearing glasses, for instance, turn blue or green Cr3+-bearing glasses into yellow (Figure 11). Like for the chemical dependence of glass coloration, there is a marked difference between transition elements depending on whether they occupy one or several sites. In the latter situation, temperature modifies the equilibrium between the site populations whereas in the former, the site of the coloring element expands with increasing temperature. Because of the difficulty of recording hightemperature optical absorption spectra, however, data are scarce so that we will restrict ourselves to discussing investigations made below Tg. We nonetheless warn that important modifications of the optical spectra may take place in the molten state.

5.1

Coexistence of Well-Defined Sites: Ni2+

In a classic piece of work, Lin and Angell [15] investigated the optical absorption spectra of Ni2+ in a potassium triborate glass and melt to 1000 C. In the starting glass, Ni2+ is distributed between 4- and 5-coordination as in most oxide glasses (see Section 3.1). Major changes occur in the vicinity of Tg, above which the proportion of [4]Ni2+ increases. This is likely related to

the temperature-induced coordination changes of boron, as shown by the reaction NaCC + BO4

BO3 + ONBO + NaNM

5

where NaCC and NaNM stand for charge-compensating and network-modifying Na, respectively, and ONBO for nonbridging oxygen. The [4]B to [3]B conversion between glass and melt increases alkali activity and then provides further charge compensation for [4]Ni, inducing the coordination change of Ni. In the borate composition investigated, the [4] Ni/[5]Ni ratio is not frozen in at Tg, as these two states are separated by unusually small energy barriers. The presence of further changes down to room temperature is a direct evidence of ionic mobility while the polymeric network is frozen in. The modification of Ni- and Co-speciation in glasses at high temperature may be retained after fast quenching. This has been recently shown in Co- and Ni-bearing alkali borosilicate glasses in which the 4coordinated species, favored at high temperature, are partly retained at room temperature by a fast quenching, illustrating the importance of thermal history on glass structure [16]. 5.2 Presence of One Site: Direct Evidence of a Thermal Expansion of Cation Sites The crystal-field strength is a sensitive probe of the environment of transition elements in crystalline compounds and of its changes under high temperatures or pressures. High-temperature optical spectra of Cr3+ in glasses show a systematic linear redshift of the crystal-field transition from 300 to 800 K, with an isobestic point near 17 000 cm−1 (Figure 12). The transmission window similarly 0.4

300 K 383 K 479 K 578 K 676 K 726 K

Absorbance

0.3

0.2

0.1

0

12 000

15 000

18 000

21000

24 000

Wavenumber (cm–1)

Figure 11 Green Cr-containing glasses turning yellow at ca. 500 C, a direct illustration of the thermal expansion of cation sites in glasses. (See electronic version for color figures)

Figure 12 Modification of the optical absorption spectrum of Cr3+ in a potassium borosilicate glass from 300 to 726 K. Source: After [12]. (See electronic version for color figures)

687

688

6.2 The Color of Glass

shifts toward lower wavenumbers, giving glasses thermochromic properties [11]. Using a point charge model, one may derive the temperature-induced variation of the Cr– O distances from crystal-field splitting, Dq 10Dq =

5q r 4 R5

6

where q is the effective charge in the ligands, r the d-electron-core distance, and R the mean Cr–O distance. In this way, one estimates the linear thermal expansion coefficients of Cr3+–O bonds in glasses to be about 16–20∙10−6 K−1. These values are independent on glass composition, contrary to what is observed for bulk thermal expansion, and they are in addition generally larger than the macroscopic thermal expansion coefficients. This lack of sensitivity of Cr3+ to the average glass structure is an additional confirmation of the heterogeneous structure of silicate glasses at the atomic scale [11]: Cr3+ does not explore an average glass structure but rather adjusts its own environment.

6 Charge-Transfer Processes: From Amber Glasses to Lunar Glasses 6.1 Ligand to Metal Charge Transfer (LMCT) Charge transfer (CT) represents a shift of the electron charge density from one ion to a neighboring one. The most frequent processes involve transition metal ions such as Fe2+, Fe3+, Ti4+, Ce3+, Ce4+, and their ligands (O, S, Se…) in relation with the covalency of the chemical bond. They give rise to intense absorption bands at short wavelengths, providing a strong UV absorption in glasses that would otherwise be mostly transparent in the visible range. These glasses are thus used for solar protection and they also ensure efficient UV absorption in food containers. The reduction of glass transparency in the UV arises from the presence of Gaussian-shaped absorption bands, superimposed on an exponential Urbach absorption edge and related to the presence of ligand-to-metal CT transitions. The intensity of these bands is larger by about three orders of magnitude than that of crystal-field transitions. The O2−–Fe3+ CT band near 45 000 cm−1 dominates the shape of the UV absorption edge [17], and may be detected at low concentration down to ppm levels. For Fe2+, CT is about three times less intense and occurs at slightly higher energy than for Fe3+. Likewise, Ce3+ and Ce4+ are strong UV absorbers in glasses where, as observed for iron, absorption is more efficient (by a factor of 16) and takes place at higher wavenumbers for the oxidized than for the reduced form [18]. Other transition

metal ions show intense ligand-to-metal transitions in the UV, e.g. near 33 000 cm−1 for Ti4+ [19]. Increasing the covalency of Fe-ligand bond shifts the energy of the charge-transfer transition toward lower values. Such is the case of the well-known amber chromophore, which is widely used to efficiently absorb UV radiation and then protect radiation-sensitive liquids in glass containers (pharmaceuticals and beverages). This chromophore shows optical transition near 23 500 cm−1 with a molar extinction coefficient of about 9000 L/mol/cm (as compared to 25 L/mol/cm for the Fe2+ absorption band near 1000 nm). As a consequence, the amber chromophore contributes to glass coloration at concentrations as low as a few ppm: the high intensity of these bands causes them to extend into the visible spectrum. The continuously decreasing absorption from the violet to red gives rise to this characteristic brown coloration. The structure of this amber chromophore is still poorly known, involving [4]Fe3+ ions surrounded by one S2− and three O2− ions. Its stability field is then limited by two opposite redox reactions, i.e. the reduction of ferric iron and the oxidation of sulfide ligands. A peculiar case concerns oxyanion and oxycation complexes such as chromate (CrO4)2−, vanadate (VO4)3−, or uranyl (UO2)2+ groups. Under oxidizing conditions, these complexes are similar in glasses to those observed in crystals and aqueous solutions, retaining similar spectral properties. As a d0 system, the formal Cr(VI) or V(V) oxidation states do not have d electrons, so that the only electronic transitions occur via charge-transfer processes from ligands to the central ion, which is at the origin of the intense coloration arising from these extreme oxidation states. For instance, CT in chromate groups consists of a transfer of an oxygen p electron, constituting one of the ligand bonds of t1π symmetry, to the central ion dshell. Further splitting by crystal field gives rise to two absorption bands near 37 000 and 27 000 cm−1 [20]. Only the latter is usually observed because the former is hidden by the absorption of the matrix (Figure 12). 6.2 Intervalence Charge Transfer Another type of CT involves cations with different oxidation states, which also relies on an extended covalency of chemical bonds and give rise to absorption bands so intense that these may even result in efficient coloration at concentrations down to the ppm level. Increasing the iron content in oxide glasses, for instance, increases absorption in the visible region between ligand-to-metal CT in the near UV and crystal-field transitions in the near IR so that high-Fe glasses melted in air are black (Figure 13). Evidence has been found for a contribution near 14 500 cm−1, assigned to Fe2+–O2−–Fe3+ intervalence charge transfer (IVCT), Fe2+ and Fe3+ playing the

7 Absorption by Organized Clusters and Nanophases

(a)

(b)

Figure 13 Coloration arising from charge transfer processes. (a) Dark color of NaFeSi2O6 glass (Fe2+–Fe3+ intervalence charge transfer). (b) Orange glass (“soil”) collected during the Apollo 17 mission. Clear orange beads owe their color to Fe2+–Ti4+ intervalence charge transfer. The black color of some grains comes from the surface nucleation of olivine crystals with intergrown ilmenite (FeTiO3) crystals. Source: © Kurt Hollochern Geology Dept, Union College, NY. (See electronic version for color figures)

role of electron donor and acceptor, respectively [21]. The deep-brown to black color of these glasses is an interesting visual proof for clustering of transition element in glasses with a significant covalent bonding in and between the Fe sites. During lunar exploration, an original 3.48-billion-yearold orange glass has been found near a small crater at the Apollo 17 landing site (Figure 13). This glass color comes from a Fe2+ (donor)–O2−–Ti4+ (acceptor) charge-transfer transition near 24 000 cm−1. Synthetic glasses containing Fe or Ti and synthesized under simulated reducing lunar conditions exhibit a green or a purple color, respectively. It is only the association between the two transition elements that results in this original color [19]. This fact provides further proof of the heterogeneous distribution of transition element cations in glass structure, favoring a location in specific enriched regions. Similar Fe–Ti IVCT may be used for enhancing UV absorption in container glasses for drugs and cosmetics.

7 Absorption by Organized Clusters and Nanophases

[6] but not in silicate glasses. For decades, these features have been assigned to the presence of Ni and Co in octahedral sites within the glass structure. More recently, Niand Co–K edge EXAFS data on these glasses have revealed cation–cation correlations up to 6 Å in ordered NiO- or CoO-based clusters and characterized by three colinear, edge-sharing octahedra, which induce a specific multiple scattering feature around 6 Å. Some structural features characteristic of the bulk oxides (CoO or NiO) are missing, however, showing that these ordered domains do not correspond to pure oxide crystallites [2]. This environment is not affected by Ni or Co concentration and disappears with increasing alkali content. The presence of similarly ordered domains in low-alkali borosilicate glasses shows that [6]Ni (and probably [6]Co) is preferentially associated with a borate rather than with a silicate sublattice. This local coordination is likely favored by the geometrical constraints induced by the presence of rigid large [3]B-based superunits. But the EXAFS data indicate a less extended structural order in the NiO nanodomains, probably due to the mutual interaction between borate and silicate sublattices, which limits their extent [6].

7.1 Presence of Organized Clusters: Low-Alkali Borate and Borosilicate Glasses

7.2

Nickel- and cobalt-bearing alkali-poor borate glasses exhibit original green and light pinkish purple colorations, respectively. Similar colors are found in borosilicate

Although Ruby glasses have been known for centuries (e.g. the famous fourth-century Lycurgus cup), their deep ruby-red or yellow colors have been explained only

Metallic Nanoparticles

689

6.2 The Color of Glass

recently in terms of precipitation of Au, Cu, or Ag nanoparticles 5–100 nm in diameter [22]. These nanoparticles form during thermal treatments above the annealing temperature of colorless starting glasses prepared under reducing conditions such that the dilute (40–300 ppm) coloring metal ion is present in its reduced form (e.g. Au+). Gold reduction has been accomplished historically by using Sn as a reducing agent, following the reaction: 2+

Sn

+ 2 Au

+

4+

Sn

+ 2 Au

0

7

However, the electrons needed for gold reduction may be provided by other redox reactions and even from external irradiation. The ruby-red color of the gold nanoparticles is due to a resonant absorption of photons during the excitation of surface plasmons within the nanoparticles. It is a typical example of quantum (electron) confinement effects observed when crystallites are smaller than the wavefunction of an electronic state. This color is often referred to as striking because it suddenly appears upon heating.

100 Faded in dark overnight 80 Transmittance (%)

690

60 After 1 h in sunlight (25 °C) 40

20

0 300

400

500

600

700

800

900

Wavelength (nm)

Figure 14 Transmittance curves for the crown glass used for Photogray Extra® photochromic lens in its lightened (faded) and darkened states. Source: After [23].

7.3 Photochromic Glasses Photochromic glasses darken or change color when exposed to light or UV radiation, giving rise to a wide range of applications such as ophthalmic lenses, architectural or automotive glazing, information storage, and display devices [23]. A phenomenon that has found important practical applications in optics relies on the presence of silver halide particles of a few nm precipitated in the glass through an appropriate heat treatment. When the glass is exposed to near-UV visible light, a dark coloration rapidly appears but the glass lightens more slowly when returned to the dark. It is interesting that generally the glasses do not darken completely inside a car, because the car windows block some of the UV radiation needed for the photochromic reaction. Temperature effects are intriguing: the higher the temperature, the less dark photochromic glasses will be, as, conversely, photochromic glasses will take longer to regain their transparency under low ambient temperature. Under exposure to light, Ag+ is reduced into Ag0, the halogen ions acting as the reducing agent providing electrons for silver particle formation. This results in light absorption by the conduction electrons of metallic Ag over the entire visible range, giving a neutral coloration (Figure 14). Some sensitizers such as Cu+ may be added to speed up the process, which act as an electron donor for Ag+. The limited diffusion of halogens in the glass at room temperature is at the origin of the reversibility of the process, needed by most uses of photochromic glasses. Halogens serve as sinks for electrons as Ag oxidation proceeds during the fading stage.

8

Perspectives

Light absorption by colored glasses remains an area that has great potential for development in many fields. Conversely, there is a continuous interest in ultrawhite glass for solar energy and data transmission applications, with the necessity to model the parasitic absorption caused by absorbing centers. The ability to modify the speciation of transition metal ions by modifying glass composition or melting conditions is an important advantage of glasses over crystalline matrices. The chemical dependence of the structure of oxide glasses, wherein transition metal ions occupy a large diversity of sites, opens the way for selecting specific environments that will impart original coloration. The chemical dependence of the geometry and relative proportion of the sites occupied by transition metal ions may sometimes be combined with an adjustment of the oxidation states as a function of synthesis conditions. This unique feature will continue to open the way to novel colors in glass materials. Finally, regarding historical and cultural aspects (Ch. 10.6, 10.8), spectroscopic analyses may be used to improve our knowledge of ancient glassmaking technologies. Non-invasive portable spectrometers give information on the speciation of transition elements. The investigation of stained glasses from the 12th–13th centuries, which are blue colored by tetrahedral Co2+, shows that more reducing conditions were achieved in medieval than in modern furnaces, enhancing the blue color by favoring Fe as Fe2+ and Cu and Mn as non-coloring

References

Cu+ or weakly coloring Mn2+, respectively [23]. The colorimetric analysis of stained glasses confirms the skills of medieval glassmakers to master redox kinetics and develop innovative glass colors.

13 Villain, O., Calas, G., Galoisy, L. et al. (2007). XANES

14

References 15 1 Weyl, W.A. (1967). Colored Glasses. Sheffield: Society of

Glass Technology. 2 Calas, G., Cormier, L., Galoisy, L., and Jollivet, P. (2002).

3

4

5 6

7

8

9

10

11

12

Structure-property relationships in multicomponent oxide glasses. C. R. Chim. 5: 831–843. Calas, G., Galoisy, L., Cormier, L., and Lefrère, Y. (2006). La couleur des verres: le rôle des éléments de transition. Verre 12: 5–11. Burns, R.G. (1993). Mineralogical Applications of Crystal Field Theory. Cambridge: Cambridge University Press. Galoisy, L. (2006). Structure–property relationships in industrial and natural glasses. Elements 2: 293–297. Galoisy, L., Calas, G., Cormier, L. et al. (2005). Overview of the environment of Ni in oxide glasses and relation with the glass coloration. Phys. Chem. Glasses 46: 394–399. Jackson, W.E., Farges, F., Yeager, M. et al. (2005). Multispectroscopic study of Fe(II) in silicate glasses: implications for the coordination environment of Fe(II) in silicate melts. Geochim. Cosmochim. Acta 69: 4315–4332. Bingham, P.A., Hannant, O.M., Reeves-McLaren, N. et al. (2014). Selective behaviour of dilute Fe3+ ions in silicate glasses: an Fe K-edge EXAFS and XANES study. J. Non Cryst. Solids 387: 47–56. Villain, O., Galoisy, L., and Calas, G. (2010). Spectroscopic and structural properties of Cr3+ in silicate glasses. J. Non Cryst. Solids 356: 2228–2234. Hunault, M., Calas, G., Galoisy, L. et al. (2014). Local ordering around tetrahedral Co2+ in silicate glasses. J. Am. Ceram. Soc. 97: 60–62. Calas, G., Majérus, O., Galoisy, L., and Cormier, L. (2006). Crystal field spectroscopy of Cr3+ in glasses: compositional dependence and thermal site expansion. Chem. Geol. 229: 218–226. Chopinet, M.H., Lizarazu, D., and Rocanière, C. (2002). L’importance des phénomènes d’oxydo-réduction dans le verre. C. R. Chim. 5: 939–949.

16

17

18

19

20

21

22

23

determination of chromium oxidation states in glasses: comparison with optical absorption spectroscopy. J. Amer. Ceram. Soc. 90: 3578–3581. Lin, T. and Angell, C.A. (1984). Electronic spectra and coordination of Ni2+ in potassium borate glass and melt to 1000 C. J. Am. Ceram. Soc. 67: C33–C34. Möncke, D., Ehrt, D., Eckert, H., and Mertens, V. (2003). Influence of melting and annealing conditions on the structure of borosilicate glasses. Phys. Chem. Glasses 44: 113–116. Glebov, L.B. and Boulos, E.N. (1998). Absorption of iron and water in the Na2O-CaO-MgO-SiO2 glasses. II. Selection of intrinsic, ferric, and ferrous spectra in the visible and UV regions. J. Non Cryst. Solids 42: 49–62. Efimov, A.M., Ignatiev, A.I., Nikonorova, N.V., and Postnikov, E.S. (2013). Quantitative UV–VIS spectroscopic studies of photo-thermo-refractive glasses. II. Manifestations of Ce3+ and Ce(IV) valence states in the UV absorption spectrum of cerium-doped photothermo-refractive matrix glasses. J. Non Cryst. Solids 361: 26–37. Nolet, D.A. (1980). Optical absorption and Mössbauer spectra of Fe, Ti silicate glasses. J. Non Cryst. Solids 37: 99–110. Koepke, C., Wisniewski, K., and Grinberg, M. (2002). Excited state spectroscopy of chromium ions in various valence states in glasses. J. Alloys Compd. 341: 19–27. Bingham, P.A., Parker, J.M., Searle, T. et al. (1999). Redox and clustering of iron in silicate glasses. J. Non Cryst. Solids 253: 203–209. Ravel, B., Carr, G.L., Hauzenberger, C.A., and Klysubun, W. (2015). X-ray and optical spectroscopic study of the coloration of red glass used in 19th century decorative mosaics at the Temple of the emerald Buddha. J. Cult. Herit. 16: 315–321. G.L. Stephens and J.K. Davis, Duane’s ophthalmology, Ch. 51D Ophthalmic Lens Tints and Coatings, Lippincott Williams & Wilkins: Philadelphia (2006) http://www. oculist.net/downaton502/prof/ebook/duanes/pages/v1/ v1c051d.html (accessed 27 May 2020). Hunault, M., Bauchau, F., Loisel, C. et al. (2016). Spectroscopic investigation of the coloration and fabrication conditions of medieval blue glasses. J. Am. Ceram. Soc. 97: 60–62.

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693

6.3 Photoluminescence in Glasses Lothar Wondraczek Otto Schott Institute of Materials Research, University of Jena, Jena, Germany

1

Introduction

Photoluminescence is an inelastic scattering process whereby a material subjected to optical illumination reemits photons at the point of absorption [1]. The nature of the process has two important consequences: scattering means that the reemitted light diffuses into all directions, and inelastic means that the energy of the scattered photons changes. As a result, the observed wavelength also changes as does color if the process takes place in the visible range. The phenomenon is striking in the peculiar uranium glass, which was most popular between the second half of the nineteenth and the first half of the twentieth century and is today found in antique shops in forms ranging from beads, vases, and plates to tableware and lampshades. Here, the strong photoluminescence gives rise to a characteristic greenish or even yellow color due to uranyl ions, UO22+, in quantities of up to several thousands of ppm (Figure 1). Through exposure to sunlight (or, for better visibility, to an ultraviolet [UV] lamp), it can be readily distinguished from other glasses of similar color such as yellowish-brown uranate glasses (e.g. containing U2O72−), which are not luminescent. Also in practice, photoluminescence is routinely used to distinguish between the tin and airsides of float glass (Chapter 1.4) because impurity divalent tin ions, Sn2+, can be electronically excited by exposure to UV light: relaxation of this excited state back to the ground state occurs radiatively whereby a pale, bluish shine can be observed.

Reviewers: G. Gao, Institute of Microstructure Technology, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany M. Peng, Materials Science and Engineering, South China University of Technology, Guangzhou, China

Today, however, the most important applications of photoluminescent glasses deal with optoelectronics. The purpose of this chapter is thus to review the basic physics that is needed to understand how such applications are designed. The fundamentals of photoluminescence and inelastic light scattering will first be presented. How glass chemistry can be engineered to optimize the phenomenon will then be described. Finally, key parameters such as quantum efficiency or emission lifetimes will be discussed. In preamble, it may be useful to state how whether or not a certain glass exhibits visible or infrared photoluminescence can be determined from the electronic properties of its chemical components, in particular, of its minority species and dopants. Consider, for example, sodium oxide, Na2O, an archetypal constituent of silicate glasses (Figure 2a). With eleven electrons, the sodium atom has the configuration 1s2 2s2 2p6 3s1 = [Ne]3s1. That is, one electron on the 3s orbital is only loosely bound and can thus be readily excited, for example, to 3p or other higher-lying states. In sodium gas, relaxation from 3p occurs through emission of a “yellow” photon according to the energy gap between the 3p and 3s states. This process is the basis for sodium-vapor gas discharge lamps (Figure 2b). In glasses, however, sodium is clearly not incorporated in its atomic form, but in the oxidized Na+ state in which the 3s1 electron is missing. The energy provided by visible (or UV) light is not sufficient to excite one of the deeperlying 2s or 2p electrons so as to provide for photoluminescence. In contrast, X-rays can be employed for this purpose, which is why X-ray fluorescence is so commonly used for chemical analyses of glasses and other materials (Chapter 5.1). Obviously, weakly bound electrons are necessary, but not sufficient, to generate a visible photoluminescence in glass. These are available when the material contains Sn2+, UO22+ or a multitude of other optically

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

694

6.3 Photoluminescence in Glasses

2 Inelastic Light Scattering Through Photoluminescence

active ions within specific concentration limits. In their ionic form, some of the most prominent elements that may cause photoluminescence in glasses are summarized in Table 1. These are the transition metals, with their weakly bound outer d-electrons, and the rare earths. Among them the divalent manganese ion, Mn2+ ([Ar] 3d5), is the most commonly involved in the photoluminescence of natural minerals and has also made its way into some artistic or decorative glass products, although less prominently, generating an attractive deep reddish shine.

A beam of light with a wavelength appropriate for luminescence excitation can literally be seen, but at the specific color of luminescence, whereas this very same beam remains fully invisible in a neutral glass as long as there is no scattering toward the observer’s eye. In Figure 3, a green (right, bottom) and a red (right, top) laser beam are guided through two blocks of transparent material. One (right) is a glass doped with ~500 ppm of trivalent europium, Eu3+, and the other is a glass ceramic (Chapter 7.11) with a crystal size of ~30 nm and a crystal volume fraction of ~80%. In the glass specimen, the green laser excites Eu3+ species to emit red (fluorescent) light, visible to the observer. The red laser beam is not seen because it is scattered neither inelastically nor elastically. In the glass ceramic specimen, both beams are scattered elastically at the glass–crystal interfaces although the red one is scattered to a lower extent because of its higher wavelength relative to the crystallite size. Physically (Figure 4), photoluminescence in Eu3+containing glasses involves various sharp bands that result from the intra-configurational 4f 4f parityforbidden electronic transitions from the Eu3+ excited state of 5D0 to the states of 7FJ (J = 0, 1, 2, 3, 4) (Figure 4c). As discussed later, the local structural environment does not notably affect the energetic location of the transitions since the involved f-levels are well shielded from the surrounding anions. The probability of certain relaxation reactions is strongly affected by the ligand symmetry, however, which represents a useful

Figure 1 Photoluminescent glasses involving, from left to right, doping with Sm3+, Eu2+, Eu3+, Pr3+, Mn2+, and UO22+ in various host glasses. Photograph taken under broadband ultraviolet (UV-A) irradiation.

(a)

(b) eV

4f 4d

n=4

4p

n=3

3p

6 5

4

3d

4

3

4s

n=2 n=1

2p 2s

3

4 Energy

3s

ii

1846

3

2

819 818 1138 1140

3

i 3

iii

589 590

1s

1

iv 0

3

Figure 2 Electronic transitions in sodium. (a) Electronic configuration of atomic sodium, [Ne]3s1, providing for a characteristic yellow luminescence. (b) Photoluminescence whereby an incoming photon creates a state of excitation (i), which relaxes non-radiatively through a series of narrow jumps until the emission level is reached (ii). From the emission level, relaxation occurs predominantly radiatively, i.e. through emission of a photon (iii) to a deeper-lying basin within which further non-radiative transitions may occur (iv).

2 Inelastic Light Scattering Through Photoluminescence

Table 1 Electron configuration of some transition metal and rare earth elements. Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

3d2

3d3

3d5

3d5

3d6

3d7

3d8

3d10

3d10

4s2

4s2

4s1

4s2

4s2

4s2

4s2

4s1

4s2

Ce

Pr

Nd

Sm

Eu

Gd

Tb

Dy

Ho

6s2

6s2

7

7

6s2 1

4f 5d

6s2 1

5s25p6

2

4f 5d

6s2 1

5s25p6

3

6s2 1

5

1

4f 5d

4f 5d

5s25p6

5s25p6

4f

5s25p6

6s2 1

8

6s2 1

4f 5d

4f 5d

5s25p6

5s25p6

Figure 3 Elastic and inelastic scattering of red (top) and green (bottom) laser light through a block of Eu3+-containing glass (right) and a transparent glass ceramics (left). A red photoluminescence is excited with green light only in the glass. Photograph taken under broadband ultraviolet (UV-A) irradiation. Individual bright spots caused by residual microbubbles in the glass specimen (See electronic version for color figures).

structural probe. Technical applications rely on the broad absorption band of Eu3+ in the 350–420 nm spectral region (Figure 4a), which makes Eu3+ (and its divalent counterpart) one of the most prominent optical activators in solid-state phosphors [2]. In this context, glasses as host materials offer potential advantages such as very high compositional flexibility, simple and low-cost manufacture, versatile forming technologies, superior thermal stability, and epoxy-free assembly processes. But these advantages usually go at the expense of the absorption cross section and quantum efficiency of luminescence, which results in potentially low quantum yield. Oxide glasses are, therefore, currently not used as phosphor materials. There is a variety of photoluminescence schemes (Figure 5; see also [3]). Often depending on the desired material properties, glasses can be – at least in theory – tailored through different combinations of matrix glass

9

Er

6s2 10

Tm

6s2 1

11

Yb

6s2 1

12

6s2

1

1

4f 5d

4f 5d

4f 5d

4f 5d

5s25p6

5s25p6

5s25p6

5s25p6

4f14 5s25p6

composition to which one, two, or more optically active species are added. In each case an incoming photon generates an excited electronic state before the ground state is recovered along a certain relaxation path that involves radiative and non-radiative transitions. The latter for example occur through energy transfer to the surrounding lattice by the creation of phonons, or through excitation of electrons of other optically active species. In the simplest case (Figure 5a), after excitation, part of the absorbed energy decays non-radiatively, and the remaining part causes the emission of a new photon. The energy of this new photon is always lower than that of the incoming photon, i.e. its wavelength is longer. As an important extension of such a three-level system, the four-level system (Figure 5b) involves two nonradiative steps in between which the radiative transition is embedded. As discussed later, this case is especially relevant to laser-active materials because it allows for the so-called inversion of band occupation [4]. In some cases, a single photon of high energy may trigger the emission of two (or even more) secondary photons through a radiative cascade process (Figure 5c). This process presents an intriguing feature as it offers the possibility to enhance the quantum efficiency of the luminescence process to beyond 100 %. Vice versa, the excitation scheme can also be tailored, so two photons contribute to the excitation (Figure 5d). Materials offering such properties have been receiving much attention because they enable photons to be converted from lower (e.g. infrared) to higher energy through an upconversion process. Like two-photon process, however, upconversion suffers from a notoriously low efficiency. In many cases, the absorbing and emitting ions are not the same [5]. For example, a sensitizing species can be used to ensure adequate absorption in a certain range of wavelengths (Figure 6). The absorbed energy is then transferred to a secondary dopant species, which provides the desired emission properties (Figure 5e). In a practical application, clearly the sensitizer and emitter must be

695

6.3 Photoluminescence in Glasses

Figure 4 Spectral characteristics of photoluminescence from Eu3+-doped glasses. (a) Typical excitation spectrum, with an emission band at 612 nm (cf. text). (b) Corresponding emission spectrum for excitation at 394 nm, including emission from higher-lying states (inset). Underlying energy level diagram given in (c).

(a) λem = 612 nm

(c) 30 5G

5D

6

5D

5D 3

375

400

425

(b) λ = 394 nm ex

450 7F 2

5D 0

× 200

7F

450

20

10

540

0

600 800 1000

6

2000

4

7F

2

Eu3+

3

0

500

7F

0 7F

1

5D

7F

7F 4 1

5D

400

15

5 7F

520

5L 6 5D 3 5D 2

25

2

4

350 4

PL

5D 4

PLE

5L

Wavelength (nm)

0

Energy (x103 cm–1)

Intensity (a.u.)

7F

Intensity (a.u.)

696

7F

0

560

500 550 600 Wavelength (nm)

650

700

(a)

(b)

(c)

(d)

(e)

(f)

Figure 5 Different schemes of photoluminescence: (a) downconversion in a three-level system, (b) four-level system, (c) cascade emission, (d) upconversion, (e) energy transfer, and (f ) quantum cutting.

3 Photoluminescence and Glass Chemistry

Excitation source Excitation bands of activator species

Emission line

Intensity (a.u.)

Excitation bands of sensitizer species

Emission bands of sensitizer species

Figure 6 Sensitization through co-doping: an efficient absorption in a certain spectral range is achieved through a suitable codopant species. From this species, the absorbed energy is transferred to the primary emitting species, thus increasing the range of spectral sensitivity of the latter.

Wavelength (nm)

chosen carefully on the basis of their electronic structures to ensure efficient energy transfer. If the excitation energy is high enough to be transferred to two or even more secondary emission centers, as done in cascade emission, an efficiency higher than unity can be obtained through the so-called quantum cutting (Figure 5f ).

3 Photoluminescence and Glass Chemistry The chemical design of photoluminescent glasses typically addresses two aspects: the choice of a proper ensemble of optical activators and the search for a suitable matrix material. The activator may be a single dopant at a given concentration or a combination of multiple dopants with different functions (sensitizer, amplifier, emission center, etc.; e.g. Figure 6). Here, the immediate parameters of interest are the spectroscopic properties, that is, the excitation and emission schemes, excited state lifetime, and quantum efficiency. Secondary parameters may, for instance, include the temperature dependence of photoemission, saturation effects and the power dependence of the emission intensity, or cross-reactions such as excited state or anti-Stokes emission. All these properties depend on the matrix chemistry whose choice thus is also an important feature. Especially important in this respect is the ability of the glass matrix to dissolve the activator species at sufficiently high concentrations without triggering phase separation, clustering, or crystal nucleation. In addition, specific redox conditions are needed to stabilize the desired oxidation state (Chapter 5.6) and to secure the absence or specific presence of photooxidation or photoreduction reactions, whereas the matrix composition should ensure appropriate ligand configurations (ligand chemistry, crystal field

strength, coordination, and symmetry) and phonon energy (i.e. the possible avoidance of non-radiative relaxation that would counteract photoluminescence). Typically, glass matrices with low phonon energy are sought, e.g. tellurites, fluorides, or fluorophosphates (cf. Chapter 6.5), in which non-radiative relaxation involves the concerted action of multiple phonons and, thus, becomes less and less probable. One should not disregard seemingly secondary glass properties, however, because in practice they may play a still more important role. For example, the possibility of fiber drawing largely relies on viscosity and liquidus temperature or on the absence of crystallization upon heating above the glass transition temperature (Chapter 6.5). The thermal expansion of the glass may become problematic in high power applications if it causes the formation of mechanical stress (Chapter 3.12). As for the refractive index, Abbe number, and thermal dispersion (Chapter 6.1), they determine the numerical aperture and thermal lensing effects during laser operation or the efficiency of light extraction. Finally, nonlinear optical effects determine the damage threshold for potential laser glasses. Because these features are discussed in other chapters, however, here the focus will be placed on the activator species and the resulting mechanism of photoluminescence. Some typical elements that may play a role as activators or sensitizers in photoluminescent glasses have already been listed in Table 1. Like the sodium counterexample in the glass matrix (Figure 2), they are usually present in oxidized forms, i.e. with one or more of the outer electrons missing. The remaining electronic configuration determines the actual optoelectronic properties as already discussed for the archetypal case of Eu3+ (Figure 4). The origin of photoluminescence from the latter is an f–f transition. As seen from Table 1, such a transition is shielded from the environment by the outer 6s orbital. A typical consequence is the very low dependence

697

698

6.3 Photoluminescence in Glasses

of spectral band position on ligand situation, that is, matrix chemistry and activator coordination. The photoluminescence emission bands are, therefore, characteristically narrow as exemplified by Eu3+-, Tb3+-, or Er3+doped glasses. This feature is common among many of the rare earth activators in which f–f luminescence bands are observed. The excited state positions of the most relevant trivalent rare earth species are summarized in Figure 7. These cover the elements from cerium to ytterbium (with the exception of the unstable radioactive promethium, Pm3+). In addition to the trivalent states, other oxidation states are also of importance in glassy materials for some rare earth elements, e.g. Eu2+, Yb2+, and Sm2+. In tetravalent Ce4+, all outer electrons are missing, so, as for Na+, neither color nor photoluminescence is typically observed. Although the latter species are not considered in this chapter, we note that not only f–f but also other types of transitions may occur, in particular, f–d, in such redox states. Whereas the resonance energy of an f–f transition is typically independent on crystal field strength, the transition probability between some of the degenerate states depends on ligand symmetry through its effects on orbital distortion. As a result, the intensity ratio among certain emission peaks is a function of local symmetry. Hence, rare earth elements can be used as highly sensitive and extremely local structural probes, even in cases where other techniques such as X-ray diffraction fail to provide useful information. In addition to the f–f transitions, f–d or d–d transitions can be exploited in rare earth ions with lower valences or in transition metal ions. Here, splitting of the d-levels is strongly affected by the type and number of ligand species and, thus, matrix composition. In the

example of trivalent chromium in a phosphate glass matrix (Figure 8, [6]), Cr3+ has the electronic structure of [Ar]3d3, that is, three electrons on the outer d-level. If Cr3+ is integrated into a solid matrix, interaction with the surrounding ligands leads to crystal field splitting. The degree of splitting depends on the strength of the crystal field, i.e. on the coordination number, symmetry, and type of anions. At a given field strength (Figure 8), a certain order and energetic position of all possible states is achieved. In the present case, the corresponding optical absorption spectrum is dominated by two broad absorption bands that are associated with the characteristic 4A2 4 T1 and 4A2 4T2 transitions. A zoom on the red region reveals a further, weaker band corresponding to 4 A2 2T1 and 4A2 2E transitions. Photoemission occurs in the near-infrared (NIR) spectral region. The Tanabe–Sugano diagram is usually applied for a quantification of the effects of field strength on the electronic structure of d-elements [7]. It uses the Racah parameter B and a crystal field parameter, denoted Dq, to scale band energy and field strength. For Cr3+ (and also many other d-ions), an interesting question is that of the dependence of the lowest excited state (from which luminescence is expected) upon crystal field strength: here, one finds that an intermediate octahedral field of approximately 2.1 < Dq/B < 2.3 typically separates the low and high field regions. Between those two regions, the emitting state is either 4T2 or 2E, whereby only the 4T2 state is very sensitive to Dq/B (Figure 8). When the Cr3+ ion locates in a weaker ligand field environment, the 4T2 level is lower than the 2E level, which then results in a broadband emission arising from the spin-allowed 4T2 4A2 transition. In contrast, when the Cr3+ ion locates in a

D P

5d

2.5

G

2.0

G H

540 nm

D

/ G 600 nm

310 nm

D

F

530 nm D

F

G 1330 nm

1.0

F F

0.5

F H

F

H F

Ce3+

H

Pr3+

1060 nm

I

F F F

F / H

F

F F F F F

F

F

F F

I

H

F

Nd3+

Sm3+

I

H S

F

F

I I

F H

F F H H H H

I

F / S

610 nm

F S

1.5

0.0

G

G G

F

F F

F

Eu3+

F F

S

Gd3+

S

Tb3+

H

/ F

H

/ F

H

I

F H

I

1460 nm

I

F

H

1200 nm F F

F

I

I

F

1050 nm

F

1550 nm

H 1310 nm H

Dy3+

I

I

H

Ho3+

Er3+

Tm3+

Yb3+

Figure 7 Excited state configuration of various trivalent rare earth ions. The arrows indicate some emission reactions that have received attention for NIR lasing activity or other purposes (labels indicate emission wavelength). Pm3+, positioned between trivalent Nd and Sm, not shown.

3 Photoluminescence and Glass Chemistry

300

E (eV) Wavelength (nm)

4T

1

3 Cr3+ [Ar]3d3

4T 2

2 2G

400 500 600 700 800

4P

900

1

4F

4A 2

Free ion

Ligand field splitting

Excitation

Absorpion and emission

Figure 8 Photoluminescence from Cr3+ in a phosphate glass matrix (simplified). Depending on ligand field strength, 4T1 and 4T2 are split to different extent, which results in the characteristic variations in Cr3+-related glass color. Photoluminescent reemission occurs from the lowest excited state.

strong crystal field, the 2E level falls below the 4T2 level, and, thus, the spectrum exhibits the sharp R-line originating in the spin-forbidden 2E 4A2 transition (such as in the very prominent example of crystalline ruby lasers in which Cr3+ precipitates in the strong ligand field of Al2O3). Similar effects can be exploited in many of the d-element activator species for which the emission characteristics of a given redox state vary widely with the field strength. Beyond very popular rare earth and transition metal ions, certain activator species have been reaching a level of significant research activity for application in glasses. Here, the most prominent recent example is bismuth in its various oxidation states (Figure 9). A major interest in this species was initiated by the discovery of broadband

photoluminescence in the NIR spectral region of Bidoped silica glass [8]. Involving a broad variety of host glasses, subsequent studies have shown that this emission band covers the major part of the telecom spectral range, i.e. the range of wavelengths within which optical data are transmitted. For such data transmission, optical amplifiers are required to enable photoemission to be stimulated optically in the relevant spectral range. Today’s benchmark material is the Er3+-doped fiber amplifier (EDFA), which relies on the luminescence properties of trivalent erbium (Figure 7). It provides a unique set of properties, so it has an unchallenged efficiency in optical amplification around the 1.5 μm spectral range [9]. This is also the range where vitreous silica fiber exhibits the lowest optical loss (Chapter 6.4), thus making it a perfect

Energy (103 cm–1) 1P 1

35

2S

1/2

30

1S

0

25 3P 1

20 Bi5+

15

2P

3/2(2)

2P

3/2(1)

1D

2

Bio 3P

2

10

3P

1

5 0 Bi3+

1S 0

2P

Bi2+

3P

1/2

0

Bi+

Figure 9 Simplified representation of the electronic states in some optically active ion species of bismuth.

699

700

6.3 Photoluminescence in Glasses

match for long-range optical communication. But a problematic feature has been the limited spectral bandwidth yielded by the fundamental nature of the underlying f–f transitions in Er3+. Here, the discovery of ultrabroad NIR emission from Bi-doped glasses has been considered as offering a promising alternative although technical demonstrations have not yet been successful. Interestingly, the fundamental origin of NIR photoemission from Bi-doped glasses remains highly debated [8]. Taking a broader look at bismuth in glasses, one notices that the multiplicity of redox states in which the bismuth ion (or ion cluster) may be present allows for a broad variety of materials with fundamentally different optical activities. In Figure 9, only the archetypal cases of Bi3+, Bi2+, and Bi+ are shown. With decreasing number of electrons, the electronic band gap of these species increases, so photoluminescence occurs at increasingly high energy (low wavelength). In all three redox states, however, the transition energies depend very strongly on crystal field, so the emission properties are also highly matrix dependent. The most common form of bismuth in glasses is Bi3+, which usually exhibits blue or green photoluminescence. Divalent Bi2+, on the other hand, shows red photoemission. This contrast provides another glimpse at the rich nature of the general subject and at the enormous possibilities existing to generate a specific photoluminescence in an appropriate glass matrix.

4 Efficiency, Lifetime, and Quenching Effects The quantum efficiency is a key parameter in many applications of photoluminescence. It is in addition fundamental to understand physically the underlying relaxation process that finally leads to photon emission. It describes the ratio between the numbers of emitted and absorbed photons, that is, the probability that absorption of one single photon actually causes the photoluminescent emission of a secondary photon. That this probability is by definition lower than unity signifies that the relaxation scheme of Figure 2b represents only an ideal case: coexisting with photon emission (radiative decay), other relaxation pathways may be followed, in particular phonon excitation or energy transfer. An accurate determination of quantum efficiency is not obvious. If conducted directly, it comprises determination of the absolute photon flux upon excitation and emission. Integration spheres and careful referencing are required for this purpose. The experimental approach then distinguishes between internal and external quantum efficiency, whereby the latter acknowledges the

existence of secondary effects such as the efficiency of light extraction or the occurrence of reabsorption, which also leads to a reduction in the experimentally visible intensity of photoluminescence. Efforts on materials development, therefore, often aim at increasing the external quantum efficiency. In the specific case of glasses, however, the sole notion of quantum efficiency is often misleading in terms of practical applications because it does not provide a measure of the generated emission gain. In other words, high quantum efficiency does not guarantee high emission intensity. Regarding this parameter, the absorption cross section must also be considered so that the figure of merit is a convolution of quantum efficiency and absorption probability. Typically, this is where glasses suffer from a major drawback, i.e. they often have comparably low absorption cross section. In addition, common strategies for overcoming this problem such as increasing light–matter interaction pathlengths through multiple scattering cannot be employed because of the lack of a microstructure. On the other hand, one can increase the emission intensity either by increasing the amount of dopant or by directly enhancing the optical pathlength within the material. For both routes, glasses are particularly suitable: they can be chemically tailored to maximize the solubility of the optical activator and/or secondary dopant species, and they can be formed practically universally into any shape. In particular, in the form of optical fiber, they guarantee a maximum optical pathlength, which then often enables efficient photoluminescence even at low absorption cross sections. Regarding the increase in dopant concentration, however, solubility is not the only requirement. The maximum dopant concentration is usually limited by the occurrence of energy transfer reactions, often denoted concentration quenching. Such reactions may occur over short or long spatial ranges (e.g. Foerster transfer, Dexter transfer) and always reduce quantum efficiency. The maximum dopant concentration at which the drop in quantum efficiency is observed is termed the critical concentration, xc. Some simplistic formulas have been constructed to aid in the approximate quantification of energy transfer probabilities. For example, the critical distance Rc, representing the mean spatial separation between two emission centers at xc, is often estimated from Rc =

3

6V , πxc N

1

where N is the number of emission sites per unit volume V (usually taking the volume and number of sites of a unit cell for crystalline materials and the molar volume and

5 Applications

molar concentration for glasses). For electric dipole– dipole interactions, Rc is sometimes also estimated directly from the excitation and emission spectra: R6c =

3 × 1012 × f E4

f E F E dE,

2

where f is the oscillator strength and E the energy of maximum spectral overlap and where the integral represents the overlap of the normalized emission and excitation spectra. In a more detailed consideration of glass structure, however, the value of Rc has only little meaning because spatial relations among the atomic constituents of the glass network are determined by bond lengths, coordination numbers, and bond angles. Especially over short ranges, they cannot be approximated through simple mean-field statistics. Instead, one may calculate the probability of cluster formation across first, second, or third coordination shells, which is approximately derived from the molar concentration of the specific ion, its coordination number, and the coordination numbers of all other anionic and cationic constituents of the system. In many cases, an analysis of the lifetime of photoluminescence is a more suitable way to judge the probability of radiative relaxation. In a first approximation, a simple exponential relaxation function is often used to describe the rate at which the emission level is depopulated: I t = A exp

−t , τ

3

where τ is the decay time and A is a fit constant. This law assumes that the transition probability is independent of the population of the excited state. In certain cases, which are not considered here, stretched or compressed exponentials are observed instead. The value of τ represents the time after which the initial emission intensity has decreased to a fraction of 1/e. Non-radiative relaxation occurs very rapidly through phonon activation, in particular in narrow energy quanta, so the experimentally observed lifetime of photoluminescence is decreasing with increasing non-radiative contributions. In such a case, one can decrease the probability of non-radiative relaxation by either decreasing the temperature or by increasing the number of phonons that need to be activated collectively in order to bridge the respective energy gap between the excited and ground states. This is why glasses with low phonon energy are typically sought as host species. In the theoretical case of absolute zero temperature, no phonon relaxation would occur, which would ensure a maximum lifetime in the absence of phonons. Therefore, observing the emission lifetime as a function of dopant concentration (or other chemical variations on the system) always provides some relative

information on quantum efficiency. One then uses a temperature-dependent lifetime analysis to extrapolate this information so as to obtain also absolute data, for instance, by referencing the observed lifetime to its extrapolated value at absolute zero temperature. One can also treat electronic energy transfer processes in this way, for example, by approximating the energy transfer efficiency ηET with ηET =

1 − τs , τs0

4

where τs0 and τs represent the values of emission lifetime from an activator species in the absence and in the presence of a secondary energy acceptor species, respectively. The energy transfer rate κET between the two entities can also be estimated: 1 1 = + κ ET τs τs0

5

Such considerations often provide practical tools for exploiting or avoiding energy transfer processes by chemical tailoring.

5

Applications

Because of their emission gain and other spectroscopic properties, photoluminescent glasses do not play an important role in prominent applications such as phosphors in solid-state lighting or display. But they did find niches as irreplaceable components in various specialty sectors among which optically active fiber devices and glass lasers are the most important [10, 11]. And, from a chemical standpoint, another important application of glass photoluminescence concerns probing of shortrange structural features through the aforementioned dependence of spectroscopic properties on the ligand field in the vicinity of the active species. In particular for the d–d or f–d transitions, knowledge of the variation of band structure as a function of field strength (such as given in Tanabe–Sugano diagrams) enables the crystal field strength to be directly evaluated from the peak positions of the observed emission bands. For example, this allows the local energy density to be probed or bond distance and coordination number to be determined by comparisons with reference materials (Figure 8). In a less direct way, analysis of f–f transitions provides information of ligand symmetry. As a final perspective, the study of energy transfer may help to shed light also on longerranging structural features, including clustering and nonrandom ion precipitation.

701

702

6.3 Photoluminescence in Glasses

Table 2 Prominent examples of laser-active glasses. Lasing species

Er

3+

Laser line (μm)

Glass matrix

6

1.5

Fluorophosphates

3+

1.9

Silicate

Nd3+

0.9

(Na, Ca) aluminosilicate

1.1

(K, Ba) silicate

1.4

(La, Ba, Th) borate

0.54

Borate

1.9

(Mg, Ca, Li) aluminosilicate

1.0

(Mg, Ca, Li) aluminosilicate

Ho

Tb

3+

Tm3+ Yb

3+

Table 3 Sensitizer–activator combinations in some laser glasses. Molar ratio of activators

Lasing species

Sensitizer species

Glass matrix

Er3+

Yb3+

Fluorophosphate 1 : 8

1.5

Yb3+

Silicate

1.9

Mn2+

Phosphate

3+

Ho

Nd3+

1:1

Emission peak (μm)

1:1

1.1

Tm

Yb3+, Er3+ Silicate

1:1

2.0

Yb3+

Nd3+

1:1

1.0

3+

Borate

Perspectives

Photoluminescence is a peculiar phenomenon that unfolds particular beauty in glasses. Shining from within, this very attractive visual effect results from the combination of inelastic scattering and optical transparency and may be put to use in many ways in art and design, consumer glass products, fluorescent glazes and enamels, or fiber-illumination sources, which are beyond the scope of this chapter. But glasses are not always ideal materials for more technical applications, in particular, when one needs high emission gain, high absorption cross section, elastic scattering and light diffusion, or color quality and stability. In some niches such as optical fibers, however, luminescent glasses have become indispensable materials. Here, exploitation of the emission and excitation properties of transition metal dopants and other optically active species beyond the rare earths remains a field of challenge. In other, more exploratory areas, interesting devices, and design studies continue to evolve, including luminescent concentrators, light-emitting fibers, or three-dimensional displays.

References 1 Blasse, G. and Grabmaier, B.C. (1994). Luminescent

Materials. Berlin: Springer-Verlag.

The technical applications of active optical fiber and bulk laser glasses are dominated by rare earth-doped materials. Some prominent examples are given in Table 2. The popular Nd3+-doped glass lasers involve commercial products such as codes LG 660, LG 670, LG 680 (all Schott, Germany), LSG 91H (Hoya, Japan), or Q246 (Kigre, USA). Common to all laser glasses, they exhibit emission lifetimes above 500 μs (ideally at room temperature, occasionally at cryogenic temperature), sometimes reaching up to several ms such as in Er3+based systems. Typical combinations of sensitizer and activator are listed in Table 3. With the exception of Mn2+ in Nd3+ phosphate laser glasses, here as well, rare earth sensitizers are dominating. Beyond bulk laser glasses, vitreous silica remains the most important material for optical fiber thanks to its well-established high-purity processing schemes and the underlying materials logistics (Chapter 6.4). Consequently, optically active fiber relies on rare earth-doped silica. The dopants includes Er3+ for telecom fiber amplifiers [12], Yb3+ for high power lasers [13], and further species analogous to those shown in Table 2 for the farther infrared [14].

2 Justel, T., Nikol, H., and Ronda, C. (1998). New

3

4

5 6

7

8

developments in the field of luminescent materials for lighting and displays. Angew. Chem. Int. Ed. 37: 3084–3103. Wondraczek, L., Tyystjärvi, E., Méndez-Ramos, J. et al. (2015). Shifting the Sun: solar spectral conversion and extrinsic sensitization in natural and artificial photosynthesis. Adv. Sci. 2: 1500218. Campbell, J.H. and Suratwala, T.I. (2000). Nd-doped phosphate glasses for high-energy/high-peak-power lasers. J. Non Cryst. Solids 263: 318–341. Dexter, D.L. (1953). A theory of sensitized luminescence in solids. J. Chem. Phys. 21: 836–850. Wang, W.C., Le, Q.H., Zhang, Q.Y., and Wondraczek, L. (2017). Fluoride-sulfophosphate glasses as hosts for broadband optical amplification through transition metal activators. J. Mater. Chem. C 5: 7969–7976. Sugano, S., Tanabe, Y., and Kamimura, H. (1970). Multiplets of Transition-Metal Ions in Crystals. New York: Academic Press. Peng, M., Dong, G., Wondraczek, L. et al. (2011). Discussion on the origin of NIR emission from Bi-doped materials. J. Non Cryst. Solids 357: 2241–2245.

References

9 Mears, R.J., Reekie, L., Jauchy, I.M., and Payne, D.N.

(1987). Low-noise erbium-doped fibre amplifier operating at 1.54 μm. Electron. Lett. 23: 1026–1028. 10 Ready, J.F., Farson, D.F., and Feeley, T. (eds.) (2001). LIA Handbook of Laser Materials Processing. Berlin: Springer-Verlag. 11 Weber, M.J. (1990). Science and technology of laser glass. J. Non Cryst. Solids 123: 208–222.

12 Miniscalco, W.J. (1991). Erbium-doped glasses for fiber

amplifiers at 1500 nm. J. Lightwave Technol. 9: 234–250. 13 Paschotta, R., Nilsson, J., Tropper, A.C., and Hanna, D.C.

(1997). Ytterbium-doped fiber amplifiers. IEEE J. Quantum Electron. 7: 1049–1056. 14 Allain, J.Y., Monerie, M., and Poignant, H. (1989). Tunable cw lasing around 0.82, 1.48, 1.88, and 2.35 μm in thulium-doped fluorozirconate fiber. Electron. Lett. 25: 1660–1662.

703

705

6.4 Optical Fibers John Ballato Department of Materials Science and Engineering and the Center for Optical Materials Science and Engineering Technologies (COMSET), Clemson University, Clemson, SC, USA

1

Introduction

Whether in physical or biblical contexts, light has been illuminating the universe since its beginnings. As reviewed in Chapter 10.10, the first substantive scholarly efforts at describing light can be attributed to Euclid of Alexandria (Optica; ca 300 BC), Claudius Ptolemy (Optica, ca 150 AD), and later to such luminaries as Abū ‘Alī al-Hasan ibn al-Haytham (Book of Optics written in the 1010s), René Descartes (Dioptrique in 1637), Robert Hooke (Micrographia in 1665), Isaac Newton (Opticks in 1704), and James Clerk Maxwell (A Treatise on Electricity and Magnetism in 1873). Indeed the millennial anniversary of Ibn al-Haytham’s opus was one of several reasons for 2015 being celebrated globally as UNESCO’s International Year of Light. As relates to optical fiber, the operative principle governing light confinement and propagation is that of total internal reflection taken in a ray-optic construction. Total internal reflection was first described by Johannes Kepler in 1611, mathematically described by Willebrord Snellius (1580–1626), and eventually popularized in the mid-nineteenth century through the giant luminous fountains invented by Jean-Daniel Colladon [1] on the basis of total reflection of light at the air–water interface (Figure 1). Even though the same phenomena were observed at the same time in meter-long bent rods drawn from crown glass by Jacques Babinet [2], the potential of optical fiber would still not be more fully appreciated for nearly another century. Not until, Reviewers: M. Cavillon, Institut de Chimie Moléculaire et des Matériaux, Université Paris Sud, Orsay, France P. Dragic, Electrical and Computer Engineering, University of Illinois at Urbana Champaign, Urbana, IL, USA

that is, the advent of the laser as a coherent and collimated light source and the description of materials and loss mechanisms in waveguides at optical frequencies [3]. The latter work earned Charles Kao the Nobel Prize in Physics in 2009 for “groundbreaking achievements concerning the transmission of light in fibers for optical communication.” A global race ensued to develop optical fiber with sufficiently low loss such that (laser) light could efficiently propagate over long distances and enable high-speed and high-capacity communications. As detailed below, these goals required, at least as relates to the glasses, a wide variety of innovations that included optimized glass compositions, glass and fiber fabrication processes, and light-amplifying and optically nonlinear fibers, the specifics of which are all application specific. Though applications do abound, some of which are described below, the present and near future use of glass optical fibers remain dominated by telecommunications, at least on a volume basis. For this reason, this chapter will largely focus on the glasses and processes associated with communications. At the time of the printing of this Encyclopedia, the global production of optical fiber for communications exceeds 10 m per year for every person on Earth. The performance of an optical fiber most strongly depends on the optical properties of the constituent glasses and on the design of the fiber itself. These topics will be described first, without delving into other thermal, mechanical, or chemical properties of practical interest that are adequately dealt with in other chapters. The most common glass families employed in making practical optical properties are then discussed before the main fabrication processes used are reviewed. Finally, a variety of applications of optical fibers are briefly presented.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

706

6.4 Optical Fibers

Figure 1 Colladon’s experiment with flowing water as a waveguide [1].

2 Optical Properties and Fiber Designs 2.1 Optical Properties 2.1.1 Dispersion, Absorption and Scattering

The vast majority of optical fibers are passive in that they serve as hair-thin conduits that simply transmit light from one place to another. As with any property, the efficiency with which fibers perform this task depends upon both intrinsic and extrinsic factors. Given the maturity of optical fiber fabrication, extrinsic factors such as bubbles, striations, and inclusions will be neglected. Impurities, however, are critical impediments since they absorb light in a way that can have great impact on long-distance communication links. Given the spectral bands of significance for the primary optical-fiber applications, the most detrimental impurities tend to be hydroxyl groups, -OH, and transition metals, most notably iron (Fe2+) and copper (Cu2+).

Intrinsically, the canonical optical property of any material is the index of refraction (cf. Chapter 6.1). It is a relative measure of the speed of light in vacuum, c, to that in the material, v, such that n = c/v. Macroscopically, a general expression for the refractive index can be derived from the Newtonian dynamics of a mass/spring system under the influence of an applied field (i.e. the electric field of light). The electric field intensity of light varies as a sinusoid in time (and position), and so the dielectric displacement of the charged species within the glass follows this polarization. At optical frequencies, the relevant charged species that define the properties of optical fiber are the electrons (in the ultraviolet) and the ions/molecules (in the infrared). Further details on the macroscopic derivation of the refractive index can be found in any introductory optics or optical materials text [4]. Since the polarization of the electrons and/or ions is frequency dependent, so is the refractive index: this dependence of index upon frequency or wavelength (λ) is called the chromatic dispersion. Though not the focus of this Chapter, it is an important consideration in telecommunication optical fibers since data signals are composed of a small range of wavelengths. Since each wavelength experiences a slightly different refractive index, hence velocity, the signals spread over time (distance) and can ultimately overlap such that information is lost. For this reason, early systems were designed to work at the zero dispersion point, which for silica glass optical fibers is at a wavelength of about 1.3 μm [4, 5]. Microstructured and photonic crystal optical fibers possess dispersion properties that can be tailored via specific fiber design (Figure 2). This latter point is useful since the waveguiding properties, such as loss and dispersion, of an optical fiber depend both on the materials from which it is made as well the waveguide design itself. Within the spectral bands of conventional (bulk) optics, the refractive index of conventional glasses and optical fibers decreases with increasing wavelength (normal dispersion). As the interaction between the electric field of the light and the charged species is one of a damped resonance, there are frequencies or wavelengths where dielectric relaxation is approached. At this frequency, the dispersion becomes anomalous, and the glass becomes highly absorptive. The reason is that the refractive index is a complex function whose real part is what is typically thought of as the index of refraction and the imaginary part the absorption. Accordingly, since the refractive index changes with wavelength, so too does the absorption or, more importantly for optical fibers, the absorption per unit distance, called the attenuation (typically given in units of dB/km). As noted, absorption caused by electrons and ions/ molecules occurs in the ultraviolet and mid-infrared

2 Optical Properties and Fiber Designs

20

Dispersion flattened

NZ-DSF C+LBand

102

NZ-DSF S+C+LBand

0

–10

1600

AN

1400 Wavelength (μm)

1

L ZB

Dispersion shifted

10

O2

Attenuation (dB/km)

Dispersion compensating

–20 1200

S3 As 2

10

Si

Dispersion ps/(nm Km)

1300 nm optimized

–10

200

Dispersion ps/(km nm)

0.9 –102

100

–103 0.2

0

0.4 0.6 0.8 1

2

4

6 8 10

Wavelength (μm)

–100 d/Λ = 0.5 –200 0.50

1.00

Figure 3 “V-curves” of theoretical attenuation as a function of wavelength for selected optical fiber materials.

Λ = 1.0 μm 1.50

2.00

Wavelength (μm)

Figure 2 Dispersion curves for silica (top) and for selected MOF/ PCF fibers (bottom). Source: Reprinted with permission from [5].

ranges, respectively. In between, i.e. in the visible and near-infrared, glasses are intrinsically transparent and have potentially low attenuation. This feature is especially useful for long-haul, fiber-based telecommunication systems since the greater the distance light can travel through a fiber, the fewer amplifiers are needed to ensure that the optical signals arrive at their destination, the result being a simpler and less costly system. In addition to absorption, light can also be partially scattered by minute density fluctuations in the glass. Given that the size of the structural units causing the scattering is very small compared with the wavelength of light, the process at work is Rayleigh scattering with an intensity that depends on wavelength as λ−4. The process is generally considered a source of attenuation for transmission by a fiber over a given distance because the light can be redirected even though it is not absorbed owing to the elastic nature of the scattering. Accordingly, the intrinsic transparency of a glass optical fiber is defined by the absorption of electrons in the ultraviolet, Rayleigh scattering in the visible and near-infrared, and absorption by ions/molecules in the

mid-infrared, which differs for each glass composition. A plot of loss as a function of wavelength yields a “Vcurve,” so designated from the shape of the curve (Figure 3). Because of the maturity of the chemical vapor deposition process, the lowest loss optical fiber realized to date remains conventional telecommunication-grade silica. 2.1.2 Active Optical Properties

Though quite a few ions can generate light upon suitable excitation when doped into glass, the rare earths are the most commonly used because their 4f electrons yield efficient and narrow linewidth emissions thanks to their efficient shielding by outer lying 5d states. The amorphous structure of glass promotes inhomogeneous broadening of the rare earth dopant absorption and emission lines, however, which was originally thought to preclude the possibility of laser action. But the concern proved to be wrong as it was not long after that the first experimental realization of lasing by T.H. Maiman in 1960 with ruby (Cr3+ : Al2O3) and the first glass-based laser were reported [6]. This first glass laser employed neodymium (Nd3+) as the active dopant in a barium crown glass (N.B. a dopant is a small but important value-added constituent to the composition, whereas the presence of an impurity generally is unintended and unwanted). Since then, virtually all of the rare earth ions have been made to lase [7].

707

708

6.4 Optical Fibers

The glass host plays a critical role in determining which transition, hence wavelength, is involved and how efficient the laser action is. To first order, selection of the active dopant is based on the separation of its energy levels and on whether this difference is equivalent to the energy of the desired emission. Electrons from the ion’s ground state are excited into the necessary state via optical pumping of light. The energy of this optical pump is resonant either with the excited state from which the emission occurs or with an excited state of energy higher than it, followed by relaxation into the desired excited state. Admixing of opposite parity states breaks the symmetry restrictions that would otherwise preclude emission from intra-4f transitions: as such, the rare earths are considered weakly coupled to the host. The benefit of this weak coupling is the aforementioned narrow spectral linewidths as well as the possibility for fairly long-lived electron populations in the excited states prior to de-excitation. These excited state lifetimes, which can be of the order of micro-, through several milli-seconds, provide a metastability that facilitates the population inversion central to lasing. An electron in a metastable excited state will de-excite either radiatively or non-radiatively. Without external stimulus, the relaxation is spontaneous in the former (light-emissive) case. With an external stimulus, which would most likely be a photon for dielectric glasses, then the relaxation is stimulated provided that the photon has an energy equal to the energy difference between the populated excited state and a lower lying level. For spontaneous emissions, the light given off has no correlation in direction, polarization, or phase to any other spontaneous emissions that may occur within the host at the same time, and its energy is the difference between those of the originating and terminal electron levels. For stimulated emission, the generated photon is, in contrast, identical in all ways (direction, energy, polarization, and phase) to the photon that stimulated it. This creation of equivalent photons is a hallmark of the laser process. Further, if the stimulating and stimulated emissions are permitted to leave the host after a single pass, then the process is considered as optical amplification. If the stimulating and stimulated emissions are fed back into the host via some reflective structure in order to intensify further, then one denotes this an oscillator. Both amplifiers and oscillators are forms of lasers. The glass host is critical in the efficiency of the laser for several reasons. First, lasing requires gain that cannot apply until sufficient light is provided to offset losses, such as those from impurities or scattering sites. Accordingly, laser glasses and fibers should be of highest transparency, hence purity and homogeneity. Second, in addition to fundamental properties associated with the specific transitions of each rare earth, the so-called selection rules, the probability for a

radiative relaxation scales super-linearly with the refractive index of the host. In other words, all other things being equal, the most efficient laser hosts are glasses with the highest refractive indices. In the case of non-radiative relaxation of the excited state electrons, heat is generated rather than light. Here host phonons stimulate the de-excitation and creation of additional phonons. As such, the host glass composition is of great consequence since the interatomic bonds, and their structural arrangement, determine the phonon spectrum. Of particular importance is the highest energy (longitudinal optical, LO) vibrational modes since they involve the phonons most responsible for facilitating non-radiative relaxation. In order to reduce non-radiative relaxations, glasses can be cooled since the phonon occupancy number (number of phonons of given energy) depends on temperature and follows Bose–Einstein statistics. Alternatively, glasses with heavier and more weakly bound atoms/ions would possess lower phonon energies and therefore would exhibit reduced nonradiative relaxation rates. More specifically, heavy metal oxides, fluorides, and chalcogenides would therefore be more radiatively efficient than conventional silica-based glasses, all other things being equal. The glass composition has yet another influence on the active performance of optical-fiber amplifiers and lasers. Whereas it would normally stand to reason that more light-emissive dopant would yield more light, there is an optimum concentration for the rare earth dopant in a given glass. There are principally two reasons for this. The first relates to glass stability. Whereas phosphate and fluoride glasses tend to be highly multicomponent, and therefore more amenable to higher concentrations of any one species, most other conventional glass families – and particularly the silicates – generally have a fairly low “solubility” for rare earth ions prior to liquid–liquid immiscibility and phase separation. Other species, most commonly alumina (Al2O3), are added to reduce the immiscibility range (Chapter 5.2) and permit a greater concentration of rare earth dopants into the silica. The second reason for an optimum concentration of rare earths is the phenomenon called concentration quenching whereby electrons from one dopant can interact with electrons and energy levels of a second dopant if said dopants are in reasonably close proximity; this happens to a greater extent probabilistically as doping concentrations increase. In the specific case of concentration quenching, excited state electrons move from dopant to dopant until, as is likely, they encounter an impurity, are absorbed, and can no longer contribute to the generation of light. In order to determine the concentrationquenching limit, the radiative lifetime of a given transition is measured as a function of dopant level in a given glass. The lifetime will remain constant until the

2 Optical Properties and Fiber Designs

quenching limit is reached and the lifetime will rapidly decrease with any further increase in concentration. The ideal composition for most amplifier and laser applications is where the lifetimes are the longest just before the onset of quenching. Other ion–ion interactions may also take place at higher concentrations, including cross-relaxation and cooperative upconversion which can be either detrimental or actually useful in certain applications. For example, the cross-relaxation of thulium (Tm3+) in silica at concentrations in excess of about 4 wt % permits quite efficient emissions at a wavelength of 2 μm when this ion is pumped at a wavelength of about 780 nm. Thulium-doped fiber lasers have exceeded 1 kW in output power, and the 2 μm is considered “eyesafer” for defense applications. As with the first glass laser, the first optical fiber amplifier employed Nd3+ as the active dopant. A critical breakthrough occurred 25 years later when an optical fiber based on erbium (Er3+) doped into silica was realized [8]. The importance of this finding was that Er3+ can efficiently amplify light in the 1550 nm range, which overlaps the aforementioned minimum attenuation spectral window for silica optical fibers. Hence erbium-doped fiber amplifiers (EDFAs) provided a means to boost all-optical signals in low-loss silica optical fibers and helped usher in global communications as it is known today. A comprehensive compilation on various rare earthdoped fiber-based optical amplifiers and lasers is provided in [7]. Additionally, [9] reviews fiber- (hence glass-) based lasers for high-power (>1 kW) applications where additional complexities and systems-level considerations exist. The demands on the robustness of the glass and structure and performance of the resultant fiber are accordingly significant. 2.1.3 Nonlinear Optical Properties

Generally speaking, the previously discussed passive and active optical properties of glasses are termed linear phenomena because a linear relationship exists between cause and effect. For example, a change in the pump power incident on a glass laser will result in a linear change in the output power. The ratio of input to output is almost never unity owing to losses and inefficiencies in the system, but the changes generally are linearly related. Nonlinear effects are, in contrast, defined as ones where changes between input and output are not linearly related. With specific regard to optics, nonlinear optical properties derive from the same macroscopic mass/ spring consideration as linear optics, but higher-order terms are included to account for real anharmonicity in interatomic bonds. The refractive index, or, more appropriately, the dielectric susceptibility, is expanded as a power series in electric field as Pi(t) = εo(χ ij(1)Ej(t) + χ ijk(2)Ej(t)Ek(t) + χ ijkl(3)Ej(t)

Ek(t)El(t) + …), where P is the polarization (dipole moment per unit volume) vector as a function of time, t, driven by the electric field, E(t), vector of the light. The χ (n) values are the linear (n = 1) and nonlinear (n > 1) susceptibilities. The linear refractive index, n, is related to the linear susceptibility as n = (1 + χ (1))1/2. The amorphous structure of glass precludes even-order nonlinearities for reasons of symmetry though they can be present in acentric crystals. Accordingly, the polarization as a function of electric field given above can be recast in terms of refractive index, n. For glasses this is given by n = no + n2I, where no is the linear refractive index, n2 is the nonlinear refractive index, and I is the intensity of the light, which is proportional to E2(t). The more common nonlinear optical phenomena present in glass optical fibers include frequency-mixing processes such as third-harmonic generation (THG), sumfrequency generation (SFG), difference-frequency generation (DFG), optical-parametric amplification (OPA), and other nonlinear processes, such as the optical Kerr effect, self-focusing, self-phase modulation (SPM), optical solitons, cross-phase modulation (XPM), four-wave mixing (FWM), stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), and multi-photon absorption. Even in their earliest days, optical fibers provided a practical proving ground for understanding and utilizing nonlinear optical phenomena. The reason is that optical fibers possess two key attributes of value to nonlinear optics: long lengths over which weak effects can grow in magnitude and small core sizes that confine the light in a reduced cross-sectional area, thus greatly increasing the optical intensity (power per unit area). Interestingly, whereas nonlinear features were originally considered to be parasitic, Stolen [10] noted with respect to modern communication systems that “Fiber nonlinear optics has grown from a novel medium for the study of nonlinear optical effects, through a period where these effects appeared as system impairments, to the present day where optical nonlinearities are an integral part of high-capacity optical systems”. 2.2

Optical Fiber Designs

As a general rule, fibers are cylindrical structures whose lengths greatly exceeds their diameters. For conventional (e.g. telecommunications) optical fibers, lengths can range from meters, as for data centers, to thousands of kilometers, as in transoceanic cables. In these cases, the diameters are prescribed by convention as having an outer cladding glass diameter of 125 μm and a core diameter that depends on whether or not only a single waveguide mode propagates (core diameters of about 8 μm with numerical aperture of about 0.14 for typical communication wavelengths) or multiple ones do (core diameter

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6.4 Optical Fibers

(a) Refractive Input index profile pulse

Modal dispersion

Higher-order modes

Step-index multimode fiber

Output pulse

Lower-order modes

Modal dispersion

Graded-index multimode fiber

Step-index single-mode fiber

(b)

LP01

LP11

LP21

LP31

LP02

LP12

LP22

LP32

LP03

LP13

LP41

(c)

a

b

c

d

Figure 4 (a) Total internal reflection, single/multi/and GI fiber designs, (b) electromagnetic modes, and (c) schematic designs of photonic crystal fiber and MOF. Source: Reprinted with permission from [5].

of 62.5 μm). The fibers are doubly coated with protective polymers to resist abrasion and reduce the effects of bending such that the total fiber diameter is about 250 μm. A series of images exemplifying current standard and specialty optical fibers are provided in Figure 4.

2.2.1 Conventional Core–Clad Optical Fibers

As noted above, in the ray-optic view, optical fibers guide light via total internal reflection whereby the light is confined in the high-index core, which is surrounded by a

lower-refractive index cladding. Under this condition, i.e. light incident from a high-index region into a lower-index region, Snell’s law for light refraction is violated when the angle of incidence exceeds a critical angle (given by sin−1(nclad/ncore), where nclad is the refractive index of the clad and ncore is the refractive index of the core, and reflection, instead of refraction, occurs (Figure 4a). The index difference between core and clad need not be large and actually is one of the design parameters that define the behavior of the resultant waveguide. For simple descriptions, the ray-optic picture generally suffices. For more sophisticated designs, however, light is more correctly described as a wave, and the aforementioned ray-optic construction is replaced with a waveoptic formalism in which electromagnetic modes are confined and allowed to propagate within a higher refractive index core coaxially surrounded by a lower-refractive index cladding. In the wave-optic perspective, the transverse components of the light waves constructively and destructively interfere across the core, influenced by the cladding, yielding stable propagating fiber modes. Some of the light power inevitably extends into the cladding: this component is called the evanescent field. The exact distribution of these modes depends on the core size, refractive index contrast between core and clad (defined by the numerical aperture, NA = [ncore2 − nclad2]1/2), the wavelength of light, and the cross-sectional geometry of the core; i.e. whether rectangular, circular, elliptical, etc. Thorough reviews of conventional core/clad optical fiber designs are given in [5, 11]. One important practical consequence of the coexistence of modes in an optical fiber is modal dispersion. In communication systems, the optical fibers carry a digital (on/off ) series of packets of light. Because each mode has a different distribution, it has a different effective (mode) index, hence velocity. As a result, data packets launched into a fiber that excite multiple modes will necessarily spread in time, analogously to the chromatic dispersion of pulses noted above, such that data can be lost over time/distance. Such multimode (MM) optical fibers are not only easier to fabricate and maybe better for short distance/lower bandwidth applications where ease of handling and cost are drivers. Single-mode (SM) optical fibers generally possess a smaller core and lower numerical aperture (NA) than do MM fibers such that only the lowest-order mode propagates and no modal dispersion is present. Single-mode fibers are required for highcapacity communications over longer distances. Graded-index (GI) fibers are MM waveguides where the refractive index across the core is graded in a nearly parabolic manner, which balances the time for a given mode to propagate a certain direction. As a result, modal dispersion is significantly reduced [5, 11].

3 Optical Fiber Glasses

2.2.2 Double-Clad Optical Fiber

Optical fibers whose core has been doped with lightemissive species can be used as an optical amplifier or laser. The details and uses of these fibers are provided in Sections 2.1.2 (Active Optical Properties) and 5 (Applications), respectively, and so will not be described at length here. Suffice it to say that the excitation of the active species requires an optical pump; efficiently collecting the pump light into the fiber core can be problematic given the core’s often small size. One approach to lessen this difficulty is to pump the larger cladding, rather than the core directly. In order to do this effectively, the cladding must itself act as a waveguide: a secondary cladding of lower-refractive index surrounding the higher refractive index active core is then necessary. This “double-clad” design is particularly useful in high-power (>1 kW) fiber-based laser designs where significant pump powers are required to achieve the desired laser output power. Additionally, double-clad fibers permit the use of lower-brightness diode sources for efficient pumping of the active core through brightness conversion of light in the cladding. The cross section of this pump cladding often is shaped, such as with a flat edge or hexagonal symmetry, in order to break the circular symmetry and facilitate intersection of the helical cladding modes of the pump with the active core. This design provides a means both of efficient pumping and excitation. References [9] and [5] provide excellent additional details on doubleclad designs and uses. 2.2.3 Microstructured and Photonic Crystal Optical Fiber

MOFs and photonic crystal fibers (PCFs) constitute classes of optical fibers where the cross-sectional geometry is periodically modified in order to control the propagation characteristics of the light [12]. These periodicities in the material, whose length scales generally are commensurate with the wavelength of light, beget periodicities in the refractive index profile that create Bragg-like conditions for allowed and forbidden propagation energies and directions associated with the transverse components of the electromagnetic modes. For completeness, it is noted that some dispersion shifted/flattened (telecommunications) fibers have index structures that can be several times larger than the wavelength. A representative image of a PCF cross section is provided in Figure 4. Though MOFs and PCFs have been fabricated from a wide variety of glasses, the majority of structures are based on silica given its high strength, low loss, and commercial availability. The ability to use both silica and the fiber’s geometric structure to realize properties that a conventional silica fiber would not otherwise possess has opened many doors to important applications, such as sensing, low-latency communications, and supercontinuum (SC) generation. As the

creation of a continuous and broad spectra, SC generation arises when short, high-power laser pulses propagate through a nonlinear media (here the fiber). Such spectral broadening can rely on a variety of nonlinear effects, including SPM, FWM, soliton fission, and Raman scattering. While SC generation can be observed in many nonlinear media, MOFs and PCFs are particularly useful because they can provide for small mode sizes and tailored dispersions that facilitate enhanced nonlinearities [13].

3 3.1

Optical Fiber Glasses Silica and Silicates

As specifically relates to optical fiber, silica has always been the main glass former used in all practical and large commercial scales. This is due to the purity and vaporphase processability of the precursor SiCl4. Both as a glass and as an optical fiber, SiO2 can be produced with nearly intrinsic properties, of which the most important are transparency and strength. Within the spectral region of low intrinsic loss, silica exhibits a minimum transmission of about 0.2 dB/km at a wavelength of 1.55 μm. The V-curve for silica was provided in Figure 2. Silica glass is the only material for which the theoretical transmission and that measured in practice coincide, again a testimony of testament to the degree of engineering and optimization of the CVD processes employed in the manufacturing of silica optical fiber. For all intents and purposes, impurities have been removed from the process, though, in some cases, such as for non-commodity (i.e. specialty) designs and compositions, some impurities can still be present. Near the low-loss wavelengths in silica, transition metals, rare earths, and hydroxyl groups (OH) can limit transparency. It is worth noting that high OH concentrations in SiO2 glass do improve its ultraviolet (UV) transmission, so that optical fibers for application in the UV spectral range do typically have OH purposely included. When properly drawn and coated, silica-glass optical fibers can also exhibit nearly theoretical tensile fracture strength, in excess of 3 GPa. This is due in part to the high draw temperature, which can anneal away any cracks or scratches on the glass surface. The high strength of SiO2 glass correlates with its refractory thermal nature (both originating from the strength of the Si–O bond) and its relatively high chemical inertness and high laser damage threshold. Not surprisingly, the centrality of silica glass to all optical fiber applications of commercial consequence stems from this remarkable combination of properties; see Table 1. A variety of oxides generally are added to silica to modify its refractive index, thermal expansion coefficients, and viscosity as a function of temperature. The most

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Table 1 Representative properties for common optical fiber glasses. na

n2/nSiO2b

Transparency rangec

Tg ( C)

SiO2

1.44

1

0.3–2.1

1120

CTE (10−6/K)

0.55

Principal applications

Communications, fiber lasers

ZBLAN

1.49

1.2

0.5–5.5

265

17.2

IR fiber lasers and light transport

Phosphated

1.55

1.2

0.4–2

360

95

High gain per unit length fiber lasers

Germanated

1.8

40

0.5–4

450

100

Nonlinear fiber optics

Tellurited

2

20

0.5–4.5

300

170

Nonlinear fiber optics

As2S3

2.5

200

6 Jan

180

21

Nonlinear and IR fiber optics

As2Se3

2.9

600

1.5–9

140

24

Nonlinear and IR fiber optics

a

Refractive index at a wavelength of 1550 nm. Nonlinear refractive index at a wavelength of 1550 nm relative to that of SiO2. c Transparency range of glass in fiber form. d Representative order of magnitude values for these selected glass families. Source: After [14]. b

common are GeO2 (germanosilicates), Al2O3 (aluminosilicates), P2O5 (phosphosilicates), F (fluorinated silicates), and B2O3 (borosilicates). When added to SiO2, GeO2 increases the refractive index and enhances photosensitivity, P2O5 increases the refractive index and reduces glass viscosity, Al2O3 increases the refractive index and enhances the solubility of rare earth dopants, B2O3 reduces the refractive index and increases the coefficient of thermal expansion, and F reduces the refractive index and the glass viscosity. Doping with laser-active species, most notably the rare earths, is employed for the realization of optical-fiber amplifiers and lasers. In the case of active optical fibers based on silica, a dopant is often required to lessen phase separation of the glass and the resulting clustering of the rare earth oxide (RE2O3) since the RE2O3–SiO2 systems display considerable immiscibilities [15]. Alumina (Al2O3) is the most common additive to silica though phosphorus pentoxide (P2O5) also can be used. Greater detail on silica and silicate-based optical fibers can be found in [11, 15] as well as in references therein.

different ways to increase chemical durability and decrease the phosphate glass solubility in water and tendency to devitrify. Given the broad range of phosphate glass compositions, it is difficult to define specific draw temperatures or optical and thermal property values. Suffice it to say that phosphates are considered soft glasses; they definitely have reduced mechanical strength relative to silica and typically draw into fiber at temperatures of the order of 800 C. Attenuation values from fibers reported in the literature range from about 0.1 to several dB/m in the near IR spectral range; see Table 1. Phosphate glass optical fibers are used most notably for fiber lasers and amplifiers with high gain per unit length. As already noted, the impact of optical nonlinearities scale with distance and so shorter amplifiers and lasers imply a reduced buildup of parasitic effects as well as reduced device dimensions. Phosphates can incorporate a higher rare earth concentration prior to the onset of concentration quenching than can conventional silicate glasses. Phosphates can, for instance, accommodate rare earth (e.g. Yb3+) doping concentrations higher than silica by about one order of magnitude.

3.2 Phosphates Phosphates constitute a family of oxide glasses where the principal glass-forming species is phosphorus pentoxide, P2O5 (Chapter 7.9). The structure of phosphate glasses is based on PO42− tetrahedra whose P=O double bond is credited for the reduced thermal and mechanical properties of phosphate glasses in comparison with silicates. Although P2O5 is considered a glass former, phosphate glasses are always multicomponent with a wide range of possible network intermediates and modifiers. Of particular note are the alkaline earth oxides (i.e. MgO, CaO, SrO, and BaO), alkali oxides (i.e. Li2O, Na2O, K2O), and sesquioxides (e.g. Al2O3 and B2O3). Each contributes in

3.3 Infrared Glasses 3.3.1 General Remarks

Infrared glasses are generally defined as transmitting light at wavelengths beyond the transparency range of conventional silica-based glasses and fibers. This includes the mid-infrared spectral region, from about 2–5 μm wavelengths, and the far infrared, which ranges from about 8–12 μm wavelengths and possibly longer. Interest in these spectral regions stems from the fact that these are associated with the sensing of biological and chemical species (~3–12 μm range), thermal signature identification and countermeasures (~8–12 μm range),

3 Optical Fiber Glasses

astronomy/cosmology (~8–12 μm range), and weather forecasting (~3–5 and 8–12 μm range). In general, infrared glasses are characterized by constituents that are heavier in molar weight and/or weaker in bond strength than conventional silicates. The combination of heavier structural species and weaker bonds serves to shift to longer wavelengths the multiphonon vibrational absorption bands. Since the region of lowest intrinsic loss for a glass is near the wavelength where the edge of these absorption band intersects the attenuation associated with Rayleigh scattering, this redshift in the molecular absorption band yields an intrinsically lower-loss optical fiber. Lower-loss optical fibers are of great interest for long-haul communications and high-energy lasers. Additionally, the reduced vibrational energy also implies a lower non-radiative (multiphonon) relaxation rate for active light-emissive dopants in these glasses. As a result, light emission from infrared glasses is intrinsically more efficient than in higher phonon energy silicates. A thorough treatise on infrared optical fibers, the glasses from which they are made, how they are fabricated, their properties and applications is given in [14] and in Chapter 6.5. Accordingly, only a brief description of these important glass families is provided here. Table 1 provides a comparison of properties for selected oxide and non-oxide infrared glasses. 3.3.2 Heavy Metal Oxides

Heavy metal oxide (HMO) glasses fill a somewhat unique niche in optical-fiber glasses because they are oxides, thus exhibiting some of the beneficial properties of silicates, such as relatively high strength and thermal stability while being composed of heavier species and so possessing extended transparency into the infrared. The two systems most commonly studied and fabricated into optical fibers are the tellurites and germanates. Tellurite glasses are based on TeO2. They were first studied in 1952 and then considered for optical fiber only in 1994. Relative to silica and to other infrared glasses, tellurites enjoy a wide transmission window that extends from the UV to the mid-IR (~0.35–5 μm) and have glass and chemical stability appropriate for many applications, high linear and nonlinear refractive indices, and relatively low phonon energy (~600–800 cm−1 for tellurites versus 1100 cm−1 for SiO2). They are, however, less thermally stable with glass transition temperatures of only about 300–350 C. For optical fibers, the best-studied tellurites are related to the TeO2–ZnO–Na2O system, common dopants further including La2O3 and WO3. Tellurites, which generally are made via a melt/quench method, often possess hydroxyl (OH) impurities that limit transparency unless dehydration methods are employed not only for their precursors but also during the melting process. The lowest

tellurite fiber attenuation values achieved to date are about 0.5 dB/m at a wavelength of 2.1 μm [14]. Another important HMO glass family is germanate glasses whose structures are analogous to those of silicates because GeO2 is isostructural with SiO2. Since GeO2 is heavier than SiO2, however, germanates transmit further into the infrared and have similar intrinsic losses as SiO2 (though IR absorption is redshifted, Rayleigh scattering would be higher due to the higher refractive index) but are less thermally stable than silica. The glass transition temperature and melting point for GeO2 are about 700 C and 1115 C, respectively, whereas for SiO2 these values are ~1400 and 1726 C. Germanate glasses often are multicomponent. They are typically realized through a melt/quench process. Even though GeO2 regularly is doped into silica with one of the CVD processes, the direct formation of GeO2 core optical fibers is made difficult by significant mismatches in thermal expansion. That said, silica-clad optical fibers possessing very high GeO2 core concentrations and losses of only about 20 dB/km at 1.9 μm have been realized [16]. Of the main oxides used for optical fiber (SiO2, GeO2, P2O5, and B2O3), GeO2 has the highest (linear) refractive index, nonlinear refractive index (n2), peak Raman scattering cross section, and photorefractive effect. The large n2 value, approximately three times higher than in SiO2, suggests germanate glass optical fibers for four-wave frequency conversion devices. The high Raman gain of GeO2, approximately 10 times larger than for SiO2, marks these glasses as useful for efficient fiber-based tunable Raman fiber lasers and amplifiers. Lastly, the strong photosensitivity of GeO2, both when doped into SiO2 and as a germanate glass, suggests the ability to write Bragg gratings into the fiber at lower UV fluence levels and without hydrogen loading as is often done for silica fibers. Some useful compositional, physical, and optical properties of the more common tellurite and germanate glass optical fibers are provided in [14]. 3.3.3 Fluorides

Fluoride glasses were discovered accidently in the early 1970s through attempts to grow fluoride laser crystals. The ionicity of the fluoride bond makes fluorides nontraditional glass-forming systems relative to oxides and chalcogenides (Chapter 6.5). The melts generally exhibit low viscosities, and glass formation largely is based on the “confusion principle” whereby the presence of multiple components make it difficult for a crystal to form upon cooling of the melt. Relative to other infrared glasses, fluorides generally exhibit the lowest refractive index and optical nonlinearity, which makes them of value for high-power laser applications. The first fluoride glasses were based on ZrF4 as the main constituent. To date, the most common and

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6.4 Optical Fibers

well-studied fluoride glass is “ZBLAN” (Chapter 6.5) whose base molar composition is about 53 ZrF4– 20 BaF2–4 LaF3–3 AlF3–20 NaF. In addition to the fluorozirconate glasses, others of interest include fluoroaluminate glasses, based on aluminum fluoride, and fluoroindate glasses, based on indium fluoride. The fluoroaluminates and fluoroindates generally possess better chemical stability than do fluorozirconates. Mixed anion systems, such as the fluorophosphate and oxyfluoride glasses, have also been developed. As noted, relative to silicates, infrared glasses generally possess weaker bonding, which also means reduced thermal and mechanical properties. For example, the glass transition and fiber draw temperatures for ZBLAN optical fiber are about 260 and 310 C, respectively, whereas recent strength values of 700 MPa for 125-μm fibers have been realized. For telecommunication-grade silica optical fiber, these values are about 1100 C (Tg), 2000 C (Tdraw), and > 3GPa. The weak bonding is useful for intrinsically low-loss and higher-efficiency lasing; however extrinsic factors have always plagued the transmission of fluoride optical fibers. In theory, ZBLAN should exhibit a minimum loss of ~0.01 dB/km at a wavelength of 2.5 μm, which is approximately 20 times lower than that of silica (0.2 dB/km at 1.5 μm). Whereas the record low loss to date is ~0.4 dB/km at 2.35 μm, typical background loss of commercial fluoride fibers is ~150 dB/km for ZrF4-based glass fibers (wavelength range of 2.3–3.6 μm) and ≤ 450 dB/km for InF3-based glass fibers (wavelength range of 3.2–4.6 μ m). Only silica-based glasses are reliably manufactured with the CVD process; all other glasses being made by a melt/quench method, which leads to added impurities. In the case of the fluorides, these higher losses are associated with transition metal, rare earth, and OH impurities as well as extrinsic scattering from occasional bubbles, crystallites, and inclusions. That said, even with present loss values, the reduced phonon energies (600 cm−1 for ZBLAN versus 1100 cm−1 for silica) associated with the weak bonding have permitted a wide range of novel fluoride glass fiber lasers at wavelengths not possible with silicates. Of particular note are numerous fluoride glass fiber lasers doped with rare earths based on upconversion of near-infrared pumps to visible and UV wavelengths [7] and also the praseodymium-doped fluoride fiber that amplifies communication signals at the 1.3 μm zero dispersion wavelength. For completeness it is worth noting that fluorides are part of the broader halide family of non-oxide glasses (Chapter 6.5). Generally speaking, fluorides are more stable and possess a greater glass-forming range than do glasses based on other halide glass formers such as ZnCl2.

3.3.4 Chalcogenides

Chalcogenide glasses derive their name from the chalcogen elements from which they are formed, namely, sulfur (S), selenium (Se), and tellurium (Te); see Chapter 6.5. The glass-forming ability of this glass family tends to decrease with increasing molecular weight; i.e. it decreases in the order sulfides, selenides, and tellurides (which are based on elemental Te and thus not to be confused with the TeO2-based tellurites already described). The best-studied and commonly employed systems are in the binary systems of As with S, Se, and Ge and in the ternary systems of As–Se with Ge and Te, as well as in the Ge–As–Te, Ge–Sb–Se, and Ga–La–S families. The glass transition and fiber-draw temperatures range from 350 to 550 C and from 400 to 700 C, respectively. From the perspective of optical fiber, chalcogenides are of greatest interest for mid- and long-wave IR light propagation. The relative heaviness of the constituent elements coupled with weaker bond strengths shifts the infrared absorption out to quite long wavelengths, in some cases in excess of 20 μm. This makes such fibers of value for astronomical observations and imaging where no other glasses or fibers transmit. In addition to this extended transparency in the infrared, chalcogenides have the highest nonlinear refractive indices (n2) among optical glasses, making them of interest for low-power fibers in nonlinear optical devices. The minimum intrinsic loss of chalcogenide optical fiber is near or slightly below that of silica, though at longer wavelengths, e.g. 0.01 dB/m at 5.0 μm for As2S3. In practice, however, losses generally are considerably higher because of impurities from the melting process as well as glass and homopolar bond defects. More typical mid-infrared attenuation values are in the range of 0.1–10 dB/m. To date, the lowest loss observed in a chalcogenide is 0.012 dB/m at 3.0 μm from a multimode As2S3 optical fiber.

4

Optical Fiber Fabrication

The fabrication of optical fiber requires specific materials possessing the requisite optical, physical, chemical, and thermal properties for a given fiber design, which can, in addition, be converted from either the melt or a glass “preform” or “blank” into the resultant fiber. This section describes the basics of these two considerations.

4.1 Glass Formation There are many ways in which to make a glass. For the purposes of this Chapter, only those that are used in

4 Optical Fiber Fabrication

(a)

(b) Fumace (1200 °C)

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Figure 5 Sketch of the chemical vapor deposition process (a) modified chemical vapor deposition (MCVD), (b) plasma-enhanced chemical vapor deposition (PECVD), (c) outside vapor deposition (OVD), and (d) vapor axial deposition (VAD). Source: After [5].

reasonable scale to make glasses relevant to optical fiber are noted. Thorough reviews of conventional optical fiber fabrication are given in [11] and [5] and of photonic crystal fibers are given in [5]. Representative schematics for the CVD processes as well as the fiberdraw approach to fiber formation are provided in Figures 5 and 6. 4.1.1 Melt/Quench

Rods and tubes can be extracted from melt-quenched glass, typically via milling and polishing, from which a

core/clad preform can itself be constructed based on the optical fiber design. Judicious selection of the starting materials that are batched and melted in an appropriate crucible is critical to obtaining the requisite refractive index, thermal expansion coefficient, and viscosity– temperature relationships, among other important properties. Depending on the chemistry of the melt, and particularly on the vapor pressure of its constituents, additional conditions may be necessary such as a controlled, low-oxygen content atmosphere as in the case of fluoride glasses or sealed ampoules for the melting

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of high-quality and high-purity chalcogenide glasses. Contamination caused by dissolution of the crucible into the glass melt and by impurities resident in the precursor batch compounds can yield extrinsic absorptions and modify the physical and chemical properties that limit the performance of the subsequent glass. Additionally, contamination of the glass from atmospheric moisture can be problematic since OH species strongly absorb at many wavelengths of practical interest. Care must be given in all instances to make the melt, hence resultant glass, as free of impurities, bubbles, and chemical heterogeneities as possible for optimal fiber formation and optical performance.

whose applications to the fabrication of optical fiber is thoroughly described in [5, 11]. In all cases, the base reaction is SiCl4 + O2 SiO2 + 2Cl2. Though the processing specifics differ, the enabling chemistry is similar; i.e. the high temperature oxidation, thermophoretic deposition of glass particulate soot, and subsequent sintering and consolidation of glass soot derived from volatile halide species. The exact temperatures and times required for each of these steps differ, depending on the processing method, the size and design of the preform, and the compositions of the glasses. In addition to yielding a final glass rod that contains both core and clad region in their desired proportions, the particular power of these CVD approaches is that SiCl4 possesses a vapor pressure that is nearly 1012 times higher than those of the most detrimental impurities to optical performance, transition metals phases such as Fe2Cl6. Hence, CVD-derived silica-based optical fibers can exhibit intrinsically low attenuation values. In order to obtain silicate optical fibers, the GeO2, P2O5 B2O3, and/or F additives to the SiO2 are formed through vapor-phase reactions from their respective volatile halides: GeCl4, POCl3, BCl3, and/or SiF4. Either because BCl3 (or BBr3) and SiF4 are gases or because the GeCl4 and POCl3 precursor liquids have a suitably high vapor pressures, in both cases the doping chemical can be added directly into the SiCl4 gas stream. As done for doping with Al2O3 or light-emissive rare earth species [5, 11], one can adjust further the glass composition by doping the deposited soot via solutions with dissolved salts (e.g. AlCl3, YbCl3, and ErCl3). A complete solid solution exists between SiO2 and GeO2 and P2O5 such that glass stability is not problematic, though some volatility of the GeO2 and P2O5 can occur at the high temperatures required for preform consolidation and collapse. This volatility can lead to undesirable changes in the refractive index profile of the resultant preform, which in turn influences the performance of the resultant optical fiber. Other dopants, such as Al2O3, B2O3, and the lanthanide oxides (e.g. Yb2O3), do possess compositional regions of liquid– liquid immiscibility or a tendency to crystallize. Accordingly, more limited ranges exist for their addition into SiO2 though novel methods for obviating these traditional issues have been developed [15].

4.1.2 Chemical Vapor Deposition

4.2 Fiber Formation

All silica-based optical fiber of commercial consequence is drawn from glass fabricated using chemical vapor deposition methods, namely, outside vapor deposition (OVD), modified chemical vapor deposition (MCVD), vapor axial deposition (VAD), or plasma-enhanced chemical vapor deposition (PECVD). Representative schematics are provided in Figure 5 for these processes

As with glass formation, there are many ways to make a fiber. Whereas many polymer fibers, and indeed some non-optical glass fibers, are fabricated by extrusion, optical fibers are not because of the critical need for a pristine surface from which the strength of the resultant fiber is largely determined (see Chapter 3.12). Glass optical fibers are either formed directly from the melt in some specialty

Cooling

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Furnace

Furnace

Fiber diameter measurement Glass fiber Polymer coating applicator

Coating

716

UV polymer curing unit Polymer jacketed fiber Take-up system

Figure 6 Sketch of the fiber-draw process. Source: After [5].

4 Optical Fiber Fabrication

cases or, more conventionally, drawn from a (core/clad) glass rod directly into fiber. These processes are described in more detail below. 4.2.1 Double Crucible

Glasses such as selected chalcogenides are not sufficiently stable to yield a bulk rod. They can be formed into fibers instead by melting of the components followed by controlled flow of this melt out of an orifice at the bottom of the melter. In order to achieve a core/clad geometry, one melt stream (generally that of the core) is initiated, and a second melt stream (generally that of the cladding) is then flowed around it; these melt streams originated from concentric melters, each controlled to melt uniformly, homogenize the core or clad glass, and yield a stream with proper melt viscosity such that limited interactions between core and clad result upon fiber formation. 4.2.2 Fiber Draw

The draw process is vastly dominant to fabricate optical fibers. It is distinct from extrusion, spinning, or pultrusion in that a nozzle or die is not employed. These processes are applicable to polymer fibers (optical and non-optical) as well as non-optical glass fibers such as those used for thermal insulation or acoustic isolation (Chapter 9.3). Because fiber strength is of paramount importance, particularly in telecommunication applications, the surface of the (typically silica) optical fiber cannot be contacted, obviating the use of a die or spinneret through which the fiber is formed. Whereas the fiber is formed directly from the melt in the double-crucible method, the fiber-draw process begins with a glass rod (also called a preform or blank) that contains the core and clad glasses. The subsequent reduction from preform to fiber generally is an affine transformation whereby the diametric ratio of core and clad remains constant. If pressure or vacuum is employed during the draw, as is occasionally done in the fabrication of photonic crystal fibers, then the geometric ratios between preform and resultant fiber are not necessarily constant, and pressure is another processing parameter in the ultimate fiber design and performance. In general, glass optical fibers are formed with a vertical draw tower. The glass preform is held at the top of the tower in a down-feed unit that controllably lowers it into a furnace. Under certain circumstances, the preform can be rotated during the draw to facilitate greater uniformity of cross-sectional core diameter or to induce helical perturbations along the fiber’s length. The furnace design, often including inert atmosphere control, depends on the glass from which the fiber is made. The temperature of the furnace usually is best determined from the tension of the fiber during the draw, which is important for

maintaining good diameter control: a temperature appropriate in this respect is typically that at which the viscosity is about 106 poise (105 Pa s). For conventional silica optical fibers, these temperatures are between about 1925 and 2000 C. For softer glasses that are either prone to crystallization or have steeper viscosity–temperature relationships, the working range can be markedly shorter (ΔT ~ 10–20 K). During the beginning of the fiber-draw process, the temperature usually is raised above the eventual draw temperature in order to hasten the softening of the glass preform and its localized flow into a “drop” or “gob” that ultimately exits the furnace and defines the transition from bulk preform into fiber. This transition section is also known as the “neck” or “neck-down” region. The fiber is then pulled down the tower through a series of other instruments such as those that measure the bare (core/clad) glass fiber diameter, apply and cure polymer coatings (more detail below), display the concentricity of the coating around the glass fiber, measure the final coated fiber diameter, provide the tension for pulling the fiber from the locally softened preform (which is slowly lowered into the furnace), and ultimately collect the fiber on a spool for subsequent use. Upon sufficient cooling of the fiber, though still on-line prior to collection, one or often two polymer coatings are applied. In most cases, they provide protection of the underlying glass from the strains and abrasions of installation and use (Chapter 3.12). The first polymer layer, called the primary coating, is relatively soft and is intended to relieve the strain placed on the fiber during use so that the loss of light caused by micro-bending can be lessened. The second polymer layer, called the secondary coating, is generally hard and provides abrasion resistance. The coatings are applied in oligomeric form to the glass fiber on-line during the draw by a series of dies that do not contact the glass surface but do provide a thin separation for the coating to wet the glass with welldefined thickness. The coatings are then cured on-line with an ultraviolet lamp. Whether the primary is cured first or both primary and secondary coatings are cured simultaneously (called wet-on-wet coating) depends on the application, hence volume of fiber and draw speed. For more specialty uses, a single coating may be sufficient. One variation on this theme includes polymer clad silica (PCS) where the fiber is only composed of silica with no core/clad structure and the single (hard) polymer coating constitutes the cladding. A second variation is doubleclad fibers used in fiber laser designs, where the fiber is constructed with an active glass core, passive glass clad, and a low-refractive index polymer cladding that provides light guidance for the laser pump light in the glass cladding. A protective outer polymer coating often is used in double-clad fiber designs.

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For completeness, the aforementioned microstructured and photonic crystal optical fibers generally are formed via fiber-draw processes as well. However, the preforms from which the fibers are drawn typically are ensembles of stacked rods or tubes of requisite periodic structure. Although tedious, this “stack and draw” method does enable very sophisticated and multimaterial structures to be fabricated and drawn into fiber.

5

Applications

In 2013, the National Research Council of the United States National Academies published an updated report on the state of optics and photonics [17] whose annual global economic impact was estimated at $7.5 trillion. Optical fiber is a subset of this field, which was fully expected to continue to grow because of their many direct or indirect applications. The principal application areas are (i) communications, information processing, and data storage; (ii) defense and national security; (iii) energy; (iv) health and medicine; and (v) advanced manufacturing. It is beyond the scope of this chapter to delve deeply into each though a brief description is provided below. For more detail, the reader is referred to the report itself [17]. Much of the initial impetus behind the development of optical fibers stemmed from their potential use in communications. It can be argued that of all the applications of glass optical fibers, those for global communications remain not only the largest in scale but also the most enabling since such fibers have brought knowledge and given voice to people around the world who previously had no access to information or means for commerce. Around the turn of the twenty-first century, a meaningful transition occurred when Internet traffic associated with data surpassed that for voice-based telephony. People speaking with people approximately scales with population, which grows at a rate of only about 1% per year. Computers talking to computers do not, so very rapid increases in Internet traffic spurred a growth in the demand for glass optical fiber that continues to this day. The Internet of Things, continued growth in social media, cloud computing, and data storage will only increase this demand in the future. There have always been defense and security applications for optical fiber, and indeed, the Internet evolved from the US Department of Defense’s Advanced Research Projects Agency Network (ARPANet). The dielectric nature of glass obviates many electronic means of tapping into signals, making optical communications more secure. More recently, the use of lasers for projecting nearly instantaneous power at long distances without having to risk harm to individuals has ushered in

significant growth in high-energy lasers. Though freeelectron, chemical, and solid-state lasers are all of interest, high-energy lasers based on glass optical fibers have enjoyed considerable attention because they can be small, light, fully integrated, and meet many of the requisite power needs [9]. The main use at present of optical fiber as relates to energy is for the monitoring of oil and gas wells. In particular, glass optical fibers are employed in distributed temperature and acoustic sensor systems, which can allow for increased production and reduced risks. The high pressures, temperatures, and chemically aggressive environments have all but limited the choice of optical fibers to those made from either silica or, in some cases, pure silica cores with lower-index fluorinated silica cladding, which resist hydrogen degradation better than other glass families. There have been recent successes in using high-power lasers for actual drilling, which could greatly speed the exploration of new wells. Photonics plays an ever expanding role in health and medicine where the intrinsically small dimensions and flexibility of glass fibers are most valuable advantages. Applications include fiber bundle endoscopes for imaging within the body, fibers as light pipes to induce localized chemical reactions associated with photodynamic therapies, and more recently, though yet immature, optogenetics whose goal is to control and record neuron activity in living organisms. Infrared optical fibers – particularly fluoride glass optical fibers – are used to transmit mid-infrared light such as that at 2.8 μm from an Er : YAG laser for use in ophthalmology and dentistry. Advanced manufacturing has grown markedly over the past decade as modern conveniences continue to shrink in dimensions and increasingly complicated shapes are more rapidly fabricated. While lasers in general play enabling roles, the specific use of glass optical fiber is more limited but growing as with some of the other applications noted above. The use of fiber in advanced manufacturing, at present, largely relates to its flexibility such that laser light can be brought from the source to the part being fabricated without complex bulk optical elements where misalignment can occur in articulated robotic systems. A second and growing area for glass optical fiber in manufacturing relates to fiber-based high-power lasers where the quality of the laser beam can be considerably higher than in bulk solid-state laser systems.

6

Perspectives

To say that optical fiber is central to modern life is an understatement. The ubiquity and instantaneous availability of information, as just one example, is entirely

References

enabled by optical fibers in both passive and active forms. While silica will remain the material of choice, continued advances in infrared glasses, most likely fluorides, will open doors to new applications [5]. Ever greater control of the properties of light will be engineered into the fibers through judicious and clever combinations of geometric structuring and materials selection [8]. In addition to expanded roles in present technologies such as communications, defense, medicine, and manufacturing, applications where fibers play more enabling roles will grow and include energy independence, advanced genomics (e.g. optogenetics), autonomous vehicles, and space exploration. Only time will tell what the future holds, but there is no question that the future for glass optical fiber remains very bright!

5 Oh, K. and Paek, U. (2012). Silica Optical Fiber

6 7 8

9

10 11

Acknowledgments The author thanks the following individuals who have provided important input for the development of this chapter: Thomas (Wade) Hawkins, Max Jones, Courtney Kucera, Benoît Faugas, Maxime Cavillon, and Colin Ryan.

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References

15

1 Colladon, J.D. (1842). Sur les réflexions d’un rayon de

lumière à l’intérieur d’une veine liquide parabolique. C.R. Acad. Sci. 15: 800–802. cf. La fontaine de Colladon. La Nat. 12: 325–326 (1884). 2 Babinet, J. (1842). Note sur la transmission de la lumière par des canaux sinueux. C. R. Acad. Sci. 15: 803. 3 Kao, C. and Hockham, G. (1966). Dielectric-fibre surface waveguides for optical frequencies. Proc. IEE 113: 1151–1158. 4 Hecht, E. (2016). Optics, 5e. Harlow, UK: Pearson.

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17

Technology for Devices and Components: Design, Fabrication, and International Standards. New York: Wiley. Snitzer, E. (1961). Optical maser action of Nd3+ in a barium crown glass. Phys. Rev. Lett. 7: 444–446. Digonnet, M. (ed.) (1993). Rare Earth Doped Fiber Lasers and Amplifiers. New York: Marcel Dekker. Mears, R., Reekie, L., Poole, S., and Payne, D. (1986). Low-threshold tunable CW and Q-switched fiber laser operating at 1.55 μm. Electron. Lett. 22: 159–160. Richardson, D., Nilsson, J., and Clarkson, A. (2010). High power fiber lasers: current status and future perspectives. J. Opt. Soc. Am. B27: 63–92. Stolen, R. (2008). The early years of fiber nonlinear optics. J. Lightwave Technol. 26: 1021–1031. MacChesney, J. and DiGiovanni, D. (1990). Materials development of optical fiber. J. Am. Ceram. Soc. 73: 3537–3556. Knight, J., Birks, T., Russell, P., and Atkin, D. (1996). Allsilica single mode optical fiber with photonic crystal cladding. Opt. Lett. 21: 1547–1549. Dudley, J.M., Genty, G., and Coen, S. (2006). Supercontinuum generation in photonic crystal fiber. Rev. Mod. Phys. 78: 1135–1184. Tao, G., Ebendorff-Heidepriem, H., Stolyarov, A. et al. (2015). Infrared fibers. Adv. Opt. Photon. 7: 379–458. Ballato, J. and Dragic, P. (2013). Rethinking optical fiber: new demands, old glasses. J. Am. Ceram. Soc. 96: 2675–2692. Dianov, E.M. and Mashinsky, V.M. (2005). Germaniabased core optical fibers. J. Lightwave Technol. 23: 3500–3508. National Research Council Committee on Harnessing Light: Capitalizing on Optical Science Trends and Challenges for Future Research (2013). Optics and Photonics: Essential Technologies for Our Nation. Washington, DC: The National Academies Press.

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6.5 Fluoride and Chalcogenide Glasses for Mid-infrared Optics Bruno Bureau and Jacques Lucas Verres et Céramiques, Institut des Sciences Chimiques de Rennes UMR-CNRS 6226, Rennes, France

1

Introduction

The glass world has long been dominated by oxides because of the exceptional ability of SiO2, B2O3, and P2O5 to form strongly associated melts. In the last past decades, however, new glasses have been formed from metallic salts such as fluorides and chalcogenides whose unusual properties, primarily optical, have led to important practical applications. Research and development in this field has in fact been boosted by the need for lighttransmitting materials in the infrared (IR) region. In contrast to oxides glasses, whose opacity beyond 3 μm make them inappropriate for mid-IR technologies, fluoride and chalcogenide glasses are low-phonon materials because the vibrational modes of their glass framework shift the IR cutoff to a maximum of about 20 μm. This is why chalcogenides [1–3] and fluorides [4, 5] have found many applications, ranging from IR lenses as key components in thermal-imaging and night-vision systems to opticalwaveguide fibers transmitting IR light in energy transfer or remote analytical devices. This chapter will focus on those glasses for which applications have been found, thus excluding a number of halides (chloride, bromide, and iodine) and chalcogenides that suffer from a poor chemical durability, especially under humid conditions, or from weak mechanical properties and resistance to crystallization. The first series of materials selected encompasses complex ZrF4-based glasses known as ZBLAN, because they are a mix of Zr, Ba, La, Al, and Na fluorides, as well as metal trifluorides such as InF3, GaF3, or AlF3 [5]. The second group to be discussed deals with composition ranges where viscous liquid may be formed from chalcogens (X = S, Se, Te). This group also Reviewers: Jong Heo, Pohang University of Sciences and Technology, South Korea Steve Martin, University of Iowa, Iowa City, USA

includes glasses made from chalcogenides such as As2X3, Sb2X3, GeX2, and Ga2X3 [1, 6, 7]. After having briefly reviewed the issue of glass transparency, we will describe vitrification in these systems, then glass structure, and finally the main current uses of these materials in optics. For detailed information on important topics directly relevant to the present theme, we will refer to other chapters on floppy–rigid structural transitions (Chapter 2.7), luminescence (Chapter 6.3), silica optical fibers (Chapter 6.4), and glass ceramization (Chapter 7.11).

2 Glass Transparency in the Infrared Region At short wavelengths the optical transparency of a material is limited by the interaction of light with the electrons involved in chemical bonding. At high wavelengths, optical losses originate in absorption by the vibrating atoms, which form dipoles coupling with the oscillating electric field of light. As indicated by the simple model of the harmonic oscillator, the frequencies at which light begins to couple with network vibrations decrease with increasing atomic masses and decreasing bond strengths. In silicate glasses, the absorption rises to 50%, at about 3 μm in the near-IR (Figure 1). Hence, the most efficient strategy to expand the spectral window of glasses is to deal with atoms heavier than oxygen or silicon to lower phonon energy and shift the multiphonon cutoff to longer wavelengths. With fluorine, sulfur, selenium, and tellurium, the optical transparency indeed extends further and further in the mid-IR and even in the far-IR with the heaviness of the glass former (Figure 1). In practice, the reasons for developing glasses transmitting light in the mid-IR region are several. First, blackbody emission shifts toward the IR with decreasing temperatures. Whereas the sun, with a corona temperature of

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

6.5 Fluoride and Chalcogenide Glasses for Mid-infrared Optics

Figure 1 Influence of atomic weight and bond strength on the infrared transparency of glass families.

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Figure 2 Shift to lower wavelengths and intensity increase with temperature of blackbody radiation. Emission by the human body in the mid-infrared near 10 μm.

about 6000 K, emits most of its energy in the visible region, the radiation emitted at room temperature – for instance, by the human body – peaks near 10 μm (Figure 2). Optics operating in this region are thus necessary for thermal imaging in night-vision systems and, more generally, for all kinds of IR camera and IR transmitting optics. Second, although generally transparent in the visible region, the atmosphere exhibits two windows where light is strongly absorbed. One is the 3–5 μm region just in between the wavelength of the O–H elongation vibration and the strong bending mode of the H2O molecule. Extending from 8 μm, after water absorption, to about 13 μm where CO2 molecules begin to absorb, the second window has a greater width that makes it well suited to visualize thermal objects at room temperature such as human or animal beings. Third, as already noted, the IR region is the domain of molecular vibrations. Hence, every kind of molecules has a spectral fingerprint, which is roughly located

between 2 and 12 μm, so that chemical species can be detected and analyzed from IR spectra. For all applications, however, an important feature to be accounted for is Fresnel loss, which is caused by photon reflections at the glass surface and is proportional to the refractive index n of the material. This parameter depends on the polarization of the atoms forming the glass. It is strongly enhanced by heavy elements, so it increases from 1.5 for silicate or fluoride glasses to 2–2.5 for selenides and even to 3.2 for tellurides. As a result, reflection losses increase sympathetically from about 15 to 50%, respectively (Figure 1), which implies that the surface of chalcogenide glass lenses needs to be coated with antireflective films. Finally, a few words are probably useful to justify why these materials cannot generally be used in the visible range. At short wavelengths (Figure 1), optical absorption is due to electronic transitions associated with both bonding and nonbonding electrons. The latter gives rise to the so-called band-gap absorption, whose cutoff wavelength is λc = hc/Eg for a glass with a band gap Eg. The glass is transparent at wavelengths λ > λc where light is not sufficiently energetic to induce an electronic transition. Conversely, the material is opaque at wavelengths λ < λc where light is absorbed to promote an electronic transition. Because of band-gap absorption, a bulk glass thus filters out all visible light of wavelengths shorter than λc and can then appear colored or even black. Oxide glasses such as silicates are transparent in the visible because λc is located in the UV region at around 0.3 μ m. The same applies to fluoride glasses. Chalcogenides, in contrast, markedly absorb in the visible because their band gaps are lowered by the lone pairs of nonbonding electrons sitting at intermediate levels between the valence and conduction bands. Chalcogen elements, moreover, are regarded as semiconductors because they lie in between metals and nonmetals in the periodic table, so electronic transitions become increasingly probable from sulfur to tellurium. In sulfide glasses, the transmission limit is

3 Fluoride Glasses: Formation and Structure

slightly displaced in the middle of the visible range, making these materials yellow or orange. For selenides, the color becomes dark red or black, and definitely black for tellurides, making these materials looking like an alloy rather than a glass. In summary, fluoride and chalcogenide glasses are unique for mid-IR technology, but useless for the visible and near-IR ranges where silicate glasses remain matchless.

3 Fluoride Glasses: Formation and Structure 3.1

Glass Formation in Metal Fluorides MFx

Owing to the peculiar electronegativity of fluorine, fluorides can be roughly divided in two classes [5]. When the metal M has a high oxidation state, the formation of volatile molecular species is dominant, and the chemical bond is covalent. Typical examples are uranium hexafluoride, UF6, and silicon tetrafluoride, SiF4. If the metal is mono- or divalent (e.g. alkalis or alkaline earths), the material is highly crystalline with strong ionic bonds. This is the case of NaF or CaF2, which upon melting give rise to fluid, nonassociated liquids lacking any glass-forming ability. Trivalent MF3 or tetravalent MF4 crystals (M = transition metal belonging to the 3d or 4d series in the periodic table) form giant 3-D frameworks based on the connection of octahedra or more complex corner-sharing polyhedra. The chemical bonds causing the formation of these networks are intermediate between covalent (overlapping of orbitals) and purely ionic as typically found in AlF6, GaF6, InF6, ZrF7, or ZrF8. The connection between those units can be very rigid without any possibility of varying the bond angle M–F–M. In this case, the solid and melt have similar short-range structures, so crystallization is the rule upon cooling. In some very special situations, however, a fluoride melt can be made up of diverse MFx polyhedral units mutually connected between which bond angles are floppy and, thus, vary at little energy cost for the system. This situation leads to an associated melt showing a higher viscosity. Crystal formation then is thwarted by the existence of these nonperiodic polymeric networks, which persist when the melt is cooled down. As happening for silicate glasses, the viscosity of the metal fluoride polymer increases so much when the temperature drops that a glass forms when the viscosity reaches 1012 Pa s. To prevent crystallization, an empirical rule is to use complex compositions in which competition between different possibly nucleating crystals is maximum (the socalled principle of confusion). In the 1980s, the activity in the field was strongly boosted by the search for

ultra-transparent glasses at telecom wavelengths. Many fluoride glass compositions were then discovered, but only a few were found suitable for applications. Since interest mainly lies in widening the transparency window toward the IR, only heavy metal fluoride glasses such as ZrF4 and InF3 are relevant. In fluorozirconate glasses, the most popular composition is that of ZBLAN glass, namely (in mol %), 52 ZrF4 19 BaF2 5 LaF3 4 AlF3 20 NaF, where ZrF4, AlF3, and LaF3 are considered as glass formers and the large ions Ba2+ and Na+ as modifiers. Glasses based on InF3 are also of interest since they are stable enough to be drawn into optical fibers. The phonon energy is lower for InF3 than for ZrF4 glasses so that the former transmit better in the IR thanks to a cutoff that is slightly shifted toward longer wavelengths, at 5.5 instead of 4.6 μm for optical fibers. In practice, the composition of these glasses is also complex with molar concentration of InF3 close to 50% and various heavy metal fluorides (BaF2, PbF2, ZnF2, GaF3, or CdF2) to keep the phonon energy as low as possible and to prevent crystallization from happening. Besides, small amounts of alkali chlorides can be also added to adjust the refractive index. 3.2 Polymeric Networks Based on ZrFn Polyhedra Determining the structure of fluoride and chalcogenide glasses becomes increasingly difficult when composition becomes complex, especially when major components have themselves a complex structural role. For fluorides, the most appropriate and simplest glass for structural investigation has the ratio ZrF4/BaF2 = 2. Because this glass is very unstable, fast quenching of the melt is necessary to obtain small flakes suitable for X-ray investigations. Thanks to its rather simple composition, this BaZr2F10 glass has also been investigated by computer simulation. Examination of the fluorozirconate crystal chemistry is also bringing important information about ZrFx coordination polyhedra, where x varies from 6 to 8 with a most frequent value of 7. As a matter of fact, there exist a variety of polyhedral geometries around zirconium associated with a great flexibility of the Zr–F–Zr bond angle. Since fluoride glasses were discovered accidentally in a study of atomic substitutions in crystalline LaZrF7, it is of interest to note that, according to X-ray investigations [8], ZrF7 and LaF8 polyhedra are connected to form a 3-D network in this rare earth fluorozirconate. More generally, structural models have been established to integrate several sources of information (Figure 3). In X-ray diffraction studies, radial distribution functions (RDF) show Zr–Zr pair correlations indicative of short and longer Zr…Zr distances compatible with

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6.5 Fluoride and Chalcogenide Glasses for Mid-infrared Optics

4

Applications of Fluoride Glasses

4.1 General Considerations

Zr

F

Ba

Analyses by differential scanning calorimetry (DSC) are simple means to check that glasses have the required mechanical and thermal properties and also a strong enough resistance to devitrification [5–7]. For ZBLAN, a DSC analysis shows that its Tg is close to 260 C, i.e. well above the 120–130 C required for practical applications, but also that crystallization is signaled by an exothermic peak at Tx of about 400 C. Hence, the glass must be fiberized between these two temperatures under severely controlled viscosity conditions such that the deformation rate is high enough but crystallization remains avoided. Besides, fluoride glasses are sensitive to thermal shock because of high thermal expansion coefficients (17.2 × 10−6 K−1 for ZBLAN), which are consistent with their rather low Tg. Heavy metal fluoride glasses are stable under normal atmospheric conditions, but they are sensitive to moisture corrosion when temperature increases because the OH− ion has the same size as F−, so F/OH substitution at the glass surface is a ready source of corrosion.

Figure 3 Structure of ZrF4 glass reticulated by ZrF7 or ZrF8 polyhedral units, with large ions such as Ba2+acting as network modifiers.

4.2 Optical Fibers for Guiding Infrared Light

ZrFx polyhedra sharing edges and corners, respectively, the Ba2+ ions being a glass modifier. Interestingly, computer simulations lead to the same result with two clearly distinct Zr…Zr distances. Another important point is to establish the role played by the lanthanide atom in ZBLAN glasses. The La content being small at around 4%, Nd3+ has been used as a dopant because rare earth spectroscopy with this ion as a probe is very sensitive to the local ligand field. The Nd3+ fluorescence spectra are very similar in the glass and parent crystalline LaZrF7, indicating that La3+ is incorporated in the glass network as LaF8 polyhedra. Hence, there is a striking contrast with silicate glasses where Nd3+ absorption spectra are broad, indicating that this ion is instead a network modifier. From these results, one concludes that these associated melts vitrify when their networks have a polymeric nature. The disordered polymer is made up of a variety of polyhedral connections, including small amounts of AlF6 and LaF8 in addition to the predominant ZrF7. Variations in bond angles then cause local disorder and a lack of periodicity, whereas the Na+ and Ba2+ ions are glass modifiers. Both also contribute to foster the competition between crystalline phases that might precipitate, delaying in this way the devitrification process that remains here an issue.

Fibers are by far the main commercial product for fluoride glasses [4, 9], in agreement with the fact that one of the main reasons for investigating them was the search for ultra-transparent materials. Although electronic absorption in the UV is not so different in fluorides compared with SiO2 glass, the phonon absorption in contrast drastically shifts toward long wavelengths with phonon energies of 600 and 1100 cm−1, respectively. Glass transparency is represented by V-shaped curves (Figure 4), indicating that the minimum optical loss is 0.2 and about 0.02 dB/km for SiO2 and fluoride glasses, respectively. Because fluoride glasses have thus been considered as a substitute for silica in long-distance telecommunications, much effort has been paid to develop high-quality optical waveguides in single- or multimode configurations (i.e. depending on whether the core of the fiber is several or many times larger than the light wavelength, so single or many optical modes propagate). In both cases, however, a prerequisite for the internal reflections needed for light propagation is that the refractive index of the core be slightly higher than that of the clad glass. One thus needs to combine two glasses having similar properties, except for the refractive index. With the rod-in-tube method (Figure 5), the core glass is used for the rod and the clad glass for the tube: after strict adjustment of the rod into the tube, the preform obtained is drawn with a drawing tower and the fiber collected on a drum.

4 Applications of Fluoride Glasses

10 000.00 Visible light 1 000.00 Attentuation (dB/km)

Figure 4 Comparison between the infrared transparencies of silica and fluoride fibers. Minima of the V-shaped curves of 1 dB/km for silica near the 1.55 μm telecom wavelength and of only 0.02 dB/km for fluoride at 2.9 μm.

Silica

ZBLAN

Infrared

100.00 10.00 1.00

Theoretical best

0.10 0.01

IR multiphonon edge losses

Rayleigh scattering loss

0.001 0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Wavelength (μm)

Figure 5 Production of a single-mode preform (C) from two Se–Te vitreous alloys: one for the core rod (A) and the other for the cladding tube (B). A as a first step, the rod has to be drawn into a stick to get the requested final diameter ratio.

4.3

Passive Properties

In passive functions the fiber transmits the light from a source toward a target [9]. Critical parameters are the spectral transmission window, the optical loss, and the resistance of the fiber to high densities of light especially when the source is a laser. Since silica fibers are both reliable and inexpensive, the only market left is the region where they are no longer transparent. The lowest optical losses are found around 3 μm before transparency begins to decrease strongly in the 4–5 μm region. Single-mode fibers are used in very special sectors such as spatial interferometry in the spectral region beyond 2 μ m where silica fibers become opaque. Although the intense research made on ultralow-loss fibers for telecommunications has declined, the potential for ultratransparency is still a reality. The lowest loss obtained

A

B

A+B C

in the 1990s was about 1 dB/km around 2.9 μm, but higher transparency would be possible through reduction in the IR thanks to a cutoff that is slightly shifted toward longer wavelengths, at 5.5 instead of 4.6 μm for optical fibers. In practice, the composition of these glasses is also complex with molar concentration of InF3 close to 50% and various heavy metal fluorides (BaF2, PbF2, ZnF2, GaF3, or CdF2) to keep the phonon energy as low as possible and to prevent crystallization from happening. Besides, small amounts of alkali chlorides can be also added to adjust the refractive index.

4.4

Active Properties

When the core of a fluoride fiber is doped with luminescent rare earth elements, the device can be considered as a

725

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6.5 Fluoride and Chalcogenide Glasses for Mid-infrared Optics

Line - silica -

Input signal

Optical amplifier RE-doped fiber (Er, Tm, Pr)

Coupler

Figure 6 Optical configuration of a singlemode fluoride fiber used for laser action or optical amplification. Core glass doped with the appropriate rare earth ion.

Line - silica -

Amplified output

Coupler

Pump laser

new light source [4]. The optical configuration needs to be single mode to ensure the quality of the output light, whereas the specifications in terms of optical loss are as high as possible. The field was very active in the 1990s with the aim of developing two kinds of products, namely, optical amplifiers and fiber lasers. When a lanthanide is pumped with the appropriate source (a laser diode, for instance), the light emitted by the fiber is guided in its fiber, collected at the output (Figure 6), and serves to regenerate the telecom signal. For use as a laser, two mirrors are necessary to obtain the required oscillations. The market of optical amplifiers is entirely driven by telecommunication constraints. Since the relevant wavelength is in the low-loss region of silica at 1.55 μm, the only rare earth operating in this region is the erbium ion Er3+. Although the so-called erbium-doped fiber amplifier (EDFA) based on silica satisfies market needs thanks to their high efficiency, a potential for fluoride amplifiers resides in the use of other wavelengths located on the borderline of the silica low-loss region typically from 1.3 to 1.65 μm. Rare earth ions such as Pr3+ and Dy3+ are suitable for this region because the amplification ability is very poor in silica but very efficient in fluoride glasses. Compared with silica, however, a limitation of fluoride fibers is the impossibility of welding them with silica glass resulting from their chemical incompatibility. Fiber lasers represent an expanding market because of their intrinsic advantages. Heat dissipation is, for instance, more efficient, whereas flexibility is fundamental to guide the light toward its target. The field is also dominated by silica fibers, which are strong and easy to prepare, but rare earths may have a weak luminescence in this matrix that suffers from poor transparency beyond 2 μm. Consequently there is some room for fluoride fiber lasers (Figure 7) as their emission range covers a broad spectral domain from UV to the mid-IR. The emission in the visible is due to upconversion or photon addition mechanisms, which are very efficient in this matrix. Upconversion means that the ground-state electrons of the rare earth are first excited by photons pumped to an

upper long-life level. The same source can then promote these electrons to a higher level, from which light is emitted at wavelengths shorter than that of the pumping light. Pumping with an invisible IR source, for instance, results in the emission of a visible green light. Considering the power and the wavelength available from fluoride fibers (Figure 7), one sees that all these wavelengths are available for specific applications such as marking, cutting, or welding materials. Medical applications such as special surgery as well as analytical purposes are opening with this new kind of light sources

5

Chalcogenide Glasses

5.1 Formation with Chalcogens Chalcogen glasses are built from S, Se, and Te, which lie below oxygen in the periodic table [6, 7]. Like oxygen, these elements are characterized by an outer electronic shell of six electrons, s2 p2x p1y p1z , of which only the two odd electrons are involved in covalent bonding. Thus, these elements are generally twofold coordinated, generating crystal networks constituted of chains (Se and Te) or rings (S) in which the elements are strongly covalent bonded. The overall cohesion of these units is achieved through much weaker dipole–dipole van der Waals interchain bonds. Although the three chalcogens belong to the same family and share similar one-dimensional (1-D) crystal structures, they may be chemically “false friends” because sulfur and selenium are good glass formers whereas tellurium is not. Although sulfur- and selenium-based glasses have similar chemistries, the former have a moderate interest because of their limited transparency in the mid-IR. Selenium thus is clearly the key element to form bulk glasses displaying the desired transparency in the mid-IR up to 16 μm. The strategies for glass formation are then the same as for fluoride in that they rely on empirical rules. The key ingredient is to form a polymeric melt with

5 Chalcogenide Glasses

Figure 7 Laser emission of rare earth-doped fibers. (a) Comparison between the emissions of fluoride and silica fibers. (b) Influence of the doping rare earth on the output power of fluoride fibers (from [6]).

(a) Pr Nd Ho Er Tm

Fluoride glass

Yb Pr Nd Sm Ho

Silica glass

Er Tm Yb 0.2 0.6

1.0

1.4

1.8

2.2

2.6

3.0

3.4

3.8

Wavelength (μm)

(b) Er

Tm/Ho Ho

10

Ho/Pr Ho

Output power (W)

Tm

1 Dy

0.1

Er Tm Nd

Nd Ho

0.01

Ho

Tm

Er

Ho

Ho

Er

1E–3 1

1.5

2

2.5

3

3.5

4

Laser wavelength (μm)

highly flexible bond angles, thus yielding a floppy network keeping chemical bonds strong without periodicity. In this respect, the structure of crystalline selenium is really unique as it is similar to that of an inorganic polymer. Its weak interchain bonds are easily broken by thermal agitation, hence a low melting point of 216 C and the formation of a viscous liquid in which chain fragments persist. If Se is for this reason the only good glass-forming element, its glass transition temperature of 40 C is much too low for any practical application. To increase it to ensure acceptable mechanical and thermal properties, a network dimensionality higher than 2 is required through chain cross-linking by elements close to selenium in the periodic table. In this way the covalent character of bonding is kept, and the strength of the structural network is improved. In practice, selenium chains are cross-linked

by trivalent elements such as As or Sb or tetravalent elements such as Ge, all of them having similar electronegativities. Two basic systems are then dominating the chalcogen-based glass scenery. In the first (Se–Ge), the network is built with GeSe4 tetrahedra connected to one another by Se chain fragments. The GeSe2 composition yields a fully reticulated 3-D network where the tetrahedral units are directly corner shared. Because this stoichiometry is equivalent to that of SiO2 in silicate glasses, one would expect GeSe2 to be optimal in terms of viscosity and thermomechanical properties. On the contrary, its network is overconstrained because a lack of degree of freedom makes this glass difficult to form and unstable upon shaping. As for the GeSe4 composition, its tetrahedral units are expected to be linked by Se–Se dimers providing the

727

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6.5 Fluoride and Chalcogenide Glasses for Mid-infrared Optics

needed flexibility to the network. As discussed in the Section 3.2, however, the structure of this glass is more complex, showing that chalcogenide chemistry may be complicated too. In the second system (As–Se), the building blocks are AsSe3 pyramids connected by bridging Se chain fragments. A fully reticulated network is obtained for As2Se3, for which pyramids are expected to be directly linked by individual Se atoms. The resulting reticulated network has a 2-D planar shape and is floppy enough to provide a glass exhibiting good physical and rheological properties. This composition thus is one of the most widely used. For technical and industrial uses, it is nonetheless advisable to oppose more strongly crystallization through more complex compositions bearing at least three elements. The so-called GASIR glasses belonging to the Ge–As–Se systems have, for instance, been developed by Umicore-IR glass company for molded IR optics. In these compositions the original 2-D planar network of the As–Se system extends into a third dimension through the GeSe4 tetrahedral units incorporated, resulting in a Tg increase and in improved thermomechanical properties. The particular Ge22As20Se58 composition is the most stable selenide, which makes it matchless for molded IR lenses. Other interesting materials belong to the Te– As–Se system, where addition of tellurium aims at lowering the phonon energy to shift transparency slightly further in the mid-IR comparatively with a purely selenide glass. An example is the Te2As3Se5 glass whose network is formed of mixed Te–Se chains reticulated by trivalent As. It is stable enough to be shaped by the DIAFIR company into optical fibers for mid-IR spectroscopy. As for pure tellurium [1], its very poor vitrifiability originates in the marked metallic character of the bonds that ensure interchain cohesion, which is, for instance, indicated by an electrical conductivity several orders of magnitude higher for Te than that for Se. This metallic character also results in a delocalized π bonding cloud, shorter interchain distances, and stronger cohesion of the structure and, thus, in a melting point of 422 C much higher than 216 C of Se. As observed for alloys, Te liquid is constituted of isolated, unreticulated atoms, which is why a glass can be obtained only by splat quenching. 5.2 Network Reticulation from Selenium Chains In technologically important selenide glasses, bonding is highly covalent with small coordination spheres: Se (twofold coordinated), As (3), and Ge (4). Despite this apparent simplicity, the structure of a glass network was until recently understood more from the solid-state chemist’s intuition than from hard experimental data. It was commonly described as a network of covalent bonds obeying the 8-N rule, but no consistent information had been

obtained on medium-range order, i.e. on the actual connection of the AsSe3 and GeSe4 polyhedral building blocks. The reason was that X-ray and neutron diffraction data are not easy to interpret in chalcogenide systems because the sizes of the electronic clouds and, unfortunately, also the neutron-absorption cross sections are very close to one another for Se, As, and Ge. And because these elements are neighbors in the periodic table, the Se–Se, Ge–Se, and As–Se bond lengths are too similar to allow structural organization to be determined from RDF. A decisive step was thus taken when the first 77Se solid-state nuclear magnetic resonance (NMR) spectra were collected in the AsxSe1−x and GexSe1−x systems [10]. For As–Se binary systems, NMR results have more or less confirmed the chemist’s expectations (Figure 8). From pure Se to the famous As2Se3, the network of Serich glasses evolves from a 1-D chain structure to a 2-D pyramidal network. For pure Se, it has in particular been confirmed that the structure is built from selenium chains, as found in crystalline phases, so melting does preserve the strong intrachain covalent bonds and only de-solder the chains in a disordered but still reticulated network. For As2Se3, the glass structure as seen by 77Se solid-state NMR is also very simple: each Se does directly bridge the AsSe3 pyramids, whereas a transition to a structure with a lower dimensionality is observed at the As2Se3 stoichiometry, beyond which As-rich glasses are composed of a pyramidal backbone containing an increasing number of 0-D As4Se4 or As4Se3 units. This transition has a direct bearing on thermal and mechanical properties that, as exemplified by glass transition temperatures (Figure 8), exhibit a clear extremum at the As2Se3 composition, consistent with its technological interest. For Ge–Se systems, selenium atoms embedded into chain or ring fragments can be clearly identified from the band assigned to Se–77Se–Se neighbors in the NMR spectra. The intensity of this line is expected to decrease from pure Se to GeSe4 stoichiometry. At this point all GeSe4 tetrahedra should be bridged by Se–Se dimers, so the NMR spectrum should exhibit a unique band assigned to Ge–77Se–Se neighbors. As collected by different authors, however, 77Se NMR spectra completely disagree with such chemist’s expectations. In particular, they reveal a large contribution of selenium-chain fragments that include at least 33% of the Se atoms. In other words, weak van der Waals bonds are abundant in the GeSe4 network, which was expected instead to be fully 3-D. This feature is the reason why the thermal, mechanical, or optical properties of this material do not have any special interest with respect to other glasses of the GexSe1−x system. In conclusion, no composition in the Ge–Se system plays a role similar to that of As2Se3 in the As–Se system. Because of the lack of sufficient

5 Chalcogenide Glasses

(a)

–100

–100

AsSe3

–50

T2CPMG dimension (Hz)

T2CPMG dimension (Hz)

As2Se3

0

50

100 1500

1000 77Se

500

0

–50

0

50

100 1500

–500

1000 77Se

chemical shift (ppm)

–100

500

–100 AsSe6

–50

T2CPMG dimension (Hz)

T2CPMG dimension (Hz)

–500

chemical shift (ppm)

AsSe4.5

0

50

100 1500

0

1000 77Se

0

500

–500

–50

0

50

100 1500

1000 77Se

chemical shift (ppm)

500

0

–500

chemical shift (ppm)

(b) 240

Tg (°C)

200 160 120 80 40 0

10

20

30 40 50 As content %

60

70

Figure 8 Structure of chalcogenide glasses as determined by solid-state NMR. (a) Bands assigned to Se–77Se–Se, As–77Se–Se and As–77Se–As neighbors, illustrating the monotonously increasing reticulation of the network with the As fraction x. (b) Variation of Tg with the dimensionality of the structural network: maximum value for the most reticulated network of As2Se3, followed by a decrease at higher As contents where molecular units appear to destroy the covalent network.

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6.5 Fluoride and Chalcogenide Glasses for Mid-infrared Optics

chemical ordering, the physical and structural properties increase monotonously until the GeSe2 composition is reached, which is not a good glass former.

6

Chalcogenide Glass Applications

6.1 General Considerations Thanks to their more floppy network, chalcogenide glasses have in general an excellent resistance to devitrification as indicated by a lack of crystallization peak in their DSC thermograms. Their glass-forming region is wide enough that glasses having a suitable viscosity– temperature relationship can be selected for particular applications. A curve with a gentle slope is suitable for molding and fibering. Bonding is strong enough to ensure a good durability with respect to water corrosion. Nevertheless parasitic absorption bands are very common. They are due to contamination by oxygen atoms, which are detected in the multiphonon region. Also Se–H absorption bands in the 4–5 μm region are difficult to eliminate. Purification operations, which require special expertise, are thus of paramount importance during synthesis. Finally, the glass transition of selenide glasses is directly connected to the dimensionality of the structural network. The richer the glass composition in reticulating elements (As or Ge), the higher the Tg. Whereas Tg is 40 C for pure Se glass, it increases to 185 C for the fully reticulated As2Se3 (Figure 8). For GASIR, which is enriched in Ge, it reaches 280 C, making this glass composition suitable for application in hazardous condition as requested by the military. On the other hand, glasses with low Tg are easy to prepare but are not suitable for applications. They have in particular too high expansion coefficients, which translates into a real risk of network relaxation even at room temperature. 6.2 Infrared Glass Molding One of the factors limiting mass production of thermalimaging systems such as night-vision devices resides in the high cost of traditional IR optics. These are made from ZnS transparent ceramics or Ge single crystals

through expensive fabrication processes that include high-precision diamond turning to obtain the final product. In this respect glasses have the obvious advantage of being directly moldable to the desired shape. Chalcogenide glasses have indeed ideal rheological properties for molding operations at moderate temperature and pressure. With easily duplicated silica molds (Figure 9), complex aspheric and diffractive optical configurations can be produced with a quality that makes direct installation of the parts in an IR camera possible. Generally speaking, the definite advantage of chalcogenide over fluoride glasses lies in their much wider transparency in the mid-IR. In fibers, this transparency extends to at least 11 μm for selenide glasses and even 16 μm for telluride glasses against only 5 μm for the best fluoride. Most applications are restricted to selenide glasses, however, because tellurides are prone to crystallize and difficult to shape [1–3]. Chalcogenide glasses belonging to the domain Ge–As/ Sb–Se have best thermomechanical properties through addition of tetravalent germanium, which causes the glass transition to rise sharply to the 250–300 C range. These glasses do not absorb light in the 3–5 and 8–12 μm optical windows where the atmosphere is transparent enough to transmit blackbody radiation. They are thus used to make lenses for IR cameras mainly designed for thermal imaging and night vision. Original developments were made for defense purposes, but the cost of these advanced optics is declining, making applications possible in many civilian areas such as assistance in night driving or firefighting, heat-loss detection for energy savings, or body thermal imaging in human and veterinary medicines. Compared with the previously used crystalline Ge lenses, optics molded from chalcogenide glasses are much cheaper thanks to the reduced cost of the starting material and the more simply implemented hot-pressing technology. Technologically optimized compositions include the GASIR 1 (standard) and GASIR 2 (including Sb instead of As) IR glass optics developed and commercialized by Umicore-IR glass (Table 1). In photonic applications, partial crystallization in the form of nanocrystals and even microcrystals can be advantageous, particularly with regard to mechanical properties. But the nucleation and growth steps of the glass ceramization process must of course be strictly Figure 9 High-precision molding of chalcogenide glasses as lenses ready to be mounted in infrared optics.

6 Chalcogenide Glass Applications

Table 1 Composition and main physical properties of fluoride and chalcogenide glasses.

Targeted market

Glass transition temperature, Tg ( C)

Optical indices

Transmission domains ( μm, as a bulk)

Young’s modulus (GPa)

Name

Composition (mol %)

ZBLAN

52 ZrF4 19 BaF2 5 LaF3 4 AlF3 20 NaF

Fiber lasers, amplifiers

260

1.5

0.3–6

58

GASIR-1

22 Ge 20 As 58 Se

Mid-IR lenses, with As

292

2.5

0.8–14

18

GASIR-2

20 Ge 15 Sb 65 Se

Mid-IR lenses, As free

260

2.6

1–14

19

TAS

20 Te 30 As 50 Se

Mid-IR spectroscopy

140

2.8

2–16

17

Figure 10 Ceramization of chalcogenide glass disks in which the controlled size of the nanoparticles nucleated yields a material opaque in the visible but still transparent in the mid-IR.

controlled to make sure that the crystal size remains smaller than the light wavelength and avoid scattering optical losses. For optics operating at around 10 μm in IR cameras, the maximum size then is 1 μm (see Figure 10).

6.3

Actually the main application of these fibers is fiber evanescent-wave spectroscopy (FEWS). As indicated by its name, this technique takes advantage of the evanescent waves produced at the surface of a fiber in which light is propagating. If a substance in physical contact with the fiber has absorption bands in the IR region, the evanescent waves are partially absorbed at each reflection, leading to a measurable reduction of the fiber transmission (see Figure 12). The collected spectra extend from about 2 to 12 μm, the transmission range of the optical fiber, where one finds a wealth of molecular absorption bands. Hence, FEWS is an efficient and easy technique to record in situ and in real time IR spectra, without any sampling, which makes it especially useful in studies of pollutants in wastewater, fermentation processes, bacterial contamination in food, bacterial biofilm spreading, and identification of tumor tissues or biological liquids (serum, blood, or plasma). Basic mono-index selenide fiber is the suitable configuration for this technique. To improve sensitivity in the sensing zone, however, the fibers need to be tapered. During the drawing process, one makes it possible by changing the strain and the temperature applied to the fiber.

Fiber Evanescent-wave Spectroscopy

Optical fibers are readily drawn from selenide glasses with a tower especially adapted for low-Tg materials. One of the most interesting compositions is the aforementioned Te2As3Se5 glass (TAS) whose fibers transmit IR light from 2 to 12 μm with minimum losses of about 0.1 dB/m within the 6–9 μm region (Figure 11). This value is obviously much higher than the very low losses of silica fibers at 1.55 μm, but is sufficient for the typical couple of meters of short-distance applications such as remote spectroscopy.

6.4

Glass for Space Exploration

Chalcogenide glass optical fibers have also been developed under very different geometries and profiles. For example, mixed Se–Te glass single-mode fibers operating in the 10 μm region are developed for space exploration. They are candidates for two space programs aiming at detecting signs of life in exoplanets orbiting around stars far in the universe, namely, the “Darwin mission” conducted by the European Space Agency and the “Terrestrial Planet Finder” sponsored by NASA in the United

731

6.5 Fluoride and Chalcogenide Glasses for Mid-infrared Optics

(a)

(b) 70

Glass thickness 1 mm

60

Attenuation (dB/m)

Transmission (%)

732

50 40 30 20 10 0

0

2

4

6

8

10

12

14

16

18

10 9 8 7 6 5 4 3 2 1 0

20

Glass fiber length 1 m

0

3

4

5

6

7

8

9

10

11

12

Wavelength (μm)

Wavelength (μm)

Figure 11 The outstanding optical properties a TAS (Te–As–Se) glass fiber in the entire mid-infrared range. (a) Transmission. (b) Attenuation. Main parasitic absorptions due to oxygen and hydrogen (see the Se–H residual band at 4.8 μm).

Figure 12 Fiber evanescent-wave spectroscopy (FEWS). (a) Absorption of the energy propagating by reflection on the surface of the fiber by the sample to be analyzed. (b) IR source and detector positioned at the input and output of the fiber. With a reduction of the fiber diameter, the number of reflections and thus the sensitivity increase.

(a) Sample

Fiber Penetration depth (b) Sensing zone FTIR spectrometer

States. Because the expected signs of life on exoplanets are the presence of water, ozone, and carbon dioxide in their atmosphere, the targeted signatures are the midIR absorption bands of these gases at 6, 9, and 15 μm for H2O, O3, and CO, respectively. For their detection by space telescopes, single-mode fibers transmitting light from 4 to 20 μm must be manufactured. Such TAS glass fibers, which are the first presenting a single propagation mode at 10 μm, have been successfully designed and fabricated by the rod-in-tube method (Figure 5). As they stand, they are suitable for detecting H2O and O3 but not CO2, which absorbs at 15 μm [1, 2]. Such research programs thus are a unique and challenging incentive for the development of glasses transmitting as far as possible in the IR. This feature is exemplified by Te-based glasses, which are the only vitreous materials having so broad an optical window from 2 to 22 μm and, thus, collecting light so far into the IR. Independently of any market-driven motivation, these space programs do show that the search for new exotic materials should not

MCT detector

depend only on expected applications to remain a goal for researchers in materials science.

7

Perspectives

Chalcogenide glasses are a wonderful playground for exploring the optoelectronic properties of amorphous semiconductors. Although their applications are currently exploiting their transmission in the mid-IR, further effort in basic and technological research should lead to more sophisticated functionalities in photonics based on a coupling of their optical and electronic properties [11]. Chalcogenide glasses, for instance, have nonlinear properties about 100 times larger than silica because the electron cloud of heavy elements is much more polarizable than that of oxygen and also because of a large amount of lone pairs in the glassy network. These effects should allow for supercontinuum generation, i.e. for large

References

secondary sources emitting in the mid-IR induced by pumping of sharp laser source. This goal has already been achieved with fluoride glass, but the emission domain is then limited by the glass transparency to 4–5 μm. At this time, a strong research activity focuses on the realization of such sources from chalcogenide glass fibers or planar guides. Chalcogenide glasses are characterized by many other fascinating light-induced phenomena such as photodarkening, photo-fluidity, photo-expansion, and photocrystallization [12, 13]. All of them are induced by photons and not by thermal agitation. In any case, the wavelength of the exciting source must be close to the band gap of the glass to create electron–hole pairs that change the nature of chemical bonds and coordination numbers, triggering local structural reorganization. These phenomena are observable in the bulk but are magnified for thin films. Of interest is also the electrical switching effect, which was originally discovered in telluride glasses as a purely semiconducting phenomena. The very first application consisted in playing with the optoelectronical properties of selenium as amorphous thin film to develop electrophotographic devices. In these applications, however, devices based on crystalline silicon or amorphous silicon thin films have prevailed [7]. Especially within the ternary Ge–Sb–Te–Te system, Te alloys can vitrify as thin layers of nm thickness but only upon ultrafast quenching. Under laser-beam irradiation they undergo readily the glass to crystal phase transformation, so they are very good candidates for optical storage. Although the digital versatile disk (DVD) technology is based on the reflectivity contrast between the vitreous and crystalline phases, it might alternatively rely on electronic conductivity in view of the differences of several orders of magnitude between the properties of the two phases. In addition, a challenging research activity is underway to form stable glasses for optics based on tellurium, in particular for IR sensing. Finally, one may note that, thanks to their easy shaping, chalcogenide glasses and glass ceramics containing Li+ as a mobile ion have also a high potential as solid-state electrolyte for the development of batteries (Chapter 9.5).

References 1 Bureau, B., Boussard-Pledel, C., Lucas, P. et al. (2009).

2 3 4

5

6 7

8

9

10

11

12

13

Forming glasses from Se and Te. Molecules 14: 4337–4350. Zhang, X.H., Bureau, B., Boussard, C. et al. (2008). Glass to see beyond the visible. Chemistry 14: 432–442. Shaw, L.B. and Aggarwal, I.D. (2002). Applications of chalcogenide glass optical fibers. C. R. Chim. 5: 873–883. Zhu, X. and Peyghambarian, N. (2010). High-power ZBLAN glass fiber lasers: review and prospects. Adv. OptoElectron.: 501956. Lucas, J. (1991). Halide glasses. In: Glasses and Amorphous Materials (ed. J. Zarzycki), 455–492. Weinheim: VCH. Feltz, A. (1993). Amorphous Inorganic Materials and Glasses. VCH: Weinheim. Elliott, S.R. (1991). Chalcogenide glasses. In: Glasses and Amorphous Materials (ed. J. Zarzycki), 493–548. Weinheim: VCH. Coupe, R., Louer, D., Lucas, J., and Leonard, A.J. (1983). X-ray scattering studies of glasses in the system ZrF4BaF2. J. Am. Ceram. Soc. 66 (7): 523–529. Saad, M. (2011). Heavy metal fluoride glass fibers and their applications, Proceedings of SPIE 8307, Passive Components and Fiber-Based Devices VIII, 83070N. doi: https://doi.org/10.1117/12.915295. Bureau, B. (2014). Structure of chalcogenide glasses characterized by NMR spectroscopy. In: Chalcogenide Glasses: Preparation, Properties and Applications (eds. J.L. Adam and X.H. Zhang), 36–57. Cambridge: Woodhead Publishing. Eggleton, B.J., Luther-Davies, B., and Richardson, K. (2011). Chalcogenide photonics. Nat. Photonics 5: 141–148. https://doi.org/10.1038/NPHOTON.2011.30. Tanaka, K. and Shimakawa, K. (2009). Chalcogenide glasses in Japan: a review on photoinduced phenomena. Phys. Status Solidi B 246: 1744–1757. Tanaka, K. (2014). Photo-induced phenomena in chalcogenide glasses. In: Chalcogenide Glasses: Preparation, Properties and Applications (eds. J.L. Adam and X.H. Zhang), 139–168. Cambridge: Woodhead Publishing.

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6.6 Optoelectronics: Active Chalcogenide Glasses Jong Heo1 and Kai Xu2 1

Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Gyeongbuk, Republic of Korea 2 State Key Laboratory of Silicate Materials for Architectures (SMART), Wuhan University of Technology, Wuhan, China

1

Introduction

From lenses and mirrors to optical fibers, glasses have traditionally been used as passive components in optics and photonics (Chapters 6.1, 6.4, and 6.5). But they can serve instead as spectral converters for active optoelectronic devices when they contain luminescent elements such as transition-metal and rare-earth ions. Among those active optoelectronic glasses, chalcogenides are unique because they are either used as matrices to host rare-earth ions or they constitute themselves luminescent sources in the form of the so-called quantum dots. Including from about 100 to 10 000 atoms in particles whose size ranges from several to tens of nanometers, these nanocrystals are incorporated in an amorphous matrix generally made up of silicate or phosphate glasses. The first aim of this chapter thus is to present the most important features of rare-earth doped chalcogenide glasses for fiber-optic amplifiers and mid-infrared laser sources. As host materials, As–S, Ge–Ga–S, or Ge– Ga–Sb–Se chalcogenide glasses enhance the emission of light by rare-earth ions. The lifetimes of the excited electronic states of these ions depend much on whether or not their decays involve the simultaneous emission of multiple phonons. Because of their low-energy phonons, chalcogenide glass matrices thus ensure extended lifetimes for the excited electronic states of their host ions by making multiphonon relaxation difficult. Hence, they have potentials in fiber-optic amplifiers and mid-infrared lasers. The effect can be enhanced through addition of alkali halides such as KBr, KI, CsBr, and CsI to Reviewers: T. Wagner, General and Inorganic Chemistry, University of Pardubice, Pardubice, Czech Republic X. H. Zhang, Institut des Sciences Chimiques, Université de Rennes I, Rennes, France

chalcogenide glasses, in which cases a halide ion environment around a rare-earth ion further reduces electron– phonon coupling and, therefore, reinforce emission properties. In the second part of the chapter, attention will be paid to quantum dots in transparent dielectric matrices. Because of quantum confinement effects, chalcogenide compounds such as CdS, CdSe, PbS, and PbSe present tunable optical properties when their size reduces to tens of nanometers. Glasses bearing quantum dots can thus cover a very wide range of wavelengths from the visible to the near-infrared, so they should give rise to universal fiber-optic amplifiers and color converters to be used in fields ranging from biomedicine (Chapter 8.4) to energy. Readers not familiar with these topics are referred to Chapter 6.5 for a detailed account on the structure and properties of chalcogenide glasses and to Chapter 6.3 for a review of spontaneous light emission in glasses.

2 Active Chalcogenide Glasses Doped with Rare-Earth Ions Chalcogenide glasses doped with rare-earth ions have been considered as potential materials for mid-infrared lasers and fiber-optic amplifiers because of a low multiphonon relaxation compared with that of oxide glasses. This process competes against the desired emission, resulting in the reduction of the emission efficiency. It is more efficient in silica-based glasses whose intrinsic phonon absorption bands extend to the mid-infrared region. In contrast, chalcogenide glasses have relatively low phonon energies (Chapter 6.5, [1]) so that they can provide enhanced emission properties of certain fluorescence that are usually quenched in oxide hosts.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume I, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

6.6 Optoelectronics: Active Chalcogenide Glasses

In a pioneering work, As2S3 glasses were used as hosts of different ions such as Nd3+, Ho3+, Er3+, and Tm3+ [2]. Successful incorporation of up to 2.0 wt % rare-earth ions was achieved. In addition, mid-infrared fluorescences were reported, for instance, at 2098 and 440 nm from the Dy3+ cascading transitions 6H13/2 6H15/2 and 6 H11/2 6H13/2, respectively. Since then many other infrared emissions have been reported from Nd3+ and Ho3+ in sulfide glasses. Much effort has also been devoted to Ge–Ga (with As)–S and Ga–La–S glasses because of the high rare-earth solubility in these matrices, good glass-forming ability, and partial transparency in the visible spectrum. Indeed, infrared emissions have been observed upon doping of these glasses with Ho3+, Tm3+, or Dy3+ [3]. Recently, emissions in the telecommunication wavelengths have also been investigated for applications toward fiber-optic amplifiers. Chalcogenide glasses doped with Pr3+ and Dy3+ ions have proven interesting thanks to an original O-band centered near 1300 nm [4, 5]. Much effort is done to develop materials for amplifiers at short band (S-band) and wavelength regions outside of the conventional band (C-band).

3

Optical Fiber Amplifiers

3.1 O-Band (1260–1360 nm) Telecommunication Window The 1300 nm emission from Dy3+ or Pr3+ ions was first observed in 1994–1995 in doped Ge25Ga5S70 (at. %) glasses that had been melt quenched [4, 5]. Although this transition of Dy3+ has a larger stimulated emission cross section than that of the 1G4 ➔ 3H5 transition in Pr3+ [5], it suffers from the short 38 μs lifetime of its upper emission level (6F11/2 6H9/2) so that its quantum efficiency of 17% is low. This lifetime is in fact approximately one tenth of that measured from the 1G4 level in Pr3+ because of the high multiphonon rate of 25 000 seconds−1 of its 6F11/ 6 6 2 H9/2 ➔ H11/2 transition in sulfide glasses. These drawbacks have been remedied via the addition to the glass matrix of small amounts of alkali halides [6],

10

Emission intensity (a.u.)

736

8

(a) (b) (c) (d) (e)

0.9[Ge0.25Ga0.10S0.65]–0.1KBr 0.9[Ge0.25Ga0.10S0.65]–0.1CsBr 0.9[Ge0.25Ga0.10S0.65]–0.1KI 0.9[Ge0.25Ga0.10S0.65]–0.1CsI Ge0.25Ga0.10S0.65

(a) 6

(b)

4 (c) 2

(d) (e)

0 1200

1400

1600

1800

Wavelength (nm)

Figure 1 Effect of the nature of the alkali halide added on the emission spectra for the 1310 nm (6F11/2, 6H9/2 ➔ 6H15/2) and 1750 nm (6H11/2 ➔ 6H15/2) transitions in Dy3+-doped chalcogenide and chalcohalide glasses [6].

which markedly enhance the intensity emitted by the transitions (6F11/2 6H9/2 6H15/2) at 1310 nm and (6H11/2 6H15/2) at 1750 nm (Figure 1). As reported early [4], the intensity of the 1310 nm emission in Ge–Ga–S glasses is considerably smaller than that centered at 1750 nm. In alkali halide-bearing chalcohalide glasses, however, the 1310 nm emission intensity clearly increases at the expense of the 1750 nm fluorescence band. The lifetime of the 6F11/2 6H9/2 level is 1320 μs, i.e. it is approximately 35 times longer than that measured from Ge–Ga–S glass with a quantum efficiency approaching 100% (Table 1).

3.2 S-Band (1460–1530 nm) Telecommunication Window Other interesting materials are thulium-doped glasses. These have been investigated for S-band (1460–1530 nm) amplifiers to make use of the 1480 nm

Table 1 Calculated (τR) and measured(τm) lifetimes and quantum efficiency (η = τm/τR) of the 1310 nm fluorescence band in 0.1 at % Dy3+-doped chalcogenide and chalcohalide glasses [6]. 0.9[Ge0.25Ga0.10S0.65] –0.1KBr

0.9[Ge0.25Ga0.10S0.65] –0.1CsBr

0.9[Ge0.25Ga0.10S0.65] –0.1KI

0.9[Ge0.25Ga0.10S0.65] –0.1CsI

Ge0.25Ga0.10S0.65

τR

840

964

326

317

205

τm

735

1320

220

193

36

η

0.88

>1

0.68

0.61

0.18

3 Optical Fiber Amplifiers

Emission intensity (a.u.)

emission (Figure 2) from the Tm3+:3H4 3H6 transition [7]. Because the lifetime of the terminal emission level (3F4) is 8–10 times longer than that of the upper level, which hampers laser action, ways have been devised to achieve the required population inversion in Tm3+ ions, such as codoping with Ho3+ or Tb3+ ions [8]. As the energy gap between the 3H4 level and the one located immediately below (3H5) is approximately 4300 cm−1, the population of the 3H4 level can alternatively be quenched through multiphonon relaxation. Glasses with low phonon energy must of course be used, namely, sulfides, fluorides [8], and tellurites [9]. But the amount of Tm3+ in glasses must be kept low, however, because the lifetime and population density of the Tm3+:3H4 level is also quenched via cross relaxation (3H4, 3H6 3F4, 3F4) when the Tm3+ concentration is high. Chalcogenide and chalcohalide glasses containing CsBr provide viable solutions to these challenges. Three emission bands at 1220, 1480, and 1820 nm (Figure 2) are due to the 3H5 3H6, 3H4 3F4, and 3F4 3H6 transitions in Tm3+, respectively. The 1480 nm emission intensity x = 0.00 x = 0.05 x = 0.10 x = 0.12

1.0

3H

4

3F 4 3F

4

3H 6

0.5 3H

5

3H 6

0.0 1000

1200

1400

1600

1800

2000

2200

Wavelength (nm)

Figure 2 Effect of the CsBr fraction x on the emission spectra of Tm3+ in (1 − x) (Ge0.25Ga0.10S0.65)•xCsBr glasses. Tm3+ concentration of 0.05 mol % in all glasses [7].

increases sharply and the lifetimes of the 3H4 level also increase rapidly from 0.23 to 1.23 ms upon CsBr addition (Table 2), whereas the measured lifetimes of the 3H4 level decrease with increasing Tm3+ concentration in all glasses. In Ge0.25Ga0.10S0.65 glasses, the 3H4 level lifetimes, for example, decrease from 233 to 93 μs as the amount of Tm3+ increases from 0.05 to 0.50 mol %. These changes are due to the increased rate of cross relaxation (Tm3+:3H4, 3H6 Tm3+:3F4, 3F4) as the average distance between Tm3+ ions decreases Therefore, the concentration of Tm3+ should be carefully optimized to prevent such large lifetime decreases.

3.3 U-Band (1625–1675 nm) Telecommunication Window Another important ion is Ho3+, which has several midinfrared and visible emissions whose intensities markedly vary with the nature of the host material [3]. The 1660 nm emission from the 5I5 5I7 transition is usually quenched in oxide matrices as a result of strong multiphonon interaction because the energy gap between the 5I5 and 5I6 levels is only 2600 cm−1. An intense 1660 nm band has nonetheless been achieved in several chalcogenide glasses [10]. A large gain is realized within the U-band window (1625–1675 nm) in sulfide glasses doped with Ho3+ and Tb3+ ions. Since gain coefficients are directly proportional to the quantum efficiency of the specific transition, selenide and chalcohalide glasses are attractive host materials thanks to their phonon vibration energies that are as low as 250 cm−1. Excitation to the 5I5 level of Ho3+ with a 910 nm laser beam results in a dominant near-infrared fluorescence at 2000 nm (5I7 5I8) and in two additional bands centered at 1660 and 1180 nm (Figure 3). With an increasing Ho3+ concentration, the intensity ratios between the latter two emissions (I1.66μm/I2.00μm) considerably decrease probably because of the cross relaxation (5I5, 5I8 5 I7, 5I7). The measured lifetime of the 5I5 level is 9.38 ms (Table 3) for a high quantum efficiency of ~99%,

Table 2 Spectroscopic properties of Tm3+ in various glasses [6].

Host glass

Ge0.25Ga0.10S0.65

0.90(Ge0.25Ga0.10S0.65) –0.10CsBr

Peak emission wavelength (nm)

1460

1480

1460

1450

FWHM (nm)

87

90

76

114

Fluoride

Tellurite

Measured lifetime (ms)

0.23

1.20

0.74–1.40

0.31

Quantum efficiency (τmeas/τrad)

0.83

0.95

0.6–1.0

0.90

Emission cross section (10−20 cm2)

0.54

0.14

0.18

0.36

σ e × τmeas (10−23 cm2 s)

0.12

0.17

0.13–0.25

0.11

737

6.6 Optoelectronics: Active Chalcogenide Glasses

(a)

Ge0.25Ge0.10S0.65 glass 0.9[Ge0.25Ge0.10S0.65]–0.1CsBr glass

0.02 mol %

107

Intensity (a.u.)

0.2 mol %

(a) 5I

6

5I

5I

5

7

8

5I

1200

1400

1600

5I

7

1800

2000

2200

0.02 mol % 3

0.2 mol %

5I

8 5F 5

5S 5F 2, 4

5I

5I

8 5S 2

5I 7

5I

5I

8

4

500

600

700

(c)

Dy3+

105

Dy3+ 104

Nd3+

(d) (e)

103 Dy3+ 102

Dy3+

101

8

T = 293 K 400

(b)

8

(b) 5F

Nd3+ Nd3+

106 Multiphonon relaxation rate (s–1)

5I

1000

Intensity (a.u.)

738

800

Wavelength (nm)

Figure 3 Effect of the Ho3+ concentration on the emission spectrum of doped 0.95GGS1–0.05CsBr glasses. (a) Near-infrared region. (b) Visible region. Excitation wavelength: 910 nm. Emission intensities normalized to the intensities of the 2000 and 660 nm bands, respectively [10].

Table 3 Measured lifetimes (τm) of the Ho3+: 5I5 level at 293 K for chalcohalide glasses doped with different concentrations of Ho3+. Radiative lifetime (τr) of the 5I5 level of 9.44 ms as calculated from Judd–Ofelt analysis. Overall energy transfer rates (WET) obtained from WET = 1/τm − 1/τr. WET (s−1)

Ho3+ concentration (mol %)

τ m (ms)

0.02

9.38

1

0.05

8.41

13

0.1

6.18

56

0.2

4.16

134

which represents clear evidence for the aforementioned small phonon energy of chalcohalide glasses.

3.4 Rates of Multiphonon Relaxation The degradation of the lifetime and quantum efficiency of excited electronic states is assigned to multiphonon relaxation. Its rate (Wmp) for energy gaps (ΔE) of 900–3500 cm−1 has been calculated from the ratios

Dy3+

100 0

1000

2000

Energy gap

3000

4000

(cm–1)

Figure 4 Dependence of multiphonon relaxation rates at room temperature on energy gap for phosphate: (a), silicate (b), germanate (c), tellurite (d), and fluoride (e) glasses. Solid lines: fits to the data calculated for Ge–Ga–S and Ge–Ga–S–CsBr glasses [7].

between the radiative and measured lifetimes. For sulfide and chalcohalide glasses (Figure 4), the ΔE and calculated Wmp data show the strongly beneficial effects of CsBr addition on both intensities and lifetimes. These data are described by the simple expression Wmp = W0exp(−αΔE) where W0 is the rate extrapolated to zero-energy gap and α a material-dependent constant. For both types of glasses, the rates for the excited levels are lower than found in oxide glasses by several orders of magnitude. The temperature dependence of the multiphonon relaxation rates from the excited states of Dy3+ has been investigated to understand quantitatively changes in the local phonon mode. Up to approximately 150 K, the rates increase only slightly with temperature (Figure 5). At higher temperatures, they increase rapidly because of the stimulated emission of thermally activated phonons. Fits to the measured rates suggest that the five-phonon relaxation process of the 375 cm−1vibration mode dominates in sulfide glass, whereas it the six-phonon process of the 245 cm−1 vibration prevails in CsBr-bearing glasses (Figure 5a). Hence, these results strongly indicate that multiphonon relaxation originates in the stretching vibration of Ga─Br bonds in these glasses.

4 Mid-Infrared Lasers

Multiphonon relaxation rate (104 S–1)

(a) 4.5

Dy3+:6F11/2 - 6H9/2(ΔE = 1870 cm–1)

4.0

Experimental data

3.5 3.0 2.5 2.0 1.5 1.0 0.5 50

100

150

200

250 300

350 400

Temperature (K)

(b) Dy3+:6F5/2(ΔE = 1490 cm–1)

Multiphonon relaxation rate ( S–1)

1400

Experimental data 1200 1000 800 600 400

4

200

4.1

0 50

100

150

200

250

300

Temperature (K)

Figure 5 Temperature dependence of multiphonon relaxation rates in Dy3+ [6]. (a) From the 6F11/2–6H9/2 level in Ge–Ga–S2 glasses. (b) From the 6F5/2 level in Ge–Ga–S2–CsBr glasses. Fits to the data made with five- or six-phonon relaxation processes.

3.5

CsBr, the first coordination shell around Tm3+ ions in contrast consists of ~5.86 (1.58) Br− ions. This result again supports that the idea Tm3+ is predominantly surrounded by Br− ions in CsBr-bearing chalcohalide glasses. Large changes in emission properties upon CsBr addition suggest considerable modification of the local environment around rare-earth ions. The backbone of Ge– Ga–S glass is composed of edge- or corner-sharing GeS4/2 and GaS4/2 tetrahedra (Chapter 6.5, [11]). In CsBr-bearing glasses, Br− ions seem to bond with Ga only. The bond energy is higher for Ga─Br than for Ge─Br whereas the bonding difference with S and Br is also larger for Ga than for Ge. Hence, Ga─Br bonds are energetically more favorable than Ge─Br so that the preferred coordination of Tm3+ ions with Br instead of S is likely related to the formation of [GaS3/2Br]− structural units in the glass matrix. In this case, [GaS3/2Br]− tetrahedral units need charge compensators, which are the rareearths ions dissolved. These ions, therefore, ensure a reduced multiphonon relaxation and local refractive index compared with CsBr-free glasses, which significantly enhance emission properties [6].

The Influence of the Local Structure

Insights onto emission mechanisms can also be gained from studies of the local structure around the relevant ions, for instance, made with extended X-ray absorption fine structure (EXAFS) spectroscopy (Chapter 2.2). For Tm3+ ions, the L3-edge EXAFS spectrum is similar in CsBr-bearing chalcohalide glasses and in crystalline TmBr3. Representing the first neighbor shells around thulium in crystals, the main peak of the radial distribution function is observed at 2.74 (1) and 2.79 (1) Å (after phase correction) in TmBr3 and Tm2S3, respectively (Figure 6). Because this peak becomes similar to that of TmBr3 upon CsBr addition, one concludes that Tm3+ ions are mainly surrounded by Br− ions in these chalcohalide glasses. From fits made to the EXAFS data, the sulfur coordination number of Tm3+ ions is in fact 6.77 (85) in Ge0.25Ga0.10S0.65 glass (Table 4). Upon addition of

Mid-Infrared Lasers General Remarks

The mid-infrared range mostly refers to 3 000–25 000 nm wavelengths. It encompasses the atmospheric windows at 3 000–5 000 nm and 8 000–12 000 nm as well as the characteristic vibrational energy bands of most of gases, liquids and solids, including intermediate-reaction species and biological tissues (Chapter 6.5). Especially in the 3000–5000 nm interval, numerous mid-infrared laser sources have thus been studied for various applications including gas sensing, spectroscopy, chemical process monitoring, and military uses [11, 12]. Realistic high-power fiber lasers (>1 W) have been designed with Ho3+- or Er3+-doped ZBLAN optical fibers (Chapter 6.5), but they are operated at wavelengths shorter than 3000 nm where few applications are found. Although lasing above this wavelength is possible with ZBLAN glasses doped with Ho3+, Er3+, and Dy3+ ions, the high-power sources needed ensure only low outputs. Construction of a compact, high-powered, and economic all-fiber mid-infrared laser system is thus difficult with conventional fluoride glass fibers. In this respect, chalcogenides are more advantageous than fluoride glasses. Not only are phonon energies lower than 350 cm−1 for the former and higher than 500 cm−1 for the latter, but chalcogenides show a wide transmission window extending to above ~10 000 μm. On the other hand, rare-earth ions such as Pr3+, Tb3+, Dy3+, Ho3+,

739

6.6 Optoelectronics: Active Chalcogenide Glasses

Tm2S3

10

TmBr3

10

Figure 6 Radial distribution functions of Tm3+ ions determined from EXAFS results for the thulium sulfide and bromide crystals and the glasses indicated. Uncorrected phase shifts.

Data Fit

Magnitude of fourier transform (a.u.)

740

5

0

5

0

1

2

3

4

5

6

0

7

0

GGS glass 10

10

5

5

0

0

1

2

1

2

3

4

5

6

4

5

6

7

GGS-CsBr glass

3

4

5

6

7

0

0

1

2

3

Distance (Å)

Table 4 Coordination numbers (N), bond distances (R), and Debye–Waller factors (σ 2) of Tm─S and Tm─Br bonds in crystals and glasses, along with the R-factors of the fits. Bond

Composition

R (Å)

N

σ 2 (Å2)

R-factor

Tm─S

Tm2S3 crystal

2.74 (1)

6.50 (fixed)

0.0115 (15)

0.013

Ge0.25Ga0.10S0.65 glass

2.77 (1)

6.77 (0.85)

0.0107 (14)

0.015

Tm─Br

TmBr3 crystal

2.79 (1)

6.00 (fixed)

0.0066 (3)

0.001

0.90 (Ge0.25Ga0.10S0.65)–0.10CsBr glass

2.79 (1)

5.86 (1.58)

0.0083 (18)

0.020

Estimated uncertainties in parentheses.

Er3+, and Tm3+ have 4f–4f transitions whose wavelengths lie in the 3000–5000 nm range. When pumped to the 6 H11/2 state, dysprosium has in particular a strong emission near 3000 nm with a three-level lasing system. It has also an emission near 4300 nm, which suffers from a high multiphonon relaxation rate in other glass hosts. Praseodymium covers a wide 3500–5500 nm range but requires a suitable host matrix because of narrow energy gaps between its |4f > states ( Cs+) [16]. However, for the M2+ cations, the M─O bond strength (related to z/r2) is high, so detachment of M2+ ions is the slow step, and, thus, diffusion will increase as z/r2 decreases (i.e. Ba2+ ≈ Sr2+ > Ca2+ > Mg2+). However, the hierarchy is also affected by the degree of polymerization (i.e. Q) since the amount of free space in the melt increases with increasing Q values. Thus for high-Q melts (e.g. molten minerals), there is plenty of space, and cation detachment is the controlling factor, whereas, in lower-Q melts (e.g. metallurgical slags), there is little space, and D is determined by cation size [16]. Metallurgical slags in general have low Q values and higher concentrations of M2+ than of M+ ions. Application of the above theory to slags is a little confusing since (i) a low Q would mean D increases with decreasing cation size but (ii) the high M2+ concentration would indicate D increases with increasing cation size. More work is needed to clarify this point.

5.4 Thermal Conductivity (K) Many silicates are considered to be semitransparent media through which heat is transferred by several mechanisms (Chapter 4.5), namely, (i) phonon or lattice conduction, (ii) convection, and (iii) radiation conduction (kR, a mechanism that involves absorption of IR radiation and reemission). This complex situation poses severe measurement problems. One can minimize convection by using transient techniques such as the laser pulse (LP) and transient hot wire (THW) methods. However, the measured thermal conductivity (keff) for silicates may contain a kR contribution of unknown magnitude. For an optically thick sample (defined as α∗d > 3 where α∗ = absorption coefficient and d = thickness of sample), kR can be calculated (kR = 16σn2T3/3α∗ where n is the (a)

refractive index and σ the Stefan–Boltzmann constant); contributions from kR rise sharply with increasing temperature owing to the T3 dependence. There is some uncertainty in measured thermal conductivity values [12] since: i) At the present time, there are large differences between the values obtained with the laser pulse (kLP) and transient hot wire (kTHW) methods for temperatures higher than 1000 K (Figure 8); reported values for liquid slags of similar composition indicate kLP ≈ 5 kTHW. At this time no values of k can be recommended for slags above 1000 K. ii) One reduces contributions to radiation conduction (kR) by (i) adding transition metal oxides (e.g. FeO, NiO), which increase the absorption coefficient of solid and liquid slags, and (ii) by promoting crystallization in solid slags since crystals, grain boundaries, and pores scatter IR radiation. The temperature dependences of the thermal conductivities obtained with the LP and THW methods are similar below 1000 K but diverge markedly at higher temperatures (Figure 8a). At a certain point (denoted the critical temperature, Tcrit ≈ 1000 K), kTHW values drop sharply with increasing temperature, whereas kLP values exhibit a gentle rise with increasing temperature up to Tliq, before showing a small decrease for the liquid. This critical temperature occurs for kTHW values at the temperature where the viscosity attains a value of 106 dPa s, i.e. midway between the softening temperature (where the sample can no longer support its own weight) and the flow point (Chapter 1.1, [12, 16]). Furthermore, measurements of kTHW indicate that values of k298 increase with both increasing polymerization (Q) and increasing cation field strength (z/r2). These findings are consistent with the view that the magnitude of the thermal conductivity (kTHW) of the solid is associated with the rigidity of the silicate network.

(b) 2

2.4 2 k (W/m/K)

1.5 k (W/m/K)

852

1

1.6 1.2 0.8

0.5 0.4 0 300

700

1100 T (K)

1500

0

0

5 10 log10 η (dPa s)

15

Figure 8 Thermal conductivity of Na2O–CaO–SiO2 slags of similar composition. (a) As a function of temperature; curve = kTHW; o = kLP. (b) As a function of log10 viscosity for four different slags; dotted lines (from left) Tflow; Tsoft, Tliq.

6 Thermodynamic Properties

6 6.1

Thermodynamic Properties Thermal Expansion Coefficient

Referring to Chapter 3.5 for details, we just remind the reader that the coefficient of volume thermal expansion is given by αV = (VT − V298)/[V298 (T − 298)] where V is the molar volume. The values of αV for liquid silicates [9] decrease with: i) Increasing polymerization (i.e. Q). ii) Increasing field strength (z/r2) of the cation. The above factors also affect the thermal expansion of the solid. Values of αl and αV for both glassy and crystalline phases are similar from 298 K to Tg, but the transition from glass to supercooled liquid is accompanied by a large increase in α (α > Tg ≈ 3 α < Tg). In contrast, α values for the crystalline phase maintain a smooth relation with increasing temperature. 6.2

Density (ρ) and Molar Volume (V)

The density (ρ) and molar volume (V) are linked via ρ=

M , V

14

where M is the molecular weight of the slag and the effect of temperature on V is given by 1 + α T − 298

V T = V 298

3

15

The molar volume of a slag is slightly affected by the degree of polymerization. Reasonable estimates of the molar volumes of liquid slags can be calculated from partial molar volumes (Eq. 16) for the various slag constituents, denoted 1, 2, and 3, but a plot of XV SiO2 − X SiO2 exhibits a negative departure from linearity implying compaction in the structure. Thus polymerization results in reduction of the molar volume (or increase in density). The effect of Al2O3 on the molar volume is the reverse of that for SiO2: V = Σ XV

1

+ XV

2

+ XV

3

+…

16

Crystalline phases have higher densities than glassy slags. Crystallization of a glassy slag results in some shrinkages causing porosity in the slag. There is an increase in molar volume (ΔVfus) when crystalline slags melt, but values of ΔVfus for the supercooled liquid are much lower because of the expansion associated with the enhanced α values above the glass transition.

i) Phase diagrams for MO–SiO2 systems exhibit miscibility gaps at high SiO2 contents, the width of the gap increasing with increasing field strength of the cation (z/r2), i.e. Mg > Ca > Sr (Chapter 5.2). ii) The liquidus temperatures (Tliq) of M2O–SiO2 and MO–SiO2 systems tend to decrease with decreasing field strength of the cation. iii) The activity coefficients of SiO2 ( f ∗SiO2 ) in M2O–SiO2 and MO–SiO2 systems increase as the field strength of the cation decreases (i.e. in the hierarchy of f ∗, K2O > Na2O > Li2O > BaO > SrO > CaO > MgO). In meta-aluminous aluminosilicates (i.e. X Al2 O3 = X ΣMx O ), the order changes since f ∗SiO2 then increases as the field strength of the chargecompensating cations (i.e. in the order (Ca > Na > K) and with decreasing 2Al/(2Al + Si) ratios [8, 9]. iv) Values of the enthalpy of solution of meta-aluminous aluminosilicates in lead borate become more negative (i.e. more thermodynamically stable) as (z/r2) for the cations (doing the charge balancing) decreases (i.e. in the hierarchy K > Na > L I ≈ Ba > Sr > Ca > Mg) [17]. v) The entropy of fusion (ΔSfus) for crystalline phases increases with (i) decreasing SiO2 content and (ii) increasing field strength (z/r2) of the cation [8, 9]. vi) The heat capacity (Cp) and enthalpy (HT − H298) for crystals can be estimated in most cases to ±2% from composition-independent partial molar quantities; routines are available to estimate Cp and (HT − H298) for the supercooled liquids [9].

6.4

Sulfur and Phosphorus Capacities

Industrially, considerable effort is devoted to minimizing sulfur and phosphorus levels in molten metals because of the aforementioned deleterious effects of these elements. The concepts of S and P capacities (denoted CS and CP) have been defined to characterize the ability of a specific slag to withdraw these elements from the molten metal. These capacities are thus directly related to the partition coefficients, which for sulfur is, for instance, LS = [(% S)sl/ (% S)m]. The complication here is that the speciation of S and P must be taken into account when reactions between the molten metal and slag are considered and their equilibrium constants evaluated. In the slag, sulfur coexists as sulfide and sulfates so that one has [18, 19] 0 5S2 + O2sl− = 0 5O2 + S2sl− ,

6.3 Thermodynamics and Liquidus Temperature

K1 =

Thermodynamic properties are affected by the field strength (z/r2) of the cations present:

0 5S2 + 1 5O2 + O2sl− = 0 5O2 + SO24 − sl ,

a2S − a2O−

pO 2 p S2

17a

05

,

17b 18a

853

854

7.4 Metallurgical Slags

K2 =

a2SO−4 a2O−

pO2 p S2

05

18b

Because the oxygen activity a2O− is high, however, in a first approximation, the low sulfur activity can be assumed to be constant, a2O− = γ S, so the sulfur and sulfide capacities (Cs) simplify to [18] C s = wt

S

wt

C 2SO−4 =

05

pO 2 p S2

pO 2

,

19

SO34 − 15

p S2

20

05

0 5P2 + 1 5O2sl− = 0 75O2 + P 3sl− ,

21a

P3 − p0O75 2 , p0P25

21b

wt

0 5P2 + 1 5O2sl− + 1 25O2 = PO34 − sl , C 3PO− 4 =

wt

PO34 −

22a 22b

p1O25 p0P25 2

In practice, high S and P capacities thus are achieved with high-basicity slags.

6.5 Surface Tension (γ) and Interfacial Tension (γmsl) Surface and interfacial tensions are not bulk properties because they are affected by surfactants, which tend to occupy preferentially the surface layers of the sample; typical ones are soluble S and O in the metal phase and B2O3, K2O, CaF2 in silicates. The temperature derivative dγ/dT tends to switch gradually from a negative to a positive value with increasing SiO2 content; the crossover point is near X SiO2 > 0 5 . In metal processing, the interfacial tension (γ msl) owes its great importance to the fact that it is a major factor in slag/metal kinetics and in slag entrapment. It can be calculated from γ msl = γ m + γ sl − 2φ γ m γ sl

Property values for various slags are compared with those for minerals in Table 2. It can be seen that the viscosity increases with increasing degree of polymerization (Q). A similar comparison of the activation energy terms (BA) would show an identical trend. The principal differences between the property values of glasses and minerals and those of metallurgical slags are due to the fact that the latter have a loose structure compared with the 3-D framework of minerals.

7

Likewise [20], the analogous reactions and capacities for phosphide and phosphate capacities (C 3P − and C 3PO− 4 ) are given by

C 3P − =

6.6 Comparison of Property Values for Metallurgical and Coal Slags and Molten Minerals

05

,

23

where the interaction coefficient (φ) increases with increasing Gibbs energy of formation per mole O for the oxides present. Because surface tension tends to be three or four times higher for the metal phase than for silicate melts, it is largely controlled by the former phase and hence is sensitive to the soluble O and S contents in the metal.

Perspectives

In the past, measurements of physical properties for slags have proved useful in understanding the mechanisms causing problems in process control and product quality. That remains the case, but a new demand for slag property data is likely to emerge in the future. Over the last 30 years, mathematical modeling of processes has improved to the point that they can now give insight into the mechanisms responsible for process problems. A good example is the model of the continuous casting of steel (Figure 3), which couples fluid flow, heat transfer, and the solidification of the steel shell [19, 20]. This model has not only correctly predicted heat fluxes and the consumption of slag but also revealed the mechanisms underlying defect formation (e.g. slag entrapment) (Figure 2) and the formation of oscillation marks [20]. The model actually allows one to see into the mold even at a very high temperature of 1900 K. Mathematical modeling of processes will prove an evermore important tool in improving process control and product quality in the future. However, these models need good, reliable property values for both slag and metal phases as input data (cf. Chapter 1.7 for analogous models in glassmaking). Physical property measurements are both time consuming and costly. There is a vast range of slag compositions used in metallurgical processing, and compositions tend to vary on a daily basis. Consequently, it is unrealistic to carry out property measurements on all slags. Thus, it is necessary to develop mathematical models to calculate reliable property values from slag chemical composition data (which is available on a routine basis). This will be a major challenge for the future and will require the model to describe not only the effect of polymerization but also the various cation effects, and this, in turn, will require a reliable description of the slag structure. A final point should be noted. The continuous drive for improved process efficiency has caused the recycling of slag wastes (e.g. in cements; cf. Chapter 9.9) and energy capture from slags to become very active areas of research in recent years.

References

References 1 Motz, H., Ehrenberg, A., and Mudersbach, D. (2013). Dry

2

3

4

5 6 7 8 9

10

solidification with heat recovery of ferrous slag. Proceedings of the 3rd International Slag Valorisation Symposium, Leuven, Belgium. Leuven: KU Leuven, pp. 37–55. Feldbauer, S. and Cramb, A.W. (1995). Physical properties of mold slags that are relevant to clean steel manufacture. Proceedings of the 78th Steelmaking Conference, Nashville, TN. Warrendale, PA: ISS-AIST, pp. 655–667. Mills, K.C. and Fox, A.B. (2003). The role of mould fluxes in continuous casting – so simple yet so complex. ISIJ Int. 43: 1479–1486. Mukai, K. (1998). Marangoni flows and corrosion of refractory walls. In: Marangoni and Interfacial Phenomena in Materials Processing, vol. 692 (eds. E.D. Hondros, M. McLean and K.C. Mills), 201–212. London: Royal Society. Mysen, B.O. (1988). Structure and Properties of Silicate Melts. Amsterdam: Elsevier. Henderson, G.S., Calas, G., and Stebbins, J.F. (2006). The structure of silicate glasses and melts. Elements 2: 269–273. Henderson, G.S. (2005). The structure of silicate melts: a glass perspective. Can. Mineral. 43: 1921–1958. Mysen, B.O. and Richet, P. (2005). Silicate Glasses and Melts: Properties and Structure. Amsterdam: Elsevier. Mills, K.C., Hayashi, M., Wang, L.J., and Watanabe, T. (2014). The structure and properties of silicate slags. In: Treatise on Metallurgy, vol. 1 (ed. S. Seetharaman), 149– 286. Amsterdam: Elsevier. Gaye, H. and Welfinger, J. (1984). Modelling of the thermodynamic properties of complex metallurgical slags. In: 2nd International Symposium on Metallurgical

11

12

13

14

15

16

17

18

19

20

Slags and Glasses (eds. D. Gaskell and H.A. Fine), 357– 375. Warrendale, PA: Metallurgical Society. Zhang, G.H., Chou, K.C., and Mills, K.C. (2014). A structurally based viscosity model for oxide melts. Metal. Mater. Trans. B 45B: 698–706. Mills, K.C., Yuan, L., Li, Z., and Zhang, G.H. (2013). Estimating the thermal and electrical conductivities of slags. High Temp.-High Press. 42: 237–256. Barati, M. and Coley, K.S. (2006). Electrical and electronic conductivity of CaO-SiO2-FeOx at various oxygen potentials. Metal. Mater. Trans. B 37: 51–60. Angell, C.A., Ngal, K.L., McKenna, G.B. et al. (2000). Relaxation in glassforming liquids and amorphous solids. J. Appl. Phys. 88: 3113–3157. Zhang, Y., Ni, H.W., and Chen, Y. (2010). Diffusion data in silicate melts. Rev. Mineral. Geochem. 73: 311–408. Mills, K.C., Yuan, L., Li, Z. et al. (2012). A review of the factors affecting the thermophysical properties of molten slags. High Temp. Mater. Proc. 31: 301–322. Roy, B.N. and Navrotsky, A. (1984). Thermochemistry of charge-coupled substitutions in silicate glasses: the systems M1/nn+AlO2-SiO2 (M = Li, Na, K, Rb, Cs, mg, Ca, Sr, Ba, Pb). J. Amer. Ceram. Soc. 67: 606–610. Gaye, H. and Lehmann, J. (1995). Chapter 6a, Sulphide capacities. In: Slag Atlas. Dusseldorf: Verlag Stahleisen GmbH. Kirner, D. and Janke, D. (1995). Chapter 6b, Phosphate and phosphide capacities. In: Slag Atlas. Dusseldorf: Verlag Stahleisen GmbH. Ramirez-Lopez, P.E., Mills, K.C., Lee, P.D., and Santillana, B. (2012). A unified mechanism for the formation of oscillation marks. Metal. Mater. Trans. B 43: 109–122.

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7.5 Water Glass Hans Roggendorf Martin-Luther-Universität Halle-Wittenberg, Institute of Physics, Halle (Saale), Germany

1

Introduction

By water glass one designates not only alkali-rich silicate glasses but also the liquid phases obtained either when these glasses are dissolved into water or when a silica phase is dissolved in alkaline lyes. They are also called “soluble silicates.” Water glass has in fact a long history as it was first mentioned by the Flemish chemist and physician Joan Baptista van Helmont who reported in 1648 in his Ortus medicinae [1] that “if one melts a fine powder of glass with a large amount of alkali and exposes it in a humid place, one will presently find that all the glass dissolves into a water” (see Chapter 10.11). But a longstanding practical interest in this material was raised much later in the 1820s when the Bavarian chemist and mineralogist Johann Nepomuk Fuchs (1774–1856) described applications of materials he termed himself water glasses such as “protectant against the rapid propagation of fire in theaters, as binder and paint films” [2]. His potassium silicate glasses contained more silica than van Helmont’s and thus had the interest of being stable against moist atmospheres but still soluble in water. To optimize many more practical applications, the chemical composition of water glass has since then been varied not only through changes in the nature and concentration of the alkali cation but also through the incorporation of ammonium ions. As a result, this silicate family has become one of the most important inorganic chemicals, being added to detergents, cements, paints, adhesives, and binders, serving in water treatment and mineral ore flotation, or used as a starting product in the fabrication of ceramics or of specialty minerals such

as zeolites. Water glass provides concentrated, reactive silica in a liquid phase with a buffered alkalinity ensured by the weakly bonded alkalis. Hence, it has the great advantage of offering the versatility of silicate materials in the context of aqueous chemistry. The composition of water glass is most simply characterized by the SiO2/M2O ratio (M = Li, Na, K) on either a mol (Rm) or a weight (Rw) basis. (Note that Rm = Rw FM, where the F factors are the ratios of the molar masses of the relevant alkali oxide and silica, namely, FNa = 1.032, FK = 1.566, and FLi = 0.497). In 1998 the world production was estimated to lie between 3 × 106 and 4 × 106 tons, the majority in the form of sodium water glass. More recent data for 2010 claim the production of soluble silicates with a content of 740 000 tons of SiO2 in Western Europe alone. In this chapter we will thus review the production, structure, basic physical and chemical properties, and uses of these basic materials. As a complement, we refer the reader to a review on older literature by Vail [3] and to more recent papers by Iler [4] and Falcone [5]. Vail covered the whole range from science via technology to application available at his time, Iler treated soluble silicates in his outstanding book on silica chemistry from a more fundamental side, and Falcone took up new developments with a focus on structure. As for production processes, additional basic information can be found in handbooks on technical chemistry (e.g. [5]).

2

Fabrication of Water Glass

2.1 Process I: Glass Synthesis with Subsequent Dissolution in Water Reviewers: James S. Falcone, Institute of Chemistry, West Chester University Pennsylvania, PA, USA Ulrich Schubert, Institute of Materials Chemistry, Vienna University of Technology, Wien, Austria

The most important fabrication process of liquid water glasses is melting of raw materials to produce alkali silicate glasses, which are subsequently dissolved in water.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume II, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

858

7.5 Water Glass

Silica

Alkaline carbonates Melting

Water

Alkaline lye

Figure 1 Process scheme for the productions of water glass and related materials.

Direct dissolution Glass lumps

Glass dissolution Liquid water glass Grinding and sizing

Anhydrous glass powders

Drying, crystallization

Drying

Amorphous alkaline silicates (20 wt % H2O)

Crystalline alkaline silicates

The majority of the sodium water glasses and nearly all potassium water glasses are made by this process. As a matter of fact, the chemical durability of alkali silicate glasses with the same stoichiometry increases so much in the order K 8), however, the model predicts N4 values of 100%, which would mean that all boron atoms are in fourfold coordination. But actual 11B NMR-derived N4 values are always lower than 100% because these high modifier (Na2O) concentrations eventually lead to the creation of NBO on silicon atoms instead of additional B(IV) groups. The competing role of charge-balancing cation and network modifier exhibited by Na+ is even more complicated for other modifying oxides, especially for the alkaline earth cations, for which multinuclear NMR data have shown that cation field strength dictates the extent of B(IV) charge balancing by the modifier [21, 22]. As a result of these changes in network structure with different modifiers, the physical properties of such borosilicate glasses are also impacted, with fewer B(IV) groups and a larger number of NBO leading to network depolymerization, a drop in Tg, and a negative correlation between CTE and boron speciation. Although new models (a)

4.2 Silicon–Boron Mixing The manner in which network-forming silicon and boron mix can also be investigated by 11B MAS NMR spectroscopy. For glasses with similar amounts of Na2O (Figure 6), the impact of SiO2 : B2O3 ratio is reflected by the measured N4 fraction. As predicted by structural models (e.g. Figure 4), the coordination of boron is mainly determined by the R2O : B2O3 and SiO2 : B2O3 ratios. Compositions with high K values, such as that of Figure 6b, allow for much larger N4 values caused by mixing of the silicate and borate polyhedra, driven perhaps by relaxation of B(IV) avoidance (i.e. avoidance of B(IV)–O–B(IV) linkages) that is important for glasses containing higher amounts of B2O3 (e.g. lower K values). Mixing of silicate and borate polyhedra is not necessarily ideal, however, so some B(IV)–O–B linkages are evident from the appearance of a second B(IV) resonance in these glasses. One resonance at approximately −1.4 ppm (Figure 6b) is assigned to B(IV) with four silicon next-nearest neighbors (NNN). Owing to the low SiO2 content of this particular glass, some of the B(IV) are surrounded by fewer Si NNN, the difference being at least one B NNN. The peak at +0.2 ppm in Figure 6b is B(IV) with 3Si and 1B NNN. As shown for Pyrex in Figure 2, multiple B(IV) peaks resulting from ordering between boron and silicon are important and common features for borosilicate glasses. The relative population, Figure 6 11B MAS NMR spectra for (a) a boron-rich glass with composition 17 Na2O 60 B2O3 23 SiO2 measured at 11.7 T [20] and (b) a silica-rich glass (20.4 Na2O 21.7 B2O3 57.8 SiO2) measured at 16.4 T [24]. Solid lines are the experimental NMR data, and dashed lines represent simulations of the various B(III) and B(IV) components, as labeled.

B(IV)

(b)

B(IV)

B(III) B(III)

B(IV) peaks

“ring” B(III) peak “non-ring” B(III) peak 20 11B

10 0 NMR shift (ppm)

–10

20

10 11B

0

NMR shift (ppm)

–10

4 Structural Aspects

or extent of mixing between B and Si, is very sensitive to glass composition because B(IV)(4Si) is predominant in silica-rich glasses, in contrast to glasses having higher concentrations of B2O3, where more B(IV)–O–B linkages (e.g. B(IV)(3Si,1B) units) are common, as shown by the changes in B(IV) peak position with varying K in Figure 5. From a practical standpoint, mixing of B3+ and Si4+ in the anionic framework, made possible by association of boron with charge-compensating cations such as alkali ions, has important consequences. When added to silicates, B2O3 causes large freezing point depressions because of its very low melting temperature of 712 K, an effect that is still enhanced by the entropy of Si–B mixing. This is the reason why homogeneous glasses are obtained at lower temperatures for borosilicates than for silicates. The effect is similar to that yielded by addition of alkali oxides to silicates, but it has the important advantage of not affecting significantly the polymerization state of the material and, thus, not degrading its stability. 4.3

Superstructural Units

Another widely debated topic is the occurrence of superstructural units in the network. Six-membered rings composed of B(III) and B(IV) polyhedra (and their associated bridging oxygens) are ubiquitous in alkali borate glasses, as shown by NMR and Raman spectroscopies or other structural probes. In borosilicate glasses, some of these ring structures are thought to form through incorporation of both silicate and borate polyhedra, as in the minerals danburite [CaB2(SiO4)2] and reedmergnerite [NaBSi3O8]. As characterized by such well-defined superstructural geometries, this type of intermediaterange structure is apparently unique to borate and borosilicate glass families. Its identification is particularly effective with 11B NMR and Raman spectroscopies. As seen for Pyrex (Figure 2) and other borosilicate glasses (e.g. Figure 6), the 11B MAS NMR spectra contain considerably more information than simply on boron coordination numbers. As discussed for B(IV) peaks, the presence of multiple B(III) resonances is reflective of multiple structural environments involving BO3 polyhedra. This feature has been studied not only with 11B MAS NMR but also with 11B dynamic-angle spinning (DAS), double-rotation (DOR), and multiple-quantum magic-angle spinning (MQMAS) NMR spectroscopy. The fits made to the spectra (not shown) generally yield two distinct B(III) species having similar quadrupolar coupling parameters, but differing significantly in their isotropic chemical shifts. This chemical shielding difference of 3–4 ppm was first measured in glassy B2O3 and attributed to boroxol ring and non-ring B(III) units [25]. The multiple B(III) peaks detected in 11B NMR

experiments, like in the examples herein, have been consistently interpreted in terms of ring and non-ring B(III) species: the ring peak represents B(III) units in boroxol and modified rings (e.g. tetraborate, triborate, danburite, etc.), whereas the non-ring B(III) environment includes those of BO3 polyhedra that exist outside of these welldefined superstructural units. Over broad compositional ranges, the presence of ringtype B(III) indicates that the borosilicate glass network is characterized by a surprising amount of short- and intermediate-range order. These features have important implications for network topology and the nature of the network-forming species that control the physical and mechanical properties of the glass. One of the ongoing challenges in this field is the identification and absolute confirmation of different network polyhedra and ring structures in highly modified borosilicate glasses. For those glasses containing NBO, especially when these are bonded to boron atoms, the complexity in their NMR and vibrational spectra is significantly increased. In addition to the possibility of ring and non-ring B(III) units, as well as of multiple types of B(IV) polyhedra based on mixing between B and Si units, the presence of metaborate units (B(III) with a single NBO) would appear as yet another B(III) resonance in the 11B NMR data. The combination of multiple spectroscopies, and possibly new advances in NMR methodology, should yield better and more precise descriptions of these complex glass structures. 4.4

From NMR to Integrated Studies

To begin with oxygen, other nuclei amenable to NMR experiments are incorporated in borosilicate glasses. In particular, 17O NMR has been used to understand the network connectivity between borate and silicate groups, lending in this way support to the characterization of phase separation in binary B2O3–SiO2 glasses and to a detailed understanding of topological disorder and phase separation in multicomponent borosilicates [14, 26]. Additional NMR studies have dealt with 23Na, 6Li, 7Li, 133 Cs, 43Ca, and 25Mg modifier cations, allowing researchers to understand the local environment of these components, as well as the impact of such modifiers on the network structure and properties of borosilicates of academic or commercial interest. In this respect, Na+ and Li+ are two modifiers of significant interest in model systems and in the development of better structure– property relationships that are important in commercial glasses utilizing ion exchange for mechanical toughening (Chapter 3.12). Although NMR has become one of the mainstream characterization tools for network structure, other spectroscopies and computational methodologies have been

873

874

7.6 Borosilicate Glasses

extensively developed to learn about the physics and chemistry of borosilicate glasses. Vibrational spectroscopies, for example, continue to play a key role in understanding the network structure of borosilicate glasses. Starting with the seminal work of Konijnendijk [27], Raman spectroscopy has been instrumental in developing and contrasting structural models for borosilicates with those designed for borate and silicate glass families, for instance, with respect to danburite and reedmergnerite superstructural units [28, 29]. Whereas knowledge of the structure of borosilicate glasses has been significantly advanced over the past 50+ years, a precise description of short- and intermediate-range network structure, including mixing of the two glass-forming oxides, continues to be a challenge in both experimental and theoretical approaches. Some of the more recent advances in this arena involve a combination of experimental and modeling studies whereby empirical models are for instance complemented by theoretical calculations of NMR spectra or molecular dynamics (MD) simulations [30]. Purely computational approaches also are common and have yielded potentially important insight into these issues. As advanced during the last past decades, MD simulations have been validated in terms of reproducing boron NMR data (i.e. N4 values) and other structural details obtained by spectroscopic investigations (Chapter 2.8).

This transformation has of course a large impact on glass properties. Current understanding and related empirical models of boroaluminosilicate glasses often consider simplified interactions between modifiers and network formers by assuming that Al2O3 is preferentially stabilized in AlO4 units, with any “excess” modifier then made available for other structural changes. This assumption appears to hold generally for a great many systems, but may not be exact, so models based on this view would also be inaccurate. Recent work on boroaluminosilicates conducted by several prominent research groups does indeed show that all Al is not necessarily in fourfold coordination in charge-balanced compositions. The presence of a nonzero AlO5 population, which may also be sensitive to fictive temperature and compression of the glass, suggests a more complicated interaction between network modifiers and formers in these multicomponent borosilicate glasses. This topic thus continues to be an active area of research. Advances in both experimental and computational study will result in a better structural understanding of glass formation and properties, perhaps also leading to additional commercial and scientific opportunities.

5 Temperature and Pressure Variations of Network Structure 4.5 The Impact of Al2O3 In addition to these studies on relatively simple glasses, much experimental work has been devoted to the effects of additional glass formers on structure and properties. As a crucial component of new products, Al2O3 has been extensively investigated because the presence of such a third glass former complicates the interactions between modifiers and both B2O3 and SiO2. The ratio of modifier to Al2O3 in these boroaluminosilicates actually controls many properties, including density and Tg. These features and the concomitant changes in the glass structure have been elucidated primary by means of multinuclear NMR techniques [31, 32]. In fact, addition of Al2O3 also requires chargecompensating cations to stabilize Al in tetrahedral coordination, which lowers the fraction of network-modifying cations. As a consequence, the NBO content decreases and, if the glass is highly modified, also reduces the N4 fraction. The resulting glass network may exhibit more connectivity, in particular if Al2O3 addition reduces or eliminates NBO on both boron and silicon. In glasses containing few modifiers, for example, below the Dell et al. critical R∗ value [19], then boron is typically converted from tetrahedral units back to trigonal species.

5.1 Temperature vs. Entropy With rising temperature, the structure of a melt necessarily varies so as to ensure an increase in configurational entropy. In borosilicates, changes in boron speciation are a simple way to fulfill at least partially this requirement. Particularly in highly modified glasses [21], one can actually shift markedly the equilibrium between B(IV) and NBOs by varying the quenching rate to freeze the short-range structure at different fictive temperatures (Figure 7). Although the largest impact of Tf is on boron speciation, a modification of the line shape apparent on closer examination of B(IV) peaks (Figure 7) indicates more complicated changes in the network structure. The quenched glass has at least two types of B(IV) that are not well resolved in the 11.7 T spectra but are nonetheless indicated by the noticeable asymmetry of the B(IV) peak. Annealing induces a slight increase of the relative intensity at the upfield (more negative shift) side of the peak, which one would assign to B(IV) surrounded by 4 Si NNN. If this intensity change is meaningful (e.g. reproducible and outside of the measurement uncertainty), then such data indicate that a change in thermal history for this glass causes an overall increase in N4,

5 Temperature and Pressure Variations of Network Structure

been discussed in the context of the structural underpinnings of melt viscosity [34].

B(IV)

5.2 Quenched Annealed B(III) 25

20

15 11B

10

5

0

–5

NMR frequency (ppm)

Figure 7 Increase in the B(IV) fraction in a sodium borosilicate glass upon annealing of a quenched glass, shown by a comparison of 11B MAS NMR spectra (11.7 T) [33].

much of that change not affecting equally all B(IV), but mainly those surrounded by 4 Si. A closely related area of significant interest, but rather challenging to study with traditional characterization tools like NMR, is the structure of borosilicate melts and supercooled liquids. Most of the commercially relevant borosilicate glasses are processed from melts, so it stands to reason that a deeper knowledge of glassmelt properties and structure would be immensely beneficial. Some in situ methodologies do exist and have been used to characterize glassmelts, but even high-temperature NMR and other spectroscopies are difficult to implement and are generally restricted to specialized laboratories. One area of growing utility and popularity relates to optical interrogation of glassmelts, involving small furnaces, laser heating, and laser heating with aerodynamic levitation. These methods provide a means by which to use Raman and Brillouin light scattering, neutron diffraction, and high-energy X-ray scattering to study glassmelt chemistry and physics (Chapter 2.2). In a recent neutron diffraction examination of boron coordination in borosilicate melts, dramatic decreases in N4 on melting two borosilicate glasses were, for instance, observed, such structural insight having then Figure 8 Effects of permanent densification on the boron speciation of two borosilicate glasses, as shown by the differences between the 11B MAS NMR spectra (16.4 T) recorded for the as-made glasses (solid curves) and compressed samples at Tg and 1 GPa (dashed curves). (a) 20.4 Na2O 21.7 B2O3 57.8 SiO2 [24]. (b) 15.0 Na2O 10.1 CaO 16.5 B2O3 58.4 SiO2 [36].

(a)

Pressure vs. Volume

With increasing pressure, the structure of a melt necessarily becomes more compact to ensure the thermodynamically required density increase. For obvious reasons, the effects have been well documented for glasses of geochemical interest whose network structure has indeed been found sensitive to pressure. Hence, it should not come as a surprise that these investigations have recently been extended to borosilicate glasses. One particularly recent study, using NMR to understand changes in glass structure, but, more importantly, to correlate pressure and short-range structure with glass properties, indicates that certain changes with modest pressure may be irreversible [35]. To illustrate better the changes in glass structure with pressure, 11B MAS NMR spectra have been obtained on two borosilicate glasses before and after high-temperature compression at Tg and 1 GPa. In both glasses (Figure 8), the impact of compression on boron speciation is an overall increase in N4, much like the changes in structure with thermal history alone. In addition to N4 variations, a preferential change in the type of B(IV) is indicated for the sodium borosilicate glass (Figure 8a), as found for similar glasses having different thermal histories. Here, the peaks assigned to B(IV) with 3 Si, 1 B, and 4 Si NNN, B(IV)(3Si1B), and B(IV)(4Si), respectively, change differently upon compression, with a larger increase in the B(IV)(4Si) concentration. Closer examination of the B(III) region of these spectra gives additional insight into related changes in ring and nonring B(III) peaks with compression – something that is currently the subject of a combined NMR and Raman study of borosilicate glasses under permanent densification. One of the other structural responses to this hightemperature compression relates to the modifier environment. As mentioned earlier, NMR studies of 23Na (or (b)

B(IV)

B(IV)

B(III)

B(III)

20

10 11B

0

NMR shift (ppm)

–10

20

10 11B

0

NMR shift (ppm)

–10

875

876

7.6 Borosilicate Glasses

other modifiers) allow one to follow changes in the local environment of these cations as glasses are densified. Many NMR studies have shown a clear increase in chemical shift of 23Na for glasses densified by compression either at room or at elevated temperatures. Most of these data have been interpreted as a general reduction of the average Na─O distance in the densified glasses and not as a change in the coordination number of the alkali. Further understanding of both the glass network and the modifier environments, using advanced experimental and computational methodologies, is necessary to describe fully densification of borosilicates under high pressure and possibly during mechanical damage induced by nano- and micro-indentation.

6

of new NMR and transmission electron microscopy (TEM) capabilities have increased our ability to discern phase separation in glasses, which either account for or aid in understanding associated physical properties, as well as serve to understand better nucleation and crystallization in glasses. Finally, many challenging problems in glass science will benefit from the study of model borosilicate systems. A deeper understanding of the glass transition, intermediate-range structure, phase separation and crystallization processes, impact of temperature and pressure on glass structure and properties, etc. is continually achieved through work on borosilicate glasses. Progress in new and advanced simulation approaches and experimental capabilities will also lead to an improved understanding of these important aspects of glass science.

Perspectives

In spite of almost two centuries of study, borosilicate glasses remain intriguing materials whose incredible commercial success justifies the widespread research efforts made to characterize them better and improve their structure–property relationships. Accurate determinations of glass structure across several length scales (short and intermediate range) will continue to drive new applications as it will be difficult to optimize compositional and processing variables, including temperature and pressure, without this information. The next wave of innovation is actually underway: it is the development of ultra-strong glasses through better characterization of bulk and surface structure and properties [37]. Of particular importance in this respect are the details of flaw generation, crack growth, and overall glass durability and, in turn, the impact of these phenomena on glass structure and properties [38]. Applications of borosilicate glasses are also growing into new scientific and commercial areas, for example, in glass/polymer laminates or in biological uses. Hence, the surfaces of these materials become critical in their applications, driving the need for enhanced understanding and control of surface chemistry and properties, as well as of glass dissolution mechanisms. In all these respects theoretical simulations will also be valuable. The interatomic potentials needed in MD simulations have thus been improved to yield correct structures and properties over wide ranges of composition. But the main difficulties remaining to be overcome concern the temperature sensitivity of cation coordination and the unrealistically high quench rates currently possible. Advances in experimental and computational methodologies to understand and control better phase separation in borosilicate glasses may also lead to new and improved compositions. Even today, the development

Acknowledgments This contribution has been influenced greatly by a large community of glass and characterization scientists at Corning Incorporated. In particular, collaborations with J. Mauro (Corning, Pennsylvania State University), M. Smedskjaer and Y. Yue (Aalborg University), S. Sen (University of California at Davis), and R. Dieckmann (Cornell University) have resulted in new and exciting understanding of borosilicate glasses. Thanks are also due to H. Yamasaki (NEG) for data communication.

References 1 Faraday, M. (1859). On the manufacture of glass for

2

3

4 5

6

optical purposes. In: Experimental Researches in Chemistry and Physics, 231–291. London: Taylor and Francis. Hovestadt, H. Jenaer Glas und seine Verwendung in Wissenschaft und Technik (Jena: Fischer) (trans. Everett, J.D. and Everett, A.) [Jena Glass and its Scientific and Industrial Applications] (London: MacMillan and Co., 1902). Weyl, W.A. (1948). Boron oxide – its chemistry and role in glass technology, parts I and II. Glass Industry 29 131–136, 156, 201–205, 228. Abe, T. (1952). Borosilicate glasses. J. Am. Ceram. Soc. 35: 284–299. Kiaulehn, W. (1959). Der Zug der 41 Glasmacher or The Odyssey of 41 Glassmakers. Jena: Jenaer Glaswerk Schott & Genossen. Dyer, D. and Gross, D. (2001). The Generations of Corning: The Life and Times of a Global Corporation. New York: Oxford University Press.

References

7 Smedskjaer, M.M., Youngman, R.E., and Mauro, J.C.

8

9

10 11

12

13

14

15

16

17

18

19

20

21

(2014). Principles of Pyrex® glass chemistry: structureproperty relationships. Appl. Phys. A 116: 491–504. Wallenberger, F.T. (2010). Commercial and experimental glass fibers. In: Fiberglass and Glass Technology (eds. F.T. Wallenberger and P.A. Bingham), 3–90. New York: Springer. Gin, S., Abdelouas, A., Criscenti, L.J. et al. (2013). An international initiative on long-term behavior of highlevel nuclear waste glass. Mater. Today 16: 243–248. Schulze, G. (1913). Versuche über die Diffusion von Silber in Glas. Ann. Phys. 40: 335–367. Kistler, S.S. (1962). Stresses in glass produced by nonuniform exchange of monovalent ions. J. Am. Ceram. Soc. 45: 59–68. Acloque, P. and Tochon, J. (1962). Measurement of mechanical resistance of glass after reinforcement. In: Symposium sur la résistance mécanique du verre et les moyens de l’améliorer [Colloquium on Mechanical Strength of Glass and Means of Improving it], 687–704. Charleroi: Union Scientifique Continentale du Verre. Charles, R.J. and Wagstaff, F.E. (1968). Metastable immiscibility in the B2O3-SiO2 system. J. Am. Ceram. Soc. 51: 16–20. Lee, S.K., Musgrave, C.B., Zhao, P., and Stebbins, J.F. (2001). Topological disorder and reactivity of borosilicate glasses: quantum chemical calculations and 17O and 11B NMR study. J. Phys. Chem. B 105: 12583–12595. van Wüllen, L. and Schwering, G. (2002). 11B-MQMAS and 29Si-{11B} double-resonance NMR studies on the structure of binary B2O3-SiO2 glasses. Solid State Nucl. Magn. Reson. 21: 134–144. Morey, G.W. and Ingerson, E. (1937). Melting of danburite; study of liquid immiscibility in the system CaO-B2O3-SiO2. Am. Miner. 22: 37–48. Richet, P., Atake, T., and Yamashita, I. (2006). Boroxol rings in SiO2-B2O3 glasses: influence on low-temperature thermal properties. J. Non-Cryst. Solids 352: 3854–3858. Sorarù, G.D., Dallabona, N., Gervais, C., and Babonneau, F. (1999). Organically modified SiO2-B2O3 gels displaying a high content of borosiloxane (=B-O-Si≡) bonds. Chem. Mater. 11: 910–919. Dell, W.J., Bray, P.J., and Xiao, S.Z. (1983). 11B NMR studies and structural modeling of Na2O-B2O3-SiO2 glasses of high soda content. J. Non-Cryst. Solids 58: 1–16. Wu, X., Youngman, R.E., and Dieckmann, R. (2013). Sodium trace diffusion and 11B NMR study of glasses of the type (Na2O)0.17(B2O3)x(SiO2)0.83-x. J. Non-Cryst. Solids 378: 168–176. Wu, J. and Stebbins, J.F. (2013). Temperature and modifier cation field strength effects on

22

23

24

25

26

27 28

29

30

31

32

33

34

35

aluminoborosilicate glass network structure. J. NonCryst. Solids 362: 73–81. Wu, J. and Stebbins, J.F. (2009). Effects of cation field strength on the structure of aluminoborosilicate glasses: high-resolution 11B, 27Al and 23Na MAS NMR. J. NonCryst. Solids 355: 556–562. Smedskjaer, M.M., Mauro, J.C., Youngman, R.E. et al. (2011). Topological principles of borosilicate glass chemistry. J. Phys. Chem. B 115: 12930–12946. Østergaard, M.B., Youngman, R.E., Svenson, M.N. et al. (2015). Temperature-dependent densification of sodium borosilicate glass. RSC Adv. 5: 78845. Youngman, R.E. and Zwanziger, J.W. (1994). Multiple boron sites in borate glass detected with dynamic angle spinning nuclear magnetic resonance. J. Non-Cryst. Solids 168: 293–297. Du, L.-S. and Stebbins, J.F. (2003). Solid-state NMR study of metastable immiscibility in alkali borosilicate glasses. J. Non-Cryst. Solids 315: 239–255. Konijnendijk, W.L. (1975). The Structure of Borosilicate Glasses. Eindhoven: Philips Research Laboratories. Bunker, B.C., Tallant, D.R., Kirkpatrick, R.J., and Turner, G.L. (1990). Multinuclear nuclear magnetic resonance and Raman investigation of sodium borosilicate glass structures. Phys. Chem. Glasses 31: 30–41. Manara, D., Grandjean, A., and Neuville, D.R. (2009). Advances in understanding the structure of borosilicate glasses: a Raman spectroscopy study. Am. Miner. 94: 777–784. Charpentier, T., Menziani, M.C., and Pedone, A. (2013). Computational simulations of solid state NMR spectra: a new era in structure determination of oxide glasses. RSC Adv. 3: 10550–10578. Zheng, Q.J., Youngman, R.E., Hogue, C.L. et al. (2012). Structure of boroaluminosilicate glasses: impact of [Al2O3]/[SiO2] ratio on the structural role of sodium. Phys. Rev. B 86: 054203. Lacomb, M., Rice, D., and Stebbins, J.F. (2016). Network oxygen sites in calcium aluminoborosilicate glasses: results from 17O{27Al} and 17O{11B} double resonance NMR. J. Non-Cryst. Solids 447: 248–254. Sen, S., Topping, T., Yu, P., and Youngman, R.E. (2007). Atomic-scale understanding of structural relaxation in simple and complex borosilicate glasses. Phys. Rev. B 75: 094203. Michel, F., Cormier, L., Lombard, P. et al. (2013). Mechanisms of boron coordination change between borosilicate glasses and melts. J. Non-Cryst. Solids 379: 169–176. Smedskjaer, M.M., Youngman, R.E., Striepe, S. et al. (2014). Irreversibility of pressure induced boron speciation change in glass. Sci. Rep. 4: 3770.

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7.6 Borosilicate Glasses

36 Svenson, M.N., Bechgaard, T.K., Fuglsang, S.D. et al.

(2014). Composition-structure-property relations of compressed borosilicate glasses. Phys. Rev. Appl. 2: 024006. 37 Wondraczek, L., Mauro, J.C., Eckert, J. et al. (2011). Towards ultrastrong glasses. Adv. Mater. 23: 4578–4586.

38 Winterstein-Beckmann, A., Möncke, D., Palles, D. et al.

(2014). A Raman-spectroscopic study of indentationinduced structural changes in technical alkaliborosilicate glasses with varying silicate network connectivity. J. Non-Cryst. Solids 405: 196–206.

879

7.7 Glass for Pharmaceutical Use Daniele Zuccato1 and Emanuel Guadagnino2 1 2

Stevanato Group, Piombino Dese, Italy European Pharmacopeia Expert, Italian Delegate, Venezia, Italy

1

Introduction

One of its properties that originally made glass a highly prized material was its inertness with respect to liquids and other substances that it could contain (Chapter 10.2). The small vials for perfumes and unguents made as soon as bulk glass was produced in the late Bronze Age are a clear testimony of this ancient recognition. When it became common in the eighteenth century, the use of glass that for the storage of dry and liquid pharmaceuticals was thus the continuation of an extremely old tradition. Even though it has since then been replaced by plastics or other materials in a great many applications, glass has kept fundamental advantages in terms of chemical inertness, lack of porosity, shapability, transparency, coloration, or possibility of high-temperature sterilization. As a result, the use of glass in pharmacy keeps increasing, especially for new applications such as prefilled syringes, which are the primary way for delivering new high-technology drugs. The purpose of this chapter thus is to review the main features relevant to the use of glass in pharmacy. The pharmacopeial requirements for containers are first considered and a definition of the most common glass types provided. The current glass-tubing production processes are then presented, as well as the conversion steps to obtain containers from glass tubes. Next the factors affecting the mechanical resistance of the containers are briefly examined with a particular focus on the effects of glass forming and handling on the packaging performances. The chemical resistance of glass has important implications for the storage of pharmaceuticals. Hence, Reviewers: P. Mascheroni, Helmholtz Center for Infection Research, Braunschweig, Germany F. Nicoletti, International Commission on Glass and Stevanato Group, Piombino Dese, Italy

possibly significant interactions between the container internal surface and the enclosed therapeutic agents are reviewed, with some considerations from the perspective of glass manufacturers. An account on the current internal and external treatments to improve the chemical and mechanical performances of the containers is provided. Finally, the chapter will examine some high-technology perspectives on the future of glass containers for parenteral uses (i.e. subcutaneous or intravenous injections), focusing on innovative solutions aiming at improving the patients’ quality of life.

2

Glass Products and Types

Typical containers for pharmaceutical use are ampoules, vials, syringes, and cartridges (Figure 1):

• • •

Ampoules remain the less expensive products available on the market. Their use keeps slightly increasing worldwide in that a growth in China, Japan, and other Asian countries compensates for a decrease in Western Europe and North America. Vials show a constant increase, growing in all markets because of their universal acceptance by end users and pharmaceutical companies. Such an increase is tightly connected to a quality improvement in terms of increasing output, lower rejection rates, and decreasing cosmetic defects. A high growth is shown by cartridges in all applications, whether dental, biotechnological, and insulin related. In the last case the so-called pen applications for selfadministration are key success factors, but the highest quality is then requested in terms of cosmetic defects and dimensional tolerances because of the high cost of such drugs and the need to guarantee a very precise dosage.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume II, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

880

7.7 Glass for Pharmaceutical Use

Syringes and special devices 13%

Ampoules

Cartridges 40% 20%

27% Vials

Figure 2 Distribution of pharmaceutical glass containers in terms of production volume. Figure 1 Different glass container types: ampoule, vial, syringe, and cartridge from left to right.

•

Syringes and special devices

The high growth of syringes production is driven by prefilling. Thanks to their ease of use and dosage accuracy, these containers are already the primary packaging of choice for many healthcare users. Their major markets are either key therapies that include vaccines, low-molecular-weight heparins, biotech products or applications in combination with auto-injectors.

The use of glass for pharmaceutical preparations is ruled by pharmacopeia authorities. The European [1] and US pharmacopeias [2] acknowledge two different types of glasses, namely, neutral borosilicate and soda lime, and three different types of glass containers according to a well-established classification based on their hydrolytic resistance (Chapter 5.1). In order of decreasing cost, these are the following:

• • •

Type I glass containers are made of neutral borosilicate glass, which have intrinsically a high hydrolytic resistance. These containers can thus be used for any purpose. Type II glass containers are usually made of soda-lime glass. Being subject to alteration by contact with aqueous solutions (Chapter 5.11), they can be internally treated over a thickness of about 0.5 μm to acquire a hydrolytic resistance equivalent to that of type I glass. These containers are suitable for acidic and neutral aqueous preparations for parenteral use. Type III glass containers are made of untreated soda-lime glass. Owing to their moderate chemical resistance, they are suitable in parenteral use only for nonaqueous preparations.

The general segmentation of the overall 35–45 billion glass containers produced yearly would indicate a large preponderance of ampoules (Figure 2). In terms of value

Cartridges

Vials

Ampoules

€0

€500 000 000

€1 000 000 000 €1 500 000 000

Figure 3 Segmentation of the value (€) of the different container types, year 2017.

as expressed in euros (Figure 3), syringes and special devices generate in contrast the highest revenues, whereas ampoules provide the lowest, clearly illustrating the value added in the highly engineering part of the production.

3 Production of Pharmaceutical Glasses and Containers Pharmaceutical containers are produced from type I and III glasses in the compositional ranges shown in Table 1. Coefficients of thermal expansion (CTE) range from 49 × 10−7 to 55 × 10−7 K−1 for clear glass and from 52 × 10−7 to 54 × 10−7 K−1 for amber glass (Chapter 6.2), whereas the working points lie between 1145 and 1165 C for the former and between 1120 and 1165 C for the latter, with annealing temperatures ranging from 535 to 575 C. Type I clear glasses includes also high-borosilicate glasses (the

3 Production of Pharmaceutical Glasses and Containers

Table 1 Composition ranges of type I and III pharmaceutical glasses (type II same as type III). Type I

Type III

Oxide (wt %)

Clear tubing

Amber tubing

Molded

SiO2

72.0–75.0

69.0–71.0

69.0–75.0

B2O3

10.0–11.5

7.0–10.0

Al2O3

5.0–7.0

5.0–6.0

0.5–4.0

Na2O + K2O

7.0–8.5

7.0–8.0

12.0–16.0

CaO + BaO + MgO

0.5–3.0

2.0–3.0

10.0–15.0

Fe2O3

0.5–1.0

TiO2

2.5–3.0

0–1.0

so-called Exp.33 glasses), thus having higher boron and silica contents and lower alkali contents with a CTE of about 33 × 10−7 K−. Of course, knowledge of these parameters is of primary importance for the manufacturing process.

3.1

Glass-Tubing Production

Glass tubes or canes are produced with either the Danner or the Vello process (Figure 4). In both processes the starting point is the furnace where raw materials of the glass batch are melted. As a continuous flow, the melt then is shaped as a tube [3]. After these steps the tubing is gauged, classified for use, and cut into the desired lengths. Named after Edward Danner who was working in the 1910s at Libbey Glass (Toledo, USA), the former can make tubing of 1.6–66.5 mm in diameter and rods of 2.0–20 mm in diameter at drawing rates of up to about 7 m/s for the smaller sizes and with a maximum daily production of up to 40 tons for the largest diameters. With this process, an angled rotating sleeve allows the introduction of air to inflate the tubing. The glass flows at about 1200 C from the forehearth on a rotating, hollow, Figure 4 The Danner and Vello glass-tubing processes, drawing glass horizontally and vertically, respectively.

water-cooled mandrel. The outside diameter and the thickness of the finished tubing are then controlled at about 900 C by the flow of inflating air together with the drawing and rotation speeds and the inclination of the mandrel, which is usually 15–20 from the horizontal. Named after Leopoldo Sanchez-Vello, the second process was first patented in 1929 in France. In this case, the glass flows from a forehearth into a reservoir in which a hollow bell-shaped mandrel rotates in a ring that allows the glass to flow via the annular space to give a continuously emerging tube. Air is fed via the end of the bell where there is a hollow tip. The dimensions of the tubing are controlled by the rate of draw, the clearance between the bell and the ring, the rate of drawoff, and the pressure of the blowing air. Production rates can be twice as high as with the Danner process, so the size of the drawing line is also much longer to reach from 100 to 140 m. 3.2

Container Production from Tubing

Glass vials can alternatively be produced by blow molding of glass gobs as described in Chapter 1.5. Only the glasstubing converting technology will thus need to be described here. From tubing to vials the forming process with vertical converting machines is shown in Figure 5 in a clockwise sequence: (i) opening of tubing bottom, (ii) forming of the vial shoulder, (iii) forming of the vial mouth, (iv) cutting of the tubing, and (v) forming of another vial bottom. The whole forming process of vials and ampoules is realized by gas burners, whereas it also includes a thermal shock cutting phase for cartridges and syringes. These steps are of course part of the production procedure in a long production line (Figure 6) beginning with the feeder that supplies the converting machine with the glass tubing and ending with a fully automated system for quality checking. Specifically, the correct shape of the container is monitored at every step by a camera system that allows for self-adjustment operations in the case of small dimensional deviations. From the machine, the container is transferred to another line where its Danner mandrel

Vello mandrel

881

882

7.7 Glass for Pharmaceutical Use

Closed-end Pierced tube bottom

Heat

Pre-tool

Heat

Finishing tool

Heat narrow zone

Part vial smooth bottom

Figure 5 Forming process from glass tube to vial. The various steps include glass heating and processing with pre-finishing and finishing tools.

Packaging Tube feeder

Figure 6 Schematic representation of a glass container production line. Different manufacturing and inspection systems are shown, including a tube feeder, a rotating manufacturing stage, optical inspection devices, and an oven.

Annealing oven Visual inspection

dimensional parameters are again controlled by optical and mechanical means. Where appropriate, before being annealed it is then subjected to additional operations according to the customer requirements such as washing, sulfur treatment, etc. Finally, the container is brought to an automatic packing machine, which is confined in a protected clean area, where the final optical control for cosmetic defects is performed. This factory quality control is the key to guarantee the compliance of the final product with the specification requirements established by both the pharmacopeia and the pharmaceutical industry. Maximum care thus is taken in the converter operations to avoid scratches on the container body. Likewise, special precautions are taken in the machine feeding phase, and all container transfer and packaging operations are performed by robots.

4

Physical Resistance

The theoretical strength of a material is directly connected to the strength of its structural chemical bonds (Chapter 3.11, [4]). In silicate glasses, strong covalent

bonds are present, such as Si─O bonds with energies of about 400 kJ/mol. These features translate into very high theoretical strengths, which could be greater than 10 000 MPa for glasses and glass ceramics. But commonly used glasses have mixed covalent (strong) and ionic (weak) bonds and, moreover, present dispersed structural microheterogeneities. As a result, the theoretical tensile strength of borosilicate glasses can vary from 6500 to 9000 MPa. These values can never be met in practice since the actual strength of glass articles is substantially affected by the presence of surface flaws (Chapter 3.11). Indeed, contact with metal tools or other glass items often causes damages on the surface of glass articles. These surface flaws usually appear as scratches or micro cracks, which act as stress concentrators during mechanical loading. Eventually, the mechanical stresses generated by these defects may result in breakage of the finished container. Owing to wear and manufacturing processes, these flaws are common in all materials, but their effects are mitigated in ductile materials by plastic flow, which relieves the stress concentrations. Under typical operating temperatures and timescales, however, glasses are brittle materials that display negligible plastic flow. As a consequence, surface defects induced by wear, friction sliding,

5 Chemical Resistance

Figure 7 As apparent in a probability plot for vertical breaking of cartridges, the considerable improvement in mechanical properties of cartridges produced in a no-glass-to-glass line (right) with respect to a standard production (left).

99.9 99

Percent

90 80 70 60 50 40 30 20 10 5 3 2 1 Category A B 0.1 1000

10 000 Vertical breaking load (N)

and impacts significantly decrease the mechanical resistance of glass containers [5], so their practical tensile strength is usually about only 20–200 MPa. Interestingly, the failure of glass products also depends on the loading time and on the area subjected to the mechanical stress. Tensile stresses exerted over large periods of time may cause microscopic cracks to grow and eventually to reach critical sizes. This is why the strength of glass articles is higher for rapid than for slow mechanical loading. In addition, increasing the area subjected to mechanical stress increases the probability of triggering surface flaws, jeopardizing the resistance of the article. All these factors may differ widely from a process to another as illustrated by the considerable differences in vertical breaking probabilities between cartridges produced by two different processes (Figure 7): especially for the “weak” end of the distribution, considerable improvements are obviously provided by the no-glassto-glass line products where the flaws coming from the mutual contact of containers are avoided.

The chemical durability of soda-lime commercial glasses has been investigated for nearly a century [10, 11], so the interaction mechanism is well understood. In the field of pharmaceutical glass, borosilicates are recognized as the most durable because their interaction with semi-neutral aqueous solutions does not cause a significant pH shift. The reason is that alkalis are much more tightly bound to the silicate network when present as charge-compensating cations for B3+ in tetrahedral coordination (Chapter 7.6) than when being network modifiers as in soda-lime-silica glasses. In other words, borosilicate glasses are properly called neutral because the small amounts of alkalis and other ions released by the glass surface do not alter the neutrality of the contact solution. When an aqueous solution enters in contact with the glass surface, the first stage is the hydration of the contact glass layer according to the reaction H2 O + Si─O─Si glass ➔ Si─OH glass + HO─Si glass 1

5 5.1

Chemical Resistance Corrosion Reactions

The chemical resistance of pharmaceutical glasses is the resistance to the attack by a liquid medium [6–9]. Although glass is almost inert with respect to the majority of neutral organic media, interaction with aqueous solution causes substantial alterations of the inner contact surface (Chapters 5.11 and 5.12). The resistance to such attacks by aqueous solution is known as the chemical durability or hydrolytic resistance (Chapter 5.1).

At the same time an ion exchange reaction is initiated between alkali ions in the glass network and proton ions in the leaching solution H2 O + Na + − O─Si glass ➔ SiOH glass + Na + + OH − 2 This reaction causes a slight rise of the pH of the extraction solution, which has a negligible effect on the extraction mechanism. The silica gel layer that forms on the surface differs in mechanical properties from the bulk glass. Repeated hydration and dehydration cycles

883

884

7.7 Glass for Pharmaceutical Use

thus bring to the cracking of such layer and eventual generation of subvisible or visible particles. At this stage the quantity of extracted alkalis linearly correlates with the square root of time (t) but later on the process becomes linear with time (Chapter 5.11). The total extracted amount of alkalis (Q) can be schematically represented by the empirical expression Q = a √t + bt, where a and b depend on the glass composition and temperature [10]. For a slightly acidic medium, the following reaction takes place: H + + Na + − OSi glass ➔ SiOH glass + Na + 3 With solutions at pH lower than 4, the reaction proceeds up to the formation of an alkali-depleted layer that acts as a barrier toward further attack, whereas the pH remains substantially unchanged. For basic solutions (pH > 9), the OH− ions break oxygen bridges (Si–O–Si bonds), causing silica to dissolve according to the following dissolution mechanism: 2H2 O + glass Si─O─SI + OH − ➔ glass SiOH + H3 SiO4 − 4 −

With increasing OH concentration, the reaction shifts to the right, thus favoring the dissolution of silicic acid. In addition to pH, time, and temperature, other factors like the surface-to-volume ratio, glass composition, and the contact media determine the extent of chemical attack. For instance, buffers with a strong ionic strength (KCl and citric acid, for instance) or complexing agents such as EDTA, glutaric acid, and phosphate promote extensive interactions with the glass network and cause its total dissolution [12]. 5.2 Testing of the Hydrolytic Resistance of Containers The pharmacopeia distinguish between the resistance provided by the glass itself and that offered by the inner glass surface of the container in contact with water or, more generally, with aqueous preparations. A grain test, carried out on a glass fraction of specified grain size, is suitable to monitor the resistance offered to water attack by the glass as material. In this respect, the distinction between type I and type III glasses becomes obvious when the extract solutions are titrated with a 0.02 M HCl solution after 30 minutes water exposures at 121 C. The higher quality of borosilicate glasses (type I) manifests itself with a limit of 0.1 ml of HCl solution per gram of glass compared with a value of 0.85 ml for soda-lime glasses (type III). This test can be used also to reveal whether the glass surface has been treated or

Table 2 Comparison between glass grain test results for borosilicate glass tubes and molded soda-lime-silica glasses commercially available. Results (ml 0.02 M HCl/g glass)

Supplier

Limit value (ml 0.02 M HCl/g glass)

Schott Fiolax

0.037

0.10

NEG BS

0.035

0.10

Nipro

0.036

0.10

Corning

0.036

0.10

Soda-Lime Molded

0.44–0.54

0.85

Soda-Lime Amber

0.53–0.68

0.85

Table 3 Typical surface test results for type I vials produced by different glass-tubing converters using the same tubing raw material.

Vial capacity

Results (ml 0.01 M HCl/ 100 ml extract)

Limit value (ml 0.01 M HCl/ 100 ml extract)

Notes

3 ml

1.1

1.3

Converter A

3 ml

0.70

1.3

Converter B

10 ml

0.70

0.80

Converter C

10 ml

0.55

0.80

Converter B

20 ml

0.27

0.60

Converter B

2 ml

0.39

0.60

Converter C

not and, thus, to distinguish between type I and type II glass containers. In Table 2 typical grain test results from commercially available tubing and molded sodalime glasses are reported. A surface test is mandatorily requested to assess the alkali release from the inner surface of the containers. The latter, filled with water, are autoclaved for one hour at 121 C, and the pooled extract is titrated with a 0.01 M HCl solution. The limit values are established as a function of container capacities and glass type, being 10 times higher for type III glass containers. Typical surface test results on vials of different capacity are displayed in Table 3 where the impact of different converters is also highlighted. In particular cases the individual alkali release can be measured by flame atomic absorption spectroscopy (Chapter 5.1). 5.3 Glass Extractables There is an increasing attention paid to extractables, i.e. the substances released from the whole drug packaging system after a stress treatment (e.g. autoclaving treatment, long time and high-temperature exposure).

6 Surface Interactions with Pharmaceutical Products

Table 4 Inductively coupled plasma mass spectrometry (ICP-MS) analyses of elements extracted from 10 ml glass type I vials after an autoclaving cycle made according to the grain test. Element

Conc. (mg/l)

Element

Conc. (mg/l)

Cd

1% FeO), became dominant over much of the Roman world. It is thought to have been made in Egypt and was used alongside a continuation of the Mn-decolorized glass made on the Levantine coast. Over the next few centuries, a series of relatively abrupt changes in the composition of natron glass indicates shifts in the location of production within the South-East

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10.3 Roman Glass

Figure 7 Typical mixing line between Roman antimonydecolorized glass, with low Al2O3, and manganesedecolorized glass, with high Al2O3 [22], displayed by Roman glass fragments from the Iulia Felix wreck in the Adriatic [8].

1

MnO/(Sb2O3 + MnO)

1270

0.9

Colorless

0.8

Green-blue

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1.00

1.50

2.00

2.50

3.00

Al2O3

Mediterranean region (Figure 1). Over the same period, there is a gradual decline in the quality of glass made in the Levant, where the use of manganese decolorant diminished and the average soda content of the glass reduced until, in the eighth century, a bluish glass with around 12% Na2O and 75% SiO2 became the characteristic product (Table 1). This period of decline corresponds to the contraction of the Roman Empire and a dramatic reduction in the volume of Mediterranean trade. Indeed in the post-Roman (early medieval) societies of Europe, fresh glass from the Southeast became increasingly difficult to obtain. From Italy through to Britain, evidence of a dependence upon recycled glass becomes increasingly apparent from the end of the sixth century. An important source of this recycled material may have been the wall mosaic and window glass of the large public buildings, which were abandoned with the decline and withdrawal of Roman administration. Mosaic tesserae were important sources of material for color as well as for raw glass; for example, cobalt-blue tesserae were mixed with colorless glass to produce translucent blue sheets for windows through to the twelfth century. Limpid blue- or green-tinted transparent glass of the eighth– ninth centuries may contain copper, antimony, and lead at high levels, which could have resulted only from extensive recycling of first–third century opaque tesserae, excluding cobalt blues, which were reserved as a source of blue pigment [22]. In western Europe, much of this recycled material was likely imported from the old Roman regions in the South. By the ninth century, it could no longer satisfy the demand for glass, which included the requirements of the growing Christian churches and monasteries. A new formulation was thus developed such that glass began to be made from local sand and potassium-rich wood ash, laying the foundations for the stained glass window industry of the high medieval period (Chapter 10.8). In the Islamic East,

natron-based glass production declined in the ninth century when the natron flux was replaced by soda-rich ash, produced by burning halophytic plants from desert and coastal environments, marking an end to the Roman tradition of glassmaking. Although current opinion is that glass was no longer made from Egyptian natron after around 900 CE, natron-based glass continued to be in use through the thirteenth century for some purposes. The compositions of glass enamels on Romanesque copper-alloy reliquaries and plaques of the twelfth century correspond precisely to the opaque glasses of the second–third centuries. Writing around 1120 CE, the monk Theophilus tells us that these were obtained from the old buildings of the pagans (Romans) [23]. He also indicated that window glass was colored blue by mixing blue tesserae with contemporary wood ash glass. Analysis of medieval church windows supports this account [22].

7

Perspectives

The preservation of ancient cultures is tenuous. Analytical samples of heritage materials such as glass can be difficult to obtain, which is why the available data have been collected in a somewhat opportunistic and arbitrary fashion. For some regions they depend upon museum material that may date back to the early twentieth century or before. Even so, over the past 20 years, new archeological discoveries and improvements in the understanding of vessel chronology, along with a marked expansion in scientific investigations, have led to the development of a consistent model of Roman glass production. Detailed archeological studies focused on glass assemblages at specific sites, on shipwrecks, or on the geographical distributions of specific types of glass objects are

References

continually enlightening our understanding of the ways in which glass was perceived, valued, used, and reused. New trace element and isotopic approaches are likely to be applied to shed light on the sources of fluxes, colorants, and opacifiers. Although several primary production sites have been identified, those of some of the major types of glass remain to be discovered whereas the possibility of primary production in the West requires more attention. Modeling and experiment offer the potential to understand better furnace operation. In this respect, the determination of oxidation states in experimental glasses could allow furnace conditions to be determined. Alongside other evidence, this framework will allow glass to be used to yield important information on industry, trade, and the ancient economy. The wider reasons behind technological innovation and change, the movement of production locations, and the growth and decline in glass use will be amenable to investigation as our understanding of chronology and regional variation becomes more refined. In this way, the study of glass will bring new and valuable information on the inner workings and evolution of the Roman Empire itself.

8

9

10 11

12

13 14

References 15 1 Tait, H. (ed.) (2004). Five Thousand Years of Glass.

London: British Museum Press. 2 Price, J. (2005). Glassworking and glassworkers in cities

3

4

5

6

7

and towns. In: Roman Working Lives and Urban Living (eds. A. MacMahon and J. Price), 167–191. Oxford: Oxbow. Freestone, I.C. (2008). Pliny on Roman glassmaking. In: Archaeology, History and Science. Integrating Approaches to Ancient Materials (eds. M. Martinón-Torres and T. Rehren), 77–100. London: Routledge. Gorin-Rosen, Y. (2000). The ancient glass industry in Israel: summary of the finds and new discoveries. In: La Route du Verre (ed. M.-D. Nenna M-D), 49–63. Lyons: Maison de l’Orient Méditerranéen. Nenna, M.-D. (2015). Primary glass workshops in Graeco-Roman Egypt: preliminary report on the excavations of the site of Beni Salama, Wadi Natrun. In: Glass of the Roman World (eds. J. Bayley, I.C. Freestone and C. Jackson), 1–22. Oxford: Oxbow. Sode, T. and Kock, J. (2001). Traditional raw glass production in northern India: the final stage of an ancient technology. J. Glass Stud. 43: 155–169. Foy, D., Picon, M., Vichy, M., and Thirion-Merle, V. (2003). Caractérisation des verres de l’Antiquité tardive en Méditerranée occidentale: l’émergence de nouveaux courants commerciaux. In: Échanges et commerce du

16

17

18

19

20 21

22 23

verre dans le monde antique: Actes du colloque de l’Association Française pour l’archéologie du verre (eds. D. Foy and M.-D. Nenna), 41–78. Montagnac: M. Mergoil. Silvestri, A., Molin, G., and Salviulo, G. (2008). The colourless glass of Iulia Felix. J. Archaeol. Sci. 35: 331–341. Freestone, I.C., Jackson-Tal, R., Tal, O., and Taxel, I. (2015). Glass production at an early Islamic workshop in Tel Aviv. J. Archaeol. Sci. 62: 45–54. Degryse, P. (2014). Glass Making in the Greco-Roman World. Leuven: Leuven University Press. Schibille, N. (2011). Late byzantine mineral soda high alumina glasses from Asia minor: a new primary glass production group. PLoS One 6: e18970. Arletti, R., Quartieri, S., and Freestone, I.C. (2013). A XANES study of chromophores in archaeological glass. Appl. Phys. A 111: 99–108. Stern, E.M. (1999). Roman glassblowing in a cultural context. Am. J. Archaeol. 103: 441–484. Freestone, I.C. and Stapleton, C.P. (2015). Composition, technology and production of coloured glasses from Roman mosaic vessels. In: Glass of the Roman World (eds. J. Bayley, I.C. Freestone and C. Jackson), 61–76. Oxford: Oxbow. Barber, D.J. and Freestone, I.C. (1990). An investigation of the origin of the colour of the Lycurgus Cup by analytical transmission electron microscopy. Archaeometry 32: 33–45. Verità, M. and Santopadre, P. (2010). Analysis of goldcolored ruby glass tesserae in Roman church mosaics of the fourth to 12th centuries. J. Glass Stud. 52: 11–24. Israeli, Y. and Katsnelson, N. (2006). Refuse of a glass workshop of the second Temple period from area J. In: Jewish Quarter Excavations, vol. 3 (ed. H. Geva), 411–460. Jerusalem: Israel Exploration Society. Wardle, A. (2015). Glass Working on the Margins of Roman London. London: Museum of London Archaeology. Foy, D. and Nenna, M.-D. (2001). Tout feu tout sable: Mille ans de verre antique dans le Midi de la France. Aix-en-Provence: Édisud. Harden, D.B. (1987). Glass of the Caesars. Olivetti: Milan. Foy, D. and Fontaine, S.D. (2008). Diversité et évolution du vitrage de l’antiquité et du Haut moyen âge. Gallia 65: 405–459. Freestone, I.C. (2015). Re-use and recycling of Roman glass: analytical approaches. J. Glass Stud. 57: 29–40. Theophilus priest and monk [Roger of Helmarshausen] (1963). Diversarum Artium Schedula (trans. J. G. Hawthorne and C. S. Smith, On the Diverse Arts). Chicago: University of Chicago Press.

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10.4 Glass and the Philosophy of Matter in Antiquity Marco Beretta Università di Bologna, Bologna, Italy

1

Introduction

In Antiquity, glass, more than any other product made out of earthly materials, could be easily shaped and colored to imitate precious stones or mineral substances. Egyptian priests projected a religious meaning onto the mineral kingdom, such that each mineral was endowed with special properties that evoked the presence of the gods [1]. When it was discovered that glass could imitate lapis lazuli, Egyptian craftsmen began to reflect upon the properties of matter and the value that should be attributed to imitations. Were these mere counterfeits or faithful replicas of the natural stones? This was a critical question because, with the XVIIIth dynasty (c. 1543–1292 BCE), the production and trade of both artificial and natural lapis lazuli became an important aspect of Egyptian culture and religious rituals. The Egyptian glassmaking tradition survived in Hellenistic Alexandria, exporting both technical know-how and theoretical insights to Palestine and, during the Roman Empire, along the Mediterranean coastline. Attention to archeological data in particular reveals that Egypt played an exceptionally important role in directing the interest of early Greek philosophers and naturalists on the properties of glass. Of particular importance in this respect was the philosophy of matter first expounded by Empedocles of Agrigento (483–424) according to which everything in the sublunar world (the Earth and its atmosphere) was made up of various proportions of the four elements, fire, air, water, and earth. When Plato (c. 428–347) and his former disciple

Reviewers: F. Dell’Acqua, Dipartimento di Scienze del Patrimonio Culturale, Università degli Studi di Salerno, Fisciano, Italy M. Martelli, Humboldt-Universität zu Berlin Institut für Klassische Philologie, Berlin, Germany

Aristotle (384–322) subsequently went one step further with their own explanations for the transformations undergone by these elements, their theories had an obvious bearing on glass, whose marvelous properties such as natural luster and transparency required a rational account in terms of the action of fire upon a variety of earthly substances. And not only was glass representing the dramatic transformation of insignificant raw materials into a remarkable substance akin to gems, but it also had many common features with metals in general. Hence, glass became closely involved in alchemy when metal transmutation became an important goal of this Sacred Art, and such efforts could only increase after the technical revolution triggered by the invention of glassblowing during the first century BCE. Before examining glass within the context of ancient philosophy of matter, however, we will have to go back in time and consider how this material was originally considered in Mesopotamia and in Egypt. From Empedocles’ to Plato’s and Aristotle’s theories, we will then briefly present the basic relevant concepts before delving into the mutual relationships of glass and alchemy. Finally, the role played by Byzantium in the transmission of the alchemical tradition will be summarized.

2 2.1

Near Eastern Views on Glass Mesopotamia

From about the twelfth century BCE, Mesopotamian glass and medical texts bore a resemblance in their literary form: they prescribed instructions in the form of recipes, and some even recommended religious rituals and prayers, invoking the need to perform certain experiments during propitious days ([2], Chapter 10.11).

Encyclopedia of Glass Science, Technology, History, and Culture, Volume II, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

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10.4 Glass and the Philosophy of Matter in Antiquity

According to these early Mesopotamian recipes, the chemical operations required to produce colored glass were preceded with a ritual including the worship of images and a libation offering; when the glass was placed into the kiln, a sheep was sacrificed before images of the Gods. Such rites were important because their association with a holy discipline such as medicine underlines the scientific and literary dignity of glassmaking. One of the most important achievements of Mesopotamian glassmaking was the imitation of lapis lazuli. Given the importance of these gems in near-Eastern art and culture, the ability to produce notable quantities of artificial stone represented an important technological advance, although glass was still valued as highly as gold. Another feature revealed by Mesopotamian texts, which would have important consequences for the history of glassmaking, was the definition of glass itself: the term baŝlu abnu (molten stone), which announced the Greek líthos chytè (molten stone), eventually used by Herodotus (c. 484–420) [3] and other Greek authors. The reference to the chemical operation of melting is significant because the fusing property of glass was shared by other mineral substances, especially metals. In this respect, it seems that at a very early stage glass was not seen as an entirely artificial product but as a natural stone which, like metals, could be fused and modified. 2.2 Egypt Although the influence of Mesopotamian glassmaking on Egyptian craftsmen is now generally acknowledged, the priority disputes over the invention of this material have overshadowed the different approaches and technologies developed within the two civilizations. In fact, Egyptian craftsmen displayed an extended knowledge of primary ingredients, developed advanced metallurgical techniques that led them to produce a richer variety of colors, and, last but not least, manifested a theoretical interest in the classification of glass within a philosophy of matter apparently absent from Mesopotamian texts. The glass industry made its appearance in Egypt from 1400 BCE during the reign of Akhenaten (r. c. 1354–1338). Like in Mesopotamia, the invention of glass probably derived from the crafts of faience and glaze. These materials consisted of the same ingredients – silica, alkali oxides, and lime in modern parlance – but their technical treatment was completely different, thus resulting in many different vitreous bodies. Both glass and faience were treated as artificial precious stones, however, and Egyptian craftsmen seem to have mastered both techniques with the greatest dexterity. At least between 1400 and 1050 BCE, glass was of great importance in Egyptian culture for the production of

amulets, beads, vessels, inlays, and the imitation of precious stones. Probably because glass could imitate so many materials, the Egyptians did not coin a specific name to denote it until the third century CE, when the demotic yl was used for the first time in the magical papyrus of London [4]. Egyptian craftsmen, like their Mesopotamian counterparts, also defined glass as a “molten stone” or “molten precious stone” (aA.t-wdH). Going farther than their predecessors, however, they included glass artifacts within a comprehensive classification of metals and mineral products without finding it necessary to establish a clearcut distinction between glass and faience, on the one hand, and glazing mineral stones on the other. One definition of glass appropriated the term faience, THn.t, which was derived from the verb THn: to sparkle, to scintillate, the lightning flash. As the etymology would have been equally effective to denote colored glass, the term later became synonymous with this new artifact. While sharing the same property of being meltable, substances such as gold and lapis lazuli differed essentially by their qualities of color and brilliance. According to Hecataeus of Abdera (late fourth century BCE), a Greek skeptic philosopher who wrote a book now lost on the history of Egypt, Egyptians believed in a principle of matter which, divided into four elements, became the basis of all living beings [5]. The relation between these elements and the importance attributed by Egyptians to colors in order to classify the products of the mixtures of the four elements would eventually find an important echo in the Greek philosophy of matter. Because the gods’ influence over the mineral kingdom was so pervasive, craftsmen who were engaged in the manipulation of metals and stones were in touch with godly particles and fluids, and their capacity to transform matter thus placed them in the position of demiurges (Figure 1). It is not without significance that there was no term denoting glassmakers in Mesopotamia whereas in Egypt irw hsbd denoted the craft of “makers of (artificial) lapis lazuli,” thus showing the professionalization of a skill that would enjoy significant importance within Egyptian society and culture. As a matter of fact, craftsmen enjoyed a higher social status in Egypt than in Classical Graeco-Roman economic contexts. In Egypt, claimed the Greek physician Galen (c. 129–216), new artisanal discoveries were always submitted to the approval of scholars, who provided public notice of the new inventions through inscriptions fixed on sanctuary columns. It was the tradition of omitting inventors’ names from these inscriptions, which, according to Galen [6], caused a multitude of anonymous writings on occult sciences to be attributed to the god Hermes Trismegistus, the founder of all wisdom.

3 The Glass of the Greek Philosophers

Figure 1 Head of an Egyptian priest made of vitreous material (c. seventh century BCE) from the former Ernesto Wolf Collection. Source: Photo courtesy E.M. Stern.

3 3.1

The Glass of the Greek Philosophers From Empedocles to Plato

Even though scholars long raised doubts concerning how much was actually known in archaic Greece about glass, today it is clear that techniques had then been imported from Egypt to imitate ceramics and were already used widely. Homer’s works, which are often used to show the absence of references to glass in the eighth century BCE, in reality contain many references to a substance called kyanos designating a blue glass paste used to decorate temples [7] and warriors’ armor. In other passages of Homer and in Philostratus [8] and Aristotle after him, the term kyanos is used as an adjective designating the blue, iridescent color of stones, animals, and objects. In another sense kyanos designated an actual stone – a natural product that Pliny the Elder (23–79) identified in his Natural history [9a] with a blue pigment (caeruleum) and by his modern commentators as azurite – a blue stone similar to lapis lazuli. The Greeks identified metals with products of mineral extraction that were meltable. These included not only real metals such as gold, silver, and copper but also composite bodies, such as glass and some mineral pigments, which were not discernible within ancient philosophies of

matter and would be today designated as metallic substances. What curiously associated these materials was solely their properties of being products of mineral extraction and, above all, of being meltable materials that could change form if submitted to the action of fire through metallurgical techniques. As already noted, the most influential philosophy of matter in Antiquity was that of Empedocles. Probably the now lost treatise on metals occupied an important place in his poem On Nature. But the important point is that, from the advent of this theory, it became necessary to give an empirical foundation to the macroscopic changes visible in a material. On the assumptions that all bodies release effluences and at the same time have pores capable of absorbing other effluences commensurable with them, Empedocles understood that metals “like all other bodies possess a structure” [10] so that the differences among the elements and the compounds were due to the different configurations of their aggregate of particles. Empedocles’ theory of pores was taken up again by his pupil, Gorgias (c. 483–376 BCE) in order to explain the property common to bronze, silver, and glass of forming mirrors capable of concentrating sunlight and acting as burning mirrors [11]. By the way, we must note that, contrary to what is still often believed, the Greeks did make glass mirrors and were well aware of the differing reflecting properties of metals. To establish a distinction of this kind, it was in fact necessary to be much more familiar with the workings of glass and metals than attested to by fragmentary archeological proofs and, above all, by late Latin texts. Empedocles’ philosophical intuition on the structure of matter, based at least in part on his knowledge of metallurgical techniques, received further and more profound consideration by Plato. In his dialogue Statesman [12], no distinction was made between “gold and silver, and everything that is mined,” showing the connection between the identification of metals with the technique of their extraction. Metals were substances extracted from the Earth, which, when subjected to the action of fire, were behaving in the same way. Regarding glass, it is interesting to note that one of the first occurrences of the term hyalos in the explicit context of natural philosophy is found in Plato’s Timaeus [13a], his great cosmological dialogue. This introduction of the term hyalos in the fifth century BCE brought with it a more precise understanding of glass. According to some philologists, the substantive hyalos derived from the verb heyin (to rain), signifying water droplet, whereas others say that it derives from hals (salt): the former term exalts the physical characteristics of glass – particularly its brightness and transparency – whereas the latter alludes to its chemical constitution. Whatever

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10.4 Glass and the Philosophy of Matter in Antiquity

the correct explanation is, in both cases physics and technology were at the basis of the Greek definition of glass. As for the elements, Plato explained in Timaeus that the triangle was their building block so that the four of them represented the four fundamental regular polyhedra, namely, the tetrahedron (fire), cube (earth), octahedron (air), and icosahedron (water) [13b]. In terms of a balanced reaction, the vaporization of water upon heating was, for instance, seen as the rearrangement of the 20 equilateral triangles of one water icosahedron into the 4 triangles of one fire tetrahedron and the 16 triangles of two water octahedra [13c]. In Timaeus, Plato could then discuss the interplay of fire and water in metals and define glass [13d] as a mixture of water particles (in a larger proportion) and of earth, which, when subjected to the action of the particles of fire reached the molten state. It is fusibility, therefore, which Plato also attributed to metals, that defined the material character of glass. This concept represented a fundamental step forward in antique metallurgy and eventually also involved a better understanding of what glass was. 3.2 Aristotle Although paying careful attention to empirical research, Aristotle’s primary interest, without doubt, was to construct a coherent philosophy of matter capable of overcoming the limits encountered by that of Plato. This is what he did in the in the fourth book of his Meteorology where attention was duly paid to metals, in general, and to glass, in particular. Without falling into the wild speculations of earlier thinkers, Aristotle rejected Plato’s geometrical approach to posit instead that the elements should rather be accounted for in terms of four fundamental qualities, namely hot, cold, dry, and humid. Fire was then dry and hot, air dry and cold, water cold and humid, and earth dry and cold so that all transformations within the sublunar world was taking place through exchanges of these four qualities. On this basis, Aristotle proposed elaborate interpretations for the cause of the chemical changes to which matter was subjected. He took his cues from widespread practical and craftsmanly activities such as that of the art of the potter, when speaking of the properties of clay, or the treatment of oil, when describing differences in the solubility of liquids. Likewise, the properties of solid bodies were sifted through a system of categories derived from arts and techniques. In this way, Aristotle proposed to distinguish bodies according to a comprehensive property flow-chart: “to be apt or inapt to solidify, melt, be softened by heat, be softened by water, bend, break, be fragmented, impressed, moulded, squeezed; to be tractile or non-tractile, malleable or non-malleable, to be fissile

or non-fissile, apt or inapt to be cut; to be viscous or friable, compressible or incompressible, combustible or incombustible, to be apt or inapt to give off fumes” [14a]. Aristotle then imagined that the formation of metals and many other mineral bodies were due to the two types of exhalations generated by the Sun’s heat: the first liberated watery vapor, which constituted water and insinuated itself into the bodies of which it was a component; the second was dry and very inflammable, deriving directly from the earth. Not limiting himself to characterize metals as meltable bodies extracted from mines, as Plato did, Aristotle also sought to find out the cause of their meltability. He assigned it to the vaporous or watery exhalation, which, thanks to its intrinsic humidity, rendered these bodies susceptible to melting and thereby to reaching the liquid state. Further, the different degrees of fusibility of various metals were, according to Aristotle, due to different proportions of the two basic elements, water and earth, since “all determinate bodies in our world involve earth and water. Every body shows the quality of that element which predominates in it” [14b]. And it appeared that the aqueous element often seemed to prevail: “gold, then, and silver and copper and tin and lead and glass and many nameless stones are of water; for they are all melted by heat” [14c]. In light of Aristotle’s classification, one could think that the idea of defining glass as hyalos, deriving from the verb to rain was not altogether extraneous from the chemical property of this material to reach a molten state at high temperatures. The possibility of producing transparent glass was conditioned by the availability of furnaces capable of reaching temperatures above 1000 C. Therefore, the substitution in the fourth century BCE of the terms kyanos and lithos chytê for hyalos might have reflected an awareness of technological progress achieved especially in the art of glassmaking. From this definition, it clearly appears that the Ancients considered the philosophy of matter as distinct from manipulative procedures, thereby allowing them to recognize constitutive differences between various classes of minerals. In fact, in the majority of citations assembled here, it was technique that rendered possible the general definition of a specific class of minerals.

4

Glass and Alchemy

4.1 Art as Imitating Nature References to glass are found not only in philosophical texts, but in far greater measure in alchemical practices that were half way between philosophical speculation and empirical experimentation. Ancient alchemy played a central role primarily because it was inherent to the

4 Glass and Alchemy

Figure 2 Oil lamp with the illustration of an artisan blowing glass in a pipe. At the center, a glass furnace; on the left, another worker is holding the finished product. First century CE. Source: Courtesy Museo del Belriguardo, inv. 52196, Ferrara.

techniques and knowledge that were essential to the production of glass (Figure 2). The construction and development of furnaces capable of reaching ever higher temperatures, the acquired skill of combining an everincreasing number of ingredients, the chemical techniques of coloration just as those for counterfeiting gems and precious stones were all aspects shared by craftsmen and alchemists alike [15, 16]. It is difficult, and perhaps historically improper, to try to relate the production of glass by artisans to an attempt at providing metallurgical production with a theoretical and philosophical framework that would have been completely extraneous to practical needs. It is nonetheless odd that historians of glass have neglected alchemical sources by concentrating exclusively on archeological remains and on those texts, by Pliny the Elder in the lead, that have little technical content and, above all, do not reflect the actually widespread knowledge of this material in the ancient world. If the procedures of the Greek alchemists mostly derived from the technical tradition of Egyptian artisans,

they also depended upon philosophies of matter which, from the pre-Socratics onward, had tried to give rational explanations to the changes wrought upon matter by the action of fire. In most of the alchemical texts of late Antiquity, this is why we find among the authorities and founders of the alchemy the names of Thales, Pythagoras, Democritus, Plato, and Aristotle mixed with those of Egyptian sages. There is another profound reason why the development of Greek alchemy, which flowered in the Alexandrine epoch, was bound to classical philosophy. The idea of the transmutation among substances was an assumption not only shared by the main philosophies of matter in Antiquity, but for Aristotle it constituted one of the most important keys for explaining chemical combination in terms of only the four elements and their qualities. If all bodies of the sublunar world were composed of air, water, earth, and fire, then one could transform one into another by changing the proportions of their constituents. This basic philosophy permits us to understand how the identities of substances listed in the lapidaries, and in other works of this type, were so often confused with counterfeits or with such artificial products as glass. If one accepted the possibility of transmutations, then a sharp distinction between natural and manufactured products was clearly inconceivable. Hence, glass was often confused, or perhaps more correctly, set in relation to various crystals, metals, stones, and gems, which, in their turn, could assume characteristics similar to those it displayed. In connection with the importance that the philosophers attributed to transmutation for explaining chemical reactions, another principle must be recognized for its enormous influence on the development of classical alchemy. We have already emphasized that one of the chief preoccupations of Greek philosophers was not to oppose art (i.e. man’s operations) and nature. Attempts at reevaluating the former were, in fact, directly conditioned by the ability to demonstrate its intimacy with the latter. Art imitates nature was thus a common saying or, as reported by Pliny the Elder’s legendary history on the origins of metals and glass, nature itself generates art. In this regard, it is significant that in Plato’s Timaeus the creator of the universe is called demiourgos, the artisan. In the field of chemistry, the coexistence of art and nature was stressed repeatedly. Speaking of a sand with special properties, Theophrastus (c. 371–287), Aristotle’s main disciple, for instance, noticed a means of imitating nature efficaciously in experiment and in technology [17], thereby outlining a theoretical principle that was to be carried out by classical alchemy. Once they identified the relevant philosophical principles, alchemists could rely on an ample supply of

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technical information. Even though sufficient direct evidence is lacking, the frequent references to the learning of the Egyptians, together with the Egyptian and midEastern origin of most of the Greek alchemists, likely confirm the important influence of Egyptian arts and metallurgical techniques. 4.2 Bolus of Mendes The earliest alchemist is Bolus of Mendes, also known as Pseudo-Democritus and long confused by late antique authors with the philosopher–atomist Democritus of Abdera (c. 470–380). Even though information is scarce concerning Bolus and his life, a rather corrupt lexicon compiled toward the end of the tenth century, identified him as a follower of Pythagorean philosophy and as the author of various works among which was one dedicated to “the sympathies and antipathies of stones.” The chronology of Bolus’ life is still more difficult to establish with any precision. He was long thought to have lived in the second century BCE. However, his use of oriental sources such as Zoroaster and Ostanes translated into Greek around the first century of our era situates his life in a later period. In his Letters to Lucilius, the Roman stoic philosopher Seneca (4 BCE–65) still confused Bolus with Democritus of Abdera when he wrote [18]: “It seems to have quite slipped your memory that this same Democritus discovered how ivory could be softened, how, by boiling, a pebble could be transformed into an emerald – the same process used even to–day for colouring stones which are found to be amenable to the treatment!” The passage is revealing not only because it places the life of Bolus before 60 CE when the Letters to Lucilius were written, but shows how counterfeiting precious stones, primarily emerald, by using glass or rock crystal was not part of the craftsman tradition but was invented by an alchemist, or – as Seneca still confuses it, by a philosopher. Furthermore, as shown by the alchemical papyri of Leyden and Stockholm [19], the recipes for counterfeiting emerald represent a considerable part of late antique alchemical literature so that these recipes should have originated in Bolus’ work. Even though available sources are indirect and fragmentary, it is not difficult to understand that Bolus was a figure of certain importance and originality in the panorama of this period. The dating of Bolus between the first century BCE and the first decades of the next century is important because we know, as Pliny the Elder recounts in detail [9b], that it was just in this period that glassmaking made important technological progress. Of course, it cannot be claimed that alchemy directly originated from the development of glassmaking but rather, contrary to what has been hitherto supposed, that close relations

were usually posited between the two arts as exemplified by the Christian philosopher Aeneas of Gaza (fl. fifth century CE) who wrote in Theophrastus, his dialogue on the soul: “Change of matter to a better state is not implausible for, among us, experts in materials, taking silver and tin, making their form disappear, melting them down together and colouring them, and so changing the matter in something grander, have produced excellent gold. Again, sand is scattered and soda is abundant everywhere, but human skill has made glass out of them, new and transparent” [20]. 4.3 Glass and Counterfeited Stones As already stressed, the art of glassmaking offered a splendid example of how common materials could be transformed by the furnace into a noble and brilliant material (Figure 3). This quality became apparent in the counterfeiting of precious stones. During the Hellenistic era, gems rapidly became luxury items, which were particularly sought after for their virtues. Pompeius Magnus (106–48) and Julius Caesar (100–44) were the first to build up important collections. During his third triumph (61 BCE), Pompeius brought to Rome what he believed to be his most precious war booty, the myrrina vasa, extraordinarily beautiful vases made of such a precious material that two generations later the Emperor Nero (r. 54–68) managed to ensure for himself one single bowl at the astronomical price of 1 000 000 sesterces. Without the help of archeological evidence, the identification of myrra has been so problematic that for a long period this mysterious substance was thought to be millefiori glass [21]. Only recently has it been demonstrated beyond doubt that myrra should rather be identified with fluorite. Given the exceptional rarity of this mineral, Pliny thus reported that glass was used to imitate and counterfeit myrra. In view of the new spreading passion for gems and the peak of perfection reached by Roman glassmakers, Pliny mentioned in several chapters of his Natural History [9c] “how to make genuine stones of one variety into false stones of another” while lamenting that “to distinguish genuine and false gemstones is extremely difficult.” In addition, he mentioned the existence of treatises (commentarii), whose authors he preferred to omit, which gave “instructions how to stain crystal in such a way as to imitate smaragdus and other transparent stones, how to make sardonyx of sarda, and other gems in a similar manner.” Likewise, Pliny mentioned treatises devoted to glass. The circulation of this literature is of the greatest importance because it attests to the existence of authors who decided to write on topics that, for centuries, had been either kept secret or treated in general and encyclopedic works such as Pliny’s. The diffusion of this literature was

4 Glass and Alchemy

Figure 3 Pharmaceutical and chemical (?) glassware found in the Casa del Fabbro in Pompeii during the first half of the twentieth century. All items destroyed during WWII. Source: Courtesy Soprintendenza Archeologica di Pompei.

certainly justified by the amazing dexterity reached by Roman glassmakers in imitating precious stones. More common stones were also worked in such ways that they soon became luxury objects. Rock crystal was so highly regarded by the Romans that at the time of Pliny a single dipper was paid 150 000 sesterces by “a respectable married woman” [9d]. As a consequence of these follies, the manufacture of imitation and counterfeit was encouraged. “Glassware, said Pliny [9e] on this matters, has now come to resemble rock-crystal in a remarkable manner, but the effect has been to flout the laws of nature and actually to increase the value of the former without diminishing that of the latter.” That fake crystal artifacts did not cause prices to fall was probably due to the perfection of the counterfeits, which, without the help of chemical analysis, often remain today difficult to distinguish from true ones. By combining glass to crystal Roman artisan were able to imitate beryl, a gem particularly admired also because of his virtues [9f]. By the end of the second century CE, the connection between glassmaking, gold, and precious stones was

embodied in the description in the Apocalypse of Saint John [18, 21] of the new Jerusalem where we read: “And the building of the wall thereof was of jasper stone: but the city itself pure gold, like to clear glass.” As for opal, Pliny said that “there is no stone which is harder to distinguish from the original when it is counterfeited in glass by a cunning craftsman. The only test is by sunlight” [9g]. Also carbunculi (rubies?) were “counterfeited very realistically in glass, but, as with other gems, the false ones can be detected on a grindstone, for their substance is softer and brittle” [9h]. Whereas “no gemstone is more easily counterfeited by means of imitations in “glass” than “topaz,” Pliny added [9i], many other gems such as jasper, zephyr (?) were mentioned by him in connection to glassmaking. The imitation industry must have been flourishing at the same time when glassblowing was a widespread technique because, some decades before Pliny, the Roman encyclopedist Varro (116–27), noted in his Saturae Menippeae [22] that “to an inexperimented eye, a shell sometimes looks like a pearl, and glass like emerald” [22]. These fraudulent practices became

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eventually so common that the first Church fathers often took it as an example in their writings to show the deceptive nature of glass products.

4.4 An Elusive Art If imitation was as ancient a practice as glassmaking itself, treatises explicitly devoted to this art must have been relatively recent as no reference to them can be found in earlier sources. This literature, which would eventually be embodied in alchemical recipes, was thus contemporary to the extraordinary development of glassmaking. Although it is impossible to ascertain a direct relation between them, the number of distinguished authors who wrote extensively on the marvelous nature and history of this material makes us conclude that the progress achieved in the art also inspired a systematic reflection on the influence of glassmaking upon the traditional philosophy of matter. After enumerating gems and their imitations, Pliny concluded his Natural History by addressing his reader with the following interesting statement [9j]: “We must not forget to mention that gold, for which all mankind has so mad a passion, comes scarcely tenth in the list of valuables, while silver, with which we purchase gold, is almost as low as twentieth.” Because alchemy, from the Middle Age onward, has been principally identified with the art of transmuting vile metals into gold or with the chrysopoeia, the hierarchy of valuables mentioned by Pliny placing gems in the first nine positions, provided an authoritative reason why craftsmen preferred to produce false gems and precious stones rather than embarking in what would eventually be the main occupation of alchemists. In addition to this argument, the importance of which is usually underestimated, the existence of a literature on glassmaking reveals that it was in this context that the first systematic ideas upon the possibility of imitating minerals took place for the first time. The fact that Pliny deliberately chose not to mention the name of the authors of these treatises shows that a debate on the relation between natural and artificial stones was particularly lively and that the ambition of creating gems by the chemical arts was regarded with contempt by traditional naturalists. Inspired by a conservative philosophical standpoint Pliny, like Seneca, despised the pretentious attitude of these craftsmen who contended with nature for the act of creation. The position held by ancient philosophers seemed to be incompatible with the proliferation of opinions and practices, which, in the eyes of Pliny and Seneca, revealed the cultural and moral decadence of their contemporaries. The high social status of both authors justified their

negative attitude toward the Commentarii and their authors, but one wonders whether their perceptive attention on the recent technical progress was not a sign of the power of attraction they exerted on the intellectuals of the time. Additionally, there were authors who held a different opinion to develop new theories on the properties of matter by taking the chemical arts as point of departure. This was the case of the enthusiastic followers of the Pythagorean philosophy, which spread in Rome as early as the first century BCE and made systematic efforts to combine the arts with magic and philosophy. While describing the problematic properties of the diamond, Pliny remarked [9k]: “Now throughout the whole of this work I have tried to illustrate the agreement and disagreement that exist in Nature, the Greek term of which are respectively ‘sympathia’, or ‘natural affinity’, and ‘antipathia’ or ‘natural aversion’. Here more clearly than anywhere can these principles be discerned.” Pliny probably referred to a work entitled Perì antipatheiôn kaì sympatheiôn lìthon which evoked a doctrine that was exerting a considerable influence on natural philosophy. The author of this work is uncertain, although, given its astrological contents, Bolus of Mendes seems the most likely candidate [23]. Whatever the real identity of the alchemist was, it is important to point out the connection between the appearance of Bolus’ works and the development of glassmaking, an art which enjoyed both a high social reputation and a considerable “philosophical” importance. Such a reputation, reflected in the publication of treatises devoted to this topic, reached its peak during the first century CE when Pliny associated this literature with fraud because he felt the threatening effects of its pervasive diffusion. The chronological coincidence between the appearance of the work of the Egyptian alchemist and the progress made in glassmaking is of crucial importance because Bolus was the first author who believed that one metal might be made from another [23] and clearly referred to the possibility of the alchemical operation of transmuting substances by giving practical instructions.

5

The Byzantine Connection

Whereas many Latin authors explicitly referred to alchemical authors during the first two centuries CE, the Latin West witnessed a rapid decline of scholarly knowledge after the Barbarian invasions and fall of the Western Roman Empire. From the third century CE onward, the pursuits in alchemical research thus remained confined within the Greek and then Byzantine tradition.

5 The Byzantine Connection

Figure 4 Garden of Eden mosaic decorating the vault of the Galla Placidia Mausoleum, Ravenna. First half of the Vth century (after 425).

Glassmaking progressively migrated from the Roman centers of production to the south Eastern capital and cities. Together with several Syrian centers, the Alexandrine area and Ravenna (Figure 4), Constantinople represented from the first half of the fourth century CE to the end of the sixth a cultural site capable of assuring, though briefly, favorable conditions for scholarly and technical research. In this favorable context, the presence of an important community of glassmakers is attested in Constantinople. Unfortunately, apart from massive archeological remains, our knowledge of the Byzantine glass production and of its uses is confined to exceedingly few literary sources, most of which are late and medieval. But spectacular evidence for a flourishing glass industry during the early centuries (fourth to sixth centuries CE) of Byzantium is undoubtedly the monumental mosaics which adorned the newly conceived basilicas and mausoleums. The case of alchemy shows that Byzantine culture played a crucial role in directing the heritage of the

Greco-Egyptian tradition onto a new path. The corpus of ancient alchemical writings was collected probably for the first time in Constantinople between the seventh and the beginning of the eleventh century, when the Codex Marcianus Gr. 299 was compiled. This manuscript, preserved in the Biblioteca Marciana in Venice, is the primary source of most of the known ancient alchemical texts. It includes not only the writings of Pseudo-Democritus and Zosimus of Panopolis (third to fourth centuries), among others, but also of Byzantine authors such as Stephanos of Alexandria (c. 550–before 638) and lists the titles of lost texts attributed to authors bearing the names of the Byzantine Emperors Justinian (r. 527–565) and Heraclius (r. 610–641), indicating that alchemy attained an unprecedented high cultural and social status in Byzantium. The remarkable strength and prestige of the Byzantine alchemical tradition is further evidenced by the Epistle on the Making of Gold of Michael Psellos (1018–after 1081), the most influential intellectual of the period, where metal transmutation was accounted for in terms of the theory of the four elements [24]. Although this work does not contain anything particularly original, it demonstrates that alchemy was an integral part of high Byzantine cultural circles where, along with astrology, alchemy was likely included in higher education. The Byzantine contribution to the alchemical corpus consisted of several recipes dealing with, among other things, glass-making, the coloring of precious stones and the manufacture of pearls. It is probable that the prosperous glass industry and its prominent role in the architectural decoration of Byzantine churches and basilicas were sources of inspiration for the alchemists in their search for the transmutation of matter. This hypothesis finds a confirmation in a work of Stephanos of Alexandria included in a manuscript, the Parisinus Ms. 2327 of the Bibliothèque Nationale de France, where the author described in several recipes the fabrication of precious stones by colored glass and enamels. Many of these recipes were probably coming from the Greek-Egyptian tradition. Without textual evidence, however, it is impossible to determine what exactly was added in Byzantium. It is interesting to point out once again that the progress of glassmaking went hand in hand with the development of alchemy (Figure 5). The earliest explicit definitions of this discipline as Sacred art during the fifth century coincided with a widespread experimentation with new glass techniques. It is therefore not surprising that the definition of transmutation set forth by Aeneas of Gaza took glassmaking as his point of departure.

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Figure 5 Glass alchemical alembics illustrating the Codex Parisinus 2327 thirteenth century manuscript of Mary the Jewess’ On Furnaces and Instruments (c. second to third century) as quoted by Zosimus of Panapolis [25].

6

Perspectives

The Egyptian glassmaking tradition survived in Hellenistic Alexandria, exporting both technical know-how and theoretical insights to Palestine and, during the Roman Empire, along the Mediterranean coastline. Such an influence explains the Greek alchemists’ admiration for Egyptian culture. The survival of the Marcianus graecus ensured a future to the Greek alchemical tradition and its acquisition by the Byzantine cardinal Bessarion (1430–1472) probably favored its study in the West after 1468 when it was donated to the Biblioteca Marciana in Venice. However, interest in alchemy and in its connection with glass had then already been raised in the Western and Latin culture. Ideas circulated in the Mediterranean along with commodities and technical knowledge. Thus, the development of alchemy, like glassmaking, was the result of a fusion of multicultural traditions. Inasmuch as ancient alchemy was characterized by a remarkable attention to the chemical arts, we must always bear in mind that its first definition regarded it as a “holy” and “sacred” art, and that its philosophical and spiritual background were no less essential features of its identity than divination and magic were connotative elements of astrology. This characteristic of ancient alchemy once more underlines a debt to

Egyptian culture and religion. Religion, philosophy, and chemical know-how converged into the creation of a new body of knowledge, which remained prosperous even when all the other natural sciences were declining during the Hellenistic epoch and Late Antiquity. Historians of ancient science have neglected the remarkable development of chemical arts and the fecund connections they entertained with their culture. The history of ancient glass shows by contrast how useful it is to follow the impact of this technology among learned circles and how its breakthroughs have inspired philosophers of nature and alchemists alike to develop new ideas on the architecture of matter.

References 1 Aufrère, S. (1991). L’Univers minéral dans la pensée

égyptienne, 2 vols. Cairo: IFAO. 2 von Saldern, A., Oppenheim, L., Brill, R.H., and Barag, D.

(1970). Glass and Glassmaking in Ancient Mesopotamia. Corning: The Corning Museum of Glass Press, reprinted 1988. 3 Trowbridge, M.L. and Luella, M. (1930). Philological Studies in Ancient Glass. Urbana: University of Illinois.

References

4 Bresciani, E. (ed.) (1988). Le vie del vetro. Egitto e Sudan. 5

6

7 8

9

10 11

12

13

14

Pisa: Giardini editori. Diodorus of Sicily. Historiarum libris aliquot qui extant (I, 11:5–6, trans. C.H. Oldfather, The Library of History). Cambridge, MA: Harvard University Press, 1984. Galen (1965). Adversus ea quae Juliano in Hippocratis aphorismos enunciata sunt libellus. In: Claudii Galeni Opera Omnia, vol. 18 (ed. C.G. Kühn), 1. Hildesheim: Georg Olms. Homer, Odyssey, 7:87 (kyanos) (trans. R. Lattimore) (New York: Harper Perennial, Reed. 1991). A. Adler (ed.), Svidae Lexicon, 5 vols. Phi. 422 (Leipzig: Teubner, 1928–1938). English trans. Stoa Consortium at http://www.stoa.org/sol (June 2020). Pliny the Elder. Historia naturalis: (a) caeruleum 37:23; (b) progress in glass making 36:64 and 36:66; (c) on genuine and false stones 37:75; (d) expensive dipper 37:10; (e) glassware vs. rockcrystal 37:10; (f ) imitation of beryl 37:20; (g) proof by sunlight 37:22; (h) carbonculi 37:26; (i) topaz 37:33; (j) relative value of gold 37:78; (k) sympathy and antipathy 37:15. Books 36 and 37 trans. E. Eichholz, Natural History. Harvard: Harvard University Press, 1962. Halleux, R. (1974). Le problème des métaux dans la science antique, 70. Paris: Les Belles Lettres. Theophrastus. De igne magorum philosophorumque secreto externo et visibili (§ 73, trans. V. Coutant, De igne: A post-Aristotelian View of the Nature of Fire). Assen: Royal Vangorcum, 1971. Plato. Politicus, 288d (products of the mines) (trans. C.J. Rowe, Statesman). In: Plato Complete Works. Indianapolis: Hackett Pub. Co., 1997. Plato. Timaeus: (a) hyalos 61b; (b) fundamental polyhedra 55e–56d; (c) transformation of water into fire and air 56d; (d) glass 61b; (trans. D.J. Zeyl, Timaeus). In: Plato Complete Works. Indianapolis: Hackett Pub. Co., 1997. Aristotle. Meteorologica: (a) classification of bodies 385a; (b) fusibility 382a; (c) aqueous element predominant

15

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17

18

19

20

21 22

23

24

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389a; (trans. E.W. Webster, Meteorology). In: The Complete Works of Aristotle, vol. 1. Princeton: Princeton University Press, 1984. Beretta, M. (ed.) (2004). When Glass Matters. Studies in the History of Science and Art from Graeco-Roman Antiquity to the Early Modern Era. Florence: Leo S. Olschki. Beretta, M. (2009). The Alchemy of Glass. Counterfeit, Imitation and Transmutation in Ancient Glassmaking. Sagamore Beach: Science History Publications. Theophrastus. De lapidibus liber (trans. E.R. Caley and J.F.C. Richards, On Stones, p. 58). Columbus: The Ohio State University, 1956. Seneca. Epistulae morales ad Lucilium (XC:33, trans. R.M. Gummere, Letters to Lucilius, vol. V.2). Harvard: Harvard University Press, Reed, 1996. Anonymous. Les alchimistes grecs. Papyrus de Leyde – Papyrus de Stockholm – Fragments de recettes (ed. and transl. R. Halleux). Paris: Les Belles Lettres, 1981. Aeneas of Gaza. Theophrastus (62,1, trans. S. Gertz, J. Dillon, and D. Russell, Aeneas of Gaza Theophrastus with Zacharias of Mytilene Ammonius, p. 50). London: Bristol Classical Press, 2012. Kisa, A. (1908). Das Glas im Altertume, vol. 2, 533–535. Leipzig: Hiersemann. Varro. Saturae Menippae (fragment 379, ed. and trans. J.P. Cèbe, Satires ménippées, vol. 9). Rome: Ecole française de Rome, 1990. Pseudo-Democritus. Physika kai mystica (ed. and trans. M. Martelli, On the Making of Purple and Gold: Natural and Secret Questions). In: The Four Books of PseudoDemocritus, S79–S103. London: Maney Publishing, 2014. Psellos, M. Péri toû hopôs poièteon chryson. In: Catalogue des manuscrits alchimiques grecs, vol. 6 (ed. J. Bidez). Brussels: Maurice Lamertin, 1928. Berthelot, M. (1888). Collection des anciens alchimistes grecs, vol. 1, 161. Paris: Georges Steinhel.

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10.5 Ancient Glassworking E. Marianne Stern Amsterdam, The Netherlands

1

Introduction

Glassworking was a significant component of ancient technology. Tracing its evolution thus contributes to a better understanding of ancient societies especially since glass became a ubiquitous material of dual practical and aesthetic interest. The history of ancient glassworking is in addition relevant to modern technology or even to marketing. Whereas industrial processes such as flame finish (Chapters 3.12 and 6.7) and brand packaging still rely on innovations dating back to antiquity, most of the methods practiced today in art glass studios were already in use in the first century of our era. Glass was a by-product of metallurgy and, particularly, of ceramics. Therefore, it should come as no surprise that glass artifacts initially imitated metal and pottery work. It took of course some time to recognize the original properties of the new material and to take advantage of them in new processes. Some techniques are still well known so that historians are paying more attention to those that disappeared, often after having given rise to outstanding masterpieces. Ancient glass has kept various defects as a memory of its fabrication. Toolmarks are important because traces of cutting, pinching, stretching, twisting, indenting, grinding, or polishing relate to the processes themselves. In addition, air bubbles, folds, or chillmarks represent a frozen image of the movement of the glass during shaping. But the interpretation of these features is not always unambiguous because blowing, sagging, and pressing can, for instance, cause bubbles to stretch in the same direction. As for idiosyncrasies like lopsided ribs and scratches in unexplainable places, they too carry information that has to be unraveled.

Reviewers: S. Fünfschilling, Augusta Raurica, Augst, Switzerland D. Ignatiadou, National Archaeological Museum, Athens, Greece

Current research on ancient glass-forming techniques thus also relies on theoretical reconstructions, production of replicas, and ethnographic research. All three require experiments, be they as confirmation of the feasibility of the suggested technique or as test of ideas for making reliable replicas. Any theoretical reconstruction of a technique needs to explain all the details and idiosyncrasies provided by the ancient artifact and to agree with the technological shelf available at the time and location of its production. If experiments are needed to test the feasibility of a hypothesis, they do not need to generate a perfect replica. Successful experiments are instructive only insofar as they demonstrate the feasibility of a production method. They do not represent incontrovertible evidence for the proposed technique. Not only more than one method might achieve a specific result but, like their modern counterparts, ancient artisans were likely wont to develop their own way of doing things. It is beyond the scope of the present chapter to review all these aspects and, in particular, all diverging propositions that have been discussed in the literature. Rather, our goal here is to stress the inventiveness and artistry of ancient glassworkers by showing how they took advantage of the unique properties of glass that are discussed in many other chapters of this Encyclopedia. Material constraints will first be presented especially in terms of viscosity, temperature, and expansibility. That for 15 centuries rather viscous glass was shaped will be illustrated by techniques such as core forming, casting, and mold pressing. Excluding flat glass, which is dealt with in Chapter 10.8, the new possibilities offered by blowing will then be described. Workshops and the social and economic aspects of glassworking will finally be discussed along with some of the reasons why glass met with so much success in antiquity. In preamble, however, it needs to be stressed that a major problem of reconstructing early techniques is that

Encyclopedia of Glass Science, Technology, History, and Culture, Volume II, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

10.5 Ancient Glassworking

a glassworking furnace predating blowing has not yet been identified beyond doubt. Although potter kilns could have been used for firing glass in molds and preparing flat glass [1], accessible, open heat sources were needed for hot manipulation and tooling. Use might have been made of mobile firepots like those used by Egyptian metal smiths in the third millennium BCE or of shaft furnaces that deteriorated without leaving a trace. One would then understand why a workshop at Rhodes of the Hellenistic period (third to first centuries BCE) showed no trace of a furnace although tools and waste from bead and vessel production as well as thousands of beads, canes, and chunks of raw glass were found [2].

2

Basic Features of Glass Shaping

2.1 Physical Conditions Every glass-making operation is performed under welldefined conditions characterized by fixed viscosities (Chapters 1.1 and 4.1) and, therefore, fixed temperatures for a given composition (Figure 1). But neither concept existed before the seventeenth century. Whether glass was made from raw materials or simply shaped, it was its hotness and workability that were gauged from its color and its movement on a tool. Of particular importance were three colors interpreted as heat indicators by Late Bronze-Age glassmakers: glowing red, glowing

Soft, point 7.6

green/yellow (meaning perhaps orange/yellow), and glowing golden yellow, the highest heat they could reach [3]. We now know that a typical Roman glass (Chapter 10.3) was sufficiently homogeneous at 1050–1150 C, the range at which it was gathered from a pot or a tank furnace. The outer skin of the gob needed to be cooled to become a bit more viscous for blowing between 970 and 1020 C, the rather narrow range where the glass was neither too rigid nor too soft so that shaping it on the blowpipe was readily controlled. It became possible to draw long, thin canes at around 930–950 C when a thread could be trailed from one tool onto or around another. Above about 900 C, one could have pinched, poked, bent, pulled, and manipulated the soft glass with handheld tools or marvered it on a flat surface (i.e. roll it back and forth). Flattening was an extreme form of sagging. A sizeable chunk of raw glass began to deform and sag outwardly at about 830–875 C. It lost its shape and flattened to an equilibrium thickness of about 0.7 cm (Chapter 1.4) while its edges contracted [1] and tended to become circular as a result of surface energy minimization. One piece fused to another from 715 C whereas the lower end of the working range was about 600 C, the temperature at which glass began to bend or sag under its own weight. Glass adhered to metals and ceramics as long as both materials were hot. But a temperature difference was crucial to the success of operations: upon gathering, the tip of the blowpipe had to be cooler than the glass to let it contract around it whereas the opposite held true to let

Anneal, Strain, point point 13 14.5

Figure 1 Viscosity ranges for glassworking operations and viscosity–temperature relationship of the typical Roman glass of the Embiez shipwreck (solid curve, P. Richet, personal communication). Temperature interval of fuse-to-stick operations indicated as an example.

1000

Hot gathering Marvering 900 Trail thread Drawing cane 800 Chip casting

T (°C)

1286

Flatten to a disk 700 Fuse to stick Working range 600 Sagging Chunk gathering 3

6

9 Log viscosity (poise)

12

500 15

2 Basic Features of Glass Shaping

(a)

(b)

Figure 2 Gathering of 1–3 g mosaic glass florets (slices) on a blowpipe: final gather (a) reheated and marvered (b) after eight steps of pickup and reheating in six minutes. Source: Photos Arz.

chunks of “cold” glass stick to the pipe when they were picked up [4]. For gathering, the chunks had to be preheated to about 500 C to avoid thermal shock. After each gathering, the glass on the blowpipe was shortly reheated to ensure the sticking of the next chunks picked up (Figure 2). At the end of the process, the jumbled mass was heated to higher temperatures to be marvered and shaped into a smooth piece, which could then be blown. 2.2

The Issue of Thermal Expansion

The fundamental glassworking step was annealing, which had to be performed at about 500 C to prevent the accumulation of internal stress caused by the fictive temperature gradients created through the glass transition (Chapter 3.7). We do not know how and when it was realized that glass had to be cooled down very slowly after shaping, the larger the piece the slower the rates, or when dedicated furnaces or kilns began to be used for annealing. At least three different types of glassblower furnaces are known from the Roman period, one circular and two rectangular, but the function of the latter has not yet been identified clearly. Ancient glassblowers could have used the heat of piles or baskets of hot ashes, olive pits, or the like for annealing, but the cracks observed in many ancient glasses point to often insufficient relaxation of internal stresses. Cracks could also be caused by thermal expansion mismatch in pieces made from two or more glasses of different chemical compositions (Chapter 3.5). In the Late Bronze Age, colorants were usually added by the producers of the raw glass [5]. The composition

changes induced in this way were thus minor so that expansibility conflicts were not likely to create a problem for the brightly colored polychrome objects and vessels fashionable in Western Asia and Egypt, especially in view of the low shaping temperatures [6]. In Mycenaean Greece, where glassworking was also common in this period, the artisans rarely combined different colors within one piece. They used almost exclusively blue glass [1], which was also the preferred color at many Late Bronze-Age working sites in Central Europe and north Italy. Pliny (23/24–79 CE) reports that in his days glass was frequently colored in secondary workshops [7], which would have had the advantage that the glassblowers themselves could control the process and the danger of strain be kept to a minimum [6]. 2.3

Molding Processes

Molding was invented long before blowing. In the Late Bronze Age, the most widely used mold materials were stone and especially pottery, which shrank, but less than glass, and then also plaster. The higher the temperature and the longer the cooling, the greater was the danger that the glass would stick to the mold. Although pottery molds without undercuts were reusable, a separator substance was needed if the glass was not removed before annealing. Corundum (Al2O3) was one substance used for this purpose as indicated by the traces of this highly refractory oxide found in Greek terracotta molds dating from the late fifth or early fourth century BCE [1]. Bone ash, a substance readily available, might have been

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result from the sudden contact of hot glass with a cold marver or mold. Chill marks appear as wrinkles or ripples on the surface of the glass [9] or as the concentric depressions sometimes seen on the walls of Roman square bottles shaped freehand on a marver. Rotary scratches with a definite beginning and end are often found on shiny surfaces of the inside and bottom of non-blown ancient glass vessels such as Hellenistic sagged vessels and ribbed bowls (Figure 3). The scratches were interpreted as grinding or polishing marks until microphotos revealed that they could be accompanied by shortened horseshoe chatter marks, a phenomenon observed after a mishap with hot glass (Figure 4). Because they are found on vessels subjected to a rotary motion either during their shaping or when lifted off the molds, the rotary scratches are now ascribed to friction while the glass was hot, either by protruding particles of ancient tools or molds or to inhomogeneities in the glass [6].

3

Early Shaping Methods

3.1 The Ceramic Connection

Figure 3 Rotary scratches on the interior of a ribbed bowl fragment (Frankfurt/Main, Arch. Mus., inv. α24292) (preserved height 7.2 cm). Source: After [10].

another strong separator [1], as could also have been soot although no trace of it has been found in the rare ancient molds extant [8]. If glass sagged over a convex mold, it had to be lifted off before annealing to avoid cracking through shrinking upon cooling. Plaster molds had several advantages although they could be used only once. Plaster did not undergo volume changes with temperature and its dissolution in water made removal of the mold easy after annealing. In addition, fresh plaster contained some moisture – the so-called crystal water – that evaporated upon contact with the hot glass and acted as a separator ensuring a shiny glass surface [6]. Because of the weakening effect of this water loss, the mold tended to fall apart during or after annealing. A solution to this problem was thus to place the mold in a sturdier container, which provided extra strength during use. Likewise, moist wooden paddles for shaping and plungers for pressing glass created a shiny surface through the evaporation of moisture upon contact with hot glass. Glass is not a good heat conductor (Chapter 4.5). Whereas cold glass can fracture by thermal shock when touching a glowing-hot blowpipe or pontil, chill marks

Before the invention of blowing in the first century, glassworkers made a limited use of hot glass for both shaping and decoration. Crushed glass and small chunks of raw glass heated at the tip of a handheld tool sufficed for the production of most artifacts. Artisans actually took care not to overheat a piece, which would have been lost if the glass melted. In the Late Bronze Age, the ability to build melting furnaces was likely less problematic than long thought. Whether the Egyptian furnace at Amarna was a primary glassmaking furnace or not, a replica could reach 1150 C [11]. Hence, difficulties for remelting ingots were not the reason for low-temperature shaping there and in nearby Qantir where primary and secondary workshops were located in proximity [5]. At Amarna and Qantir, glassworking and faience production took place in parallel. The first craftsmen working with true glass had worked previously with faience and other vitreous materials. Consequently, they built on techniques familiar to them. Sintering, for instance, was a ceramic technique to transform a powder into a coherent mass without melting. The raw material was layered into or over a mold, dried, and fired in a kiln. Similarly, fine crushed glass could be layered into or over a mold or core and sintered. Another early technique that had its roots in ceramics was the pressing of crushed glass and heat-softened chunks into molds [6]. Extant artifacts show that the glassworkers gradually improved manufacturing techniques, discovered new properties of the material, and invented novel tools and techniques to make use of those properties.

3 Early Shaping Methods

(a)

(b)

(c)

Figure 4 Rotary scratches exhibiting horseshoe chattermarks so much shortened that they almost look like vertical lines: a close-up of the fragment in Figure 3 (a) and two micrographs, one of the fragment in Figure 3 (b) and the other of a mishap in hot glass (c) at Schott Glas, Mainz (Germany).

3.2

Core-Forming

The earliest glass vessels were made by core-forming, a generic term for a number of techniques that involved deposition of glass on a rigid core that was subsequently scraped out. In the Late Bronze Age, the deposition of cold pieces of glass was a Western Asiatic specialty.

Vessels known from several sites display colorful figural scenes and zigzag patterns created with short segments of opaque red, yellow, blue, and white canes with circular sections. The individual pegs or canes look as if they had been held together by bitumen, which would have burned off during firing [3]. The vessel’s exterior, which was

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exposed to the heat, fused better than the interior stuck to the bitumen coating of the core. All these vessels lacked handles and applied decoration, which would have required tooling while the glass was hot [12]. Most Western Asiatic and Egyptian core-formed and rodformed vessels carry tooled decoration applied to a monochrome underground, the “body” of the vessel [1, 13]. It has been often claimed that the core was immersed into a pot filled with hot molten glass to produce the body. Archeological research and experiments [14, 15] do not support this statement, however, because pots able to withstand hot molten glass are not known at Late Bronze-Age sites [5]. Those used at Amarna and Qantir were much too small to accommodate core-formed vessels that could be from 16 to 26–40 cm in height, like the amphoras found in the tomb of the pharaoh Amenhotep II (r. fifteenth century). Pots for remelting glass actually did not become common until the third century CE, but they still would have been too small. Moreover, the strain induced by a mass of hot molten glass cooling and shrinking around a core would have induced cracks, a phenomenon that has not been attested. An ancient core-formed bottle from Iraq provided important clues as to manufacturing techniques in the Late Bronze Age [12]. Experiments show that a moldformed core made from a 10 : 1 mix of sand and clay, that is prefired at about 815 C, works well [14, 15]. It was mounted on a metal mandril (supporting rod), coated with a liquid slip of the same materials, and fired at c. 700 C after which the core was thoroughly wetted with water to let finely crushed glass stick to it like wet sand. Upon sintering at about 590 C, the glass glazed over and fused to the core. After further heating up to about 860 C, successive layers of crushed glass were added by rolling the core back and forth on a flat surface in a way that shaped the vessel and smoothed its wall. This process accounts for the observation that the glass of the bottle from Iraq was layered parallel to the surface of its wall and that bubbles trapped in between these layers were spherical because the glass was not stretched in a particular direction while hot [12]. The handles and decorative trails were made with colored canes prepared independently, while zigzag patterns, festoons, feather patterns, and the like were created with a pointed tool or hook that dragged the threads up and/or down. Crucial to the success of these experiments was the use of a furnace with a vertical heat chamber, which was open at the top (Figure 5). Because of vertical heat rise, the artisan could manipulate the glass-coated core and the glass canes while controlling the temperature on the relevant side of the piece by a slow rotation of the mandril. In addition, a slit in one side of the opening at the top of the furnace made it easier to work lower down in the heat, for example, when the decorative glass threads were dragged back and forth.

Figure 5 Core-forming furnace open at the top (height 52 cm) as designed and drawn by D. Giberson. Source: After [10].

Although vessels had become much smaller, coreforming enjoyed a prolonged revival from the mid sixth through the end of the first century BCE. [1, 13]. Now, the body was sometimes made from a hot trail of glass wound around the core, with the decorative trails going in the opposite direction [1]. This technique was probably made possible by the discovery that small pieces of preheated raw glass could be picked up on the glowing tip of a solid metal rod and sufficiently heated to create a gob of glass from which trails could be wound around the core. The furnace would still have been open at the top. Working directly above, and at times in the heat, the artisan could manipulate core and trail simultaneously, while controlling the temperature of both. The orientation of the heat with respect to the core made it possible to apply an endless thread of glass as observed in the Hellenistic period.

3.3 Casting In the Late Bronze Age, glassworkers developed the chip casting technique reminiscent of faience firing in that its first step was the filling of a mold at room temperature with a finely crushed glass [1]. Upon firing at about 870 C, more crushed glass was added with a funnel-shaped sprue to fill the mold entirely, as shown by funnel remains on the rim fragments of glass-coloring pots at Qantir [16]. The best evidence for chip casting is provided by the headrests of Tutanchamen (r. fourteenth century). Weighing about 2 kg, the largest one was cast in one piece 17.5 cm high, 28.3 cm wide, and 10 cm deep [17]. The molds would have been made from the same materials as the glass melting

3 Early Shaping Methods

pots used at Qantir, which were lined with a parting layer and specially designed to optimize heat conduction from the outside. A similar parting layer in the molds would have ensured that only a final surface polishing was needed to remove any roughness after annealing [5, 17]. In antiquity, chipcasting was primarily a means of making a single hollow object after a wax model had first been made. Early cast vessels made of transparent colorless glass evoking rock crystal were precious, individual pieces, often imitating the shapes of silver vessels decorated with petals that were convex on the exterior and concave on the interior. Both the wax model and the mold were destroyed in the process: the wax model when the artisan burned it out of the mold in preparation for casting and the mold after the piece was fired. Made of plaster, the mold was broken away to extract the piece. 3.4

Mold Pressing

An important evolution took place when the artisan used a moist wooden plunger to press a gob of glass inserted as hot as possible into a mold to shape at the same time the external and internal surfaces of a vessel, whether plain or decorated with relief. Solid objects, such as amulets, inlays, beads, pendants, and other small artifacts could be pressed in reusable open molds, either with sintered crushed glass or with small pieces of softened glass [1, 13]. Again the technique was closely related to faience. In Bronze Age Egypt, ceramic molds were used, but Mycenaean (Greek) beads and inlays were usually made in steatite molds that could have been used as well for the production of gold ornaments. The numerous techniques used in antiquity for the production of beads and other small objects have been extensively discussed [1, 18] so that they will not be included here. More important was another form of mold pressing that supplanted the time-consuming casting in the fourth century BCE because the same kind of production could be achieved faster. This was not possible for vessels with a decoration that was convex on the exterior and concave on the interior. However, by far the majority of glass vessels decorated with relief on the exterior now had smooth interiors that presented no obstacle to pressing in concave molds. One created easily exterior ridges by making a simple groove or drawing a thin line in the interior of the mold [19]. Glass vessels decorated with high relief are commonly assumed to have first been blown and their decoration cut after annealing [19]. But the walls of the ancient vessels are entirely smooth between the elements in high relief and show no signs of grinding or polishing. Hence, the high relief was probably mold-formed [6, 10]. A wax model with the decoration applied to the surface served to create a sturdy plaster mold, which was filled with hot glass. While the mold was turned with some device, a moist wooden

plunger pressed the glass into it. After annealing, the plaster mold fell apart. Simple motifs, ridges, and letters (in reverse) could be engraved directly into the mold. 3.5

Rotary Mold-Pressing

When the mold was put on a turntable or potter’s wheel (Figure 6), the combination of vertical pressing and rotary rubbing made pressing at relatively low temperatures possible and ensured a more uniform distribution of the glass for open vessels with a simple cylindrical or outward curving profile. The earliest evidence for the technique comes from Ionia (southwest coastal Turkey) and Greek Macedonia [20] where colorless glass bowls decorated with fine vertical ribs or petals imitating silver work appeared in the middle of the fourth century BCE. Mold-forming is familiar from the production of moldmade Hellenistic pottery, thought to have been invented in Athens in the last quarter of the third century BCE. The main difference was that potters used molds for mass production, whereas glassworkers could not reuse molds with decoration in relief because they disintegrated and/or had to be broken away from the finished product. Rotary mold-pressing was also used to case glass, i.e. to fuse one layer of glass with another usually of a different color. Cased glass cups, often with a paper-thin, opaque white lining became a specialty in the second quarter of the first century CE. The lining enhanced the transparent colored glass on the exterior. Whereas the layers of colors

Figure 6 Rotary pressing: gob of hot glass pressed with a moist wooden plunger in a turning plaster mold. Source: After [10].

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in an experimental bowl are thick, mold-pressing made it possible to create an internal lining even thinner than achieved by blowing. In that case, two plungers were needed, one for the external glass of the vessel and another, slightly smaller, for pressing the internal glass [10].

Grinding the exterior of the rim area, which became common in workshops in Italy and northwestern Europe during the first century CE [19], would have required no more than 5 or 10 minutes. Certain mosaic glass ribbed bowls suggest that the distortion of the pattern was not a problem because it made the glass look like a semiprecious stone [1, 19].

3.6 Rib Making Toward the beginning of our era, the most popular type of glass vessels were ribbed bowls [1, 13, 19]. They are thus regarded as a hallmark for the Julio-Claudian period. No two bowls are exactly the same because irregularities in the length and placement of the ribs show that each one was tooled individually [19]. The ribs were shaped either while a mass of hot viscous glass was sagging over a convex mold placed on a slowly turning turntable (Figure 7) or they were pinched into a preformed disk of glass, which was then sagged [21]. Ancient ribbed bowls can be replicated with both techniques. The former yields relatively thick ribs that often curve slightly in one direction and have lopsided profiles like the mass-produced ancient bowls of natural bluish green or more expensive colored glass. The latter yields in contrast thin ribs, usually vertical, like those seen in ancient ribbed bowls executed in expensive luxury glass [21]. A monochrome ribbed bowl could be tooled on a turntable in one or two minutes. No polishing was required because the glass was smooth except for occasional rotary scratches [6, 10]. The rims often show toolmarks from pressing the glass against the mold to stem the flow.

3.7 Coiling and Striping: Reticella Vessels Reticella (network) vessels were made from the eponym reticella canes and trails created by application of one or two thin monochrome canes to a transparent, colorless bit of heat-softened glass, which was then twisted and lengthened (Figure 8). For the spiral bowls, made from the second century BCE, hot and pliable trails were coiled around a convex mold placed on a turntable (Figure 8). For the parallel reticella vessels, [13, 19] produced a little bit later, cane segments were first fused parallel to each other to form a striped disk which was then sagged over a stationary convex mold. In the former, the spiral trail and the bowl were created simultaneously, the trail going from the bottom center toward the rim [1, 10]. The rotary scratches occasionally observed on both types of reticella bowls are an indication that the glass was still hot when it was scratched, either during the turning of the mold or when the vessel was lifted off (Figure 8). A bowl made from three alternating trails would have required four artisans: three for holding and turning the hot bits of glass of the reticella trails and one for

Figure 7 Making of a ribbed bowl: sagging or flowing down of hot glass over a slowly turning convex mold; rim pressed against the mold, cooling the glass and thus stopping its flow; interstices between the ribs then pressed, pushing up the glass on one side with mold turning. Source: After [10].

3 Early Shaping Methods

(a)

(b)

(c)

(d)

(e)

Figure 8 Making of spiral reticella vessel: drawing of the thread from a rotating conical bit of colorless glass on which two colored canes have been deposited; coiling of the thread around the mold, and final attachment of the rim made of a thicker thread of dark glass (Source: After [2]). Spiral reticella bowl (height 7.0 cm, rim diameter 12.8 cm.). Probably second half of second century BCE. Stuttgart, Landesmuseum Württemberg, inv. Arch 97/W73. Formerly Ernesto Wolf Collection. Source: After [1].

turning the wheel and pressing the trails against the mold with a moist wooden paddle to obtain smooth walls on either side [6]. No grinding or polishing was possible because the canes were not protected by transparent

colorless glass. A striking feature of spiral reticella bowls is the uninterrupted winding of several-meter length that could be involved, which would have been very difficult to achieve with a stiff thin cane.

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3.8 Miscellaneous Apparently invented in the early second century BCE, a curious technique was used exclusively for the production of small round, lidded boxes known as Cretan pyxides. As done by the potter’s hands, a moist wooden paddle was applied against a rotating piece of glass in the middle of which a plunger was sunk (Figure 9). This technique did not spread, however, in contrast to sagging with which the mass production of vessels began in the first century BCE [1, 13]. With this simple technique, a straight, flat-sided tool pressed a sagging gob or disk of hot viscous glass against a convex mold placed on a turntable, creating at the same time the rim of the bowl. Probably made of baked clay, the mold was reusable, just requiring the finished vessel to be lifted off before annealing and consecutive glass

shrinkage. Mosaic glass bowls [1, 13, 19] required working with a preformed disk composed of mosaic glass slices or florets fused together like the parallel striped reticella bowls [13, 19]. Before the sagging stage, such disks had to be heated at relatively low temperatures to avoid distortion of the fused patterns during sagging. Small bulbous bottles predating the discovery of inflation were composed of bands of colored glass or, occasionally, of gold foil sandwiched in between two glass layers [13, 19]. As in mosaic glass bowls, the bands extended through the thickness of the wall continuing on the bottom of the bottles without a seam (Figure 10). The trick could have been to let a preformed glass bowl sag vertically under its own weight over a raised support [6, 10]. Pressing the free-hanging glass toward the stake supporting a plaster mold would have created the neck. Depending on the

Figure 9 Making a Cretan pyxis: cylindrical plunger pressed into a gob of hot glass placed on a turntable; moist wooden paddle then raising the displaced glass by pressing it against the plunger; and final of the flattening the vessel’s foot. Source: After [10].

(b)

(a)

Figure 10 Making of a bulbous colorband bottle: preheated colorband disk or bowl flowing down and contracting on a raised plaster mold, while the neck is shaped with a moist wooden paddle pressing the glass against a turning stake. Source: After [10]. Goldband bottle (height 6 cm, maximum diameter 5.8 cm). Early first century Split (Croatia), Archeological Museum, inv. no. AMS-G-87. Source: Photo T. Seser, courtesy the Museum.

4 The Slow Blowing Revolution

shape of the mold, the colorband bottles had bulbous or straight sides. Glass vessels with angular, often carinated profiles reminiscent of contemporary pottery and metal shapes were popular as fine tableware during the early Roman Empire (c. 25 BCE–50 CE) [13]. They were produced in attractive, usually translucent colors, opaque red, and mosaic glass. But it is not yet known whether they were mold-formed, pressed with a counter mold, and finished by polishing, or rotary pressed. Far from Italy, seamless glass bangles were a Celtic specialty relying on the enlarging of a bead. The bead was mounted either on a rod-shaped mandril and widened through stretching with a second tool or on a mandril shaped as a cone and widened by centrifugal force.

4 4.1

The Slow Blowing Revolution A Late Invention

Like other major advances, the discovery that hot air expands heat-softened glass was probably accidental at a time when the wealth of techniques already available was not a strong incentive to invent a completely new

one. Keen observers not only noticed this original feature but were curious enough to take unknowingly advantage of the fact that, in modern physical jargon, molten silicates are Newtonian liquids that can thus deform under very small stresses (Chapter 4.1). At the relevant viscosities, this is why the glassblower could combine the pressure of the breath with gravitational and centrifugal forces to shape glass in especially complex ways with the help of simple tools and the marver [1]. For the earliest blow vessels, the weight was lower than 100 g, with values generally in the lower 7–20 g range. The earliest archeological evidence for inflation comes from the waste of a Jerusalem workshop active in the mid first BCE or slightly later. The finds include glass tubes pinched closed at their lower end and inflated through their upper end, of which the edge was pulled outward to create a rim (Figure 11) [23]. Glass tubes, made by drawing a hollow bit of hot glass from a metal working rod, were common because chopping them up was a simple way to create beads with a thread hole. That the earliest inflated glass happened to be a tube was crucial for the development of blowing and the blowpipe [9]. But more than 100 years of experiments, discoveries, inventions, and improvements separated the first inflated glass tubes from full-fledged Roman glassblowing

Figure 11 Fragments of inflated tubes from a first century BCE Jerusalem workshop: fire-closed inflated bulbous ends, necks, and pulled-out rims. White and black bars: 1 cm. Source: After [22].

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in the second half of the first century CE. The introduction of the iron blowpipe, the construction of a new type of glassworking furnace with a horizontal, closed heat chamber, the use of hot molten glass, and the pontil technique for fire-finishing the rim of the vessel were the most important steps in this development [4, 9]. Most, but not all of the tools now taken for granted as integral to the craft were invented during this period.

was a solid rod. It was attached to the bottom of the vessel with a small wad of hot glass and usually left a scar in the form of gashes or adhesions of glass, which were not removed. The circular form of the earliest scars suggests that the glass remaining on the blowpipe after cracking off the vessel was reheated and the blowpipe itself served as a pontil [4]. 4.3 Mold Blowing

4.2 Blowing: Pipe and Pontil As they had done previously with a solid metal rod, the earliest glassblowers throughout the Roman Empire gathered preheated chunks of glass at the tip of the blowpipe, a practice that was still common when blown mosaic glass was produced in the late first to early third centuries (Figure 2) [24]. In the beginning, the glassblowers took care not to let the glass get too hot because it might have dripped off the pipe and be wasted. When they learned how to gather a gob of hot drippy glass, the glassblowers cooled it immediately, either by gentle rotation of the blowpipe or by rolling on the marver. Only after cooling the outer skin could the glass be blown. The rims of early vessels were often ground after annealing or simply left unworked. For finishing the rim, the vessel was held with a clamp, or the artisan blew a bubble of glass on a second blowpipe against the vessel’s underside while it was still on the blowpipe [4]. The pipe with the bubble was a precursor of the pontil and the bubble itself became the vessel’s base after cracking off. Invented at an as yet undetermined date in the second half of the first century, the pontil technique was the last major step in the development of glassblowing since it allowed the mouth of a vessel to be shaped while the piece was firmly held by its opposite end (Figure 12). The pontil

To combine blowing with molding was an obvious further step. Three main types of molds were designed, each with its own specific use and purpose. Mold blowing began as a technique to give vessels a surface decoration in relief that could vie with that of chased silver. While free or “offhand” blowing was being perfected in Italy, glassblowers on the Syro-Palestinian coast explored the intricacies of the multipart mold, which determined the size, shape, and decoration of the object [19]. As time went on, the construction became simpler with fewer mold parts. By the second half of the first century, many molds in Italy had just two [9]. Another type of mold, developed in Italy around the middle of the first century, was the box mold, made of stone or terracotta, with four or more smooth walls, that speeded up mass production of prismatic bottles and jars and had the additional economic advantage of not requiring the help of an assistant since the molds did not need to be opened and closed. The vessels’ prismatic shapes facilitated packing in wooden boxes, while the base molding enabled recognition of the mold maker, the container, or the content. The realization that mold-blown vessels could be mass produced was probably one of the reasons for the significant drop in production of mold-blown decorated vessels in the third quarter of the first century. Figure 12 Pontil attachment on a newly blown glass. Source: Photo Arz.

5 Decoration

Figure 13 Replica of five-part mold for a beaker, showing mythological scenes. Source: Carving and photo by David Hill.

Multipart molds were usually made of terracotta clay and provided with a series of matching bosses and cavities to ensure they fit together as closely as possible (Figure 13). No such ancient mold has been identified beyond doubt, but the number of their parts is revealed by the seams left by the glass that seeped in between [9]. The mold (Figure 14) had to be open to admit the parison, but then it had to be quickly closed and opened again to release the piece without damaging the decoration, which usually had undercuts. The mold was held firm by an assistant while the glass itself was blown rapidly to avoid thermal shock. Necks and rims were usually free blown afterward [8, 9, 19, 25]. The surface of some early Roman mold-blown vessels suggests they were blown into metal molds [8, 9], as was a distinct group of pilgrim vessels decorated with Christian and Jewish symbols produced near Jerusalem in the late sixth and early seventh centuries [9, 19]. Decorative mold blowing experienced a revival in the fourth century with the invention of the dip mold to decorate the base and walls of free blown vessels with an attractively ribbed surface pattern [8]. These delicate vessels evoked the luxury of fine-fluted silverware without the odium of mass production, because after exiting the mold, each piece was shaped individually to yield effects comparable to optic blowing. The difference was that both the exterior and the interior of the vessel had ribs [19].

Dip molds were always open at the top. They owe their name to the fact that the blower simply dipped the parison on the pipe into them and blew. After lifting the glass out of the mold, the blower could twist the vertical ribs into spirals and even reinsert the piece into the mold to create the basketry patterns seen on some late vessels from the Eastern Mediterranean (Figure 15). Decorated glass cups, tumblers, and bowls blown into shallow dip molds, with a design carved into the bottom, were a specialty of northwest Europe. The central medallion frequently featured a Greek cross or a Christogram surrounded by stylized vines, baskets, birds, wreaths, palm fronds, and trees. One preserved mold is made of limestone. Upon extraction from the mold, the relief decoration was often blurred and farther disfigured by a pontil scar. In spite of the Christian symbolism, most of the vessels were used as secular, domestic tableware [26].

5

Decoration

Shapes and decorative techniques initially imitated contemporary pottery, stone, and metal until it was discovered that glass made new types of decoration possible through controlled manipulation and/or expansion of ornaments applied to the surface, and the use of colored

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10.5 Ancient Glassworking (a)

(b)

Figure 14 Mold blowing: loading of the parison in the sooted, five-part mold of Figure 13 and recovery of the mold-blown flask whose seams are clearly visible. Source: Photos Arz.

Figure 15 The basketry pattern of a cylindrical jug (height 21 cm). Syro-Palestinian production of the end of fourth to mid fifth centuries. Stuttgart, Landesmuseum Württemberg, inv. Arch 03/W148. Formerly Ernesto Wolf Collection.

glass. Hot decorative techniques involved the application of trails and bits of glass to the vessels’ wall as well as pinching, nicking, poking, and twisting the applied ornament or even the wall itself. Colored trails and crushed glass applied before blowing could be manipulated to create marbled patterns that imitated precious stone, whereas threads in relief or prefabricated designs made of trails nicked with a specialized tool were welded after full inflation to prevent them from melting back into the wall. Early on, the zarte Rippenschale combined spirally wound trails with thin ribs pinched before full inflation of the parison. Cold decoration involved faceting, engraving, and painting. Either by hand or with the aid of a rotary tool, grinding and polishing with water and an abrasive were the earliest methods used to modify glass surfaces as shown by the linear patterns present on the undersides of fourth century BCE colorless glass bowls imitating the decoration of contemporary metal vessels. Many sagged and ribbed bowls were decorated on the interior, below the rim, and/or lower down on the body, with horizontal grooves which looked like molded ridges when seen through the glass walls. The exterior of the rims of ribbed bowls was frequently ground to remove toolmarks. After the invention of glassblowing, cut decoration became common, especially on vessels and objects made of colorless glass. Its practice was tricky, however, if the glass had not been properly annealed. Facet cutting was

6 Special Techniques

an Italian innovation, which predated the eruption of Vesuvius in 79. Round, oval, and non-touching deep facets were the hallmark of early Roman cast colorless fine dishes and plates of the first and the early second centuries. Their optical illusion of evoking raised knobs in transmitted light was probably discovered when the interior of clear vessels was decorated with horizontal grooves that looked like moldings. In contrast, closeset, shallow circular or oval facets cut into the exterior surface of glass beakers, cups, and bowls were meant to be seen with reflected light, each facet reflecting it differently to create a dazzling shimmer. In the second century, cutters began to arrange the facets in horizontal zones divided by linear grooves, which was often less labor intensive than covering the entire surface with facets and facilitated the creation of more complex designs. Like facets, engraving showed up best on colorless, transparent pieces so that the technique was most common when this type of glass was in fashion. Some vessels were cut or abraded by a stone or a fine metal wheel whereas others were incised free hand, probably with a flint or possibly a diamond point. Many engravers used more than one technique on a single vessel. Sophisticated cold work, such as painting and figural engraving, probably was executed by specialized artisans. But very little is known about their relationships with the glassblowers, the organization of the trade in blanks, or the role of patrons. As was true in other trades, glass engravers probably relied on model books. Differences in cutting techniques and cutting styles suggest that glass engravers had a firsthand knowledge of threedimensional models, perhaps through plaster casts. Freehand engraving with linear shading imitated the darkened outlines of paintings and mosaics. Dulled, abraded areas created color effects and the cutting of glass in intaglio recalled the raised relief of metal. Egypt, Rome, and the Rhineland were home to some of the most prestigious workshops. Reflecting the Christianization of the empire, several workshops added Christian subjects to their repertoires in the second quarter of the fourth century.

6 6.1

Special Techniques Hellenistic and Roman Gold Glass

The most luxurious glasses of antiquity have long puzzled researchers. The earliest are double-walled gold glass vessels first made in the Hellenistic period and again in the “Roman” fourth century, but in a totally different way. In the former (Figure 16), the technique for cutting and applying the floral gold foil decoration closely resembles the Japanese kirikane, which is eminently appropriate for ornamental motifs [27]. The elegant floral patterns

Figure 16 Hellenistic sandwich gold glass bowl (height 10.7 cm, rim diameter 24.7 cm), mid third century BCE. Source: British Museum 1871,0518.2, © The Trustees of the British Museum.

sandwiched between two close-fitting colorless glass bowls were remarkable for their lack of cracks, an indication that the gold foil was not subjected to excessive heat. If the two glass bowls were formed by rotary pressing, three moist wooden plungers would have been needed: two larger ones of the same size for the outer bowl and the gold foil pattern, and a third, slightly smaller one, for the inner bowl (Figure 17) [10]. The late Roman gold glasses served a different purpose. They were not extravagant gifts for the happy few, but often became grave markers in catacombs after having been crudely chipped to shape. They depicted Christian, Jewish, pagan and mythological themes, married couples, portraits, animals and secular events like horse races, and often bear Latin mottos wishing their owners to prosper (vivere) or drink well (bibere). In most designs and mottos, the gold foil of the figural scene and inscriptions was applied onto the surface of the cold glass with water or a light adhesive [19]. The bowl and the foot were blown separately. To prevent thermal shock, the part of the bowl bearing the decoration needed to be reheated before the glassblower blew and shaped a second bubble (the bowl or the foot) and fused it hot to the part bearing the decoration. As a result, the gold foil was always full of tiny crisscross cracks.

6.2

Cameo Glass

As exemplified by the famous Portland vase in the British Museum (Figure 18), cameo vessels were usually blue and decorated with opaque white relief. It is generally claimed

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Figure 17 Three-step making of gold glass: pressing of the gob of the outer bowl in the mold, deposition of the gold-foil pattern adhering to a plunger of the same size, and pressing of the gob of the inner bowl with a slightly smaller plunger. Source: After [10].

that the molded white decoration was carved from bicolored blanks [28]. Some of these vessels are very large and heavy, however, and date from the very beginning of blowing when the new vessels were tiny and light weight. In addition, the pontil technique, which played a basic role in the production of blown blanks, had not yet been invented and the cross-cutting shears needed for creating the rims were also unknown. The presence of rotary scratches and the fact that the decorative relief never extends beyond the shoulders of Cameo vessels rather point to a first step of rotary mold pressing in a decorated plaster mold (Figure 19). First, the cavities for the decoration were filled with powdered opaque white glass. A drop of water held the powder together until it was dried. Then the hot blue glass was rotary pressed into the mold, melting with its heat the white glass. For a higher relief, powdered glass could be sintered in the plaster mold before rotary pressing of the hot blue glass.

6.3 Cage Cups Figure 18 Cameo glass: the Portland vase (height 24.5 cm, maximum body diameter 17.7 cm, weight 1.306 kg). Late first century BCE. Source: British Museum 1945,0927.1, © The Trustees of the British Museum.

The diatreta (cage cups) are probably the most outstanding pieces of glass ever produced (Figure 20). Their decoration consisted of figural or network patterns. The earliest true cage cup is figural and dates from the late third century [29], preceding the network cage cups made

6 Special Techniques

Figure 19 Two step-making of a cameo glass: model of wax or clay serving for the hollowed out interior decoration of a plaster mold, whose cavities are then filled with powdered white glass before pressing of hot blue glass into the mold with a plunger. Source: After [10].

Figure 20 Diatrete, Cage cup (preserved height 12.1 cm, rim diameter 10.1 cm). Köln, Römisch-Germanisches Museum 60.1. Source: Photo Cornelius Steckner, courtesy the Museum.

from the fourth century. Similarities with high-relief glass suggest that the earliest precursors might have been produced in a workshop specialized in high relief. The figures are often undercut so that many details stand free from the background [29], in imitation of contemporary repoussé silver vessels. Carving of thick-walled blanks would have been a possibility because the water mill, indispensable for supplying energy to the cutting tools, had become common throughout the Roman Empire by the fourth century [22]. However, in addition to extremely severe breakage and cracking problems, the time spent on cutting and polishing would have been considerable. A much quicker and safer alternative [6, 30] is to assume that one made cage cups by pressing a double-walled blank on a turning wheel (Figure 21). After pressing the first gob of hot molten glass into the mold (the future cage), the glassblower inserted a smaller, perforated plaster mold into the hot glass and used a smaller plunger to press a second gob of hot glass into the mold to form the main body and to force at the same time some glass through the perforations. The tiny bridges connecting the cage to the inside bowl thus became integral parts of the main body as actually observed, although occasionally the two glasses meet somewhere along the bridge if some of the glass from the outer bowl (the future cage) was forced back into the perforations when the inside bowl was pressed.

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Ridge

Crosscut

Figure 21 Four-step making of a double-walled blank for subsequent cutting of a diatrete: pressing of a first gob for the outer bowl of the network cage, insertion of a perforated plaster mold, pressing of a second gob for the inner cup and the bridges through the plaster mold, and creation of a ridge while the rim is shaped. Cross section of the double-walled blank with the perforated plaster cup still inside also shown. Source: After [6].

7

Secondary Glassworking

7.1 Workshops In antiquity, glass making and working remained two separate crafts, each with its own pyrotechnology and ancillary techniques. Unlike primary production (Chapter 10.3), the shaping of glass was not bound to a specific location. Secondary workshops could be located near primary workshops, as in Israel and Egypt, but all they needed was a supply of raw glass which could come from afar (Chapter 10.3). How this trade was organized is not clear, but ingots, chunks, and even cullet found in ancient shipwrecks point to transport by sea, frequently as inexpensive ballast. Textual evidence indicates that recycling became an important source of supplies from about 70 CE on [4, 31]. Secondary glass workshops were located either on the edge of town in northwest Europe (to minimize the risk of fire) or more centrally in the Eastern Mediterranean. At Bet She’an (Israel), a downtown workshop destroyed by a sixth to early seventh century earthquake had a courtyard and two connecting rooms showing traces of shelves for storing glass vessels [32]. Most of the vessels were kept in the front room, where the furnace was located next to the wall of the doorway, surrounded by moils or crack-offs from the blowpipe, knock-offs from the pontil, and glass drops. On either side of the furnace, blown vessels and olive pits (known for their heat-storing properties) were found in heaps of black ash, which probably served as rudimentary annealing lehrs. Piles of glass chunks lay ready for use. The storeroom contained additional shelves of vessels, sacks filled with cullet, and a large jar full of chunks of raw glass.

7.2 Furnaces Some Roman oil lamps depict a worker blowing a tallnecked bottle while sitting on a low stool in front of a marver depicted as a small ledge protruding from the furnace (Figure 2, Chapter 10.4). The piece attached to the blowpipe could be entered horizontally into the furnace’s upper compartment through the working port at the center. The lower compartment served for stoking. The rectangular blocks on the floor in front of the furnace were probably blocks of raw glass waiting to be used, but what the squatting man was doing on the left is unclear. With respect to the core-forming furnace, the most significant change was the closed, horizontal heat chamber. It allowed not only higher temperatures to be reached but also ensured that the glass heated evenly on all sides, which was crucial for expanding evenly during inflation. The new glassblower’s furnace was thus a revolutionary invention. It had one major disadvantage, however, which persists today: because the artisan cannot shape the glass and simultaneously control its temperature, all the shaping has to be done outside the furnace in between successive reheating steps. The basic distinction made between short and long glasses (Chapter 4.1) is thus a direct consequence of the invention of the glassblower furnace. The remains of the lower structures of theses furnaces have been found all over Europe. The majority are circular, with an inner diameter of about 45–70 cm. Pots for remelting raw glass were rare before the third century, but common later on. Tank furnaces have been assumed to exist as early as the mid first century because glass drippings were observed on their floors, but no pots were found [33]. It has been argued, however, that tank furnaces did not become common until the third quarter

7 Secondary Glassworking

of the first century, when polychrome vessels went out of fashion and blowers began to use mostly natural bluish green glass [34]. This meant that one color of molten hot glass sufficed. As observed at other mid first century furnaces [35], the drippings on the floor resulted from small chunks of raw glass that got too hot and melted when they were picked up on the tip of the blowpipe.

7.3

Tools

Neither the commonly held opinion that ancient blowpipes were made of iron from the beginning, nor the hypothesis that ceramic blowpipes were used at an intermediate stage [1] can be proved or disproved at this moment. The earliest evidence for the use of iron blowpipes is the presence of oxidized iron in mid first century waste glass, originating from the crack-offs remaining attached to the blowpipe after separation of a completed vessel [35]. In addition to the blowpipe and the pontil, the U-shaped iron shears with parallel blades were the most important glassblower’s tool of antiquity. Originally a Celtic invention, this forfex was the universal cutting tool of the Greco-Roman world, thanks to the springy blades that opened automatically when not pressed together (Figure 2, Chapter 10.9). The tool could not cut hot viscous glass, however, which is why Roman glassblowers usually began the handle of a vessel at the shoulder, pulled the glass up, and attached it at the upper end where they drew the extra glass out thin and snapped it off. Often they folded the extra glass back and forth to create interesting folds and spurs at the upper end of the handle [19]. For most ancient glassblowing techniques, these simple iron tools sufficed along with a wooden board for shaping and a wooden stick for widening rims. An interesting feature seen on many Roman blown vessels is the firepolished rim that resulted from the wooden stick catching fire through contact with the hot glass. When shaping was completed, a gentle tap on the pontil let the piece slide onto a wedge-shaped branch to be deposited for annealing.

7.4

Blowers

Unlike pottery, glassblowing did not develop into a largescale enterprise in antiquity. The Roman glassblower furnace was small, imposing physical restrictions on the number of persons who could work simultaneously [4, 34, 35]. Nevertheless, a glassblower could have averaged 100 vessels per day or 330 000 in 30 years. That such a long period of activity may have been possible is

suggested by the tombstone of the opifex artis vitriae Julius Alexsander who died in Lyons at age 75 [4, 31]. Little is known about the financial and social position of glassblowers although quite a few names are known. Ennion, who specialized in fine mold-blown tableware, stood out above all others in the first century eastern Mediterranean. The addition of the Cypriot or from Sidon in signatures found on mold- and free blown tableware, respectively [9, 31], suggests that others too moved through the Roman Empire as did Julius Alexsander, who was born in Africa. As for the aforementioned Roman oil lamps (Chapter 10.7, Figure 4), the names of the glassblowers added on one of them may indicate that they were Athenian liberti (freemen) working in Italy [4]. According to papyri, legal documents and epigraphic sources, glassworkers in Egypt were regarded as a group for tax purposes in the early first century and as a guild in the fourth [4, 31]. Elsewhere, artisans appear to have been independent entrepreneurs probably leasing their facilities as did potters [4, 31]. If clearance on exit had been a general condition in leases, that would explain the existence of large deposits of waste glass and cullet buried in pits as found in glass workshops at Saintes (France), London, and Nijmegen (The Netherlands) [31]. In antiquity, women were active in beadmaking and glassblowing. Also known as Didyme, a Sarapodora is mentioned in a mid third century contract along with two male glassworkers from Koptos [36]. Female names are also found in basemarks on the undersides of square bottles [37]. Sentia Secunda (late first to early second centuries) added the information that she made VITR (vitrum or vitra) glass (or glass vessels) at Aquileia (Italy). The price of glass varied depending on the kind of production. Raw glass and smooth (i.e. undecorated) glass vessels were sold by the pound. According to the Edict of Maximum Prices issued in 301 by the emperor Diocletian (r. 284–305), the 25 denarii daily wage of an unskilled laborer would have bought one or two vessels of Judaean (naturally colored bluish green) glass or one vessel of Alexandrian (colorless) glass of average size. Even though these prices were 10–20 times higher than that of an equivalent pottery vessel, they were probably lower than the production cost of Judaean glass [4, 38]. As for window glass (Chapter 10.8), the maximum price was 8 or 6 denarii per pound depending on quality. A 25 × 25 cm window pane would have weighed about 2.2 Roman pounds and cost 17.6 or 13.2 denarii for the best and lower qualities, respectively [38]. As the main function of window panes was to bring in light without losing warmth [39], glazing did not require the same quality as vessels, which is why the former glass was much less expensive than the latter [38].

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8

A Short Retrospective Overview

8.1 The Spread of Glass Vitreous materials had been around for more than a millennium before true glass was made on a regular basis, from c. 1550 BCE onward (Chapter 10.2). Because the new material did not prove indispensable for any specific function, it owed its initial success to the brightness of its rich colors, which surpassed those of natural stones and the glow of faience. Glass was used first as beads, jewelry, and decorative inlays in furniture, boxes, and coffins, and even in architectural context as wall decoration [13], then as colorful core-formed vessels. As an intermediate production step, colorless and natural bluish green colored glass was not valued as such [5]. Clear colorless glass, purposely decolorized with antimony (and in later periods often with manganese), made its first appearance at Gordion (Phrygia) in the eighth to seventh centuries BCE. Wide, shallow bowls were decorated with a petal motif that was convex on the exterior and concave on the interior in imitation of metal vessels. The fashion was revived in the late fifth to fourth centuries BCE with bowls that were usually smooth on the interior. The glass itself obviously imitated rock crystal, with which such shapes would have been difficult to create because of polishing difficulties and of the risk of disfiguration or breakage caused by a small mishap. The ease of shaping glass led to several new applications of transparent glass in the Roman period. Again its acceptance began much earlier as a thing of beauty reserved at first for temples as dedications to the gods and for luxury items such as jewelry. From the mid fourth century BCE colorless glass vessels began to grace the tables of the wealthy [20]. In Greece, the optic qualities of clear colorless glass were a source of fascination from the moment it became available. In addition, transparent glass played a role in the construction of mechanical devices and gadgets and especially in the beginnings of optical studies (Chapter 10.10). It is usually thought that the invention of glassblowing revolutionized the ancient glass industry because vessels could be made much faster. However, it was taking longer to blow a ribbed bowl than to make one by tooling on a turntable. The first mass-produced glass vessels, Hellenistic grooved and sagged bowls, predated the first blown vessels, as did ribbed bowls, which were still being sold in Herculaneum at the time of the Vesuvius eruption in 79 when blown drinking vessels had ousted pottery thanks to their already well-known advantages. Blowing enlarged the existing repertoire of vessels with a wide range of shapes so that the use of glass in households increased greatly during the first century CE. Much

of it was blown, but blown luxury wares were nonetheless rare before the introduction of the pontil. Glass lamps became common from the fourth century onward [4] especially in Italy and the Eastern Mediterranean. However, it was for windows that transparent glass had the most impact in antiquity (Chapters 10.3 and 10.8), and it was during the Roman Empire that wall and floor mosaics made of colored glass cubes became common in private villas and public buildings.

8.2 The Slow Rise of Glass Blowing After the discovery of inflation in the eastern Mediterranean, it took at least one century until the novel blowing technique spread widely, even to western Europe, after it had been perfected in Italy. As usual, older materials, techniques, and concepts survived for a considerable time. The first successful innovation in glassworking had been core-forming, which transformed a ceramic technology into a widely accepted technique of glassworking. Primarily (but not exclusively) a means for the production of attractively colored bottles, core-forming was so successful that it remained in use for 1500 years. The earliest blown vessels were small glass bottles, commonly called unguentaria or balsamaria. By far the easiest and most simple shape to produce with the novel technique, many bottles were blown in attractive transparent colors. Even more bottles were blown from natural bluish green glass, which was less expensive. These bottles were much lighter than their core-formed equivalents, not a negligible factor in an economy where glass vessels were sold by weight. In addition, blowing was considerably faster than forming around a core that had to be scraped out laboriously and left an uneven surface that contaminated the interior and hampered reuse. The invention of glassblowing caused the death of coreforming. The new blown bottles fulfilled a real need as containers for medicinal preparations. Thousands of unguentaria have come to light all over the Roman Empire in civil and funerary contexts. Glassblowers soon enlarged their repertoire with bottles, jugs, and jars, which were difficult to produce by rotary pressing because the diameters of their neck and/or rim were smaller than their maximum diameters. Rotary-mold pressing was nonetheless the most serious rival of glassblowing. Like coreforming, it stemmed from ceramic technology, but it gave rise to many other techniques predating blowing and took great advantage of the properties of plaster for making molds. Thus, innovation was slow with respect to fine glass tableware, especially for open shapes with a rim diameter equal to or larger than the maximum diameter.

9 Perspectives

Throughout the first and well into the second century, rotary pressing and related older techniques remained important production methods next to blowing. Eventually, glassblowing became dominant for all vessel glass, but rotary pressing did not disappear entirely. The development of glassblowing was hindered by the slow acceptance of the pontil technique. Many workers apparently did not trust the transfer from blowpipe to pontil when blowing large heavy pieces such as cremation urns with massive, decorative glass handles. The absence of pontil scars suggests that the glassblowers reverted to earlier techniques such as the use of a clamp to hold the vessel. The three types of molds invented in antiquity each had a different impact and different history with respect to innovation. Decorative mold-blowing with the aid of multipart molds began in the Eastern Mediterranean during the first quarter of the first century CE as a way to emulate contemporary silver vessels decorated with repoussé relief [9, 40]. The technique may have been introduced into Italy in the early first century. However, unlike the small free-blown bottles, which were an immediate success, vessels blown into multipart decorated molds did not thrive in the West before the mid first century [41]. After the technique gained a foothold in Italy, the construction of the molds was simplified. Many pieces were blown into two-part molds. The introduction of box molds for the mass production of prismatic vessels caused general recognition that mold-blown decorated vessels were not individually crafted. As a result, decorative mold-blowing fell out of favor in the West [9, 40]. The box mold for blowing prismatic bottles and jars was invented in Italy around the mid first century CE or slightly later. It was an immediate success. In the eastern part of the Roman Empire, the use of box molds was never as universal as in the west. In the late third or fourth century, glassblowers invented a technique for blowing window glass, the cylinder technique [39], which would eventually oust cast flat glass of the matt/glossy type and remain in use for the production of flat glass until the twentieth century (Chapter 10.8). In this domain, too, innovation was slow. In the east, the older technique persisted in use for some time. The fourth century was actually an innovative period in the history of glassblowing [9]. Syrian blowers began to expand geometric surface motifs created in multipart molds by continuing to blow after exiting the mold. Expanded concentric circles were the commonest motif. Although this technique remained a regional curiosity, it pointed the way to a novel use of decorative molds that would dominate mold-blowing for all times to come, namely, the dip mold. Syro-Palestinian glassblowers used these molds to create bowls with barely expanded

honeycomb patterns, which were appreciated east and west. The real success story, however, was the vertically ribbed or fluted dip mold. Easy to make and easy to use it enabled the glassblower to produce a large variety of expanded vertical and spiral rib patterns in imitation of contemporary silverware.

9

Perspectives

The scenario of a gradual development and anchoring of ancient glassworking techniques based on rotary moldpressing makes sense from a historical and technological viewpoint. Although experiments have demonstrated the feasibility of the proposed reconstructions, dissent among specialists is polarizing the community of glass researchers in many fields of research from art historians and archeologists to chemists, laboratory scientists, conservators, and glassblowers. With Lierke’s theoretical reconstruction drawings in hand [6, 10], a new generation of glassblowers can begin to experiment and/or attempt to produce reliable replicas of ancient glass vessels. For the shaping of vessels with carinated profiles, made perhaps on a raised support, the lack of an appropriate furnace for working above and in the heat may be an issue that needs first to be resolved. The advantages and disadvantages of working glass with such furnaces have yet to be fully explored. The price of gold foil sufficiently thick for experiments to replicate Hellenistic gold glass may be an obstacle of a more prosaic kind. Two quite different projects will finally be mentioned to illustrate the diversity of approaches followed to understand better ancient processes. The first aims at making basic information on important pieces as widely available as possible through an open-access database set up at the Römisch-Germanisches Zentralmuseum in Mainz (Germany). Its goal is to document Roman cage-cups thoroughly through high-quality photographs of both vessel and surface [42]. Hopefully, the documentation will include microphotos of the reverse of the cage and the interior wall of the cup where details such as shortened horseshoe chattermarks suggesting double-walled pressing might be detected. Launched at the initiative of the Australian National University at Canberra, the second project highlights the use of state-of-the art techniques applied in industrial or academic glass studies (Chapters 2.1 and 2.2). Through high-resolution X-ray scanner tomography combined with a visualizing software program, the important question addressed in this case is the production of cameo-glass vessels and, in particular, the nature of the interface formed between the white and the blue glasses during the shaping process.

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References

16 Rehren, T. and Pusch, E.B. (2005). Late Bronze Age glass

1 Stern, E.M. and Schlick-Nolte, B. (1994). Early Glass of

2 3

4 5

6

7

8

9

10

11

12

13

14 15

the Ancient World. 1600 B.C.–A.D.50. Ernesto Wolf Collection. Ostfildern: Verlag Gerd Hatje. Weinberg, G.D. (1969). Glass manufacture in Hellenistic Rhodes. Archaiol. Deltion 24: 143–151. Oppenheim, A.L., Brill, R.H., Barag, D., and von Saldern, A. (1970). Glass and Glassmaking in Ancient Mesopotamia. An Edition of the Cuneiform Texts Which Contain Instructions for Glassmakers with a Catalogue of Surviving Objects. Corning, NY: The Corning Museum of Glass Press. Stern, E.M. (1999). Roman glassblowing in a cultural context. Am. J. Archaeol. 103: 441–484. Rehren, T. and Pusch, E.B. (1997). New kingdom glassmelting crucibles from Qantir-Piramesses. J. Egypt Sci. 83: 127–141. Lierke, R. (2009). Die nicht-geblasenen antiken Glasgefässe/The Non-Blown Ancient Glass Vessels. Offenbach/Main: Deutsche Glastechnische Gesellschaft. Pliny the Elder. Natural History (36.193, Books 36 and 37 trans. E. Eichholz, Natural History), 1962. Harvard: Harvard University Press. Stern, E.M. (2010). Souffler le verre dans des moules. In: D’Ennion au Val Saint-Lambert, Le verre soufflé-moulé (ed. C. Fontaine-Hodiamont), 25–37. Brussels: Institut royal du patrimoine artistique. Stern, E.M. (1995). Roman Mold-Blown Glass. The First through Sixth Centuries. Rome: L’Erma di Bretschneider and the Toledo Museum of Art. Lierke, R. (1999). Antike Glastöpferei: Ein vergessenes Kapitel der Glasgeschichte. Mainz: Verlag Philipp von Zabern. Nicholson, P.T. and Jackson, C.M. (1998). ‘Kind of blue’: glass of the Amarna period replicated. In: The Prehistory & History of Glassmaking Technology (eds. P. McCray and W.D. Kingery), 105–120. Westerville, OH: The American Ceramic Society. Stern, E.M. (1998). Interaction between glassworkers and ceramists. In: The Prehistory & History of Glassmaking Technology (eds. P. McCray and W.D. Kingery), 183–204. Westerville, OH: The American Ceramic Society. Grose, D.F. and The Toledo Museum of Art (1989). Early Ancient Glass: Core-Formed, Rod-Formed, and Cast Vessels and Objects from the Late Bronze Age to the Early Roman Empire, 1600 B.C. to A.D. 50. New York: Hudson Hills Press. Giberson, D.F. (1996). Ancient glassmaking. Its efficiency and economy. Ornament: 76–79. Giberson, D.F. (1998). A Glassblower’s Companion: A Compilation of Studio Equipment Designs, Essays, and Glassmaking Ideas. Warner, NH: The Joppa Press.

17 18

19

20

21

22

23

24

25

26

27

28

production at Qantir-Piramesses. Science 308: 1756–1758. Broschat, K. and Rehren, T. (2017). The glass headrests of Tutanchamen. J. Glass Stud. 59: 377–380. Spaer, M. (2001). Ancient Glass in the Israel Museum: Beads and Other Small Objects. Jerusalem: The Israel Museum. Harden, D.B., Hellenkemper, H., Painter, K., and Whitehouse, D. (1987). Glass of the Caesars. Milan: Olivetti. Ignatiadou, D. (2013). Διαφανής γαλος για την αριστοκρατία της αρχαίαϛ Мακεδονίαϛ [Colorless Glass for the Elite in Ancient Macedonia]. Thessaloniki: Ekdoseis Ziti. Freestone, I.C. and Stapleton, C.P. (2015). Composition, technology and production of coloured glasses from Roman mosaic vessels. In: Glass of the Roman World (eds. J. Bayley, I. Freestone and C. Jackson), 61–76. Oxford & Philadelphia: Oxbow Books. Wikander, Ö. (2008). Sources of energy and exploitation of power. In: The Oxford Handbook of Engineering and Technology in the Classical World (ed. J.P. Oleson), 137– 157. New York, NY: Oxford University Press. Israeli, Y. (1991). The invention of blowing. In: Two Centuries of Roman Glass (eds. M. Newby and K. Painter), 46–55. London: The Society of Antiquaries. Fünfschilling, S. (2015). Die römischen Gläser aus Augst und Kaiseraugst. Kommentierter Formenkatalog und ausgewählte Neufunde 1981–2010 aus Augusta Raurica. Forschungen in Augst 51. Augst: Augusta Raurica. Hill, D. (2016). Ennion and mold-blown Roman glass vessels of the first century AD at the Borg Furnace Project 2014. In: Experimentelle Archäologie: Studien zur römischen Glastechnik 1 (eds. B. Birkenhagen and F. Wiesenberg), 24–41. Merzig: Römische Villa Borg. Foy, D., Vrielynck, O., van Wersch, L., and Cabart, H. (2010). Les coupelles à décor chrétien soufflés dans un moule (seconde moitié Ve – première moitié VIe siècle). État de la documentation. In: D’Ennion au Val SaintLambert, Le verre soufflé-moulé (ed. C. FontaineHodiamont), 267–313. Brussels: Institut royal du patrimoine artistique. Namiki, H. and Fujii, Y. (2017). A study of the cut gold leaf decoration techniques on ancient gold sandwich glass, with emphasis on the Hellenistic kirikane technique. In: Annales du 20e Congrès de l’Association Internationale pour l’Histoire du Verre, Fribourg/Romont 2015 (eds. S. Wolf and A. de Pury-Gysel), 68–72. Rahden/ Westf: Verlag Marie Leiderdorf. Roberts, P., Gudenrath, W., Tatton-Brown, V., and Whitehouse, D. (2010). Roman Cameo Glass in the British Museum. London: The British Museum Press.

References

29 Whitehouse, D., Gudenrath, W., and Roberts, P. (2015).

30

31

32

33

34

Cage Cups: Late Roman Luxury Glasses. Corning, NY: The Corning Museum of Glass. Lierke, R. (2013). On the manufacture of diatreta and cage cups from the Pharos Beaker to the Lycurgus Cup. In: New Light on Old Glass: Recent Research on Byzantine Mosaics and Glass. Research Publication 179 (eds. C. Entwistle and L. James), 89–102. London: The British Museum. Price, J. (2005). Glass-working and glassworkers in cities and towns. In: Roman Working Lives and Urban Living (eds. A. MacMahon and J. Price), 167–191. Oxford: Oxbow Books. Gorin-Rosen, Y. (2000). The ancient glass industry in Israel: summary of the finds and new discoveries. In: La route du verre. Ateliers primaires et secondaires du second millénaire av. J.-C. au Moyen Âge (ed. M.-D. Nenna), 49–63. Lyon: Travaux de la Maison de l’Orient Méditerranéen 33. Shepherd, J. (2015). Gazetteer of glass working sites in Roman London. In: Glass of the Roman World (eds. J. Bayley, I. Freestone and C. Jackson), 33–43. Oxford & Philadelphia: Oxbow Books. Stern, E.M. (2012). Blowing glass from chunks instead of molten glass: archaeological and literary evidence. J. Glass Stud. 54: 33–45.

35 Amrein, H. (2001). L’atelier de verriers d’Avenches:

36

37

38 39

40

41

42

l’Artisanat du verre au milieu du 1er siècle après J.-C. Lausanne: Cahiers d’archéologie romande, 87. Stern, E.M. (2013). Glass producers in Late Antique and Byzantine texts and papyri. In: New Light on Old Glass: Recent Research on Byzantine Mosaics and Glass. Research Publication 179 (eds. C. Entwistle and L. James), 82–88. London: The British Museum. Foy, D. and Nenna, M.-D. (eds.) (2006–2011). Corpus des signatures et marques sur verres antiques, vol. 3 vols. Aixen-Provence Lyon: Association Française pour l’Archéologie du Verre. Stern, E.M. (2007). Ancient glass in a philological context. Mnemosyne 60: 341–406. Foy, D. (ed.) (2005). De transparentes spéculations. Vitres de l’Antiquité et du Haut Moyen Âge (Occident-Orient). Bavay: Musée/site d’archéologie de Bavay. Stern, E.M. (2015). Roman glass from east to west. In: Glass of the Roman World (eds. J. Bayley, I. Freestone and C. Jackson), 77–94. Oxford & Philadelphia: Oxbow Books. Price, J. (1991). Decorated mould-blown glass tablewares in the first century AD. In: Two Centuries of Roman Glass (eds. M. Newby and K. Painter), 56–75. London: The Society of Antiquaries. Broschat, K. (2016). Open access database for Roman Cage-cups planned. J. Glass Stud. 58: 294–295.

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1309

10.6 Glazes and Enamels Philippe Colomban MONARIS, UMR CNRS 8233, Sorbonne Université, Paris, France

1

Introduction

Glass has long been highly valued in the form of thin layers termed enamel or glaze depending on whether the substrate on which it is deposited is smooth (e.g. metal and glass) or porous (e.g. porcelain). From Egypt, Phoenicia, and Mesopotamia to the Indus Valley, glazed artifacts date back to about 2000–1500 BCE [1]. There is actually evidence that bulk glass was a by-product of glazes, once the great aesthetic and practical value of the new material had been acknowledged in the Middle East (Chapter 10.2). Such coatings were used not only for decoration purposes (Figure 1) but also for tightening a porous body and hardening its surface, which made, for instance, possible to keep safely liquids or other substances in large pottery vessels. In the Western world, the first enamels date back to at least 1500 BCE in Cyprus [2] whereas an older written mention of an enameled shield is found in the Iliad (eighth BCE). From diverse areas, famous artifacts include an eleventh century BCE enameled bronze wine ladle from the early Western Zhou dynasty (British Museum) or numerous Celtic enamels on brass, bronze, gold, and iron made from at least the fourth BCE with blue, red, green, yellow, and black hues [3]. As to millefiori (1000 flowers, in Italian) enamels, they appeared in Ireland during the seventh century CE. Since then, a great many new applications have been designed, ranging from porcelain or glass isolators coated with iron oxide-rich enamels to improve the electrical insulation of wire supports in wet atmospheres [4] to

Reviewers: F. Casadio, Conservation Department, Art Institute of Chicago, Chicago, IL, USA K. Janssen, Department of Chemistry, University of Antwerp, Antwerpen, Belgium

the development of advanced ceramics such as particular dielectric passive components (e.g. capacitors, substrates, sockets) that are at the roots of the development of microprocessors and computers. Glazes are also deposited on alumina electronic substrates to be used in standard or harsh conditions [4] whereas, following a tradition originating in the glazes deposited on stone in ancient Egypt [1], enameled lava remains used in contemporary building décor. Regardless of their functions and of the possibly complex shapes of their substrates, the deposited glass layers must not exhibit any puddle but have a constant thickness. Hence, it is obvious that enameling and glazing technologies involve much more than the preparation and firing of glass compositions. Without trying to deal with all varieties of enamels and glazes (Figures 1 and 2), this chapter will review their current preparation and the technical constraints exerted in particular by thermal expansion matching, describe the most pertinent innovations regarding composition and color, and finally present an overview of the history of enamels and glazes. In preamble, some definitions are in order: stoneware designates nonporous pottery or ceramics fired at temperatures higher than 1200 C; fritware, pottery in which some ground glass has been mixed with the starting clay and sand material to promote partial melting upon firing to cement the grains with the molten frit; porcelain, various kinds of white wares that share a common vitreous surface and a nonporous body as first made from 3000 to 1500 BCE during the Chinese Shang and Shang-Zhou dynasties (in the form of protoporcelains, which were already fired up to about 1200–1250 C) [5]; celadon, a green Chinese porcelain as named in France in the seventeenth century; and cloisonné and champlevé, enamels prepared with two different kinds of techniques.

Encyclopedia of Glass Science, Technology, History, and Culture, Volume II, First Edition. Pascal Richet. © 2021 The American Ceramic Society. Published 2021 by John Wiley & Sons, Inc.

(a)

(b)

(d)

(c)

(e)

(f)

Figure 1 A variety of glass coatings. (a) Enameled Venetian chalice (circa 1480–1500, Sèvres Cité de la Céramique Coll.); (b) HispanoMoresque luster pottery (fifteenth century, Sèvres Cité de la Céramique Coll.); (c) glazed Ottoman Kütahya bowl (end of seventeenth century, Sèvres Cité de la Céramique Coll.); (d) Chinese cloisonné (sixteenth century, UCAD Coll.); (e) Han Viet pottery glazed with ashes (before sixth century, Private Coll.); (f ) Raku tea bowl (twentieth century) voluntarily broken and restored with the golden lacquer technique (Source: Courtesy Andoche Praudel, potter, Private Coll.); diameter ~20 cm, except (e) (~12 cm) and (f ) (~15 cm). Source: Photos Ph. Colomban.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 2 Limoges enamels. (a) Plaque depicting Jesus before Ponce Pilate tentatively assigned to Penicaud (sixteenth/seventeenth century, UCAD Coll., partially restored); (b) plaque depicting King Henry IV (initial seventeenth century dating, actually a nineteenth century fake; UCAD PE1640); (c) Gallé enameled glass (UCAD Coll.); (d) Sceaux porcelain were decorated with Cassius Purple enamel (Sèvres Cité de la Céramique Coll.); (e) Medici porcelain plate (sixteenth century, Sèvres Cité de la Céramique Coll.); (f ) rhinoceros from Pilnitz garden (J. F. Böttger, Meissen, early eighteenth century, Sèvres Cité de la Céramique Coll.); largest dimension ~20 cm, except (a), (b) (~12 cm) and (f ) (~150 cm). Source: Photos Ph. Colomban.

2 Preparation and Thermal Constraints

2 Preparation and Thermal Constraints Coatings, in general, are made from either glass precursors through in situ reaction and melting or with ready-to-use glass frits. An aqueous slurry is prepared from these materials if the substrate is an unfired or a porous pottery. The slurry is deposited by immersion of the object or painting with a brush or spray dried. The slurry must have the right viscosity, thixotropy, etc., which are optimized with specific additional ingredients such as clays, kaolin, or polymers and glues. If the substrate is not porous, water is replaced with organic solvents/media and glues or similar additives are incorporated. The coated items are then heated to form the glass coating and to develop a specific color and/ or gloss. The coating thickness ranges from a few tenths of microns in salted stoneware to a few millimeters in celadon and cloisonnés. The coating must readily melt upon firing to yield a nice gloss and join smoothly with the substrate, which requires the precursor mixture to consist of

(a)

(d)

a fine powder. Along with firing, grinding is the most energy-intensive operation in the Arts du Feu, which might be why mechanized grinding techniques were developed only in the Middle-Ages with water mill energy. To get fine powders, ancient craftsmen thus relied instead on the firing of plants (ashes), shells and calcareous stone (chalk), bones (ashes), and flint pebbles (silica) together with water washing to eliminate impurities. In this way, they sometimes achieved directly the right composition (Figure 1e) [6]. However, craftsmen have long known that composition is not the sole parameter that governs final quality [6–11]. For a given composition, the glaze can be matt or glossy, well coated (Figure 1c), or crawled (Figure 3c) depending on grinding time. The glaze ingredients used to be ground in a mortar or in a rotating barrel of water containing flint or quartz pebbles (now steel, alumina, or zirconia balls depending on glaze composition). Upon firing, the reaction rate increases with the initial compaction of the deposit and it also depends on temperature, duration, heating rate, particle size, volatile content, and on the reducing or oxidizing nature of the gas atmosphere.

(b)

(c)

(e)

Figure 3 Firing defects on glazes and enamels. (a) Celadon crackled glaze (nineteenth century, Qing Dynasty, Private Coll., ~5 × 8 cm2); (b) high-quality Mamluk enameled glass bottle (diameter: ~15 cm), exhibiting a high-quality glossy enamel and (c) Mamluk enameled mosque lamp (diameter: ~30 cm), where the glaze has failed to adhere to or wet the body on firing (crawling) (fourteenth century, Louvre Museum Coll.); (d) Cuerda seca-like technique: a line hinders the glaze to go out of the defined area (fifteenth century, Ottoman Empire, Private Coll., ~ 4 × 9 cm2); (e) micro-crazed red glaze of a gilded Meissen Bottger’ stoneware (Sèvres Cité de la Céramique Coll., ~4 × 6 cm2). Source: Photos Ph. Colomban.

1311

10.6 Glazes and Enamels

s.p. Tg Thermal expansion

1312

α–β 100

300

500

700

900

1100

Temperature (°C)

Figure 4 Control of the glaze quality: comparison between the thermal expansion of a quartz-rich ceramic body (solid line, α–β phase transition) and a glaze (dashed line; Tg: glass transition temperature; s.p.: softening point).

Because sintering is driven by atomic diffusion, longer heating times have similar effects as temperature increases or grain size decreases. Controlling the contact angle between the melted coating and its substrate is mandatory to ensure complete wetting and also to keep the thickness constant. Bonding between the substrate and the coating is also very important. For metal substrates, a ground or under coat is generally needed to ensure adherence and accommodate the thermal expansion mismatch between upper coating and substrate [4]. Cobalt and nickel oxides were the best materials in this respect, followed by cupric, manganese, and iron oxides. Glazes for decorative purpose were then applied on the ground coat. Coatings widely differ in composition because of the thermal-expansion match that must be achieved with a great many different substrates during the firing and cooling operations (Figure 4). Two different techniques are distinguished in this respect. With the Grand Feu (Great Fire), for instance, used to make porcelain, the coating and its substrate are simultaneously fired at temperatures ranging from 1200 to 1400 C. With Petit Feu (Small fire), Muffle fire, or minaï (in Iran), lower temperatures of 600–1000 C suffice because the substrate has been separately fired once or twice at higher temperatures [10, 11]. In practice, the thermal expansion coefficients of metals range from 100 to 220 × 10−7 K−1 (steel, 90–180; gold, 140; brass/bronze/copper, 180–160; silver, 195; aluminum, 220 × 10−7 K−1). These coefficients are generally lower than 100 × 10−7 K−1 for ceramics (amorphous silica, 1–0; SiC, 35; mullite, 50; porcelain, 65; alumina, 75; zirconia, 105 × 10−7 K−1) and can even be negative for β spodumene/eucryptite (−10 to −5 × 10−7 K−1, cf. Chapter 7.11).

A further complexity results from the α–β phase transition of quartz, which causes a highly anomalous expansion near 565 C (Figure 4) for quartz-rich raw materials. As for silicate glasses, their thermal expansion coefficient increases from 30 to 80 × 10−7 K−1 from borosilicates to lead-based materials, and decrease when SiO2, B2O3, CaO, MgO, or ZnO are substituted for Na2O and K2O [4, 7]. Although thermal expansion of solids is a complex phenomenon determined at the atomic level by the number of bonds per unit volume and their anharmonicity, it has long been accounted empirically with coefficients first assigned to the constituting oxides by ceramist Hermann Seger (1839–1893). Optimized calculators are now available [12]. Another important property is tensile stress. As usual, it is much smaller on tension than on compression for silicate glasses. Because of its thinness, a coating should not be put under tension but gently compressed by the substrate. The slow expansion experienced by porous ceramics with time if exposed to humidity must also be accounted for. Upon cooling below the softening point, i.e. the temperature at which the coating layer sticks on the substrate (Figure 4), the contraction of the glass coating is monitored by the thermal expansion mismatch [4]. To result in a compressive stress, the thermal expansion of the glass should be lower than that of the substrate. On the contrary, a glaze cracks when the substrate expansion is too low (Figure 3) whereas too high a compressive strength causes peeling. The most common defects of coatings are volume bubbles, craters, and pinholes induced by gas formation, generally from the body-interface reaction when glaze and body are fired together. However, small, micron-sized bubbles are specially developed in celadon (Figure 3a) and opal glazes [9, 10, 13] for opacification or aesthetic effects.

3

Composition and Microstructure

3.1 Pottery Glaze The raw materials actually used are not oxides, but mineral substances such as stones: clays, feldspars, talc, quartz, flint, or carbonates, the components to which craftsmen refer [4, 6–9, 14]. Because the compositions of these natural substances are highly variable, even within a given quarry, craftsmen mix raw materials from different places or, better, from different origins to average out differences and limit chemical fluctuations. When adjustments could not be made in the past in response to composition changes, then the quality of the production was decreasing and the factory might even disappear. Like materials scientists, archeologists and art historians usually report glaze and enamel compositions in

3 Composition and Microstructure

Table 1 Modern porcelain glaze compositions expressed in terms of either oxide or raw materials (wt %, after [16]). Raw materials

Standard kaolin (ECC)

Oxide

a

Calcined kaolin (Dorkamul)b c

NG6 glaze

NG33 glaze

SiO2

63.16

73.87

Al2O3

17.87

14.31

CaO

11.46

4.95

K2O

5.72

4.85

Na2O

1.37

1.16

Fe2O3

0.19

0.14

TiO2

0.05

0.03

MgO

0.19

0.69

8.70

7.85

13.16

8.75

Quartz (Norquartz 45)

6.89

33.35

Feldspar (Norflux 45)c

45.67

38.45

Wollastonite FW325 (Partek)d

25.58

8.90

Dolomite (Microdol 1)e

—

2.70

Firing temperature ( C)

1340

1400

a

English China Clay (St. Austell, UK). Dorfner (Hischau, Germany). c North cape Minerals (Stjernoy, Norway). d Partek (Helsinki, Finland). e Norwegian talc (Bergen, Norway). b

terms of oxides or elements as determined from chemical analysis (Chapter 5.1, [15–17]). Potters and enamelers put the emphasis instead on raw materials, which actually determine the actual firing process relevant to their batch (Table 1). They do it by following another procedure designed by Seger who distinguished acid [SiO2], amphoteric [Al2O3], and basic [flux: CaO, Na2O, K2O, and MgO] oxides [4, 6, 14]. The temperature, at which a liquid phase forms, a basic parameter for the reaction/bonding of the coating with the substrate, is then determined more by the particular raw materials used than by the mean chemical composition. Because the advancement of reactions (through atomic diffusion) depend on both temperature and time, Seger in addition designed reference cones made up of specific mixtures, which deforms and melts according to given controlled firing conditions (temperature and heating rate) in the wide temperature interval 500–1520 C [12]. The interest of the procedure is apparent in Table 2 where firing temperatures range from ~600 (Cone 022) to ~1430 C (Cone 15). Compounds such as lead oxide are highly volatile and diffuse rapidly in the substrate, however, in which cases compositions obtained from elemental analyses slightly differ from those of the precursors. Low-firing lead-free glazes maturing at 1050 C or less (Seger Cone #2) have one to two parts of silica per part of the other ingredients.

Higher-firing glazes melting at ~1250 C (Cone 10) have three to five parts of silica per part of others. Hightemperature fired porcelain glazes have ~10 parts or more of silica (Table 1). These empirical rules are now complemented by fundamental insights derived from advances made through studies of structure–composition–property relationships (cf. Section 2). Lowering of the melting temperatures by network-modifying cations such as Ca, Na, K, Li, or Pb is well understood, as are the opposite polymerizing effects induced by the addition of Al. Raman spectroscopy (Chapter 2.2) is in particular used for rapid and nondestructive analyses of chemical bonds. The degree of polymerization of the coating is, for instance, derived from the ratio between the peak areas of SiO4 bending and stretching modes (Figure 5), which markedly increases from fully depolymerized lead-rich glasses melted at about 700 C to 3-D connected silicarich glazes melted at about 1400 C (Figure 5b and c) [14, 15, 18–22]. This direct relationship clearly illustrates how craftsmen have been unknowingly playing with the composition and degree of polymerization of their coatings to achieve the required properties. Finally, the duration of the complete heating and cooling cycle is of course another important parameter, which is largely determined by the thermal resistance efficiency

1313

Table 2 Modern glaze compositions expressed with Seger formula. Acid

Amphoteric

SiO2

Al2O3

0.8333

0.0833

Basic (flux) ZrO2 (SnO2)

Fe2O3

MgO

Glaze type

Cone

Silica-rich

15 7

0.7143

0.0816

Alkali-rich

11

0.6593

0.1209

4

0.6275

0.0784

4

0.638

0.0673

4

0.6679

0.081

0.0223

1

0.6688

0.0495

0.0274

Tableware Majolica Low expansion Lead-based

0.0204

0.6477

0.0646

0.1062

0.5805

0.161

0 0.0113

0.6281

0.0753

0.6599

0.0719

4

0.5795

0.0886

Crackle

06

0.5461

0.0848

Raku

06

0.587

0.0723

Celadon

6

0.7422

0.0918

Chun/red

8

0.7718

0.0619

Ash

4

0.316

8

0.4611

Li2O

0.0751

K2O

Na2O

ZnO

0.044

0.1429

0.0408

0.1319

0.022

0.022

0.049

0.049

0.098

0.0251

0.0063

0.0752

0.0878

0.0899

0.0638

0.0911

0.0061

0.0547 0.0262 0.1973 0.0684

0.0152

0.0607

0.0506

0.0223

0.0983

0.079

0.0215

0.0138

Source: After [4].

0.0185

0.0295

PbO (P2O5)

0.0165

0.0277 0.0204

0.0418

0.076

0.0606

0.076 0.2682

~1830

Co-olivine

Olivine

Co2SiO4

Blue

>1500

Sèvres blue

Spinel

CoAl2O4

Blue

>18th

Egyptian blue

Amorphous

CaCuSi4O10

Blue

3000 BCE

Egyptian green

CaCuSi5O12

Green

3000 BCE

Han blue

BaCuSi4O10

Blue

500 BCE

BaCuSi2O16

Violet

~200 BCE

Han violet Smalt

Amorphous

Bone white

Co in glass

>1300

Ca3(PO4)2

White

Roman

Rutile

Rutile

TiO2

White

>20th

Quartz

Quartz

SiO2

White

>5th

Tin oxide

Cassiterite

SnO2

White

>5th

Wollastonite

Ca3Si3O9

White

>18th

Arsenate

Na1-x-yKxCayPb4(AsO4)3

White

>16th

Uranyl yellow

UO

Cadmium sulphide-selenide

Wurtzite

Naples yellow type 1

Pyrochlore

Naples yellow type 2 Naples yellow pyrochlore Zinc yellow

Spinel

Mussif gold

2+

Yellow

>19th

CdS1 − xSex

in (lead)glass

Yellow to red

>20th

PbSn1 − xMxO4

Yellow

Roman

PbSn1 − xSixO4

Yellow

Roman

PbSb2 − xMxO7

Yellow

Antiquity

ZnCrO4

Yellow

>19th

SnS2

Gilding

>13th

Hercynite

Spinel

Fe2 − x(Al,Ti,Mn)xO3

Orange

Roman

Hematite

Corundum

Fe2 − x(Al,Ti,Mn)xO3

Red

Roman

Pseudobrookite

Brookite

Fe2−x(Al,Ti)xO5

Red

Roman

Gold

Metal nanoparticle

Au

Red purple

15th

Copper

Metal nanoparticle

Cu

Red