Geological Melts 9781501510939, 9781946850089

Citation preview

REVIEWS in MINERALOGY and GEOCHEMISTRY Volume 87

2022

Geological Melts EDITORS Daniel R. Neuville

Université de Paris, France

Grant S. Henderson

University of Toronto, Canada

Donald B. Dingwell

Ludwig-Maximilians-Universität München, Germany

Series Editor: Ian Swainson MINERALOGICAL SOCIETY of AMERICA GEOCHEMICAL SOCIETY

COVER ILLUSTRATIONS Background: Simultaneous effusive/explosive activity of the 2021 Cumbre Vieja euption, La Palma (Photo credit: Ulrich Kueppers: 7 October 2021). Lower right inset: Glass structure visualized from molecular dynamics simulations (Le Losq et al. 2017). Upper left inset: SEM photo of volcanic ash from the submarine eruption of Serreta off Terceira, Azores (Kueppers and Cimarelli 2018). Lower left inset: Scanning calorimetric glass transition determination of a Pantellerite glass. (redrawn schematically from Gottsmann and Dingwell 2002). Upper right inset: Raman spectra of a basaltic glass (redrawn from Amalberti et al. 2021). Amalberti J et al. (2021) Raman spectroscopy to determine CO2 solubility in mafic silicate melts at high pressure: Haplobasaltic, haploandesitic and approach of basaltic compositions (2021) Chem Geol 582:120413. https://doi.org/10.1016/j.chemgeo.2021.120413 Gottsmann J, Dingwell DB (2002) The thermal history of a rheomorphic air-fall deposit: The 8 ka pantellerite flow of Mayor Island, New Zealand. Bull Volcanol 64:410–422 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. https://doi.org/10.1038/s41598-017-16741-3 (CC-BY-4.0, http://creativecommons.org/

Reviews in Mineralogy and Geochemistry, Volume 87

Geological Melts

ISSN 1529-6466 (print) ISSN 1943-2666 (online) ISBN 978-1-946850-08-9 Copyright 2022

The MINERALOGICAL SOCIETY of AMERICA 3635 Concorde Parkway, Suite 500 Chantilly, Virginia, 20151-1125, U.S.A. www.minsocam.org The appearance of the code at the bottom of the first page of each chapter in this volume indicates the copyright owner’s consent that copies of the article can be made for personal use or internal use or for the personal use or internal use of specific clients, provided the original publication is cited. The consent is given on the condition, however, that the copier pay the stated per-copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other types of copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. For permission to reprint entire articles in these cases and the like, consult the Administrator of the Mineralogical Society of America as to the royalty due to the Society.

Geological Melts 87

Reviews in Mineralogy and Geochemistry

iii

87

PREFACE

The initiative for the development of this volume arose from preliminary discussions between the editors that it had been 25 years, and a whole generation, since RIMG had dedicated a special issue to the topic of silicate melts and their many roles in materials and geological sciences. Back in 1995 silicate melts were being rediscovered as a vital component of the earth sciences in the wake of an increasing awareness of their structural complexity, the development of new experimental techniques and their application to the determination of structure and properties of these melts, as well as, the partially unexpected results of such studies. A further overriding theme was the emerging consensus of the concept of the glass transition as a key to the interpretation and extrapolation of structure and property determinations and as a fundamental physical transition governing many phenomena in petrology and volcanology. The result of that confluence of interests and ambitions has been a remarkable quarter century of opportunities for the study of the molten state in both materials and geological sciences and involving national programs and international collaborations on an unprecedented scale. Collected in this volume are a compact set of chapters covering fundamental aspects of the nature of silicate melts and the implications for the systems in which they participate, both technological and natural. The contents of this volume may perhaps best be summarized as structure – properties – dynamics. The volume contains syntheses of short and medium range order, structure-property relationships, and computation-based simulations of melt structure. It continues with analyses of the properties (mechanical, diffusive, thermochemical, redox, nucleation, rheological) of melts. The dynamic behavior of melts in magmatic and volcanic systems, is then treated in the context of their behavior in magma mixing, strain localization, frictional melting, magmatic fragmentation, and hot sintering. Finally, the non-magmatic, extraterrestrial and prehistoric roles of melt and glass are presented in their respective contexts. This volume is the cumulative effort of many people whom we gratefully thank, especially the authors of the chapters for their contributions and patience, and the reviewers for their comments and suggestions. We thank Ian Swainson and Rachel Russell for all their work. Finally, we hope graduate students and researchers new to the field will find the volume helpful as a starting point to these fascinating areas of such great importance for understanding the workings of the Earth System and realms beyond. D.B. Dingwell (Munich) Grant Henderson (Toronto) Daniel -R. Neuville (Paris)

1529-6466/22/0087-0000$00.00 (print) 1943-2666/22/0087-0000$00.00 (online)

http://dx.doi.org/10.2138/rmg.2022.87.00

Geological Melts 87

Reviews in Mineralogy and Geochemistry

87

TABLE OF CONTENTS

1

The Short-Range Order (SRO) and Structure GS Henderson, JF Stebbins

INTRODUCTION.....................................................................................................................1 ACRONYMS AND ABBREVIATIONS...................................................................................2 WHAT IS SHORT-RANGE ORDER (SRO)?...........................................................................3 The Si–O bond, O–Si–O and Si–O–Si angles................................................................4 Techniques used to probe the SRO in glasses and melts................................................6 NETWORK-FORMING OXIDES AND CATIONS...............................................................15 Silicon coordination in oxide glasses and melts...........................................................16 Aluminum coordination...............................................................................................19 OXYGEN ANION SPECIATION...........................................................................................22 Order/disorder among bridging oxygens......................................................................22 Effects of modifier oxides: non-bridging oxygens.......................................................25 Measurements of distributions of non-bridging oxygens.............................................26 The connection between network cation coordination and non-bridging oxygens......28 Higher oxygen anion coordination numbers................................................................30 “Free” oxide anions......................................................................................................31 DISTRIBUTIONS OF NBO AND BO AROUND NETWORK CATIONS: Q SPECIES...........................................................................................................................34 Variations on a theme: issues of fitting and data analysis............................................38 Modifier and charge compensating cations..................................................................40 ACKNOWLEDGEMENTS.....................................................................................................43 REFERENCES........................................................................................................................43

2

From Short to Medium Range Order in Glasses and Melts by Diffraction and Raman Spectroscopy JWE Drewitt, L Hennet, DR Neuville

INTRODUCTION...................................................................................................................55 X-RAY, NEUTRON, AND RAMAN SCATTERING OF GLASSES AND MELTS.............57 X-ray and neutron diffraction.......................................................................................57 Raman spectroscopy.....................................................................................................59 The boson peak: A signature of SRO or MRO?...........................................................61 MULTICOMPONENT SILICATE GLASSES........................................................................62 Binary silicate glasses..................................................................................................62 v

Geological Melts ‒ Table of Contents Diffraction measurements............................................................................................63 Raman spectroscopy measurements.............................................................................65 Lead silicate glasses.....................................................................................................68 Aluminosilicate glasses................................................................................................68 Diffraction and Raman measurements along the tectosilicate join..............................69 Charge compensator versus network modifier.............................................................71 GLASS AND MELT STRUCTURE UNDER EXTREME CONDITIONS............................72 High temperature containerless processing..................................................................73 Aluminate melts...........................................................................................................73 Aluminosilicate melts...................................................................................................79 Iron silicate melts and glasses.....................................................................................80 Glasses and melts at high pressure...............................................................................83 Pressure induced modifications in MRO and SRO in SiO2 and GeO2 glass.................84 Silicate melt structure at high pressure.........................................................................86 Al coordination change at high pressure......................................................................87 SUMMARY AND FUTURE PERSPECTIVES......................................................................88 ACKNOWLEDGEMENTS.....................................................................................................89 REFERENCES........................................................................................................................89

3

Link between Medium and Long-range Order and Macroscopic Properties of Silicate Glasses and Melts DR Neuville, C Le Losq

INTRODUCTION.................................................................................................................105 Glass structure versus macroscopic properties...........................................................105 Thermodynamic approach to glass transition.............................................................109 Viscosity and glass transition.....................................................................................109 Configurational properties and glass structure...........................................................110 Pressure–temperature space.......................................................................................113 SILICATE GLASSES AND MELTS.....................................................................................113 Alkali or earth alkaline silicate glasses and melts......................................................113 Viscosity of silicate melts...........................................................................................115 Ideal mixing: mixing alkali or alkaline-earth in silicate glasses and melts................116 Mixing alkali and alkaline-earth elements in silicate glasses.....................................120 Silicate glasses and others network formers...............................................................125 Silicate melts: how can we use existing structural knowledge to model melt properties.........................................................................................................127 ALUMINOSILICATE GLASSES AND MELTS..................................................................131 Molar volume, coordination number and structure....................................................132 Proportion of Al in five-fold coordination..................................................................133 Molar volume, AlO44− and implications for the coordination number of metal cations...........................................................................................................135 Glass transition temperature.......................................................................................136 Link between structure and properties of aluminosilicate melts: example of the CaO–Al2O3–SiO2 system............................................................................................136 From the CAS system to other chemical systems......................................................140 Alkaline-earth mixing in aluminosilicate glasses and melts......................................142 Models for alkali aluminosilicate melts.....................................................................144 ALUMINATE GLASSES AND MELTS...............................................................................147 vi

Geological Melts ‒ Table of Contents Al2O3...........................................................................................................................148 Al2O3–CaAl2O4 compositions.....................................................................................148 CA–C3A compositions...............................................................................................149 C3A–CaO compositions.............................................................................................149 Link with observations in other binary systems.........................................................149 CONCLUSION AND PERSPECTIVES...............................................................................150 REFERENCES......................................................................................................................152

4

Topology and Rigidity of Silicate Melts and Glasses M Micoulaut, M Bauchy

INTRODUCTION.................................................................................................................163 ROLE OF NETWORK RIGIDITY.......................................................................................164 Rigidity theory of network glasses.............................................................................164 The situation in silicate glasses..................................................................................165 Rigidity Hamiltonians and floppy modes...................................................................169 Temperature dependent constraints............................................................................170 MOLECULAR DYNAMICS AND RIGIDITY....................................................................172 Bond-bending and bond-stretching............................................................................173 Behavior in the liquid phase.......................................................................................174 ISOSTATIC RELAXATION..................................................................................................175 Reversibility windows................................................................................................176 OTHER APPLICATIONS .....................................................................................................180 Diffusivity anomalies.................................................................................................180 Prediction of glass hardness.......................................................................................181 Prediction of glass stiffness........................................................................................182 Origin of fracture toughness anomalies......................................................................183 Prediction of dissolution kinetics...............................................................................184 Other applications and conclusion.............................................................................185 REFERENCES......................................................................................................................185

5

Molecular Simulations of Oxide and Silicate Melts and Glasses S Jahn

INTRODUCTION.................................................................................................................193 SIMULATION METHODS...................................................................................................193 Classical potentials.....................................................................................................194 Electronic structure methods......................................................................................196 Molecular dynamics simulations................................................................................197 Monte-Carlo simulations............................................................................................198 Data analysis...............................................................................................................198 SIMULATIONS OF OXIDE AND SILICATE MELTS AND GLASSES............................203 Oxide melts and glasses at ambient pressure.............................................................203 Silicate melts and glasses at ambient pressure...........................................................206 Melts and glasses at high pressure.............................................................................212 CONCLUSIONS....................................................................................................................218 REFERENCES......................................................................................................................219 vii

Geological Melts ‒ Table of Contents

6

Mechanical Properties of Oxide Glasses BP Rodrigues, T To, MM Smedskjaer, L Wondraczek

INTRODUCTION.................................................................................................................229 ELASTIC CONSTANTS AND POISSON’S RATIO...........................................................230 FRACTURE AND BRITTLENESS......................................................................................232 EXPERIMENTAL METHODS FOR STRENGTH AND TOUGHNESS TESTING...........236 Biaxial test..................................................................................................................237 Uniaxial test................................................................................................................238 Fracture toughness test...............................................................................................239 WEIBULL DISTRIBUTION AND PROBABILITY PLOTS...............................................240 STRESS CORROSION AND FATIGUE...............................................................................243 Region 0: environmental limit....................................................................................244 Region I: stress corrosion...........................................................................................244 Region II: transport kinetics.......................................................................................245 Region III: inert crack growth....................................................................................246 Stress corrosion mechanism.......................................................................................246 INDENTATION HARDNESS, SCRATCH RESISTANCE AND CRACKING...................246 Stress fields.................................................................................................................247 Deformation mechanism............................................................................................248 Hardness.....................................................................................................................249 Strain-rate sensitivity..................................................................................................249 Indentation cracking...................................................................................................250 Scratch resistance.......................................................................................................253 FRACTOGRAPHY................................................................................................................254 Crack branching pattern and angle.............................................................................254 Fracture surfaces (mirrors, mist and hackle)..............................................................255 RESIDUAL STRESS AND METHODS FOR ENHANCING THE PRACTICAL STRENGTH OF GLASSES...............................................................256 Thermal strengthening................................................................................................257 Chemical strengthening..............................................................................................258 MECHANICAL PROPERTY EXAMPLES..........................................................................260 Fracture toughness versus Young’s modulus..............................................................260 Fracture energy versus Poisson’s ratio.......................................................................260 Properties related to Poisson’s ratio...........................................................................261 Stress optical coefficient and persistent anisotropy....................................................262 PERSPECTIVE: TOPOLOGICAL CONSTRAINT THEORY............................................262 PERSPECTIVE: STRUCTURAL HETEROGENEITY AND NON-AFFINE DEFORMATION.............................................................................264 PERSPECTIVE: MODELING AND SIMULATION...........................................................266 Finite element methods..............................................................................................266 Peridynamics..............................................................................................................268 Molecular dynamics...................................................................................................268 Machine learning........................................................................................................270 OUTLOOK............................................................................................................................270 ACKNOWLEDGEMENT.....................................................................................................271 REFERENCES......................................................................................................................272 viii

Geological Melts ‒ Table of Contents

7

Diffusion in Melts and Magmas Y Zhang, T Gan

INTRODUCTION.................................................................................................................283 FUNDAMENTALS OF DIFFUSION...................................................................................284 Fick’s laws..................................................................................................................284 Various kinds of diffusion and diffusivities................................................................286 Dependence of D on temperature, pressure, and melt composition...........................287 SOME USEFUL SOLUTIONS TO THE DIFFUSION EQUATION AND EXPERIMENTAL DESIGNS FOR OBTAINING DIFFUSIVITY...................................289 Diffusion couples .......................................................................................................289 Sorption or desorption ...............................................................................................290 Diffusion in melts during diffusive mineral dissolution ............................................291 Thin-source diffusion ................................................................................................292 Isotropic diffusion in spheres ....................................................................................293 Variable diffusivity along a profile ............................................................................293 Diffusion distance and square root of time relation ..................................................295 MULTICOMPONENT DIFFUSION....................................................................................295 Effective binary diffusion ..........................................................................................296 Multicomponent diffusion theory...............................................................................298 Recent studies of multicomponent diffusion..............................................................300 TRACER AND EFFECTIVE BINARY DIFFUSION DATA...............................................307 H2O diffusion .............................................................................................................308 Diffusion of alkalis.....................................................................................................312 Cu diffusion................................................................................................................313 Diffusion of Sc, Y, and REE.......................................................................................315 Diffusivities of Li, Rb, Sr, Ba, Sn, V, Zr, Hf, Th, U, Nb and Ta.................................317 SiO2 diffusion ............................................................................................................318 Self diffusion of O, Si, Mg and Ca, and interdiffusivity of Ni and Co in a peridotite melt..........................................................................................................319 Diffusion of Mo and W..............................................................................................320 Diffusion of F, Cl, and S.............................................................................................320 Major and trace element diffusion (OEBD) in shoshonite–rhyolite diffusion couple.......................................................................................................321 DIFFUSIVE ELEMENTAL AND ISOTOPE FRACTIONATION DURING MAGMATIC PROCESSES................................................................................................322 DIFFUSIVITY IN CRYSTAL-BEARING AND BUBBLE-BEARING MAGMAS............325 Crystal-bearing magmas.............................................................................................328 Bubble-bearing magmas.............................................................................................329 CONCLUSIONS....................................................................................................................331 ACKNOWLEDGEMENT.....................................................................................................331 REFERENCES......................................................................................................................331

ix

Geological Melts ‒ Table of Contents

8

Silicate Melt Thermochemistry and the Redox State of Magmas R Moretti, G Ottonello

INTRODUCTION AND RATIONALE.................................................................................339 THE EMERGENCE AND RISE OF THE CONCEPT OF OXYGEN FUGACITY............345 Oxygen exchange between metals and their oxides...................................................345 Oxygen fugacity and iron-bearing solid phases.........................................................348 MODELLING THE REDOX STATE OF SILICATE MELTS..............................................350 Non-reactive species-based approaches to iron redox................................................350 The ionic approach and the role of the ligand............................................................357 Oxygen fugacity, sulfur and joint Fe–S redox exchanges..........................................368 THE (FULL) AB-INITIO PERSPECTIVE: THE CASE OF IRON REDOX..........................................................................................374 Electron transfer and solute–solvent interactions in melts.........................................374 The normal oxygen electrode.....................................................................................376 Ab-initio iron redox ...................................................................................................382 REMARKS AND PERSPECTIVES.....................................................................................387 CODE AVAILABILITY........................................................................................................390 APPENDIX ...........................................................................................................................391 Isolated molecules (gaseous state).............................................................................391 Neutral and charged species in solution ....................................................................392 ACKNOWLEDGEMENTS...................................................................................................397 REFERENCES......................................................................................................................397

9

Nucleation, Growth, and Crystallization in Oxide Glass-formers. A Current Perspective M Montazerian, ED Zanotto

INTRODUCTION.................................................................................................................405 TABLE OF SYMBOLS.........................................................................................................407 CRYSTAL NUCLEATION AND CLASSICAL NUCLEATION THEORY........................408 Recent findings that warrant further research: Examples of experimental tests........413 BASIC MODELS OF CRYSTAL GROWTH IN SUPERCOOLED LIQUIDS....................416 Experimental tests......................................................................................................420 OVERALL CRYSTALLIZATION AND GLASS-FORMING ABILITY: THE JOHNSON–MEHL–AVRAMI–KOLMOGOROV APPROACH...............................422 Glass stability against crystallization.........................................................................426 PERSPECTIVES...................................................................................................................426 ACKNOWLEDGMENTS......................................................................................................427 REFERENCES......................................................................................................................428

x

Geological Melts ‒ Table of Contents

10

Thermodynamics of Multi-component Gas–Melt Equilibrium in Magmas: Theory, Models, and Applications P Papale, R Moretti, A Paonita

INTRODUCTION.................................................................................................................431 FUNDAMENTAL EQUATIONS OF EQUILIBRIUM THERMODYNAMICS..................435 Fundaments of thermodynamic equilibrium..............................................................435 Terms in the equilibrium equations............................................................................440 REGULAR SOLUTION MODELING APPROACH TO VOLATILE–MELT THERMODYNAMICS......................................................................444 Excess Gibbs energy...................................................................................................444 Early models...............................................................................................................446 The SOLWCAD model (Papale et al. 2006)..............................................................447 The MagmaSat model (Ghiorso and Gualda 2015)....................................................451 Performance of the SOLWCAD and MagmaSat models...........................................452 REACTIVE SPECIES-BASED APPROACHES TO VOLATILE–MELT EQUILIBRIA....455 Making solubility models (nearly) ideal: the Burnham model for water solubility...455 General aspects of the reactive species-based approaches to volatile–melt equilibria............................................................................................458 H2O models revisited: the role of speciation in ionic polymeric-approaches ...........459 Speciation-based CO2 models....................................................................................469 The VolatileCalc model..............................................................................................473 Acid–base compositional control on volatile speciation............................................476 Sulfur solubility..........................................................................................................482 Modeling sulfur solubility in silicate melts: the CTSFG model................................485 Additional models for sulfur solubility in silicate melts............................................494 Combined C–H–O–S–(±Cl) saturation models .........................................................497 Halogen solubility......................................................................................................503 First principles and molecular dynamics approaches.................................................505 NOBLE GASES.....................................................................................................................507 General aspects of noble gas solubility in magmas....................................................507 Basic thermodynamics of noble gas solubility in silicate melts.................................508 Pure noble gases and noble gas mixtures...................................................................509 Reference state and activity–composition relationships.............................................510 Models based on statistical mechanics.......................................................................514 Models accounting for melt composition...................................................................515 Modeling mixed H2O–CO2–noble gases....................................................................518 Ar solubility as a proxy for N2 solubility...................................................................521 Applications................................................................................................................521 Determination of magma storage conditions..............................................................522 Interpretation of volcano degassing data....................................................................529 Using noble gases with major volatiles......................................................................533 Constraining and modeling magma and eruption dynamics......................................537 CONCLUDING REMARKS.................................................................................................543 REFERENCES......................................................................................................................543

xi

Geological Melts ‒ Table of Contents

11

High Pressure Melts T Sakamaki, E Ohtani

INTRODUCTION.................................................................................................................557 EXISTENCE OF MAGMA IN THE INTERIOR OF THE EARTH.....................................557 Evidence for mantle melting......................................................................................557 H2O in Earth’s mantle.................................................................................................558 Mantle transition zone................................................................................................558 Ultralow velocity zone at the base of lower mantle...................................................558 PHYSICAL PROPERTY OF HIGH PRESSURE MELTS...................................................559 Density of melt at high pressure.................................................................................559 Viscosity of melt at high pressure..............................................................................560 H2O-BEARING MELTS........................................................................................................562 Generation of hydrous magma in the interior of the Earth.........................................562 H2O effect on the melt density....................................................................................563 The behavior of hydrous magmas above and below the mantle transition zone........564 H2O effect on the melt viscosity.................................................................................565 CO2-BEARING MELTS........................................................................................................566 CO2-rich magma in the interior of the Earth..............................................................566 CO2 effect on the melt density....................................................................................566 CO2 effect on the melt viscosity.................................................................................567 Viscosity of carbonate melt........................................................................................567 MAGMA OCEAN IN THE EARLY EARTH.......................................................................568 Melting in the early Earth’s mantle............................................................................568 Dynamics of the magma ocean crystallization...........................................................568 REFERENCES......................................................................................................................569

12

Volatile-bearing Partial Melts in the Lithospheric and Sub-Lithospheric Mantle on Earth and Other Rocky Planets R Dasgupta, P Chowdhury, J Eguchi, C Sun, S Saha

INTRODUCTION.................................................................................................................575 THE EFFECTS OF MAJOR VOLATILES ON MELTING OF THE EARTH’S MODERN MANTLE.........................................................................576 Solidus of CO2, H2O, and CO2+H2O-bearing peridotite.............................................577 The effects of CO2 and H2O contents and major element bulk composition on the solidus...........................................................................................................578 Carbonated peridotite solidus during open system processes....................................581 The composition of H2O–CO2-bearing partial melts from nominally volatile-free mantle—beneath oceans and continents.............................................582 THE EFFECTS OF VOLATILE STORAGE IN ACCESSORY PHASES VERSUS MAJOR MANTLE MINERALS........................................................................586 Mobilization of carbon versus sulfur-bearing accessory phase during melting of the Earth’s mantle................................................................................................587 Sulfur mobilization by incipient melt in the Earth’s mantle......................................588 Extraction of C–S–H volatiles from other rocky mantles in the Solar System..........591 xii

Geological Melts ‒ Table of Contents Carbon contents of graphite-saturated mantle melts—application to planetary mantles.....................................................................................................593 Sulfur concentrations at sulfide saturation—application to planetary mantles..........596 Fractionation of carbon and sulfur during mantle melting at varying oxygen fugacity..........................................................................................596 Carbon, sulfur and water as a function of melting degree and mantle redox.............597 CONCLUDING REMARKS.................................................................................................600 ACKNOWLEDGMENTS......................................................................................................601 REFERENCES......................................................................................................................601

13

Decrypting Magma Mixing in Igneous Systems D Morgavi, M Laumonier, M Petrelli, DB Dingwell

INTRODUCTION.................................................................................................................607 HISTORICAL PERSPECTIVE (1851 TO MODERN TIMES)............................................607 DEFINITIONS AND FIELD EVIDENCE OF MAGMA MIXING.....................................610 Definitions of mixing and mingling...........................................................................610 Mixing and mingling structures ................................................................................610 SCALING RULES AND NUMERICAL MODELLING......................................................612 Stretching and folding plus diffusion: kinematic description of magma mixing.......612 Complete fluid dynamic description of magma mixing.............................................615 EXPERIMENTAL STUDIES FOR DECIPHERING THE COMPLEXITY OF MAGMA MIXING.............................................................................................................623 Reproducing the textural evidences of magma mixing..............................................623 Rheological constraints .............................................................................................625 Flow regimes in magma chambers and mixing .........................................................627 Experiments involving crystal disequilibrium during magma mixing.......................629 CHEMICAL INVESTIGATIONS: FROM A SIMPLE LINEAR RELATION TO A COMPLEX INTERPLAY WITH SYSTEM DYNAMICS ......................................629 IMPLICATION OF MAGMA MIXING AND FUTURE DEVELOPMENTS ....................630 ACKNOWLEDGEMENTS...................................................................................................631 REFERENCES......................................................................................................................632

14

Magma / Suspension Rheology S Kolzenburg, MO Chevrel, DB Dingwell

THEORETICAL CONSIDERATIONS.................................................................................639 CONVENTIONAL DESCRIPTIONS OF RHEOLOGICAL DATA....................................640 EXPERIMENTS ON ANALOGUE MATERIALS...............................................................646 Particle suspension analogues....................................................................................647 Bubble suspension analogues.....................................................................................648 Experimental materials and measurement strategies..................................................649 EXPERIMENTS ON HIGH TEMPERATURE SILICATE MELT SUSPENSIONS...........650 Concentric cylinder experiments................................................................................652 Bubble bearing suspensions.......................................................................................662 Parallel plate experiments...........................................................................................663 Torsion experiments...................................................................................................668 FIELD RHEOLOGY.............................................................................................................672 xiii

Geological Melts ‒ Table of Contents Falling sphere.............................................................................................................674 Penetrometers.............................................................................................................674 Rotational viscometers...............................................................................................675 Toward parameterization: requirements for future field viscometry..........................677 PARAMETERIZATION STRATEGIES...............................................................................679 Particle suspensions....................................................................................................679 Parameterization of the relative suspension viscosity ηr.......................................................................... 679 Parameterization of the yield stress ty........................................................................................................................... 689 Bubble suspensions....................................................................................................692 The yield stress dilemma............................................................................................702 TECHNOLOGICAL ADVANCES........................................................................................704 OUTSTANDING CHALLENGES........................................................................................705 Models for multiphase rheology.................................................................................705 Reactive flow and phase dynamics.............................................................................706 Filling data gaps.........................................................................................................707 Connecting magma rheology and rock mechanics.....................................................707 Exploiting multidisciplinary datasets.........................................................................708 Characterizing nanoscale processes...........................................................................708 ACKNOWLEDGMENTS......................................................................................................709 REFERENCES......................................................................................................................709

15

Strain Localization in Magmas Y Lavallée, JE Kendrick

INTRODUCTION.................................................................................................................721 MATERIAL DEFORMATION AND STRAIN LOCALIZATION.......................................722 Evidence for strain localization in magmas: the geologic record..............................722 Strain regimes.............................................................................................................724 Stress and strain regimes in magmatic environments.................................................724 Evolution of properties and conditions during magma transport...............................725 Deformation modes: ductile vs brittle........................................................................726 STRAIN LOCALIZATION: AN INTERPLAY BETWEEN DEFORMATION MECHANISMS....................................................................................728 Viscous flow and energy dissipation..........................................................................728 Bubble deformation and alignment............................................................................729 Crystal alignment and deformation............................................................................734 Multiphase magma rupture.........................................................................................739 Fault processes............................................................................................................748 CONSEQUENCES OF STRAIN LOCALIZATION IN MAGMAS....................................750 Brittle versus ductile deformation modes in rocks and magmas................................750 Construction versus destruction of permeability........................................................751 Implications for magma seismicity and tilt at volcanoes...........................................752 Transport in volcanic conduits and during volcanic eruptions: a model....................754 ACKNOWLEDGEMENTS...................................................................................................757 REFERENCES......................................................................................................................757

xiv

Geological Melts ‒ Table of Contents

16

Magma Fragmentation B Scheu, DB Dingwell

INTRODUCTION.................................................................................................................767 SILICATE LIQUIDS—THE BASIS OF MAGMA...............................................................768 FRAGMENTATION—A MATERIALS TRIGGER.............................................................769 EXPERIMENTAL VOLCANOLOGY OF MAGMATIC FRAGMENTATION...................773 Early experimental approaches...................................................................................774 Fragmentation experiments using magma analogues.................................................776 Fragmentation experiments using silicate melts and volcanic rocks..........................777 THEORETICAL MODELS AND CRITERIA FOR MAGMA FRAGMENTATION..........778 MAGMA FRAGMENTATION BEHAVIOR.....................................................................780 Fragmentation threshold.............................................................................................780 Influence of permeability on magma fragmentation..................................................782 Speed of magma fragmentation..................................................................................783 Timescales of magma ascent and fragmentation—Implications for eruption styles.. 785 PRODUCTS OF MAGMA FRAGMENTATION..................................................................787 Energetic considerations of magma fragmentation....................................................787 Grain size distribution of fragmentation products......................................................788 SECONDARY FRAGMENTATION.....................................................................................790 EXPLOSIVE AND NON-EXPLOSIVE MAGMA WATER INTERACTION.....................791 NON-MAGMATIC FRAGMENTATION: STEAM-DRIVEN ERUPTIONS......................792 CONCLUDING REMARKS AND FUTURE PERSPECTIVES.........................................793 ACKNOWLEDGEMENTS...................................................................................................794 REFERENCES......................................................................................................................794

17

Hot Sintering of Melts, Glasses and Magmas FB Wadsworth, J Vasseur, EW Llewellin, DB Dingwell

INTRODUCTION TO SINTERING IN VOLCANIC ENVIRONMENTS..........................801 Families of sintering phenomena................................................................................803 Phenomenology and internal texture..........................................................................804 Conceptual approaches...............................................................................................807 THEORETICAL MODELS FOR SINTERING UNDER NO EXTERNAL LOAD............808 ‘Free sintering’ of many particles or sintering under zero applied load.....................810 Extending sintering models to polydisperse systems.................................................813 ‘PRESSURE SINTERING’ OR SINTERING UNDER EXTERNAL LOAD......................813 The extended Mackenzie–Shuttleworth model (Wadsworth et al. 2019)...................814 The extended Scherer model (Scherer 1986).............................................................814 The Quane and Russell (2005) model. ......................................................................814 PORE SIZES, SURFACE AREA AND INTER-PARTICLE DISTANCES IN SINTERING SYSTEMS...............................................................................................815 Pore sizes....................................................................................................................815 Specific surface area...................................................................................................818 Inter-particle distance.................................................................................................818 EXPERIMENTAL APPROACHES.......................................................................................818 Sintering under equilibrium pressures........................................................................820 Sintering under differential pressures.........................................................................822 xv

Geological Melts ‒ Table of Contents EMPIRICAL DATA AND ANALYSIS.................................................................................822 Fundamental quantities specific to the data used here...............................................822 Sintering of two droplets or particles.........................................................................823 Sintering of large systems of many droplets..............................................................824 SINTERING OF MORE COMPLEX SYSTEMS.................................................................826 The effect of rigid crystals..........................................................................................827 Sintering with diffusive hydration or dehydration......................................................828 PHYSICAL PROPERTIES OF SINTERED SYSTEMS......................................................830 The sintered filter: permeability during sintering (Wadsworth et al. 2021)...............830 Elastic properties........................................................................................................831 Compressive strength of sintered materials................................................................832 SINTERING DYNAMICS MAPS.........................................................................................833 RECIPES FOR SINTERING AND APPLICATIONS..........................................................834 OUTLOOK............................................................................................................................836 ACKNOWLEDGMENTS......................................................................................................836 REFERENCES......................................................................................................................837

18

Models for Viscosity of Geological Melts JK Russell, K-U Hess, DB Dingwell

INTRODUCTION.................................................................................................................841 EXPERIMENTAL DETERMINATION OF MELT VISCOSITY........................................842 Measurement techniques............................................................................................843 Viscosity data for natural silicate melts......................................................................846 MODEL CONSIDERATIONS..............................................................................................846 TEMPERATURE DEPENDENCE OF MELT VISCOSITY................................................848 Non-Arrhenian functions for melt viscosity...............................................................848 THE HIGH-TEMPERATURE LIMIT TO MELT VISCOSITY (A).....................................851 Practical application of a high-T limit........................................................................852 Implications of a common A......................................................................................853 EARLY MODELS AND MODELLING OF GEOLOGICAL MELTS................................856 MODELS FOR HYDROUS SILICIC MELTS.....................................................................861 Hydrous low-P models for silicic melts.....................................................................861 Hydrous high-P models for silicic melts....................................................................863 OTHER MODELS FOR RESTRICTED COMPOSITIONAL RANGES............................866 Models for melts from the Phlegrean Field................................................................866 A model for natural Fe-bearing silicate melts............................................................867 A model for extraterrestrial melts...............................................................................868 MULTICOMPONENT MELT MODELS FOR GEOLOGICAL SYSTEMS.......................871 Non-Arrhenian multicomponent melt models (anhydrous).......................................871 Non-Arrhenian multicomponent melt models (hydrous)...........................................873 GRD MODEL (2008)...........................................................................................................874 Attributes....................................................................................................................875 Weaknesses.................................................................................................................878 QUO VADIMUS....................................................................................................................880 CLOSING THOUGHTS........................................................................................................881 ACKNOWLEDGEMENTS...................................................................................................882 REFERENCES......................................................................................................................882 xvi

Geological Melts ‒ Table of Contents

19

Non-terrestrial Melts, Magmas and Glasses G Libourel, P Beck, J-A Barrat

INTRODUCTION.................................................................................................................887 CHONDRULES: THE EARLIEST MOLTEN DROPLETS OF THE SOLAR SYSTEM................................................................................................888 Extraterrestrial igneous droplets.................................................................................889 Chondrule thermal history..........................................................................................891 Evidence for gas–melt interaction during chondrule formation.................................894 Astrophysical implications.........................................................................................896 MAGMATIC MELTS FROM PROTOPLANETS.................................................................896 Alkali-depleted protoplanetary basalts.......................................................................897 Andesitic or trachyandesitic achondrites....................................................................901 IMPACT-RELATED MELTS AND GLASSES.....................................................................902 Impact induced melting and vaporisation, lessons from terrestrial impactites..........902 Impact-related amorphization of minerals: dense glass or not...................................903 High-pressure melting, and high-pressure phase bearing melt..................................904 Transported glass fragments and glass beads in extra-terrestrial regolith and regolith breccias.......................................................................................................906 Prospects.....................................................................................................................911 ACKNOWLEDGEMENTS...................................................................................................912 REFERENCES......................................................................................................................912

20

Frictional Melting in Magma and Lava JE Kendrick, Y Lavallée

INTRODUCTION.................................................................................................................919 FAULT FRICTION................................................................................................................921 Identifying pseudotachylytes......................................................................................921 Fault slip in tectonic and volcanic environments.......................................................923 Dynamics of frictional sliding....................................................................................926 FRICTIONAL MELTING.....................................................................................................928 The history of experimental approaches.....................................................................928 Mechanical response to melting.................................................................................929 Selective melting........................................................................................................932 Frictional melt rheology.............................................................................................937 Viscous remobilization...............................................................................................944 Thermal vesiculation..................................................................................................945 Elevated ambient temperature....................................................................................947 Fault healing and cyclic rupture.................................................................................951 SUMMARY AND CONCLUDING REMARKS..................................................................952 ACKNOWLEDGEMENTS...................................................................................................953 REFERENCES......................................................................................................................953

xvii

Geological Melts ‒ Table of Contents

21

Non-Magmatic Glasses MR Cicconi, JS McCloy, DR Neuville

OVERVIEW ..........................................................................................................................965 ACRONYMS AND GLOSSARY..........................................................................................965 INTRODUCTION ................................................................................................................966 The composition and origin of natural glasses...........................................................966 METAMORPHIC GLASSES................................................................................................968 Pyrometamorphic glasses...........................................................................................968 Pseudotachylite or frictionites....................................................................................972 GLASSES FROM HIGHLY ENERGETIC EVENTS...........................................................974 Impactites...................................................................................................................974 Tektites and microtektites...........................................................................................977 Enigmatic impact glasses...........................................................................................982 Fulgurite.....................................................................................................................987 Trinitite or nuclear glass.............................................................................................993 GLASS PROPERTIES...........................................................................................................996 Liquid immiscibility...................................................................................................996 Reduced iron species..................................................................................................997 Glass structure..........................................................................................................1000 CONCLUDING REMARKS...............................................................................................1005 ACKNOWLEDGMENTS....................................................................................................1005 REFERENCES....................................................................................................................1005

22

Silicate Glasses and Their Impact on Humanity RE Youngman

INTRODUCTION...............................................................................................................1015 HISTORY AND IMPACT OF SILICATE GLASSES.........................................................1016 Glass before and during the Age of Antiquity..........................................................1016 Silicate glasses during the Middle Ages...................................................................1019 Silicate glasses in modern and contemporary history..............................................1022 Summary and perspectives on the Glass Age...........................................................1035 ACKNOWLEDGEMENTS.................................................................................................1037 REFERENCES....................................................................................................................1038

23

Glass as a State of Matter—The “newer” Glass Families from Organic, Metallic, Ionic to Non-silicate Oxide and Non-oxide Glasses D Möncke, B Topper, AG Clare

OVERVIEW.........................................................................................................................1039 INTRODUCTION...............................................................................................................1039 The glassy state of matter.........................................................................................1042 The glass family tree................................................................................................1042 Glass models.............................................................................................................1043 xviii

Geological Melts ‒ Table of Contents ORGANIC GLASSES.........................................................................................................1044 Man-made polymeric glasses...................................................................................1046 Amber.......................................................................................................................1047 Organic metal framework glasses.............................................................................1047 INORGANIC METALLIC GLASSES................................................................................1048 INORGANIC NON-METALLIC NON-OXIDE GLASSES...............................................1049 Chalcogen(ide) glasses.............................................................................................1049 Fluoride glasses........................................................................................................1052 Other ionic and molecular glasses............................................................................1055 Nitride glasses..........................................................................................................1055 SIMPLE INORGANIC OXIDE GLASSES........................................................................1058 Phosphate glasses.....................................................................................................1058 Borate glasses...........................................................................................................1066 Tellurite glasses........................................................................................................1071 Germanate glasses....................................................................................................1073 Other glasses.............................................................................................................1075 GLASS FAMILIES IN COMPARISON..............................................................................1076 CONCLUDING REMARKS...............................................................................................1078 ACKNOWLEDGEMENTS.................................................................................................1078 REFERENCES....................................................................................................................1079

xix

1

Reviews in Mineralogy & Geochemistry Vol. 87 pp.1-53, 2022 Copyright © Mineralogical Society of America

The Short-Range Order (SRO) and Structure Grant S. Henderson Department of Earth Sciences University of Toronto 22 Russell St Toronto Ontario, M5S 3B1 Canada [email protected]

Jonathan F. Stebbins Department of Geological Sciences Stanford University Stanford California 94305–2115 USA [email protected]

INTRODUCTION Magmas are mixtures of melt, crystals and dissolved gasses with or without crystalline material (Mysen and Richet 2019). They play an important role in igneous processes particularly those influenced by their viscosity, density, and other physical properties. Much of the research to date has used quenched melts (or glasses) as proxies for studying the melt portion of magmas. Studies of glasses and melts at elevated temperatures or in-situ have been carried out since the late 1970s (cf., Waseda and Egami 1979; Exarhos et al. 1988) but remain difficult experiments to perform due to technical difficulties dealing with high temperatures and molten liquids. Problems can arise from, for example, thermal broadening of spectroscopic peaks (often reflecting important dynamics in the liquid state), black body radiation, and motional averaging, as well as challenges of thermal gradients, volatilization, accurate P/T measurement, etc. Another complication is the complex chemical compositions of natural melts and glasses which can make it difficult to analyze and interpret data. Therefore, the glasses studied are usually simple synthetic, rather than natural compositions. The assumption is that the structure of the glass resembles that of the melt at the glass transition temperature, the temperature at which there is a transition from liquid-like to solid-like properties and behavior. One of the key issues is the quality and information content of data obtainable on glasses vs. liquids. A more complete definition of a glass is given by Zanotto and Mauro (2017). Several recent books provide greater detail on glass and melt structure and properties than can be included here (e.g., Greaves and Sen 2007; Le Losq et al. 2019b; Musgraves et al. 2019; Mysen and Richet 2019; Varshneya 2019; Greaves 2020; Richet 2020) including high pressure studies (Kono and Sanloup 2018). Other RiMG volumes on silicate melts (Stebbins et al. 1995) and on spectroscopic methods (Henderson et al. 2014b) as well as other chapters in this volume provide extended and complementary information as well. 1529-6466/22/0087-0001$10.00 (print) 1943-2666/22/0087-0001$10.00 (online)

http://dx.doi.org/10.2138/rmg.2022.87.01

Henderson & Stebbins

2

ACRONYMS AND ABBREVIATIONS

AWAXS

Anomalous wide-angle X-ray scattering

MAS

Magic angle spinning (NMR)

Ab Initio

First principles

MBO

Bridging oxygen (Si–O–Si) with one or more alkali or alkaline-earth cations attached to it.

BE

Binding energy

MD

Molecular dynamics

BO

Bridging oxygen

MQ

Multiple quantum (NMR)

CA

CaO–Al2O3 or CaAl2O4

NBO

Non-bridging oxygen

CA2

CaO–Al2O3 or CaAl4O7

NMR

Nuclear magnetic resonance

C3A

3CaO–Al2O3 or Ca3Al2O6

NRIXS

Non resonant inelastic X-ray scattering (same as XRS)

C2A

2CaO–Al2O3 or Ca2Al2O5

O2−

Free oxide (same as FO)

CMAS

CaO–MgO–Al2O3–SiO2 or CaMgAl2SiO7

PCA

Principle component analysis

CN

Coordination number

PCF

Pair correlation function

CQ

quadrupolar coupling constant (NMR)

PSF

Partial structure factor

CSA

Chemical Shift Anisotropy (NMR)

RDF

Radial distribution function

DAS

Dynamic Angle Spinning (NMR)

RMC

Reverse Monte Carlo

DAXS

Diffraction anomalous X-ray scattering

SRO

Short-range order

DFT

Density functional theory

tricluster

A group of three network cations, each of which has three or four oxygen first neighbors which share a single oxygen i.e., OAl3

DOR

Double Rotation (NMR)

UV

Ultraviolet

ELNES

Energy loss near-edge spectroscopy

XANES

X-ray absorption near-edge structure

EPSR

Empirical potential structure refinement

XAFS

X-ray absorption fine structure spectroscopy (same as EXAFS)

eV

Electron volt

XAS

X-ray absorption spectroscopy

EXAFS

Extended X-ray absorption fine structure

XPS

X-ray photoelectron spectroscopy

FO

Free Oxide (same as O2−)

XRS

X-ray Raman spectroscopy (same as NRIXS)

FWHM

Full width at half maximum

2D

Two-dimensional (NMR)

IR

Infrared also NIR (Near IR) and MIR (Mid IR)

3Q

Triple quantum (NMR)

keV

Kilo electron volt

The Short-Range Order (SRO) and Structure

3

WHAT IS SHORT-RANGE ORDER (SRO)? The interatomic forces that link atoms in glasses and melts are the same as those in crystalline materials (Zachariasen 1932). Crystal structures can be defined by a unit cell, lattice type, atom positions, point and space group symmetry. Glasses form extended threedimensional structures like crystalline materials, but in a glass, there is no lattice and no translational symmetry. No formal unit cell can be defined. The lack of well-ordered periodic structure like that of a crystal means that the structure of a glass must be defined using an alternative approach. The most common way of defining the structure of glasses is to use concepts of order even though the presence of order in glasses cannot be precisely defined. The degree of order is usually interpreted in terms of short, intermediate or medium range order. It is the lack of long-range order that differentiates a glass from a crystal. Drewitt et al. (2022, this volume) discuss the intermediate-range order in glasses and melts. Wright (1994) defined four ranges: (I) the structural unit, (II) the interconnection of adjacent structural units, (III) the network topology (medium-range order), and (IV) longrange fluctuations in density (long-range order). The first two ranges of order defined by Wright (1994) are generally grouped together to define short-range order. In simple silicate glasses the basic building block is the SiO4 tetrahedron. The arrangement of atoms around the tetrahedron and how it is linked to its immediate tetrahedral neighbours constitutes one key aspect of the short range order (SRO). Other factors such as coordination of non-network cations also play a role. SiO4 tetrahedra are made up of 4 Si–O bonds and 4 O–Si–O angles. The latter are generally close to 109.4° and tend to be relatively limited (ranging from 98–122°) except at high pressures (P) and temperatures (T). If the oxygens are shared with the Si atoms of the adjacent tetrahedron they are referred to as bridging oxygens (BO) and link the tetrahedra together. The number of bridging oxygens associated with a tetrahedron defines what is termed a Qn species (based on chemical nomenclature for a ‘quaternary’ group with four bonds) where n is the number of bridging oxygens and can vary between 0–4 (Fig. 1). If an oxygen is bonded to only one Si atom (or other element such as Al, B, or P, with high charge and small coordination number) it is termed a non-bridging oxygen (NBO). This type of bond has excess negative charge on the oxygen resulting in the need for the charge to be balanced by the close approach of one or usually several “charge balancing cations” such as an alkalis or alkaline-earths. There are a number of parameters that can be defined which fully describe the nature of the tetrahedron and its linkage to adjacent tetrahedra.

Q0

Q1

Q4

Q3

Q2

MBO

O tricluster

Figure 1. Qn species: NBO (sky blue), BO (red), MBO (blue). Q0 tetrahedron with no BO; Q1 with 1 BO; Q2 with 2 BO; Q3 with 3 BO; partial structure of α-Na2Si2O5 showing Q3 tetrahedra with regular BO (red) and MBO (blue) with Na (green) attached; and an oxygen tricluster (orange) being shared with 3 AlO4 tetrahedra.

4

Henderson & Stebbins

Figure 2. Parameters that define the SRO: α intertetrahedral angle, δ bond torsion angles, d Si–O distance, Φ O–Si–O angle. Reprinted from The structure of silicate melts: a glass perspective. Henderson GS Canadian Mineralogist 43: 1921–1958. Copyright Mineralogical Association of Canada (2005).

These are: the Si–O bond length (d); the tetrahedral (O–Si–O) bond-angle (φ); the intertetrahedral (Si–O–Si) or dihedral bond-angle (α); the bond-torsion angles (δ1 and δ2), and the Si coordination number (N). These parameters are shown in Figure 2. There is little difference between a tetrahedron in a glass and a crystal. This is because the parameters associated with individual tetrahedra are relatively fixed. However, the wide variation in α (116–180° in silica glass), and δ1 and δ2 distinguishes a glass from its corresponding crystalline analogue: disorder begins with the interconnection of adjacent tetrahedra (Mozzi and Warren 1969).

The Si–O bond, O–Si–O and Si–O–Si angles Excellent reviews of the nature and behaviour of the Si–O bonds and angles found in crystalline silicates and in glasses are given in Liebau (1985) and Mysen and Richet (2019). Only a brief overview will be given here. It is important to remember that the bond distances and angles determined for glasses are generally average distances and not explicit distances as determined for crystalline materials. This is because of the nature of the disorder in glasses. In silica glass the average Si–O bond length is ~1.59–1.62 Å, with a Si–O–Si angle varying from ~120–180° (Mozzi and Warren 1969; Mei et al. 2007). An often stated Si–O–Si average angle is 144° as determined by Mozzi and Warren. However, this value is significantly different from nearly every other study (using multiple techniques) of the Si–O–Si angle in SiO2 glass where the average angle is around 147–151°. The difference can be attributed to the manner in which Mozzi and Warren (1969) calculated their Si–Si bond distance distribution. A discussion of this and further references are given in Wright (1994); Henderson (2005); Mei et al. (2007) and Trease et al. (2017). The average O–O distance is ~2.62–2.65 Å and Si–Si distance ~3.06–3.12 Å (Mozzi and Warren 1969; Konnert and Karle 1973; Wright 1994). The bridging oxygen bond lengths in silicate glasses and crystals lengthens with decrease in the Si–O–Si angle and with increase in coordination of Si (Liebau 1985). Furthermore, Si–NBO distances are shorter than Si–BO distances because of the weaker attraction to lower-charged cations. In crystalline silicates the Si–NBO distance is typically 1.58 Å and Si–BO about 1.63Å. The coordination of the oxygen atoms also influences the Si–O distance and Si–O–Si angle: Si–O bond lengths increase as the coordination of O increases while the Si–O–Si angle tends to decrease (cf., Liebau 1985; Gibbs et al. 1997). Recently, Nesbitt et al. (2015a) were able to detect at least two types of Si–O–Si. One type of BO was connected to 2 Si atoms with a coordination of 2 while another termed MBO (where M = alkali or alkaline-earth) had alkali or alkaline-earth cations bonded to the BO resulting in the oxygen being 3-fold or higher coordinated. Such bonds must be present because while one Na atom produces 1 NBO its coordination number is around 5 and consequently some of the 5 bonds must be to bridging oxygens. Discriminating between the close approach of an alkali to the BO as opposed to actual formation of a bond with the BO, however, remains a challenging issue. Extensive molecular orbital calculations do show that such bonds are likely and energetically favoured (Gibbs 1982; Gibbs et al. 1997, 2009) Furthermore, they are very common in alkali

The Short-Range Order (SRO) and Structure

5

silicate crystal structures such as α-Na2Si2O5 where chains of SiO4 tetrahedra consist exclusively of Q3 tetrahedra but with 2 MBOs and one regular BO (Pant and Cruickshank 1968). The presence of these MBOs can influence the peaks or bands observed in the Raman spectra of alkali and alkaline-earth silicate glasses and alter binding energies (BE) in O 1s XPS spectra (see below). While there are many models of the possible structure of SiO2 and silicate glasses (see Henderson 2005 for a more extensive discussion and Wright 2019) there are two principal models that are widely referred to when describing the structure of such glasses. These are the crystallite theory (cf., Lebedev 1921, Randall et al. 1930 and Porai-Koshits 1958) and the random network model (cf., Zachariasen 1932, Warren 1933) or modified random network (MRN) model of Greaves et al. (1981), Greaves (1985) and Greaves and Sen (2007). Briefly the crystallite hypothesis treats the extended structure of the glass as regions of crystal-like structure (crystallites, 8–15 Å in size) which have more disordered areas at the interface between the crystallites. The random network model treats the glass as a continuous random network of SiO4 tetrahedra which are fully bonded through BOs to adjacent tetrahedra making up the network. Zachariasen (1932) recognised that certain elements made up such networks, and termed them network formers (Si, Al, P, As, B). On the other hand, addition of oxides of other elements tended to break the network up. The latter he termed network modifiers and includes the alkalis and alkaline-earths. The added oxide ions convert the BOs to NBOs when added to the network in excess of T3+ cations. Some elements (e.g., Fe, Ti) were termed “intermediate” since they may act as either a modifier or former depending upon the composition of the glass and/or T and P conditions (Varshneya 2019). Greaves et al. (1981) suggested that modifier cations were not homogeneously distributed in silica glass and did not randomly break up the fully connected network. They suggested that the alkalis (Na in the study) were heterogeneously distributed in the glass with the Na–NBO linkages tending to form “percolation” channels within a silica rich network (Fig. 3). This model is the most widely accepted model in geological glass and melt research. However, it should be mentioned that direct structural evidence of channels remains elusive although classical (Cormack et al. 2003; Du and Cormack 2003) and first principles or ab initio molecular dynamics simulations do suggest their presence (Fig. 3). However, the “channels” in melt simulations are not channels in the sense suggested by Greaves (1985) but “dynamic trajectories” of the diffusion of Na through the simulated structure.

a)

b)

c)

Figure 3. Examples of a modified random network containing a) channels (reprinted from, The structure of silicate melts: a glass perspective. Henderson GS Canadian Mineralogist 43:1921–1958. Copyright Mineralogical Association of Canada (2005), b) with MBOs present near the channels (Reprinted from Journal of Non-crystalline Solids, Nesbitt HW, Henderson GS, Bancroft GM, Ho R 409:139–148), Copyright (2015), with permission from Elsevier and c) from a computer simulation showing dynamic trajectories of the Na atoms (Reprinted with permission from Meyer A, Horbach J ,Kolb W, Kargl F, Schober H Physical Review Letters 93:027801(2004) Copyright (2004) by the American Physical Society. http://dx.doi.org/10.1103/ PhysRevLett.93.027801).

6

Henderson & Stebbins

Techniques used to probe the SRO in glasses and melts There are a wide range of techniques that are employed in studying the structure of glasses and melts (cf., Stebbins et al. 1995; Henderson et al. 2014b; Affatigato 2015; Henderson 2020). Some are direct structural probes, such as neutron and X-ray diffraction (scattering) while others investigate specific types of atoms such as Nuclear Magnetic Resonance (NMR), X-ray absorption spectroscopy (XAS), Mössbauer and X-ray photoelectron spectroscopy (XPS) or structural groups and vibrational properties (Raman spectroscopy, infrared (IR) and Brillouin spectroscopy). Regardless of the technique employed, the data represent the contributions from all of the local structural configurations. Furthermore, these contributions may be highly overlapping in the observed spectrum and thus difficult to uniquely evaluate. Unlike crystalline materials, in which individual site occupancies and geometries can be determined, information on specific atom sites is not possible in glasses and melts. In addition, for melts, temperature-induced structural changes with changing T are important to obtain. However, one needs to be aware of the time scale of the experimental technique used to probe the structure and the rate of changes in the melt. A large discrepancy between the two provides information on a time-averaged structure and not individual structural features. Space is too limited to give overviews of every technique and interested readers are referred to Henderson (2020) or the specialized chapters given in Henderson et al. (2014b), Affatigato (2015), Musgraves et al. (2019), and Richet (2020). Nevertheless, we will briefly describe the most commonly used techniques. X-ray and neutron diffraction techniques. Neutron (Hannon 2015) and X-ray diffraction (Benmore 2015) (also called scattering when applied to amorphous materials like glasses and melts) are extensively used to determine average bond lengths, coordination numbers and angles over both short and intermediate range length scales. Neutron diffraction and its variant “isotope substituted” neutron diffraction (see below) is frequently used to study lighter elements and elements that are close to each other in the periodic table for which X-rays have difficulty discriminating, because X-rays interact with the electron cloud of an element while neutrons interact with nuclei and their neutrons. Consequently, neutrons provide better spatial resolution than X-rays. However, neutron scattering experiments generally require much larger samples than X-ray scattering (e.g., 50 g vs. 1 mg), sometimes limiting applications. Figure 4 shows the powder diffraction pattern for crystalline quartz versus the glass slide on which the sample sits. The crystalline sample shows well defined diffraction peaks, or “reflections”, which can be used to identify the sample, and, with Rietveld techniques, to determine the crystallographic parameters necessary to solve the crystal structure. On the other hand, the glass pattern is very weak and essentially consists of one or more very broad humps in the trace (Fig. 4 inset). Despite the seemingly low resolution, useful information about bond distances, angles and coordination can be extracted from the glass data using appropriate methods. One of the following references should be consulted for a more thorough discussion (Fischer et al. 2006; Benmore 2015; Hannon 2015). The most common approach is to determine the Radial Distribution Functions (RDF), and the total and pair correlation functions (PCF). The RDF is a one-dimensional representation of the three-dimensional structure which is averaged over the entire system. It represents the probability of finding a given atom at any distance r from an atom at the centre of the system. As in diffraction from crystals the angle between incident and scattered beams is 2θ and λ the X-ray or neutron wavelength, the wave or scattering vector is then given by 4π sin θ/λ. This vector is denoted by s or k in X-ray diffraction and Q in neutron scattering.

The Short-Range Order (SRO) and Structure

7

Figure 4. Powder diffraction traces for crystalline SiO2 (quartz) and the glass slide on which the sample was mounted (red, dash/dot). The inset shows the glass diffraction trace enlarged to give an indication of the difference in intensity between a glass and crystalline sample.

Since diffraction data provides information about the average structure of the glass, the RDF peaks indicate average interatomic distances and average bond distance variations (peak widths). The areas under the peaks are related to average coordination number. RDF peaks are relatively high and narrow at low radial distances, but broader and of lower intensity at longer distances. This indicates the structure is less variable at shorter distances than longer ones. This enables the identification of the interatomic distances at low r but longer distance peaks are more ambiguous as there are more than one contribution to the peaks. By collecting data to high k space one can minimize the overlapping contribution: Neutron data is often collected out to Q (k) ranges of ~40–50 Å−1 while X-ray data is obtained using X-ray photons (> 40 keV) with wavelengths lower than 0.03 nm which improves k to ≥ 30 Å−1. An alternative approach is to use techniques that can separate the individual PSFs (e.g., anomalous X-ray scattering or isotope substitution, see below). Analysis and interpretation of X-ray and neutron diffraction data is often performed in conjunction with molecular dynamics (MD) simulations. The simulations in turn may use some sort of model such as empirical potential structure refinement (EPSR) to interpret the data. Care must be taken as to what is reported, the actual pair correlation functions and experimental distances, versus MD or EPSR distances. Isotope substituted neutron diffraction (c.f., Cormier 2019) uses the dependence on number of neutrons in the sample. This enables one to more clearly discriminate the different atom pairs contributing to the RDF and enables a more unambiguous interpretation. There are, however, some caveats that must be considered (cf., Hannon 2015; Cormier 2019).

8

Henderson & Stebbins

Vibrational techniques (Raman, IR, Brillouin). The reader is referred to relatively recent reviews of Raman (Dubessy et al. 2012; Rossano and Mysen 2012; Neuville et al. 2014; Almeida and Santos 2015), Infrared (McMillan and Hofmeister 1988; Kamitsos 2015) and Brillouin (Speziale et al. 2014; Kieffer 2015) spectroscopy for more comprehensive discussions of these techniques, or Henderson (2020) for an overview. Infrared (IR), Raman and Brillouin spectroscopy each probe various vibrational properties of a glass. Incident electromagnetic radiation of appropriate frequencies (IR–Visible regions) interact with the vibrational and rotational modes of structural units making up the structure of the glass. IR spectroscopy involves the absorption of photons in the infrared region of the EM spectrum while Raman is based on photon inelastic scattering. The latter is by far the most common vibrational spectroscopic technique used to probe the Qn speciation, as well as the intermediate-range structure of glasses. Brillouin spectroscopy is primarily used to investigate the elastic properties of glasses and involves the interaction of photons with acoustic waves or phonons in the glass. Infrared spectroscopy (IR). In IR spectroscopy incident photons from an IR source are absorbed by the vibrating atoms of the sample. Two energy ranges are usually recognised: far IR (~10–400 cm−1) and mid-IR regions (~400–5000 cm−1). Absorption occurs when there is a change in the induced dipole moment of the bonds that are vibrating. It is the change in the incident versus transmitted or reflected IR radiation that is measured, and these changes are strongest in polar molecules and asymmetric vibrations. Currently, reflectance IR is probably the most common IR spectroscopy method used to investigate glass structure while absorption studies are generally used to investigate volatiles such as water (see Fig. 5 and Behrens et al. 2009) and CO2 in glasses (cf., Kamitsos 2015). The peaks observed in IR spectra are characteristic of molecular groups or atomic vibrational motions that make up the SRO of the glass.

Figure 5. IR absorption spectra of albite glass (Alb1) from Behrens et al. (2009). Spectra are plotted with an offset for clarity. (a) MIR. Bold lines represent measured spectra. Figure 5. To evaluate the carbonate band intensity a spectrum of the starting glass scaled to same thickness was subtracted from the sample spectrum. A linear baseline (dashed) was fitted to the raw spectrum to quantify the 3550 cm–1 band intensity and subtraction spectrum to measure the peak heights of the carbonate peaks. (b) NIR. Linear baselines (dashed) were employed to evaluate the peak heights of the NIR combination bands. Note that the Fe-related band at 5600 cm–1 disappeared and the OH combination bands splits into two peaks in the spectrum of the water-rich sample Alb1_24. This observation indicates alteration during quench.

The Short-Range Order (SRO) and Structure

9

Raman spectroscopy. As noted above, Raman spectroscopy is widely used to investigate both the short and intermediate range structure of glasses and melts. It is particularly sensitive to elucidating the different types of Qn species in glasses although quantification of the different species remains problematic. The reader should refer to one of the references noted above, as well as, Dubessy et al. (2012) for descriptions of the different types of spectrometers. Essentially, Raman spectroscopy relies on measuring the change in photon energy when photons from a laser are scattered from the vibrating atoms or molecular groups in the sample. During the collisional process, a few of the incident photons can gain or lose energy (most are scattered with no change in energy). This gain or loss in energy is detected and is characteristic of the atoms and molecular groups involved in the vibrational motion. The difference in energy is termed the Raman shift (∆ν) and is reported in terms of cm−1. The Raman shift results from inelastic interactions between the incident photons and the electron cloud around the vibrating molecules. When the electron cloud is easily deformed it is said to be Raman active and the deformation is termed the polarizability. Vibrations and molecular motions that are polarizable are Raman active. In mineralogical applications, Raman spectroscopy is primarily used to characterize mineralogical phases, as well as, inclusions contained within gems and crystals (See Beyssac and Pasteris 2020). This approach uses Raman spectra as a fingerprinting technique comparing an unknown spectrum with some sort of crystalline standard. With glasses and melts the Raman spectrum is more commonly used to discriminate different vibrations and vibrational groups contained within the glass. In particular for SRO, it is the NBO and BO vibrations in the 800–1300 cm−1 region of the spectrum that are important. Figure 6a shows the Raman spectrum for SiO2 glass and for SiO2 glass with 5 mol% Na2O added. Clearly there are significant changes in the high frequency region as network modifier (Na2O) is added to the fully connected SiO2 network composed entirely of Q4 tetrahedra where all the oxygens attached to Si are BOs. The addition of a modifier creates NBOs and other types of Qn (n = 1–3) species. Figure 6b (O’Shaughnessy et al. 2020) is a plot of a series of sodium silicate glasses with increasing modifier content. It shows the progressive change in shape and intensity of the bands in the high frequency region of the spectrum. Both Q3 (at 1100 cm−1) and Q2 bands (at 980 cm−1) are clearly observed at higher alkali contents.

Figure

Figure 6. Unpolarized Raman spectra for a) SiO2 glass and of Na-silicate glass with 5 mol% Na2O added. Note the increase in intensity in the 1100 cm−1 region due to the presence of NBOs, as well as, increased ina) b) tensity of the A1 band a) of pure SiO2; b) Full range of spectra for 5–30 mol% Na2Ob)added showing the rapid n increase Figurein6.Q bands as Na2O increases. Republished with permission of John Wiley & Sons - Books from The influence of modifier cations on the Raman stretching modes of Qn species in alkali silicate glasses, 6.C O’Shaughnessy, GS Henderson, HW Nesbitt, GM Bancroft, DR Neuville, Journal of the American Ceramic Society 00:1–11, https://doi.org/10.1111/jace.17081, copyright (2020) permission conveyed through Copyright Clearance Center, Inc.

10

Henderson & Stebbins

Raman peak or band positions depend primarily on the types of atoms undergoing vibration and the nature of the bonding between the atoms involved. The intensity is primarily related to the polarizability of the interatomic bonding as well as the types of atoms involved. The SiO2 spectrum shown in Figure 6a can be used to aid interpretation of more complex compositions. The Boson peak at 10–200 cm−1 is characteristic of glasses and while still somewhat controversial is related to longer-range interactions. The broad feature labelled “main” in Figure 6a is at around 440 cm−1 and primarily related to asymmetric vibrations associated with BOs in rings containing > 5 SiO4 tetrahedra with a mean of around 6 tetrahedra per ring. The sharp features labelled D1 and D2 (for defect band 1 and defect band 2) at 490 and 606 cm−1, respectively are due to the breathing motion of oxygens in small 4- and 3-membered rings. The feature labelled C at ~800 cm−1 is a combination of two peaks whose origin is rather vague. They have been assigned to various “cage rattling” motions of the Si and O, as well as BO bending and symmetric stretch. The features labelled T2 and A1 are both due to motions of the BO in Q4 tetrahedra (Fig. 7). T2 involves the motion of 2 BO toward the Si atoms while the other 2 BOs move away from the Si, while the A1 mode is the motion of all the BO toward and away from the Si. The A1 band is actually 2 bands whose origin is unclear. a) a) b) b) Furthermore, it remains present over an extensive compositional range when modifiers are band is somewhat controversial in that some added to the glass. On the other hand, the T 2 Figure 6. authors propose that it is present in all glasses while others suggest that it becomes inactive upon modifier addition (see discussion of curve fitting and text below).

a)

b)

a) Figure 7. Q4 vibrational modes. a) T2 a) b) vibrate toward and away from the Sib) mode where pairs of oxygens atom and b) A1 mode where all the oxygen move toward and away from the Si atom.

Figure 7. With the addition of a network modifier, additional bands are observed in the 850–1300 cm−1 region. These additional bands are due to the presence of NBO symmetric stretch vibrations and they occur at relatively fixed positions for the different Qn (where n = 0–3) species. However, there are a number of issues that are worth pointing out. In order to quantify the relative proportions of the different Q species the high frequency envelope is often “curve fit” or “deconvolved” by fitting a series of Gaussian curves to the envelope. However, in the vast majority of studies the number of bands observable in the high frequency envelope exceeds the number of Qn species present, and, consequently, additional bands must be added to obtain reasonable fits. These additional bands have been assigned to a range of possible structural species from two Q3 and Q2 bands (Matson et al. 1983) to the presence of the T2 band (cf., Le Losq et al. 2014), to assignments such as Si–O0 (cf., Franz and Mysen 1995).

Use of pure Gaussian line shapes may be responsible for some of these ambiguities. For example, Kamitsos and Risen (1984) noted that Raman bands of silicate glasses were 4 4 predominantly Lorentzian rather than Gaussian. And more recently, Bancroft et al. (2018) and Nesbitt et al. (2018) have explored the lineshapes and linewidths of bands in the high frequency envelope of alkali and alkaline-earth silicate glasses. Bancroft et al. (2018) and O’Shaughnessy et al. (2020) point out that the additional bands are required because a) Gaussian line shapes do not fit the side wings of the high frequency Raman bands well;​

The Short-Range Order (SRO) and Structure

11

b) there are additional bands in the spectral envelope due to MBO vibrations; c) the additional MBO bands make the Q3 vibrational peak asymmetric; and d) the A1 mode of the Q4 tetrahedra is present even to high alkali contents and occurs as two peaks which merge together at 20 mol% added alkali (O’Shaughnessy et al. 2020). An example of their fits for two sodium silicate glass compositions with 15 and 30 mol% added Na2O are shown in Figure 8. However, it should be noted that these findings are only for alkali and alkaline-earth containing silicate glasses. When Al or other elements (e.g., Ti, P) are present, the high frequency envelope is more complex. Line shapes and assignments may well be different (cf., Le Losq et al. 2014). Care should be used when interpreting data for aluminosilicate glasses and other compositions: interpretations based on studies of alkali or alkaline-earth silicate glasses may not be applicable. It is important to note that when curve fitting the high frequency envelope, care should be taken as to the nature of the vibrations. Authors may refer to the same vibrational motion using different terminology and it is important to have a good understanding of the terminology and nature of the motions i.e., rocking, bending, asymmetric, symmetric, rattling, twisting, torsional. Furthermore, in both infrared and Raman spectra, the area of a fitted component is not necessarily directly proportional to the actual fraction of a given structural species, as absorption or scattering cross sections are expected to be affected to some degree by the structure itself. Independent constraints of mass-balance, or ‘calibration’ from independent measurements by other methods (e.g., NMR spectroscopy), have been applied to this problem (Mysen and Richet 2019). Full, quantitative calculation of vibrational spectra for glasses is potentially very important for resolving such empirical issues but remains a challenging problem. Recent Raman spectral simulations on alkali silicate glass structures (determined from classical MD simulations) suggest that component lineshapes for some Qn species may be highly non-Gaussian and more complex, than conventional deconvolution functions (cf., Kilymis et al. 2019).

Figure 8. Fits for sodium silicate glasses with 15 mol% (Na15) and 30 mol% Na2O (Na30). Q3–1 is Q3 tetrahedra without an alkali attached to the BO while Q3–2 and Q3–3 have 1 or 2 alkalis attached to the BO. Similarly, for the Q4 and Q2 tetrahedra. Note the asymmetry in the most intense band in Na30 due to the presence of multiple types of Q3 species (BO, MBO). An alternative explanation for the additional peaks is second neighbour effects on the Qn species (Olivier et al. 2001). In this model the Qn units may be clustered with Qn,ijkl where ijkl are adjacent Q species of varying character i.e., Q0, Q1, Q2, Q3 etc.

Brillouin Spectroscopy. Brillouin spectroscopy is a technique (cf., Speziale et al. 2014) that uses the interaction between optical photons from an incident laser and phonon vibrations in a solid, to probe the elastic properties and acoustic velocities of the sample. It measures the scattered light within 10−2 to  1/2 and are thus also subject to nuclear ‘quadrupolar’ interactions (MacKenzie and Smith 2002; Stebbins and Xue 2014). The most important parameter, the ‘quadrupolar coupling constant’ (CQ) depends on the distortion of the local chemical environment from purely cubic local symmetry. In an ordered crystal, this produces a characteristic peak shape and shift down in frequency that can be analyzed to give structural information; for comparable sites in glasses, structural disorder generally yields a shifted, broadened, asymmetric peak that can only be approximated by fitting with several adjustable variables and distributions of parameters. Fortunately, quadrupolar shifts and broadening decrease greatly with ever higher magnetic field strengths, giving increasing resolution, quantitation, and information content. At higher fields, the chemical shift contribution to the spectrum begins to dominate, often simplifying extraction of structural information. Nuclear magnetic interactions (like those observed in some other spectroscopies) generally depend on the orientation of a molecule, crystal, or structural group in the external magnetic field. In a polycrystalline or an amorphous solid, this can lead to a large spreading out of the signal and loss in resolution and reduction in signal to noise ratio. Some such ‘anisotropic’ effects (chemical shift anisotropy and nuclear dipole couplings) can be averaged out by rapid rotation of the sample on an axis at the ‘magic angle’ (about 54.7°, ‘magic angle spinning’ or MAS NMR) to the external field, usually resulting in much narrower peaks (at the ‘isotropic chemical shift’) and much enhanced resolution. In some cases, the anisotropy itself can carry useful structural information, as sometimes seen in ‘static’ NMR experiments (non-spinning) or in advanced experiments such as ‘Magic Angle Flipping’ (Davis et al. 2010, 2011). Quadrupolar broadening is only partially averaged by MAS but can be eliminated by 2-dimensional ‘multiple quantum’ (MQMAS) NMR. Accurate quantitation of intensities in the latter can be complicated, however. Dynamic Angle Spinning (DAS) and Double Rotation (DOR) NMR can also eliminate quadrupolar effects but may be technically more difficult to implement (Florian et al. 1996). In liquids (and even in some mobile solids), reorientation may be rapid about multiple, random axes, completely averaging all anisotropic effects, and yielding the very narrow NMR lines typical of molecular liquids. This effect is routinely exploited in 1H NMR in organic chemistry. If, at the same time, bond-breaking and exchange among different structural environments is rapid compared to the frequency width of NMR spectrum, only a single, averaged NMR signal will be observed. This situation is common in very high temperature, in situ NMR experiments on oxide liquids (Stebbins and Farnan 1992; Florian et al. 1995; Massiot et al. 1995, 2008; Capron et al. 2001; Kanehashi and Stebbins 2007), for example when Al3+ cations may have 4 vs. 5 vs. 6 oxygen neighbors. Spectra still will contain useful, quantitative information about the average local structure, and effects on temperature and composition.

14

Henderson & Stebbins

In the intermediate dynamical regime, typically up to a few hundred °C above the glass transition temperature, viscosity is still high enough, and structural exchange slow enough, so that in some cases the dynamics of bond breaking in the liquid can actually be measured by NMR (Farnan and Stebbins 1990a,b, 1994). Many advanced NMR experiments take advantage of the interactions between like or between unlike nuclear spins to gain unique information about ordering and structure. Indeed, it is this potential to directly probe element-specific, interatomic interactions that may be the most unique capability of NMR spectroscopy. Such interactions can be through-space and highly sensitive to distance (dipole-dipole interactions) or through-bond and highly sensitive to bonded connections (‘J’ couplings). In such experiments, which are described by a plethora of acronyms (Duer 2004), two or more nuclear spin systems may be perturbed simultaneously or sequentially. Data are often recorded as two-dimensional spectra, with two frequency axes derived from variation of some time interval during the experiment. In oxide glasses, most such ‘double (or even triple) resonance’ experiments rely on pairs of nuclides with strong nuclear dipolar couplings, such as 1H with 29Si or 27Al, or other pairs such as 11B–27Al and 27 Al–31P (van Wüllen et al. 1996a,b; Chan et al. 1999; Zhang and Eckert 2006). However, recent advances have yielded results with more weakly coupled pairs such as 17O–27Al and 17 O–29Si (Jaworski et al. 2015; LaComb et al. 2016; Sukenaga et al. 2017). Other advanced NMR experiments, relying on interactions between like pairs of nuclides (e.g., 29Si–29Si) can provide unique information on longer range structure, including the extent of phase separation (Martel et al. 2011, 2014). As in any complex experiment, careful testing and even calibration of results on crystalline materials of known structure is very helpful in validation. X-ray absorption and X-ray Raman. X-ray absorption spectroscopy (XAS) consists of two principle techniques: X-ray absorption near-edge structure (XANES) spectroscopy (cf., Henderson et al. 2014a) and Extended X-ray absorption spectroscopy (EXAFS) (cf., Newville 2014). The XAS spectrum is composed of 3 regions: XANES (0–50 eV above the X-ray absorption edge); EXAFS (~ 50–1500 eV above the X-ray edge), and the pre-edge at ~20–30 eV below the edge (Fig. 9). Sincea)both EXAFS and XANES are element specific, they can potentially be obtained from any element at concentrations as low as ~ 100 ppm. Figureprobe 8. the structural environment of specific types of atoms but of course Both techniques the information extracted is for the average structure of the element over all possible sites in

Figure 9.for Si K-edge showing the XANES and EXAFS regions, as well as the pre-edge Figure 9. XAS spectrum which is used to discriminate different transition metal coordination states. It is not possible to obtain EXAFS for elements with excitation energies below 1.8 keV because of interference effects from overlapping elemental edges.

b)

The Short-Range Order (SRO) and Structure

15

the glass. EXAFS is primarily used to determine the first shell or nearest neighbour interatomic distances and angles around the element of interest. It can also determine features out to 2nd and 3rd neighbours (it is limited to maximum distances of ~10 Å), as well as the coordination of the element. XANES provides information about the electronic structure of the element, the oxidation state, and for transition metals, the average coordination. XANES data are qualitative while interatomic distances and static disorder or Debye–Waller parameters determined by EXAFS are quantitative. X-ray Raman spectroscopy (XRS) or Near-Edge Inelastic X-ray scattering (NRIXS) is similar to XANES producing spectra that are qualitatively similar. However, the excitation mechanism is different and uses momentum transfer (similar to optical Raman) of hard X-rays (>10 keV) to excite the electronic transitions of interest. The great advantage of X-ray Raman is that it excites all the elements in the sample and can be used for high T and P in-situ studies. It is currently the only technique that can probe light elements ( Na+ > K+) promoted by the increasing degree of concentration of negative charge around the modifier (Brandriss and Stebbins 1988; Maekawa et al. 1991; Stebbins et al. 1992), analogous to that noted above for bridging oxygen species. For example, well-studied Na2Si2O5 glass has about 10% Q2 groups, a corresponding fraction of Q4 groups, and about 80% Q3 groups. This is more disordered than in the crystal, but less so than predicted by a random model of NBO distribution over the tetrahedra (25% Q2). For a given silica content, the resulting higher Q4 concentrations in the liquids with higher field strengths correlates with the higher thermodynamic activity of silica (the Q4-like component), the latter long known by comparisons of the binary phase diagrams (Ryerson 1985; Stebbins 2016). As mentioned above for NBO distributions, this effect of modifier field strength on speciation and activities is correlated with the energetics that drive liquid–liquid phase separation. NMR studies of glasses with varying cooling rates, and thus fictive temperature, show that k3 increases with higher temperature (Reaction (12) is pushed to the right by a positive reaction enthalpy, Brandriss and Stebbins 1988). This finding has been confirmed and greatly extended by high temperature, in situ Raman spectroscopy (Mysen and Frantz 1993; Malfait et al. 2007b, 2008). The mixing of Qn species contributes significantly to overall configurational entropy and heat capacity of melts (e.g., Le Losq and Neuville 2017) but is far from explaining totals. In binary alkaline earth silicate systems, the range of compositions that can be quenched into single-phase glasses is narrower than in the alkali silicates, and, in both NMR and Raman spectra, component peaks assignable to different Qn groups are even less well resolved because of greater overall disorder. Fitting of conventional 1-D 29Si MAS NMR spectra become highly model-dependent, for example. 29Si NMR, using the advanced ‘magic angle flipping’ method and 2-D data collection, has allowed greater distinctions to be made for Qn species, based on their local asymmetry (chemical shift anisotropy) instead of simply their isotropic chemical

The Short-Range Order (SRO) and Structure

37

shifts (Davis et al. 2010, 2011). In compositions such as MgSiO3 (Davis et al. 2011) and CaSiO3 (Zhang et al. 1997) glass, the available data indicate that k3 (as well as the analogous k2) values are highest values are higher than in the alkali systems, as the divalent modifier cations are even more effective at concentrating the negative charges on the NBO. In the latter composition (Fig. 24), total NBO/Si, as estimated from a fitted model, was slightly lower than expected from composition and the conventional assumptions discussed above, possibly allowing for about 1% ‘free’ oxide ion; whether this is significantly different from zero is not certain given uncertainties in the fitting process. In MgSiO3 glass and in a composition close to Mg2SiO4, the estimated NBO/T values were also below those expected from composition, again suggesting the presence of a few % ‘free’ oxide ion in these low silica, high field-strength compositions. 4006 J. Phys. Chem. B, Vol. 101, No. 20, 1997

Zhang et al.

Q4



Q3

Q4

MAS dimension (ppm)



Q3

Q2

90˚ dimension (ppm)

Q3

Q2



Q3 Q1

Q0

Q2

Q1

data fitted model ‘slices’ through 2-D spectrum (ppm)

Figure 3. Contour plot with projection on each dimension. Twenty equally spaced contour lines are drawn at levels ranging from 3 to 93% of the maximum intensity in the spectrum. On the right are selected cross sections and their “best-fit” curves. Forty-five cross sections from ‰iso ) -65.31 29 deviation of 75.32. ppm to -108.56 ppm were analyzed. ‘magic The averageangle ¯2Ó valueflipping’ was 48.47, with a standard Figure 24. Two-dimensional (MAF) Si NMR spectra for CaSiO3 glass. In the

90˚ dimension, the line shapes are influenced by the chemical shift anisotropy (CSA), which helps in distinguishFigure 1, it is clear from the 90° dimension that in the region n ing among the aQlow-intensity species. A fitted model successive slices in the MAS dimension is shown at the right. of -110 ppm symmetric line shapefor attributed species can be observed.forMoving to less negative EachtofitQ(4)includes components no more than two Qn species with distinct CSA’s, although low intensities of chemical shifts in the -100 ppm region, anisotropic chemical othershift components must make minor contributions to the line shapes. Reprinted with permission from Anionic line shapes characteristic of negative axiality and nearly 29 species in CaSiO two-dimensional Si NMR. Zhang P, Grandinetti PJ, Stebbins 3 glass zero determination asymmetry parameters are observed and using are attributed to In the region of -85 ppm the anisotropic line Copyright (1997) American Chemical Society. Q(3) species. JF. Journal of Physical Chemistry B101:4004–4008. shapes are dominated by anisotropic chemical shift, and line shapes with Ë ) 0.70 are attributed to Q(2) species. In Figure 2B the same spectrum is plotted with the least negative isotropic chemical shifts in the MAS dimension to the front. In the region of -65 ppm a very weak symmetric line shape attributed to Q(0) species is observed. Moving to more negative chemical shifts in the -75 ppm region, anisotropic chemical shift line shapes characteristic of positive axiality are observed and are attributed to Q(1). The anisotropic4line shapes in the individual cross sections taken parallel to the 90° dimension were least-squares analyzed to obtain the relative contribution of each Q(n) species to the MAS intensity at the MAS frequency correlated to that cross n section. A contour plot along with representative cross sections and best-fit simulations is also shown in Figure 3. Again, this approach has the advantage that the parameter uncertainties in each cross section are completely uncorrelated with parameter uncertainties in other cross sections. The chemical shift anisotropy line shape for each site was modeled using five parameters. These were (1) an isotropic chemical shift position ‰iso, (2) a chemical shift tensor axiality ¢, (3) a chemical shift tensor asymmetry parameter Ë, (4) an integrated intensity, and n (5) a Gaussian smoothing function. All sites in each cross section shared the same isotropic frequency and that value was fixed by the isotropic dimension. In least-squares analyses those cross sections dominated by one Q(n) species showed little variations in ¢, Ë, and Gaussian line broadening for the line shape of the dominant species. Therefore, in the final leastsquares analysis of each cross section the chemical shift tensor

As well as statements of equilibria among Qn species, reactions such as Reaction (12) . The recon4. Separated isotropic line shapes for each are often considered in terms of accounting forFigure mass and charge balance as Qmelt and glass structed Si MAS spectrum of CaSiO glass from the sum of the five structure change with composition, temperatureisotropic and line pressure. For example, shapes is shown above, along with thewith observedthe MASsimple shown in black dots. approximations mentioned above (negligible FOspectrum and constant network coordination numbers), 2 Q(n) site were axiality ¢ andby asymmetry parameter Ëin for Q a given an increase (or other species an increase in Q species is expected to be accompanied held fixed at the values obtained when that Q(n) site was the with n  0.5) two clear Pb–O peaks at 2.26  Å and 2.66  Å are resolved, corresponding to Pb in 4- and 6-fold coordination, respectively. Takaishi et al. (2005) report a higher Pb–O bond length of 2.78 Å in Pb-silicate glasses from neutron diffraction measurements. However, these authors failed to consider correlations at longer distances, especially Pb–Si and Pb–Pb (Fig. 7), which have a strong influence on the position of the Gaussian functions fitted to their real-space pair distribution functions. Takaishi et al. (2005) also assign a peak at 2.65 Å to O–O bonds in their Gaussian fit. In our XRD measurements of Pb-silicate glasses, the O-O correlations are poorly weighted (WOO = 0.090 (x = 0.3), 0.046 (x = 0.5) and 0.025 (x = 0.7)) and contribute little to the measured signal. Since the intensity of the peak at 2.66 Å is strongly influenced by the fraction of Pb present in the glass, we assign this peak to mainly Pb–O bonds in 6-fold coordination. We note that this relationship is also visible in the data published by Takaishi et al. (2005), which clearly show an increase in intensity of the peak at 2.65 Å at the highest Pb content when the weighting of Pb–O correlations becomes higher than for O–O correlations. The Gaussian fits presented in Figure 7 reproduce very well the experimental total correlation functions T(r) considering the two well defined PbO4 and PbO6 contributions. While the presence of PbO5 units cannot be ruled out, their contribution will lie between the PbO4 and PbO6 and are difficult to determine unambiguously.

Drewitt et al. a) (CaO)x(SiO2)1-x

12 11 10

Si-O

9 8 7

Si-Si O-O

x=0

6 5

x = 0.4

4 3 2 1 0

Ca-O

0

2

Ca-Ca

x = 0.5

4 6 8 Distance, r (Å)

Pair distribution function, G(r)

Pair distribution function, G(r)

64

10

b) (PbO)x(SiO2)1-x

12 11 10

Si-O

9 8 7

Si-Si O-O

x=0

6 5

x = 0.3

4 3 2 1 0

x = 0.5 PbPb

x = 0.7

PbO4 PbO6

0

2

4 6 8 Distance, r (Å)

10

Figure 6. Total pair distribution functions G(r) SiO2 and silicate glasses in the system (MO)x(SiO2)1-x for a) M = Ca and b) M = Pb (previously unpublished XRD measurements made at beamline ID11 at the European Synchrotron Radiation Facility (ESRF), Grenoble, France).

10 T(r) Partial fits Total fit

8

6

Pb-Pb (Mostly)

PbO4

SiO4

T(r)

PbO6

4

2 PbO6 and/or O-O from SiO4

Pb-Si

0

1

2

3 4 Distance, r (Å)

5

6

Figure 7. Total correlation functions T(r) obtained from the XRD data for (PbO)x(SiO2)1-x for x = 0.3 (top), 0.5 (middle), 0.7 (bottom) from Figure 6, presented together with partial Gaussian fits (red curves) and their combined totals (blue curves).

From Short to Medium Range Order in Glasses and Melts

65

Although Pb and other heavy elements are strongly probed by XRD, lighter elements such as Ca are probed less strongly. Neutron diffraction with isotope subsitution (NDIS) is a powerful tool for isolating these weaker or heavily overlapped pair correlations. Figure 8 shows the first order (Eckersley et al. 1988) and second order “double” (Gaskell et al. 1991) difference functions from 44Ca/natCa NDIS measurements of CaSiO3 (Ca50) glass (with 3 mol.% Al2O3 added to prevent nucleation, Eckersley et al. 1988). The results reveal well defined Ca–O and Ca–Ca distances indicating ordering of the modifier Ca2+ cations up to 10 Å. Originally attributed by Gaskell et al. (1991) to sheets of edge shared CaO6 octahedra, subsequent MD simulations have revised this model of medium range cationic ordering to more chainlike clusters or channels of Ca-centered polyhedra (Mead and Mountjoy 2006; Benmore et al. 2010a; Skinner et al. 2012a; Cormier and Cuello 2013). A similar distribution of Mg-centered polyhedra contributing to MRO is observed from a 25Mg/natMg NDIS study of MgSiO3 glass (Cormier and Cuello 2011). These inhomogeneous distributions of cation centered polyhedra pervading the silicate network appears to substantiate the Greaves MRN model (Fig. 1b). Further NDIS measurements revealing the development of cationic MRO on vitrification of oxide melts are discussed later in this chapter.

∆G(r) (10-8 m2)

0.4

Ca-O

(a)

Ca-Si, Ca-Ca

0.2 0.0 -0.2

0

1

2

3

4

5

6

7

8

9

10

dCaCa(r)

Distance, r (Å) 8 6 4 2 0 -2 -4 -6

(b)

0

Ca-Ca

1

2

3 4 5 Distance, rCaCa (Å)

Ca-Ca

6

7

8

Figure 8. (a) First order difference function ΔG(r) and (b) reduced partial pair distribution function dCaCa(r) = 4π rρ0 [gCaCa(r) − 1] by double difference from the 44Ca/natCa NDIS results reported in Eckersley et al. (1988) and Gaskell et al. (1991) for (CaO)0.48(SiO2)0.49(Al2O3)0.03 glass. The peak at ~2.2 Å in the unphysical low-r features below the first Ca–Ca interatomic distance (dashed curve) in (b) arises from an incomplete subtraction of partials gαβ≠CaCa(r).

Raman spectroscopy measurements We now consider unpolarized Raman spectra for the full range of M-silicate compositions shown in Figure 9, for which distinct and progressive changes are observed with the type and proportion of M cation content. In the following, we discuss the structural information provided by these spectra with respect to the four key spectral regimes; the boson (20–200 cm−1), low (200–600 cm−1), intermediate (600–800 cm−1), and high (800–1200 cm−1) wavenumber regions.

66

Drewitt et al.

The boson region: At low wavenumbers, the BP generally experiences an increase in frequency with reducing SiO2 concentrations, indicating a correlation between the BP frequency and glass depolymerization (Neuville 2006, 2014a; Richet 2012). The BP is also influenced by the introduction of different network modifiers, where at constant SiO2 concentration the BP shifts to higher frequency with the addition of small or medium sized ions and lower frequency with the introduction of larger heavier ions (Neuville 2005, 2006). These changes are accompanied by a narrowing of the BP width for glasses containing heavier elements (Ba, Pb) compared to lighter elements (Na, Li, Mg, Ca), consistent with a very narrow boson peak observed in the Raman spectra of cesium silicate glasses (O’Shaughnessy et al. 2017). This appears to point towards a modification of MRO in the silicate glasses, and perhaps the development of ordering of the modifier cations. Changes in intensity and position of the BP may also be explained by distortion of the SiO4 tetrahedra (Hehlen et al. 2002). The low frequency region: With the addition of modifier oxides, the R, D1, and D2 bands in the spectral domain between ~250 and 600 cm−1 originating from ≥ 5-, 4-, or 3-membered rings, respectively, evolve into a broad peak in the region of the D2 vibration at ~580 to 680 cm–1, reflecting the breaking of Si–O–Si bonds and introduction of NBO leading to a reduction in the size of the ring structures formed from interconnected SiO4 tetrahedra. However, for lighter modifier elements (e.g. Li-silicate glass) the spectrum retains significant resemblance to the pure SiO2 glass spectrum indicating the presence of silica-rich regions in the glass (Matson et al. 1983). This has been interpreted as consistent with the MRN model, where Li atoms form MRO clusters within an underlying silicate network (Le Losq et al. 2019a). Although Figure 9 shows only unpolarized spectra, the R, D1, and D2 bands are highly polarized. Polarized Raman measurements of Na-silicate glasses, where spectra are recorded with parallel (VV) or perpendicular (VH) polarizations of incident and scattered light, reveal a strong reduction in intensity of the R-band accompanied by the development of a strong narrow band between ~540 to 600 cm−1 in VV polarized spectra with increasing Na2O fraction (Hehlen and Neuville 2015). This is consistent with a reduction in the Si–O–Si angle due to a reduction in ring size and increasing preponderance of D2 modes. The R, D1, and D2 bands are inactive in the VH polarized spectra which instead reveal the development of a peak at ~350 cm−1 and a lower frequency peak at ~175 cm−1 with increasing cation concentration attributed to cation motions (Hehlen and Neuville 2015). This will be discussed in more detail below, in relation to the dual role of cations as network modifiers or compensators in aluminosilicate compositions. The intermediate frequency region: The asymmetric band observed in silica and silica-rich glasses at around 800 cm−1 is attributed to bending vibrations in SiO4 tetrahedra (Sarnthein et al. 1997; Taraskin and Elliott 1997; Spiekermann et al. 2013). It is, however, interesting to note the presence of a high frequency shoulder in this peak for pure SiO2. This asymmetry has been attributed to two different structures of SiO4 units with distinct inter-tetrahedral Si–O–Si angles coexisting in the glass (Seifert et al. 1982; Neuville and Mysen 1996; Kalampounias et al. 2006). However, direct structural studies have not observed a bimodal distribution of the Si–O–Si angle in SiO4 units. We note that different n-membered rings exhibit different Si–O–Si angles such that this observation could be simply explained by the variation in Si–O stretching frequency in tetrahedral units as a function of ring size (Le Losq et al. 2019a). This is supported by the loss of this high-frequency shoulder with the addition of modifier cations and hence reduction in the ring size and Si–O–Si distributions. However, since the Si–NBO frequency is related to the bond force constant other explanations are also possible, including e.g. a change in Si–O–Si angle as alkali atoms bond to the BO or by the presence of an alkali as a charge compensator. The high frequency region: The high frequency Raman bands for silicate glasses centered at ~1100  cm−1  are associated with Si–O stretching vibrations in different Qn tetrahedral units and are typically interpreted by spectral deconvolution (Mysen et al. 1982a,b; McMillan 1984), as discussed in detail in Henderson and Stebbins (2022, this volume). Here we provide additional details for selected glass compositions.

From Short to Medium Range Order in Glasses and Melts

67

Figure 9. Unpolarized Raman spectra of SiO2 and silicate glasses in the system (MO)x(SiO2)1-x for M = Li2, Na2, K2, Mg, Ca, Ba, Pb. The spectra are labelled MX for cation fraction X in mole%. Original data are in Neuville et al. (2014) and Ben Kacem et al. (2017).

Spectral deconvolution of these high-frequency bands into their constituent components by Gaussian curve fitting is illustrated in Figure 10 for Ca40 and Na40 glass spectra (Neuville 2006). Here the Gaussian bands at ~900 cm−1, 960 cm−1, and 1080 cm−1 can be attributed to the vibrations of Q1, Q2, and Q3 species, respectively. To fully model the high-frequency region, it is necessary to include an additional band at 1020 cm−1 for Ca40 and 1040 cm−1 for Na40. This contribution can be compared to the band observed at ~1070 cm−1 in the pure SiO2 glass spectrum (Fig. 4). This band has been attributed to the T2 stretching mode of Q4 units (Neuville et al. 2014a; Henderson and Stebbins 2022, this volume) although recent studies (Bancroft et al. 2018, O’Shaughnessy et al. 2020) assigned this band to Q3 tetrahedra close to alkali cations. The Raman spectrum of the Na1 glass (Fig. 9) shows that the addition of only 1 mol% of Na2O in silica leads to a slight increase of the intensity of the peak at 1070 cm–1. Further addition of modifier ions, however, leads to a large increase in the intensity corresponding to the higher frequency Q4 A1 mode for higher alkali composition silicate glasses (Bancroft et al. 2018; O’Shaughnessy et al. 2020; Henderson and Stebbins 2022, this volume). At low alkali oxide contents, the A1 mode is composed of two bands. These bands merge into a single band after the addition of 20 mol% of Cs oxide (O’Shaughnessy et al. 2020).

68

Drewitt et al.

Figure 10. Gaussian deconvolution of Raman spectra for Ca40 and Na40, redrafted from (Neuville 2006). Band assignments (from low to high frequency) are: Q1, Q2, T2s, Q3 and Q4. No Q4 species are present in the Na40 glass.

The band at 1135 cm−1 in the Ca40 spectrum is attributed to the A1 stretching mode of Q4 units. Substitution of Ca by Na reduces the network polymerization as evident by the complete absence of this Q4 band in the Na40 glass spectrum. With increasing modifier cation concentration, increasingly depolymerized species are present, including Q0 and Q1 species, leading to a significant shift in the intensity maximum of the Si–O stretching bands to lower frequencies (see e.g. the spectra for Mg62 and Mg56 and Fig. 12 of Neuville et al. 2014a).

Lead silicate glasses The high-frequency domain, 850–1300 cm−1, in the Raman spectra of lead silicate glasses appears less intense compared to other glass compositions. This is a result of the normalization process as Pb-silicate glasses exhibit the highest intensity peaks at low frequency. Two very intense low-frequency peaks at 100 cm−1 and 141 cm−1 are dominant features in Raman spectra of Pb-silicate glasses (Worrell and Henshall 1978; Furukawa et al. 1978; Ohno et al. 1991; Zahra et al. 1993; Feller et al. 2010, Ben Kacem et al. 2017). The peak at 141 cm−1 is attributed to covalent Pb–O–Pb bonding in interconnected tetrahedral PbO4 units (Furukawa et al.1978; Worrell and Henshall (1978); Zahra et al.1993) and correlates with NMR spectra which show the proportion of Pb–O–Pb linkages increases with PbO content (Lee and Kim 2015). The Raman band at 100 cm−1 has been attributed to ionic Pb–O bonds associated with NBO atoms in PbO6 units (Worrell and Henshall 1978; Ohno et al. 1991) A variety of charge balancing models have been reported which predict MRO in the form of different extended networks of interconnected Pb-centered units in the glass, including dimeric zigzag chains of covalently bonded PbO4 tetrahedra (Morikawa et al. 1982), screw chains of PbOn polyhedra (n = 3 or 4) (Imaoka et al. 1986), Pb cations in predominantly edge-shared PbO3 trigonal pyramid arrangements (Takaishi et al. 2005), and pyramidal PbOn units with a mix of corner and edge sharing with electron lone-pairs organizing to form voids in the glass (Alderman et al. 2013). XRD reveals Pb can adopt both 4- and 6-fold coordinated sites in Pb-silicate glasses (Figs. 6 and 7), where Pb in 4-fold coordination forms an interconnected sub-network mixing mechanically with the SiO4 tetrahedral network without chemical interaction (Neuville and Le Losq 2022, this volume). This is supported by the glass transition temperature for PbO–SiO2 glasses which varies almost linearly between 30 and 90 mol.% of SiO2 fraction (Ben Kacem et al. 2017) implying heterogenous mixing. Pb in 6-fold coordination plays a similar role to alkali or alkaline-earth elements breaking up the silicate network polymerization by forming NBOs.

Aluminosilicate glasses Aluminosilicate glasses and their melts are of interest due to their relevance to natural magmas. Aluminum is classed as an intermediate glass former due to its ability to both compete with Si to form a 4-fold coordinated network structure or to behave as a network modifier

From Short to Medium Range Order in Glasses and Melts

69

assuming 5- or 6-fold coordination and reducing the glass network connectivity via the formation of non-bridging oxygens (Sun 1947). This behavior is particularly sensitive to the relative proportions of Al and other modifier cations (Bista and Stebbins 2017). To form a perfectly connected network of AlO4 tetrahedra the Al:O ratio needs to be precisely 1:2 such that any two Al atoms are connected by a single bridging oxygen. For the (MO)x(Al2O3)1-x compositions this occurs at the ratio R = MO/Al2O3 = 1 (x = 0.5), where modifier cations, assuming a uniform distribution, will perfectly charge compensate AlO4 units which have an overall charge of -1. Aluminosilicate compositions along this join are denoted tectosilicate or meta-aluminosilicate glasses. Peraluminous aluminosilicates, classified as glasses with the ratio R = MO/Al2O3 < 1, have an excess of Al and are unable to form an ideal charge compensated corner-sharing network of AlO4 tetrahedra (Mysen and Richet 2019). This oxygen deficiency may be compensated for by the formation of highly coordinated AlO5 and AlO6 units and/or a change in network connectivity. In peralkaline glasses (R = MO/Al2O3 > 1) there are excess modifier cations which will act to charge compensate AlO4 tetrahedra and potentially depolymerize the network. There is, however, increasing evidence for deviations from this simple model, with significant proportions AlO5 and even 5-fold coordinated SiO5 units observed in glasses that are sufficiently charge compensated by metal cations (Stebbins 1991, et al. 1997; Toplis et al. 2000). Significant fractions of AlO4 have also been observed in the alumina-rich glasses (Mysen and Richet 2005) in which charge neutrality may be accomplished by the formation of O:(Al/Si)3 triclusters in which one O atom is shared by three Al/Si tetrahedral units (Lacy 1963; Toplis et al. 1997, 2000; Stebbins and Xu 1997; Stebbins et al. 2001; Mysen and Toplis 2007).

Diffraction and Raman measurements along the tectosilicate join

Neutron total pair distribution function, G(r)

The G(r) functions from neutron diffraction experiments and Raman spectra for MO– Al2O3–SiO2 (M = Ca, Sr) glasses along the tectosilicate join (R = MO/Al2O3 = 1) are shown in Figures 11 and 12. Compositions are denoted by concatenating the modifier element M with the mole fraction X of SiO2 and Y of Al2O3 in per cent (MX.Y). With increasing substitution of Si by Al the nearest neighbor peak T–O in G(r) is broadened and shifts to higher distances from 1.60 Å in pure SiO2 to 1.76 Å in silica-free Ca0.50 glass. This results from Al–O correlations with longer nearest neighbour lengths overlapping the shorter Si–O correlations (Cormier et al. 2000, 2003; Hennet et al. 2016). For the Ca-aluminosilicate glasses, the peak at ~2.30 to 2.35 Å 12 11 10 SiO2

9 8

SA75.12

7

SA63.18

6

CA50.25

5 4 3

SA33.33

CA19.40

SA20.40

CA12.44

2

CA00.50

1 0

SA50.25

CA33.33

1

2

3

4 5 Distance, r (Å)

6

7

8

Figure 11. Neutron total pair distribution functions for M-aluminosilicate (M = Ca,Sr) glasses along the tectosilicate (R = 1) join (data from Bowron 2008; Kozaily 2012; Hennet et al. 2016; Charpentier et al. 2018). Compositions are denoted by MX.Y for mole per cent fraction X of SiO2 and Y of Al2O3, where the fraction MO = 100 – (X + Y).

70

Drewitt et al.

Figure 12. Raman spectra for calcium aluminosilicate glasses along the tectosilicate (R = 1) join (data from Neuville et al. 2004, 2010, 2014a). Compositions are denoted by the notation CaX.Y for mole per cent fraction X of SiO2 and Y of Al2O3, where the fraction CaO = 100 – (X + Y).

is attributed to the first Ca–O bond and becomes increasingly conspicuous with reducing SiO2 concentration due to higher weighting on the gCaO(r) partial pair distribution functions. It is difficult to precisely determine the Ca–O coordination environment using conventional x-ray or neutron diffraction due to considerable overlap by the gOO(r) partial pair distribution functions (Hannon and Parker 2000; Benmore et al. 2003; Mei et al. 2008a,b; Drewitt et al. 2011; Hennet et al. 2016). Direct measurements of the first Ca–O coordination shell in both calcium-silicate (as previously discussed) and -aluminate glasses by NDIS provide average Ca–O coordination numbers of ~6.2 to 6.5 (Eckersley et al. 1988; Drewitt et al. 2012), with MD simulations revealing a broad distribution of Ca–O polyhedra centered on ~6 (Drewitt et al. 2012; Jakse et al. 2012). Despite the larger neutron scattering length bSr = 0.702(2) fm, compared to bCa = 0.470(2) fm (Sears 1992), the nearest neighbour Sr–O correlations are not discernible in the G(r) functions for Sr-aluminosilicate glasses. This is due to the larger ionic radius of Sr2+ cf. Ca2+ (Shannon 1976) due to both higher atomic number and larger Sr–O coordination number of ~8 to 9 (Novikov et al. 2017; Charpentier et al. 2018). Furthermore, the O–O correlations associated with these highly coordinated Sr-centered polyhedra are shifted to lower distances compared to Ca-aluminosilicate measurements. As a result, the nearest neighbour peak in gSrO(r) is completely overlapped by the gOO(r) correlations (Florian et al. 2018). This highlights a need for future diffraction studies of Sr-aluminosilicate glasses using element specific techniques. In Raman spectra of aluminosilicate glasses, similar spectral features and vibrations are observed for Al as for Si, where Al can adopt Q4, Q3 and Q2 speciation depending on silica fraction (McMillan and Piriou 1983; Neuville et al. 2008a,b, 2010; Licheron et al. 2011). The substitution of Al for Si in tetrahedral positions leads to detectable shifts in frequency, broadening, and reduction in spectral resolution of the Raman bands relative to the SiO2 glass spectrum (Mysen et al. 1981; Seifert et al. 1982; McMillan et al. 1982; McMillan and Piriou 1982, 1983; McMillan 1984; Neuville and Mysen 1996; Neuville et al. 2004, 2006, 2008a,b; Le Losq and Neuville 2013; Le Losq et al. 2017). In particular, the T–O stretching vibrations shift to lower wavenumber, with a corresponding increase in position of T–O–T bending modes, as a result of a reduction in the (Si,Al)–O force constant and/or Si,Al coupling (Rossano and Mysen 2012). These changes are illustrated for calcium aluminosilicate glasses in Figure 12 showing the Raman spectra along the tectosilicate join. Along this join (tectosilicate), glasses are fully

From Short to Medium Range Order in Glasses and Melts

71

polymerized and Al3+ substitutes for Si4+ in Q4 tetrahedral sites regardless of the modifier element (Neuville and Mysen 1996; Neuville et al. 2004, 2006, 2008a,b; Le Losq and Neuville 2013; Novikov et al. 2017; Le Losq et al. 2017; Ben Kacem 2017). This is illustrated in Figure 13a, where the Q4I, Q4II vibrational modes (assigned to Q4 tetrahedra with 2 different Si–O–Si angles, see Henderson and Stebbins (2022, this volume) and T2s mode (the T2 mode associated with Q4 tetrahedra observed in SiO2 glass, see Henderson and Stebbins 2022, this volume) determined by Gaussian deconvolution, experience a linear shift to lower wavenumbers with increasing substitution of Si for Al associated with a continuous shift from the Si–O–Si vibration to pure Al–O–Al vibrations in the CA50.00 glass (McMillan and Piriou 1983; Neuville and Mysen 1996; Neuville et al. 2004, 2006, 2008a,b, 2010; Licheron et al. 2011; Novikov et al. 2017). This variation correlates well with the 27Al NMR chemical shift for Al in four-fold coordination and the T–O bond length measured by diffraction (Fig. 13b), which both increase linearly with increasing Al fraction (Neuville et al. 2004, 2006, 2008a,b). Modifier cations nano-segregate into percolation channels at high Al/Si and high modifier content, with their presence indicated by an increase of the D1 and D2 peak intensity (Le Losq et al. 2017). (a)

(b)

Figure 13. a) Wavenumber of the 3 Gaussian bands as a function of SiO2 for NAS, MAS, CAS, SAS and BAS tectosilicate glasses (Neuville and Mysen 1996; Neuville et al. 2004, 2006, 2008; Novikov et al. 2017) and b) 27Al NMR chemical shift, diso and T–O distance obtained from the G(r) as a function of SiO2 for CAS glass system (Fig. 11).

Charge compensator versus network modifier As noted above the substitution of an alkali or alkaline-earth element by Al has a significant influence on the Raman spectra of aluminosilicate glasses. Some of the changes are related to whether the added alkali or alkaline-earth cations behave as charge compensators or network modifiers. The dual role of the cations can be explored through analysis of the VH component of polarized Raman spectra. (Hehlen and Neuville 2015, 2020). The VH Raman spectra of calcium aluminosilicate glasses along the 50% SiO2 join are shown in Figure 14. A strong band is apparent at ~350 cm−1 for the alumina-free calcium silicate glass (Ca50.00) which is not visible in unpolarized Raman spectra of the Ca50.X series (Fig. 9). The intensity of this peak reduces with decreasing CaO/Al2O3 ratio and its position is sensitive to the mass of the cation (Na: 350 cm−1, Mg: 360 cm–1, Ca: 352 cm–1, Sr: 334 cm–1, Ba: 310 cm–1, Hehlen and Neuville 2015, 2020). This low frequency vibration is attributed to cations acting as network modifiers. When cations adopt a charge compensation role for the AlO4− tetrahedra this vibration disappears.

Drewitt et al.

Intensity (arbitrary units)

72

Ca50.00 Ca50.06 Ca50.12 Ca50.18 Ca50.25 Ca50.30 Ca50.40

25 20 15 10 5 0

0

200

800 1000 600 400 Wavenumber (cm-1)

1200

Figure 14. VH Raman spectra of calcium aluminosilicate glasses along the 50% SiO2 join (redrafted from Hehlen and Neuville 2015).

This change in role of modifier cations with varying CaO/Al2O3 ratio is supported by a preedge shift observed in Ca K-edge x-ray absorption near edge structure (XANES) measurements of Ca-aluminosilicate glasses from Ca50 to Ca50.25 compositions (Cicconi et al. 2016). A similar change in the structural role of Na+ ions from network modifier to charge compensator are indicated by an evolution of the 23Na NMR chemical shift of Na-aluminosilicate glasses (Le Losq et al. 2014). This also appears to correlate with the disappearance of the peak at 350 cm−1 observed in the VH Raman spectra between sodium silicate and sodium tectosilicate glasses (Hehlen and Neuville 2015). Being able to determine the behavior of alkali and alkaline-earth cations as charge compensators or network modifiers is very useful. Clearly, there is potential in examining the VH spectra and more work needs to be done.

GLASS AND MELT STRUCTURE UNDER EXTREME CONDITIONS Despite decades of research focused on aluminosilicate glasses, much less direct information is available on the structure of magmas in their high temperature liquid state (Henderson 2005) or under the high p conditions of deep planetary interiors (Kono and Sanloup 2018). This is due to the challenges associated with making measurements above the high melting temperatures of aluminosilicates (> 1500 K), where conventional furnaces present a high risk of chemical reaction with a sample, spectroscopy measurements are inhibited by thermal radiation (Papatheodorou et al. 2010), and the thermal motions and structural disorder lead to weaker spectroscopy or diffraction signals compared to the solid glass. Measurements at high-p and/or -T are doubly challenging, requiring specialized instrumentation to generate these extreme conditions while simultaneously allowing good accessibility to the sample and minimizing unwanted contributions from the sample environment. As a result, quenched glasses have long been used as analogues for the study of melts (Henderson 2005). However, while important, information obtained on glass structure is not always representative of melts in their natural liquid state (Wilding et al. 2010; Drewitt et al. 2012). This is particularly apparent for so-called fragile liquids such as depolymerized silicate melts (Giordano and Dingwell 2003) in which dynamical properties and viscosity exhibit a marked deviation from Arrhenius behavior compared to more traditional strong glass forming liquids such as pure silica (Angell 1991, 1995). Glasses and melts also experience significant reorganization in SRO and MRO under compression such that measurements made at high-p conditions are necessary to understand the full nature of magmas at depth.

From Short to Medium Range Order in Glasses and Melts

73

High temperature containerless processing In recent years, containerless techniques such as aerodynamic-levitation with laser-heating have enabled in situ diffraction and spectroscopy measurements of the structure of liquid oxides (Price 2010; Papatheodorou et al. 2010; Hennet et al. 2011a; Benmore and Weber 2017). Levitating liquids on a stream of inert gas eliminates the possibility of chemical reaction with containment material and experiments provide clean data sets of the liquid sample enabling advanced techniques such as NDIS to be applied (Drewitt et al. 2012, 2017, 2019; Skinner et al. 2012a). The high flux of synchrotron sources means that XRD measurements using ultra-fast millisecond acquisition times are possible with large area detectors. This enables diffraction patterns to be measured as an oxide liquid is supercooled into the solid glass state (Hennet et al. 2007, 2011b; Benmore et al. 2010a; Skinner et al. 2013a; Drewitt et al. 2019). Another key advantage of containerless processing is the suppression of heterogenous nucleation thereby promoting deep supercooling which, combined with rapid quenching, facilitates the formation of glass compositions such as peridotite (Auzende et al. 2011) or pure aluminates (Drewitt et al. 2019) that cannot ordinarily be formed using conventional methods.

Aluminate melts Pure liquid alumina has a poor glass forming ability and cannot be quenched to a glass (Skinner et al. 2013b; Shi et al. 2019). However, the glass forming ability of aluminate compositions is enhanced significantly by the addition of alkali, alkaline earth, or metal oxides in combination with containerless processing or other fast quenching techniques. Extensive experimental and simulation studies have been made to understand the structure of silica-free calcium aluminate glasses and their melts (McMillan and Piriou 1983; Morikawa et al. 1983; Poe et al. 1993, 1994; Massiot et al. 1995; McMillan et al. 1996; Daniel et al. 1996; Hannon and Parker 2000; Weber et al. 2003; Benmore et al. 2003; Iuga et al. 2005; Kang et al. 2006; Thomas et al. 2006; Hennet et al. 2007; Mei et al. 2008a,b; Cristiglio et al. 2010; Neuville et al. 2010; Mountjoy et al. 2011; Licheron et al. 2011; Drewitt et al. 2011, 2012, 2017, 2019; Liu et al. 2020). Other compositions have also been investigated, including barium (Licheron et al. 2011; Skinner et al. 2012b), strontium (Weber et al. 2003; Licheron et al. 2011; Novikov et al. 2017), lead (Barney et al. 2007), and rare-earth aluminates (Wilding et al. 2002; Weber et al. 2004a; Du and Corrales 2007; Barnes 2015). A liquid–liquid phase transition (LLPT) has even been proposed in the yttria–aluminate system, inferred from the observation of coexisting low-density and high-density phases in the supercooled melts (Aasland and McMillan 1994; Wilding et al. 2002, 2005, 2015; Weber et al. 2004a,b; Wilson and McMillan 2004; Greaves et al. 2008), although this result is disputed by subsequent measurements which find no structural or thermal signatures consistent with a LLPT (Barnes et al. 2009) and the observations may instead be attributed to nanocrystalline inclusions forming within the glassy material (Nagashio and Kuribayashi 2002; Tangeman et al. 2004; Skinner et al. 2008; Barnes et al. 2009). Molten calcium aluminates are very fragile refractory liquids. Fragile liquids tend to exhibit greater variation in SRO and MRO compared to strong glass forming liquids and encounter high potential energy barriers during supercooling such that they become trapped in deep local energy minima on approach to the glass transition (Drewitt et al. 2019). The comprehensive range of techniques applied to the calcium aluminate system reveal significant transformations in SRO and MRO structure taking place in these liquids during glass formation. Neutron and XRD G(r) functions for (CaO)x(Al2O3)1-x glasses and melts with x  =  0.5 (CaAl2O4, CA) and x = 0.75 (Ca3Al2O6, C3A) are shown in Figure 15 (Drewitt et al. 2011, 2012, 2017, 2019). The results of MD simulations made using aspherical ion model (AIM) potentials, which consider polarization effects up to the quadrupolar level (see Jahn 2022, this volume), are also shown (Drewitt et al. 2011, 2012, 2019). The first peak in G(r) for the melts at ~1.78 Å is attributed to the nearest neighbour Al–O bond, while the second peak at ~2.3 Å

Drewitt et al.

74

a) XRD

5

Al-O Ca-O

Total pair distribution function, G(r)

4

CA

Ca-O

4

Glass

3

2

2

Liquid

1 0

0

2

1

2

3 4 5 Distance, r (Å)

Glass

3 2

Liquid

1

C3A

4

Glass

3

Liquid

1

C3A

4

0

CA

Al-O

5 Glass

3

b) Neutron

6

Liquid

1 6

0

1

2

3

4

Distance, r (Å)

5

6

Figure 15. Total pair distribution functions G(r) from a) x-ray and b) neutron diffraction of CA and C3A glasses (solid black curves) and liquids (solid red curves) together with the corresponding functions computed directly from MD simulations (dotted curves) (data from Drewitt et al. 2011, 2012, 2017, 2019).

arises from Ca–O correlations (Drewitt et al. 2011). On vitrification, the intensity and resolution of the Al–O and Ca–O peaks is significantly enhanced, reflecting the thermal motions and higher overall structural disorder in the liquid state. The Al–O and Ca–O peak positions experience shifts to ~1.75 Å and ~2.35 Å, consistent with a reduction and increase in Al–O and Ca–O coordination numbers, respectively. However, accurate quantification of these coordination numbers is hindered by the penetration of Ca–O correlations into the first Al–O coordination shell and considerable overlap with other atom-atom interactions at higher bond lengths. This is particularly acute for the liquids, but also affects the glass measurements (Hannon and Parker 2000; Mei et al. 2008a,b; Drewitt et al. 2011). Element selective techniques are, therefore, required to isolate the Al and Ca coordination environments. This represents a significant challenge at high temperatures: 27Al NMR spectroscopy measurements observe the fast exchange limit such that individual coordination populations cannot be resolved in the high temperature melts (Coté et al. 1992; Poe et al. 1993, 1994; Massiot et al. 1995; Florian et al. 2018), 43Ca NMR is limited by low sensitivity and natural abundance (Dupree et al. 1997), x-ray absorption measurements of high temperature levitated melts are difficult to perform, and NDIS is limited by the sample size and neutron flux. Despite the small size (~2–3 mm diameter) of levitated melt droplets, neutron diffraction with isotope subsitution (NDIS) has nevertheless been successfully applied to precisely measure the Al–O and Ca–O coordination environments in levitated liquid CA and C3A (Drewitt et al. 2012, 2017). The pseudo-binary pair distribution functions gmm(r) and gCam(r) for the CA and C3A melts and the quenched CA glass are shown in Figure 16. In gmm(r) all interactions involving Ca are eliminated and the function contains contributions from µ–µ (µ = Al, O) pair

From Short to Medium Range Order in Glasses and Melts

1.2

75

Al-O

1.0 O-O

g (r) (barn)

0.8 0.6

CA glass

0.4 0.2 CA melt

0.0

Figure 16. The real-space pseudo-binary pair distribution functions gµµ(r) and gCaµ(r) for the CA (Drewitt et al. 2012) and C3A (Drewitt et al. 2017) melts from NDIS measurements (solid curves) and AIM-MD (dotted curves) simulations (Drewitt et al. 2011, 2012). (Reprinted from Drewitt et al. 2019, doi:10.1088/17425468/ab47fc © SISSA Medialab Srl. Reproduced by permission of IOP Publishing. All rights reserved).

-0.2 -0.4

C3A melt

gCa (r) (10-1 fm)

-0.6 Ca-O

2.0

CA glass

1.0

CA melt

0.0

C3A melt

-1.0 1

2

3

4 5 6 Distance, r (Å)

7

8

correlations only, showing well resolved peaks corresponding to Al–O nearest neighbors and O–O bonds. In contrast, gCam(r) is comprised solely from Ca–µ pair correlations and the main peak corresponds to the Ca–O nearest-neighbors. The NDIS experiments for liquid C3A and CA glass go one step further to provide direct measurement of the gCaCa(r) partial pair distribution function, as shown in Figure 17. The AIM-MD model is in good general agreement with the neutron and XRD total structure measurements and the NDIS difference functions. The CA composition has an Al:O ratio of 1:2 such that it is feasible to form a fully polymerized network of Q4-species in which any two Al atoms are connected by a single bridging oxygen. The C3A composition on the other hand is significantly depolymerized with a theoretical mean number of 2 bridging oxygens per Al atom. The combined NDIS, XRD, and AIM-MD results reveal that the structure of liquid CA deviates from this simple network model containing 83% AlO4 tetrahedra with 12% non-bridging oxygens and 15% AlO5 units, many of which share edges (Drewitt et al. 2012). Considering all Al–O pairs, 18% oxygen atoms have a coordination > 2, with 7% “formal” triclusters involving AlO4 tetrahedra only. Liquid C3A is composed of a higher fraction of AlO4 tetrahedra (93%) with 60% non-bridging oxygen and 36% bridging oxygen atoms (Drewitt et al. 2017), where the latter is slightly higher than expected from the O:Al ratio (Skinner et al. 2012b). This is accounted for by the presence of 3 to 4% “free oxygen” ions, which do not participate in Al–O bonding, and ~1% oxygen triclusters. While the majority of AlO4 tetrahedra in C3A melt belong to a single infinitely connected network, 15 to 20% belong to smaller clusters with ~10% forming Al2O7 dimers or isolated AlO4 tetrahedra.

Drewitt et al.

76

gCaCa(r)

2

CA glass

1 0

C3A melt

-1 -2 2

4

6 8 Distance, r (Å)

10

12

Figure 17. The partial pair distribution function gCaCa(r) for CA glass (Drewitt et al. 2012) and C3A melt (Drewitt et al. 2017) determined directly from NDIS experiments (solid curves) and generated from the AIM-MD simulations (Drewitt et al. 2011, 2012). (Reprinted from Drewitt et al. 2019, doi:10.1088/17425468/ab47fc © SISSA Medialab Srl. Reproduced by permission of IOP Publishing. All rights reserved).

On vitrification, the over coordinated CA glass structure reorganizes to form a predominantly corner shared network of AlO4 tetrahedra. The C3A glass is also characterised by a preponderance (99%) of aluminium in AlO4 tetrahedra with 85% belonging to a single infinite network. This is consistent with 27Al NMR (Neuville et al. 2006, 2007) and XANES spectroscopy at the L and K-edges (Neuville et al. 2008b, 2010) which show Al is predominantly four-fold coordinated by oxygen in glasses with compositions x = 0.5 to 0.75. There is, however, a residual 3.5% Al in AlO5 units remaining in CA glass (Neuville et al. 2006) and the AIM-MD results indicate the presence of ~4% residual AlO5 units in CA glass, accompanied by 7% non-bridging oxygens and 5% “formal” oxygen triclusters (Drewitt et al. 2012). This latter result is consistent with 5% oxygen triclusters detected in the glass by heteronuclear correlation NMR spectroscopy (Iuga et al. 2005). Differences in network connectivity are apparent from the Raman spectra of CA, C12A7 (x = 0.632, Ca12Al14O33) and C3A glasses shown in Figure 18. All spectra exhibit a Boson peak at ~90 cm−1, a strong band at ~560 cm−1 with significant asymmetry at higher wavenumbers, and another strong band at ~780 cm−1, which increases in intensity relative to the 560 cm−1 band with increasing CaO content. The 560 cm−l band is attributed to transverse motions of bridging oxygens in Al–O–Al linkages, with the high frequency asymmetry caused by Al–O stretching vibrations of the fully polymerized tetrahedral aluminate groups (McMillan and Piriou 1983). This band experiences a shift to higher frequencies and reduction in intensity with increasing CaO content associated with changes in polarizability of the Al–O–Al vibrations resulting from an increase in the Al–O force constant as Q2 species are introduced into the glass network. This is consistent with a shift to lower energies of the L2,3-edge in Al XANES spectroscopy measurements attributed to the presence of Q2 species and associated stronger hybridization of non-bridging oxygens (Neuville et al. 2010). The weak band in the CA glass spectrum at 780 cm−1, and shoulder at 910 cm−1, are attributed to Al–O stretching vibrations of Q4 Al species. The increase in intensity and shift to lower frequencies of the 780 cm−1 band with increasing CaO content is attributed to increasing fractions of non-bridging oxygens giving rise to more intense vibrations compared to bridging oxygens (McMillan and Piriou 1983). This is consistent with 27Al NMR (Neuville et al. 2006) and Al K-edge XANES results (Neuville et al. 2008a,b), which suggest Al units predominantly in Q2 and Q3 speciation in C3A glass. It also implies that the C12A7 glass contains a significant fraction of NBO.

From Short to Medium Range Order in Glasses and Melts

77

Figure 18. Raman spectra of CA, C12A7, C3A glasses (data from Neuville et al. 2006, 2010; Licheron et al. 2011). The arrow indicates the increase in intensity of the 780 cm−1 band and corresponding shift to lower frequencies with increasing CaO concentration.

Calcium has a broad distribution of 4- to 9-fold Ca–O coordination sites, with average Ca–O coordination numbers of 6.2 in CA (Drewitt et al. 2012) and 5.6 in C3A (Drewitt et al. 2017) melts, compared to ~5 in liquid CaSiO3 (Skinner et al. 2012a). In CA melt, edgeand face-sharing Ca-centered polyhedra form small clusters contributing to MRO. In C3A melt all Ca-centered units are connected by corners to a single network with 90% edge- and face-sharing. The direct measurement of gCaCa(r) by NDIS (Fig. 17) gives an average Ca–Ca coordination number of ~8 (~8.5 from AIM-MD) compared to a value ~5 in CA melt, reflecting the greater fraction of Ca in the C3A composition and hence greater tendency towards clustering. The average Ca–O coordination in C3A glass reduces slightly to 5.5 (Drewitt et al. 2019). However, on vitrification, the CA glass experiences a remarkable development of cationic MRO with edge- and face-sharing Ca-centered polyhedra with an average Ca–O coordination of 6.4 which form large branched chainlike clusters that weave through the glass network (Fig. 19) (Drewitt et al. 2012). Similar clusters of Ca-centered octahedra are observed in CaSiO3 glass (Benmore et al. 2010a; Skinner et al. 2012a) and it has been argued that Ca-clustering is in fact an essential requirement for glass formation and is responsible for the fragile behavior of the melt (Skinner et al. 2012a).

(a) Melt

(b) Glass

Figure 19. Snapshots illustrating the largest clusters of edge-sharing Ca-centred polyhedra in the AIMMD simulations of CaAl2O4 from Drewitt et al. (2012) for (a) the melt 2500 K and (b) the glass at 350 K. The clusters are represented by the light (yellow), dark (blue), and medium (green) shaded units which involve 16, 9, and 8 Ca atoms in the liquid or 44, 24, and 19 Ca atoms in the glass, respectively. Reprinted figure with permission from Drewitt et al. Physical Review Letters 109:235501 (2012) doi:10.1088/09538984/24/9/099501. Copyright (2012) by the American Physical society.

78

Drewitt et al.

In summary, at the Al2O3-rich limit of the glass forming region of calcium aluminate melts up to 20% of the Al reside in AlO5 coordination sites (Drewitt et al. 2011), increasing to over 30% in pure alumina (Skinner et al. 2013b). These highly coordinated Al units are incompatible with glass formation. However, although the equimolar (CA) melt contains 15% AlO5 polyhedra (Drewitt et al. 2011), these highly coordinated units and oxygen triclusters breakdown on vitrification and the supercooled melt structure reorganizes to form a predominantly corner-shared AlO4 tetrahedral glass network (Drewitt et al. 2012). This is accompanied by the development of medium range cationic ordering associated with the formation of long clusters of edge- and face-sharing Ca-centered polyhedra (Fig. 19). While significantly depolymerized, the structure of C3A melt remains largely composed of AlO4 tetrahedra (Drewitt et al. 2011). Although many of these tetrahedra belong to a single infinite network, ~20% aluminum in C3A melt belong to smaller clusters with ~10% unconnected Al2O7 dimers and AlO4 monomers (Drewitt et al. 2017). On vitrification, C3A glass is characterized by a tetrahedral aluminate network structure, where 85% of AlO4 units belong to a single infinite structure with only 5% isolated tetrahedra or dimers (Drewitt et al. 2019). Beyond the CaO-rich limit of the glass forming region, the number of isolated AlO4 units is expected to increase such that the glass can no longer support the formation of an infinitely connected network of AlO4 units (Drewitt et al. 2017). The significant transformations that take place in SRO and MRO during glass formation in the calcium aluminate glasses are captured by time-resolved measurements of aerodynamically levitated liquid calcium aluminates recorded during solidification of the high temperature melts through their glass transition (Hennet et al. 2007; Drewitt et al. 2019). In particular, the changes in MRO associated with the development of cationic ordering is indicated by the evolution of the FSDP in S(Q) attributed to cation–cation correlations (Fig. 20). The work reviewed here for a representative fragile glass-forming system demonstrates that caution is required when considering glasses as analogues for geological melts. Similar differences in the local structural environment have also been observed in fragile MgO–SiO2 liquids (Wilding et al. 2010) and natural silicate melts in the CaO–MgO–Al2O3–SiO2 (CMAS) system encompass a range of kinetic fragilities (Giordano and Dingwell 2003; Giordano and Russell 2007; Giordano et al. 2008). As such, measurements made on glasses cannot be assumed to be representative of melts in their natural liquid state and models should be based, where possible, on liquid-state measurements.

Figure 20. Time resolved synchrotron XRD measurements of the structure factors S(q) of aerodynamically levitated liquid (a) CA and (b) C3A during glass formation with 30 ms acquisition times. (Reprinted from Drewitt et al. 2019 doi:10.1088/1742-5468/ab47fc © SISSA Medialab Srl. Reproduced by permission of IOP Publishing. All rights reserved).

From Short to Medium Range Order in Glasses and Melts

79

Aluminosilicate melts As for aluminates, aluminosilicate melts have high melting points and only a few diffraction studies have been reported, mainly using laser heating with aerodynamic levitation at neutron sources (Jakse et al. 2012, Hennet et al. 2016, Florian et al. 2018) or levitation inside the bore of a NMR spectrometer (Poe et al. 1992; Florian et al. 2018). Alternatively, wire furnace methods, in which a small quantity of sample is placed in a small hole (~500 µm diameter) in a Pt–Ir alloy wire and melted by resistive heating (Mysen and Frantz 1992; Richet et al. 1993; Neuville et al. 2014b), have been adopted for x-ray absorption spectroscopy (XAS) (Neuville et al. 2008b), Raman spectroscopy (Daniel et al. 1995; Neuville and Mysen 1996), XRD (Neuville et al. 2014b), and small angle x-ray scattering (SAXS) (di Genova et al. 2020) of aluminosilicate melts. In contrast to aluminate melts, which can be stably levitated for days without significant mass loss (Drewitt et al. 2012, 2017), aerodynamically levitated laser heated silicate melts experience significant sample vaporization at high SiO2 fractions. This leads to significant changes in composition, as experienced by in situ XRD measurements of liquid SiO2 (Mei et al. 2007; Skinner et al. 2013a) and NDIS measurements of CaSiO3 melt (Skinner et al. 2012a) for which sample mass loss is particularly detrimental due to the requirement for the different isotopically enriched samples to have identical composition. Thus, neutron diffraction experiments of aluminosilicate melts, which require counting times of several hours, have been limited to compositions up to about 33% of silica in melts containing CaO (Hennet et al. 2016) and 42% in melts containing SrO (Florian et al. 2018). Figure 21a shows a comparison of the neutron structure factors measured for a range of calcium aluminosilicates melts along the charge compensator line together with the corresponding glass. On melting, the FSDP becomes less distinct with lower intensity and increased broadening, which is indicative of increased disorder in the organization of polyhedra on medium range length scales. This augmentation of disorder is also evident in the broadening and reduction in structure of the peaks over the full Q-range. Similar changes are observed for other CaO/Al2O3 ratios (Hennet et al. 2016). Along the join R = 1, this disorder is mainly related to an increase of the proportion of AlO5, which is apparent from the asymmetric high-r broadening of the first peak in G(r) (Fig. 21b), related to a slight increase of the Al–O distance (Drewitt et al. 2012).

Figure 21. Total structure factors S(Q) of some CAS glasses measured using neutron scattering (a) and corresponding total pair distribution functions (b). The liquid temperatures are reported in the figure. (Data from Hennet et al. 2016).

80

Drewitt et al.

As previously observed for glasses, the CaO correlation, which was largely overlapped with the O–O correlations belonging to SiO4 tetrahedra, is now fully overlapped at high temperature complicating the interpretation of the measurements. Thus, molecular dynamics simulations have been employed to provide more insight on the liquid structure, revealing the AlO5 units are accompanied by increased proportions of NBO and oxygen triclusters (Jakse et al. 2012). The MD simulations reveal that the addition of silica to aluminate compositions reduces the quantity of AlO5 present from ~18% in Ca0.50 to ~10% in Ca12.44 and Ca19.40 melts. These melts contain ~14% OAl3 triclusters and ~12% NBO. The simulations reveal a continuous development in the AlO4 network and corresponding reduction in AlO5 units, oxygen triclusters, and NBOs during supercooling to a glass. Calcium occupies a distribution of coordination sites ranging from 4 to 8 with an average Ca–O coordination number of ~6. The potentials used to describe this structural environment also provide a relatively accurate model of the dynamical properties of these melts (Bouhadja et al. 2013). Neutron diffraction measurements of SrO–Al2O3–SiO2 melts reveal similar SRO associated with the Al and Si atoms as for calcium aluminates with an increase in the fraction of AlO5 units in the melts estimated at 5–6% (Florian et al. 2018). As for the glasses, it is difficult to extract information from the SrO contribution, which is overlapped by O–O correlations arising from Si–O and Al–O tetrahedra and highly coordinated Sr–O polyhedra (cf. Fig. 11). By looking at the possible O–O correlations attributed to these Sr–O polyhedra, the Sr–O coordination number was estimated to be ~8 for the join R = 3 and somewhat less for R = 1 (Florian et al. 2018). The in situ high temperature NMR experiments (Florian et al. 2018) provide more information on the network structure. With increasing ratio X = Si/(Al+Si), along the R = 1 join, the network composed mainly from AlO4 units at low Si content is gradually replaced by a network of SiO4 tetrahedra. For X > 0.7, the same behavior is observed along the R = 3 join. However, below this ratio, AlO4 units contain NBOs which break up the aluminosilicate network. Consequently, for a given silica content, the addition of SrO reduces the medium range order (smaller ring sizes for R = 3 than for R = 1). For per-aluminous compositions, large amounts of 5- and 6-fold coordinated aluminum are found in the melts. Different mechanisms than those observed along the joins R = 1 and 3, especially at low silica content could also suggest the presence of oxygen triclusters.

Iron silicate melts and glasses As the fourth most abundant element in the Earth’s crust, iron plays an important role due to its high mass having a strong influence on the density and viscosity of natural volcanic magmas. Iron adopts a dual character as both a network former and modifier in silicate glasses. This behavior is modulated by the coexistence of ferrous (Fe2+) and ferric (Fe3+) iron cations which adopt different structural roles. The redox ratio Fe3+/∑Fe is strongly influenced by chemical composition, temperature, and oxygen fugacity (Wilke 2005). This mixed valency complicates the interpretation of the local coordination environment in structural measurements. In general, Fe3+ is predominantly a network former with 4-fold coordination in silicate glasses (Burkhard 2000), although this is highly dependent on composition and oxidation state, and higher coordinated Fe3+ sites have been observed (Virgo and Mysen 1985; Hannoyer et al. 1992; Keppler 1992; Kim and Lee 2020). In early models of iron silicate glasses, Fe2+ was assumed to occupy 6-fold coordinated sites as in corresponding silicate minerals (Boon and Fyfe 1972; Binsted et al. 1986). However, a wide distribution of 4-, 5-, and 6-fold coordination with oxygen has been reported in synthetic and natural iron silicate glasses by using x-ray, Mössbauer and optical absorption spectroscopies (Calas and Petiau 1983; Virgo and Mysen 1985; Binsted et al. 1986; Iwamoto et al. 1987; Dingwell and Virgo 1988; Hannoyer et al. 1992; Keppler 1992; Wang et al. 1993; Rossano et al. 1999, 2000a,b; Wu et al. 1999; Galoisy et al. 2001; Giuli et al. 2002; Farges et al. 2004; Wilke et al. 2004, 2007;

From Short to Medium Range Order in Glasses and Melts

81

Jackson et al. 2005; Mysen 2006; Bingham et al. 2007; Giuli et al. 2011, 2012; Nyrow et al. 2014; Zhang et al. 2016, 2018; Alderman et al. 2017a; Cottrell et al. 2018 Nayak et al. 2019) and x-ray and neutron diffraction (Johnson et al. 1999; Holland et al. 1999; Weigel et al. 2006, 2008a,b; Drewitt et al. 2013; Wright et al. 2014). More limited direct information is available on the local coordination environment of iron in silicate melts by comparison with the quenched glass. Using a conventional XRD source, Waseda et al. were the first to report the structure of iron silicate melts suggesting a reduction in Fe–O coordination from 6- to 4-fold with increasing SiO2 fraction (Waseda and Toguri 1978; Waseda et al. 1980). However, serious inconsistencies have been found in this data including the assignment of unrealistically small Fe–Si bond distances and Fe–O–Si bond angles (Jackson et al. 1993; Drewitt et al. 2013). High temperature XAS measurements have indicated Fe2+ residing solely in 4-fold sites in alkali silicate (Waychunas et al. 1988) melts, and a complete conversion from 6-fold Fe2+ sites in crystalline fayalite (Fe2SiO4) to 4-fold in the melt (Jackson et al. 1993). A subsequent XAS study found only slightly higher quantities of low coordinated Fe2+ in reduced silicate melts (Wilke et al. 2007). This is confirmed by in situ synchrotron XRD measurements of laser heated silicate liquids, including Fe2SiO4 and FeSiO3, levitated on an Ar gas stream in air (Drewitt et al. 2013). Here, two distinct Fe–O peaks are resolved (Fig. 22) with bond lengths 1.93 and 2.20 Å corresponding to FeO4 and FeO6 units, respectively, with average Fe–O coordination numbers of 4.8 (Fe2SiO4) and 5.1 (FeSiO3). Both Fe–O peaks are also apparent in the measurements of a basalt glass and melt. Although only two Fe–O peaks are

Figure 22. Gaussian fits to the main peaks in T(r) = 4πrr0G(r) from synchrotron XRD measurements by Drewitt et al. (2013) for (a) liquid fayalite (Fe2SiO4) and (b) liquid ferrosilite (FeSiO3). The black circles are the measured data and the solid black curves are the superposition of the fitted Gaussian functions. Reprinted figure with permission from Drewitt et al. Physical Review B 87:224201 (2013) http://dx.doi. org/10.1103/PhysRevB.87.224201. Copyright (2013) by the American Physical Society.

82

Drewitt et al.

apparent, the results do not exclude the presence of up to ~10–25% FeO5 units in the iron silicate melts and glasses studied (Drewitt et al. 2013). The coexistence of 4-, 5-, and 6-fold coordinated iron in silicate melts has important implications for the partitioning behaviour of iron in natural melts or transport properties of magmas. The ratio of these different units is affected by oxygen fugacity, with in situ Fe K-edge XANES and synchrotron XRD measurements of levitated fayalitic melts revealing average Fe–O coordination numbers increasing from 4.4 in the reduced melt to 4.7 at higher Fe3+/∑Fe (Alderman et al. 2017b). Raman spectroscopy has also been used to interpret the structural role of iron in silicate glasses and melts and link the redox equilibrium to the silicate structure (Mysen et al. 1980, 1984, 1985; Fox et al. 1982; Wang et al. 1993, 1995), and more recently to quantify the Fe redox ratio (Magnien et al. 2006, 2008; Roskosz et al. 2008; Di Muro et al. 2009; Cochain et al. 2012; Di Genova et al. 2015, 2016, 2017; Le Losq et al. 2019b). Raman spectra of iron silicate glasses and melts vary systematically with varying Fe3+/∑Fe ratio due to the different roles of Fe2+ and Fe3+ influencing the network structure and Qn speciation in different ways (Le Losq et al. 2019b). Samples with high Fe3+/∑Fe ratio have characteristically strong intensity at ~900 cm−1 assigned to Fe3+-O stretching vibrations (Wang et al. 1995; Magnien et al. 2004, 2006, 2008; Di Muro et al. 2009; Cochain et al. 2012; Le Losq et al. 2019b). This is illustrated in Figure 23 for an iron-pyroxene glass composition with variation of the redox state Fe3+/ΣFe from 0.09 to 0.97. Here the intensity of the Fe3+–O stretching band at 910  cm−1 increases progressively with increasing Fe3+ fraction consistent with the formation of tetrahedral ferric iron, as indicated from the Fe pre-edge XANES (Wilke et al. 2001).

Figure 23. a) Raman spectra at room temperature for a series of iron-pyroxene glasses (redrafted from Magnien et al. 2006). The Fe3+/ΣFe redox ratio is indicated and the spectra are displaced vertically for clarity. The spectra were normalized to the maximum intensity of the spectra corrected from the excitation lines (see Neuville et al. 2014). b) Deconvolution of Raman spectrum of pyroxene glass with redox ratio Fe3+/ΣFe = 0.09, and c) Fe3+/ΣFe = 0.99.

From Short to Medium Range Order in Glasses and Melts

83

Glasses and melts at high pressure Pressure can lead to considerable reorganization of SRO and MRO in glasses and melts. The structural response of melts to high p determines the density and dynamical properties of natural magmas in deep planetary interiors. Understanding the link between structure and properties of melts at high-p is, therefore, integral to understanding a range of problems including the distribution and causes of chemical alteration (metasomatism) of the mantle due to upward or lateral migration of melts, large scale differentiation from an early magma ocean, and mantle melting at mid-ocean ridges and subduction zones. Gravity driven melt transportation is proportional to melt mobility, which is dependent upon the viscosity of the melt and the density contrast between the melt and solid mantle. Early equation of state data for melts indicated that basaltic magmas are more compressible than mantle minerals leading to the possible existence of a melt–crystal density crossover at depth (Stolper et al. 1981; Rigden et al. 1984; Agee and Walker 1988). Many network glasses experience permanent densification upon recovery from cold (i.e. room temperature) compression associated with irreversible changes due to a collapse in MRO and void space, with the local coordination environments typically returning to their ambient structures (Bridgman and Šimon 1953; Grimsditch 1984; Polian and Grimsditch 1990; Susman et al. 1991; Ishihara et al. 1999; Inamura et al. 2001; Trachenko and Dove 2002; Sampath et al. 2003; Huang and Kieffer 2004a,b; Champagnon et al. 2008; Rouxel et al. 2008). Heat treatment during compression promotes rebonding and further permanent densification of recovered samples (Polian and Grimsditch 1990; Ishihara et al. 1999; Trachenko and Dove 2002; Inamura et al. 2004; Martinet et al. 2015), where highly coordinated local environments reminiscent of the high-p state are recoverable to ambient conditions in glasses equilibrated at high-p–T above the liquidus (Stebbins and McMillan 1989; Li et al. 1995; Yarger et al. 1995; Ohtani et al. 1985; Xue et al. 1989, 1991; Stebbins and Poe 1999; Allwardt et al. 2004; Kelsey et al. 2009) or at high-p close to the glass transition (Allwardt et al. 2005a,b; Gaudio et al. 2008, 2015; Guerette et al. 2015; Stebbins and Bista 2019). Nevertheless, in order to unequivocally capture the evolution in SRO and MRO in glasses and melts at high p there is no substitute for in situ experiments, and such studies are clearly essential for melts which do not quench to a glass. Recent advances in experimental and analytical techniques now allow for the measurement of the structure and properties of glasses and melts to be measured in situ at high-p. Pressure cells used for high-p research can be classified into two main types: large volume devices, such as a piston cylinder devices and multi anvil (MA) apparatus (Ito 2007), or the much smaller volume diamond anvil cell (DAC) (Mao and Mao 2007). Large volume devices are typically used for ex situ phase equilibrium experiments under simultaneous high-p–T conditions using resistive heating. Piston cylinder devices can achieve moderate p up to 5–6 GPa and 1800 °C (Holloway and Wood 1988), corresponding to upper mantle or lunar core conditions. As the name suggests, the MA apparatus utilizes multiple anvils to compress a sample from four or more directions to generate conditions of up to 30 GPa and 3000 °C (Holloway and Wood 1988), corresponding to mid to lower mantle conditions. Use of sintered diamond MA cubes, in place of standard tungsten carbide cubes, allows p as high as 90 GPa to be generated (Zhai and Ito 2011), providing access to deep lower mantle conditions. MA devices with x-ray transparent apertures are now commonplace at most third-generation synchrotron radiation sources (Liebermann 2011) and have been exploited for in situ high-p measurements of the structure and properties of silicate glasses and melts (Funamori et al. 2004; Ohtani et al. 2005). However, MA devices are expensive to build and operate and sample accessibility is limited by the large-scale bulky nature of the apparatus. The Paris–Edinburgh (PE) cell is a large volume press specifically designed to optimize sample accessibility for in situ powder neutron diffraction experiments at p up to ~25 GPa (Besson et al. 1992; Klotz et al. 1995) where developments made within the last decade allow for high-quality in situ neutron diffraction measurements to be made of cold-compressed glass in the gigapascal regime

84

Drewitt et al.

(Drewitt et al. 2010; Salmon et al. 2012; Salmon and Zeidler 2015). The PE cell has been adapted for high-p–T synchrotron XRD experiments (Besson et al. 1996; Mezouar et al. 1999; Crichton and Mezouar 2005) and used for in situ x-ray scattering measurements of silicate melts (Yamada et al. 2011; Sakamaki et al. 2012; Kono et al. 2014). Recently, a double-stage large volume cell was developed by incorporating a pair of secondary diamond anvils into a primary-stage PE cell to generate pressures in the megabar (1 Mbar = 100 GPa) regime (Kono et al. 2019) and has been used for measuring structure of different glasses at ultrahigh pressure (Kono et al. 2016, 2018; Ohira et al. 2019; Shibazaki et al. 2019; Wilding et al. 2019). The DAC generates extremely high static pressures by compressing a sample between two opposing single crystal diamond anvils (Bassett 2009). High-p experiments up to ~1 megabar (1 Mbar = 100 GPa) are routine in the DAC (Li et al. 2018), with multimegabar pressures feasible by employing beveled (Bell et al. 1984) or toroidal (Dewaele et al. 2018) anvils to provide access to static p corresponding to Earth’s core and beyond, with p in the Terapascal (1000 GPa) regime achievable using secondary micro-ball nanocrystalline diamond anvils (Dubrovinsky et al. 2012; Dubrovinskaia et al. 2016). The DAC is an extremely versatile and portable device with relatively low manufacturing costs. The transparency of diamonds across the electromagnetic spectrum offers a key advantage over other high-p methods, including the ability to observe a sample in situ under compression using optical microscopy, spectroscopy, and x-ray scattering techniques. Laser heating techniques can also be employed to heat samples at high-p to temperatures up to ~5000 K. Dedicated laser heated diamond anvil cell (LHDAC) setups for in situ high-p–T structure measurements are now widely available at synchrotron sources around the world (Watanuki et al. 2001; Shen et al. 2001; Meng et al. 2006; Caldwell et al. 2007; Liermann et al. 2010; Petitgirard et al. 2014). The LHDAC method combined with synchrotron XRD has been exploited in the Earth Sciences to study metallic (Shen et al. 2004; Morard et al. 2013, 2017) and silicate (Sanloup et al. 2013b; Drewitt et al. 2015) melt structure under deep mantle and core conditions. Simultaneous high-p–T conditions may also be achieved in a resistively heated (RH)-DAC. Although the maximum attainable temperature is lower than for the LHDAC, the RHDAC has the distinct advantage of providing homogeneous heating over the whole sample allowing the measurement of larger wholly molten samples without contamination from thermal insulation media or laser coupling material (de Grouchy et al. 2017; Louvel et al. 2020; Drewitt et al. 2020). Regardless of whether large volume or DAC apparatus are used, measuring glass or melt structure in situ at high-p requires accurate characterization of the p-dependent background scattering from the cell to extract a precise measurement of the diffuse glass or melt signal (Shen et al. 2003; Drewitt et al. 2010). This background scattering can be reduced using spatial collimation (Mezouar et al. 2002) or by reducing the fraction of non-sample components within the path of the incident beam: e.g. much of the x-ray Compton scattering from DAC anvils can be eliminated by using perforated diamonds (Soignard et al. 2010).

Pressure induced modifications in MRO and SRO in SiO2 and GeO2 glass In situ high-p spectroscopy (Grimsditch 1984; Hemley et al. 1986; Williams and Jeanloz 1988; Zha et al. 1994; Polsky et al. 1999; Lin et al. 2007; Champagnon et al. 2008; Murakami and Bass 2010), and x-ray (Meade et al. 1992; Inamura et al. 2004; Sato and Funamori 2008, 2010; Benmore et al. 2010b; Shen et al. 2011; Prescher et al. 2017; Kono et al. 2020) and neutron (Zeidler et al. 2014a) diffraction have been used extensively to determine the p-induced structural modifications of pure SiO2 glass. Extensive spectroscopy (Itié et al. 1989; Durben and Wolf 1991; Polsky et al. 1999; Hong et al. 2007; Vaccari et al. 2009; Baldini et al. 2010; Dong et al. 2017; Spiekermann et al. 2019), and x-ray (Guthrie et al. 2004; Hong et al. 2007, 2014; Mei et al. 2010; Kono et al. 2016) and neutron (Guthrie et al. 2004; Drewitt et al. 2010; Salmon et al. 2012; Wezka et al. 2012) diffraction measurements reveal GeO2 glass undergoes analogous p-induced transformations to SiO2 but over a much lower-p regime.

From Short to Medium Range Order in Glasses and Melts

85

There is firm consensus from these studies for the operation of two key densification mechanisms in pure SiO2 and GeO2 glass starting with a steady collapse in MRO associated with the closure of open ring structures which is accompanied at higher pressures by a continuous transformation from a tetrahedral to octahedral glass network. The changes in MRO are evident in the reciprocal space diffraction patterns from a shift in position of the FSDP at 1.55 Å−1 at ambient-p to higher Q values with increasing p (Fig. 24). This change is accompanied by the development of a second peak at ~3 Å−1. The emergence of a new peak observed at ~3 Å−1 in S(Q) for SiO2 and GeO2 glass at high-p is observed for many other types of oxide glasses and melt compositions including calcium aluminate (CaAl2O4) and anorthite (CaAl2Si2O8) (Drewitt et al. 2015), forsterite (Mg2SiO4) (Benmore et al. 2011; Adjaoud et al. 2008), enstatite and wollastonite (Salmon et al. 2019), jadeite (NaAlSi2O6), albite (NaAlSi2O6) and diopside (CaMgSi2O6) (Sakamaki et al. 2014a,b). In SiO2 glass, this peak has been attributed to the breakdown of MRO and emergence of SiO6 octahedra (Meade et al. 1992; Benmore et al. 2010b). More generally, this peak is consistent with the development of shortrange topological ordering arising from a more densely packed structure (Elliot 1995; Salmon et al. 2005, 2006; Sakamaki et al. 2014b; Drewitt et al. 2015). Advances made in neutron diffraction methodologies for high precision in situ measurements of glasses at high p (Drewitt et al. 2010) have enabled NDIS measurements of GeO2 glass to directly measure the individual Ge and O environments (Wezka et al. 2012). From these measurements, the p-dependence of the mean Ge–O–Ge bond angle was found, which reduces with increasing p consistent with compaction of the open corner shared tetrahedral network structure. 8.0 GPa

Total structure factor, S(Q)

1

5.8 GPa

0

4.9 GPa

-1

4.0 GPa

-2

2.2 GPa

-3

ambient

-4 -5

0

2

4

6

8

10

12

14

16

-1

Scattering vector, Q (Å )

Figure 24. Total structure factors S(Q) for GeO2 glass as measured by in situ neutron diffraction at high pressure in the PE cell from ambient to 8.0 GPa. The changes in intensity and position of the FSDP and principal peak are indicated by the arrows. (Data from Drewitt et al. 2010).

The transformation in SRO from a tetrahedral to octahedral glass network occurs over the p range of ~10 to ~40 GPa (SiO2) and ~5 to 30 GPa (GeO2). The onset of coordination change in network forming structural motifs for a wide range of oxide glasses can be rationalised in terms of the oxygen packing fraction (Wang et al. 2014; Zeidler et al. 2014b; Zeidler and Salmon 2016; Salmon 2018). The upper limit of stability for tetrahedral motifs in both SiO2 and GeO2 glass occurs at and oxygen packing fraction of ~0.58, consistent with random loose packing of hard spheres. The conversion to an octahedral network is largely completed at an oxygen packing fraction of ~0.64 which corresponds to random close packing of hard spheres (Zeidler et al. 2014b). Molecular dynamics simulations reveal that GeO5 and SiO5 units act as important intermediaries on transformation towards an octahedral glass, where the coordination changes primarily from 4 → 5 and 5 → 6 (Wezka et al. 2012; Zeidler et al. 2014a).

86

Drewitt et al.

This is supported by the measured mean O–Ge–O bond angle from NDIS (Wezka et al. 2012) and can be understood in terms of a ‘zipper’ mechanism for ring closure developed for SiO2 glass in which a tetrahedral SiO4 unit belonging to a ring structure forms a new bond with a bridging oxygen within the ring, leading to the formation of a distorted square pyramidal SiO5 unit and a threefold coordinated oxygen atom (Wezka et al. 2012; Zeidler et al. 2014a). This demonstrates a striking interrelation between the changes experienced in SRO and MRO which is underscored by a correlation between the position of the FSDP in S(Q), relative to its position at ambient-p, and the onset of coordination change (Zeidler and Salmon 2016; Salmon 2018). Some studies using in situ XRD (Sato and Funamori 2010), Brillouin spectroscopy (Murakami and Bass 2010) and Kβ′′ x-ray emission spectroscopy (Spiekermann et al. 2019) suggest a plateau in octahedral coordination persisting in SiO2 and GeO2 glass beyond 100 GPa. However, molecular dynamics simulations of both SiO2 and GeO2 glass (Brazhkin et al. 2011) and SiO2 melt (Karki et al. 2007) indicate a continuous increase in coordination number > 6 at 100 GPa. Recent in situ XRD measurements for SiO2 in a DAC up to 172 GPa (Prescher et al. 2017) and in a double-stage large-volume cell to 120 GPa (Kono et al. 2020), as well as GeO2 glass up to 91.7 GPa (Kono et al. 2016), appear to confirm this.

Silicate melt structure at high pressure In situ diffraction measurements of the structure of silicate melts at high p have advanced significantly in the last decade. Exploratory in situ synchrotron XRD measurements of molten silicates were first reported for CaSiO3 and MgSiO3 melts up to 6 GPa using a cubic multi-anvil device (Funamori et al. 2004). In the last decade, the structure of a range of silicate melts have been measured by diffraction using large volume pressure cells at p up to ~10 GPa including forsterite–enstatite (Mg2SiO4–MgSiO3) (Yamada et al. 2007, 2011), albite (NaAlSi3O8) (Yamada et al. 2011), jadeite (NaAlSi2O6) (Sakamaki et al. 2012, 2014a; Wang et al. 2014), fayalite (Fe2SiO4) (Sanloup 2013a), diopside (CaMgSi2O6) (Wang et al. 2014), and basaltic melts (Sakamaki et al. 2013; Crépisson et al. 2014). A compilation of structure, density, and viscosity data of silicate melts at high pressure reveals a reduction in isothermal viscosity of polymerized melts up to ~3–5  GPa where it encounters a turnover to a normal (positive) p-dependence (Schmelzer et al. 2005; Wang et al. 2014). Wang et al. (2014) attribute this viscosity turnover to the tetrahedral packing limit, below which the structure is highly compressible with transformations dominated by changes in network connectivity and the collapse of MRO resulting in a reduction in inter-tetrahedral bond angle, and above which the structural response is dominated by the increase in nearest neighbor atom-atom coordination numbers. Structural measurements of molten fayalite reveal an increase in average Fe–O coordination from 4.8 GPa at ambient-p (Drewitt et al. 2013) to 7.2 at 7.5 GPa (Sanloup et al. 2013a). It is suggested that this rapid increase in Fe coordination is responsible for the higher compressibility of fayalite melt compared to molten Mg-rich San Carlos olivine (Guillot and Sator 2007, Sanloup et al. 2013a). To date, only two studies have been reported for the in situ structure of silicate melts beyond 10 GPa. Both studies utilise the LHDAC combined with synchrotron XRD, with molten basalt reported to lower mantle conditions up to 60 GPa using Yb-fibre laser heating (Sanloup et al. 2013b) and liquid anorthite reported to 32.5 GPa using CO2 laser heating (Drewitt et al. 2015). The measurements of molten basalt reveal an increase in Si–O coordination change from 4 at ambient-p (Drewitt et al. 2013) to 6 at 35 GPa, consistent with the results for pure SiO2 glass discussed above. By normalising the x-ray intensities using an iterative procedure that minimises the unphysical low-r oscillations below the first interatomic bond distance (Eggert et al. 2002) a converged solution for melt density was determined directly from the liquid diffraction measurements. The results reveal that molten basalt experiences a density crossover with the solid mantle and may be gravitationally stable in the deep lower mantle

From Short to Medium Range Order in Glasses and Melts

87

(Sanloup et al. 2013b). In situ density measurements of silicate glasses using x-ray absorption contrast techniques similarly predict the accumulation of Fe-rich silicate melts above the core mantle boundary (Petitgirard et al. 2015, 2017), consistent the formation of a dense basal magma ocean in the Earth’s early mantle (Labrosse et al. 2007).

Al coordination change at high pressure NMR and x-ray spectroscopy measurements of permanently densified aluminosilicate glasses, synthesised from high-p melts (up to 12 GPa) in multi anvil apparatus and recovered to ambient conditions, revealed the development of highly coordinated AlO5 and AlO6 populations occur at far lower pressures than changes observed for Si–O coordination and as such has a greater influence on controlling melt mobility and magmatic processes in the shallow upper mantle (Li et al. 1995; Yarger et al. 1995; Allwardt et al. 2005a,b; Kelsey et al. 2009). It is likely, however, that these early ex situ studies significantly underestimate the population of highly coordinated units recoverable from high-p due to large transient drops in pressure during temperature quench (Stebbins and Bista 2019). Direct in situ synchrotron XRD measurements of Al coordination change in CaAl2O4 and CaAl2Si2O8 (anorthite) glasses to 30 GPa reveal a continuous increase in Al–O coordination reaching an average value of ~6 by 25 GPa (Drewitt et al. 2015). The only reported in situ measurements of Al–O coordination change in a melt at high-p, made for liquid CaAl2Si2O8 to 32.4 GPa using synchrotron XRD in a DAC with CO2 laser heating, reveals the change in local Al structure is comparable to the corresponding glass with an average Al–O coordination of 5 by ~10 GPa and 6 by ~30 GPa (Drewitt et al. 2015). The increase in Al–O coordination from 4-, to 5-, to 6-fold up to 30 GPa measured for molten anorthite is consistent with the results of MD simulations (de Koker 2010; Drewitt et al. 2015). At ambient pressure, chemical ordering dominates in the form of AlO4 and SiO4 tetrahedra. On initial pressurization, the relatively open network structure is compressed and destroyed (Drewitt et al. 2015). This is supported by in situ Raman measurements of the glass which reveal a rapid reduction in the inter-tetrahedral bond angle below 2 GPa (Moulton et al. 2019). The increase in Al–O coordination number increases almost immediately on compression with the formation of AlO5 motifs and increasing fractions of AlO6 units after ~5 GPa (Drewitt et al. 2015). At 10–15 GPa, the fraction of AlO5 units reaches a maximum fraction of ~50% and are increasingly replaced by AlO6 units to become the dominant feature at ≥ 30 GPa (Fig. 25a). These changes in coordination are accompanied by a reduction in NBO fraction to only a few per cent by 10–15 GPa (Drewitt et al. 2015), consistent with Raman spectroscopy measurements which indicate that depolymerized Q2 and Q3 AlO4 units are the first to transform to higher coordination (Muniz et al. 2016). The Si–O coordination number follows a similar behaviour as for pure SiO2 glass. The Ca–O coordination begins to increase immediately on compression, rising continuously to an average value of ~10 at 30 GPa. The increase in highly coordinated Al and Ca units is accompanied by a development in polyhedral connectivity. At 10 GPa, ~95% Ca and 50% Al atoms belong to single large clusters, increasing to 100% Ca and 90% Al atoms by 30 GPa (Fig. 25b). At higher pressures, recent in situ synchrotron XRD measurements of an aluminosilicate glass using a double-stage PE cell suggest the Al–O coordination number remains constant at ~6 up to 110 GPa (Ohira et al. 2019). However, MD simulations indicate a continuous increase in Al–O coordination number in aluminosilicate glasses and melts, approaching values of ~7 at 100 GPa (de Koker 2010; Bajgain et al. 2015; Ghosh and Karki 2018). We note that it is not possible to separate the Si–O and Al–O nearest neighbour contributions in the total pair distribution functions of aluminosilicate glass measured by Ohira et al. (2019). This contrasts with the measurements reported by Drewitt et al. (2015) where the Al–O coordination environment was quantified directly from the measurement of silica-free CaAl2O4 glass.

Drewitt et al.

88

(a) AlOx coordination

ambient

10 GPa

30 GPa

(b) Clustering of edge- and face-sharing AlOx polyhedra

ambient

10 GPa

30 GPa

Figure 25. Snapshots from MD simulations of liquid CaAl2O4 at 2500 K at ambient, 10 GPa, and 30 GPa. (a) AlOx coordination with x = 4 (yellow), 5 (red), 6 (blue), and 7 (brown). (b) clusters of > 100 (blue), 10–100 (red), 5–9 (orange), 2–4 (green), and 1 (yellow) of edge- and face-sharing AlOx polyhedra. Reprinted figure with permission from Drewitt et al. Journal of Physics: Condensed Matter 27:105103 (2015) http://dx.doi.org/10.1088/0953-8984/27/10/105103 Copyright (2015) by the Institute of Physics.

SUMMARY AND FUTURE PERSPECTIVES In this chapter we demonstrate the high complementarity between x-ray or neutron diffraction and Raman spectroscopy techniques for measuring SRO and MRO in geologically relevant silicate and aluminate glasses and their melts. Nevertheless, despite decades of research important questions remain unresolved. For example, the origin of the Boson peak, a ubiquitous feature in Raman spectra of glass, remains a mystery with competing theories invoking both MRO and SRO structure (Greaves and Sen 2007). Secondly, understanding the incorporation of modifier cations into aluminosilicate glasses and melts is important for understanding the viscous behavior of natural melts. While cationic percolation channels appear to be a general feature of MRO in alkali silicates (Greaves 1985; Meyer et al. 2004; Du and Cormack 2004; Cormier and Cuello 2011; Le Losq et al. 2017), more research is needed to elucidate if these cation diffusion channels are a general feature of alkaline-earth and transition-metal aluminosilicate melts and to understand their influence on the dynamic behavior of natural melts. This work will benefit from the further application of element selective diffraction techniques such as NDIS of glasses and their high-T melts (Drewitt et al. 2012, 2017) combined with advanced molecular dynamics simulation techniques (Jahn 2022, this volume). Recent technological developments have facilitated diffraction and spectroscopy measurements of aluminosilicate glasses and their melts to be made in situ under extreme high-T and/or -p conditions experienced in planetary interiors. In situ high pressure measurements of silicate glasses and their germanate analogues have revealed a collapse in MRO associated with ring structures at ambient conditions followed by a development in SRO associated with

From Short to Medium Range Order in Glasses and Melts

89

increasing local coordination number. These changes are intimately linked to magmatic transport properties at depth, with an interplay between their viscosity and compressibility arising from collapsing MRO and subsequent increase in SRO at depth (Wang et al. 2013). There exists a striking interrelation between the destruction of MRO via ring closure events and the development of highly coordinated network forming units at high-p, underscored by the correlation between the relative position of the FSDP in S(Q) measured at high-p and the onset of coordination change (Zeidler and Salmon 2016; Salmon 2018). However, while these measurements have improved our understanding of the structural modifications in simple silicate glasses at high p, much less information is available on other cations. Also, although important, information obtained on glass structure is not always representative of melts in their natural liquid state (Wilding et al. 2010; Drewitt et al. 2012) and as such in situ high-p–T measurements of the melts are highly desirable. The last decade has seen a significant improvement in high-p–T technology and a wide range of in situ measurements of silicate melts have been reported (Kono et al. 2014). Nevertheless, despite these developments only two measurements of the in situ structure of silicate melts have been reported beyond 10 GPa, both utilising the LHDAC and synchrotron XRD (Sanloup et al. 2013b; Drewitt et al. 2015). The next decade is, therefore, likely to see an increase in LHDAC or RHDAC (Louvel et al. 2020) experiments applied to melts assisted by the increased flux and micro/nano focus capabilities of next generation highenergy synchrotron radiation facilities. The LHDAC methods used in XRD studies could also become more routinely adopted for Raman spectroscopy measurements to monitor changes in MRO in aluminosilicate melts at T > 2000 K by applying methods such as Coherent AntiStokes Raman Scattering Microscopy (CARS) (Cheng and Xie 2004; Baer and Yoo 2005) to overcome the deleterious effect of blackbody radiation on the Raman scattering signal. Finally, future developments in PE cell technology could include neutron transparent heating assemblies so that NDIS can be employed at high-p–T to reveal unprecedented resolution of the short and medium range cationic ordering in geological melts at high-p.

ACKNOWLEDGEMENTS We thank Grant Henderson and an anonymous reviewer for their helpful comments on the original manuscript. JD acknowledges funding from NERC (NE/P002951/1) and EPSRC (EP/V001736/1).

REFERENCES Aasland S, McMillan PF (1994) Density-driven liquid–liquid phase separation in the system AI2O3–Y2O3. Nature 369:633–636 Adjaoud O, Steinle-Neumann G, Jahn S (2008) Mg2SiO4 liquid under high pressure from molecular dynamics. Chem Geol 256:185–192 Alderman OLG, Hannon AC, Holland D, Feller S, Lehr G, Vitale AJ, Hoppe U, Zimmerman M, Watenphul A (2013) Lone-pair distribution and plumbite network formation in high lead silicate glass, 80PbO–20SiO2 Phys Chem Chem Phys 15:8506–8519 Alderman OLG, Wilding MC, Tamalonis A, Sendelbach S, Heald SM, Benmore CJ, Johnson CE, Johnson JA, Hah H-Y, Weber JKR (2017a) Iron K-edge x-ray absorption near-edge structure spectroscopy of aerodynamically levitated silicate melts and glasses. Chem Geol 453:169–185 Alderman OLG, Lazareva L, Wilding MC, Benmore CJ, Heald SM, Johnson CE, Johnson JA, Hah H-Y, Sendelbach S, Tamalonis A, Skinner LB, Parise JB, Weber JKR (2017b) Local structural variation with oxygen fugacity in Fe2SiO4+x fayalitic iron silicate melts. Geochim Cosmochim Acta 203:15–36 Allwardt JR, Schmidt BC, Stebbins JF (2004) Structural mechanisms of compression and decompression in highpressure K2Si4O9 glasses: an investigation utilizing Raman and NMR spectroscopy of glasses and crystalline materials. Chem Geol 213:137–151 Allwardt JR, Stebbins JF, Schmidt BC, Frost DJ, Withers AC, Hirschmann MM (2005) Aluminum coordination and the densification of high-pressure aluminosilicate glasses. Am Mineral 90:1218–1222

90

Drewitt et al.

Allwardt JR, Poe BT, Stebbins JF (2005b) The effect of fictive temperature on Al coordination in high-pressure (10 GPa) sodium aluminosilicate glasses. Am Mineral 90:1453–1457 Almeida RM, Santos LF (2015) Raman spectroscopy of glasses. In: Modern Glass Characterisation, Affatigato M (Ed), John Wiley and Sons, USA, p 158–240 Agee CB, Walker D (1988) Static compression and olivine flotation in ultrabasic silicate liquid. J Geophys Res 93:3437–3449 Angell CA (1991) Relaxation in liquids, polymers and plastic crystals—strong/fragile patterns and problems. J NonCryst Solids 131–133:13–31 Angell CA (1995) Formation of glasses from liquids and biopolymers. Science 267:1924–1935 Auzende A-L, Gillot J, Coquet A, Hennet L, Ona-Nguema G, Bonnin D, Esteve I, Roskosz M, Fiquet G (2011) Synthesis of amorphous MgO-rich peridotitic starting material for laser-heated diamond anvil cell experiments— application to iron partitioning in the mantle. High Press Res 31:199–213 Baer BJ, Yoo C-S (2005) Laser heated high density fluids probed by coherent anti-Stokes Raman spectroscopy. Rev Sci Instr 76:013907 Bajgain S, Ghosh DB, Karki BB (2015) Structure and density of basaltic melts at mantle conditions from firstprinciples simulations. Nature Commun 6:8578 Baldini M, Aquilanti G, Mao H-k, Yang W, Shen G, Pascarelli S, Mao WL (2010) High-pressure EXAFS study of vitreous GeO2 up to 44 GPa. 81:024201 Baggioli M, Zaccone A (2019) Universal origin of boson peak vibrational anomalies in ordered crystals and in amorphous materials. Phys Rev Lett 122:145501 Bancroft M, Nesbitt HW, Henderson GS, O’Shaughnessy C, Withers AC, Neuville DR (2018) Lorentzian dominated lineshapes and linewidths for Raman symmetric stretch peaks (800–1200 cm−1) in Qn (n = 1–3) species of alkali silicate glasses/melts. J Non-Cryst Solids 484:72–83 Barnes AC (2015) A comparison of structural models of Tb3Al5O12 and Nd3Al5O12 glasses obtained when using x-ray data alone and when x-ray and neutron data are combined. Z Phys Chem 230:387–415 Barnes AC, Skinner LB, Salmon PS, Bytchkov A, Pozdnyakova I, Farmer TO, Fischer HE (2009) Liquid–liquid phase transition in supercooled yttria–alumina. Phys Rev Lett 103:225702 Barney ER, Hannon AC, Holland D, Winslow D, Rijal B, Affatigato M, Feller SA (2007) Structural studies of lead aluminate glasses. J Non-Cryst Solids 353:1741–1747 Barrio RA, Galeener FL, Martínez E, Elliot RJ (1993) Regular ring dynamics in AX2 tetrahedral glasses. Phys Rev B 48:15672–15689 Bassett WA (2009) Diamond anvil cell, 50th birthday. High Press Res 29:163–186 Bell PM, Mao H-k, Goettel K (1984) Ultrahigh pressure: beyond 2 megabars and the ruby fluorescence scale. Science 226:542–544 Ben Kacem I, Gautron L, Coillot D, Neuville DR (2017) Structure and properties of lead silicate glasses and melts. Chem Geol 461:104–114 Benmore CJ (2015) X-ray diffraction from glass. In: Modern Glass Characterisation, Affatigato M (Ed), John Wiley and Sons, USA, p 241–270 Benmore CJ, Weber JKR (2017) Aerodynamic levitation, supercooled liquids and glass formation. Adv Phys X 2:717–736 Benmore CJ, Weber JKR, Sampath S, Siewenie J, Urquidi J, Tangeman JA (2003) A neutron and x-ray diffraction study of calcium aluminate glasses. J Phys: Condens Matter 15:S2413–S2423 Benmore CJ, Weber JKR, Wilding MC, Du J, Parise JB (2010a) Temperature-dependent structural heterogeneity in calcium silicate liquids. Phys Rev B 82:224202 Benmore CJ, Soignard E, Amin SA, Guthrie M, Shastri SD, Lee PL, Yarger JL (2010b) Structural and topological changes in silica glass at pressure. Phys Rev B 81:054105 Benmore CJ, Soignard E, Guthrie M, Amin SA, Weber JKR, McKiernan K, Wilding MC, Yarger JL (2011) High pressure x-ray diffraction measurements on Mg2SiO4 glass. J Non-Cryst Solids 357:2632–2636 Besson JM, Nelmes RJ, Hamel G, Loveday JS, Weill G, Hull S (1992) Neutron powder diffraction above 10 GPa. Physica B 180–181:907–910 Besson JM, Grima P, Gauthier M, Itié JP, Mézouar M, Häusermann D, Hanfland M (1996) Pretransitional behavior in zincblende HgTe under high pressure and temperature. Phys Stat Sol 198:419–425 Binsted N, Greaves GN, Henderson CMB (1986) Fe K-edge x-ray absorption spectroscopy of silicate minerals and glasses. J Phys Colloques 47:C8-837–840 Bingham PA, Parker JM, Searle TM, Smith I (2007) Local structure and medium range ordering of tetrahedrally coordinated Fe3+ ions in alkali–alkaline earth–silica glasses. J Non-Cryst Solids 353:2479–2494 Bista S, Stebbins JF (2017) The role of modifier cations in network cation coordination increases with pressure in aluminosilicate glasses and melts from 1 to 3 GPa. Am Mineral 102:1657–1666 Brink T, Koch L, Albe K (2016) Structural origins of the boson peak in metals: From high-entropy alloys to metallic glasses. Phys Rev B 94:224203 Boon JA, Fyfe WS (1972) The coordination number of ferrous ions in silicate glasses. Chem Geol 10:287–298

From Short to Medium Range Order in Glasses and Melts

91

Börjesson L, Hassan AK, Swenson J, Torell LM, Fontana A (1993) Is there a correlation between the first sharp diffraction peak and the low frequency vibrational behavior of glasses? Phys Rev Lett 70:1275–1278 Bouhadja M, Jakse N, Pasturel A (2013) Structural and dynamic properties of calcium aluminosilicate melts: a molecular dynamics study. J Chem Phys 138:224510 Bowron DT (2008) An experimentally consistent atomistic structural model of silica glass. Mater Sci Eng B 149:166–170 BrazhkinVV, Lyapin AG, Trachenko K (2011) Atomistic modeling of multiple amorphous-amorphous transitions in SiO2 and GeO2 glasses at megabar pressures. Phys Rev B 83:132103 Bridgman PW, Šimon I (1953) Effects of very high pressures on glass. J Appl Phys 24:405–413 Buchenau U, Prager M, Nücker N, Dianoux AJ, Ahmad N, Phillips WA (1986) Low-frequency modes in vitreous silica. Phys Rev B 34:5665–5673 Buchenau U, Galperin YM, Gurevich VL, Schober HR (1991) Anharmonic potentials and vibrational localization in glasses. Phys Rev B 43:5039 Buchenau U, Galperin YM, Gurevich VL, Parshin DA, Ramos MA, Schober HR (1992) Interaction of soft modes and sound waves in glasses Phys Rev B 46:2798–2808 Burkhard DJM (2000) Iron-bearing silicate glasses at ambient conditions. J Non-Cryst Solids 275:175–188 Calas G, Petiau J (1983) Coordination of iron in oxide glasses through high-resolution K-edge spectra: Information from the pre-edge. Solid State Commun 48:625–629 Caldwell WA, Kunz M, Celestre RS, Domning EE, Walter MJ, Walker D, Glossinger J, MacDowell AA, Padmore HA, Jeanloz R, Clark SM (2007) Laser-heated diamond anvil cell at the advanced light source beamline 12.2.2. Nucl Instr Meth Phys Res A 582:221–225 Champagnon B, Martinet C, Boudeulle M, Vouagner D, Coussa C, Deschamps T, Grosvalet L (2008) High pressure elastic and plastic deformations of silica: In situ diamond anvil cell Raman experiments. J Non-Cryst Solids 354:569–573 Charpentier T, Okhotnikov K, Novikov AN, Hennet L, Fischer HE, Neuville DR, Florian P (2018) Structure of strontium aluminosilicate glasses from molecular dynamics simulation, neutron diffraction, and nuclear magnetic resonance studies. J Phys Chem B 122:9567–9583 Cheng J-X, Xie XS (2004) Coherent anti-Stokes Raman scattering microscopy: instrumentation, theory, and applications. J Phys Chem B 108:827–840 Crichton WA, Mezouar M (2005) Methods and application of the Paris–Edinburgh Press to X-ray diffraction structure solution with large-volume samples at high pressures and temperatures. Chapter 17 In: Advances in HighPressure Technology for Geophysical Applications, Chen J, Wang Y, Duffy TS, Shen G, Dobrzhinetskaya LF (eds) Elsevier, Holland, p 353–369 Chumakov AI, Monaco G, Monaco A, Crichton WA, Bosak A, Rüffer R, Meyer A, Kargl F, Comez L, Fioretto D, Giefers H, Roitsch S, Wortmann G, Manghnani MH, Hushur A, Williams Q, Balogh J, Parliński K, Jochym P, Piekarz P (2011) Equivalence of the Boson Peak in glasses to the transverse acoustic van Hove singularity in crystals. Phys Rev Lett 106:225501 Cicconi MR, de Ligny D, Gallo TM, Neuville DR (2016) Ca neighbors from XANES spectroscopy: a tool to investigate structure, redox and nucleation processes in silicate glasses, melts and crystals. Am Mineral 101:1232–1235 Cicconi MR, McCloy JS, Neuville DR (2022) Non-magmatic glasses. Rev Mineral Geochem 87:965–1014 Cochain B, Neuville DR, Henderson GS, McCammon CA, Pinet O, Richet P (2012) Effects of iron content, redox state and structure of sodium borosilicate glasses: A Raman, Mössbauer and boron K-edge XANES spectroscopy study. J Am Ceram Soc 95:962–971 Cormack AN, Du J (2001) Molecular dynamics simulations of soda–lime silicate glasses. J Non-Cryst Solids 293– 295:283–289 Cormier L (2019) Neutron and X-ray diffraction of glass. In: Handbook of Glass, Musgraves JD, Hu J, Calvez L (eds) Springer Nature, Switzerland pp 1045–1092 Cormier L, Cuello GJ (2011) Mg coordination in a MgSiO3 glass using neutron diffraction coupled with isotopic substitution. Phys Rev B 83:224204 Cormier L, Cuello GJ (2013) Structural investigation of glasses along the MgSiO3–CaSiO3 join: Diffraction studies. Geochim Cosmochim Acta 122:498–510 Cormier L, Neuville DR, Calas G (2000) Structure and properties of low-silica calcium aluminosilicate glasses. J Non-Cryst Solids 274:110–114 Cormier L, Ghaleb D, Neuville DR, Delaye J-M, Calas G (2003) Chemical dependence of network topology of calcium aluminosilicate glasses: a computer simulation study. J Non-Cryst Solids 332:255–270 Coté B, Massiot D, Taulelle F, Coutures J-P (1992) 27Al NMR spectroscopy of aluminosilicate melts and glasses. Chem Geol 96:367–370 Cottrell E, Lanzirotti A, Mysen B, Birner S, Kelley KA, Botcharnikov R, Davis FA, Newville M (2018) A Mössbauer-based XANES calibration for hydrous basalt glasses reveals radiation-induced oxidation of Fe. Am Mineral 103:489–501 Crépisson C, Morard G, Bureau H, Prouteau G, Morizet Y, Petitgirard S, Sanloup C (2014) Magmas trapped at the continental lithosphere-asthenosphere boundary. Earth Planet Sci Lett 393:105–112 Cristiglio V, Cuello GJ, Hennet L, Pozdnyakova I, Leydier M, Kozaily J, Fischer HE, Johnson MR, Price DL (2010) Neutron diffraction study of molten calcium aluminates. J Non-Cryst Solids 356:2492–2496

92

Drewitt et al.

Daniel I, Gillet P, McMillan PF, Richet P (1995) An in situ high-temperature structural study of stable and metastable CaAl2Si2O8 polymorphs. Mineral Mag 59:25–33 Daniel I, McMillan PF, Gillet P, Poe BT (1996) Raman spectroscopic study of structural changes in calcium aluminate (CaAl2O4) glass at high pressure and high temperature. Chem Geol 128:5–15 de Grouchy CJL, Sanloup C, Cochain B, Drewitt JWE, Kono Y, Crépisson C (2017) Lutetium incorporation in magmas at depth: Changes in melt local environment and the influence on partitioning behaviour. Earth Planet Sci Lett 464:155–165 de Koker N (2010) Structure, thermodynamics, and diffusion in CaAl2Si2O8 liquid from first-principles molecular dynamics. Geochim Cosmochim Acta 74:5657–5671 Dewaele A, Loubeyre P, Occelli F, Marie O, Mezouar M (2018) Toroidal diamond anvil cell for detailed measurements under extreme static pressures. Nat Commun 9:2913 Di Genova D, Morgavi D, Hess K-U, Neuville DR, Borovkov N, Perugini D, Dingwell DB (2015) Approximate chemical analysis of volcanic glasses using Raman spectroscopy. J Raman Spectr 46:1235–1244 Di Genova D, Kolzenburg S, Vona A, Chevrel MO, Hess K-U, Neuville DR, Ertel-Ingrisch W, Romano C, Dingwell DB (2016) Raman spectra of Martian glass analogues: A tool to approximate their chemical composition. J Geophys Res Planets 121:740–752 Di Genova D, Vasseur J, Hess K-U, Neuville DR, Dingwell DB (2017) Effect of oxygen fugacity on the glass transition, viscosity and structure of silica- and iron-rich magmatic melts. J Non-Cryst Solids 470:78–85 Di Genova D, Brooker RA, Mader HM, Drewitt JWE, Longo A, Deubener J, Neuville DR, Fanara S, Shebanova O, Anzellini S, Arzilli F, Bamber EC, Hennet L, La Spina G, Miyajima N (2020) In situ observation of nanolite growth in volcanic melt : A driving force for explosive eruptions. Sci Adv 6:eabb0413 Di Muro A, Métrich N, Mercier M, Giordano D, Massare D, Montagnac G (2009) Micro-Raman determination of iron redox state in dry natural glasses: Application to peralkaline rhyolites and basalts. Chem Geol 259:78–88 Dingwell DB, Virgo D (1988) Viscosities of melts in the Na2O–FeO–Fe2O3–SiO2 system and factors controlling relative viscosities of fully polymerized silicate melts. Geochim Cosmochim Acta 52:395–403 Dong J, Yao H, Guo Z, Jia Q, Wang Y, An P, Gong Y, Liang Y, Chen D (2017) Revisiting local structural changes in GeO2 glass at high pressure. J Phys Condens Matter 29:465401 Drewitt JWE, Salmon PS, Barnes AC, Klotz S, Fischer HE, Crichton WA (2010) Structure of GeO2 glass at pressures up to 8.6 GPa. Phys Rev B 81:014202 Drewitt JWE, Jahn S, Cristiglio V, Bytchkov A, Leydier M, Brassamin S, Fischer HE, Hennet L (2011) The structure of liquid calcium aluminates as investigated using neutron and high energy x-ray diffraction in combination with molecular dynamics simulation methods. J Phys Condens Matter 23:155101 Drewitt JWE, Hennet L, Zeidler A, Jahn S, Salmon PS, Neuville DR, Fischer HE (2012) Structural transformations on vitrification in the fragile glass-forming system CaAl2O4. Phys Rev Lett 109:235501 Drewitt JWE, Sanloup C, Bytchkov A, Brassamin S, Hennet L (2013) Structure of (FexCa1-xO)y(SiO2)1-y liquids and glasses from high-energy x-ray diffraction: Implications for the structure of natural basaltic magmas. Phys Rev B 87:224201 Drewitt JWE, Jahn S, Sanloup C, de Grouchy C, Garbarino G, Hennet L (2015) Development of chemical and topological structure in aluminosilicate liquids and glasses at high pressure. J Phys: Condens Matter 27:105103 Drewitt JWE, Barnes AC, Jahn S, Kohn SC, Walter MJ, Novikov AN, Neuville DR, Fischer HE, Hennet L (2017) Structure of liquid tricalcium aluminate. Phys Rev B 95:064203 Drewitt JWE, Jahn S, Hennet L (2019) Configurational constraints on glass formation in the liquid calcium aluminate system. J Stat Mech 104012 Drewitt JWE, Turci F, Heinen BJ, Macleod SG, Qin F, Kleppe AK, Lord OT (2020) Structural ordering in liquid gallium under extreme conditions. Phys Rev Lett 124:145501 Du J, Cormack AN (2004) The medium range structure of sodium silicate glasses: a molecular dynamics simulation. J Non-Cryst Solids 349:66–79 Du J, Corrales R (2007) Understanding lanthanum aluminate glass structure by correlating molecular dynamics simulation results with neutron and x-ray scattering data. J Non-Cryst Solids 353:210–214 Dubrovinskaia N, Dubrovinsky L, Solopova NA, Abakumov A, Turner S, Hanfland M, Bykova E, Bykov M, Prescher C, Prakapenka VB, Petitgirard S, Chuvashova I, Gasharova B, Mathis Y-L, Ershov P, Snigireva I, Snigirev A (2016) Terapascal static pressure generation with ultrahigh yield strength nanodiamond. Science Adv 2:e1600341 Dubrovinsky L, Dubrovinskaia N, Prakapenka VB, Abakumov AM (2012) Implementation of micro-ball nanodiamond anvils for high-pressure studies above 6 Mbar. Nat Commun 3:1163 Dupree R, Howes AP, Kohn SC (1997) Natural abundance solid state 43Ca NMR. Chem Phys Lett 276:399–404 Durben DJ, Wolf GH (1991) Raman spectroscopic study of the pressure-induced coordination change in GeO2 glass. Phys Rev B 43:2355 Duval E, Boukenter A, Champagnon B (1986) Vibration eigenmodes and size of microcrystallites in glass: observation by very-low-frequency Raman scattering. Phys Rev Lett 56:2052–2055 Eckersley MC, Gaskell PH, Barnes AC, Chieux P (1988) Structural ordering in a calcium silicate glass. Nature 335:525–527

From Short to Medium Range Order in Glasses and Melts

93

Eggert JH, Weck G, Loubeyre P, Mezouar M (2002) Quantitative structure factor and density measurements of highpressure fluids in diamond anvil cells by x-ray diffraction: Argon and water. Phys Rev B 65:174105 Elliot S (1991) Medium-range structural order in covalent amorphous solids. Nature 354:445–452 Elliot S (1992) A unified model for the low-energy vibrational behaviour of amorphous solids. Europhys Lett 19:201–206 Elliot SR (1995) Second sharp diffraction peak in the structure factor of binary covalent network glasses. Phys Rev B 51:8599–8601 Faber TE, Ziman JM (1965) A theory of the electrical properties of liquid metals: III. the resistivity of binary alloys. Phil Mag 11:153–173 Farges F, Lefrère Y, Rossano S, Berthereau A, Calas G, Brown Jr GE (2004) The effect of redox state on the local structural environment of iron in silicate glasses: a combined XAFS spectroscopy, molecular dynamics, and bond valence study. J Non-Cryst Solids 344:176–188 Feller S, Lodden G, Riley A, Edwards T, Croskrey J, Schue A, Liss D, Stentz D, Blair S, Kelley M, Smith G, Singleton S, Affatigato M, Holland D, Smith ME, Kamitsos EI, Varsamis CPE, Loannou E (2010) A multispectroscopic structural study of lead silicate glasses over an extended range of compositions. J Non-Cryst Solids 356:304–313 Fischer HE, Barnes AC, Salmon PS (2006) Neutron and x-ray diffraction studies of liquids and glasses. Rep Prog Phys 69:233–299 Florian P, Novikov A, Drewitt JWE, Hennet L, Sarou-Kanian V, Massiot D, Fischer HE, Neuville DR (2018) Structure and dynamics of high-temperature strontium aluminosilicate melts. Phys Chem Chem Phys 20:27865–27877 Fox KE, Furukawa Y, White WB (1982) Transition metal ions in silicate melts. Part 2. Iron in sodium silicate glasses. Phys Chem Glasses 23:169–178 Funamori N, Yamamoto S, Yagi T, Kikegawa T (2004) Exploratory studies of silicate melt structure at high pressures and temperatures by in situ X-ray diffraction. J Geophys Res 109:B03203 Furukawa T, Brawer SA, White WB, (1978) The structure of lead silicate glasses determined by vibrational spectroscopy. J Mater Sci 13:268–282 Galeener FL (1982a) Planar rings in vitreous silica. J Non-Cryst Solids 49:53–62 Galeener FL (1982b) Planar rings in glasses. Solid State Commun 44:1037–1040 Galeener FL, Leadbetter AJ, Stringfellow MW (1983) Comparison of the neutron, Raman, and infrared vibrational spectra of vitreous SiO2, GeO2, and BeF2. Phys Rev B 27:1052–1078 Galoisy L, Calas G, Arrio MA (2001) High-resolution XANES spectra of iron in minerals and glasses: structural information from the pre-edge region. Chem Geol 174:307–319 Gaskell PH, Eckersley MC, Barnes AC, Chieux P (1991) Medium-range order in the cation distribution of a calcium silicate glass. Nature 350:675–677 Gaudio SJ, Sen S, Lesher CE (2008) Pressure-induced structural changes and densification of vitreous MgSiO3. Geochim Cosmochim Acta 72:1222–1230 Gaudio SJ, Lesher CE, Maekawa H, Sen S (2015) Linking high-pressure structure and density of albite liquid near the glass transition. Geochim Cosmochim Acta 157:28–38 Geissberger AE, Galeener FL (1983) Raman studies of vitreous SiO2 versus fictive temperature. Phys Rev B 28:3266–3271 Ghosh DB, Karki BB (2018) First-principles molecular dynamics simulations of anorthite (CaAl2Si2O8) glass at high pressure. Phys Chem Mater 45:575–587 Giordano D, Dingwell DB (2003) The kinetic fragility of natural silicate melts. J Phys: Condens Matter 15:S945 Giordano D, Russell JK (2007) A rheological model for glassforming silicate melts in the systems CAS, MAS, MCAS. J Phys: Condens Matter 19:205148 Giordano D, Russell JK, Dingwell DB (2008) Viscosity of magmatic liquids: A model. Earth Planet Sci Lett.271:123–134 Giuli G, Pratesi G, Cipriani C, Paris E (2002) Iron local structure in tektites and impact glasses by extended x-ray absorption fine structure and high-resolution x-ray absorption near-edge structure spectroscopy. Geochim Cosmochim Acta 66:4347–4353 Giuli G, Paris E, Hess K-U, Dingwell DB, Cicconi MR, Eeckhout SG, Fehr KT, Valenti P (2011) XAS determination of the Fe local environment and oxidation state in phonolite glasses. Am Mineral 96:631–636 Giuli G, Alonso-Mori R, Cicconi MR, Paris E, Glatzel P, Eeckhout SG, Scaillet B (2012) Effect of alkalis on the Fe oxidation state and local environment in peralkaline rhyolitic glasses. Am Mineral 97:468–475 Goldstein M (1969) Viscous liquids and the glass transition: a potential energy barrier picture. J Chem Phys 51:3728–3739 Greaves GN (1985) EXAFS and the structure of glass. J Non-Cryst Solids 71:203–217 Greaves GN, Sen S (2007) Inorganic glasses, glass-forming liquids and amorphizing solids. Adv Phys 56:1–166 Greaves GN, Wilding MC, Fearn S, Langstaff D, Kargl F, Cox S, Van QV, Majérus O, Benmore CJ, Weber R, Martin CM, Hennet L (2008) Detection of first-order liquid/liquid phase transitions in yttrium oxide–aluminum oxide melts. Science 322:566–570 Grigera TS, Martin-Mayer V, Parisi G, Verrocchio P (2003) Phonon interpretation of the ‘boson peak’ in supercooled liquids. Nature 422:289–292 Grimsditch M (1984) Polymorphism in amorphous SiO2. Phys Rev Lett 52:2379–2381 Gross E, Romanova M (1929) Über die Lichtzerstreuung in Quarz und festen amorphen Stoffen, welche die Gruppe SiO2 enthalten. Z Physik 55:744–752

94

Drewitt et al.

Guillot B, Sator N (2007) A computer simulation study of natural silicate melts. Part II: High pressure properties. Geochim Cosmochim Acta 71:4538–4556 Guerette M, Ackerson MR, Thomas J, Yuan F, Watson EB, Walker D, Huang L (2015) Structure and properties of silica glass densified in cold compression and hot compression. Sci Rep 5:15343 Gurevich VL, Parshin DA, Pelous J, Schober HR (1993) Theory of low-energy Raman scattering in glasses. Phys Rev B 48:16318–16331 Guthrie M, Tulk CA, Benmore CJ, Xu J, Yarger JL, Klug DD, Tse JS, Mao H-k, Hemley RJ (2004) Formation and structure of a dense octahedral glass. Phys Rev Lett 93:115502 Hannon AC, Parker JM (2000) The structure of aluminate glasses by neutron diffraction. J Non-Cryst Solids 274:102–109 Hannon AC (2015) Neutron diffraction techniques for structural studies of glasses. In: Modern Glass Characterisation, Affatigato M (Ed), John Wiley and Sons, USA, p 158–240 Hannoyer B, Lenglet M, Dürr J, Cortes R (1992) Spectroscopic evidence of octahedral iron (III) in soda-lime silicate glasses. J Non-Cryst Solids 151:209–216 Hehlen B, Neuville DR (2015) Raman response of network modifier cations in alumino–silicate glasses. J Phys Chem B 119:4093–4098 Hehlen B, Neuville DR (2020) Non network-former cations in oxide glasses spotted by Raman scattering. Phys Chem Chem Phys 22:12724–12731 Hehlen B, Courtens E, Vacher R, Yamanaka A, Kataoka M, Inoue K (2000) Hyper-Raman scattering observation of the Boson peak in vitreous silica. Phys Rev Lett 84:5355–5358 Hehlen B, Courtens E, Yamanaka A, Inoue K (2002) Nature of the Boson peak of silica glasses from hyper-Raman scattering. J Non-Cryst Solids 307–310:87–91 Hemley RJ, Mao HK, Bell PM, Mysen BO (1986) Raman spectroscopy of SiO2 glass at high pressure. 57:747–750 Henderson GS (2005) The structure of silicate melts: a glass perspective. Can Mineral 43:1921–1958 Henderson GS, Stebbins JF (2022) The short-range order (SRO) and structure. Rev Mineral Geochem 87:1–53 Hennet L, Pozdnyakova I, Bytchkov A, Price DL, Greaves GN, Wilding M, Fearn S, Martin CM, Thiaudière D, Bérar J-F, Boudet N, Saboungi M-L (2007) Development of structural order during supercooling of a fragile oxide melt. J Chem Phys 126:074906 Hennet L, Cristiglio V, Kozaily J, Pozdnyakova I, Fischer HE, Bytchkov A, Drewitt JWE, Leydier M, Thiaudière D, Gruner S, Brassamin S, Zanghi D, Cuello GJ, Koza M, Magazù S, Greaves GN, Price DL (2011a) Aerodynamic levitation and laser heating: Applications at synchrotron and neutron sources. Eur Phys J 196:151–165 Hennet L, Pozdnyakova I, Bytchkov A, Drewitt JWE, Kozaily J, Leydier M, Brassamin S, Zanghi D, Fischer HE, Greaves GN, Price DL (2011b) Application of time resolved x-ray diffraction to study the solidification of glassforming melts. High Temp High Press 40:263–270 Hennet L, Drewitt JWE, Neuville DR, Cristiglio V, Kozaily J, Brassamin S, Zanghi D, Fischer HE (2016) Neutron diffraction of calcium aluminosilicate glasses and melts. J Non-Cryst Solids 451:89–93 Hiraoka Y, Nakamura T, Hirata A, Escolar EG, Matsue K, Nishiura Y (2016) Hierarchical structures of amorphous solids characterized by persistent homology. PNAS113:7035–7040 Holland D, Mekki A, Gee IA, McConville CF, Johnson JA, Johnson CE, Appleyard P, Thomas M (1999) The structure of sodium iron silicate glass—a multi-technique approach. J Non-Cryst Solids 253:192–202 Holloway JR, Wood BJ (1988) Simulating the Earth: Experimental Geochemistry. Boston: Unwin Hyman. Hong X, Shen G, Prakapenka VB, Newville M, Rivers ML, Sutton SR (2007) Intermediate states of GeO2 glass under pressures up to 35GPa. Phys Rev B 75:104201 Hong X, Ehm L, Duffy TS (2014) Polyhedral units and network connectivity in GeO2 glass at high pressure: An X-ray total scattering investigation. Appl Phys Lett 105:081904 Hosokawa S, Bérar J-F, Boudet N, Pilgrim W-C, Pusztai L, Hiroi S, Maruyama K, Kohara S, Kato H, Fischer HE, Zeidler A (2019) Partial structure investigation of the traditional bulk metallic glass Pd40Ni40P20. Phys Rev B 100:054204 Huang L, Kieffer J (2004a) Amorphous-amorphous transitions in silica glass. I. Reversible transitions and thermomechanical anomalies. Phys Rev B 69:224203 Huang L, Kieffer J (2004b) Amorphous-amorphous transitions in silica glass. II. Irreversible transitions and densification limit. Phys Rev B 69:224204 Imaoka M, Hasegawa H, Yasui I (1986) X-ray diffraction analysis on the structure of the glasses in the system PbO– SiO2. J Non-Cryst Solids 85:393–412 Itié JP, Calas G, Petiau J, Fontaine A, Tolentino H (1989) Pressure-induced coordination changes in crystalline and vitreous GeO2. Phys Rev Lett 63:398 Ishihara T, Shirakawa Y, Iida T, Kitamura N, Matsukawa M, Ohtori N, Umesaki N (1999) Brillouin scattering in densified GeO2 glasses. Jpn J Appl Phys 38:3062–3065 Inamura Y, Arai M, Nakamura M, Otomo T, Kitamura N, Bennington SM, Hannon AC, Buchenau U (2001) Intermediate range structure and low-energy dynamics of densified vitreous silica. J Non-Cryst Solids 293–295:389–393 Inamura Y, Katayama Y, Utsumi W, Funakoshi K (2004) Transformations in the intermediate-range structure of SiO2 glass under high pressure and temperature. Phys Rev Lett 93:015501

From Short to Medium Range Order in Glasses and Melts

95

Ito E (2007) Multianvil cells and high-pressure experimental methods. In: Treatise on Geophysics: Theory and Practice (second edition), Elsevier, Holland 2:197–230 Iuga D, Morais C, Gan Z, Neuville DR, Cormier L, Massiot D (2005) NMR heteronuclear correlation between quadrupolar nuclei in solids. J Am Chem Soc 127:11540–11541 Iwamoto N, Umesaki N, Atsumi T (1987) EXAFS and x-ray diffraction studies of iron ions in a 0.2(Fe2O3) · 0.8(Na2O · 2SiO2) glass. J Mater Sci Lett 6:271–273 Jackson WE, Mustre de Leon J, Brown Jr GE, Waychunas GA, Conradson SD, Combes J-M (1993) High-temperature XAS study of Fe2SiO4 liquid: reduced coordination of ferrous iron. Science 262:229–233 Jackson WE, Farges F, Yeager M, Mabrouk PA, Rossano S, Waychunas GA, Solomon EI, Brown Jr GE (2005) Multi-spectroscopic study of Fe(II) in silicate glasses: Implications for the coordination environment of Fe(II) in silicate melts. Geochim Cosmochim Acta 69:4315–4332 Jakse N, Bouhadja M, Kozaily J, Drewitt JWE, Hennet L, Neuville DR, Fischer HE, Cristiglio V, Pasturel A (2012) Interplay between non-bridging oxygen, triclusters, and fivefold Al coordination in low silica content calcium aluminosilicate melts. Appl Phys Lett 101:201903 Jahn S (2022) Molecular simulations of oxide and silicate melts and glasses. Rev Mineral Geochem 87:193-227 Johnson JA, Johnson CE, Holland D, Mekki A, Appleyard P, Thomas MF (1999) Transition metal ions in ternary sodium silicate glasses: a Mössbauer and neutron study. J Non-Cryst Solids 246:104–114 Kalampounias AG, Yannopoulos SN, Papatheodorou GN (2006) Temperature-induced structural changes in glassy, supercooled, and molten silica from 77 to 2150 K. J Chem Phys 124:014504 Karki BB, Bhattarai D, Stixrude L (2007) First-principles simulations of liquid silica: Structural and dynamical behavior at high pressure. Phys Rev B 76:104205 Kang E-T, Lee S-J, Hannon AC (2006) Molecular dynamics simulations of calcium aluminate glasses. J Non-Cryst Solids 352:725–736 Kelsey KE, Stebbins JF, Mosenfelder JL, Asimow PD (2009) Simultaneous aluminum, silicon, and sodium coordination changes in 6 GPa sodium aluminosilicate glasses. Am Mineral 94:1205–1215 Keppler H (1992) Crystal field spectra and geochemistry of transition metal ions in silicate melts and glasses. Am Mineral 77:62–75 Kim H, Lee SK (2020) Extent of disorder in iron-bearing albite and anorthite melts: Insights from multi-nuclear (29Si, 27Al, and 17O) solid-state NMR study of iron-bearing NaAlSi3O8 and CaAl2Si2O8 glasses. Chem Geol 538:119498 Kohara S, Suzuya K (2005) Intermediate-range order in vitreous SiO2 and GeO2. J Phys: Condens Matter 17:S77-S86 Kono Y, Sanloup C (Eds.) (2018) Magmas Under Pressure, Elsevier, Holland Kono Y, Park C, Kenney-Benson C, Shen G, Wang Y (2014) Toward comprehensive studies of liquids at high pressures and high temperatures: Combined structure, elastic wave velocity, and viscosity measurements in the Paris–Edinburgh cell. Phys Earth Planet Inter 228:269–280 Kono Y, Kenney-Benson C, Ikuta D, Shibazaki Y, Wang Y, Shen G (2016) Ultrahigh-pressure polyamorphism in GeO2 glass with coordination number > 6. PNAS 113:3436–3441 Kono Y, Shibazaki Y, Kenney-Benson C, Wang Y, Shen G (2018) Pressure-induced structural change in MgSiO3 glass at pressures near the Earth’s core–mantle boundary. PNAS 115:1742–1747 Kono Y, Kenney-Benson C, Shen G (2019) Opposed type double stage cell for Mbar pressure experiment with large sample volume. High Press Res 40:175–183 Kono Y, Shu Y, Kenney-Benson C, Wang Y, Shen G (2020) Structural evolution of SiO2 glass with Si coordination number greater than 6. Phys Rev Lett 125:205701 Kozaily J (2012) Structure and dynamics of calcium aluminosilicate melts. Ph.D. thesis, University of Orléans http:// www.theses.fr/2012ORLE2003/document Klinger MI (2010) Soft atomic motion modes in glasses: Their role in anomalous properties. Phys Rep 492:111–180 Klotz S, Besson JM, Hamel G, Nelmes RJ, Loveday JS, Marshall WG, Wilson RM (1995) Neutron powder diffraction at pressures beyond 25 GPa. Appl Phys Lett 66:1735–1737 Labrosse S, Hernlund JW, Coltice N (2007) A crystallizing dense magma ocean at the base of the Earth’s mantle. Nature 450:866–869 Lacy ED (1963) Aluminium in glasses and melts. Phys Chem Glasses 4:234–238 Laird BB, Schober HR (1991) Localized low-frequency modes in a simple model glass. Phys Rev Lett 66:636–369 Le Losq C, Neuville DR (2013) Effect of Na/K mixing on the structure and rheology of tectosilicate silica-rich melts. Chem Geol 346:57–71 Le Losq C, Neuville DR, Florian P, Henderson GS, Massiot D (2014) The role of Al3+ on rheology and structural changes in sodium silicate and aluminosilicate glasses and melts. Geochim Cosmochim Acta 126:495–517 Le Losq C, Neuville DR, Chen W, Florian P, Massiot D, Zhou Z, Greaves GN (2017) Percolation channels: a universal idea to describe the atomic structure of glasses and melts. Sci Rep 7:16490 Le Losq C, Cicconi MR, Greaves GN, Neuville DR (2019a) Silicate glasses. In: Handbook of Glass, Musgraves JD, Hu J, Calvez L (eds) Springer Nature, Switzerland pp 441–503 Le Losq C, Berry AJ, Kendrick MA, Neuville DR, O’Neill HStC (2019b) Determination of the oxidation state of iron in Mid-Ocean Ridge basalt glasses by Raman spectroscopy. Am Mineral 104:1032–1042

96

Drewitt et al.

Lee SK, Kim EJ (2015) Probing metal-bridging oxygen and configurational disorder in amorphous lead silicates: insights from 17O solid-state nuclear magnetic resonance. J Phys Chem C 119:748–756 Lee SK, Stebbins JF (2003) The distribution of sodium ions in aluminosilicate glasses: a high-field Na-23 MAS and 3Q MAS NMR study. Geochim Cosmochim Acta 67:1699–1709 Le Roux S, Jund P (2010) Ring statistics analysis of topological networks: New approach and application to amorphous GeS2 and SiO2 systems. Comp Mater Sci 49:70–83 Le Roux S, Petkov V (2010) ISAACS—interactive structure analysis of amorphous and crystalline systems. J Appl Cryst 43:181–185 Levelut C, Gaimes N, Terki F, Cohen-Sohal G, Pelous J, Vacher R (1995) Glass-transition temperature: Relation between low-frequency dynamics and medium-range order. Phys Rev B 51:8606–8609 Li D, Secco RA, Bancroft GM, Fleet ME (1995) Pressure induced coordination change of Al in silicate melts from Al K edge XANES of high pressure NaAlSi2O6–NaAlSi3O8 glasses. Geophys Res Lett 22:3111–3114 Li B, Ji C, Yang W, Wang J, Yang K, Xu R, Liu W, Cai Z, Chen J, Mao H-k (2018) Diamond anvil cell behavior up to 4 Mbar. PNAS 115:1713–1717 Licheron M, Montouillout V, Millot F, Neuville DR (2011) Raman and 27Al NMR structure investigations of aluminate glasses: (1-x)Al2O3-x MO, with M=Ca, Sr, Ba and 0.5 < x < 0.75). J Non Cryst Solids 357:2796–2801 Liebermann RC (2011) Multi-anvil, high pressure apparatus: a half-century of development and progress. High Press Res 31:493–532 Liermann H-P, Morgenroth W, Ehnes A, Berghäuser A, Winkler B, Franz H, Weckert E (2010) The Extreme Conditions Beamline at PETRA III, DESY: Possibilities to conduct time resolved monochromatic diffraction experiments in dynamic and laser heated DAC. J Phys: Conf Ser 215:012029 Lin J-F, Fukui H, Prendergast D, Okuchi T, Cai YQ, Hiraoka N, Yoo C-S, Trave A, Eng P, Hu MY, Chow P (2007) Electronic bonding transition in compressed SiO2 glass. Phys Rev B 75:012201 Liu H, Chen W, Pan R, Shan Z, Qiao A, Drewitt JWE, Hennet L, Jahn S, Langstaff DP, Chass GA, Tao H, Yue Y, Greaves GN (2020) From molten calcium aluminates through phase transitions to cement phases. Adv Sci 7:1902209 Louvel M, Drewitt JWE, Ross A, Thwaites R, Heinen BJ, Keeble DS, Beavers CM, Walter MJ, Anzellini S (2020) The HXD95: a modified Bassett-type hydrothermal diamond-anvil cell for in situ XRD experiments up to 5 GPa and 1300 K. J Synchrotron Rad 27:529–537 Mao H-K, Mao WL (2007) Diamond-anvil cells and probes for high P–T mineral physics studies. In: Treatise on Geophysics: Theory and Practice (second edition), Elsevier 2:263–291 Magnien V, Neuville DR, Cormier L, Mysen BO, Briois V, Belin S, Pinet O, Richet P (2004) Kinetics of iron oxidation in silicate melts: A preliminary XANES study. Chem Geol 213:253–263 Magnien V, Neuville DR, Cormier L, Roux J, Hazemann J-L, Pinet O, Richet P (2006) Kinetics of iron redox reactions: A high-temperature X-ray absorption and Raman spectroscopy study. J Nucl Mater 352:190–195 Magnien V, Neuville DR, Cormier L, Roux J, Hazemann J-L, de Ligny D, Pascarelli S, Vickridge I, Pinet O, Richet P (2008) Kinetics and mechanisms of iron redox reactions in silicate melts: The effects of temperature and alkali cations. Geochim Cosmochim Acta 72:2157–2168 Marruzzo A, Schirmacher W, Fratalocchi A, Ruocco G (2013) Heterogeneous shear elasticity of glasses: the origin of the boson peak. Sci Rep 3:1407 Martinet C, Kassir-Bodon A, Deschamps T, Cornet A, Le Floch S, Martinez V, Champagnon B (2015) Permanently densified SiO2 glasses: a structural approach. J Phys: Condens Matter 27:325401 Massiot D, Trumeau D, Touzo B, Farnan I, Rifflet J-C, Douy A, Coutures J-P (1995) Structure and dynamics of CaAl2O4 from liquid to glass: A high-temperature 27Al NMR time-resolved study J Phys Chem 99:16455–16459 Masson O, Thomas P (2013) Exact and explicit expression of the atomic pair distribution function as obtained from X-ray total scattering experiments. J Appl Crystallogr 46:461–465 Matson DW, Sharma SK, Philpotts JA (1983) The structure of high-silica alkali-silicate glasses. A Raman spectroscopic investigation. J Non-Cryst Solids 58:323–352 McCloy JS (2019) Frontiers in natural and un-natural glasses: An interdisciplinary dialogue and review. J Non-Cryst Solids: X 4:100035 McMillan PF (1984) Structural studies of silicate glasses and melts—Applications and limitations of Raman spectroscopy. Am Mineral 69:622–644 McMillan P, Piriou B (1982) The structures and vibrational spectra of crystals and glasses in the silica–alumina system. J Non-Cryst Solids 53:279–298 McMillan P, Piriou B (1983) Raman spectroscopy of calcium aluminate glasses and crystals. J Non-Cryst Solids 55:221–242 McMillan P, Piriou B, Navrotsky A (1982) A Raman spectroscopic study of glasses along the joins silica–calcium aluminate, silica–sodium aluminate, and silica–potassium aluminate. Geochim Cosmochim Acta 46:2021–2037 McMillan PF, Poe BT, Gillet P, Reynard B (1994) A study of SiO2 glass and supercooled liquid to 1950 K via hightemperature Raman spectroscopy. Geochim Cosmochim Acta 58:3653–3664 McMillan PF, Petuskey WT, Cote B, Massiot D, Landron C, Coutures JP (1996) A structural investigation of CaO– Al2O3 glasses via 27Al MAS-NMR. J Non-Cryst Solids 195:261–71

From Short to Medium Range Order in Glasses and Melts

97

Mead RN, Mountjoy G (2006) A molecular dynamics study of the atomic structure of (CaO)x(SiO2)1-x Glasses. J Phys Chem B 110:14273–14278 Meade C, Hemley RJ, Mao HK (1992) High-pressure x-ray diffraction of SiO2 glass. Phys Rev Lett 69:1387 Mei Q, Benmore CJ, Weber JKR (2007) Structure of liquid SiO2: A measurement by high-energy x-ray diffraction. Phys Rev Lett 98:057802 Mei Q, Benmore CJ, Siewenie J, Weber JKR, Wilding M (2008a) Diffraction study of calcium aluminate glasses and melts: I. High energy x-ray and neutron diffraction on glasses around the eutectic composition. J Phys Condens Matter 20:245106 Mei Q, Benmore CJ, Weber JKR, Wilding M, Kim J, Rix J (2008b) Diffraction study of calcium aluminate glasses and melts: II. High energy x-ray diffraction on melts. J Phys Condens Matter 20:245107 Mei Q, Sinogeikin S, Shen G, Amin S, Benmore CJ, Ding K (2010) High-pressure x-ray diffraction measurements on vitreous GeO2 under hydrostatic conditions. Phys Rev B 81:174113 Meng Y, Shen G, Mao H-k (2006) Double-sided laser heating system at HPCAT for in situ x-ray diffraction at high pressures and high temperatures. J Phys: Condens Matter 18:S1097-S1103 Mermet A, Duval E, Etienne S, G’Sell C (1996) Low frequency Raman scattering study of the nanostructure of plastically deformed polymer glasses. J Non-Cryst Solids 196:227–232 Meyer A, Horbach J, Kob W, Kargl F, Schober H (2004) Channel formation and intermediate range order in sodium silicate melts and glasses. Phys Rev Lett 93:027801 Mezouar M, Le Bihan T, Libotte H, Le Godec Y, Häusermann D (1999) Paris Edinburgh large-volume cell coupled with a fast imaging-plate system for structural investigation at high pressure and high temperature. J Synchrotron Rad 6:1115–1119 Mezouar M, Faure P, Crichton W, Rambert N, Sitaud B, Bauchau S, Blattmann G (2002) Multichannel collimator for structural investigation of liquids and amorphous materials at high pressures and temperatures. Rev Sci Instr 73:3570–3574 Morard G, Siebert J, Andrault D, Guignot N, Garbarino G, Guyot F, Antonangeli D (2013) The Earth’s core composition from high pressure density measurements of liquid iron alloys. Earth Planet Sci Lett 373:169–178 Morard G, Nakajima Y, Andrault D, Antonangeli D, Auzende AL, Boulard E, Cervera S, Clark AN, Lord OT, Siebert J, Svitlyk V, Garbarino G, Mezouar M (2017) Structure and density of Fe–C liquid alloys under high pressure. J Geophys Res Solid Earth 122:7813–7823 Morikawa H, Takagi Y, Ohno H (1982) Structural analysis of 2PbO–SiO2 glass. J Non-Cryst Solids 53:173–182 Morikawa H, Marumo F, Koyama T, Yamane M, Oyobe A (1983) Structural analysis of 12CaO.7Al2O3 glass. J NonCryst Solids 56:355–360 Moulton BJA, Henderson GS, Martinet C, Martinez V, Sonneville C, de Ligny D (2019) Structure—longitudinal sound velocity relationships in glassy anorthite (CaAl2Si2O8) up to 20 GPa: An in situ Raman and Brillouin spectroscopy study. Geochim Cosmochim Acta 261:132–144 Mountjoy G, Al-Hasni BM, Storey C (2011) Structural organisation in oxide glasses from molecular dynamics modelling. J Non-Cryst Solids 357:2522–2529 Muniz RF, de Ligny D, Martinet C, Sandrini M, Medina AN, Rohling JH, Baesso ML, Lima SM, Andrade LHC, Guyot Y (2016) In situ structural analysis of calcium aluminosilicate glasses under high pressure. J Phys Condens Matter 28:315402 Murakami M, Bass JD (2010) Spectroscopic evidence for ultrahigh-pressure polymorphism in SiO2 Glass. Phys Rev Lett 104:025504 Mysen BO (2006) The structural behavior of ferric and ferrous iron in aluminosilicate glass near meta-aluminosilicate joins. Geochim Cosmochim Acta 70:2337–2353 Mysen BO, Frantz JD (1992) Raman spectroscopy of silicate melts at magmatic temperatures: Na2O–SiO2, K2O–SiO2 and Li2O–SiO2 binary compositions in the temperature range 25–1475°C, Chem Geol 96:321–332 Mysen BO, Richet P (2005) Silicate Glasses and Melts. Developments in Geochemistry Volume 10, Elsevier, Holland, 1st edition Mysen BO, Richet P (2019) Silicate Glasses and Melts, Elsevier, Holland, 2nd edition Mysen BO, Toplis MJ (2007) Structural behavior of Al3+ in peralkaline, metaluminous, and peraluminous silicate melts and glasses at ambient pressure. Am Mineral 92:933–946 Mysen BO, Seifert FA, Virgo D (1980) Structure and redox equilibria of iron-bearing silicate melts. Am Mineral 65:867–884 Mysen BO, Virgo D, Kushiro I (1981) The structural role of aluminum in silicate melts—a Raman spectroscopic study at 1 atmosphere. Am Mineral 66:678–70 Mysen BO, Finger LW, Virgo D, Seifert FA (1982a) Curve-fitting of Raman spectra of silicate glasses. Am Min 67:686–695 Mysen BO, Virgo D, Seifert FA (1982b) The structure of silicate melts: implications for chemical and physical properties of natural magma. Rev Geophys Space Phys 20:353–383 Mysen BO, Virgo D, Seifert FA (1984) Redox equilibria of iron in alkaline earth silicate melts: relationships between melt structure, oxygen fugacity, temperature and properties of iron-bearing silicate liquids. Am Mineral 69:834–847 Mysen BO, Virgo D, Neumann E-R, Seifert FA (1985) Redox equilibria and the structural states of ferric and ferrous iron in melts in the system CaO–MgO–SiO2–Fe–O: relationships between redox equilibria, melt structure and liquidus phase equilibria. Am Mineral 70:317–331

98

Drewitt et al.

Nagashio K, Kuribayashi K (2002) Spherical yttrium aluminum garnet embedded in a glass matrix. J Am Ceram Soc 85:2353–2358 Nakayama T (2002) Boson peak and terahertz frequency dynamics of vitreous silica. Rep Prog Phys 65:1195–1242 Nayak MT, Desa JAE, Reddy VR, Nayak C, Bhattacharyya D, Jha SN (2019) Structures of silicate glasses with varying sodium and fixed iron contents. J Non-Cryst Solids 509:42–47 Neuville DR (2005) Structure and properties in (Sr,Na) silicate glasses and melts. Phys Chem Glasses 46:112–118 Neuville DR (2006) Viscosity, structure and mixing in (Ca, Na) silicate melts. Chem Geol 229:28–42 Neuville DR, Le Losq C (2022) Link between medium and long-range order and macroscopic properties of silicate glasses and melts. Rev Mineral Geochem 87:105–162 Neuville DR, Mysen BO (1996) Role of aluminum in the silicate network: In situ, high-temperature study of glasses and melts on the join SiO2–NaAlO2. Geochim Cosmochim Acta 60:1727–1737 Neuville DR, Cormier L, Massiot D (2004) Al environment in tectosilicate and peraluminous glasses: A 27Al MQMAS NMR, Raman, and XANES investigation. Geochim Cosmochim Acta 68:5071–5079 Neuville DR, Cormier L, Massiot D (2006) Al coordination and speciation in calcium aluminosilicate glasses: Effects of composition determined by 27Al MQ-MAS NMR and Raman spectroscopy. Chem Geol 229:173–185 Neuville DR, Cormier L, Montouillout V, Massiot D (2007) Local Al site distribution in aluminosilicate glasses by 27 Al MQMAS NMR. J Non-Cryst Solids 353:180–184 Neuville DR, Cormier L, Montouillout V, Florian P, Millot F, Rifflet JC, Massiot D (2008a) Structure of Mg- and Mg/Ca aluminosilicate glasses: 27Al NMR and Raman spectroscopy investigations. Am Mineral 93:1721–1731 Neuville DR, Cormier L, Flank AM, de Ligny D, Roux J, Flank A-M, Lagarde P (2008b) Environments around Al, Si and Ca in aluminate and aluminosilicate melts by x-ray absorption spectroscopy at high temperature. Am Mineral 93:228–234 Neuville DR, Henderson GS, Cormier L, Massiot D (2010) The structure of crystals, glasses, and melts along the CaO–Al2O3 join: Results from Raman, Al L- and K-edge X-ray absorption, and 27Al NMR spectroscopy. Am Mineral 95:1580–1589 Neuville DR, de Ligny D, Henderson GS (2014a) Advances in Raman spectroscopy applied to earth and material sciences. Rev Mineral Geochem 78:509–541 Neuville DR, Hennet L, Florian P, de Ligny D (2014b) In situ high-temperature experiments. Rev Mineral Geochem 78:779–800 Nyrow A, Sternemann C, Wilke M, Gordon RA, Mende K, Yavaş H, Simonelli L, Hiraoka N, Sahle ChJ, Huotari S, Andreozzi GB, Woodland AB, Tolan M, Tse JS (2014) Iron speciation in minerals and glasses probed by M2/3edge X-ray Raman scattering spectroscopy. Contrib Mineral Petrol 167:1012 Novikov VN, Sokolov AP (1991) A correlation between low-energy vibrational spectra and first sharp diffraction peak in chalcogenide glasses. Solid State Commun 77:243–247 Novikov AN, Neuville DR, Hennet L, Gueguen Y, Thiaudière D, Charpentier T, Florian P (2017) Al and Sr environment in tectosilicate glasses and melts: viscosity, Raman and NMR investigation. Chem Geol 461:115–127 Ohira I, Kono Y, Shibazaki Y, Kenney-Benson C, Masuno A, Shen G (2019) Ultrahigh pressure structural changes in a 60 mol.% Al2O3–40 mol.% SiO2 glass. Geochem Perspect Lett 10:41–45 Ohno H, Nagasaki T, Igawa N, Kawamura H (1991) Neutron irradiation effects of PbO–SiO2 glasses. J Nucl Mater 179–181:473–476 Ohtani E, Taulelle F, Angell CA (1985) Al3+ coordination changes in liquid aluminosilicates under pressure. Nature 314:78–81 Ohtani E, Suzuki A, Ando R, Urakawa S, Funakoshi K, Katayama Y (2005) Viscosity and density measurements of melts and glasses at high pressure and temperature by using the multi-anvil apparatus and synchrotron X-ray radiation. Chapter 10 In: Advances in High-Pressure Technology for Geophysical Applications, Chen J, Wang Y, Duffy TS, Shen G, Dobrzhinetskaya LF (eds) Elsevier, Holland, p 195–209 Onodera Y, Kohara S, Salmon PS, Hirata A, Nishiyama N, Kitani S, Zeidler A, Shiga M, Masuno A, Inoue H, Tahara S et al. (2020) Structure and properties of densified silica glass: characterizing the order within disorder. NPG Asia Mater 12:85 O’Shaughnessy C, Henderson GS, Nesbitt HW, Bancroft GM, Neuville DR (2017) Structure-property relations of caesium silicate glasses from room temperature to 1400 K: Implications from density and Raman spectroscopy. Chem Geol 461:82–95 O’Shaughnessy C, Henderson GS, Nesbitt HW, Bancroft GM, Neuville DR (2020) The influence of modifier cations on the Raman stretching modes of Qn species in alkali silicate glasses. J Am Ceram Soc 103:3991–4001 Papatheodorou GN, Kalampounias AG, Yannopoulos (2010) Raman spectroscopy of high temperature melts. Chapter 20 In: Molten Salts and Ionic Liquids: Never the Twain? Gaune-Escard M, Seddon KR (Eds) John Wiley and Sons, Inc. NJ, USA, p 301–340 Parshin DA (1993) Soft potential model and universal properties of glasses. Physica Scripta T49:180–185 Pasquarello A, Car R (1998) Identification of Raman defect lines as signatures of ring structures in vitreous silica. Phys Rev Lett 80:5145–5147 Petitgirard S, Salamat A, Beck P, Weck G, Bouvier P (2014) Strategies for in situ laser heating in the diamond anvil cell at an X-ray diffraction beamline. J Synchrotron Rad 21:89–96 Petitgirard S, Malfait WJ, Sinmyo R, Kupenko I, Hennet L, Harries D, Dane T, Burghammer M, Rubie DC (2015) Fate of MgSiO3 melts at core–mantle boundary conditions. PNAS 112:14186–14190

From Short to Medium Range Order in Glasses and Melts

99

Petitgirard S, Malfait WJ, Journaux B, Collings IE, Jennings ES, Blanchard I, Kantor I, Kurnosov A, Cotte M, Dane T, Burghammer M, Rubie DC (2017) SiO2 glass density to lower-mantle pressures. Phys Rev Lett 119:215701 Phillips JC (1984) Microscopic origin of anomalously narrow Raman lines in network glasses. J Non-Cryst Solids 63:347–355 Poe BT, McMillan PF, Coté B, Massiot D, Coutures J-P (1992) Silica–alumina liquids: in-situ study by hightemperature 27Al NMR spectroscopy and molecular dynamics simulation. J Phys Chem 96:8220–8224 Poe BT, McMillan PF, Coté B, Massiot D, Coutures JP (1993) Magnesium and calcium aluminate liquids: in situ high-temperature 27Al NMR spectroscopy. Science 259:786–788 Poe BT, McMillan PF, Coté B, Massiot D, Coutures J-P (1994) Structure and dynamics in calcium aluminate liquids: high-temperature 27Al NMR and Raman spectroscopy. J Am Ceram Soc 77:1832–1838 Polian A, Grimsditch M (1990) Room-temperature densification of a-SiO2 versus pressure. Phys Rev B 41:6086–6087 Polsky CH, Smith KH, Wolf GH (1999) Effect of pressure on the absolute Raman scattering cross section of SiO2 and GeO2 glasses. J Non-Cryst Solids 248:159–168 Prescher C, Prakapenka VB, Stefanski J, Jahn S, Skinner LB, Wang Y (2017) Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures. PNAS 114:10041–10046 Price DL (1996) Intermediate-range order in glasses. Curr Opin Solid State Mater Sci 1:572–577 Price DL (2010) High-Temperature Levitated Materials. Cambridge University Press Price DL, Moss SC, Reijers R, Saboungi M-L, Susman S (1989) Intermediate-range order in glasses and liquids. J Phys: Condens Matter 1:1005–1008 Rahmani A, Benoit M, Benoit C (2003) Signature of small rings in the Raman spectra of normal and compressed amorphous silica: A combined classical and ab initio study. Phys Rev B 68:184202 Richet P (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 Richet P, Gillet P, Pierre A, Bouhifd MA, Daniel I, Fiquet G (1993) Raman spectroscopy, x-ray diffraction, and phase relationship determinations with a versatile heating cell for measurements up to 3600 K (or 2700 K in air). J Appl Phys 74:5451–5456 Rigden SM, Ahrens TJ, Stolper EM (1984) Densities of liquid silicates at high pressures. Science 226:1071–1074 Roskosz M, Toplis MJ, Neuville DR, Mysen BO (2008) Quantification of the kinetics of iron oxidation in silicate melts using Raman spectroscopy and assessment of the role of oxygen diffusion. Am Mineral 93:1749–1759 Rossano S, Mysen B (2012) Raman spectroscopy of silicate glasses and melts in geological systems. In: Raman spectroscopy applied to Earth sciences and cultural heritage, Dubessy J, Caumon M-C, Rull F (eds) EMU Notes Mineral 12:321–366 Rossano S, Balan E, Morin G, Bauer J-P, Calas G, Brouder C (1999) 57Fe Mössbauer spectroscopy of tektites. Phys Chem Mineral 26:530–538 Rossano S, Ramos A, Delaye J-M, Creux S, Filippono A, Brouder C, Calas G (2000a) EXAFS and molecular dynamics combined study of CaO−FeO−2SiO2 glass. New insight into site significance in silicate glasses. Europhys Lett 49:597–602 Rossano S, Ramos AY, Delaye J-M (2000b) Environment of ferrous iron in CaFeSi2O6 glass; contributions of EXAFS and molecular dynamics. J Non-Cryst Solids 273:48–52 Rouxel T, Ji H, Hammouda T, Moréac A (2008) Poisson’s Ratio and the densification of glass under high pressure. Phys Rev Lett 100:225501 Rull F (2012) The Raman effect and the vibrational dynamics of molecules and crystalline solids. In: Raman spectroscopy applied to Earth sciences and cultural heritage, Dubessy J, Caumon M-C, Rull F (eds) EMU Notes Mineral 12:1–60 Sakamaki T, Wang Y, Park C, Yu T, Shen G (2012) Structure of Jadeite Melt at High Pressures up to 4.9 GPa. J Appl Phys 111:112623 Sakamaki T, Suzuki A, Ohtani E, Terasaki H, Urakawa S, Katayama Y, Funakoshi K-I, Wang Y, Hernlund JW, Ballmer MD (2013) Ponded melt at the boundary between the lithosphere and asthenosphere. Nat Geosci 6:1041 Sakamaki T, Wang Y, Park C, Yu T, Shen G (2014a) Contrasting behavior of intermediate-range order structures in jadeite glass and melt. Phys Earth Planet Inter 228:281–286 Sakamaki T, Kono Y, Wang Y, Park C, Yu T, Jing Z, Shen G (2014b) Contrasting sound velocity and intermediaterange structural order between polymerized and depolymerized silicate glasses under pressure. Earth Planet Sci Lett 391:288–295 Salmon PS (1994) Real space manifestation of the first sharp diffraction peak in the structure factor of liquid and glassy materials. Proc R Soc Lond A 445:351–365 Salmon PS (2018) Densification mechanisms of oxide glasses and melts. Chapter 13 In: Magmas Under Pressure, Kono Y, Sanloup C (Eds.), Elsevier, Holland, p 343–369 Salmon PS, Zeidler A (2013) Identifying and characterizing the different structural length scales in liquids and glasses: an experimental approach. Phys Chem Chem Phys 15:15286 Salmon PS, Zeidler A (2015) Networks under pressure: the development of in situ high-pressure neutron diffraction for glassy and liquid materials. J Phys: Condens Matter 27:133201 Salmon PS, Martin RA, Mason PE, Cuello GJ (2005) Topological versus chemical ordering in network glasses at intermediate and extended length scales. Nature 435:75–78

100

Drewitt et al.

Salmon PS, Barnes AC, Martin RA, Cuello GJ (2006) Glass fragility and atomic ordering on the intermediate and extended range. Phys Rev Lett 96:235502 Salmon PS, Drewitt JWE, Whittaker DAJ, Zeidler A, Wezka K, Bull CL, Tucker MG, Wilding MC, Guthrie M, Marrocchelli D (2012) Density-driven structural transformations in network forming glasses: a high-pressure neutron diffraction study of GeO2 glass up to 17.5 GPa. J Phys: Condens Matter 24:439601 Salmon PS, Moody GS, Ishii Y, Pizzey KJ, Polidori A, Salanne M, Zeidler A, Buscemi M, Fischer HE, Bull CL, Klotz S, Weber R, Benmore CJ, Macleod SG (2019) Pressure induced structural transformations in amorphous MgSiO3 and CaSiO3. J Non-Cryst Solids: X 3:100024 Sampath S, Benmore CJ, Lantzky KM, Neuefeind J, Leinenweber K, Price DL, Yarger JL (2003) Intermediate-range order in permanently densified GeO2 Glass. Phys Rev Lett 90:115502 Sanloup C, Drewitt JWE, Crépisson C, Kono Y, Park C, McCammon C, Hennet L, Brassamin S, Bytchkov A (2013a) Structure and density of molten fayalite at high pressure. Geochim Cosmochim Acta 118:118–128 Sanloup C, Drewitt JWE, Konopkova Z, Dalladay-Simpson P, Morton DM, Rai N, van Westrenen W, Morgenroth W (2013b) Structural change in molten basalt at deep mantle conditions. Nature 503:104–107 Sarnthein J, Pasquarello A, Car R (1997) Origin of the High-Frequency Doublet in the Vibrational Spectrum of Vitreous SiO2. Science 275:1925–1927 Sato T, Funamori N (2008) Sixfold-coordinated amorphous polymorph of SiO2 under high pressure. Phys Rev Lett 101:255502 Sato T, Funamori N (2010) High-pressure structural transformation of SiO2 glass up to 100 GPa. Phys Rev B 82:184102 Schirmacher W (2013) The boson peak. Physica Status Solidi (b) 250:937–253 Schirmacher W, Ruocco G, Scopigno T (2007) Acoustic attenuation in glasses and its relation with the boson peak. Phys Rev Lett 98:025501 Schirmacher W, Scopigno T, Ruocco G (2015) Theory of vibrational anomalies in glasses. J Non-Cryst Solids 407:133–140 Schmelzer JWP, Zanotto ED, Fokin VM (2005) Pressure dependence of viscosity. J Chem Phys 112:074511 Sears VF (1992) Neutron scattering lengths and cross sections. Neutron News 3:26–37 Seifert F, Mysen BO, Virgo D (1982) 3-dimensional network structure of quenched melts (glass) in the systems SiO2– NaAlO2, SiO2–CaAl2O4 and SiO2–MgAl2O4. Am Mineral 67:696–717 Shannon RD (1976) Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst A32:751–767 Sharma SK, Mammone JF, Nicol MF (1981) Raman investigation of ring configurations in vitreous silica. Nature 292:140–141 Shen G, Rivers ML, Wang Y, Sutton SR (2001) Laser heated diamond cell system at the Advanced Photon Source for in situ x-ray measurements at high pressure and temperature. Rev Sci Instr 72:1273–1282 Shen G, Prakapenka VB, Rivers ML, Sutton SR (2003) Structural investigation of amorphous materials at high pressures using the diamond anvil cell. Rev Sci Instr 74:3021–3026 Shen GY, Prakapenka VB, Rivers ML, Sutton SR (2004) Structure of liquid iron at pressures up to 58 GPa. Phys Rev Lett 92:185701 Shen G, Mei Q, Prakapenka VB, Lazor P, Sinogeikin S, Meng Y, Park C (2011) Effect of helium on structure and compression behavior of SiO2 glass. PNAS 108:6004–6007 Shi Y, Neuefeind J, Ma D, Page K, Lambersona LA, Smith NJ, Tandia A, Song AP (2019) Ring size distribution in silicate glasses revealed by neutron scattering first sharp diffraction peak analysis. J Non-Cryst Solids 516:71–81 Shi C, Alderman OLG, Berman D, Du J, Neuefeind J, Tamalonis A, Weber JKR, You J, Benmore CJ (2019) The structure of amorphous and deeply supercooled liquid alumina. Front Mater 6:38 Shibazaki Y, Kono Y, Shen G (2019) Compressed glassy carbon maintaining graphite-like structure with linkage formation between graphene layers. Sci Rep 9:7531 Skinner LB, Barnes AC, Salmon PS, Crichton WA (2008) Phase separation, crystallization and polyamorphism in the Y2O3–Al2O3 system. J Phys: Condens Matter 20:205103 Skinner LB, Benmore CJ, Weber JKR, Tumber S, Lazareva L, Neuefeind J, Santodonato L, Du J, Parise JB (2012a) Structure of molten CaSiO3: Neutron diffraction isotope substitution with aerodynamic levitation and molecular dynamics study. J Phys Chem B 116:13439–13447 Skinner LB, Barnes AC, Salmon PS, Fischer HE, Drewitt JWE, Honkimäki V (2012b) Structure and triclustering in Ba-Al–O glass. Physical Review B 85:064201 Skinner LB, Benmore CJ, Weber JKR, Wilding MC, Tumber SK, Parise JB (2013a) A time resolved high energy x-ray diffraction study of cooling liquid SiO2. Phys Chem Chem Phys 15:8566–8572 Skinner LB, Barnes AC, Salmon PS, Hennet L, Fischer HE, Benmore CJ, Kohara S, Weber JKR, Bytchkov A, Wilding MC, Parise JB, Farmer TO, Pozdnyakova I, Tumber SK, Ohara K (2013b) Joint diffraction and modelling approach to the structure of liquid alumina. Phys Rev B 87:024201 Soignard E, Benmore CJ, Yarger JL (2010) A perforated diamond anvil cell for high-energy x-ray diffraction of liquids and amorphous solids at high pressure. Rev Sci Instr 81:035110

From Short to Medium Range Order in Glasses and Melts

101

Sokolov AP (1999) Vibrations at the boson peak: random- and coherent-phase contributions. J Phys:Condens Matter 11:A213–A218 Sokolov AP, Kisliuk A, Soltwisch M, Quitmann D (1992) Medium-range order in glasses: comparison of Raman and diffraction measurements. Phys Rev Lett 69:1540–1543 Spiekermann, G, Steele-MacInnis, M, Kowalski PM, Schmidt C, Jahn S (2013) Vibrational properties of silica species in MgO–SiO2 glasses obtained from ab initio molecular dynamics. Chem Geol 346:22–33 Spiekermann G, Harder M, Gilmore K, Zalden P, Sahle CJ, Petitgirard S, Wilke M, Biedermann N, Weis C, Morgenroth W, Tse JS, Kulik E, Nishiyama N, Yavaş H, Sternemann C (2019) Persistent octahedral coordination in amorphous GeO2 Up to 100 GPa by Kβ′′ X-Ray Emission Spectroscopy. Phys Rev X 9:011025 Stavrou E, Tsiantos C, Tsopouridou RD, Kripotou S, Kontos AG, Raptis C, Capoen B, Bouazaoui M, Turrell S, Khatir S (2010) Raman scattering boson peak and differential scanning calorimetry studies of the glass transition in tellurium–zinc oxide glasses. J Phys: Condens Matter 22:195103 Stebbins JF (1991) NMR evidence for five-coordinated silicon in a silicate glass at atmospheric pressure. Nature 351:638–639 Stebbins JF, Bista S (2019) Pentacoordinated and hexacoordinated silicon cations in a potassiumsilicate glass: Effects of pressure and temperature. J Non-Cryst Solids 505:234–240 Stebbins JF, McMillan P (1989) Five- and six-coordinated Si in K2Si4O9 glass quenched from 1.9 GPa and 1200 °C. Am Mineral 74:965–968 Stebbins JF, Poe BT (1999) Pentacoordinate silicon in high-pressure crystalline and glassy phases of calcium disilicate (CaSi2O5). Geophys Res Lett 26:2521–2523 Stebbins JF, Xu Z (1997) NMR evidence for excess non-bridging oxygen in an aluminosilicate glass. Nature 390:60–62 Stebbins JF, Oglesby JV, Xu Z (1997) Disorder among network-modifier cations in silicate glasses: New constraints from triple-quantum 17O NMR. Am Mineral 82:1116–1124 Stebbins JF, Oglesby JV, Kroeker S (2001) Oxygen triclusters in crystalline CaAl4O7 (grossite) and in calcium aluminosilicate glasses: 17O NMR. Am Mineral 86:1307–1311 Stolper E, Walker D, Hager BH, Hays JF (1981) Melt segregation from partially molten source regions: the importance of melt density and source region size. J Geophys Res 86:6261–6271 Sun K-H (1947) Fundamental condition of glass formation. J Am Ceram Soc 30:277–281 Susman S, Volin KJ, Price DL, Grimsditch M, Rino JP, Kalia RK, Vashishta P, Gwanmesia G, Wang Y, Liebermann RC (1991) Intermediate-range order in permanently densified vitreous SiO2. A neutron-diffraction and moleculardynamics study. Phys Rev B 43:1194–1197 Takaishi T, Takahashi M, Jin J, Uchino T, Yoko T, Takahashi M (2005) Structural study on PbO–SiO2 glasses by x-ray and neutron diffraction and 29Si MAS NMR measurements. J Am Ceram Soc 88:1591–1596 Takahashi Y, Osada M, Masai H, Fujiwara T (2009) Crystallization and nanometric heterogeneity in glass: In situ observation of the boson peak during crystallization. Phys Rev B 79:214204 Tangeman JA, Philips BL, Nordine PC, Weber JKR (2004) Thermodynamics and structure of single- and two-phase yttria–alumina glasses. J Phys Chem B 108:10663–10671 Taraskin SN, Elliott SR (1997) Nature of vibrational excitations in vitreous silica. Phys Rev B 56:8605–8622 Taraskin SN, Elliot SR (1999) Low-frequency vibrational excitations in vitreous silica: the Ioffe–Regel limit. J Phys Condens Matter 11:A219–A227 Taraskin SN, Loh YH, Nataranjan G, Elliott S (2001) Origin of the boson peak in systems with lattice disorder. Phys Rev Lett 86:1255–1261 Thomas BWM, Mead RN, Mountjoy G (2006) A molecular dynamics study of the atomic structure of (CaO)x(Al2O3)1−x glass with x = 0.625 close to the eutectic. J Phys: Condens Matter 18:4697–4708 Tomoshige N, Mizuno H, Mori T, Kim K, Matubayasi N (2019) Boson peak, elasticity, and glass transition temperature in polymer glasses: Effects of the rigidity of chain bending. Sci Rep 9:19514 Toplis MJ, Dingwell DB, Lenci T (1997) Peraluminous viscosity maxima in Na2O–Al2O3–SiO2 liquids: The role of triclusters in tectosilicate melts. Geochim Cosmochim Acta 61:2605–2612 Toplis MJ, Kohn SC, Smith ME, Poplett IJF (2000) Fivefold-coordinated aluminum in tectosilicate glasses observed by triple quantum MAS NMR. Am Mineral 85:1556–1560 Trachenko K, Dove MT (2002) Densification of silica glass under pressure. J Phys: Condens Matter 14:7449 Umari P, Pasquarello A (2002) Modeling of the Raman spectrum of vitreous silica: concentration of small ring structures. Physica B 316–317:572–574 Umari P, Gonze X, Pasquarello A (2003) Concentration of small ring structures in vitreous silica from a first-principles analysis of the Raman spectrum. Phys Rev Lett 90:02741 Vaccari M, Aquilanti G, Pascarelli S, Mathon O (2009) A new EXAFS investigation of local structural changes in amorphous and crystalline GeO2 at high pressure. J Phys Condens Matter 21:145403 Virgo D, Mysen BO (1985) The structural state of iron in oxidized vs. reduced glasses at 1 atm: A 57Fe Mössbauer study. Phys Chem Min 12:65–76 Waasmaier D, Kirfel A (1995) New analytical scattering-factor functions for free atoms and ions. Acta Cryst. A51: 416–431

102

Drewitt et al.

Wang Z, Cooney TF, Sharma SK (1993) High temperature structural investigation of Na2O·0.5Fe2O3·3SiO2 and Na2O·FeO·3SiO2 melts and glasses. Contrib Mineral Pet 115:112–122 Wang Z, Cooney TF, Sharma SK (1995) In situ structural investigation of iron-containing silicate liquids and glasses. Geochim Cosmochim Acta 59:1571–1577 Wang Y, Sakamaki T, Skinner LB, Jing Z, Yu T, Kono Y, Park C, Shen G, Rivers ML, Sutton SR (2014) Atomistic insight into viscosity and density of silicate melts under pressure. Nature Commun 5:3241 Wang Y, Hong L, Wang Y, Schirmacher W, Zhang J (2018) Disentangling boson peaks and Van Hove singularities in a model glass. Phys Rev B 98:174207 Warren BE (1934a) Identification of crystalline substances by means of x-rays. J Am Ceram Soc 17:73–77 Warren BE (1934b) The diffraction of x-rays in glass. Phys Rev B 45:657–661 Warren BE (1934c) X-ray determination of the structure of glass. J Am Ceram Soc 17:249–254 Warren BE, Krutter H, Morningstar O (1936) Fourier analysis of x-ray patterns of vitreous SiO2 and B2O3. J Am Ceram Soc 19:202–206 Waseda Y, Toguri JM (1978) The structure of the molten FeO–SiO2 system. Metall Trans B 9:595–601 Waseda Y, Shiraishi Y, Toguri JM (1980) The structure of the molten FeO–Fe2O3–SiO2 system by X-ray diffraction. Trans Jpn Inst Met 21:51–62 Watanuki T, Shimomura O, Yagi T, Kondo T, Isshiki M (2001) Construction of laser-heated diamond anvil cell system for in situ x-ray diffraction study at SPring-8. Rev Sci Instr 72:1289–1292 Waychunas GA, Brown Jr GE, Ponader CW, Jackson WE (1988) Evidence from X-ray absorption for networkforming Fe2+ in molten alkali silicates. Nature 332:251–253 Weber JKR, Benmore CJ, Tangeman JA, Siewenie J, Hiera KJ (2003) Structure of binary CaO–Al2O3 and SrO–Al2O3 liquids by combined levitation-neutron diffraction. J Neutron Res 11:113–121 Weber JKR, Abadie JG, Hixson AD, Nordine PC, Jerman GA (2004a) Glass formation and polyamorphism in rareearth oxide–aluminum oxide compositions. J Am Ceram Soc 83:1868–1872 Weber JKR, Benmore CJ, Siewenie J, Urquidi J, Key TS (2004b) Structure and bonding in single- and two-phase alumina-based glasses. Phys Chem Chem Phys 6:2480–2483 Weigel C, Cormier L, Galoisy L, Calas G (2006) Determination of  Fe3+  sites in a NaFeSi2O6 glass by neutron diffraction with isotopic substitution coupled with numerical simulation. Appl Phys Lett 89:141911 Weigel C, Cormier L, Calas G, Galoisy L, Bowron DT (2008a) Intermediate-range order in the silicate network glasses NaFexAl1−xSi2O6 (x = 0:0.5:0.8:1): A neutron diffraction and empirical potential structure refinement modeling investigation. Phys Rev B 78:064202 Weigel C, Cormier L, Calas G, Galoisy L, Bowron DT (2008b) Nature and distribution of iron sites in a sodium silicate glass investigated by neutron diffraction and EPSR simulation. J Non-Cryst Solids 354:5378–5385 Wilding M, Bingham PA, Wilson M, Kono Y, Drewitt JWE, Brooker RA, Parise JB (2019) CO3+1 network formation in ultra-high pressure carbonate liquids. Sci Rep 9:15416 Wezka K, Salmon PS, Zeidler A, Whittaker DAJ, Drewitt JWE, Klotz S, Fischer HE, Marrocchelli D (2012) Mechanisms of network collapse in GeO2 glass: high-pressure neutron diffraction with isotope substitution as arbitrator of competing models. J Phys: Condens Matter 24:502101 Wilding MC, McMillan PF, Navrotsky A (2002) Thermodynamic and structural aspects of the polyamorphic transition in yttrium and other rare-earth aluminate liquids. Physica A 314:379–390 Wilding MC, Wilson M, McMillan PF (2005) X-ray and neutron diffraction studies and MD simulation of atomic configurations in polyamorphic Y2O3–Al2O3 systems. Phil Trans R Soc A 363:589–607 Wilding MC, Benmore CJ, Weber JKR (2010) Changes in the local environment surrounding magnesium ions in fragile MgO–SiO2 liquids. Europhys Lett 89:26005 Wilding MC, Wilson M, McMillan PF, Benmore CJ, Weber JKR, Deschamps T, Champagnon B (2015) Structural properties of Y2O3–Al2O3 liquids and glasses: An overview. J Non-Cryst Solids 407:228–234 Wilke M (2005) Fe in magma—An overview. Ann Geophys 48:609–617 Wilke M, Farges F, Petit P-E, Brown GE, Martin F (2001) Oxidation state and coordination of Fe in minerals: An Fe K-XANES spectroscopic study. Am Mineral 86:714–730 Wilke M, Partzsch GM, Bernhardt R, Lattard D (2004) Determination of the iron oxidation state in basaltic glasses using XANES at the K-edge. Chem Geol 213:71–87 Wilke M, Farges F, Partzsch GM, Schmidt C, Behrens H (2007) Speciation of Fe in silicate glasses and melts by insitu XANES spectroscopy. Am Mineral 92:44–56 Wilson M, McMillan PF (2004) Interpretation of x-ray and neutron diffraction patterns for liquid and amorphous yttrium and lanthanum aluminum oxides from computer simulation. Phys Rev B 69:054206 Williams Q, Jeanloz R (1988) Spectroscopic evidence for pressure-induced coordination changes in silicate glasses and melts. Science 239:902–905 Worrell CA, Henshall T (1978) Vibrational spectroscopic studies of some lead silicate glasses. J Non-Cryst Solids 29:283–299 Wright AC, Clarke SJ, Howard CK, Bingham PA, Forder SD, Holland D, Martlew D, Fischer HE (2014) The environment of Fe2+/Fe3+ cations in a soda–lime–silica glass. Phys Chem Glasses: Eur J Glass Sci Technol B 55:243–252

From Short to Medium Range Order in Glasses and Melts

103

Wu Z, Bonnin-Mosbah M, Duraud JP, Métrich N, Delaney JS (1999) XANES studies of Fe-bearing glasses. J Synchrotron Rad 6:344–346 Xue X, Kanzaki M, Trønnes RG, Stebbins JF (1989) Silicon coordination and speciation changes in a silicate liquid at high pressures. Science 245:962–964 Xue X, Stebbins JF, Kanzaki M, McMillan PF, Poe B (1991) Pressure-induced silicon coordination and tetrahedral structural changes in alkali oxide–silica melts up to 12 GPa: NMR, Raman, and infrared spectroscopy. Am Mineral 76:8–26 Yamada A, Inoue T, Urakawa S, Funakoshi K-I, Funamori N, Kikegawa T, Ohfuji H, Irifune T (2007) In situ X-ray experiment on the structure of hydrous Mg-silicate melt under high pressure and high temperature. Geophys Res Lett 34:L10303 Yamada A, Wang Y, Inoue T, Yang W, Park C, Yu T, Shen G (2011) High-pressure x-ray diffraction studies on the structure of liquid silicate using a Paris–Edinburgh type large volume press. Rev Sci Instr 82:015103 Yarger JL, Smith KH, Nieman RA, Diefenbacher J, Wolf GH, Poe BT, McMillan PF (1995) Al coordination changes in high-pressure aluminosilicate liquids. Science 270:1964–1967 Zachariasen WH (1932) The atomic arrangement in glass. J Am Chem Soc 54:3841–3851 Zahra AM, Zahra CY, Piriou B (1993) DSC and Raman studies of lead borate and lead silicate glasses. J Non-Cryst Solids 155:45–55 Zeidler A, Salmon PS (2016) Pressure-driven transformation of the ordering in amorphous network-forming materials. Phys Rev B 93:214204 Zeidler A, Drewitt JWE, Salmon PS, Barnes AC, Crichton WA, Klotz S, Fischer HE, Benmore CJ, Ramos S, Hannon AC (2009) Establishing the structure of GeS2 at high pressures and temperatures: a combined approach using x-ray and neutron diffraction. J Phys: Condens Matter 21:474217 Zeidler A, Wezka K, Rowlands RF, Whittaker DAJ, Salmon PS, Polidori A, Drewitt JWE, Klotz S, Fischer HE, Wilding MC, Bull CL, Tucker MG, Wilson M (2014a) High-pressure transformation of SiO2 glass from a tetrahedral to an octahedral network: a joint approach using neutron diffraction and molecular dynamics. Phys Rev Lett 113:135501 Zeidler A, Salmon PS, Skinner LB (2014b) Packing and the structural transformations in liquid and amorphous oxides from ambient to extreme conditions. PNAS 111:10045–10048 Zha C-s, Hemley RJ, Mao H-k, Duffy TS, Meade C (1994) Acoustic velocities and refractive index of SiO2 glass to 57.5 GPa by Brillouin scattering. Phys Rev B 50:13105–13112 Zhai S, Ito E (2011) Recent advances of high-pressure generation in a multianvil apparatus using sintered diamond anvils. Geosci Front 2:101–106 Zhang HL, Hirschmann MM, Cottrell E, Newville M, Lanzirotti A (2016) Structural environment of iron and accurate determination of Fe3+/ΣFe ratios in andesitic glasses by XANES and Mössbauer spectroscopy. Chem Geol 428:48–58 Zhang HL, Cottrell E, Solheid PA, Kelley KA, Hirschmann MM (2018) Determination of Fe3+/ΣFe of XANES basaltic glass standards by Mössbauer spectroscopy and its application to the oxidation state of iron in MORB. Chem Geol 479:166–175

3

Reviews in Mineralogy & Geochemistry Vol. 87 pp. 105-162, 2022 Copyright © Mineralogical Society of America

Link between Medium and Long-range Order and Macroscopic Properties of Silicate Glasses and Melts Daniel R. Neuville and Charles Le Losq Géomatériaux, Institut de physique du globe de Paris CNRS, Université de Paris Cité Paris, France [email protected] [email protected]

INTRODUCTION The two first chapters of this volume focus on the structure of magmas at different scales: short and medium range order. A quick review of the glass literature, from the 90’s or older, reveals that most published papers focused on the structure of glasses, or on properties of glasses or melts. Depending on their original discipline, the work of the scientific community in those areas are different. Physicists published papers on glass structure, including the structure of SiO2, GeO2, B2O3 as seen by X-ray or neutron diffraction and Raman spectroscopy for example (Galeener et al. 1983; Wright 1990; Gaskell et al. 1991). Chemists worked on more complex glass compositions, like chalcogenide (Poulain and Lucas 1970; Poulain 1983), or focused their work on specific properties of glasses like refractive index, density or the oxidation state of multivalent elements (Schreiber 1986). Earth scientists worked on properties of melts involved in geologic phenomena, like diffusivity, heat capacity, density or viscosity (Bottinga and Weill 1970, 1972; Bacon 1977; Carmichael et al. 1977; Robie et al. 1979; Ryan and Blevins 1987). This has changed over time. Since the 2000’s, it is easier to simultaneously investigate the structure and properties of glasses. Industrial and technological needs evolved, and the interest of the Earth sciences community became more and more focused on the acquisition and interpretation of in situ data to address problems requiring insights about silicate melts at high temperature and high pressure. As a result, the scientific community became more unified, performing more and more studies that simultaneously investigated the structure and properties of glasses and melts. Presently, we have reached a point where it is possible to link together experimental and structural/thermodynamic data to build models for solving industrial or Earth sciences problems. The aim of this chapter is to show how this is possible.

Glass structure versus macroscopic properties Among the most important questions about glasses and melts, one is critical for many applications and studies: how the melt/glass structure affects macroscopic properties? For Doremus (1973), a glass is an amorphous solid. The term solid implies a high viscosity, usually greater than 1010 Pa·s. This viscosity therefore limits the flow of the body. The amorphous term implies the absence of long-range order (see Fig. 5A in Drewitt et al. 2022, this volume), which reveals an analogy with the liquid state. So, a glass is a solid whose properties are similar to those of liquids. Parks and Huffman (1926) even talk about “a fourth state of matter”. However, no consensus exists regarding glass, and the nature of glass and the glass transition are two fundamental questions that remain open in condensed matter physics (e.g., see the different definitions in and debate between Zanotto and Mauro 2017; Popov 2018; Schmelzer and Tropin 2018). 1529-6466/22/0087-0003$10.00 (print) 1943-2666/22/0087-0003$10.00 (online)

http://dx.doi.org/10.2138/rmg.2022.87.03

106

Neuville & Le Losq

An important point is that glasses can exhibit very different chemical compositions and can be prepared by different means. Mineral (i.e., silicate), oxide, non-oxide, metal and organic glasses exist (see for an exhaustive description in Musgraves et al. 2019). In fact, glasses are found regardless of the type of chemical bonds that link the atoms they contain: covalent, ionic, metallic, Van der Waals or hydrogen bonding. The glassy state is a characteristic of condensed matter. Glasses can be obtained by the rapid quench of liquids, or of a gas by solid condensation, by amorphization of a crystalline phase or by sol-gel methods (Descamps 2017). The most common method for obtaining a glass is by the rapid quench of a liquid1. During the quench, viscosity continuously increases up to a value so high that the final state can be considered as solid. One can therefore imagine the structure of the glass as being similar to that of a liquid whose movements are hindered. Glasses, like undercooled liquids, have a disordered structure that was frozen in at the glass transition temperature. A fundamental question is what happens when a liquid crosses the glass transition temperature? The latter is the temperature (often abbreviated Tg, and more realistically it is a small temperature interval) at which second order thermodynamic properties like heat capacity show a transition, revealing the locking-in of the atoms in fixed (but undetermined) positions. In essence, Tg is the temperature at which a number of thermodynamic properties go from liquid-like to solid-like values. Unlike a crystallized solid, it is not possible to introduce the term of melting temperature for the glassy state. The solidification of a liquid into glass is accompanied, in fact, by a continuous and gradual increase in viscosity upon cooling, without the appearance of a crystalline structure (Fig. 1). This behavior remains true regardless of the glass/melt chemical composition (silicate, aluminosilicate, borate, borosilicate, germanate, chalcogenate, tellurate, metallic, organic... see for details regarding each glass family the Musgraves et al. 2019). This shows the continuous transition from glass to liquid for a property such as viscosity (Tamman 1925; see Fig. 1). The glass transition is a dynamic phenomenon that characterizes the loss of internal thermodynamic equilibrium. Indeed, the properties of a glass no longer depend solely on pressure and temperature, but also on the temperature at which the glass transition occurs. Finally, Tamman (1925) sums the concept as “The viscosity of a liquid increases with increasing undercooling, and in a rather narrow temperature interval it increases very rapidly to values characteristic of solid crystals. A brittle glass is thus formed from an easily mobile liquid. This change in viscosity does not correspond to the behavior of the other properties, which in this temperature interval change relatively only slightly. The change in viscosity is a continuous one and no temperature can be chosen as the freezing-point, the point at which the liquid becomes solid. Glasses are undercooled liquids.” The simplest and earliest characterization of the glass transition is due to Parks and Huffmann (1927), who investigated organic liquids. They note Nernst (1911) has stated that heating a glass “externally it has the properties of a solid, owing to great viscosity and considerable rigidity, produced by strong mutual action of the molecules. An amorphous body differs from a crystal, however, in its complete isotropy and absence of a melting point; on heating, it passes continuously from the amorphous to the usual liquid state, as its properties show steady change with rise of temperature, and no breaks anywhere.” In fact, Parks and Huffmann (1927) stated “While there is no definite temperature, comparable to the melting point of a crystal, at which all properties undergo a sharp change, there is nevertheless a temperature interval, definite and reproducible, in which a number of properties change with a rapidity approaching that observed in the case of the melting process of a crystal. In brief, there is a softening region instead of a melting point. The glass as it exists below this softening region differs so markedly from the liquid existing above that it might well be considered as a different state of the substance.” 1

“Rapid cooling rate” means 15°/min, the term “classic cooling rate” is also used.

Link between MRO, LRO and Properties of Silicate Glasses and Melts 14

SiO

Or

2

Ab

107

Diop

12

Viscosity, log Pa.s

Wo

10

8

bas

6

4

LGM

2

Figure 1. Viscosity versus 1/T curves for different melt compositions. LGM and CLA are rhyolite and andesite melts from Neuville et al. (1993), bas is a basalt melt from Villeneuve et al. (2008), SiO2 is silica melt from Heterington et al. (1964) and Urbain et al. (1982), Ab and Or are albite, NaAlSi3O8, and orthoclase, KAlSi3O8 melts from (Le Losq and Neuville 2013; Le Losq et al. 2017); Py, Wo, Diop, are pyrope, Mg3Al2Si3O12, wollastonite, CaSiO3, and diopside, (CaMg)SiO3, melt compositions (Neuville and Richet 1991).

Py CLA

0

5.2

6.5

7.8 4

9.1

10.4

-1

10 /T, K

From an energetic point of view, Moyniham et al. (1974) showed that the variations in relative enthalpy and heat capacity with temperature for two different cooling or heating speeds exhibit a sudden change in temperature and corresponds to a dampened variation of these two properties. They showed that for the same liquid, the glass transition temperature varies with the cooling or heating rate. The higher the cooling rate, the higher relative enthalpy or heat capacity (Fig. 2). The glass transition thus corresponds to a small temperature and pressure interval upon which properties such as heat capacity undergo a second order transition (Moyniham et al. 1974). This interval is at higher temperatures at high cooling rates (situation A in Fig. 2), and moves to lower temperatures at slower cooling rates (situation B in Fig. 2).

 
 








Figure 2. Relative enthalpy and heat capacity versus temperature for two different cooling rates, A and B correspond respectively to fast and low temperature change (redrafted from Moyniham et al. 1974). Cpl and Cpg correspond to the heat capacities of the liquid and the glass, respectively. TB and TA correspond to the glass transition at the two different rates A and B, respectively.

 

 








   

108

Neuville & Le Losq

It is theoretically possible to obtain identical variations for all properties as a function of time at the same temperature (thermal expansion, viscosity for example) but it is not necessary (Moyniham, et al. 1974). With sudden changes in temperature, variations of the liquid properties linked to atomic mobility require some time to reach a new equilibrium. This time is called the relaxation time, τ. A liquid has a large number of different configurational states (Goldstein 1969, 1976). Each state corresponds to a minimum in potential energy and when temperature decreases, the number of possible configurations decreases as the domains for structural rearrangement become larger and larger. As a result, the time for structural relaxation, τ, of the liquid increases. Crossing the glass transition leads to the atoms trapped in given but disorganised positions. This results in quenching the liquid into a glass. The configuration state of the glass does not change from Tg to 0 K, as shown by the fact that the residual entropy of glass remains constant below Tg (e.g., see Richet et al. 1986, 1991; Richet and Neuville 1992; Tequi et al. 1993; Goldstein 2011; Schmelzer et al. 2018 and references cited therein). It should be noted that Raman and infrared vibrational spectroscopy data suggest that the structure of a glass is an image of the instantaneous configuration of the liquid at Tg (Sharma et al. 1978; Shevyakov et al. 1978; Kashio et al 1980; Kusabiraki and Shiraishi 1981; Kusabiraki 1986; Neuville and Mysen 1996). The uniform cooling of a liquid at a rate q = dT/dt can be likened to a series of instant temperature jumps DT = Tfi − Ti, where Tfi and Ti are the final and initial temperatures, each jump being followed by a Dt period during which the temperature remains constant and equal to Tfi. Just after each jump, the viscosity of the liquid, hl, is still worth hTi and differs from hTfi – hTi from the new balance value, hTfi. This is called relaxation, the process by which the liquid tends to reach the state of equilibrium associated with the final temperature Tfi. To characterize the kinetics of this evolution, we can define a viscous relaxation time tη as equal to: tη = (hl − hTfi) / (dη/ tη)

(1)

Experimentally, tη increases when T decreases. Three cases can be distinguished: 1. Dt ≫ tη, the substance has a relatively long time to equilibrate its structure at the new temperature. We are in the liquid state or in a glass state at the thermodynamic equilibrium for which the equilibrium viscosity is reached almost instantaneously. During cooling, the viscosity increases to its equilibrium value. 2. Dt ∼ tη, this corresponds to the glass transition domain. Viscosity depends on both the time and temperature to which the glass was previously subjected. 3. Dt ≪ tη, the relaxation time is much higher than the measurement time. No configurational rearrangement is then possible. The liquid freezes. Only the vibrational part of the heat capacity remains, which is close to the heat capacity of the crystal. Relaxation times depend heavily on temperature (Simmons et al. 1970, 1974; Rekhson 1975, 1989; Dingwell and Webb 1990), as well as on the structure and therefore glass composition; e.g., borosilicate glasses have higher relaxation times than silicate or aluminosilicate glass compositions (Sipp et al. 1997). Figure 3 shows, for a soda-lime silicate glass, that relaxation time increases with decreasing temperature: e.g., equilibrium is reached after 500, 1200, 1600 min respectively at 795, 788 and 777 K. However, it is important to note that there is no reason why the relaxation times of the various properties should be identical at equal cooling speeds. Moynihan et al. (1976a) indicate that “for example, the enthalpy changes occurring during the approach to equilibrium of a network glass following a change in temperature could be considered to arise from the breaking of some of the network bonds, while the volume changes are due to rearrangement of the structure into less densely packed configurations. One cannot say a priori, however, which

Link between MRO, LRO and Properties of Silicate Glasses and Melts

109

of these two processes should on the average occur earlier in time. That is, bond breaking might be a necessary precursor to volume-changing rearrangements of the structure, so that one would expect H to relax faster than V. On the other hand, configurational rearrangements leading to large volume changes might occur early in time, stressing the network and leading to subsequent bond breaking, so that one would expect V to relax faster than H.” In practice, it appears that the differences in relaxation time between volumetric and calorimetric relaxation times are relatively small, if not almost non-existent, and are essentially due to differences in cooling or heating rates (Sasabe et al. 1977; Moynihan and Gupta 1978; Dingwell and Webb 1990). Differences between relaxation times for the same material but determined with methods sensitive to different properties are clearly visible when comparing data from dilatometry, calorimetry and viscosimetry. For example, in the case of alkaline-earth aluminosilicate glass compositions, drop calorimetry Tg are generally found at temperatures at which viscosities are of 10.7 ± 0.5 log Pa·s, a value lower than that of ~12 log Pa·s that is known to be the reference for the determination of the viscous Tg (Neuville and Richet 1991; Tequi et al. 1991).

Thermodynamic approach to glass transition We have seen that temperature and pressure are not sufficient parameters to characterize the state of glass. Tool and Eichlin (1931) introduced the concept of fictive temperature, Tfic, to characterize a glass at constant pressure. It can be defined as the temperature at which the glass would be in an equilibrium state (as a melt) if it could be heated and measured instantly. The fictive temperature can be defined during cooling in dilatometry or calorimetry, as the glassy transition temperature. It is possible to give a formal thermodynamic definition of the fictive temperature, considering it as an order parameter. Moynihan et al. (1974, 1976a,b) discussed fictive temperatures, their influence on enthalpy properties and order parameters. It can be recalled, that the glass transition looks like a second-order transition for which volume, enthalpy and viscosity are continuous functions of T but not heat capacity, dilatation and compressibility coefficients. For the latter parameters, a steep transition is observed when temperature crosses the glass transition. In reality, fictive temperature is a critical parameter as it reflects how viscosity, hence relaxation time, can show non-equilibrium behavior and can depend on time in the supercooled domain. In Figure 3, the effect of fictive temperature is clearly visible. The downward curve is obtained from a sample that has a fictive temperature below the measurement temperature. Similar behaviors are visible for density, or refractive index (Winter 1943; Ritland 1954). When the fictive temperature of the glass is higher than the measurement temperature, the glass has a more disordered configurational state than the state it should have if the glass were in thermodynamic equilibrium, i.e., its “fictive” configuration entropy is too high. It has a lower viscosity than its equilibrium viscosity, so its viscosity increases over time until the fictive temperature equals the measurement temperature. For a fictive temperature lower than that of measurement, the viscosity decreases until the establishment of the thermal equilibrium characterized by the equality of the two temperatures. In Figure 2, the relaxation curves over time for the cases of cooling or heating are asymmetrical. This is because a liquid increases its entropy faster with an increase in temperature (Rekhson 1980; Dingwell and Webb 1990; Sipp et al. 1997)2.

Viscosity and glass transition The glass transition is closely related to transport phenomena and more specifically to viscosity (Gibbs and Dimarzio 1958; Adam and Gibbs 1965; Goldstein 1969; Grest and Cohen 1980; Richet 1984; Scherer 1984), one of the fundamental properties of liquids that intervenes in transport processes. For the experimentalist, liquid viscosity also can be considered as a structural probe. Many models attempt to describe the variation of viscosity with temperature. 2 A fictive pressure, Pfic, can be defined as the pressure at which the glass would be in an equilibrium state if it were subjected instantly to pressure equal to Pfic, at constant temperature.

Neuville & Le Losq

110

14.5

Viscosity, log Pa.s

777 K 14.0

788 K

13.5

795 K 13.0

soda-lime silicate glass 12.5

0

400

800

1200

1600

2000

2400

Time, min

Figure 3. Viscosity versus time for a soda-lime silicate glass at different temperatures (redrafted from Sipp et al. 1997). We can note that increasing viscosities represent relaxation after previous measurements performed at higher temperatures, whereas decreasing viscosities indicate relaxation after annealing at lower temperatures.

Among them, we can cite the empirical Arrhenius and Tamman–Vogel–Flucher (TVF) equations, or the thermodynamic Adam–Gibbs (AG) model (see also the section Silicate glasses and melts) allows linking melt mobility to its thermodynamic properties such as heat capacity and configurational entropy, and can be used for viscosity predictions and extrapolations (Neuville and Richet 1990). Le Losq and Neuville (2017) further showed that the AG model allows linking melt structural knowledge to thermodynamic properties and viscosity, in order to build complete, extensive models for property predictions.

Configurational properties and glass structure Configuration properties are the key to understand the difference between liquids and glasses. To illustrate the importance of such configurational aspects, consider the second order thermodynamic properties of crystal, glass and liquid pyrope (Mg3Al2Si3O12). Table 1. Heat capacity of pyrope and Mg3Al2Si3O12, glass and liquid in J·mol−1·K−1. Data are from Tequi et al. (1991). T(K)

Crystal

Glass

298

325.6

327.8

1020

492.2

504.4

1700

522.6

Liquid 665.7 689.5

Above room temperature, the glass and crystalline phase have similar heat capacities, Cp. On the contrary, the Cp of the liquid is 25% higher than that of solids (crystal or glass). Moreover, it should also be noted that the Cp of the liquid usually increases with temperature of the liquid and cannot be considered as a constant. These differences can have a significant impact when you integrate with temperature or pressure, as shown by the example of pyrope and Mg3Al2Si3O12 liquid. For instance, a simple extrapolation of the heat capacity of the Mg3Al2Si3O12 liquid to low temperatures would produce a liquid with a lower entropy than that of its crystalline form below 694 K (Fig. 4A). This temperature actually corresponds to the Kauzmann temperature, a temperature below which the liquid entropy would become lower than that of a crystal with the same composition. Such a system does not exist because

Link between MRO, LRO and Properties of Silicate Glasses and Melts

111

Figure 4. A) entropy versus temperature (Tequi et al. 1991), B) schematic representation of the complex higher dimensional potential energy hypersurface of an N-particle system in terms of a two-dimensional diagram of chemical potential versus some collective configuration coordinate Z*, which defies precise definition, but the width of the funnel represents entropy (Angell 1991; Mossa et al . 2002), and C) viscosity versus temperature for the Mg3Al2Si3O12 composition (Neuville and Richet 1991). The same numbers are all connected together in the three figures. 1 is the Pyrope crystal that presents the minimum potential energy. 1′ is a metastable crystal, mc, that can have a potential energy higher than that observed for the glass. 2 is the liquid with a low viscosity, high entropy and high potential energy, in which atoms can move rapidly from one position to one other. 3 is the glass, in which atoms can move very slowly, there is a relaxation time, viscosity increase and entropy decrease, and the atom can fall in different potential energy minima and stay inside or jump to another with a lower potential energy. Tm is melting temperature, Tg, glass transition temperature, TK Kauzmann temperature, ΔSf entropy of melting at the melting temperature. Supercooled liquids are liquids between melting temperature and glass transition temperature.

a property of a liquid like the entropy should always remain higher than that of its crystalline form at a given temperature. The violation of this idea is known as the Kauzmann paradox (Kauzmann 1948)3. The pyrope example shows that configuration terms play an important role on the properties of liquids. It is therefore necessary to understand how configurational properties vary, and their link to melt and glass structure. Figure 4A shows the variation of the entropy of a crystal, glass and liquid for the Mg3Al2Si3O12 composition as a function of temperature. It is clear that the residual entropy corresponds to the difference between the entropy of the glass and that of the crystal at 0 K. This residual entropy is very small compared to the entropy of glass, crystal and liquid. This residual entropy is called configurational entropy, Sconf, and it is the key to understanding glasses and liquids. To determine Sconf, it is necessary to solve the entropic cycle represented in Figure 4A. However, this is only possible for minerals that melt congruently, and with a composition that can exist in a stable form as crystal, liquid and glass. Measuring the heat capacity of the crystal, Cpc, from 0 K to the melting temperature, Tm, allows determining its absolute entropy Sc at Tm: Tm

C pc (2) dt T 0 By adding the entropy of fusion of the crystal, ΔSf, to Sc, the entropy of the liquid Sl is then obtained at Tm. Measuring the heat capacity between the melting temperature, Tm, and the glass transition temperature, Tg, allows determining the heat capacity of the liquid and the

Sc =

3



This well-known paradox in temperature is recently proposed via pressure, but without any experimental basis, see the papers of Schmelzer et al. (2016) and Mauro (2011).

Neuville & Le Losq

112

supercooled liquid, Cpl. The measurement of the heat capacity of the glass between Tg and 0 K provides Cpg. Finally, the residual entropy, also known as the so-called configurational entropy Sconf, is obtained at 0 K via: Tm

Sconf (0 K) =

T

g 0 C pc Cpl C pg d t t d dt + DS + + f 0 T T T  T T m

(3)

g

This calculation is illustrated in Figure 4A for a composition of Mg3Al2Si3O12 (Tequi et al. 1991). As this Figure shows, Sconf represents a small difference between large numbers, and its value will be affected by a very large error if calorimetric measurements are not made with the highest possible accuracy. For this purpose, the studies focused on determining Sconf from calorimetry measurements require high-precision measurements of thermal capacity: heat capacities need to be determined better than 0.2% by adiabatic calorimetry between 0 K and ambient, and better than 0.5% by high-temperature drop calorimetry (e.g., Tequi et al. 1991). Aside from the time and the difficulty of performing such high precision heat capacity measurements, one of the main drawbacks of the calculation of the configurational entropy through the thermodynamic cycle is the necessity to study minerals that melt congruently, with compositions existing as glass, liquid and crystal as stated previously. Only a few chemical compositions can be studied in this way. Fortunately, as we shall see later, Sconf can be determined through the use of the Adam and Gibbs model combined with viscosity measurements. Figure 4B schematically illustrates the positions of atoms in a crystal as a function of the collective configuration coordinate, as determined by local minima of interatomic potentials that are at specific positions, allowing the building of a repetitive pattern characterized by long range order. In a glass, the bond angles and interatomic distances are not constant but extend over a range of relatively close values. Long-range order does not exist, and one can represent the interatomic potentials as a plane showing minima separated by barriers with varying shapes and heights. As a result, glass entropy is higher than that of crystal at given temperature (point 3, Fig. 4). The ideal glass with the minimum potential exists, but also other minima can exist with higher potential for the glass state or even the metastable crystal (point 1′). Now suppose that a certain amount of heat is brought instantly to the glass. Below the glass transition, the thermal energy brought upon increasing temperature is accommodated as vibrations, via an increase in average vibration amplitudes. The specific heat is vibrational in nature and the material behaves like a solid. At and above Tg, the thermal energy becomes important enough to allow the atoms to cross the energy barriers that separate the different configurational states (Richet and Neuville 1992). This configurational contribution is necessarily positive, and the liquid or glass states can be defined by the existence or absence of this contribution (Davis and Jones 1953). In a way, the glass transition can be seen as the beginning of the exploration by atoms of positions corresponding to the highest values of interatomic potential (Goldstein 1969). This distribution of configurations over increasingly high potential energy states is the main characteristic of atomic mobility and low viscosity or relaxation time (point 2, Fig. 4). If we now look at the changes in volume in an amorphous material, we notice that a general characteristic of interatomic potentials is their anharmonic nature, i.e., that the forces applied to the vibrational atoms are not exactly proportional to the movements in relation to the equilibrium positions of these atoms (Richet and Neuville 1992). An increase in vibration amplitudes therefore leads to an increase in interatomic distances. Like solids, liquids also have such anharmonic vibrational expansion, but higher-energy patterns that begin to be explored over the glass transition are generally associated with increased interatomic distances. This is why the thermal expansion coefficient generally increases significantly at the glass transition (Richet and Neuville 1992).

Link between MRO, LRO and Properties of Silicate Glasses and Melts

113

Pressure–temperature space As we have mentioned before, there is a glassy transition pressure (Rosenhauer et al. 1979), which allows one to place the glass transition in a pressure-temperature plane for a given cooling or heating rate. However, the effects of pressure and temperature on the properties of glasses are actually different. High pressure can produce irreversible configurational changes. So, for given experimental quench rates or measurement time scales, the kinetics of configurational changes are markedly different depending on whether they are caused by pressure or temperature. The main reason for this difference is that the shape of potential energy wells varies little with temperature but significantly with pressure. If high kinetic energy is required to cross the potential barriers at constant pressure, changes in these barriers with pressure can lead to new configurational states at lower temperatures, if the pressure is high enough. The processes occurring at high pressure in glasses are likely similar to those that occur in liquids. Since the 2000’s, many papers have shown significant changes in the glass structure with increasing pressure, more or less linked to changes in their properties (e.g., Poe et al. 2001; Suzuki et al. 2002; Wang et al. 2014). In this volume, an exhaustive chapter can be found on the effect of pressure on the structure and properties of melts and glasses by Sakamaki and Ohtani (2022, this volume).

SILICATE GLASSES AND MELTS Alkali or earth alkaline silicate glasses and melts As depicted in the previous two chapters, silica glass is a material well-connected at the molecular scale, built from a three-dimensional network of tetrahedral units composed of covalently bonded central Si and apical O atoms (a.k.a. Bridging Oxygens or BO). However, contrary to a-quartz that forms perfect trigonal crystals, SiO2 glass is built by SiO4 tetrahedra distributed disorderly yet not totally randomly (e.g., see Fig. 5A in Drewitt et al. 2022, this volume). The relative density d of silica glass equals 2.20 (molar volume Vm = 27.311 cm3), a value lower than that observed for a-quartz (d = 2.65 gcm−3, Vm = 22.673 cm3) that presents a compact and well-ordered structure. This implies that silica glass presents a rather porous structure, with possibly a minor amount of Non-Bridging Oxygen (NBO, see Henderson and Stebbins 2022, this volume) atoms not connected to 2 Si atoms (Brückner 1970; Fanderlik 1990). The fraction of NBO in silica is usually considered as negligible, making the silica structure a very strong one. As an alkali oxide is added, Na2O for example, more and more NBO are created until reaching the possibility to create isolated SiO4 tetrahedra linked together by only ionic Na–O bonds. For alkali silicates, this corresponds to a theoretical view because Na4SiO4 glasses do not exist. However, in the Ba-silicate system, it is possible to obtain glasses with 33% and 37% silica with classic cooling rate (Bender et al. 2002), while in the Mg-silicate system it is possible to obtain glasses up to 62 MgO in mole percent (38% SiO2) but below 50 percent of silica, it is necessary to use a fast cooling rate as shown in Raman spectra (Neuville et al. 2014a). Glass formation in the SiO2–Na2O system is actually not possible for amounts of Na2O lower than that of the metasilicate composition Na2SiO3 (Schairer and Bowen 1956). At higher Na2O contents, up to 58 mole percent, it is possible to obtain Na silicate glasses only via high-speed quenching of a small quantity of melt (a few grams; Imaoka and Yamazaki 1963). Stable, large pieces of glass cannot be formed below 60 mol% of SiO2 in this system (Neuville 2006). For other alkali-silicate glasses, it is possible to make glasses up to 35 and 55 mole% of Li2O and K2O, respectively (Imaoka and Yamazaki 1963; Levin et al. 1964). To summarize, alkali silicate glasses can be easily obtained at normal cooling rates in the 60 to 99 mole% SiO2 range (see Raman spectra of silicate glasses in Neuville et al. 2014), and alkaline-earth silicate glasses between 33 and 75 mol% SiO2, particularly with heavy alkalineearth elements like Ba. For Mg, the glass forming domain is smaller, and ranges between

Neuville & Le Losq

114

37 and 55 mole% SiO2 (Imaoka and Yamazaki 1963; Richet et al. 2009). In the CaO–SiO2 system between 99 and 62 mole% SiO2, the melts at temperatures just above the liquidus consists of two immiscible phases (Imaoka and Yamazaki 1963; Levin et al. 1964; Hudon and Baker 2002a,b; Neuville 2006). Alkali or alkaline-earth silicate glasses show almost linear variations in molar volume with addition of M2+O in silica glasses (Fig. 5). Molar volumes obtained from density measurements for CaO–Al2O3–SiO2 and Na2O–Al2O3–SiO2 are also available in the literature (Seifert et al. 1982; Doweidar 1998, 1999) but we have chosen not to report them on the figures for two reasons: i) they show similar trends to ours, ii) they are made with different cooling rate than ours (not mentioned in the articles). The molar volume (Vm) of silicate glasses increases or decreases as a function of the cation size4. In the case of cations presenting an ionic radius larger than O2− (132 pm), like Cs+, Rb+ or K+, the glass molar volume increases with cation addition. For cations presenting an ionic radius lower than that of O2−, like Na+ and Li+, Vm of silicate glasses decreases both with the cation size and its amount. A similar behavior is observed in alkaline-earth silicate glasses. In Ca and Mg silicate glasses, Vm varies almost linearly with the glass SiO2 (Fig. 5). In Figure 5, a dotted straight line is drawn between SiO2 and MgO with Mg in 6-fold coordination, and it is clearly observed that the Vm of Mg-silicate glasses are below this line, which suggests that the CN of Mg is significantly less than 6 in amorphous magnesium silicates. Such an interpretation agrees with 25Mg Nuclear Magnetic Resonance (NMR) spectroscopy that shows that Mg is essentially in four-fold coordination in silicate glasses (Fiske and Stebbins 1994; Georges and Stebbins 1998; Kroeker and Stebbins 2000; Shimoda et al. 2007a,b), as well as with XANES at the Mg K-edge (Trcera et al. 2009) while Ca is essentially in six fold coordination in silicate glasses as shown by XANES at the Ca K-edge (Cormier and Neuville 2004; Neuville et al. 2004b; Ispa et al. 2010; Cicconi et al. 2016). These gentle variations may indicate that Ca and Mg remain almost in the same coordination number, CN, in silicate glasses, this CN being slowly affected by the SiO2 content or by the variation in the number of bridging oxygens around Si.

Molar volume, cm

3

35

Cs O 2

30

Al O 2

KO

Rb O 2

2

3

[6]

Al

25

BaO

PbO

Na O 2

Li O

SrO

20

SiO

2

2

[6]

Ca O

15

[6]

Mg O

10

0

20

40

60

mole % SiO

80

100

2

Figure 5. Molar volume of glasses at room temperature: data for Ca, Mg, Na, K, Li silicate glasses are original data from Neuville, Sr and Ba Novikov (2017) Rb, Cs from O’Shaughnessy et al. (2017, 2020); Pb-silicate from Ben Kacem et al. (2017) and Al-silicate glasses from Wang et al. (2020). Molar volume of [6]Al corresponds to Al2O3, and MgO and CaO are from Robie et al. (1979). Density of MA44.00 and MA38.00 glasses are respectively 2,807 and 2,881, Raman spectra of these two glasses are given by Neuville et al. (2014). 4

Cation sizes are given in Whittaker and Muntus (1970) and molar volumes are from Robie et al. (1979).

Link between MRO, LRO and Properties of Silicate Glasses and Melts

115

Viscosity of silicate melts In Figure 6A, the viscosity of SiO2 and soda silicate melts are plotted as a function of reciprocal temperature. Silica shows the highest viscosity of all glass compositions, as well as a strongly linear behavior indicating an Arrhenian behavior (slope is equal to an activation energy). The fact that silica easily forms a glass, albeit a strong one with a very high viscosity, directly indicates that Si is a network former cation. Other elements, presenting lower valence and larger ionic radius, can play different roles in the glass structure. For instance, the introduction of Na2O in silica glass yields to breaking the covalent Si–O–Si bridges, and, hence, to the formation of Non-Bridging Oxygens, NBO. Na is considered, in this case, as a network modifier cation. Na fits into the glass structure as cations linked to the surrounding oxygens by bonds that are much more ionic and thus weaker than Si–O covalent bonds. Thus, the structure of sodium silicate glasses is weaker than that of vitreous silica. This translates into a lowering of the viscosity at given temperature when adding Na2O in SiO2 (Fig. 6A). Furthermore, the introduction of Na2O in silica glass produces a non-Arrhenian behavior that increases with x for the NSx glass; x corresponds to the ratio of SiO2/Na2O in mole percent (Fig. 5A). When viscosity varies with 1/T following an Arrhenian behavior, it follows this equation: log η = A + B/T

(4)

with A the viscosity at infinite temperature and B an activation energy. This equation can only be used for a few chemical compositions like SiO2, GeO2, NaAlSi3O8 or KAlSi3O8. An Arrhenian behavior implies that the activation energy, B, is independent of temperature,

SiO2

NS6

NS4 NS3

A)

13

Viscosity, Pa.s

11 9 7

NS2

5 3 NS1.5 1

3

6

9

104/T, K-1

12

14 B)

15

K2O

Viscosity, log Pa.s

12 10 8 6

Na2O

750 K 800 K

4 2

1400 K 0 50 60

70 80 Mole of SiO2 %

90

100

Figure 6. A) viscosity versus reciprocal temperature (SiO2 NS6, NS4, NS3, NS2, NS1.5, data from Neuville 2006 and Le Losq et al. 2014). NSx: x corresponds to the ratio of SiO2/Na2O in mole percent (e.g., NS4: x = 4 = 80/20: 80% SiO2 and 20% Na2O); B) viscosity versus SiO2 content for Na- and K-silicate glasses (data from Poole 1948; Bockris et al. 1955; Neuville 1992, 2006).

116

Neuville & Le Losq

and, hence, that the process underlying melt viscous flow remains the same regardless of temperature. For melts showing a strong non-Arrhenian behavior like NS3, the activation energy term, B, decreases from 2000 kJ mol−1 at 1000 K down to 300 kJ mol−1 at 1800 K. In such conditions, it is no longer possible to use the Arrhenian equation. For this reason, Tamman, Vogel and Fulcher proposed the so-called TVF equation (Vogel 1921; Fulcher 1925; Tamman and Hesse 1926) to link viscosity and temperature: log η = A + B/(T − T1)

(5)

A, B, and T1 are just fitting parameters without physical meaning. The TVF equation is very useful to fit and interpolate viscosity data at low and/or at high temperature (Neuville and Richet 1990). This equation has been used in many different papers and is at the basis of several viscosity models (Bottinga and Weill 1971; Shaw 1972; Persikov 1991; Giordano et al. 2008; Giordano and Russell 2018). The empirical parameters A, B, T1 can be linked to glass structure (Giordano and Russell 2018). However, while finding very practical applications, this equation remains purely empirical. Aside from the empirical Arrhenius or TVF equations, the Adam–Gibbs equation, derived from the theory of Adam and Gibbs (1965), is one of the best candidates to fit and extrapolate viscosity measurements for silicate melts (Urbain 1972; Wong and Angel 1976; Richet 1984; Scherer 1984; Neuville and Richet 1990, 1991; Mauro et al. 2009). The strength of this equation is that it allows relating viscosity measurements to heat capacity and configurational entropy data (Urbain 1972; Wong and Angell 1976; Richet 1984; Scherer 1984). The Adam– Gibbs theory and equation will be discussed in more details in the next section. No other equation allows relating thermodynamic to dynamic variables in a simple way. The variations observed and described previously for sodium silicate glasses are similar for all alkali oxides, as for instance visible for K2O in Figure 6B. Generally, the addition of a few percent of alkali in silica glass produces an important viscosity decrease of a few orders of magnitude (Lecko et al. 1977). Ten mole percent of alkali oxides decreases the viscosity by ~ 10 orders of magnitude at 1400 K, this decrease being larger at low temperature near the glass transition temperature. After 10 mol% of added alkali oxides, the decrease in viscosity with increasing alkali content becomes less pronounced and the viscosity varies almost linearly at high temperature. These viscosity variations for more than 10% of added alkali are well correlated with increases in thermal expansion and heat capacity of the liquid which vary almost linearly as a function of chemical change at high temperature (Bockris et al. 1955; Lange and Carmichael 1987; Lange and Navrotsky 1992).

Ideal mixing: mixing alkali or alkaline-earth in silicate glasses and melts In the section Viscosity of silicate melts, we observed that molar volumes, as well as viscosity and glass transition temperature of alkali and alkaline-earth silicate glasses all changes with the addition of network modifiers. Mixing different metal cations (like Ca and Mg, or Na and K) in silicate glasses results in large variations in their properties, such as large decreases of their glass transition temperatures or large increases in their electrical conductivity (Day 1976). This is the so-called mixed alkali effect, MAE, reviewed many times (Richet 1984; Neuville and Richet 1991; Allward and Stebbins 2004; Cormier and Cuello 2013; Le Losq and Neuville 2013; Le Losq et al. 2017; Bødker et al. 2020) in the literature for alkali silicate glasses since the work of Day (1976). In this section, we show and introduce some terminology about mixing elements and their effect on the structure and macroscopic properties of melts and glasses. Ca and Mg are very important elements in Earth and material sciences, and it thus it is particularly important to understand how they mix in silicate melts. To understand this, we can look at how viscosity varies along the CaSiO3–MgSiO3 binary. Neuville and Richet (1991) have shown that at constant temperature, the viscosity of (Ca,Mg)SiO3 composition is always lower than the viscosity of the end-member, CaSiO3 or MgSiO3 (Fig. 7A).

Link between MRO, LRO and Properties of Silicate Glasses and Melts

117

B)

MAS dimension, ppm

A)

C) C)

Ca Mg Ca-Mg

BO

Mg-NBO Ca-NBO isotopic dimension, ppm

Figure 7. A) Viscosity versus xi = Ca2+/(Ca2++Mg2+) at constant temperature and B) configurational entropy for Ca/Mg mixing data from dashed line correspond to the total configurational entropy and full line to the topological variation of the entropy see text (Neuville and Richet 1991) C) 17O triple-quantum NMR spectrum redrafted from Allwardt and Stebbins (2004).

By using the Adam–Gibbs equation, it is possible to determine the configurational entropy, Sconf. Adam and Gibbs (1965) theory of relaxation processes is based on the idea that transporting matter in a viscous liquid requires a cooperative change in the fluid configuration. A liquid with zero configuration entropy would be analogous to a perfect crystal, and no material displacement could occur since a single configuration would be available. The viscosity would then be infinite. If only two configurations were possible, a movement of matter could only occur if all the atoms of the liquid changed position simultaneously. The probability of such a cooperative movement would be very low and viscosity extremely high, but no longer infinite. More generally, as Sconf grows, cooperative configurational changes can occur independently of each other in increasingly smaller volumes of the liquid. At the same time, viscosity decreases and is predicted by: log η = Ae − Be / TSconf(T)

(6)

where Ae is a pre-exponential term and Be a measure of the Gibbs free energy barriers hindering configurational rearrangements in the liquid. Sconf(T) can be written as: Cpconf  T  dt T Tg T

and

Sconf(T) = Sconf(Tg)+ 

Cpconf(T) = Cpl(T) − Cpg(Tg)

(7) (8)

where Cpl and Cpg are the heat capacity of the liquid and the glass. Cpconf is the melt configurational heat capacity, equal to the difference between the heat capacity of the liquid Cpl and the heat capacity of the glass at Tg, Cpg(Tg) (Richet et al. 1986). Those values can be measured or modelled with the existing parametric equations (Richet and Bottinga 1984; Stebbins et al. 1984; Richet 1987; Tangeman and Lange 1998; Russell and Giordano 2017), see for examples and details Neuville (2005, 2006), Le Losq et al. (2014) and Le Losq and Neuville (2017). One may also note that Cpg(Tg) ~ 3R, the Dulong and Petit

118

Neuville & Le Losq

limit (Petit and Dulong 1819), such that it can be easily estimated from this simple calculation (Richet 1987). The configurational heat capacity is a very important term, in particular, the higher Cpconf is, the faster Sconf increases with T, and the lower the Be/ Sconf ratio. The importance of these differences between configurational Cp is illustrated in Figure 1, where in the case of NaAlSi3O8, the liquid Cpconf represents less than 10% of that of the glass, and deviations from Arrhenius behavior are small. On the contrary, CaSiO3 or Mg3Al2Si3O12 have a Cpconf representing 30% of the Cp of the glass, and the viscosity versus 1/T curves depart significantly from a straight line. Because of the importance of Cpconf, it is therefore imperative to know the heat capacity of liquids and glasses for a given temperature and chemical composition. We can note that the configurational heat capacity Cpconf(T) depends essentially on the heat capacity of the liquid, Cpl, and in the case of alkaline-earth silicate melts, Cpl is independent of T and varies mostly linearly with melt composition (Stebbins et al. 1984; Richet and Bottinga 1985; Lange and Navrotsky 1992). This explains the pseudo-linear variations of viscosity observed at high temperature (1750 K, Fig. 7A). However, near Tg, the melt viscosity depends strongly on Sconf(Tg), which shows large non-linear variations with melt composition. This explains the large, non-linear viscosity changes at supercooled temperature upon mixing alkaline-earth elements in silicate melts (Fig. 7A). Using Equation (6) in conjunction with viscosity data and heat capacity values (from data or models), Sconf can be calculated. Sconf along the CaSiO3–MgSiO3 binary is plotted in Figure 7B. To reproduce Sconf variations with composition, it is necessary to look at the contributions to Sconf(Tg) in Equation (7). Sconf records topological contributions from the melt structure (bond angle and interatomic distance distributions, etc.) as well as excess entropy arising from chemical mixing effects. It thus is common to express Sconf as the addition of those two sources (Neuville and Richet 1991): Sconf (Tg) = Stopo + Smix

(9)

with Smix the term embedding all mixing contributions and Stopo the entropy arising from the topology of the glass network. The topology of the network for the two end-members is distinctly different and is also different compared to the crystalline analogues. Stopo, the topological configuration entropy can be approximated as a linear variation of the configurational entropy of the end-members and calculated as Σ xi Sconfi(Tg), with Sconfi(Tg) the configurational entropy of CaSiO3 and MgSiO3 glasses (Neuville and Richet 1991). This Stopo term corresponds to a mechanical mixing between the two end-members without necessary chemical or physical interaction. Stopo can be expressed from the glass structure and varies linearly with composition (Le Losq and Neuville 2017). Smix corresponds to a chemical mixing term that can be ideal or non-ideal. In the case of Ca/Mg mixing, the simplest hypothesis that can be made is that Smix = Sideal, and thus can be written as: Sideal=−n R∑ xi ln xi

(10)

where R is the perfect gas constant and n is the number of atoms exchanged per formula units, 1 in this case, and xi = Ca2+/(Ca2++Mg2+). From a thermodynamic point of view, the ideal solution implies that end-members components mix randomly in solution. The excellent agreement (Fig. 7B) between entropies obtained from viscosity measurements and values predicted using Equations (6–10) shows that the ideal mixing hypothesis for Ca/Mg is consistent with the data. It should be noted that the mixing effect is predominant near Tg. The configuration entropy of the intermediate compositions is therefore

Link between MRO, LRO and Properties of Silicate Glasses and Melts

119

much higher than that of the end-members, explaining the minimum in viscosity observed upon Ca/Mg mixing. When temperature increases, the entropy of the end-members increases rapidly and Smix, which is constant, eventually becomes small compared to Σ xi Sconfi(Tg) in Equation (9). Therefore, at high temperatures, Smix is negligible and this results in a quasilinear variations in viscosity, driven by the linear variation of Cpl upon Ca/Mg mixing. These macroscopic conclusions about Ca/Mg mixing are in very good agreement with nanoscale investigations made by 17O NMR (Allwardt and Stebbins 2004) and neutron diffraction and RMC (Cormier and Cuello 2013). From neutron diffraction, the silicate network shows small but significant changes with the Mg/Ca exchange and a significant intermixing of Ca and Mg can be observed (Cormier and Cuello 2013). From another point of view, 17O NMR spectra of the diopside glass (CaMg)SiO3 shows that only one broad non-bridging oxygen atom (NBO) peak is visible, and encompasses the entire range of chemical shifts ranging from Ca-NBO to Mg-NBO. Comparison of the isotropic projections from 3QMAS NMR to 1D spectra predicted using a random model show that Ca/Mg mixing in Ca/Mg-silicate glasses is generally highly disordered (Allwardt and Stebbins 2004), except maybe near the glass transition temperature where a more ordered glass is possible as shown by neutron diffraction made on CaSiO3 glass by Gaskell et al. (1985). Validity of the viscosimetry approach to determine Sconf(Tg). We have just shown that it is possible to determine configurational entropies using viscosity measurements and the AG theory. Are those values of Sconf(Tg) truly representative of the glass residual entropy? To answer this question, we can compare Sconf(Tg) obtained from calorimetric measurements to those obtained from fitting viscosity data. Data from 11 very different compositions, including B2O3, SiO2 or KAlSi3O8, show very good agreement between Sconf(Tg) values retrieved from viscosity measurements or calorimetric measurements (Fig. 8). This thus validates the use of Equation (6) to determine Sconf(Tg) of melts. In the case of Na/K mixing in silicate melts, only one set of measurements is available from Poole (1948). Using those data, Richet (1984) proposed that an ideal, random Na/K mixing occurs in silicate melts, and viscosity can be modelled using the ideal mixing calculation of Sconf; some differences between calculated and measured viscosity in the supercooled silicate melts are visible in Richet (1984) work, however they arise from the way the data and model are represented. The more recent study of Le Losq and Neuville (2017) resolved this, showing that it is clearly possible to model the viscosity of Na–K silicate melts while assuming a random mixing of the alkalis (see the section Silicate glasses and others network formers). 60 Mg3Al2Si3O12

Sconf vis, J/mol.K

50 CaAl2Si2O8

40

NaAlSi3O8

KAlSi3O8

30 CaMgSi2O6

20 10 0

B2O3

GeO2 SiO2 NaAlSiO4

0

10

MgSiO3 CaSiO3

20

30

40

Sconf cal, J/mol.K

50

60

Figure 8. Viscosimetry configurational entropy versus calorimetry configurational entropy for 10 different oxide glasses for which determination of calorimetric measurements are possible. Calorimetric data are from Richet (1984) for SiO2, NaAlSi3O8, KAlSi3O8, de Ligny and Westrum (1996) for GeO2 and B2O3, Richet et al. (1991) for NaAlSiO4, Tequi et al. (1991) for Mg3Al2Si3O12, and Richet et al. (1986) for MgSiO3, CaSiO3, CaMgSi2O6 and Ca2Al2Si2O8. Viscosity data are from Hetherington et al. (1964) and Urbain et al. (1982) for SiO2, Neuville and Richet (1991) and Le Losq and Neuville (2013) and Le Losq et al. (2017) for alkali and alkaline-earth silicate and aluminosilicate compositions, from Fontana and Plummer (1966) for GeO2, and from Eppler (1966), Macedo and Litovitz. (1965), Napolitano et al. (1965) for B2O3.

Neuville & Le Losq

120

Mixing alkali and alkaline-earth elements in silicate glasses Most industrial and geologic glasses are silicate and aluminosilicate glasses containing a mixture of alkali and/or alkaline-earth elements. Igneous rocks (Morey and Bowen 1925) as well as nearly 90% of industrial glasses contain mixtures of alkali and alkaline-earth elements. We can cite the particular case of soda-lime silica glasses, extensively used for the construction of conventional windows and container glasses. The importance of M2+O– M+2O–SiO2 glasses (with M+ an alkali and M2+ an alkaline-earth element) further increased recently because they also are used for the development of bioactive glasses (Hench 1991; Kim et al. 1995; Clupper and Hench 2003; Hill and Brauer 2011; Brauer 2015). Given the importance of alkali and alkaline-earth metal cations in glasses, many studies were performed to understand the M2+O–M+2O mixing in silicate glasses. They are essentially focused on the glass mechanical properties or devitrification (Morey 1930; Frischat and Sebastian 1985; Koike and Tomozawa 2007; Koike et al. 2007), on glass structure (Buckerman and MüllerWarmuth 1992; Lockyer et al. 1995; Jones et al. 2001; Lee and Stebbins 2003; Lee et al. 2003, Neuville 2005, 2006, Hill and Brauer 2011; Brauer 2015; Moulton and Henderson 2021 and references therein) or thermodynamic properties (Natrup et al. 2005; Neuville 2005, 2006; Richet et al. 2009b; Inaba et al. 2010; Sugawara et al. 2013). Given the above-mentioned importance of M2+O–M+2O–SiO2 glasses, we will in this section bring new insights to the effect of M2+O–M+2O mixture on the properties of silicate glass and melt. Glass formation domains. The substitution of alkali elements by alkaline-earth elements allows extending the glass forming domain of silica glasses to lower silica contents (Fig. 9), and, more generally, it allows improving many glass properties (Moore and Carey 1951; Imaoka and Yamazaki 1963; Tomozawa 1978, 1999; Gahay and Tomozawa 1989, 1984; Neuville 2005, 2006). For M2+O and M+O2 bearing silicate glasses, the vitrification domain starts near 50 mol% silica in most cases. For Mg silicates, it starts at 45.7 mol% (Moore and Carey 1951). It was generally accepted that the presence of Mg–O bonds allows preserving somehow the continuity of the silicate network, with Mg acting to some extent as a network former (Moore and Carey 1951), an idea in agreement with the low coordination number of Mg discussed previously. In the case of CaO–Na2O–SiO2 glasses, the first phase diagram was made by Morey and Bowen (1925). It revealed the domain where glasses can be formed, but also an immiscibility domain SiO2

50

CaO-Na2O

SiO2

50

50

M+2O

M2+O

CaO-K2O

SiO2

50

50

M+2O

M2+O SiO2

50

M2+O

SrO-Na2O

MgO-Na2O

50

M+2O

M2+O SiO2

50

50

M+2O

M2+O

SrO-K2O

50

M+ 2O

Figure 9. The upper part of the ternary diagram corresponds to the glass forming region of glass between M2+O and M+2O, with M2+=Mg2+, Ca2+, Sr2+ and M+=Na+, K+ (redrafted from Imaoka and Yamazaki 1963 and Levin et al. 1964). The white areas are the glass making domain, the light dotted areas are the crystallization domains, the dark dotted lines correspond to the glass making domain, but strongly hygroscopic, and the gray areas to unmixed glass.

Link between MRO, LRO and Properties of Silicate Glasses and Melts

121

in which phase separation is observed. This immiscibility domain is very large near the CaO– SiO2 binary, extending between 62 and 100 mol% of silica. It decreases rapidly with addition of Na2O in the glass (Morey and Bowen 1925; Greig 1927; Hudon and Baker 2002a,b). In the immiscibility domain, different phases exist: cristobalite, SiO2, wollastonite CaSiO3, sodium disilicate Na2Si2O5, devitrite Na2Ca3Si6O16, and a non-defined compound Na2Ca2Si3O9. The proportion of these phases vary as a function of the bulk composition and the cooling rate (Morey and Bowen 1925; Greig 1927; Tomozawa 1978, 1999; Gahay and Tomozawa 1989; Hudon and Baker 2002a,b; see also the Schuller chapter in Neuville et al. 2017). Similar observations can be made in the other M+2O–M2+O–SiO2 systems, with M+ = Li+, Na+, K+ and M2+ = Mg2+, Ca2+, Sr2+, Ba2+. Generally, a pyrosilicate phase, M2+SiO3, and one or two phases M+yM2+xSizOu crystallize at high silica contents (> 70 mol%, x,y,z,u are different proportions of each crystalline phases), except for M2+ = Ba2+ where the glass forming domain is large but mostly unconstrained. Bender et al. (2002) achieved the synthesis of Ba silicate glasses up to the BS7 (BaO/SiO2 = 7 in mol%) composition, and Frantz and Mysen (1995) investigated some of those glass compositions by Raman spectroscopy. To summarize, in all of the M+2O–M2+O–SiO2 ternary diagrams, the glass forming domains are relatively small and essentially exist at silica contents higher than 50 mol%, with exception of barium silicates. In the case of sodium and potassium silicates, a large zone of high hygroscopicity exists below the glass forming domain, typically between 66 and 50 mol% of silica for sodium silicate glasses and between 70 and 50 mol% for potassium silicate glasses (Tomozawa 1978, 1999; Gahay and Tomozawa 1989). In general, one should be careful with potassium silicate glasses that are always highly hygroscopic. Viscosity variations. Figure 10A shows viscosity measurements of silicate melts for M2+–Na mixing with M2+ = Ca2+, Sr2+. Ca- and Sr-silicate melts show similar behavior. The addition of those elements produces a large increase in melt viscosity at constant temperature, in agreement with previous measurements (English 1923). The lack of measurement between 102 and 109 Pa·s results from the very rapid rate of crystallization in this viscosity-temperature range for mixed alkali and alkaline-earth silicate glasses (Meiling and Uhlmann 1977; Mastelaro et al. 2000; Neuville 2005, 2006). In the Figure 10B, we clearly observe that addition of 10 mole% Na2O in an alkaline-earth silicate melt has a stronger effect on melt viscosity than addition of 10 mole% M2+O to a soda-silicate melt composition. This indicates that a sodium silicate glass network can incorporate alkaline-earth elements more easily than the opposite. A striking difference exists in the behavior of the viscosity between pure Na-silicate melts and pure alkaline-earth silicate melts (CN60.00 or SN60.00). Indeed, at constant viscosity and near Tg (Fig. 10B), i.e., near 1000 K, the viscosity of the end-member compounds differ by 10 orders of magnitude. This difference decreases with temperature: it is less than 0.5 order of magnitude at 1600 K. Furthermore, at 1600 K, the viscosity of the Na2O–M2+O–SiO2 melts decreases almost linearly with Na2O/(Na2O + M2+O). Similar behaviors were already observed by English (1923) in the same system with 75 mole% SiO2 and 25 mole% Na2O, and with a substitution of Na2O by up to 12 mole% CaO. The viscosity variations observed in Figure 10 can be understood using Equations (6–9). It is possible to determine how configurational entropy varies upon the mixing of Na2O with M2+ in the glasses (Fig. 11A). Sconf can be decomposed in Stopo and Smix (Eqn. 9). Stopo is equal to the sum of endmembers. Smix, in the case of M+/M2+ mixing, has a complex expression that depends on the way the cations mix into the glass structure. Between the calcium and sodium silicate glasses, Sconf(Tg) varies non-linearly with Na2O/(Na2O + CaO). It increases rapidly with increasing Na2O / (Na2O+CaO) to 0.2, then it slightly decreases with further substitution Ca2+ by Na+. Similar observations are made in the SrO–Na2O–SiO2 system (Neuville 2005). The observed variations strongly depart from the

Neuville & Le Losq

122 14

Viscosity, log Pa.s

CN60.00

A)

12

SN60.00

CN60.20

SN60.20

10 XN60.40 NS1.5

8 6

Figure 10. A) Viscosity versus 1/T for silicate melts ranging from the pure alkaline-earth silicate melt) to pure soda silicate (XN60.40) composition names are: XN60.Y, X = C or S for the Ca or Sr system, Y corresponds to Na2O content, 60 to SiO2 in mole percent, and X = 100 − (60 + Y) all in mole percent. B) Viscosities of Na/ M2+ silicate melts versus Na2O/(Na2O + M2+O) at constant temperature, M2+=Ca, Sr, dashed lines correspond to the linear viscosity variation at 1000 K, 1050 K and 1600 K, solid and open symbols correspond to the CaO–Na2O–SiO2 and SrO–Na2O–SiO2 systems, respectively compiled from Neuville (2005, 2006).

4 2 0

6

8

10

12

104/T, K

14

14

B) 1000K

10 8 6 1050K

4 2 0

1600K

0

CN60.00 SN60.00

0.2

0.4

0.6

Na2O/(M"O+Na2O)

0.8

1 XN60.40 NS1.5

B)

234"'5'(3$+.653""

89:1'4;489:1'

A)

2342 60 wt. % SiO2 (i.e., Andesites to Rhyolites) with only a few examples of measurements at lower silica contents (Fig. 4.2). These experiments are typically performed just above the melt’s glass transition temperature (i.e., in the supercooled liquid state). This is because these high viscosity systems have comparatively slow crystallization and vesiculation kinetics, which allows negligible textural and or chemical change of the sample over the course of the experiment and to maintain a steady state suspension viscosity over the measurement timescales (minutes to hours). Other rheometric methods such as fibre elongation (Li and Uhlmann 1970; Webb and Dingwell 1990a), falling body viscometry (Mackenzie 1956; Kushiro et al. 1976) or three point bending (McBirney and Murase 1984), that have proven useful to investigate for example the influence of pressure on melt viscosity or non-Newtonian effects in unrelaxed, high viscosity melts have largely been abandoned for suspension rheology. The same is true for centrifuge experiments that were initially attempted for two and three phase rheometry by Roeder and Dixon (1977). Micro-penetration, that simulates the geometry of a falling sphere experiment (Hess and Dingwell 1996) has proven inadequate for determination of suspension rheology in the laboratory since it probes a comparatively small volume of melt adjacent to the indenter rather than the bulk of the sample. However, the penetration method is well suited when scaled for field measurements, where the penetrating rod is much larger than the average crystal (see “Field Rheology” section later in this chapter). Since both method and apparatus place tight constraints on measurement conditions, we review the advances in magma suspension rheometry grouped by the three most common experimental methods 1) concentric cylinder, 2) parallel plate and 3) torsion. Parallel Plate

14

Phonolite

Concentric Cylinder Torsion

12 Tephry-phonolite Trachydacite

2

2

Na O +K O (wt%)

10

Phono-Tephrite

Foidite

Rhyolite Trachy-Andesite

8 Tephrite-Basanite

Basaltic Trachy-Andesite

6

Trachy-Basalt

4

2

0

PicroBasalt

37

41

Basalt

45

49

Basaltic Andesite

53

Dacite

Andesite

57

SiO (wt%)

61

65

69

73

77

2

Figure 4.2. Total alkali versus silica diagram showing the compositions of published multiphase rheology measurements on lavas. Measurements of low viscosity suspensions (Foidite to Basaltic Andesite) are performed exclusively via concentric cylinder methods, whereas high viscosity magmas (Andesite to Rhyolite) are almost exclusively performed via parallel plate and torsional viscometry.

Concentric cylinder experiments Concentric cylinder viscometry has long been a go-to technique for measuring the viscosity of silicate melts at super-liquidus temperatures (Shaw 1969; Cukierman et al. 1972;

Magma / Suspension Rheology

653

Dingwell and Virgo 1987; Spera et al. 1988). It is commonly employed in combination with viscosity measurements near the glass transition temperature, e.g., via micro-penetration viscometry (Hess and Dingwell 1996) or estimation of the melt viscosity by application of shift factors to calorimetric data (Stevenson et al. 1995; Gottsmann et al. 2002; Giordano et al. 2005, 2008b) to interpolate the theoretical temperature-dependent viscosity of the pure melt across the crystallization interval (Tammann and Hesse 1926). This theoretical curve of the temperature–viscosity relationship of the crystal free melt is required to quantify the contribution of crystals and/or bubbles on the rheology of the bulk sample. The temperature range covered by concentric cylinder viscometry spans from 800 to 1700 °C. Theoretically, concentric cylinder viscometry allows imposing a vast range of strain rates but, in practice, the range of accessible strain rates is largely limited by the rheometer used for measurement and the method of sample containment. In current experimental geometries, the strain-rate limit is defined by either the torque limit of the rheometer or by the strength of the coupling between sample container and its holder, as the sample container may start slipping at high torque. Strain rates imposed in published data range from ~0.005 s−1 to ~9 s−1. (Dingwell and Virgo 1988; Stein and Spera 1998; Vona and Romano 2013; Kolzenburg et al. 2018b, 2020) In most experiments, temperature is not measured directly in the suspension because insertion of a thermocouple would disturb flow within the sample and thus affect the rheological measurement. Instead, the furnace control temperature is calibrated to the measured temperature of a non-crystalizing melt that is measured directly via insertion of a thermocouple (commonly platinum–rhodium alloys; type S or B). Concentric cylinder measurements are usually performed at atmospheric pressure and in air but experimentation under controlled atmospheres (e.g., more reducing conditions) is possible (Dingwell and Virgo 1987; Chevrel et al. 2014; Kolzenburg et al. 2018c, 2020). The importance of measurements at varying oxygen fugacity is increasingly recognized due its effect on melt viscosity (for example by reduction of Fe3+ to Fe2+) and on the onset of crystallization as well as phase equilibria. To date, no apparatus exists that allows for concentric cylinder viscometry under pressure, a key component affecting crystal phase assembly and bubble nucleation and growth dynamics in magmatic systems but there are active efforts to expand concentric cylinder measurement capacity in that direction (see section “Technological Advances” later in this chapter). For concentric cylinder experiments, the sample is melted in a cylindrical container and housed in a box or tube furnace. A cylindrical spindle is then inserted into the melt, generating the concentric cylinder measurement geometry (Fig. 4.1A). All parts in contact with the melt are commonly made of Pt–Rh alloys to withstand the high experimental temperatures and to avoid reaction between the melt and the container or spindle. More cost-effective materials, such as alumina ceramics, Pt–Rh alloys sheathed alumina ceramics or graphite, that allow for extraction of the entire sample without disturbing sample texture have been used with limited success. Alumina ceramics have proven inadequate for experiments involving low viscosity melts and high temperatures since they are soluble in the melt and induce contamination. Such contamination changes the melt composition and, with that, its viscosity, phase relations and crystallization kinetics. Nonetheless, ceramics are promising candidates for experimentation with high viscosity melts and at relatively low temperatures, which would result in negligible contamination during experimentation for durations of several days due to the much lower diffusivities in high viscosity systems and at low temperature. Graphite containers and spindles require low oxygen fugacity to avoid combustion during the experiment, which would in turn induce changes in the measurement geometry or, at worst, result in crucible failure and leakage into the furnace. Concentric cylinder measurements quantify the torque exerted by the magmatic liquid or suspension on the rotating spindle immersed into the sample. This torque is proportional to the apparent viscosity of the sample at the imposed experimental conditions.

Kolzenburg et al.

654

A

B

1144 °C

log ηapp (Pa s)

Thermal relaxation

log apparent viscosity

4.5

t4

1152 °C 1157 °C 1168 °C

1180 °C

3.5

Incubation t0

1162 °C 1162°C-bis

4

t1

Crystallization t2

time

Stable crystal content t3

3

0

1

2

3

4 5 6 time (105 s)

7

8

9

Figure 4.3 A) Schematic viscosity-time path of crystallization experiments, after Vona and Romano (2013) and Chevrel et al. (2015). As a general trend, four regions can be recognized with increasing time (t): 1) t0–t1: viscosity increase due to thermal equilibration of the melt to the experimental temperature; 2) t1–t2: “incubation time” time-invariant viscosity of the metastable liquid before crystallization. 3) t2–t3: viscosity increase due to crystallization; 4) t3–t4: time-invariant viscosity of the crystal–melt suspension with a constant crystal content (thermodynamic and textural equilibrium). B) Sample Dataset of the time and temperature dependence of the evolution of apparent viscosity during experiments at constant sub-liquidus temperature and constant shear rate; from Chevrel et al. (2015).

Experiments can be performed at either constant strain rate (i.e., torque is measured while the spindle is rotated at a constant rate) or constant stress (i.e., rotation rate is measured while the spindle is rotated at a constant torque). Standard concentric cylinder viscometry aims to achieve a linear velocity profile across the liquid (i.e., between inner and outer cylinder). However, linear velocity profiles are only achieved when the gap between the two cylinders is narrow, a geometry which does not lend itself to the study of particle suspensions. Therefore, most experiments on natural silicate melts are performed in wide gap geometries, where the flow velocity field is non-linear. This method can be employed to study silicate melt suspensions since it allows sufficient space to accommodate crystals and/or bubbles in the gap between cylinder and spindle while returning accurate viscosity measurements. Further, the concentric cylinder geometry allows for continuous viscosity measurement as a function of varying experimental conditions or textural changes in the sample, and infinite strain. This makes it more flexible than other methods that have limitations in total achievable strain (e.g., parallel plate viscometry). Following Couette theory, the shear stress (σ) and shear strain-rate (  ) measured at the inner cylinder are described by:  

2 2    Ri  n   n 1     Ro    

(4.1)

M 2 rRi2l

(4.2)



where Ω is the angular velocity, M the measured torque, Ri and Ro the radii of the inner and outer cylinder, respectively, l is the effective immersed length of the spindle and n is the flow index. The value of the flow index (n) is determined as the slope of M vs. Ω in loglog space. From Equations (4.1) and (4.2) the sample’s flow curve (σ vs.  ; Fig. 2.1) can be constructed to describe the rheological behavior of the measured suspension. As apparent from Equation (4.1), the wide gap setup has the disadvantage that the shear strain-rate depends on both the measurement geometry and the flow index value (n).

Magma / Suspension Rheology

655

Alternatively, the torque-viscosity relationship can be calibrated against materials of known viscosity over the desired range of torque and rotation rate, as routinely done for viscometry of pure silicate melts. The most frequently used standards for calibration are glasses from either the National Institute of Standards and Technology (NIST; formerly National Bureau of Standards, NBS) or from the Deutsche Glas Gesellschaft (DGG) for which the temperature viscosity relationships are accurately known. Using linear fits to the calibration data, a torque measurement at a certain rotation rate corresponds to the apparent viscosity of an unknown suspension. Tying sample texture to the rheological response of a suspension fundamentally relies on accurate quantification of textural parameters including crystal or bubble content, shape (aspect ratio) and size-distribution, and particle surface roughness (see also the "Parameterization Strategies"section later in this chapter). Recovering these data in combination with rheological measurements lies at the heart of the motivation for most available measurements of concentric cylinder suspension rheometry. The vast majority of studies address the effect of crystals on suspension rheology and only few concentric cylinder experiments measure bubble bearing melts. This is because concentric cylinder measurements are commonly performed near the melt's liquidus temperature (i.e., at low viscosities), where the large density differential between bubbles and melt allow for bubble percolation (i.e., buoyant separation of the exsolved gas phase) over the course of the experiment and, thus, thermomechanical equilibrium cannot be achieved for most magma compositions. The much lower density differential between common crystals and silicate melts allows maintaining textural homogeneity (i.e., constant crystal contents and shapes) over timescales sufficiently long for experimentation (hours to days). Hence, concentric cylinder viscometry is an ideal method to study magmatic low viscosity melt–particle suspensions. In the following, we review measurements of melt + crystals suspensions under equilibrium and disequilibrium conditions and their use for mapping of the full rheological behavior of crystallising lava. We also include a review of the few measurements of melt + bubble suspensions employing this experimental approach. Crystal-bearing suspensions at equilibrium conditions. For experimentation at equilibrium conditions, the sample is first molten at super liquidus temperatures to determine the viscosity of the crystal free melt. Subsequently, the sample is cooled to sub-liquidus temperatures at which crystallization is expected to occur. The environmental parameters (temperature, oxygen fugacity and shear-rate) are then maintained constant and the rheological response of the sample is monitored as a fuction of time. Some of the first experiments of this type were inspired by and combined with field measurements, which are reviewed later in this chapter. These were performed on lavas from Hawaii (Shaw 1969) and Etna (Gauthier et al. 1973). Both studies note profound sub-liquidus deviations from the liquid viscosity trend as well as from Newtonian behavior at deformation rates relevant to lava flows. Subsequent studies, such as Ryerson et al. (1988) and Pinkerton and Stevenson (1992), began to focus on systematic laboratory experimentation, and the combination with field measurements was discontinued after the work of Pinkerton and Norton (1995); see the “Field Rheology” section later in this chapter. While the aforementioned studies attempted connecting measurements of crystal contents to the rheological data using complementary petrological experiments, none of them present systematic textural analyses of the experimental samples themselves. This combination was introduced by Sato (2005) who highlighted the need for more detailed experimentation by documenting a profound discrepancy between the rheology of elongate plagioclase bearing suspensions with respect to suspensions of spherical particles (Marsh 1981) (see section “Parameterization strategies” later in this chapter for more details). Efforts to recover textural data and crystallization kinetics of the experimental samples were developed only later (Ishibashi and Sato 2007, 2010; Ishibashi 2009). These studies provided unprecedented detail on the non-Newtonian effects of magmatic suspensions including thixotropy, shear thinning and apparent yield stress. Some other studies (Sonder et al. 2006; Hobiger et al. 2011) present systematic mapping of shear rate effects on magmatic suspensions at various temperatures but omit textural data, thus impeding parameterization.

656

Kolzenburg et al.

Continuous temporal monitoring of the viscosity evolution from super liquidus to steady state sub-liquidus conditions, which allows commenting on the process kinetics, combined with systematic mapping of shear rate effects and analysis of textural features of the sample were first presented about a decade ago (Vona et al. 2011) but are starting to become more numerous in recent years (Vetere et al. 2013, 2017, 2019; Vona and Romano 2013; Sehlke et al. 2014; Chevrel et al. 2015; Sehlke and Whittington 2015; Campagnola et al. 2016; Soldati et al. 2016, 2017; Liu et al. 2017; Morrison et al. 2020). Figure 4.3 shows the schematic temporal evolution of viscosity in this type of experiment. The data show a profound time dependence and follow a characteristic four stage evolution: 1. During the initial temperature drop from super-liquidus temperatures to the experimental sub-liquidus temperature, the measured viscosity increases rapidly due to the temperature dependence of melt viscosity (thermal relaxation). 2. A period of constant, or very slowly increasing, viscosity, commonly termed “incubation time”, which has been shown to range from minutes to days. The duration is a function of both the degree of undercooling (i.e., temperature difference between sample temperature and liquidus temperature) and meltviscosity. The detailed kinetics of this incubation period remain poorly understood and incubation times are poorly reproducible in experiment. Nonetheless, systematic changes are documented and, generally speaking, increasing undercooling decreases incubation time, whereas increasing viscosity increases incubation time. 3. A relatively sharp increase in viscosity that is a result of the effect of crystal growth throughout the sample. It has been shown that crystallisation is often not homogeneous but propagates through the crucible from the walls of both the crucible and the spindle toward the sample center, a result of increased nucleation efficiency at both surfaces (Chevrel et al. 2015; Kolzenburg et al. 2018). This increase of viscosity gradually decelerates until reaching thermodynamic equilibrium (i.e., constant crystal content) and mechanical equilibrium (i.e., homogenous crystal alignment within the flow field). 4. A plateau in the measured viscosity, which represents the apparent viscosity of the suspension after reaching thermodynamic and textural equilibrium (i.e., sample temperature, crystal content and torque measurement are constant). When reaching this plateau, it is common to vary the shear rate to investigate the non-Newtonian behavior of the suspension. At the end, the measurement is stopped, and the sample is quenched for textural analyses. Attaining this equilibrium state (t4 onward) prior to any further rheological investigation of the sample (such as variations in shear rate) or quenching of the sample for textural analyses is important because the sample temperature is not measured directly. Constant thermal conditions as well as cessation of crystal growth are assumed to be achieved once a steady torque reading is reached. The time required to reach this steady state depends strongly on the sample composition and the melt viscosity since both affect the crystallization kinetics. In this type of experiment, the equilibrium state can be reached within few hours for low viscosity samples (Vona et al. 2011), while it may take several days for higher viscosity samples (Chevrel et al. 2015). Detailed studies on this incubation time are few and mostly provide measurements of nucleation delay in the absence of deformation (Swanson 1977; Couch et al. 2003; Hammer 2004). These studies also provide quantitative descriptions of nucleation and growth rates and note that the incubation time varies systematically as a function of proximity to the melt liquidus (i.e., degree of undercooling), where a lower degree of undercooling results in longer incubation times. Systematic understanding of the nucleation delay requires extensive experimental efforts coupled with thermodynamic modeling. Recently, Rusiecka et

Magma / Suspension Rheology

657

al. (2020) have performed such work and developed a model predicting the nucleation delay of olivine, plagioclase, and clinopyroxene in basaltic melts, and alkali feldspar and quartz in felsic melts that is based on classical nucleation theory and benchmarked with experimental data from experiments performed in the absence of deformation in a piston cylinder apparatus. Since the sample reaches a quantifiable textural equilibrium in these experiments, the data allow establishing the relationships between texture and rheology as it is commonly done in experiments on analogue materials (see “Analogue Materials” and “Parameterization Strategies” sections later in this chapter). Systematic experimentation has, however, shown that the sample texture attained in the steady state is heavily dependent on the thermal- and deformation-history of the sample in the stages before reaching thermomechanical equilibrium (Kouchi et al. 1986; Vona and Romano 2013; Kolzenburg et al. 2018b). As such, the recovered experimental data are pertinent to making quantitative ties between texture and rheology but data from the rheological evolution of the sample on the path to the equilibrium state, are tightly restricted to the specific experimental conditions. Further, strain accommodation in the sample may vary from being homogenously distributed to being heavily localized. Therefore, a complete analysis requires the textures to remain undisturbed during quench. In an effort to do so, Chevrel et al. (2015) employed a new kind of spindle, where an alumina ceramic is wrapped in thin Pt-foil, allowing to maintain the entire sample undisturbed during quench without sacrificing much precious metal lab ware. Their results show strong textural organization and crystal alignment during the crystallisation stage (t3). All available concentric cylinder measurements at equilibrium conditions are performed on relatively low silica content and low viscosity melts (Fig. 4.2), where the fast crystallization kinetics allow experimentation over manageable timeframes. Further, they are dominantly measured in air and at atmospheric pressures. Therefore, most data are acquired and interpreted with respect to the emplacement of lava flows. With decreasing temperature (i.e., increasing degree of undercooling) all studies observe increasing effective viscosity as a result of increasing crystal fraction. The onset of non-Newtonian, shear thinning, behavior is documented at crystal contents above ~5 vol% and becomes more pronounced as undercooling, and therewith crystal content, increases. While some studies comment on the potential existence of thixotropy (Sato 2005; Ishibashi and Sato 2007, 2010; Campagnola et al. 2016) in the measured magmatic suspensions, conclusive evidence is not available to date. This is likely because strain-dependent changes in the textural configuration of the experimental sample impede reproducing previous textural states that would be required to ascertain thixotropic behavior (Barnes 1997). Overall, the available data highlight that detailed knowledge of magma and lava undercooling, as well as strain and strain-rate dependent effects on the crystallization kinetics, is required to assess the resulting changes in rheology and, therewith, flow velocity of magmas and lavas. This outlines the necessity of incorporating the complex feedback mechanisms between flow environment (i.e., slope for lavas and pressure differential for magma plumbing), flow velocity and lava rheology into transport models of magmatic suspensions. Crystal-bearing suspensions at disequilibrium conditions. The experimental efforts reviewed above are dedicated to understanding the multiphase rheology of lava at constant environmental and textural conditions. This is because this type of experiment provides the data required to derive empirical rheologic laws from the experimental data (see section “Parameterization Strategies” for details later in this chapter). However, the conditions of subsurface magma migration and flow of lava on the surface of Earth and other Planets are inherently dynamic and induce disequilibrium. Measured and modelled cooling rates of basaltic lavas during flow and ascent range from 0.01 to 20 °C/min (Huppert et al. 1984; Flynn and Mouginis-Mark 1992; Hon et al. 1994; Cashman et al. 1999; Witter and Harris 2007; La Spina et al. 2015, 2016; Kolzenburg et al. 2017). These values are mostly representative of conduit wall contacts and lava flow crusts and can, therefore, be taken as maximum values

658

Kolzenburg et al.

that are expected to be lower in the interior of well insulated systems. Decompression during ascent is another factor promoting crystal growth and influencing its kinetics (Hammer and Rutherford 2002; Blundy et al. 2006; Arzilli and Carroll 2013). In addition, shear-rates during viscous transport in volcanic plumbing systems can range from ∼70 s−1 in Plinian eruptions (Papale 1999) to as low as 10−9 s−1 in slowly convecting magma chambers (Nicolas and Ildefonse 1996) and effusion-rates for basaltic eruptions range between 1–1000 m3s−1 (Harris and Rowland 2009; Coppola et al. 2017). For common lava flow geometries (thickness between 2 and 10 m; widths between 200–1000 m) this translates to shear-rates between ∼0.001– 2.5 s−1. Further, magmas are generated at low oxygen fugacities (f O2) and then transported and erupted on Earth’s surface, moving towards increasingly oxidizing environments. The effect of oxygen fugacity on the viscosity and structure of silicate melts relevant to natural compositions has been investigated for a range of compositions (Hamilton et al. 1964; Mysen and Virgo 1978; Mysen et al. 1984; Dingwell and Virgo 1987; Dingwell 1991; Herd 2003; Liebske et al. 2003; Sato 2005; Vetere et al. 2008; Chevrel et al. 2013a; Kolzenburg et al. 2018). Oxygen fugacity also strongly affects the stability of Fe-bearing phases, the onset of crystallization and degassing, as well as the melts crystallization-path and -kinetics and glass transition temperature (Tg) under both static (i.e., constant T and P) and dynamic (decreasing P and T) conditions (Hamilton et al. 1964; Sato 1978; Toplis and Carroll 1995; Bouhifd et al. 2004; Markl et al. 2010; Arzilli and Carroll 2013; La Spina et al. 2016; Kolzenburg et al. 2020). Therefore, evaluating the influence of the evolving environmental parameters on the transport and emplacement dynamics of magmatic suspensions requires systematic characterization of their rheological properties at non-isothermal and non-equilibrium conditions. The importance of disequilibrium effects on crystal growth has been recognized for decades (Walker et al. 1976; Pinkerton and Sparks 1978; Coish and Taylor 1979; Gamble and Taylor 1980; Lofgren 1980; Long and Wood 1986; Hammer 2006; Arzilli and Carroll 2013; Vetere et al. 2015; Arzilli et al. 2018; Kolzenburg et al. 2020) and has inspired experimental studies investigating the cooling- and shear-rate dependence of the dynamic rheology of crystallizing silicate melts at conditions near those of natural emplacement scenarios (Kouchi et al. 1986; Ryerson et al. 1988; Giordano et al. 2007; Vona and Romano 2013; Kolzenburg et al. 2020). The number of published rheological studies at disequilibrium conditions is, however, low and systematic mapping of the effects of cooling rate (Giordano et al. 2007; Kolzenburg et al. 2016, 2017, 2019; Vetere et al. 2019), shear rate (Kolzenburg et al. 2018b) and oxygen fugacity (Kolzenburg et al. 2018c, 2020) as well as their interdependence is only beginning in recent years. This is largely because disequilibrium experimentation does, to date, not allow for textural characterization of the sample during experimentation, which would be necessary for standard rheological parameterization (see the “Parameterization Strategies” section later in this chapter). Diffusion and crystal growth are very rapid at the high degrees of undercooling reached in constant cooling disequilibrium experiments and it is therefore not possible to extract and quench the experimental charges sufficiently fast to investigate their textures. Quantification of textures during disequilibrium experiments would require data at high spatial and temporal resolution, such as in situ tomographic data, as it is starting to become available for analogue materials (Dobson et al. 2020). Further, variations in the thermal inertia of the experimental apparatus induce characteristic thermal paths in the investigated melts which require in situ thermal monitoring of the sample. This was hindered in concentric cylinder viscometry, as hard-wired data transmission compromises the highly sensitive torque measurements for accurate viscosity determination. In temperature-stepping experiments this can be overcome by calibrating the sample against the furnace temperature (Dingwell 1986). At disequilibrium, however, the release of latent heat of crystallization (Settle 1979; Lange et al. 1994; Blundy et al. 2006), redox foaming (i.e., liberation of oxygen gas bubbles during reduction of Fe2O3 to FeO; see also Dingwell and Virgo (1987)), heat advection and changing heat capacity may also influence the samples’ thermal state. Further, temperature calibration without deformation, cannot assess viscous-heating effects potentially

Magma / Suspension Rheology

659

acting at high viscosities and/or high shear rates (Hess et al. 2008; Cordonnier et al. 2012a). A new experimental device that allows for in situ thermal characterization of rheological measurements was presented in Kolzenburg et al. (2016) and may serve to address the above questions in the future (see for example Kolzenburg et al. 2020).

Log 10 apparent viscosity (Pa s)

The available disequilibrium data document that, at the conditions charted to date, cooling rate is the governing parameter determining the rheological evolution of magma and shear rate and oxygen fugacity play smaller roles. All presented experimental data describe a systematic sub-liquidus rheological evolution (Fig. 4.4). The measured apparent viscosity initially follows the pure liquid curve and once crystallization occurs, the apparent viscosity of the suspension (also sometimes called the effective viscosity; Petford, 2009) deviates from this curve towards higher viscosity values. Over the course of the experiment, the apparent viscosity of the magmatic suspension gradually increases with increasing undercooling until reaching a point where the apparent viscosity of the suspension rises steeply, terminating its capacity to flow at the “rheological cut off temperature” (Tcutoff); see Kolzenburg et al. (2017). This point is commonly assigned as the stopping condition for cooling limited lava flow behavior (Wilson and Head 1994; Harris and Rowland 2009) but systematic experimental determination of this temperature only started over the past few years. The available data show that increasing cooling rate delays the crystallisation onset and hence decreases the temperature at which the initial departure from the liquid curve occurs as well as reducing Tcutoff. Decreasing oxygen fugacity decreases the temperature of the crystallisation onset and hence decreases the temperature at which the suspension viscosity departs from liquid viscosity and the Tcutoff (Kolzenburg et al. 2018c, 2020). Conversely, increasing shear-rate promotes crystallization (Kouchi et al. 1986; Vona and Romano 2013; Kolzenburg et al. 2018b; Tripoli et al. 2019) and therefore acts to increase both the temperature of the departure from liquid viscosity and Tcutoff. This is the case for any investigated cooling rate and composition. Currently available data (see Fig. 4.4. as example) suggest that, while inducing important changes, shear-rate does not out-scale the effects of cooling-rate or oxygen fugacity (Kolzenburg et al. 2018b). While standard rheological parameterization of disequilibrium data is not possible due to the lack of quantitative textural data, Tcutoff measurements present a promising approach to develop an empirical understanding of stopping criteria that can be implemented in magma and lava transport models at low computational cost (Harris and Rowland 2001; Chevrel et al. 2018). 3.5

Liquid viscosity

3

5 K/min 3.06 sec

-1

1 K/min 3.06 sec

-1

3 K/min 3.06 sec -1 0.5 K/min 3.06 sec-1

2.5

0.5 K/min 1.53 sec-1 -1

0.5 K/min 0.77 sec

2 1.5 1 1100

1150 1200 1250 Temperature (C)

1300

Figure 4.4. Evolution of apparent viscosity under constant cooling at various cooling and shear rates; data from Kolzenburg et al. (2017). All data describe a similar trend, where during constant cooling from superliquidus to sub-liquidus temperatures the apparent viscosity initially follows the pure liquid curve and once crystallization occurs, the apparent viscosity deviates from this curve towards higher viscosity values.

Kolzenburg et al.

660

Rheological mapping of crystal-bearing suspensions. To describe the full rheological evolution of a magma batch over the course of its journey to and on the surface requires rheological characterization over a wide range of sub-liquidus temperatures and shear-rate conditions. This can be done by combining data from equilibrium and disequilibrium experiments as well as from other techniques (e.g., parallel plate). An example of such a rheological map, representing the physical behavior of a given starting bulk rock composition from superto sub-liquidus (crystal-bearing suspension) conditions, is given in Figure 4.5. The melt compositions of Vona et al. (2011) and Kolzenburg et al. (2018c), albeit stemming from different eruptions, are within analytical error for all major oxides and hence all variations in the rheology of the crystallizing basalt are controlled by variations in the volumetric fractions of crystals and bubbles rather than melt composition. The megacryst-bearing lava measured in Vona et al. (2017) is slightly more silicic (~ +4 wt.% SiO2) and hence somewhat more viscous. Comparison of the pure liquid viscosity of the re-melted bulk rock and the separated groundmass presented in Vona et al. (2017) document that, for basaltic melts, crystallization induced variations in melt composition result in small changes ( 1200 °C) via concentric cylinder, 2) low temperature ( 0.2; highest temperature) 2) the relative viscosity starts to increase exponentially (gray symbols; ηr > 2; intermediate temperature) 3) the measurement limit at which the sample exceeds the torque limit of the rheometer and its relative viscosity tents towards infinity i.e., solidification (black symbols). Dotted and bold lines represent the crystallization onset and the rheological cut off, respectively.

Fournaise (La Réunion) has higher liquidus temperatures (hence the higher temperatures of the crystallization onset and solidification point) and faster crystallization kinetics (hence the shorter times required to reach both the crystallization onset and solidification point) than the Holuhraun lavas (Iceland). A prominent feature when comparing data from equilibrium and disequilibrium experiments is that at thermal equilibrium (Fig. 4.6A), the crystallization process shows a dominant time dependence (solidification occurs from left to right in the diagram), whereas at thermal disequilibrium (Fig. 4.6B), the crystallization process shows a dominant temperature dependence (solidification occurs from top to bottom in the diagram for any given cooling rate). This is because the available disequilibrium data are restricted to rather high cooling rates (> 0.5 K/min) and it is expected that at lower cooling rates (approaching equilibrium conditions), the dependence of temperature would decrease while the time dependence would increase thus merging the two experimental datasets. The measurements on the lava from Piton de la Fournaise suggest an increase in the time dependence of the process between the highest and lowest cooling rate but, to date, no coherent dataset exists that investigates this transition for a single composition and a broad range of cooling rates.

Bubble bearing suspensions Concentric cylinder rheometry data on bubble bearing suspensions are scarce. This is largely due to the thermal and mechanical constraints of the method. Retaining bubbles in a melt at high temperatures for the duration of rheology experiments (several hours to days) requires relatively high melt viscosities (>105 Pa s) to minimize bubble percolation (i.e., volatile

Magma / Suspension Rheology

663

exsolution and loss upwards through the melt). This, in turn, requires a device design that permits high torques. Only few datasets on concentric cylinder measurements of bubble bearing suspensions are published (Stein and Spera 1992, 2012; Bagdassarov and Dingwell 1993a) and few studies describe devices that could access such experimental conditions in the laboratory (Stein and Spera 1998; Morgavi et al. 2015; Kolzenburg et al. 2016). Alternatively, it was suggested that field rheometry could be used for measuring the rheology of bubble-bearing low viscosity suspension (Chevrel et al. 2018), but to date no systematic study has been published.

Parallel plate experiments Parallel plate suspension viscometry is largely dedicated to understanding the multiphase rheology of lava and magma at constant environmental and textural conditions. The compositions used in studies employing this approach vary from Andesites to Rhyolites with few examples of Basalts (Fig. 4.2). This method allows for simple experimentation on multiphase suspensions of synthetic or natural samples, since the samples can be readily recovered by core drilling from any glass bearing rock sample. This permits detailed characterization of sample texture, an important factor for parameterization of the rheological data (see the “Parameterization Strategies” section later in this chapter). For accurate measurement it is crucial to ensure parallel faces of the sample surfaces in contact with the compacting pistons since uneven faces result in anomalously high strain-rates due to the reduced initial contact area and thus underestimation of the samples viscosity. The cylindrical cores are loaded in a uniaxial press (Fig. 4.1B) and heated to the desired experimental temperature. Sample temperature can be monitored by insertion of thermocouples or by calibration to reference samples. Experiments are performed near the melt’s glass transition (i.e., in the supercooled liquid state), where the viscosity is sufficiently high to neglect crystallization and vesiculation timescales relative to the duration of the experiment. This minimises textural and chemical change of the sample over the course of the experiment and maintains steady state suspension viscosity over the measurement timescales (minutes to hours). Parallel plate viscometry uses cylindrical samples that are deformed in uniaxial compression either at constant load or at constant strain-rate. Constant strain-rate experiments record stress-time relationships sensed via a load cell. Constant load experiments record straintime relationships measured by dilatometry. Although the experiments involve relatively small total strains it is still possible to run stress or strain-rate stepping experiments (Fig. 4.7A). The simplest approach to calculate the apparent viscosity of the sample in uniaxial compression parallel plate experiments is to derive it directly from the ratio of the recorded stress (σ, i.e., load over surface area in contact with the piston) and engineering-strain-rate ( e; i.e., variation of the sample length (Δl/l) per unit time) (Quane and Russell 2005; Avard and Whittington 2012; Heap et al. 2014; Ryan et al. 2019a): app 

 e

(4.3)

However, at the imposed strains (up to ~30–40 %), the sample geometry changes, and the sample strain cannot simply be described as Δl/l. Thus, Recovering the samples shear viscosity from parallel-plate viscometry requires that the geometrical change is accounted for. This approach rests on the mathematical description of the flow process by two differential equations, the Navier–Stokes equation and the continuity equation, following the Wallace plastimeter methodology (Rowlatt 1956). For isothermal conditions and with some simplifying assumptions, an analytical solution to these was obtained by Gent (1960). Based on experiments on coal tar and cross correlation with concentric cylinder viscometry, Gent (1960) validated the proposed, geometry independent (isovolumetric), theoretical formulation to recover shear viscosity from parallel plate experiments. Following this approach, calculation of the samples’ shear viscosity (hs) from the experimental data rests on one of two geometrical assumptions for the deformation mechanism.

Kolzenburg et al.

664

13

A

Log apparent viscosity modelled

Log apparent viscosity (Pa s)

11 10.8 10.6 10.4

-3.5 -1

10

s

-4

10

10.2

s

-1

-4.5 -1

10

s

10-5 s -1

10 0

0.05

0.1

0.15 Strain

0.2

B

12.5 12 11.5 11 10.5 10

Lavallée et al., 2007 Award and Whittington 2012

9.5 9 9

0.25

10 11 12 Log apparent viscosity measured

13

Figure 4.7. (A) Plot of apparent viscosity vs. strain for a strain rate stepping experiment on Chaos Crags (USA) dome lava (unpublished data by Kolzenburg et al.). For a given strain rate, the recorded load (and thus also the measured viscosity) initially increases rapidly until reaching a constant value equivalent to the relaxed rate of continuous sample deformation. The data describe clear shear thinning behavior (i.e., increasing strain-rate decreases apparent viscosity). (B) Comparison between the non-Newtonian models of Lavallée et al. (2007) and Avard and Whittington (2012) derived from uniaxial parallel plate experiments (plot modified after Avard and Whittington 2012 Fig, 12a). Note that this figure compares the model of Lavallée et al. (2007) to the one presented in Avard and Whittington (2012). As such, this is not an assessment of overall quality of one model over the other but a demonstration of the fact that that neither of these non-Newtonian models can comprehensively describe the rheology of dome lavas but each one is applicable only within the framework it was developed in. This highlights the need for further and systematic rheometry in order to derive a holistic rheological model.

1. The “no slip” condition, where the contact surface area between the sample and the parallel plates remains constant and the cylinder accommodates all deformation by bulging/barrelling. In this case the shear viscosity is calculated as follows:

2 Fh5 (4.4) h 3V 2 h3  V t where F the applied force, h the sample height, V the sample volume and t is time. Dt and DV are time and volume variation, respectively s 

2.





The “perfect slip” condition, where the contact surface area between the sample and the plates increases with deformation while the cylinder does not bulge (i.e., retains vertical sides). In this case the shear viscosity is calculated as follows:

h2 F (4.5) h 3V t Both equations are valid only for experimental geometries where the sample diameter is smaller than the diameter of the parallel plates (i.e., no sample extrusion) and the sample is assmed to be both incompressible and stay cylindrically symmetrical (i.e., not sagging under its own weight). s 

Further, at high porosity, vesicular melts may behave in pure uniaxial compression, meaning that neither bulging nor sample translation occurs. It is important to note here, that the deformation of bubbles contributes a significant volume viscosity to the macroscopic flow of vesicular materials and due to the compressibility of pore fluids or gases, the sample volume does, in most cases, not remain constant during experimentation. In this case, the measured viscosity is equivalent to the samples’ bulk (or longitudinal) viscosity (Eqn. 2.6) and therefore additional determination of shear or volume viscosity is required to completely resolve the samples’ rheology.

Magma / Suspension Rheology

665

The main limitation of parallel plate viscometry for application to natural magmatic suspensions has long been the relatively small sample size. Most common parallel plate viscometers are restricted to cylindrical sample diameters below 10-15 mm, largely because of the balance between the high stresses required for deformation of high viscosity samples near the glass transition and the limitations in compressive strength of the materials used as pistons driving the parallel plates (ceramics, silica glass or high temperature metal alloys). For a sample to be representative of the whole rock texture, however, its diameter sample should be ~8–10 times that of the largest crystal or bubble present (Ulusay and Hudson 2006). Seeing as bubble and crystal sizes in igneous rocks commonly range from hundreds of microns up to a few centimetres, rheological studies were initially limited to microlite bearing melts with crystal sizes below ~350 micron (Lejeune and Richet 1995; Stevenson et al. 1996) and bubble sizes below 1 mm (Bagdassarov and Dingwell 1992). Although the available experimental data are few, only a limited number of studies were presented following the initial qualitative descriptions in the aforementioned contributions and there is significant potential for expansion and improvement. The first magmatic suspensions studied with parallel plate viscometry concerned vesicular rhyolite and were presented in Bagdassarov and Dingwell (1992). However, as outlined above, the equations provided by Gent (1960) are valid only for isovolumetric systems. On first glance this makes them inapplicable to bubble bearing systems, since bubbles contain compressible gas. Several approaches have been presented to account for this issue but all of them remain to be validated by cross correlation with other rheometric methods. Bagdassarov and Dingwell (1992) modify the perfect slip equation provided in Gent (1960) by expanding sample volume to: V  h  Seff

(4.6)

And then simplifying Equation (4.5) to: s 

hF h 3Seff t

(4.7)

Note that they introduce Seff, the effective surface area of the sample, which is corrected for the sample’s surface porosity in contact with the plates: Seff  Sabs  (1   b )

(4.8)

where Sabs being the total sample surface area in contact with the plates and Φb the bubble volume fraction. Vona et al. (2016) also adapted the equation for perfect slip conditions and expanded it to account for variations in sample volume over the course of the experiment. They achieve this by measuring sample volume before and after the viscosity measurement and then distributing the volume reduction linearly over the course of the experiment:

app 

h2 F

(4.9) h t where V0 is the initial sample volume and k is a coefficient tracking the porosity loss. It is defined as k = 0.01(ff – fi) / tf , where fi is the initial porosity, ff is the final porosity, and tf is the final time. This linear distribution of volume reduction, however, does not account for the compressibility of the gas phase in the bubble, which induces a non-linear transition from simple core shortening during the initial deformation phase to the perfect slip condition reached at the end of the experiment. As such this approach is only applicable for low strain experiments.

3 V0 1  kt  

Kolzenburg et al.

666

Bubbly silicate melts or foams are essentially impermeable unless they undergo bubble wall fragmentation (Taisne and Jaupart 2008; Takeuchi et al. 2008, 2009; Caricchi et al. 2011; Shields et al. 2014; Von Aulock et al. 2017; Ryan et al. 2019a,b). Hence they can act as gas springs due to the compressibility of the pore gas (Jellinek and Bercovici 2011). It would therefore be favorable to treat the sample as one volumetric unit and use the entire sample (melt + bubbles) surface area when converting measurement data to viscosity values (see Eqn. 4.10). This approach could, in principle, be developed to also account for the non-linear compressibility of gases for the study of suspensions of pressurized bubbles. Ultimately, the simplest and most favorable way to recover shear viscosity from parallel plate experiments is a modified version of the method proposed by Bagdassarov and Dingwell (1992) that uses the absolute sample surface area (rather than a porosity correction) in the form of: app 

hF h 3Sabs t

(4.10)

Due to the range of proposed data reduction approaches reviewed above, rigorous comparison of published date is not possible and hence systematic parameterization of bubble suspension and three phase suspension rheology has been impeded to date. In the following we present a review of published experimental work on magmatic suspensions, focusing on the employed apparatuses, textural variations and core findings of the respective studies. The first experiments on bubble-free particle suspension obtained with parallel plate viscometry were performed with unimodal enstatite spherules suspended in an enstatite melt (Lejeune and Richet (1995). This study describes Newtonian behavior up to crystal volume fractions of Φ = 0.4. Beyond the Φ = 0.4 threshold Stevenson et al. (1996) document nonNewtonian shear thinning effects and the development of an apparent yield stress. At Φ > 0.7 the deformation behavior is reported to evolve towards non-uniform distribution of crystals and melt with the onset of brittle processes (solid-like behavior). The authors state that the data support the simple Einstein–Roscoe model (see “Parameterization Strategies” section later in this chapter for details) for suspensions of spherical particles but also noted that crystal size distribution and shape may be of importance to fully describe textures relevant to natural samples. The latter point was demonstrated by Stevenson et al. (1996) who performed measurements on obsidian containing prismatic to needle shaped microlites and demonstrated the Einstein–Roscoe model may drastically underestimate the effective suspension viscosity once particle shapes deviate from spherical. The sample size limitation was addressed by Quane et al. (2004) who introduced a new device capable of high temperature (up to 1100 °C) experimentation on samples of up to ~7 cm diameter and loads of up to ~1100 kg. This high-temperature, low-load apparatus was employed in a number of studies, dominantly aimed at quantifying the rheological behavior of welding and compacting volcaniclastic deposits, on both natural and analogue materials at atmospheric conditions (Quane and Russell 2005, 2006; Quane et al. 2009; Heap et al. 2014) and was later modified to allow for experimentation at elevated H2O pore fluid pressures (Robert et al. 2008). Based on some of these data, Russell and Quane (2005) developed an empirical rheological model for welding and compacting deposits that has found wide application in numerical studies, e.g., Kolzenburg et al. (2019). The observed strain (eT) is ascribed to a combination of a time-dependent viscous compaction (ev) and a time-independent mechanical compaction (em) described by:

T 

1  0  ln 1  

 

0 t   exp10   0 x  10   E 1  0 

(4.11)

Magma / Suspension Rheology

667

where f0 is the original porosity, σ is the stress acting on the sample, and η0x and E are the viscosity and Young’s modulus of the deposit at zero porosity, respectively. In this model, the effective viscosity of the crystal-bearing melt without bubbles (i.e., η0x where f0 = 0) is determined as a function of temperature. The α value is used to predict the bulk viscosity of the mixture as a function of porosity, and the increase in relative viscosity with decreasing porosity (Quane et al. 2009). Published values of α range from ~0.7 to ~5.5 (Ducamp and Raj 1989; Quane and Russell 2005; Quane et al. 2009; Heap et al. 2014) and vary as a consequence of differences in sample microstructure (i.e., porosity, crystal content, pore size and shape, particle size and shape, and pore and particle size distribution, amongst others). See Wadsworth et al. (2022, this volume) for further details on sintering and welding. A similar device to that introduced in Quane et al. (2004) was also employed by Vona et al. (2017) to study the multiphase rheology of megacryst-rich magmas. This study documents the lava’s complex rheological response related to a non-homogenous deformation of the natural sample (e.g., viscous and/or brittle shear localization), favored by the presence of bubbles. The authors argue that the obtained flow parameters can be considered as representative of the bulk rheology of natural magmas, characterized by similar non-homogeneous deformation styles. The optimal scaling relation of sample size ≫ largest crystal or bubble could however not be reached by this study due to machine limitations.

To date there are only few parallel plate devices that are capable of performing high load high temperature experiments on large samples. The design for a high load, high temperature deformation apparatus was introduced in Hess et al. (2007) and allows measurements on geologically relevant sample dimensions (up to 100 mm in both length and diameter). This resulted in several seminal contributions advancing the understanding of non-Newtonian effects such as viscous heating in pure melts (Hess et al. 2008) as well as strain-rate dependent rheology and viscous limit of flow during dome building eruptions (Lavallée et al. 2007, 2008, 2012; Cordonnier et al. 2009, 2012b); see also Lavallée and Kendrick (2022, this volume) . The large sample size and high load capacity directed use of this device towards investigating magma failure and shear localisation (Lavallée et al. 2008, 2012, 2013; Coats et al. 2018); mapping the boundary between viscous and elastic deformation mechanisms and exploring suspensions of high crystal volume fractions Φ = 0.5–0.6. The first published datasets suggested that highly crystalline suspensions of varying composition and texture can be described by a single nonNewtonian rheological law (Lavallée et al. 2007). Successive experiments, however, showed that their behavior is more complex, involving decreases in viscosity with increasing total strain and strain-rate, resulting from changes in sample texture (i.e., breaking of crystals and textural reorganization rather than true non-Newtonian flow behavior). Therefore, further systematic characterization is needed in order to derive holistic rheological laws for magmatic three phase suspensions at eruptive conditions (Cordonnier et al. 2009; Avard and Whittington 2012). Some interesting non-isothermal parallel plate viscometry experiments were presented in Bouhifd et al. (2004) and Villeneuve et al. (2008), in which samples of glassy basalt were heated from below their glass transition temperature to 1250 °C and 1300 °C, respectively. This induced crystallization of the glassy basalt sample while passing from the supercooled liquid state through the crystallization window to super-liquidus temperatures. The results highlight the profound effect that crystallization has to increase the effective viscosity of basaltic melts and also indicate that decreasing oxygen fugacity may inhibit crystallization in the supercooled liquid field. Unfortunately, neither of the studies provided accurate determinations of the viscosity–crystal fraction relationships or textural characterization, rendering the data not suitable for parameterization and derivation of rheological flow-laws. Dynamic experiments tracking rheological changes during vesiculation of synthetic three phase magmas were presented in Pistone et al. (2017). The experiments document that during foaming (i.e., nucleation and growth of gas-pressurised bubbles) and inflation, the rheological

Kolzenburg et al.

668

lubrication of the system is dictated by the initial crystallinity. At Φ  0.8), vesiculation leads to large overpressures, triggering extensive brittle fragmentation. This novel approach to using parallel plate viscometry as a method to probe dynamic changes in flow behavior of three phase suspensions magma is very promising and presents a potentially very fruitful research path to be explored for natural magmas in the years to come.

Torsion experiments Oscillatory torsion measurements. The first high temperature viscometry experiments on magmatic suspensions performed in torsion used a custom built forced sinusoidal torsion deformation device that induced very small oscillatory strain (e  Δ log η (T)

12 8

Crystallization Interval

6

Δ log η (X) ∼ Δ log η (T)

2 0 -2

4

6

8

10

(A) 12

10000/T(K) A

B 14

10

(Pa s)

D

R

Δ log η (X) >> Δ log η (T)

12

log

845

8

Crystallization Interval

6

Figure 3. Compilation of modern measurements of viscosity for a range of geological melts (sources in Giordano et al. 2008). (A) Viscosity measurements (N = 945) on 59 anhydrous silicate melts at controlled temperature and atmospheric pressure. (B) Viscosity values (N = 843) of volatile-bearing (H2O, F) silicate melts. Note change in scale of x-axis; grey shaded field denotes the log η–T(K) space corresponding to measured values for anhydrous melts. Crystallization on the time-scales of the experiments creates a data gap between low and high viscosity measurements. The top bar on each panel denotes the range of formation and eruption temperatures for anhydrous to hydrous natural basalts (B), andesite (A), dacite (D) and rhyolite (R).

4 2

Δ log η (X) < Δ log η (T)

0 -2

4

6

8

10

12

(B) 14

10000/T(K)

16

18

20

The micropenetration and parallel plate techniques have been widely applied to the determination of the viscosity of supercooled metastable melts, both dry and hydrous. The hydrous melts are synthesized at high-T and high-P superliquidus conditions using a conventional piston–cylinder or hydrothermal bomb (Lejeune et al. 1994, Giordano et al. 2004; Vetere et al. 2006). At low-T, the viscosity measurement can often be accomplished in less time than the time required for significant water loss via diffusion and this is a prerequisite for the ure 3: MSA_Viscosity_review_2020 determination of the viscosity of hydrous melts in a metastable state. At higher temperatures and lower viscosities, phase separation may ensue in the form of foaming, crystallization or liquid– liquid unmixing (depending on melt composition). The common gap in data between 105 Pa s and 108 Pa s (Fig. 3) is an experimental artifact resulting from this competition between the timescale of melt relaxation (i.e., minimum measurement timescale) and timescales of processes that may modify the material properties (i.e., crystallization, vesiculation or liquid-unmixing). On occasion, innovative methods have been developed and used to address specific questions that cannot be constrained by a combination of the more common low-viscosity (e.g., concentric-cylinder) and high viscosity (e.g., micropenetration) measurements. Notably, Dorfman et al. (1996) used a centrifuge-assisted falling-sphere technique to measure melt viscosity at intermediate temperatures that are commonly experimentally inaccessible due to enhanced crystallization rates. A similar methodology was used by Ardia et al. (2008) to

846

Russell et al.

measure the viscosity of hydrous silicic melts under pressure. In both cases, the centrifugeassisted method ensured the timescale of viscometry was shorter than for crystallization or foaming in these peralkaline and hydrous (respectively), rhyolitic melts. For some melt compositions, these unique datasets can be critical for more accurately constraining the nature of the melt’s temperature dependence (e.g., Arrhenian vs. non-Arrhenian; Russell et al. 2002).

Viscosity data for natural silicate melts Figure 3 illustrates the range and quality of melt viscosity data available as a result of modern experimentation (sources in Giordano et al. 2008). The dataset includes a wide range of melt compositions that cover the compositional range of most common natural melts (Fig. 1A, B). The parameter NBO/T (ratio of nonbridging oxygens to tetrahedrally coordinated cations) and the SM parameter (CaO + MgO + MnO + 0.5 FeOTotal + Na2O + K2O mol.%; Giordano and Dingwell 2003), both calculated from melt compositions, serve as chemical proxies for the structural organization of the melt and degree of polymerization (Mysen et al. 1982; Mysen 1988). The melt viscosity dataset (Fig. 3) spans and parallels the range of NBO/T and SM values of the common natural melts indicating the experimental data include melts of a wide range polymerisation (Fig. 1C). The anhydrous dataset of 952 measurements (Fig. 3A) spans temperatures of 535–1705 oC and viscosities of 10−1 to 1014 Pa s. At high temperature, the effects of composition and temperature on the range of viscosity values are similar (Fig. 3A). The corresponding data for volatile-rich melts comprise 843 measurements on 143 different compositions and are dominated by variations in H2O and F contents (Fig. 3B). The magnitude of the range of viscosity values is more or less the same as for the anhydrous melts (10−0.1 to 1013.4 Pa s) but the corresponding temperature range is to much lower values (245–1580 oC) reflecting the marked decrease in melt viscosity with increasing volatile content (Dingwell et al. 1996; Baker 1996; Hess and Dingwell 1996). At low values of viscosity, the effects of composition are subordinate to temperature whereas at high viscosities (low temperature) compositional (i.e., volatiles) effects dominate. The relative effects of melt composition and temperature on viscosity can be summarized using calculated isokom temperatures (i.e., constant viscosity) for a variety of melt compositions (Fig. 4). The melt compositions range from polymerized (low NBO/T and SM) to highly depolymerized (high NBO/T and SM) (data from Giordano and Russell 2018). At low viscosities (104 to 106 Pa s) isokom temperatures decrease markedly with increasing SM and NBO/T. At higher viscosities approaching 1012 Pa s the decrease in isokom temperature with composition is less apparent. Two calculated isokoms for equivalent melts with 1 wt.% dissolved H2O illustrate the strong effect of H2O on melt viscosity (cf. Hess and Dingwell 1996; Dingwell 1998; Giordano et al. 2004). Again the effect of H2O is most pronounced in more polymerized melts with low NBO/T and SM).

3. MODEL CONSIDERATIONS Scientific models have the main purpose of representing ideas, replicating data or observations, and making pertinent predictions and reliable extrapolations. Greenwood (1989) eloquently summarized the minimum requirements for a model to be deemed useful and scientifically acceptable. He suggested, “we should reserve the word ‘model’ for a well constrained, logical construct (not necessarily mathematical), that has necessary predictable and testable consequences.” To reproduce a set of data does not suffice. A model having no predicted and testable consequences is at risk of being unverifiable, sterile, and of limited use (Popper 1968). The more rigorous the model, the more consequences it implies—each of which is a test of that model.

Models for Viscosity of Geological Melts 0.02

1800

0.15

104

Temperature (K)

0.45

0.96

1.5

Tg ~ 1012 Pa s

1600 1400

NBO/T

108

Figure 4. Isokom temperatures for viscosities of 104, 108, and 1012 Pa s plotted as T(K) for 23 melt compositions spanning a wide range of compositions and degrees of polymerization (i.e., NBO/T and SM). The 1012 Pa s isokom (solid circles) marks the glass transition temperature (Tg). Blue circles show depression of isokom temperatures for melts having 1 wt.% dissolved water.

104

1200 12 1000 10

800 600

0

847

10

20

30

SM Parameter

40

50

The main goal of viscosity models for geological melts (silicate and otherwise) is to reliably predict melt viscosity at the conditions found in natural systems. Conceptually, good models incorporate abundant and accurate experimental observations and return a reliable tool that reproduces the data and can be extrapolated to domains where data are absent or scant. Our need for models that accurately predict the viscosity of geological melts at conditions relevant to melt production, storage and transport continues to grow as the compositional range of geological melts on Earth and other planets expands (Fig. 1). These models are also required to support the ever more sophisticated numerical models we use for simulating igneous and volcanic processes. Melts in geological systems are susceptible to continuous and dramatic changes in temperature (T) and chemical composition (X) driven by crystallization, mixing with other melts, assimilation of foreign material, changes in redox state, or exsolution or re-dissolution of volatiles. Whilst experiments cannot be expected to cover all of these T-X-driven variations in melt viscosity, models can. Lastly, it is worth recalling that although terrestrial melts have restricted and characteristic formation and eruption temperatures (Spera 2000; Lesher and Spera 2015), laboratory experiments cover a substantially greater T(K)–log η space (cf. Fig. 3A, B). However, models Figure 4: MSA_Viscosity_review_2020 that can be extrapolated over an even wider range of melt compositions (or temperatures and fO2 conditions) can accommodate potential, unforeseen, extreme compositions arising from protracted differentiation (as stated above), partial melting of crustal rocks, melts produced by frictional heating, lightning strikes or meteor impacts, as well as, new melts discovered on other planetary bodies. The ideal viscosity model for geological melts will, in addition to reproducing the original data, have the following attributes. It should span all of the compositional range (including volatiles) found in naturally-occurring volcanic rocks and it should be computationally continuous across the entire compositional and temperature spectrum of the database. Viscosity experiments performed at lower temperatures and higher viscosities have shown geological melts to vary in their T-dependence from near Arrhenian (i.e., more polymerized melts with low NBO/T or SM values) to markedly non-Arrhenian (i.e., depolymerized melts having high NBO/T or SM values) (Fig. 3). Thus, an effective model for viscosity of geological melts must also be able to accommodate both strong near-Arrhenian and non-Arrhenian T-dependent behaviour of silicate melts (e.g., Angell 1985).

Russell et al.

848

As noted above, an ideal model should also have predictable and testable consequences (e.g., Popper 1968; Greenwood 1989). For example, models for the viscosity of geological melts should support the calculation of derivative transport properties that can be tested independently, such as melt fragility (m) and glass transition temperature (Tg). Angell (1985) recognized two extreme behaviours of glass-forming liquids depending on their behaviour as they cool to their Tg: strong vs. fragile. Melt fragility is a measure of the degree to which the T-dependence of viscosity deviates from Arrhenian behaviour. In his early work, Angell suggested that strong liquids are near-Arrhenian and characterized by small changes in heat capacity as they cross the glass transition temperature. Conversely, fragile melts are associated with larger changes in heat capacity at the transition and are more strongly non-Arrhenian in their T-dependence. The degree of fragility is commonly tracked by the model-independent “steepness index” (m; Angell 1985; Plazek and Ngai 1991), which characterizes the slope of the viscosity and the associated average structural relaxation time of the melt with temperature as it approaches Tg. Essentially, it is the slope of the viscosity curve evaluated a temperatures approaching Tg: m

d  log10  where T  Tg T  d g   T

(1)

where Tg is defined as the temperature at which the melt viscosity ~1012 Pa s. Lastly, models should be internally consistent with the original tenets or assumptions adopted in the model (i.e., assumed Tg values, constant high-T limit, etc.).

4. TEMPERATURE DEPENDENCE OF MELT VISCOSITY Melts of different composition can have very different viscosities at equal temperatures (Fig. 4) and can have different temperature dependences (Fig. 3). The simplest temperature dependence shown by silicate melt viscosity is Arrhenian:   Ae  Ea / RT

(2)

where Ea is the activation energy for viscous flow and the pre-exponential term A represents the viscosity at infinite temperature (η∞). The values of the two adjustable parameters A and Ea are commonly taken as characteristic for individual melt compositions although theory and practice suggest A is a constant independent of melt composition (see below; Bottinga and Weill 1972; Shaw 1972; Persikov 1991; Persikov and Bukhtiyarov 2009; Russell et al. 2002, 2003). In general, at high-temperatures activation energy (i.e., slope of log η vs. 1/T) is highest in high viscosity liquids and decreases with decreasing viscosity. Early experimental measurements of melt viscosity were limited to super-liquidus temperatures where many silicate melts show near-Arrhenian behaviour over the observed temperature range. Ultimately, additional experimental strategies were developed that extended the range of measurements down to temperatures near Tg confirming that many geological melts can exhibit non-Arrhenian T-dependence (i.e., see Richet and Bottinga 1986, 1995; Dingwell et al. 1993).

Non-Arrhenian functions for melt viscosity Non-Arrhenian melts require higher-order functions to describe the non-linear T-dependence in their viscosity. Numerous functions have been developed to capture the non-Arrhenian temperature dependence and most involve three adjustable parameters (for simplicity referred to here as A, B, C). The reader is referred to Sturm (1980), Bottinga et al. (1995), Richet and Bottinga (1995), Russell et al. (2002, 2003), Russell and Giordano (2005), Mauro et al. (2009), and Kondratiev and Khvan (2016) for discussion of the merits of each of these. Here we briefly review four of these functions.

Models for Viscosity of Geological Melts

849

The Vogel–Fulcher–Tammann (VFT) equation is an empirical means of accommodating the non-Arrhenian temperature dependence of viscosity (Angell 1991; Richet and Bottinga 1995; Bottinga et al. 1995; Rössler et al. 1998): log  AVFT 

BVFT T  CVFT

(3)

where AVFT, BVFT, CVFT are adjustable parameters specific to individual melts. The parameter AVFT is the value of log η (Pa·s) at infinite temperature (log η∞). The parameter BVFT corresponds to the pseudo-activation energy associated with viscous flow and is thought to represent a potential energy barrier obstructing the structural rearrangement of the melt. The CVFT parameter is the temperature (K) at which viscosity becomes infinite. The VFT function is an effective descriptor of the viscosity over the compositional range of most geochemically important melts. The Adam–Gibbs (AG) functions are based on configurational entropy theory and provide a connection between the transport properties, relaxation timescales of melts, and their thermochemical properties (Adam and Gibbs 1965; Richet 1984; Bottinga et al. 1995; Richet and Bottinga 1995; Bottinga and Richet 1996; Toplis et al. 1997; Russell and Giordano 2017). The T-dependence of melt viscosity (η) is described by: log A 

B TSc  T 

(4)

where Sc is the configurational entropy of the melt at temperature (T), B is proportional to the activation energy for viscous flow, and A is again the high temperature limiting viscosity (Adam and Gibbs 1965; Richet 1984). The AG function can be expanded by introducing the concept of the glass transition temperature: B T Cp T (5)    dt  T  Sc  Tg    Tg T   where Sc(Tg) is the residual configurational entropy of the investigated sample at Tg. Assuming that configurational heat capacity of the melt is constant above Tg and that Sc ~0 at Tg (Richet 1984; Angell 1991; Toplis et al. 1997) simplifies the AG function to three adjustable parameters: log A 



BAG (6)  T  T  log   CAG  where CAG is the temperature of the glass transition. Under these conditions, the VTF and AG equations are operationally equivalent (Angell 1991; Bottinga et al. 1995; Richet and Bottinga 1995; Bottinga and Richet 1996; Toplis et al. 1997). log  AAG 

The Avramov and Milchev (1988) model determines the temperature dependence of the average jump frequency of moving entities (in their wording “molecules”) and, through it, the viscosity. The main assumption is that energy barriers of different heights appear, with a distribution depending on entropy. The viscosity depends therefore on total entropy, not on configurational entropy alone. Adopting a reference (glass transition) temperature corresponding to a melt viscosity 1012.5 Pa s and further assuming that the heat capacity of the liquid is independent of temperature they advocated a function (AV) of the form (i.e., Avramov 1998): B  log  AAV   AV   T 

CAV

(7)

Russell et al.

850

Recently, Mauro et al. (2009) has explored the attributes of another three-parameter equation (MYEGA: MY) for the temperature dependence of melt viscosity that was first described by Waterton (1932): log  AMY 

BMY CTMY e T

(8)

Their derivation starts by linking the configurational entropy from the Adam–Gibbs approach to a topologically determined number of degrees of freedom per atom. CMY is a normalised activation energy describing the intact degrees of freedom per atom with rising temperature. BMY is essentially the normalised BAG of the Adam–Gibbs equation (Fotheringham 2019). 16

An ( n=6 7

)

(A)

14

10 8 6

)

02 (n

2

)

70

(n= Ab

4

=1

Log 10

(Pa s)

12

Di

0 -2 4 16 14

5

6

7

8

10000/T(K)

9

10

11

(B)

10 8 -1

6

Log 10

-2 -4 -5

2

-6

0

-7

-2

-9

-8

4

- VFT (A = -4.69)

The parameter A in each of the four model equations represents the value of melt viscosity at infinite temperature (log η∞).

-3

4

A VFT

(Pa s)

12

These four functions (Eqn. 3, 6–8) have been fitted to viscosity data sets for three simple (synthetic) silicate melts (Fig. 5): CaMgSi2O6 (Diopside, Dp), CaAl2Si2O8 (Anorthite, An), and NaAlSi3O8 (Albite, Ab). One attribute of these melts is the abundance of measurements spanning a large range of temperature (685 to 2175 oC) and viscosity (10−1.2 to 10−14.5 Pa s) (sources in Li et al. 2020). Furthermore, two of the melts have NBO/T values of 0 and one has an NBO/T of 2, whereas two melts are nonArrhenian and one melt is near-Arrhenian in their T-dependence. The optimal adjustable parameters A, B and C (Table 2) for each melt differ between the four model equations (Eqn. 3, 6–8) because of differences in their form but each function reproduces the data well (Fig. 5A). The greatest discordance occurs at high-T and low viscosity where the AV function shows the largest misfits.

0.6 0.4

5

6

7

200

8

10000/T(K)

400

9

600 C VFT

800

10

1000

11

(C)

0.2 0

log

-0.2 -0.4 -0.6 -0.6

-0.4

-0.2

log

0

0.2

- VFT

0.4

0.6

Figure 5. Models for the temperature dependence of melt viscosity fitted to data for melts (Di, An, Ab): (A) Comparison of model curves based on VFT (solid line), Adam–Gibbs (AG, dash line), Avramov (AV, dash-dot line), and MYEGA (MY, blue dash line) functions. The four functions reproduce the data well and predict similar values of Tg and m (Table 2). (B) The VFT function fitted to the Di, An, and Ab database assuming a common value of A (log η∞) (solid line) and compared to VFT function for individual melts (dashed lines). Inset shows 99% confidence limits on values of A and C (solid squares) from the individual fits; horizontal line denotes the optimal value for a common A (−4.69 ± 0.99; Table 4). (C) Misfits to data from fitting individual datasets (Di, An, Ab) vs. fitting with a common A.

Models for Viscosity of Geological Melts

851

Interestingly, each function defines very different restricted ranges of A for the three melts (Table 2, AVFT: −5 to −4.6, AAG: −3.7 to −3.6, AAV: −2.1 to −1.4, AMY: −4.2 to −2.3) (Russell et al. 2002; Kozmidis−Petrovic 2014). The optimal values of A may suggest which functions are best for geological melts. For example, the values of AAV are only slightly lower than the lowest measured values of log η (−1.29) whereas model values of AMY span 2 orders of magnitude for these three melts (see below). Each of these four functions (Eqn. 3, 6−8) allows for the calculation of the derivative properties. Table 3 lists the expressions for calculating values of Tg, taken as the temperature where η ~ 1012 Pa·s, and melt fragility m from the optimal parameters A, B, and C. This provides an additional means of illustrating the differences between these non-Arrhenian parameterisations by comparing the derivative properties implied by the optimal parameters A, B, and C. Values of Tg and m for the three melts are reported in Table 3 based on the four model equations. All four models predict very similar values of Tg even though the functional forms are very different. Fragility values (m) predicted with the VFT, AG and AV model equations also agree well; notably, the MY function predicts a substantially lower value for m.

Table 2. Formulas to calculate derivative properties (Tg and m) from model values1 of A, B, C. Tg (K)2

Model

VFT

AG

AV2

MYEGA

TgVFT

Fragility (m)3 mVFT 

BVFT   CVFT 12  AVFT

T BAG roots  TgAG ln gAG 12  AAG CAG

TgAV 

mAG 

BAV

12.5  AAV 

1

 C  TgVFT 1  VFT   TgVFT 

CMY

TgMY

2

 TgAG   1 C AG   T ln gAG CAG

12  AAG   ln

B  mAV  CAV  AV   TgAV 

CAV

roots 12  AMY  TgMY  BMY e

BVFT

mMY 

CAV

BMYCMY CMY TgMY e TgMY 2

Notes: 1 Values of A, B, C are adjustable parameters for each function (see text) fitted to viscosity data. 2 Tg is taken as T(K) at which melt has a viscosity of 1012 Pa s except AV model which adopts 1012.5 Pa s 3 Fragility (m) is taken as the steepness index (see text).

5. THE HIGH-TEMPERATURE LIMIT TO MELT VISCOSITY (A) The parameter A in the four functions discussed above (Eqn. 3, 6–8) is the value of log η∞ and, conceptually, represents the high-temperature limit to silicate melt viscosity. Russell et al. (2002, 2003) reviewed the concept of A as a constant for all geological melts (i.e., independent of composition) implying that at high-T all melts ultimately converge to a single, common value of viscosity. This assertion is supported practically and theoretically (Myuller 1955; Eyring et al. 1982; Angell 1985; Russell et al. 2002, 2003).

Russell et al.

852

Table 3. Parameterization of compiled datasets1 of T(K)–log η for diopside (Dp), anorthite (An), and albite (Ab) melts using VTF, AG, AV, and MYEGA (MY) empirical equations (see text). Melt Composition

Dp

An

Ab

No. Experiments

102

67

70

2

0

0

NBO/T SM Parameter VFT

AG

AV

MYEGA

50

25

12.5

AVFT

−4.63

−4.71

−5.01

BVFT

4,520

5,536

11,513

CVFT

721.1

797.9

410.7

Tg (K)

993

1129

1087

m

60.7

57.0

27.3

AAG

−3.62

−3.68

−3.57

BAG

2,350

2,988

9,887

CAG

700.5

766.0

283.5

Tg (K)

993

1130

1088

m

60.4

56.1

27.1

AAV

−1.39

−1.62

−2.13

BAV

1,801

2,242

4,359

CAV

4.36

3.81

1.91

Tg (K)

993

1130

1090

m

58.4

51.9

27.0

AMY

−2.36

−2.65

−4.21

BMY

631.4

1127.4

8938.39

CMY

3096

3037

738.8

Tg (K)

993

1130

1088

m

44.8

39.4

11.0

Note: 1Data sources as in Li et al. (2020).

Practical application of a high-T limit We demonstrate the practical aspects of the “common A concept” using two separate datasets: i) the 3 synthetic silicate melts An–Ab–Di (Fig. 5); and ii) 23 multicomponent natural melts (sources in Giordano and Russell 2018). Simple System: Di−An−Ab. VFT functions have been fit simultaneously to the An–Ab−Di dataset assuming that all three melts share a common but unknown high−temperature limiting value of viscosity (i.e., A = log h∞) whilst allowing for individual values of BVFT and CVFT (Table 4). The optimal solution for AVFT is −4.69 (± 0.99) and the experimental data are reproduced exceptionally well (Fig. 5C) despite using two fewer adjustable parameters (i.e., single value for A rather than three). Furthermore, the model functions exactly overlap the individually fitted functions despite the differences in values of A, B, and C (cf. Table 3 vs. Table 4). As discussed by Russell et al. (2002), the adjustable parameters (i.e., A, B, and C) for individual melts are strongly correlated and the nature of the covariation mainly reflects the distribution (in temperature) of the data. Confidence envelopes on the values for A and C (solid squares) obtained from fitting the three datasets individually (Fig. 5B; Inset) emphasize several important facts. Firstly, they show the strong, model-induced covariance between

Models for Viscosity of Geological Melts

853

adjustable parameters inherent in the VFT function, which will be also true for any of the other parametric equations (Eqns. 3–7). This is a caution against attributing “apparent” correlations between parameters (e.g., A, B, and C) solely to variations in melt composition. Secondly, they delineate the range of model values (i.e., A and C) that, when combined in a non-arbitrary way, will reproduce the original data accurately (e.g., Russell et al. 2002). In the case of albite melts the much larger A–C confidence envelope results from applying the 3-parameter VFT function to a near-Arrhenian dataset (linear). The optimal value for the common A (−4.69; Fig. 5B Inset) is well within the confidence limits for the individual model fits. Table 4. Model parameters from simultaneously fitting the VFT function to the T(K)–log η data for the melts diopside (Dp), anorthite (An), and albite (Ab) (See Fig. 5). The model assumes the three melts share a common high-temperature limiting value (A) and individual values for B and C. Values in brackets are the 99% confidence limits on the optimal model parameters. Melt Composition

Dp

No. Experiments VFT

χ

2

min

102 AVFT

An

Ab

67

70

−4.69 (0.99)

BVFT

4,582 (1156)

5,507 (1352)

10,907 (2074)

CVFT

718 (57)

799 (63)

434 (99)

Tg (K)

992

1129

1087

m

60.2

57.0

27.8

6.61

5.56

6.27

Application to Natural melts. The practicality and mathematical viability of a common A are equally applicable to natural multicomponent melts. We have fit VFT functions to a set of 413 viscosity experiments performed on 23 (n) different anhydrous silicate melt compositions (Giordano and Russell 2018). The experimental data span much of the compositional range found in natural systems and include both near-Arrhenian and strongly non-Arrhenian melts. Fitting the VFT function to the 23 melts individually requires 69 parameters (Table 5) whilst a VFT optimization based on a common single value of A uses 47 (2n + 1) parameters: B and C values for individual melts and a single value for AVFT (−4.48). The original data are reproduced well (±0.5 log units) with fewer parameters (Fig. 6A). Values of B and C for the 23 melt compositions vary between 4,400 and 12,100, and between 245 and 670, respectively (Table 5; Fig. 6C). In contrast, the individual VFT fits generate a much larger range of parameter values (Fig. 6A–C) some of which are unrealistic: A (−11.38 to −3.63), B (4100 to 34,000), and C (−530 to 690). For example, the values of A are excessively low for polymerized melts (i.e., low SM values; Fig. 6B) which tend to have more Arrhenian T-dependence. Values of fragility calculated from the individual VFT functions versus values associated with a common value of A are compared in Figure 6D. The agreement between the two sets of values indicates that even with ~30% fewer adjustable parameters, the fundamental properties of the original data (i.e., departure from Arrhenian) are preserved. The single discordant data point is a near-Arrhenian (low fragility) rhyolite melt which is essentially overfitted by the 3-parameter VFT function resulting in an infeasible negative value for C (−531) and an unrealistically high value of B (34,000).

Implications of a common A The modelling based on a single unknown value of A generates results that are indistinguishable from those achieved by fitting data sets individually (Fig. 6). Mathematically, the concept of a common high-T limit to silicate melt viscosity is valid regardless of the model adopted (VTF vs.

Russell et al.

854 14

-2

(A)

12

[Cst A]

8

log

4

ACstT -4.48

-4

10

-6

AVFT

6

ACstT -4.48

2 -2 -2

0

2

4

log

6

8

[Measured]

10

35

12

14

-12 -600

) Cst A

Fragility (m

20 15

5 0 -600

-200

0

C

200

400

600

800

VFT

50

25

10

(B) -400

(D)

60

(C)

30

B VFT (kJ mol -1 K-1 )

-10

23 Melt Compositions (N = 413)

0

Infeasible Solutions [C < 0]

-8

Infeasible Solutions [C < 0] -400

-200

0

200

CVFT (K)

400

600

800

40 30

Infeasible Solutions [m < 12 - A]

20 10 0

10

20

30

40

Fragility (m

)

50

60

VFT

Figure 6. VFT functions fitted to viscosity data (N = 413) for 23 multicomponent silicate melts (Table 5). (A) Comparison of measured log η to VFT model values constrained to have a common A (log η∞ = −4.48). (B) Values of A and C for 23 individual melts fitted independently to VFT functions (grey symbols). Values of C less than 0 are infeasible. Black symbols denote values of C assuming a common A value (−4.48; dashed line). (C) Comparison of values of B and C for VFT functions fitted to individual datasets (open circles) vs. values assuming a common A (solid circles). (D) Values of fragility (m) calculated from the individual VFT functions vs. the VFT functions with a common A. Dashed line indicates limit to fragility defined by 12 − AVFT where A is a constant.

AG vs. MY vs. AV, etc); however, the optimal value of A will be model dependent (Russell et al. 2003). There are (at least) two very real tangible benefits of a constant A for modelling the viscosity of silicate melts. Firstly, it suggests that all effects of melt composition, including water content, can be ascribed to only two (B and C) of the three parameters. Additionally, the common A constraint reduces the overall uncertainties on all of the adjustable parameters as illustrated by Russell et al. (2002, 2003). The non-linear character of the non-Arrhenian models ensures that there are strong covariances between model parameters which allow for a wide ranges of acceptable values (i.e., A, B, C) for individual melts. In particular, the fitted confidence limits on A for a single melt can easily span 5 log units (i.e., −1 to −7). This is true even where the data are numerous, well-measured, and span a wide range of temperatures and viscosities. Stated another way, there is a substantial range Figure 6: MSA_Viscosity_review_2020 of model values which, when combined in a non-arbitrary way, can accurately reproduce the experimental data. However, when we invoke a common A, the main result is that the acceptable range of A becomes very tight and the “permissive” range of B and C values is greatly reduced. Further details on the numerical justification for a parameterization assuming a common A are provided in Russell et al. (2002, 2003).

8.98

17.15

14.47

15.23

17.35

10.17

18.86

16.86

19.69

16.01

22.22

23.49

25.23

24.15

24.50

25.58

29.77

31.22

31.15

35.92

43.61

Mercato1600

PVC

MNV

AMS_B1

Newberry

NYT_lm*13*

UNZ

MST

CI_OF104

FR_a

Pompei TR

MRP

Ves_W

Ves_G

Min_2b

Pollena GM

ETN

Ves_Gt

NYI

EIF

9.22

Lipari_RR

MDV_snt

SM 8.12

Label Rattlesnake Tuff

1.16

0.73

0.53

0.51

0.44

0.30

0.28

0.26

0.26

0.23

0.19

0.16

0.15

0.14

0.12

0.02

0.10

0.07

0.06

0.05

0.05

0.01

NBO/T 0.00

10

23

16

10

15

25

14

14

22

17

27

20

21

20

24

16

11

19

25

23

17

13

No. Data 11

−4.24

−3.97

−4.98

−4.84

−4.09

−3.66

−6.34

−6.76

−3.84

−4.08

−4.66

−5.44

−4.25

−3.63

−3.97

−11.38

−3.82

−6.05

−5.68

−5.32

−6.43

−6.75

A −7.43

4171

4257

6987

6019

5648

5629

11559

12183

5636

7014

7437

11387

7308

6879

7390

34019

9056

13654

13004

11667

16039

17422

B 19766

687.9

677.5

532.0

602.4

593.2

572.1

304.8

265.8

600.8

501.8

523.9

336.0

503.0

545.1

514.1

−530.9

362.2

165.0

205.4

247.6

184.0

90.8

C 52.9

945

944

944

960

944

932

935

915

957

938

970

989

953

985

977

924

935

922

941

921

1054

1020

Tg (K) 1070

VFT Individual Fits

59.8

56.5

38.9

45.2

43.3

40.6

27.2

26.4

42.6

34.6

36.2

26.4

34.4

35.0

33.7

14.8

25.8

22.0

22.6

23.7

22.3

20.6

m 20.4

4476

4911

6202

5477

6167

6861

8320

8101

6579

7830

7151

9452

7695

8247

8245

12057

10309

10305

10393

9927

11421

11593

B 12096

671.8

643.5

570.2

629.0

568.8

510.7

436.7

434.1

554.2

446.1

537.0

421.8

484.9

479.3

474.2

245.7

305.8

303.3

316.5

322.8

370.1

337.2

C 355.2

943

941

947

961

943

927

942

926

953

921

971

995

952

980

974

977

931

929

947

925

1063

1041

Tg (K) 1089

57.2

52.1

41.5

47.7

41.5

36.7

30.7

31.0

39.4

32.0

36.9

28.6

33.6

32.3

32.1

22.0

24.5

24.5

24.8

25.3

25.3

24.4

m 24.5

VFT Fits with Common A (−4.48)

Table 5. VFT parameters for fitting T(K)–log η datasets (N = 413) for 23 multicomponent silicate (Giordano and Russell 2018) individually and assuming a common value for A. Also reported are chemical proxies for melt structure (NBO/T, SM) and values of Tg and m.

Models for Viscosity of Geological Melts 855

Russell et al.

856

The concept of a high-T limit to silicate melt viscosity cannot be tested directly because it requires observations at extreme temperatures well outside the range of conventional experimental methods. We can state, however, that the value of A (constant or not) must be less than any of our physical measurements of melt viscosity (e.g., ≤ 10−1 Pa s for peridotitic melt; Dingwell et al. 2004). Persikov (1991), Russell et al. (2002) and others have argued that at super-liquidus temperatures, all silicate melts become highly dissociated liquids regardless of their structural arrangement at lower temperatures and will converge to a lower limiting value of viscosity. Indeed, there is no direct evidence to suggest that “fragile”, “intermediate” and, even, “strong” silicate melts maintain different rheological properties at temperatures well above their respective liquidus temperatures. The implication is that natural melts, as diverse as basalt and rhyolite, should converge to a common viscosity at high-T. The concept of a constant A is consistent with studies of low-T glass-forming systems including polymer melts, organic liquids or liquid elements (e.g., Angell 1991, Scopigno et al. 2003). In these lower temperature systems, experiments performed at T ≫ Tg show that both strong and fragile melts converge to a fixed viscosity of ~10−5 Pa s (e.g., Eyring et al. 1982; Angell 1991; Persikov 1991; Russell et al. 2003; Scopigno et al. 2003). The Maxwell relationship (τ = η0 / G∞), which informs on the time scales of relaxation processes in melts (Eyring et al. 1982; Angell 1991; Richet and Bottinga 1995; Toplis 1998; Russell et al. 2003; Scopigno et al. 2003 and references therein), provides some constraints on the lower limit to melt viscosity (η0). The quasilattice vibration period (~10−14 s) representing the time between successive assaults on the energy barriers to melt rearrangement limits the relaxation time scales (τ) of melt. Assuming an average value of ~1010 Pa for the bulk shear modulus (G∞) of the melt at infinite high frequency suggests a lower limiting value to viscosity (η0) of ~10−4 ± 2 Pa s (e.g., Dingwell and Webb 1989; Toplis 1998). This accords well with the values returned by our optimization based on the VFT function assuming a common unknown A (i.e., 10−4.7 to −4.5).

6. EARLY MODELS AND MODELLING OF GEOLOGICAL MELTS Here, we review published models for predicting the viscosity of geological melts at geological conditions. The models are diverse in that they adopt different functional forms and span specific and different ranges of melt composition, volatile contents, temperature, and pressure (Table 1). Our analysis clearly illustrates the increasing sophistication and the overall advancement we are making as a scientific community and is also intended to point the way forward. Pioneering (Arrhenian) models It is ca. 50 years since Shaw (1972) and Bottinga and Weill (1972) published empirical methods for predicting silicate melt viscosities as a function of temperature (T) and composition. These models are still used to provide estimates of melt viscosity in studies concerning magmatism, volcanism, and planetary differentiation although the citation record shows a substantial decline as more comprehensive models have become available (Fig. 2). These models were built on an experimental database that was limited in three main ways. Firstly, the database of viscosity measurements on natural silicate melts was sparse. Secondly, the available experimental data did not completely overlap or span the range of natural melt compositions. Thirdly, the majority of data derived from super-liquidus experiments. On this basis, both Shaw (1972) and Bottinga and Weill (1972) adopted an Arrhenian temperature dependence for melt viscosity and the seminal contribution made by these two papers was to provide the first tools for predicting the viscosity of geological melts as a function of composition and temperature.

Models for Viscosity of Geological Melts

857

Bottinga and Weill (1972). The Bottinga and Weill (1972) model (BW) for melt viscosity was calibrated on 2440 log η–T (K) data points derived from 31 synthetic, anhydrous silicate chemical systems spanning 35−91 mol% SiO2 over a temperature range of 1100–1800 oC. Their model predicts viscosity as a function of melt composition and temperature as: n

ln  xi Di

(9)

i

where xi and Di are the mole fraction of the ith component and an empirical constant for that component, respectively. The components relevant to natural systems in the BW model include: SiO2, TiO2, FeO (total), MgO, CaO, Na2O, K2O, and alumina was distributed across the components KAlO2, NaAlO2, CaAl2O4, MgAl2O4 and MnAl2O4. Unique values of Di for each of these 12 oxide components were determined for 5 restricted ranges of SiO2 contents: 35–45, 45–55, 55–65, 65–75 and 75–81 mol%. Furthermore, for fixed melt compositions, the Di values varied every 50 oC over the temperature interval 1200–1800 oC. This bootstrap model reproduced the original datasets well over the range of viscosities 10−1 to 105 Pa s where most melts show a near-Arrhenian temperature dependence. The BW model can be applied to natural systems (Fig. 7A) but the calculations tend to be laborious because a lookup table prescribes the values of Di depending on the composition and, then, the temperature of the melt. A more important consideration is the lack of continuous functions describing Di values as a function of composition and temperature. This is exemplified in the original figure of Carmichael et al. (1974, Fig. 4.7) where they used the BW model to calculate viscosity for 6 liquids at temperatures of 1050–1500 oC (reproduced here as Fig. 7A). Careful examination of the model points they used to define each line (see original) shows slight discontinuities arising from jumping from one set of Di values to another. This is also apparent in the original paper of Bottinga and Weill (1972, see their Fig. 7) where they computed viscosity for 7 melts over the temperature interval 1200–1800 oC. This issue would only be further exacerbated when modelling viscosities of evolving melts as a function of, both, temperature and composition. Ideally, a predictive model should be continuous across the variable space of interest. Shaw (1972). Shaw (1972), based on the compilation and calculations of Bottinga and Weill (1972), developed an alternative predictive model (SH) for geological melts viscosity. He took a different approach where he expanded the Arrhenian function (Eqn. 1) to the form:  10 4  ln  C  CT s  s   T  K    

(10)

where s is a characteristic slope calculated from melt compositions and Cη and CT are model constants: −6.4 and 1.5, respectively. The innovation in the SH model is that the compositional effects on viscosity are encapsulated in s which is calculated from the oxides with only 5 model parameters. The model is continuous in temperature and composition space and includes the effects of H2O. Figure 7B is a recalculation of viscosity curves for hydrous (0 to 10 wt.% H2O) rhyolite using the Shaw (1972) model as explored by Carmichael et al. (1974, Fig. 4.6). Superimposed on those curves are the inferred solidus and liquidus of felsic intrusive magmas which effectively delineate (reduce) the portions of the model log η–T(oC) curves that are relevant to magmatic processes. The SH model rapidly became, and remained for over 30 years, the primary method of predicting melt viscosity in geological systems (Fig. 2). Giordano et al. (2008) illustrated the application of the Shaw model to a database of modern viscosities for anhydrous and hydrous natural multicomponent melts (reproduced here in Fig. 7). The SH model is Arrhenian and therefore systematically underestimates anhydrous melt viscosity at lower temperatures (Fig. 7C). This results from an Arrhenian extrapolation to lower temperatures combined with the fact that viscosity curves for all non-Arrhenian silicate

Russell et al.

858 5

ToC

1500

1000

(B)

12

rs)

o

ite

l yo Rh

(M

on

ller

te Pan

a) ast

. Sh Mt

3

e( esit

d An

e hyt

trac

lite

no Pho

2

tarc (An

10

a) eny

(K ite

log η (Pa s)

log η (Pa s)

4

e at Cr

) tica

)

en

1

salt

Ba Al Hi-

ass t. L

U

0

6.0

ite Granodior

(A)

6.4

6.8

6% 8% 10%

800

15

T ( o C)

1000

1200

Hydrous Melts 10

(Shaw'72)

5

5

log

(Shaw'72)

% 1%

2% 4%

600

7.2 7.6

10

log

Liquidus

2

Anhydrous Melts

0 -5 -5

0% 0.5

4

)

10,000 / T(K)

15

us

lid

So

da

an

Ug

e( dit

itic

an Gr

6

(M

n ga

5.6

8

(C) 0

log

5

(Measured)

10

0 -5 -5

15

(D) 0

log

5

(Measured)

10

15

Figure 7. Petrological applications of early non-Arrhenian models for viscosity of geological melts. (A) Melt viscosity as a function of temperature for a range of anhydrous volcanic rock compositions calculated with the Bottinga and Weill (1972) model (cf. Carmichael et al. 1974, Fig. 4-7). All calculations are performed at temperatures in excess of the inferred liquidus temperatures (dashed vertical lines). (B) Viscosity curves for hydrous rhyolite melts calculated with the Shaw (1972) model and plotted vs. T (oC) (labels are wt.% H2O). Also shown are the approximate granite solidus and granodiorite liquidus (cf. Carmichael et al. 1974, Fig. 4-6). (C, D) Viscosity values predicted by model of Shaw (1972) for dataset shown in Figure 3: (C) anhydrous melts and (D) hydrous melts.

melts are concave up (Fig. 3) and, thus, steepen with decreasing temperature (increasing Figure 7: MSA_Viscosity_review_2020 viscosity). However, the model does a remarkably good job of reproducing melt viscosity at high temperatures (Fig. 7C, D), especially, considering the sparseness of the data that was available to Shaw (1972). The model replicates high-T viscosity data well because most silicate melts show only minor deviations from Arrhenian behaviour above liquidus temperatures. However, it is also testimony to the cleverness of Shaw’s parameterization for composition based on 5 model coefficients and 2 constants. The Shaw model also predicts the high-temperature viscosity of hydrous melts well (Fig. 7D). Hydrous melts of basic and intermediate chemistry tend to be more Arrhenian-like than their anhydrous counterparts and, consequently, the Shaw model probably can be applied to hydrous melts over larger ranges of temperatures. However, at sub-liquidus temperatures, the Shaw model results in much scatter and, both, overshoots and undershoots measurements of viscosity drastically (Fig. 7D). A final attribute of the Shaw model deserving comment is the high-temperature behaviour of melt viscosity that is implicit to the model’s parameterization. In Equation (10) the implied high-temperature limit to melt viscosity (i.e., A (Pa s) = log h∞) is expressed as: log  

C



 CT s 

2.303

1

(11)

Models for Viscosity of Geological Melts

859

In the Shaw model, there is a compositional dependence to log η∞ (i.e., AShaw) embedded in the term CTs but it is slight. Values of AShaw calculated for this same database are restricted to between −6.6 and −4.8 for, both, anhydrous and hydrous melts. Notably, this range is very close to the model AVFT value (−4.48) obtained earlier where we fit a common A to data for 23 anhydrous melts (i.e., Fig. 6 and Table 5, Giordano and Russell 2018). The SH model estimate of a high-T limit to melt viscosity is significantly more restricted and more sensible than the range of values one gets by fitting melts for individual values of A (i.e., Table 5, A = −11.4 to −3.6). Persikov (1980’s to 2000’s). The work of Persikov (1984, 1991) has resulted in another important set of Arrhenian models for predicting magmatic melt viscosity. He and his coauthors (Persikov and Bukhtiyarov 2009) offer an alternative approach to modelling (PB) melt viscosity at temperatures above and near liquidus conditions as a function of composition including volatiles, temperature, and, both, total and fluid pressure. Their Arrhenian model predicts melt viscosity at temperature and pressure ( ηTP ) based on the equation:  E xP   RT  K  

TP   e

(12)

where the pre-exponential constant η∞ is the high-temperature limit to melt viscosity. Based on theory, Persikov (1991) assigned a priori a constant value (independent of composition and pressure) of 10−3.5 dPa (10−4.5 Pa s) to η∞ (Persikov and Bukhtiyarov 2009). The effects of variable composition on melt viscosity are accounted for by the variable E xP representing the activation energy for viscous flow. Operationally, model values of viscosity (dPa s) are calculated from:

log TP 

E xP  3.5 4.576T  K 

(13)

The activation energy term, E xP, depends on a variable K which is proportional to the NBO/T of the melt (K = 100 NBO/T) as calculated from the oxide composition in a manner prescribed by Persikov (1984). At low NBO/T, K is adjusted to account potentially for pronounced structural reorganization in the melt based on ratios of Al/(Al + Si). Values of K are also adjusted to account for dissolved H2O (Table 6). The main attribute of the Persikov and Bukhtiyarov (2009) viscosity model is its capacity to accommodate the effects of composition, including a wide range of dissolved volatile contents, and pressure. Its main limitation is the Arrhenian basis which limits its application to near liquidus conditions or strong liquids. Table 6. Empirical functions and coefficients from Persikov and Bukhtiyarov (2009) for calculating E xP for anhydrous and hydrous melts at 1 atm pressure. K(1) = 100(NBO/T) ε = Aliv/(Aliv + Siiv)

E 1X (for P = 1 atm)

ε < 0.25

Eε = 98 – 158 ε + 152 ε2 E1X1= (K/17) (51.6 – Eε) + Eε

ε > 0.25

E1X1 = 68 – 0.965 K

K < 17

17 < K < 100

—

E1X 2= 54.4 – 0.165 K(2)

100 < K < 200

—

E1X 3= 42.4 – 0.045 K

200 < K < 400

—

E1X 4 = 34.4 – 0.005 K

Notes: 1 Values of K for water content: KH2O = KDry – (KDry – 2) × H2O (wt.%)/100 1 2 Author supplied spreadsheet (2019) uses: E X 2 = 52.4 – 0.165 K

Russell et al.

860

Figure 8 compares the measured values of viscosity for anhydrous and hydrous natural multicomponent melts (i.e., data from Giordano et al. 2008) to values predicted by the PB model. Here, we are using the PB model under a restricted range of conditions (i.e., 1 atm) relative to its full capability. The PB model is best at reproducing melt viscosity at high temperatures (Fig. 8A–B) where silicate melts are near-Arrhenian. As with the Shaw model, the PB model cannot capture departures from Arrhenian behaviour that are most apparent in fragile melts and at lower temperatures and systematically underestimates melt viscosity at lower temperatures for the anhydrous dataset (Fig. 8A). For hydrous melts at subliquidus conditions temperatures, some viscosities are predicted well by the PB model whilst others are scattered and, both, overshoot and undershoot measured values (Fig. 8B). 15

(P&B, 2009)

Anhydrous Melts

10

Hydrous Melts

10

5

log

log

5

0

(A)

8

log

5

10

(Measured)

(Pa s) P&B, 2009

6

H2O Contents 0 - 10 wt. %

4

log

2 0

NBO/TDRY = 1.5 600

800

1000

T ( o C)

1200

0

5

log

14

(C)

NBO/TDRY = 0.5

(B)

0

15

1400

(Pa s) (P&B, 2009)

0

12

log

(P&B, 2009)

15

2

10

15

(Measured)

(D)

K < 17

10

17 < K < 100

8

100 < K < 200

200 < K < 400

6

600 oC

4

0 0

0.5

1

1.5

2

2.5

1300 oC 3 3.5

NBO/T (after Persikov)

Figure 8. Prediction of melt viscosity using model of Persikov (1991) and Persikov and Bukhtiyarov (2009) (PB). Measured values of log η (as in Fig. 3) vs. values calculated with PB model for (A) anhydrous and (B) hydrous melts. (C) The PB model effects of H2O (0.5, 1, 2, 4, 6 and 10 wt.%) on dry melts (heavy line) having NBO/T values of 0.5 and 1.5 corresponding to a strong, near-Arrhenian and fragile, non-Arrhenian melt, respectively. (D) PB viscosities as a function of NBO/T (cf. Persikov 1984) and contoured for temperature. The PB algorithm uses a composition-dependent parameter K (= 100 NBO/T) which changes discontinuously at critical values of K. At low values of K (i.e., < 17), there are two trends (red dashed lines) for melts with low (< 0.25) and normal ratios of Al/(Al+Si).

We have used the PB model to explore the model effects of H2O on melt viscosity. Specifically, we calculate the T-dependant viscosity as a function of H2O content for a more (NBO/T ~ 0.5; strong) and less (NBO/T ~ 1.5; moderately fragile) polymerized melt using NBO/T as a proxy for melt structure. The PB model suggests that < 2% water has little effect ( 0.25, Tg is nearly constant and shows only a slight decrease with increasing H2O content. Hess and Dingwell (1996) published the first non-Arrhenian model (HD) based on the VFT function for predicting melt viscosity in hydrous haplogranitic melts. Their six parameter model has the form: log   3.545  0.833 ln  wH2O  

9601  2368 ln  wH2O 



T  K   195.7  32.25 ln  wH2O 



(16)

Russell et al.

862

where wH2O is the wt.% of dissolved H2O in the melt. The HD model does a better job than the Baker (1996) model and other Arrhenian models in reproducing melt viscosity in hydrous silicic systems (see Hess and Dingwell 1996). One inconvenience is that the term ln wH2O is undefined at zero water content, however, the authors suggest that this condition is never met in Nature. A water content of 1 wt.% reduces the function to: 9601 Baker (1996) T  K  X 195.7

15

XH20

H20

< 0.25

1.5

> 0.25 A calibration based on the term ln (1 + wH2O) would circumvent that issue.

(Pa s)

10

(17)

Δ log η at XH20 = 0.25

1

[Eq 15 - Eq 16]

log   3.545 

0.5 0

-0.5

Δ +’ve Δ -’ve

-1

In addition to reproducing the experimental data well, the main attributes of the HD 500 oC model are that it is continuous across water content and temperature (Fig. 9B) and predicts reasonable and experimentally validated decreases in Tg with increasing H2O content. The o Shaw (1972) model, although purely Arrhenian, 5compares reasonably well800 with C the refined HD non-Arrhenian model in, both, predicting melt viscosity (Fig. 9B) and Tg (Fig. 9C) as a function of H2O content. To a large extent, this reflects the fact that these melts are strong o (A) geological melts and their departures from Arrhenian behaviour are moderate. 1100 C 0 -1.5 500

700

800

900

1000

T( oC)

1100

log

600

0

XH20 > 0.25

(Pa s)

10

-0.5

(A)

800

o

900

T( C)

1000

1100 C 4

6

8

Wt. % H2O

15

Hess & Dingwell (1996)

500 oC

1100

log

700

o

2

10

10

600

800 oC

0

8

Δ -’ve

-1.5 500

5

6

Δ +’ve

-1

500 oC

0

0.5 0

15

Δ log η at XH20 = 0.25

1

[Eq 15 - Eq 16]

XH20 < 0.25

log

1.5

Baker (1996)

4

Wt. % H2O

(Pa s)

15

2

5

0

10

800 oC 1100 oC

(B) 0

2

4

1200

Hess & Dingwell (1996)

6

8

Wt. % H 2 O

10

(C)

500 oC 5

0

Tg (K) (~ 10

log

(Pa s)

10

12

Pa s)

1000

800 oC 1100 C o

(B) 0

2

4

Hess & D

ingwell (1

600 400

6

8

10

996)

Baker (1996)

200

Wt. % H 2 O

1200

800

0

2

4

6

Wt. % H2O

8

Pa s)

Figure 9. Models for viscosity of hydrous silicic melts. (A) The viscosity of granitic melts calculated (C) with Arrhenian model of Baker (1996) for H2O contents of 0–10 wt.% and over the temperature range 1000 500–1100 oC. Vertical dashed line denotes a discontinuous transition in empirical equations used for xH2O contents below and above 0.25 (see text). Inset shows the magnitude of discontinuity (i.e., ∆log η) as a 800 of temperature. Red dashed line is model of Shaw (1972) for same melt composition at 800 oC. function Hess & D ingthe (B) Values of viscosity calculated with model of Hess and Dingwell (1996) over the same wellnon-Arrhenian (1996) H2O600 contents and temperature as in (A). Red dashed line as in (A). (C) Values of Tg (K) predicted by the two models and calculated for a range of H2O contents (see text). Also shown are Tg values implied by the Shaw (1972) model (red dashed line).

Tg (K) (~ 10

12

Figure 9: MSA_Viscosity_review_2020

400

Baker (1996)

200 0

2

4

6

8

10

10

Models for Viscosity of Geological Melts

863

Hydrous high-P models for silicic melts Ardia et al. (2008) performed a series of innovative centrifuge-aided experiments to measure the viscosity of hydrous (0.15−5.24 wt.%) rhyolite melts as a function of temperature (580−1640 oC) and pressure (5−24 kbar) (Table 1). Using these new data and data from the literature (e.g., Schulze et al. 1996), they parameterized the BVFT and CVFT in the VFT function (i.e., Eqn. 3) to account for mol. % water content (mH2O) and pressure (P) in kilobars as: BVFT  b1  b2 mH2 O  b3 P

(18)

CVFT  c1  c2 ln(1  mH2 O ).

(19)

and

They assumed AVFT was a constant (−4.28) and did not account for compositional variations other than H2O contents. Allowing A to have a dependence on H2O content did not improve the fit. This is one of the first generalized models for predicting the viscosity of hydrous (H2Oundersaturated) silicic melts at elevated temperature and pressures. Their model predicts a strong decrease in melt viscosity with temperature and H2O content and pressure to have a variable and minor effect (Fig. 10A). The greatest effect of pressure is at low pressures, low T and low H2O contents. Model values of Tg decrease with increasing water contents and are lower than predicted by HD; increasing pressure causes a slight further reduction in Tg (Fig. 10B) Melt fragility decreases slightly with H2O content but is insensitive to pressure (Fig. 10B, inset). Their model reproduces the original experimental data well, yet has several limitations. Firstly, the model values of BVFT and CVFT calculated for a range of H2O contents become unrealistic at H2O contents > 1.54 wt.%. Calculated values of CVFT become negative and aphysical requiring a substantial corresponding decrease in BVFT (Fig. 10C). The anhydrous melt has BVFT and CVFT values of 11660 and 289K, respectively, whereas at 10 wt.% H2O the values are 9168 and −228K. Furthermore, at higher water contents the model curves of log η vs. 10000/T(K) are concave down which is unrealistic and may undermine their efforts to calculate model values for activation energy associated with viscous flow of these melts (cf. Ardia et al. 2008). Hui et al. (2009) followed the work of Ardia et al. (2008) to develop a similar model for the viscosity of hydrous rhyolite at pressure based on their new data and compiled literature data. They adopted the Zhang et al. (2003) low-pressure model and fit for additional parameters to account for pressures of 3 GPa over water contents of 0–8 wt.% H2O. Their model uses a pair of exponential expressions in P and T. One of the exponential functions is multiplied by a term involving water content and having a total of 10 adjustable parameters. The model reproduces the compiled dataset well. Interestingly, the Hui et al. (2009) model agrees well with the Hess and Dingwell (1996) model in terms of the 1 atm. 800 oC isopleth (Fig. 10A) and in terms of calculated values of Tg (Fig. 10B). The Hui et al. (2009) model also shows pressure to have a subordinate effect on viscosity relative to temperature and H2O content. One disadvantage of the Hui et al. (2009) model is that it is difficult to explicitly extract derivative properties such as Tg and fragility. A second concern is that values of A are independent of H2O content but are dependent on pressure (Fig. 10D) and unreasonable. Over a pressure range of ~3.5 GPa, A increases from −8 to −5.8 Pa s. Two other models concerning the viscosity of hydrous silicic (dacite to rhyolite) melts are Whittington et al. (2009) and Romine and Whittington (2015). Whittington et al. (2009) contributed experiments on 6 dacite liquids having water contents (w) up to 5 wt.% and then parameterized the VFT function for water content (log10 w + 0.26). Their model adopts a common

Russell et al. 15

1200

(A)

1000

Tg (K) (1012 Pa s)

ΔP (Pa s)

10

500 C 1000 oC ΔP 0

800 C o

0

13 12

1300 oC 2

4

6

8

Wt. % H 2O

Increasing H20

B

15 Kb H 2O > 1.54 wt% -200

-100

C

2

0

6

4

Wt. % H2O

400 200

ΔP

(B) 0

8

2

4

6

8

Wt. % H2O

10

Range of A Values

Ardia et al. (2008)

-5

5 Kb

10

0

600

-4

1 Atm

20 10

800

-3

Aphysical Values of C

11

9

10

30

A

log

o

5

40

Fragility

864

(C) 0

100

200

-6

)

l. (2009

Hui et a

-7 -8 -9

(D) 0

0.5

1

1.5

2

P (GPa)

2.5

3

3.5

Figure 10. Models for viscosity of silicic melts as a function of temperature, H2O content, and pressure including Ardia et al. (2008) and Hui et al. (2009). (A) Ardia et al. (2008) model values of log η vs. wt.% H2O at 1 atm. and contoured for temperature (500, 800, 1000, and 1300 oC); dashed lines denote the effects of increasing pressure (5 and 15 Kb) at 500 oC and 1300 oC. Also shown are models of Hess and Dingwell (1996, dashed red line) and Hui et al. (2009) (solid red line) for melts at 800oC and 1 atm. (B) Values of Tg as a function of H2O content from Ardia et al. (2008) for pressures of 1 atm, 5 Kb, and 15 Kb (black lines); inset shows model fragility values at 1 atm., 5 and 15 Kb. Tg values (1 atm) from Hess and Dingwell (1996) and Hui et al. (2009) are shown as in A. (C) Ardia et al. (2008) parameters B and C calculated for hydrous silicic melts at 1 atm, 5 and 15 Kb. B and C values are highest for anhydrous end-member melts (black circles) and decrease with increasing H2O content. At H2O contents greater than 1.54 wt.% values of C are negative and aphysical. (D) Comparison of Ardia et al. value of A (i.e., log η∞ ~ -4.25) to values implicit to Hui et al. (2009) model as function of pressure (see text).

value for A of −4.43 (following Russell et al. 2003). Relative to the 800oC (0.1 MPa) viscosity isopleth of other melt viscosity models (e.g., Hess and Dingwell 1996; Ardia et al. 2008; Hui Figure 10: MSA_Viscosity_review_2020 et al 2009; Romine and Whittington 2015), the Whittington et al. (2009) model predicts lower viscosities (> 1 log unit) at low H2O contents (Fig. 11A). However, Tg–H2O values (Fig. 11B) predicted by their model agree with all other models except Ardia et al. (2008). This suggests, again, that the Ardia et al. (2008) model may not predict derivative properties well. One anomaly of the Whittington et al. (2009) model concerns the model effects of H2O content on BVFT and, thus, CVFT (Fig. 11B). The model values of BVFT and CVFT are positively and linearly correlated. For a single melt composition with variable H2O content, this is not necessarily surprising as H2O is expected to decrease both activation energy (~α to BVFT) and Tg (~α to CVFT). However, across a wide range of H2O contents (0–12 wt.%) BVFT values are near-constant varying by less than 0.5% (7600–7629). A second issue involves the term (log10 w + 0.26) which goes to zero at H2O contents of 0.74 wt.% (i.e., rather than at 0 wt.%) and defines a base value for BVFT of 7618. Water contents less than 0.74 cause an increase in BVFT and H2O contents > 0.74 wt.% cause a decrease in BVFT values. Regardless of this idiosyncrasy, the overall pattern of BVFT is as expected and shows a non-linear decrease, albeit very minor, with H2O content (Fig. 11B). Romine and Whittington (2015) produced new viscosity experiments (N = 211) on hydrous rhyolite melts at 1 atm. Then using these data and low and high-pressure data compiled (N = 480)

Models for Viscosity of Geological Melts

865

from the literature they created an empirical model for silicic melt viscosity that accounts for temperature, H2O content and pressure. Their model uses a VFT function where the BVFT and CVFT terms are explicitly expanded to accommodate H2O contents (wt.%) and an additional term is added that accounts for both pressure (P, MPa) and water content. They optimize

log (Pa s)

12

(A)

1200 1000

Tg (K)

14

10 8

200

W

4 0

2

B (kJ mol-1 K-1)

10 9

ΔP 0

2

4

6

6

R

Aphysical Values of C

10

g

in as

re

Inc

12

ΔP

8

Wt. % H2O

(B)

0 H2

H 2O ~ 9 wt%

W

8 7

10

8

Wt. % H2O

R 4

13

11

R

800 oC

14

12

W

600 400

6

2

800

-200

0

200

C (K)

400

Figure 11. Viscosity models for silicic melts of Whittington et al. (2009, solid black lines, W) and Romine and Whittington (2015, red lines, R at 1 atm and 15 Kb). (A) Model values of log η vs. wt.% H2O at 800 oC and 0.1 MPa; arrow denotes effects of increasing pressure for Romine and Whittington (2015) model. Also shown are models Hess and Dingwell (1996) and Hui et al. (2009) (dashed black lines). Inset shows corresponding Tg values including 1 atm and 15 kb values from Ardia et al. (2008) (solid blue lines). (B) The values of B and C from models of Whittington et al. (2009) and Romine and Whittington (2015). B and C values are highest for anhydrous end-member melt and decrease with increasing H2O content. The grey shaded field denotes an aphysical region defined by C < 0; the Romine and Whittington (2015) model reaches this space at H2O > 9 wt.%. Whittington et al. (2009) model has a near constant value of B over a wide range of H2O contents.

600

for a common value for A (−4.40) approximating a high-temperature limit to melt viscosity. The model reproduces the 800 oC (1 atm) viscosity isopleth of Hess and Dingwell (1996) to < 1 log unit and shows pressure to have a small but significant effect on viscosity at high H2O contents (Fig. 11A). Their model matches the Tg–H2O curves of the other silicic melt models to within 50oC (Fig. 11A, inset) which improves on the Ardia et al (2008) model (Fig. 10B). The model predicts a significant decrease in Tg with pressure, as suggested by Ardia et al. (2008), that becomes more pronounced at high H2O contents (Fig. 11A, Inset). The values of BVFT and CVFT for this model also covary strongly, positively and linearly and both decrease with H2O in a non-linear (but correlated) manner. The highest values of BVFT and CVFT are associated with the anhydrous melt and the lowest with the highest water contents. One irregularity is that at H2O contents ≥ 9 wt.%, model values of C are negative and physically unreasonable. Lastly, the value of A (−4.40) in their model does not represent the high-temperature limits to melt viscosity. Rather, that is given by: log   A  P  0.00082  0.000051w 

(20)

At 0.1 MPa pressure and high temperatures, the model viscosity converges to a fixed value close to −4.40 but with a very weak, linear dependence on H2O content. However, at high pressures (≥ 1000 MPa), the model converges to very different lower values of viscosity. These high-temperature limits also show a strong linear dependence on H2O content: at 1500 MPa the model converges to log η∞ ~ 10−5.6 (dry) and 10−6.6 (12 wt.% H2O).

Figure 11: MSA_Viscosity_review_2020

866

Russell et al. 8. OTHER MODELS FOR RESTRICTED COMPOSITIONAL RANGES

Several other important non-Arrhenian models have been developed for restricted ranges of melt composition that address specific geological issues or questions. They have the potential attribute of predicting very accurately the viscosities of silicate melts that are relevant to the particular problem. One of the countervailing limitations is that they cannot be extrapolated past their original calibration datasets and the adjustable parameters are commonly less meaningful or even aphysical—a concession made to improve the reproducibility of the data of primary concern.

Models for melts from the Phlegrean Field Romano et al. (2003) produced new viscosity data on two volcanic materials from Vesuvius (V1631W/G) and the Phlegrean fields (AMS B1/D1) deemed critical for understanding the potential for explosive volcanism in the highly populated region of Naples. They measured the temperature-dependent (400 to 1500 oC) viscosity for two dry melts and the same melts with variable dissolved water contents (0 to 3.8 wt.%). Viscosity measurements for each of these two melts spanned 102 to 1012 Pa s. They also compiled viscosity data on four other hydrous melts (i.e., trachyte, phonolite and haplogranitic) from the literature (Dingwell et al. 1996, HPG8; Whittington et al. 2001, W Tr, W Ph; Giordano et al. 2000, T Ph). Each dataset for the individual melts, including the anhydrous end-member and their hydrous counterparts, was fit to individual VFT functions modified to accommodate H2O content: log  a1  a2 ln w 

b1  b2 w T  K   (c1  c2 ln w)

(21)

where w is the wt.% H2O and ai, bi, and ci are adjustable parameters unique to each of the six melts considered here. Thus, there are 6 adjustable parameters for each anhydrous melt composition (i.e., a total of 18 parameters). The form of Equation (21) is very similar to that proposed by Hess and Dingwell (1996) except that the numerator term involves w (i.e., wt.% H2O) rather than ln w. Romano et al. (2003) used this modification to allow for zero water content (i.e., undefined condition ln w at w = 0). The model does a good job of reproducing the original data and provides a solid means of tracking the effects of H2O content on the behaviour and values of melt viscosity for these anhydrous or hydrous melts at geological temperatures (Fig. 12A). Increasing water content causes a significant decrease in viscosity (Fig. 12A). Their study also provides preliminary insight into how H2O content can be accommodated in models for melt viscosity (i.e., Eqn. 21). However, there are some issues with the model. Firstly, the model is mathematically undefined at water contents of zero although virtually all geological melts contain some dissolved H2O. This inconvenience could be remedied, for example, by replacing the term [c1 + c2 ln w] in Equation (21) by [c ln (1 + w)] using one less adjustable parameter. A second issue is that the model correctly predicts a decrease in fragility with increasing H2O content (e.g., Giordano et al. 2008) but, at higher H2O contents, fragility increases in four of the six melts (Fig. 12B). This is a case where the model cannot be extrapolated past the limits of the calibration data (i.e., H2O > 4 wt.%). The model functions for all six melts show a pronounced and probably unrealistic decrease in Tg with increasing H2O content from anhydrous values of 900–1175 K to < 500 K at 10 wt.% H2O (Fig. 12C). Furthermore, the functional form of these models (Eqn. 21) ascribes a strong unrealistic compositional (H2O content) dependence to the high-T viscosity limit (i.e., A): dry melts have values of −6.7 to −4.2 whilst H2O-rich melts have values of −7 to −1. Three melts show a pronounced increase in A with H2O content and three show a strong decrease. Misiti et al. (2011) produced new data and a predictive model for two other alkaline rock compositions associated with the Campi Flegrei caldera complex. They performed 95 measurements of viscosity on anhydrous and hydrous (0.02 to 3.3 wt.%) equivalent melts of

Models for Viscosity of Geological Melts 14 12

35

(A)

Fragility (m)

6

20

4

6

8

10

10000/T(K)

1200 1000

12

10

14

0

Misiti et al. (2006)

800 600

Rom

ano

(C) 0

2

4

Romano et al. (2003) 0

2

4

6

H2O Content (wt.%)

(D)

8

10

Romano et al. (2003)

-2 -4

Misiti et al. (2006)

log

Tg (K)

15

Romano et al. (2003) Anhydrous & 2 wt. % H2O

2

(Pa s)

(Pa s) log

25

8

400

(B)

30

10

0

867

-6

et a

l. (20

6

H O Content (wt.%)

03)

8

10

-8

0

2

4

6

H O Content (wt.%)

8

10

2

2

Figure 12. Models for viscosity of hydrous alkaline melts (Romano et al. 2003, solid lines; Misiti et al. 2006, dashed lines). (A) Values of log η vs. 10000/T(K) predicted by model of Romano et al. (2003) for six anhydrous (black) silicate melts and for the same melts having 2 wt.% H2O (blue). (B) Model values of fragility for six melts of Romano et al. (2003) as a function of H2O content. (C) Calculated values of Tg as a function of H2O content. (D) Values of log η∞ implied by the two models as a function of H2O.

shoshonitic (Min) and latitic (FR) composition. Melt viscosity was measured at temperatures of 840 to 1870 K and 1 atm and under a pressure of 500 MPa; viscosity values ranged from 101.5 to 1010 Pa s. They fit the anhydrous and hydrous data for each melt to an equation of the form: 

log   a 

w 

 g b d T  K    e  T K   c T K   e

(22)

where w is the wt.% H2O and a–g are adjustable parameters unique to each melt. Their analysis included previously published data (Misiti et al. 2006) on a trachytic melt composition (dry and hydrous) from Agnano Monte Spina (AMS). The form of the model is an improvement in that it is mathematically defined at zero H2O. A complication is that model values of Tg and fragility cannot be calculated explicitly but need to be solved for numerically. Calculated values Figure 12: MSA_Viscosity_review_2020 of Tg for the three melts initially decrease appropriately with increasing H2O contents before remaining constant at H2O > ~1% (Fig. 12C). The model allows for H2O-content independent high-temperature limit (i.e., log η∞), however, the implication of fitting Equation (22) to the individual datasets for each melt composition is that each melt has a different high-temperature limit (log η∞ = −5 to −6.6; Fig. 12D). Lastly, we have also calculated viscosity isotherms for the three melts (not plotted); viscosity decreases with increasing H2O content. The nature of decrease, however, is very strange for the shoshonitic and latitic melts in that the isothermal melt viscosity is constant at water contents > 1%. The model isothermal curves for the trachytic melt (Misiti et al. 2006) are more reasonable suggesting there may be problems with some of the Misiti et al. (2011) datasets.

A model for natural Fe-bearing silicate melts Most natural silicate melts contain some amount of iron and some terrestrial melts can have 15−18 wt.% FeO(T) (e.g., Williams-Jones et al. 2020). The iron occurs in two main valence states depending on the redox state of the melt: ferrous (Fe2+) and ferric (Fe3+). There is clear evidence on the importance of iron oxide speciation (i.e., FeO vs. Fe2O3) for affecting melt viscosity (Dingwell and Virgo 1987; Dingwell 1991; Chevrel et al. 2013, 2014;

Russell et al.

868

Kolzenburg et al. 2018). Duan (2014) developed a melt viscosity model, based on data from the literature, that accounted for melt composition (including H2O), temperature, pressure and redox state of the iron. The Duan (2014) is calibrated on a compilation of ~200 experiments on 19 Fe-bearing melts spanning a temperature range of 733–1873 K. The model is calibrated for anhydrous to hydrous (100 different hydrous melt compositions. The latter dataset included viscosity values measured at significantly lower experimental temperatures: 245–1580 °C. The melt database has calculated NBO/T values that span 0 to 1.8 and the range of oxide contents (wt.%) is: SiO2 (41–79), TiO2 (0–3), Al2O3 (0–23), FeO (0–12), MnO (0–0.3), MgO (0–32), CaO (0–26), Na2O (0–11), K2O (0.3–9), P2O5 (0–1.2), H2O (0–8), and F (0–4). Their model is built on the VFT equation (Eqn. 3) and they assumed A to be a single constant (to be solved for) and ascribed all compositional dependencies of viscosity to the terms BGRD and CGRD. They represented BGRD and CGRD as linear combinations of oxide components and a subordinate number of combined oxide cross-terms. The melt viscosity model was calibrated against the viscosity–T(K)–melt composition dataset and reduced to 18 adjustable parameters including: i) A = −4.55 ± 0.21, ii) 10 coefficients to capture the compositional controls on BGRD, and iii) 7 coefficients for CGRD. Operationally, the temperature dependence of melts is calculated from the mole fractions of oxides (mi, ni) and oxide combinations (M1j, M2 j, N1, N2) as:

Models for Viscosity of Geological Melts

875

14

(A)  b m10  b M1 M 2 log   4.55  T  K    c n  c N1 N 2 8 12

7

3

(Pa s) (GRD)

i i i 1  j 1 1, j

1, j

1, j

6

1,1

i 1 i i

1,1

1,1

(28)

 

where bi and ci are the optimized coefficients (see6 Table 7). log

4 The model describes the original data well (RMSE ~ 0.40 log units) and the average misfit is between ±0.25 log units for the anhydrous melts2 and ±0.35 for hydrous melts (Fig. 17). They suggest that the model should be accurate to within ~ 5% relative error; the largest deviations 0 are for low-T, high viscosity (> 108 Pa s) data (Fig. 17B). 0

14 (Pa s) (GRD)

10

log

12

4

2

4

log

6

8

10

12

14

(Pa s) (Observed)

(B)

(A)

8 6 2 0 0

2

4 log

6

8

10

12

14

(Pa s) (Observed)

(B)

Figure 17. Quality of fit of Giordano et al. (2008; GRD) model. (A) Crossplot comparing measured values of log η to predicted values for anhydrous (grey) and volatile-rich (blue) melt compositions. (B) Histogram of absolute values of ∆log η organized by experimental temperature. Most deviations are less than 0.5 log units; greater values of ∆log η correspond to the lower temperature (higher viscosity) measurements for both anhydrous and volatile-rich datasets.

Attributes The GRD model is continuous in composition and temperature space, predicts the viscosity of natural volatile-bearing silicate melts (including H2O and F), and can predict other transport properties including glass transition temperatures and melt fragility. Model values of BGRD and CGRD for their melt compositions vary from 4450 to 12,000 J mol−1, and 0 to 668 K, respectively (Fig. 18A). Values BGRD and CGRD for their anhydrous melts show a strong, negative, linear covariation reflecting the effects of depolymerization on both parameters (Fig. 18A, C, D). The values of BGRD are highest where NBO/T is ~0 whereas CGRD values are highest for melts having the highest NBO/T (Fig. 18C, D). The pattern between BGRD and CGRD values changes dramatically but coherently for volatile-rich melts (Fig. 18). Dissolved H2O causes a marked decrease in values of CGRD (Fig. 18A, D) whereas the effects of H2O on BGRD are varied and less apparent (Fig. 18A, C).

Figure The GRD model can also be17: usedMSA_Viscosity_review_2020 to calculate derivative transport properties including the glass transition temperature (Tg) and the fragility m of silicate melts. Calculated values of Tg and m for all the melts in the database (Fig. 18B) show a wide range in fragility (m) indicating the presence of both strong and moderately fragile melts. Values of Tg for the anhydrous melts vary slightly (Fig. 18B) and are not strongly correlated with fragility. Values of, both, Tg and m are strongly affected and depressed by volatile contents (Fig. 18B). The major decrease in Tg with increased volatile content accords well with experimental studies (Hess and Dingwell 1996).

e

3.85 H2O

562.42 0.00 P2O5 17.6 (1.8) (Al2O3)*(NK) b13

–1239.33 4.49 K2O –0.91 (0.3) (SiO2+TA+P2O5)*NK+H2O) b12

2.35 Na2O –2.43 (0.3) (SiO2 +TiO2)*(FM) b11

–235.04

log hg

4.05

18.7 57.685

– P2O5)×(NK+V)

(Al2O3+FM+CaO

0.30 (0.04)

CaO c11 141.5 (19) V + ln(1+H2O) b7

3.13

2135.35

700

–258.961 m ln(1+V)

–99.5 (4)

MgO c6 –84.1 (13) Na2O + Vc b6

0.35

–1235.83

79.50

–61.397 Tg(K) NKf

–12.3 (1.3)

MnO c5 –39.0 (9) CaO b5

b4

CaO

10.2 (0.7)

FeO c4 75.7 (13)

0.05

–127.00

10264.0

33.232 CVFT 38.37

–4.55

MgO

0.99

BVFT 11.252

101.130 AVFT –1107.53 0.06

60.98 8.3 (0.5)

15.7 (1.6)

FeO(T)+MnO+P2O5 b3

FMe

Al2O3 b2

TAd

Al2O3 c3 72.1 (14)

TiO2 c2 –173.3 (22)

11.16

C’s

196.558

B’s

11411.65

Wt. %

73.57 SiO2 2.75 (0.4) SiO2

Oxide

c1 159.6 (7) SiO2+TiO2 b1

cib Oxides bib Oxides

Table 7. GRD coefficients for calculating VFT parameters B and C; A = -4.55 ± 0.21 and an example calculationa.

Notes: aRhyolite melt with 4 wt.% H2O. bNumbers in brackets indicate 95% confidence limits on values of model coefficients. cH2O + F2O− 1; dTiO2 + Al2O3; FeO(T) + MnO + MgO; fNa2O + K2O. glog h (Pa s) = A + B/(T(K) − C) and predicted value for this melt at 1273 K is 4.05 Pa s.

Russell et al.

876

The GRD model predicts a nearlinear decrease in fragility with increased volatile content; for their database m is 20–58 for anhydrous melts vs. 12–49 for volatile-rich equivalents (Fig. 18B). The implication is that volatiles cause melts that are moderately depolymerized to become less fragile (e.g., stronger as defined by the m parameter) such that dry non-Arrhenian melts tend to become more Arrhenian with increasing volatile content. Strong melts that are moderately polymerized become even more Arrhenian with increased H2O content (Fig. 18B). We have illustrated the utility of the GRD by calculating transport properties of melts within a ternary defined by endmembers basanite, rhyolite and hydrous rhyolite (4 wt.% H2O). The endmembers have significantly different compositions and distinct temperaturedependent viscosities as illustrated by the calculated fragilities (18.7–57.7; Fig. 19). Melts resulting from mixing the end-members have intermediate viscosity values and are bounded by basanite and rhyolite at high temperature and rhyolite and hydrous rhyolite at lower temperatures (Fig. 19A). Values of Tg and melt fragility are also bounded by the end members (Fig. 19B) and vary nearly linearly on the two joins involving hydrous rhyolite but distinctly nonlinear between basanite and rhyolite. As stated above, one of the main attributes of the GRD model is its potential for calculating derivative melt properties that are not directly measured (e.g., Tg and m). Activation energy (Ea) represents the energy barrier for viscous flow and incorporates the temperaturedependent structural relaxation times for molecular rearrangement. The original definition of activation energy (Ea) derives from the Arrhenian equation (Glasstone et al. 1941) and is taken as:

Models for Viscosity of Geological Melts 14 12

600

6

0

200

14

In

cre

12

as

400

C (K)

600

400 10

800

(C)

in

gM

od

20

800

30

40

rs

8

Vo l

at il

1

NBO/T

1.5

-200

2

es

200 0

0.5

60

(D)

Modifiers

400

6

0

50

Fragility (m)

600

ifie

10

4

Volatiles

C90% olivine, PP = porphyritic pyroxene with >90% pyroxene, POP = porphyritic olivine and pyroxene). A further chondrule classification refers to the initial (unequilibrated) FeO content of olivine and pyroxene (Jones et al. 2018): Chondrules which have Fa and Fs 10 mol %, are designated as type II (Fa = atomic Fe/(Fe+Mg) in olivine; Fs = atomic Fe/(Fe+Mg+Ca) in pyroxene). Most type I chondrules, particularly in carbonaceous and enstatite chondrites, have Fa < 2 mole %. Type I and type II chondrules differ in several important petrologic respects. For example, type I chondrules contain abundant Fe,Ni metal blebs suggesting reducing conditions of formation, i.e., with log fO2 (oxygen fugacity) well below the Fe/FeO (IW) buffer curve. Olivine and pyroxene grains in type II chondrules (Fig. 2) are often larger than those in their type I counterparts, and commonly show significant Fe–Mg core to rim zoning arising from disequilibrium growth. Type I

Low

Fe metal

-Ca

Olivine

Cryptocrystalline pyro

xe n

e

Fe metal

Glass

Olivine

Low -Ca pyr o xe ne

Lo w

-Ca

pyro

xen

e

Type II

Barred Barred Glass Olivine

Olivine

Olivine Glass

Olivine

Glass

Olivine

Low -Ca

pyroxene

100 µm

Figure 2. Typical textures of natural chondrules from a variety of chondrites (backscattered electron images). Nonporphyritic chondrules include cryptocrystalline (CC), barred (or dendritic) and radiated (not shown) textures. Radiating textures are commonly pyroxene (P)-rich (RP); barred and dendritic textures are commonly olivine (O)-rich (BO). Porphyritic (P) textures include olivine-rich (PO, or type A), olivineand pyroxene-rich (POP, or type AB), and pyroxene-rich (PP, or type B). Chondrules with MgO-rich (Mg# >90) primary olivine and pyroxene compositions are designated type I, and chondrules with more FeO-rich (Mg#  b (i.e., positive a − b), or velocity weakening where a 0.1 m.s-1) contact temperature increases rapidly. Assuming an infinitesimally thin slip zone over which heating is active, and that heat can only be lost perpendicular to that slip surface, then this relationship is described by the diffusion equation of Carslaw and Jaeger (1959), and the temperature change (DT) caused by a given slip event of time tx can be computed via: T 

Ve Cp

tx k

(9)

where r is mass density, Cp is heat capacity and k is diffusivity, and when the frictional work rate or power density (Wp) is considered constant (after Nielsen et al. 2010b), given that: Wp = tVe

(10)

Temperature increase can result in dynamic weakening via a number of mechanisms, including: thermal pressurization of pore fluid (Sibson 1973); elastohydrodynamic lubrication (Brodsky and Kanamori 2001); chemical decomposition (relevant to rocks containing volatilebearing minerals; e.g., Han et al. 2007; Hirose and Bystricky 2007); mineral breakdown (Noda et al. 2011); silica gel formation (Di Toro et al. 2004; Kirkpatrick et al. 2013); flash heating at asperity contacts, resulting in thermal (Rice 2006; Beeler et al. 2008) and mechanical weakening (Weber et al. 2019) and frictional melting (Spray 1993; Hirose and Shimamoto 2005b; Di Toro et al. 2006). In the case of ascending magma at elevated temperatures in a conduit, such assertions are vital to understand the occurrence and impact of fault slip. Indeed, melting of the crystal cargo in magma (and of the conduit wall rock) may be an inevitable consequence of faulting in hot magmas and lavas, and as such here we will focus on the mechanisms which result in frictional melting to produce pseudotachylyte, and specifically those advances elucidated by experimentation.

FRICTIONAL MELTING The history of experimental approaches Laboratory experimentation allows for the probing of contributing factors towards an observed phenomenon. In the case of frictional melting, experimentation has been conducted over the last several decades in order to unravel the physical conditions that lead to and follow frictional melting on a slip plane, as well as the chemical processes taking place during melting. In the case of frictional sliding, the motivation for this research is to unravel the effect of the established mechanics on ongoing slip processes. Historically, many shear configurations have been implemented to study fault friction, including direct shear (Wang et al. 1975), double shear (Dieterich 1972), biaxial (Scholz and Engelder 1976) and triaxial (Byerlee 1967) set-ups, with good agreement of findings across each method and apparatus (Byerlee 1978). Subsequently many such approaches have been used to study frictional melting, for example: Spray (1987) used a frictional welding machine to reproduce pseudotachylytes, providing an excellent description of the melting process, though lacking the constraints of the causal conditions;

Frictional Melting in Magma and Lava

929

Serendipitously, Killick (1990) noted the production of pseudotachylyte whilst drilling Proterozoic lavas at 2.4 km depth; Lockner et al. (2017) amongst others developed frictional melts over short slip distances in triaxial cells at simulated deep crustal confining pressures, yet the fault geometry in such tests prohibits decoupling of shear and normal stresses. To date, none of these approaches offer the dynamism of the high-velocity rotary shear apparatus first designed by Shimamoto in the late 1980’s (Shimamoto and Tsutsumi 1994), and since modified to tackle different aspects and conditions of extreme fault friction by several research groups around the world. The rotary shear apparatus sees two cylindrical (rock) samples placed end-on-end to simulate a slip surface and allows the collection of torque (used to calculate shear stress) and axial shortening data at an applied rotation rate and axial stress over large total displacements (e.g., Ma et al. 2014). The only disadvantage of the cylindrical set-up is the variation in slip rate across the slip surface, which is minimized by using hollow cores. Following Shimamoto and Tsutsumi (1994) a nominal equivalent rotation velocity (Ve) can then be calculated from the rotation rate (R) and the outer and inner radii of the hollow cylinders (r0 and ri respectively) via: Ve 



2 4 R ro 2  rr i o  ri



3(ro  ri )

(11)

Assuming that the shear stress is constant over the sliding surface area (S) in this geometry: S = p(ri2 − r02)

(12)

Then, the rate of frictional work (W) may also be given by: W = tVeS

(13)

Kitajima et al. (2010) explored this assumption in more detail, but here as in other studies (e.g., Lin 2007; Boulton et al. 2017) we abide by the assumption that shear stress acts uniformly over the sliding surface. Because geometrical constraints of the apparatus mean that normal stress often cannot exceed ~10 MPa, several authors have posited that the advantage of using W (or by extension frictional work rate or power density) to compare response to slip, is that larger displacements can substitute for unattainable higher normal stresses (Lin 2007; Lockner et al. 2017); although, during melting and fault slip in the presence of a frictional melt layer, such substitutions may not suffice.

Mechanical response to melting As many natural pseudotachylytes have been observed in intrusive igneous rocks the majority of work on frictional melting has been conducted on them. A number of studies have recreated the geometry and properties of frictional melt using rotary shear experiments (Fig. 2), that also allow us to interpret the conditions leading to their formation (Shimamoto and Tsutsumi 1994; Tsutsumi and Shimamoto 1997; Lin and Shimamoto 1998; Hirose and Shimamoto 2005a,b; Di Toro et al. 2006; Nielsen et al. 2008, 2010b; Del Gaudio et al. 2009; Lavallée et al. 2012a, 2015a; Kendrick et al. 2014a; Violay et al. 2014; Hornby et al. 2015). Such tests can be challenging due to decomposition of phases and differential thermal expansion during such rapid heating rates, which can result in sample rupture. Rocks containing quartz (such as granites) present a particular challenge due to the increased rate of expansivity across the α–β transition resulting in fracturing (Ohtomo and Shimamoto 1994). Glass-rich materials may experience a similar outcome when they undergo viscous remobilization (when crossing the glass transition), which can make the experimental study of volcanic materials undergoing frictional slip difficult (Lavallée et al. 2015).

Kendrick & Lavallée

930

A

C

B

D

Figure 2. Pseudotachylyte in volcanic rocks: (A) Hand-specimen from an andesitic block at Soufriere Hills volcano (Montserrat), showing multiple generations of interlayered pseudotachylyte and cataclasite which have been viscously remobilized in the partially molten magma prior to eruption, so that they laterally pinch in and out. (B) The same material as in A in a backscattered electron image of a thin section, showing the coarse phenocrysts and finer glassy groundmass of the porous host andesite, with grain size reduction from the host material to the cataclasite, and densified pseudotachylyte comprising rounded surviving phenocrysts and an equant, interlocking mineral assemblage. (C) An example of a pseudotachylyte generated in a dacite from Mount St. Helens (USA) using a high velocity rotary shear test at 2 MPa of normal stress and 1 m.s-1 slip rate. (D) The same material as in C in a backscattered electron image of a thin section, showing large phenocrysts and glass-bearing porous groundmass in the host rock, with a dense pseudotachylyte layer of comparable thickness to the natural example in B, with a number of surviving plagioclase crystal fragments held in suspension in an interstitial glass (i.e., the pseudotachylyte). Textural differences may result from the duration of melting (unconstrained in the natural example) and the more rapid cooling of pseudotachylyte generated experimentally.

During fault slip at constant normal stress and at velocities that result in melting, shear stress on the slip plane evolves (Fig. 3A). This evolution was examined by Hirose and Shimamoto (2005b) who dissected gabbros subjected to different slip distances to propose a model for the progression of fault slip. At the onset of sliding an initial phase of grain plucking and comminution results in an early peak shear stress (hence, peak friction; P1 in Fig. 3A), which is followed by an initial weakening phase corresponding to flash heating and smoothing of asperities, reaching a preliminary period of steady-state sliding (stable shear stress and friction coefficient; SS1). A second peak in shear stress then initiates, which is interpreted as the production of isolated melt patches as frictional melting ensues (Hirose and Shimamoto 2005b). As the melt patches grow, shear stress increases further until a second peak (P2) at which point a continuous molten layer exists on the slip plane. Shear stress then decreases over a characteristic distance (Dc; Fig. 3B), which corresponds to the melt thickening, until a second steady-state period of sliding is achieved (SS2 in Fig. 3A). Numerous studies have shown that the onset of melting strengthens the slip zone, i.e., shear resistance increases to a higher second peak than that achieved during rock–rock sliding (Hirose and Shimamoto 2005b). This is attributed to a lubricating cataclastic gouge layer on the contact surface during the initial period of slip (P1 to SS1 in Fig. 3) which comminutes and allows minor shear-weakening within the first few meters of slip (Hetzel et al. 1996; Reches and Lockner

Frictional Melting in Magma and Lava

931

Figure 3. (A) Friction experiment on a dacite (after Kendrick et al. 2014) showing how frictional sliding produces an early peak (P1) as slip ensues, followed by slip weakening to an initial steady-state shear stress (SS1) due to flash heating and lubricating gouge, followed by a rapid increase in shear stress as melt patches begin to form on the slip interface, the melt layer coalesces at a second peak (P2), shear stress then decreases as the melt zone widens before attaining steady state slip (SS2) controlled by the viscosity of the melt. Shortening begins as the melt layer coalesces at P2 and accelerates until also reaching a steady state, where melt is produced and expelled at a constant rate. Temperature monitored on the sample surface reaches an initial plateau due to flash heating and then increases as melt becomes visible at the sample surface just before P2. (B) Area-averaged thickness of melt patches and a frictional melt layer plotted against the displacement after P1 during friction experiments at 1.2–1.5 MPa normal stress in gabbros, the dashed line is the least squares fit (after Hirose and Shimamoto 2005). Melt thickness initially increases slowly as patches appear, then accelerates quickly to a peak, and then stabilizes.

2010; Spagnuolo et al. 2016), during this stage the temperature monitored on the sample surface is relatively stable. The ultra-fine crystal fragments produced during this stage then begin to preferentially melt due to their larger surface area (Spray 1992), generating heterogeneously distributed melt patches on the slip surface (Tsutsumi and Shimamoto 1997; Hirose and Shimamoto 2005b; Chen et al. 2017). The small melt patches act as a viscous brake and rapidly increase shear resistance (Tsutsumi and Shimamoto 1997; Fialko and Khazan 2005; Hirose and Shimamoto 2005b) and correspondingly locally raise temperatures further (Fig. 3A). As the temperature increases, melt patches coalesce resulting in a molten layer with abundant crystal fragments (e.g., Fig. 4), as seen at the onset of melting (e.g., Wallace et al. 2019b). With further melting the volume of melt to crystals increases until a critical melt fraction is reached (Fialko and Khazan 2005; Rosenberg and Handy 2005; Chen et al. 2017) and temperature stabilizes. Once melt is present, the shear resistance during slip is strongly influenced by the melt’s rheological properties; melt viscosity, suspended pores and particles and the strain-rate (Spray 1993; Hirose and Shimamoto 2005a,b; Lavallée et al. 2012a; Hornby et al. 2015). The heat source may essentially be considered as viscous shear, and heat is similarly depleted by

Figure 4. A frictional melt zone (FMZ) generated in a dacite (from Mount Unzen, Japan) during a rotary shear experiment with a slip rate of 1.45 m.s−1, normal stress of 3 MPa and total displacement of 19.6 m. The sample exhibits embayment of the FMZ into adjacent hydrous amphibole (Am) crystals as they preferentially melt, with one showing a reaction front (black band) along the melt contact. Also shows viscous remobilization in the adjacent glassy groundmass identified by rotation of the microlites in the direction of shear in the host rock, and suspension of plagioclase crystals in the melt as they have higher melting temperatures (modified from Hornby et al. 2015).

932

Kendrick & Lavallée

conduction, latent heat and removal of melt. The apparent viscosity (happ) of the melt plus suspended crystals on the slip plane can be calculated from the monitored shear stress and shear strain rate ( ) via: app 

 

(14)

 

Ve d

(15)

where  is:

For a given melt layer thickness (d) and equivalent velocity (Ve). As melt thickness cannot be accurately characterized during slip, thickness must be measured from dissected experimental specimens. Thickness of the melt layer increases during slip due to further melting and may stabilize during steady-state sliding (e.g., Ferrand et al. 2021). Thickening generally results in a reduction in shear stress (e.g., Tsutsumi and Shimamoto 1997), from P2 to SS2 (Fig. 3), as the distance between the two opposing interfaces increases, referred to as the Stefan problem (Hirose and Shimamoto 2005a). The Stefan problem describes the migration of the melt–solid interface (the melting surface) into the bulk rock under non-linear conditions (Nielsen et al. 2010b), i.e., at conditions prior to achieving steady state under a constant slip rate (Hirose and Shimamoto 2005a; Nielsen et al. 2008). The melting surface migration is controlled by the melting of the rocks’ constituent phases (see section Selective melting), which depending upon the temperature gradient around the slip zone, also dictates the roughness of this interface (Nielsen et al. 2010a). Once steady state slip is achieved in the presence of melt, a simple diffusion equation yields a relatively accurate thermal profile and provides a solution for shear stress, melt viscosity, and thickness (Nielsen et al. 2008). Analysis has shown that preserved pseudotachylyte thickness is proportional to displacement across scales from the laboratory to the field for a wide range of lithologies (Ferrand et al. 2021). For a given rock type, melt thickness varies as a function slip velocity and normal stress (Nielsen et al. 2008), but can be highly variable within a single slip zone: A study by Hornby et al. (2015) measured slip zone thicknesses in experimentally generated pseudotachylytes in dacites, which showed variability of >100 µm within single slip zone (Fig. 4). In volcanic rocks, a potential contributing factor in addition to the impact of the mineralogical assemblage is the presence of volcanic glass in the host rock, which may facilitate viscous remobilization of areas adjacent to frictional melts (see Fig. 1), widening the slip zone and contributing to the evolution of the frictional melt zone (Lavallée et al. 2012a; Kendrick et al. 2014a; Violay et al. 2014; Hornby et al. 2015). Solutions for apparent viscosity based on mechanical data provide good approximations and are useful to compare the relative behavior of different materials where the use of the friction coefficient may not be entirely appropriate (i.e., in the presence of melt). Apparent viscosity measurements may be validated using careful geochemical analysis of frictional melts and modeling of the non-Arrhenian melt viscosity plus the effect of suspended survivor clasts. For a description of fault slip in the presence of a melt layer see the section Frictional melt rheology.

Selective melting The onset of melting and growth of a molten zone during fault slip are controlled by the mineralogy of the host rocks (e.g., Spray 1992). To accurately constrain the processes of frictional heating during fault slip and understand the progression of frictional melting, quantification of temperature during experiments is vital. In natural pseudotachylytes temperature has commonly been estimated from its mineral assemblage, assuming recrystallisation occurred under equilibrium (e.g., Magloughlin and Spray 1992). Yet, frictional melting is a rapid, dynamic and chemically chaotic process (Sibson 1975) that results from

Frictional Melting in Magma and Lava

933

conversion of thermomechanical energy on a slip plane to heat at strain-rates >10−2 s−1 and slip velocities > 0.1 m s−1. Thermal monitoring of experiments has recorded heating rates of >1000 oC.s-1 (e.g., Lavallée et al. 2012a, 2015a; Kendrick et al. 2014a), and the geochemical signatures of natural and experimentally-derived pseudotachylytes show that frictional melts are formed by selective melting of their host rocks (e.g., Magloughlin and Spray 1992; O’Hara 1992; Lavallée et al. 2015b; Wallace et al. 2019b). The constituent rock-forming minerals thus control the progression of frictional melting (Fig. 5), where selective melting occurs in the order of their  solidus temperatures (Spray 1992). As such, frictional melting can be defined as a non-equilibrium process (Sibson 1975; Spray 1992; Lin and Shimamoto 1998) and the compositional evolution of frictional melts may be used to constrain the conditions of formation of natural pseudotachylytes, especially duration of slip (e.g., Jiang et al. 2015). A framework for the progressive melting of constituent mineral phases (under nonisothermal conditions) is given in Spray (2010), whereby minerals with the lowest strength and breakdown temperatures are preferentially comminuted and melted to create a polyphase suspension comprising mineral and rock fragments enclosed within a liquid. Comminution is the process of crushing and grinding a solid material to form smaller particles, which often results in a power-law particle-size distribution represented by a large number of small fragments, an intermediate number of mid-size fragments, and a small number of large fragments (e.g., Sammis et al. 1987; Guo and Morgan 2006; Spray 2010; Kennedy and Russell 2012). von Rittinger (1867) proposed that the energy consumed in the size reduction of solids is proportional to the new surface area produced, a theory which appears to be supported by comminution products which show that the normally scale-invariant power-law distribution falls apart at very fine grain size (which has been termed the comminution limit) because fracturing smaller particles requires disproportionately more energy than fracturing larger ones (e.g., Lowrison 1974). Moreover, comminution is relatively inefficient; compared to the mechanical energy input only 1–2% contributes to grain size reduction (Tromans 2008), with the bulk of remaining energy converted to heat. Since melting then ensues in the comminuted gouge, it follows that the progression of melting is highly dependent upon yield strength and fracture toughness of the material which controls this comminution, as well as the breakdown or melting temperature of the constituent minerals involved (Fig. 5). Amongst rock-forming minerals the types of bonds control their fracture toughness, covalent-bonded minerals exhibit the highest fracture toughness (e.g., diamond), followed by ionic-bonded (e.g., metal oxides), then ionocovalent (e.g., silicates) phases and finally ionocovalent or van der Waals bonded minerals (i.e., many phyllosilicates). This trend is approximately comparable with other metrics of hardness and toughness including yield strength (Fig. 5); for a comprehensive description of the variability of yield strength, fracture toughness, Mohs number and indentation hardness for rock-forming minerals, see Spray (2010). As comminution and heating progress, thermal conductivity also becomes important. The contrasting thermal conductivity of minerals means some (i.e., poor conductors) are more prone to undergo thermally induced fracturing. Decrepitation (fracture by differential thermal expansion) can be triggered, contributing to grain size reduction (Spray 2010). This secondary phase of fragmentation mechanisms occurs in addition to the grain size reduction by comminution and may be more effective in different (less conductive) phases. This contributes to the non-linearity of the melting process (e.g., Fig. 3), since the Gibbs–Thomson equation dictates that the smaller the fragment of a mineral, the lower the melting temperature becomes (e.g., Lee et al. 2017), and thus melting onset can occur during frictional sliding at much lower temperatures than their equilibrium melting temperature. Here we will focus exclusively on the progression of frictional melting in magmas and lavas. Differences in mineral assemblages are expected both between volcanic systems, and within a single system. In a given magmatic center (especially intermediate volcanic systems) mineralogy and crystallinity can be naturally variable over short to long duration, either

Kendrick & Lavallée

934

Melting/ breakdown temperature (oC)

Diamond Orthosilicates and oxides

2000 1600

Inosilicates I

Tectosilicates

1200 800

Phyllosilicates Inosilicates II

400

0 Mohs number 1 Yield strength 0.17

2

3 0.33

4 0.67

5

6 1.67

7

8 3.33

9 6.66

Figure 5. Mineral stability at temperature. Approximate melting or breakdown temperature is shown versus Mohs number and yield strength (in GPa) for groups of rock-forming minerals (after Spray 2010). Following the nomenclature of Spray et al. (2010) inosilicates I refers to single-chain inosilicates such as ortho- or clinopyroxene, and inosilicates II refers to double-chain inosilicates such as amphiboles. Orthosilicates and oxides include rutile, zircon and corundum; tectosilicates include quartz, plagioclase and orthoclase; and phyllosilicates include mica and serpentine.

reflecting magma recharge or changes in storage or ascent conditions (Smith and Leeman 1987; Scott et al. 2013). For example, previous studies have reported that elevated magmawater content in a plumbing system which introduces hydrous phases, often coincides with an increase in explosivity (Luhr and Carmichael 1990). In terms of frictional behavior, the presence of hydrous phases (e.g., amphibole, gypsum, zeolite, clays, phyllosilicates) are likely to bring forward melting onset and impact the rheology of the frictional melts produced due to their typically lower melting points and the associated release of water (e.g., Allen 1979). Thus, it is important to ascertain the effect of mineralogical changes on frictional melting, and the feedback this will have on magma ascent dynamics. Experiments on volcanic rocks demonstrate the propensity for frictional melting after a few cm’s slip at upper conduit conditions (Kendrick et al. 2014a; Wallace et al. 2019a). Selective melting of minerals in different volcanic materials have been shown to produce heterogenous melts (Lavallée et al. 2012a; Hornby et al. 2015; Wallace et al. 2019b). This results from chemically distinct “protomelts” or “schlieren”, the products of melting of individual minerals or partial mixing of these protomelts (Masch et al. 1985; Grunewald et al. 2000; Hornby et al. 2015; Wallace et al. 2019b). Protomelts represent minerals with the lowest melting temperatures (e.g., Shimamoto and Lin 1994; Hirose and Shimamoto 2005a,b; Lavallée et al. 2012a; Hornby et al. 2015). Selective melting occurs both within the comminuted gouge formed during initiation of slip, and once initiated, it is also the process by which the melt layer grows, melting the adjacent host rock by contact heating, and melting minerals with low melting temperatures further away by conduction or diffusion of heat from the slip interface. Thus, selective melting also enables the suspension of survivor clasts (that is un-melted restite lithic or crystal fragments) and contributes to embayments in the otherwise planar frictional melt boundary as certain minerals are preferentially consumed (Fig. 4). Here the Gibbs–Thomson effect may once again come into play, where the local melting temperature of a mineral’s external surface (in contact with the melt zone) is reduced along the irregular surface topology (Hirose and Shimamoto 2003; Nielsen et al. 2010a; Lee et al. 2017; Wallace et al. 2019b).

Frictional Melting in Magma and Lava

935

It therefore follows that the melting surface (i.e., the melt–solid interface) topology is sensitive to the rate of melting; with faster rates leading to lower roughness (Nielsen et al. 2010a). Recently Wallace et al. (2019b) undertook a systematic study host-rock mineralogy on compositional and textural homogenization in different lavas. Specifically, the effect of the presence of hydrous amphibole was considered by comparing an amphibole-bearing andesite from Soufrière Hills Volcano (Montserrat) to an amphibole-free andesite from Volcán de Colima (Mexico). Results showed that the amphibole-bearing andesite began melting after a shorter slip distance at the same velocity and normal stress, corresponding to the lower melting temperature of the amphibole (Fig. 5). The amphibole-bearing lava also reached a lower peak and steady state shear stress (Wallace et al. 2019b). The frictional melt zone progressively homogenized during fault slip, as revealed by textural examination and chemical transects at different slip distances beyond the attainment of steady-state slip (Fig. 6; Wallace et al. 2019b). At all stages of slip, survivor clasts were suspended in the melt. The proportion of suspended crystals remained relatively constant throughout slip (at steady state), though the size and rounding of the suspended clasts appeared to increase as the melt zone matured (Fig. 6). The Gibbs–Thomson effect states that local melting temperature of a mineral in contact with melt is lowered in proportion to its curvature (Nielsen et al. 2010a), an effect which both enhances the rounding of suspended particles, and increases the complexity of the melt–rock interface during the sustained presence of frictional melt (Hirose and Shimamoto 2003). Careful chemical timeseries of frictional melting products can elucidate the mineral contributions to the frictional melt (Wallace et al. 2019b). For example, for amphibole-bearing and amphibole-free andesites (Fig. 7), variability in major element oxide compositions were

A

Starting material

Melting onset

Steady state onset

5 m at steady state 10 m at steady state

90

50 µm

B

80

Interstitial glass Bulk rock

70

CaO (wt. %)

SiO2 (wt. %)

Melting onset

Steady state onset

5 m at steady state

60 10 m at steady state

90

90

90

90

80

80

80

80

70

70

70

70

60

60

60

60

50

50

50

50

40 12 0 10

100

200

300

8 6 4 2 0

0

100

200

300

Distance (µm)

40 40012 0 10 8 6 4 2 0 0 400

100

200

40

12 0

100

200

10 8 6 4 2 0

6 4 2 200

Distance (µm)

0

0

100

200

Distance (µm)

40

40 300 12 0

10 8

100

50

300

0

0

100

200

300

100

200

300

100

200

300

Distance (µm)

Figure 6. Physical and chemical homogenization of a frictional melt in an andesite from Soufrière Hills (Montserrat) containing plagioclase, hornblende, clinopyroxene and orthopyroxene, iron-titanium oxides and rhyolitic interstitial glass deformed in rotary shear at 1 m.s−1 and normal stress of 1 MPa. (A) A time series of frictional melt textures generated at melting onset, at the attainment of steady state sliding plus 5 m and 10 m slip at steady state, compared to the host groundmass, showing increasing size of suspended clasts as the melt zone thickens towards steady-state sliding. (B) Example profiles of major element oxide compositions across the frictional melts at the same slip distances in A, showing variability in the melts around the bulk rock composition, with variability decreasing, indicating homogenization with increasing slip distance (data from Wallace et al. 2019b).

400

Kendrick & Lavallée

936

 #






 










$"+%
















$"+%





 


























$"+%




$"+%


$"+%
















$"+%


$"+%





 #  





  


$"+%

!




























 
 













  













 



 
!












"












 
 











(













'&













'(


Figure 7. Binary plots showing the evolution of frictional melt composition for representative major element oxides (SiO2, CaO, FeO and MgO) in an amphibole-free andesite from Volcán de Colima (Mexico) and an amphibole-bearing andesite from Soufrière Hills (Montserrat) with increasing slip displacement from the onset of melting until 15 m sliding beyond the attainment of steady-state slip. For comparison, the bulk rock composition, host-rock plagioclase, interstitial glass, and amphibole (where present) are plotted. In the presence of amphibole, the frictional melt composition is much more variable, and slowly converges towards a more mafic composition than the bulk, whereas in the amphibole-free case, the frictional melt has little variability from the outset, and homogenizes towards the bulk composition with increasing slip distance “(data from Wallace et al. 2019b).

considerably higher in the amphibole-bearing andesite, suggesting that greater heterogeneity results from slip in rocks which have mineral compositions with disparate melting points. Throughout slip, the chemical composition of the frictional melts trended towards that of the bulk rock for amphibole-free lava, whereas the amphibole-bearing sample melt became progressively more mafic than the host (Wallace et al. 2019b), as has been noted in natural pseudotachylytes (Camacho et al. 1995). More broadly, the melting of polyphase rocks by selective melting may produce frictional melt that is more ferromagnesian and basic than the bulk rock, forming pseudotachylytes of distinct composition to the host materials (Spray 2010). Detailed examination of the onset of melting and the progression of homogenization, characterized experimentally, may help unravel the timeframes of fault slip to create natural pseudotachylytes. An examination of the slip distance after which melting may be achieved in different lithologies reveals that the mineralogical assemblage of each lava composition systematically controls melting onset distance (Fig. 8A). In the lithologies examined, we note that for a given slip rate and normal stress condition there is a clear tendency for basalts to melt most rapidly, followed by andesites, with dacites taking the longest slip distance to melt (note that distance to melt here is identified by the peak shear stress caused by melt, P2 in Fig. 3, not the inflection from SS1 to P2 caused by the first appearance of melt patches, which may follow a different sequence). For a given slip velocity, increasing normal stress non-linearly shortens the distance required to melt to as little as a few cm’s slip at > 5 MPa at slip velocities >1 m.s-1 (e.g., Kendrick et al. 2014a; Violay et al. 2014). At a given normal stress, slip velocity controls the distance over which melting is achieved, showing the interplay between how rapidly heat is produced versus dissipated/ conducted away from the slip zone (as described by Eqn. 9). Hirose and Shimamoto (2005b) posited that the slip weakening distance (Dc) would be directly controlled by the rate of melting of the mineral assemblage as the melt–solid interface

Frictional Melting in Magma and Lava

937

migrates into the host rock (as described previously). In their further examination of the problem, they proposed that both slip weakening and the thickening of the molten layer are characterized by exponential changes with comparable characteristic distances, and thus they proposed that Dc can be explained by the thickening of the melt zone in both experimental and natural faults (Hirose and Shimamoto 2005a). Slip rate also has an important control on the slip weakening distance (Fig. 8B); Dc is reduced at faster slip rates (e.g., Niemeijer et al. 2011) likely due to the interplay between heat production and loss described by the Stefan problem (Nielsen et al. 2010b). The data shown in Figure 8B are for a narrow range of normal stresses, 1.2–1.5 MPa, yet, previous work has found that slip weakening distance decreases inversely with normal stress for a given rock type (Nielsen et al. 2008; Niemeijer et al. 2011); although a systematic study remains to be conducted. Following weakening, once steady-state slip is achieved, the rheology of the melt, plus any suspended particles, controls fault slip and the temperature generated by shear heating (Fig. 1).

Figure 8. Characteristics of frictional melting dynamics. (A) Distance to melting, defined as the second peak in shear stress (P2 in Fig. 3), as a function of applied normal stress for basalt, andesite and dacite samples at a range of slip rates. Data shows that the slip distance required for melting decreases nonlinearly with increasing applied normal stress, and at a given normal stress faster slip rate results in melting over shorter distances (e.g., note the dacite’s distance to melting decreasing from >11 m to ~1 m as slip velocity is increased from 0.1 to 1.5 m.s-1 at 5 MPa normal stress). A clear tendency for basalts to melt most rapidly, followed by andesites, with dacites taking the longest slip distance to melt is seen. Dashed lines are illustrative least squares fits through the dataset available and do not capture the slip rate variation. Data for the andesite and dacite are from Kendrick et al. (2014a), data for the basalt is unpublished. (B) Once a frictional melt layer covers the slip surface, shear stress begins to decrease from a peak (P2 in Fig. 3) to its steady state condition (SS2) as the melt thickens. The distance over which weakening occurs is described by the slip weakening parameter, Dc, which is approximately linearly dependent on slip rate, as demonstrated with gabbro samples from Hirose and Shimamoto (2005a).

Frictional melt rheology Shear stress. Pseudotachylyte generation greatly alters the dynamics of fault slip (e.g., Otsuki et al. 2003; Di Toro et al. 2006; Nielsen et al. 2010b) such that melt rheology controls the slip zone properties (Tsutsumi and Shimamoto 1997; Hirose and Shimamoto 2005a,b; Nielsen et al. 2008; Niemeijer et al. 2011; Lavallée et al. 2012a, 2015a; Kendrick et al. 2014a; Hornby et al. 2015). Selective melting controls melt onset and homogenization timescale as the melt chemically evolves and lithic and crystal restites become suspended (Hornby et al. 2015; Wallace et al. 2019b). The final pseudotachylyte (including melt and suspended clasts) may approximate the bulk chemistry of the host rock in natural (Kendrick et al. 2012, 2014b) and experimental samples (Hornby et al. 2015), or may be more mafic than the host rock, especially where hydrous phases are present, again, as demonstrated by natural (Lin 1994b; Camacho et al. 1995; Andersen et al. 2008) and experimental (Wallace et al.

938

Kendrick & Lavallée

2019b) pseudotachylytes. Whilst friction coefficient is not, in principle, appropriate to describe fault slip in the presence of melt, the relationship of monitored shear stress to imposed normal stress and slip rate conditions still elucidates the shear resistance imposed on the fault, and is occasionally termed the effective friction coefficient. In the presence of a molten layer the rheological properties (i.e., strain-rate dependent melt viscosity, suspended particles and bubbles) dictate materials’ ongoing response to sliding (Spray 1993; Hirose and Shimamoto 2005a; Di Toro et al. 2006; Nielsen et al. 2008, 2010b; Niemeijer et al. 2011; Lavallée et al. 2012a, 2015a; Kendrick et al. 2014a; Violay et al. 2014; Hornby et al. 2015; Wallace et al. 2019b). Importantly, the composition of frictional melts, controlled by the composition and mineralogical componentry of the rock, dictates the shear resistance imposed by them (Fig. 9). Frictional melts in more mafic rocks, such as basalts, tend to lubricate slip zones (e.g., Violay et al. 2014), imposing lower effective friction coefficients than that predicted from Byerlee’s law (Eqn. 1). In felsic and intermediate rocks, including andesite and dacite, frictional melts tend to act as viscous brakes, causing high shear stresses, and effective friction coefficients higher than the Byerlee frictional envelope, especially at low normal stresses relevant shallow faulting environments including volcanic centers (Fig. 9; Lavallée et al. 2012a; Kendrick et al. 2014b; Hornby et al. 2015; Wallace et al. 2019b). This observation is matched by modeling results, which further suggest that viscous braking becomes less effective at higher normal stresses (Fialko and Khazan 2005), for example in subduction zone faulting. At these conditions frictional melt appears to lubricate slip, seemingly irrespective of melt composition (e.g., Di Toro et al. 2006). In all compositions, waning slip velocity may result in the viscous brake effect coming into play (e.g., Spray 2005), as a decrease in shear rates increases the apparent viscosity of shear thinning suspensions and decreases thermal input, thus promoting cooling which increases the melt viscosity (Lavallée et al. 2012a; Kendrick et al. 2014a).

Figure 9. Shear resistance of basalt, andesite and dacite rocks. The data were collected from a suite of experiments performed at variable normal stresses and two slip rates, showing peak shear stress (P2) and steady-state shear stress (SS2) response of the rocks undergoing frictional melting. Typically, at low normal stresses the peak shear stress is higher than the shear resistance anticipated with Byerlee’s law (grey area), and in more silicic compositions (dacite) the shear stress remains elevated at steady-state sliding conditions. Thus, at the onset of melting shear resistance may be higher than would be in an intact rock and thus the material acts as a viscous brake. As normal stress is increased the shear stress response increases at lower rate, dropping below the zone given for frictional sliding by Byerlee, and thus the melt may be lubricating with respect to intact rock. Data for the basalt is unpublished and data for andesite and dacite is from Kendrick et al. (2014a).

Frictional Melting in Magma and Lava

939

An aspect of frictional melting which is commonly overlooked is the high shear resistance imposed during the onset of melting. The onset of frictional melting always imposes marked strengthening of faults (Tsutsumi and Shimamoto 1997; Hirose and Shimamoto 2005b; Chen and Rempel 2014). This transitional period in which shear resistance ramps from an early stable sliding period of the rock–rock contact (SS1 in Fig. 3) to a second peak shear resistance (P2 in Fig. 3) can last several meters, especially at modest slip rates or normal stresses (Tsutsumi and Shimamoto 1997; Lavallée et al. 2012a; Kendrick et al. 2014b; Hornby et al. 2015; Wallace et al. 2019b). The peak shear stress exceeds the shear stress of steady-state sliding in the presence of a thickened melt layer (SS2 in Fig. 3), and often significantly exceeds the frictional envelope of Byerlee (solid symbols, Fig. 9). This may be highly relevant for frictional melts observed in certain short-lived slip events (e.g., Sibson 1975). As such there is a discrepancy in the way that melt is discussed as a lubricator or viscous brake, as all melts when first generated serve to temporarily increase resistance to slip. As such, situations where flash heating plays a role but melting can be avoided may have the lowest friction coefficients of all (e.g., Tsutsumi and Shimamoto 1997; Rice 2006), whereas those situations in which melting is able to begin may hinder or even halt slip. After the fault zone passes from hosting individual melt patches to hosting a molten layer (e.g., Hirose and Shimamoto 2005b), and the melt zone thickens, melt can be a brake or lubricator controlled by its rheology. Tsutsumi and Shimamoto (1997) stress the importance of the inclusion of such non-linear dynamics into modeling of earthquake initiation processes, and such considerations are equally relevant to faulting in volcanic environments. Theoretical solutions. Several studies have attempted to describe the effect of slip in a thin melt layer. A suite of constitutive relations and differential equations describe the thickness, temperature and viscosity during viscous fluid flow on a slip plane (Fialko and Khazan 2005; Nielsen et al. 2008, 2010b). Under steady-state conditions, the diffusion equation (which yields a simple thermal profile) further allows constraint of the shear stress (e.g., Nielsen et al. 2008). As the primary aims of these studies are to interpret and mimic experimental observations such that the model may be extended or extrapolated to the study of earthquake source parameters at depth, the models mathematically capture the essential characteristics of the dynamics of fault slip in the presence of melt (e.g., Nielsen et al. 2010b). The summation is that a theoretical solution describing the coupling of shear heating, thermal diffusion, and melt expulsion can be obtained to describe shear stress at steady state slip conditions, via: 1 4

 A    n    r

 2V   V  V    V 

log 

e

c

(16)

e

c

after Nielsen et al. (2010b), where is r the radius of the contact area, A  is a dimensional normalizing factor (incorporating rock and melt parameters and another geometrical factor) and Vc is a characteristic rate (that may be considered a critical slip velocity where a behavior transitions from a velocity-hardening to velocity-weakening). Such solutions offer a reasonable fit to laboratory data and are invaluable in the upscaling of laboratory work to various crustal scenarios, and yet the subtleties of slip dynamics are not captured. For example, equivalent viscosity of the melt only depends on slip rate and a series of fixed constitutive parameters; and as a consequence, for fixed velocity, the shear stress will vary only because of changes in thickness of the melt layer. For systems where direct observation is possible (e.g., the laboratory), it is thus advisable to also take a direct approach to the quantification of viscosity. Melt viscosity. Numerous experimental investigations have noted that slip is velocity weakening (~rate weakening) in the presence of a molten layer (Fig. 10A; Tsutsumi and Shimamoto 1997; Kendrick et al. 2014a; Violay et al. 2014). This means that for a given normal stress, an increase of slip rate results in a decrease in monitored shear stress (and hence decrease in effective friction coefficient). This relationship follows a non-linear reduction in shear stress

940

Kendrick & Lavallée

Figure 10. Mechanics of frictional melt. (A) The steady-state shear stress in the presence of a frictional melt (SS2) is velocity weakening, with shear stress decreasing as slip rate increases at a given normal stress. Here, glass-bearing and glass-free basalts (from Violay et al 2014) during frictional sliding at 10 MPa normal stress illustrate the effects of shear thinning rheology on shear stress during slip, and highlight that the presence of glass may serve to increase shear stress at a given slip condition, potentially due to widening of the slip zone by viscous remobilization of the adjacent host rock at temperatures above the glass transition. (B) Steady-state sliding ensues once a melt layer is produced and has achieved a stable thickness, where melt is expelled at an equivalent rate to its production. Melt production and expulsion is monitored via shortening, shown here as a function of normal stress. Experiments on variably porous basalts (unpublished) demonstrate that shortening rate (measured in millimeters per meter of slip) is faster at higher normal stress, and for a given normal stress is higher for more porous samples.

as a function of slip rate, with the degree of reduction controlled by the specific frictional melt viscosity (Fig. 10A). Tsutsumi and Shimamoto (1997) attribute this to a thicker melt layer at a higher velocity caused by a higher production rate of melt. Whilst such transient phenomena likely contribute to the velocity weakening of melt-bearing faults, experiments by Kendrick et al. (2014a) where slip rate was fluctuated showed the near-instantaneous response of shear stress, more rapidly acclimatizing to the new slip rate than the predicted equilibration to a new melt zone thickness in both the case of velocity increase and decrease. Such observations are key in unravelling the rheology and viscosity of frictional melt suspensions. As described in the section Mechanical response to melting, apparent viscosity of a slip zone can be retrieved from the mechanical data during a friction experiment using Equation (13). This solution relies on constraint of melt thickness, which is assumed to be constant throughout steady state slip due to achieving a balance between melt production rate (controlled by slip rate and normal stress) and melt expulsion (Nielsen et al. 2008; Niemeijer et al. 2011). During experiments shortening is monitored, and as shortening rate achieves a steady state then the melt zone is interpreted to have a stable thickness. In the presence of melt, shortening rate is faster at higher normal stress and faster at higher slip rate, but structural heterogeneities in the host rock, such as grain size or porosity variation can also impact melt thickness. Using experiments on variably porous basalts with the same bulk chemistry and mineralogical assemblages, Figure 10B shows how steady state shortening rate (due to equilibrated melting and melt expulsion) varies as a function of host rock porosity during direct shear experiments: Higher shortening rates are achieved in more porous samples, which is interpreted to be due to the increased ability for melt to infiltrate the host rock at higher porosity, enhancing melting (Hirose and Shimamoto 2005b; Nielsen et al. 2010a). This suggests that higher porosity host rocks could result in thicker melt zones, and that local porosity heterogeneities may impact melt thickness, which has been relatively overlooked to date. This is likely to be important in volcanic rocks which have anisotropic porous networks and porosities spanning 0–98% (e.g., Gonnermann and Manga 2007; Cashman and Scheu 2015).

Frictional Melting in Magma and Lava

941

An approach which takes the chemical composition of the frictional melt, the monitored temperature, thickness and volume of suspended particles to accurately model the apparent viscosity of the frictional melt zone has been utilized by a number of studies (e.g., Lavallée et al. 2012a; Hornby et al. 2015; Hughes et al. 2020). Silicate melts are viscoelastic bodies (Dingwell and Webb 1989). Work on the viscosities of silicate melts has resulted in a statistically robust dataset over a wide compositional range, all displaying strong non-Arrhenian temperaturedependence (Hess and Dingwell 1996; Giordano et al. 2006). A substantial body of work over the last 4–5 decades has dissected through the chemical composition, temperature, pressure and strain rate dependence of silicate melts’ viscosity (see this volume). The temperature dependence of melt viscosity is well constrained for a range of compositions, presented as an interactive calculator by Giordano et al. (2008). Their viscosity calculator uses 10 major and minor oxide components and the volatile phases H2O and F, calibrated against a large dataset that spans the range of most frictional melts which could be formed by selective or wholesale melting of many rocks. Thus, by taking the major and trace element oxide composition of the frictional melt, analyzed by electron probe micro analysis (EPMA), one can estimate the temperaturedependence of melts’ viscosity; the range of viscosities of dry rhyolitic, andesitic and basaltic melts are shown in Figure 11A. Hornby et al. (2015) showed how the more mafic early stage melts (protomelts) exhibited lower viscosities than the more evolved melts produced following longer slip durations, thus frictional melts may transiently move through the compositional, temperature and hence viscosity space represented by Figure 11A during their development. Water may be incorporated into the slip zone during frictional melting, either by the release of volatiles from the melting of hydrous phases, from hydrated interstitial glass in the host rock or from liquid water in pore space (Magloughlin 2011; Lavallée et al. 2015b). The presence of dissolved water in silicate melts serves to decrease their viscosity (Fig. 11B; Hess and Dingwell 1996); the effect is non-linear for a given temperature, such that the first 1% addition of H2O reduces viscosity more significantly than any subsequent fraction. Water solubility is temperature dependent (see section Thermal vesiculation), so in situations where shear heating increases the temperature of frictional melts, the solubility of water decreases (Liu et al. 2005), triggering volatile exsolution which would cause a net increase in the melt viscosity (Hess and Dingwell 1996); yet, this chemical effect would be accompanied by the physical presence of vesicles, which also modify the flow field and the resultant apparent viscosity of the suspension (e.g., Manga et al. 1998). Pseudotachylytes, especially protomelts from selective melting, and those formed in shallow crustal settings are often characterized by vesicular textures (Maddock et al. 1987; Takagi et al. 2007; Lavallée et al. 2015b; De Blasio and Medici 2017; Hughes et al. 2020). Suspension viscosity. Pseudotachylytes frequently preserve evidence of both vesicles and crystals in suspension. Selective melting during frictional melt production means that minerals with higher melting points may survive as suspended clasts within frictional melt, and vesicles are formed by the incorporation of fluids from mineral breakdown, interstitial glass / melt devolatization or trapping of groundwater. A substantial body of work has demonstrated the influence of suspended crystals or bubbles on non-Newtonian viscosity and numerous parameterizations have been generated, yet few have tackled their combined impact (Lejeune and Richet 1995; Manga et al. 1998; Llewellin et al. 2002; Caricchi et al. 2007; Lavallée et al. 2007; Costa et al. 2009; Cimarelli et al. 2011; Mueller et al. 2011; Mader et al. 2013; Lesher and Spera 2015; Truby et al. 2015). As an illustrative example of the impact of suspended crystals on viscosity, a range of particle concentrations are plotted in Figure 11C. As particle fraction increases, melt viscosity nonlinearly increases (Fig. 11D), following the relationship commonly referred to as the EinsteinRoscoe equation, whereby relative viscosity (hrel) is related to crystallinity (ϕ) and the maximum packing fraction (ϕ0) via:

942

Kendrick & Lavallée    rel app  1   m  0 



5 2

(17)

where happ is the viscosity of the suspension (apparent viscosity) and hm is the melt viscosity (see Lesher and Spera (2015) for a review of suspensions’ apparent viscosity). For simplicity here, we represent the relative viscosity of a suspension in Figure 11C assuming spherical particles (due to the rounding of suspended particles in a melt following Gibbs–Thomson theory), and a maximum packing fraction of 64% (based on monodisperse spheres). Spherical particles may reasonably approximate equant crystals, but in the presence of elongate crystals, the maximum packing fraction would decrease. Changing aspect ratio or polydispersity of the suspended crystal cargo would change the amount of relative viscosity increase as a function of crystallinity (Fig. 11D), and hence change the absolute viscosities of the suspension at given crystal fractions (Fig. 11C). What Equation (11) fails to capture (Fig. 11C), and which has been demonstrated by a number of studies (e.g., Caricchi et al. 2007), is the reduction in relative viscosity as a function of increasing strain rate (Fig. 11D) owing to the shear thinning nature of magmatic suspensions. This may be caused by the concentration of stress and strain around the bubbles and particles, which has been shown to reduce the maximum shear strain rate that can be relaxed by ~2 orders of magnitude (e.g., Gottsmann et al. 2009; Cordonnier et al. 2012; Coats et al. 2018). Particle size, aspect ratio, dispersity (of size and shape) and maximum packing dictate the magnitude of the reduction in relative viscosity as a function of strain rate (for an example see Fig. 11E). A further impact of suspensions (as opposed to pure melts) during deformation, is that they can evolve with strain, exhibiting strain hardening or strain weakening behavior, for example resulting from pore collapse, or crystal alignment, respectively (Lavallée and Kendrick 2020) adding further to the complexity of suspensions’ response to evolving conditions of fault slip. A few authors have implemented complex non-Newtonian suspension rheology solutions to frictional melts (Fig. 10F; Lavallée et al. 2012a; Hornby et al. 2015; Wallace et al. 2019b; Hughes et al. 2020). In these examples the apparent viscosity of the frictional melt suspension was estimated using the strain rate-dependent rheological model for magmatic suspensions of Costa et al. (2009) using fitting parameters from the experimental data of e.g., Caricchi et al. (2007), and maximum packing fraction estimates with the model of Mueller et al. (2011) for the restite clast population aspect ratio distribution. The temperature monitored during the experiment (either by thermal camera or by thermocouples adjacent to the slip surface) was then mirrored by the viscosity evolution as a function of slip (Fig. 11F), though assumptions must still be made as to strain rate over an evolving thickness of frictional melt. Modeled values of apparent viscosity can be compared to the viscosity experimentally determined from the mechanical data using Equation (14). The comparison yields the observation that apparent viscosity from mechanical data is lower than that which is modeled, suggesting a number of contributing factors: (1) The temperature monitored on the surface of the sample is likely a minimum value, and on the slip zone may be higher, which means viscosity would be lower than that modeled due to the viscosity of the melt phase itself being lower; (2) Both methods rely upon melt thickness, which is either estimated or based upon dissected samples; in the mechanical case this directly impacts the strain rate and accordingly the apparent viscosity (via Eqns. 13 and 14, respectively) and in the modeled case melt thickness impacts the calculated strain rate (Eqn. 13), which dictates the degree of shear thinning of the suspension; (3) The geometry of the experiment means that slip rate varies across the annular contact zone, and because the suspension is non-Newtonian, this means shear resistance is not equal at all distances from the center of rotation.

Frictional Melting in Magma and Lava

943

Figure 11. The rheology of silicate melts: (A) Effect of chemical composition on melt viscosity. Illustrative examples are given for the range of basalt, andesite and rhyolite compositions (dry endmembers). The effect of increasing SiO2 is shown, though other major and trace element oxides also exert a control. (B) Effect of dissolved water concentration on viscosity of an andesitic melt across a range of temperatures. (C) Effect of crystallinity (up to 60 vol.%) on the viscosity of a suspension containing an andesitic melt (the same as in B) across a range of temperatures, modeled using spherical particles (similar to rounded survivor clasts’ geometry) and a maximum packing fraction of 64%, using the method Einstein–Roscoe equation, Eqn. 17 (see Lesher and Spera 2015). (D) The impact of crystallinity in C on the relative viscosity (i.e., the suspension viscosity divided by the melt viscosity) of suspensions for static conditions; with increased strain rate the relative viscosity of the suspension decreases. (E) Plot of the strain rate dependence of relative viscosity for a melt with 30 vol.% crystallinity computed with the Costa et al. (2009) viscosity model (after Lavallée et al. 2012); the data suggests a rate-independent viscosity regime at very low strain rate, although this remains poorly constrained. (F) Evolution of apparent viscosity of a frictional melt zone (using the suspension modeled in E based on corrected temperature (monitored by thermocouples near the slip zone) during a rotary shear experiment (using averaged strain rate), with shear stress, shortening and temperature shown. Viscosity decreases rapidly as the melt patches coalesce (during strengthening) and as the melt zone widens (during weakening).

944

Kendrick & Lavallée

The brittle field. As frictional melts are viscoelastic bodies, they exhibit components of both viscous and elastic materials, in different proportions (e.g., Dingwell and Webb 1989; Webb and Dingwell 1990). The point at which the dominant deformation mechanism switches from one (e.g., viscous) to the other (e.g., elastic) is referred to as the glass transition, Tg, which divides the liquid state from the solid state. In the liquid state, the melt can relax a stress and the body behaves as a Newtonian liquid. In the glass transition interval, the melt struggles to relax the applied stress and may suffer structural breakdown, promoting a non-Newtonian rheology. In the solid state, the melt behaves like a glass and cannot relax the applied stress, so if sufficient stress is accumulated, the material may rupture (e.g., Dingwell and Webb 1989; Webb and Dingwell 1990). The glass transition is a thermo-kinetic barrier, requiring both consideration of temperature and timescale; and thus, strain rates and heating/ cooling rates. The glass transition reflects the relaxation timescale or conversely, the relaxation rate; i.e., if the relaxation rate exceeds the strain rate experienced, then the melt flows viscously, but if it is too slow, the melt may rupture. For convenience, the glass transition is often stated to occur when the melt viscosity exceeds 1012 Pa.s, but in detail, the strain rate and heating / cooling rate control the temperature and thus the viscosity at which Tg is crossed. Thus during slip of a melt-bearing fault, the frictional melt may be forced to succumb to the glass transition via several scenarios (e.g., Lavallée et al. 2015a). For example: (1) Intuitively, as slip velocity wanes and thermal input by shear heating decreases, the melt may cool, causing an increase in frictional melt viscosity, and a decrease in relaxation rate; this may result in quenching to a glass or if the strain rate (or applied stress) is great enough it may lead to fragmentation; (2) An increase in slip rate that cannot be equilibrated by thickening of the melt zone resulting in increased strain rate; (3) Local narrowing of the slip plane (e.g., between resistant clasts or minerals) that locally elevates strain rate; (4) A change in the crystal cargo or vesicularity, since suspended clasts or bubbles increases relaxation timescale compared to their pure melt equivalent, which means that the same conditions are more likely to result in brittle failure (Lavallée and Kendrick 2020). Such transient behavior suggests that slip in the presence of frictional melt is not controlled merely by viscosity, but also by an interplay of viscoelastic forces, centered around the glass transition, involving an element of brittle fracturing of the molten phase. This may provide a mechanism for the concurrent formation of pseudotachylytes and cataclasites, and may force us to reassess the active modes of deformation during fault slip, both in volcanic settings and traditionally considered tectonic occurrences.

Viscous remobilization The presence of glass in many volcanic rocks, and as such the provision of the glass transition, demands for a broadening of the definition of frictional melts, and pseudotachylytes, during faulting in volcanic rocks. Since volcanic rocks often contain a fraction of interstitial groundmass glass the area adjacent to the slip zone may be subject to viscous remobilization during frictional heating (e.g., Lavallée et al. 2012a; Hornby et al. 2015; Wallace et al. 2019b). As previously stated, the temperature of the glass transition is dictated by rates (whether strain rate or heating/ cooling rate) and the silicate melt composition. Faster heating rates or faster shear rates push Tg to higher temperatures (Webb and Dingwell 1990; Gottsmann and Dingwell 2001). Neglecting consideration of rates (and simplifying Tg to a viscosity of 1012 Pa.s) Tg ranges from ~600 oC for basaltic glasses to up to ~800 oC for rhyolitic compositions (e.g., Giordano et al. 2008). It is important to note that interstitial glass is more silicic than the bulk composition of volcanic rocks, being the product of fractional crystallization, and that glass is rare in more mafic rocks whose kinetics favor crystallization. During heating in the approach to Tg the structure of a glass begins to seek a state of local equilibrium (with respect to pressure and temperature conditions) via configurational changes in its structure. As Tg is reached, it relaxes any predisposed stress, manifest by a rapid increase in the volumetric expansion rate (Dingwell and Webb 1989). Above Tg the glass behaves as a liquid, able to

Frictional Melting in Magma and Lava

945

dissipate applied stresses by relaxation. This characteristic means that adjacent to frictional melts, e.g., that may exceed 1100 oC (Lavallée et al. 2012a, 2015b; Kendrick et al. 2014a; Hornby et al. 2015), the interstitial glass in the wall rock is hot and able to viscously flow. For example Hornby et al. (2015) recognized, via the alignment of microlites, bands of viscous remobilization more than 200 mm wide on either side of experimentally generated frictional melts in dacite lavas with rhyolitic interstitial glass (Fig. 4). The presence of glass may thus widen shear zones, which could lead to the incorporation of more suspended clasts into the shear zone (e.g., Violay et al. 2014) as minerals with higher melting temperature become entrained as the melt/ solid boundary migrates into the rock. Viscous remobilization may also contribute towards the strengthening phase of fault evolution, as melt patches begin to form on the slip surface, potentially serving to increase the magnitude of strengthening at melting onset. Moreover, viscous remobilization could account for the higher shear stress observed in glass-bearing compared to glass free materials (Fig. 10A; Violay et al. 2014). These areas will serve to dissipate strain, reducing the proportion of shear stress exerted on frictional melt (thus promoting an increase in apparent viscosity). In a natural fault slip environment, the presence of glass-bearing wall rocks could facilitate viscous coupling to the frictional melt, increasing the shear resistance during faulting events and potentially hindering slip (Lavallée et al. 2012a; Kendrick et al. 2014a,b; Violay et al. 2014; Hornby et al. 2015; Wallace et al. 2019a). The remobilized areas will have long structural relaxation timescales, and exhibit relatively high viscosities (compared to the frictional melt zone) meaning they may still experience brittle failure if the strain rate exceeds this timescale or shear stress exceeds the strength (Lavallée et al. 2015a). Using single-phase amorphous silicate glasses Lavallée et al. (2015a) showed how the heating rate at which Tg was met controlled the response to frictional sliding, whereby the relaxation timescale, controlled by the melt viscosity according to Maxwell’s law of viscoelasticity, enables slip to persist in the solid state until sufficient heat is generated to reduce the viscosity and allow remobilization in the liquid state. Complementarily, in their shear experiments on crushed obsidian at high temperature Okumura et al. (2015) noted cataclastic processes in rapidly sheared shards above Tg, highlighting that comminution may still occur in hot magmas, depending on strain rate, as has been evidenced in several magmatic shear zones (e.g., Cashman et al. 2008; Kendrick et al. 2014b; Wallace et al. 2019a).

Thermal vesiculation The volatiles dissolved (i.e., primarily water), in frictional melt and in the interstitial melt or glass phase of adjacent magma or wall rock, respectively, can exsolve to form vesicles. Water solubility in melt (Fig. 12A) is dependent on pressure and temperature conditions (Liu et al. 2005); water solubility is retrograde at low pressure, but prograde above ~500 MPa (Paillat et al. 1992). Thus, in volcanic settings and shallow tectonic contexts, the exsolution of water may be triggered by either decompression or by increasing temperature. The latter case may thus be prompted by frictional heating on a slip plane within glass-bearing rocks (Lavallée et al. 2015b). Recently, careful examination of experimental products and volcanic ash generated along active faults during lava dome eruptions showed evidence for thermal vesiculation by volatile release from the interstitial glass of the host andesite (Lavallée et al. 2015b). But the same mechanism may be true for both interstitial glass in the host rock, and for the melt produced by frictional melting. Once melt is present, water can be released, or conversely resorbed, by perturbations of pressure or temperature (Fig. 12). The amount of water released due to fault slip will depend on the magnitude of the heating event, but also on the local pressure conditions which dictates the initial volatile solubility and hence water content of the melt (Fig. 12). Devolatilisation also results in an increase in melt viscosity (see Fig. 11B), and the degree to which water loss increases viscosity depends upon its initial concentration and so, saturation level, the consequence of which is that a devolatilisation of the same amount will more drastically increase the viscosity of a shallow-dwelling melt than a deeper one.

946

Kendrick & Lavallée

Figure 12. Water solubility in melt: (A) Water solubility shown as dissolved H2O as a function of pressure for a range of temperatures, calculated using the relationship presented in Liu et al. (2005) for a rhyolitic melt composition. (B) Thermobarometric limits on water concentration from Liu et al. (2005) show how a heating event such as frictional heating induces exsolution of water, and the magnitude of the exsolution for a given heating event depends on pressure conditions. Calculated using a rhyolitic frictional melts, after Lavallée et al. (2015).

The vesiculation triggered by rapid heating may be sudden, and could even induce fragmentation (due to rapid strain rates, cf. Dingwell 1996), thanks to the increasing viscosity of dehydrating melt (Hess and Dingwell 1996), and lower strength of vesicular materials. This could manifest in a number of ways in conduit-derived volcanic pseudotachylytes. For example, thermal vesiculation may: (1) Be the cause of small sacrificial fragmentation events, whereby localized areas of a lava dome and magmatic conduit experience intense frictional work producing heat, which then vesiculates and fragments in response, producing a small gas-and-ash explosion, but which allows the remainder of the magma to go unperturbed, prolonging its structural stability (Lavallée et al. 2015b; De Angelis et al. 2016); (2) Explain the very steep temperature profiles observed during frictional slip in volcanic rocks deformed experimentally (e.g., Fig. 3A), by causing grain size reduction by fragmentation, increasing surface area and decrepitation, hence lowering melting temperatures via the Gibbs–Thomson equation; (3) Act as a feedback mechanism, with rapid straining allowing melt to remain in the brittle regime, explaining the diachronous occurrence of cataclasites and pseudotachylytes (e.g., Kendrick et al. 2014b), as described in the section on Brittle failure. In other shallow settings such as shallow faults, sector collapses, debris avalanches and gravity slides, vesicular pseudotachylytes have also been noted (Maddock et al. 1987; Takagi et al. 2007). It may be possible to discern if thermal vesiculation played a part in their formation, although distinguishing thermal vesiculation from the incorporation of water from breakdown of hydrous phases during melting of minerals or from saturated rocks is challenging. Identifying thermal vesiculation is further complicated by preservation of pseudotachylytes which is hindered by numerous overprinting mechanisms (Kirkpatrick and Rowe 2013) and the tendency for water to resorb in melt during cooling (Fig. 12), such that porous structures and volatile contents of pseudotachylytes are unlikely to represent their formation characteristics. Where rapid quenching is possible, for example in injection veins or fragments of vesicular pseudotachylytes that are preserved in cataclasite, it may be possible to interpret porous structures for formation conditions (e.g., Maddock et al. 1987). Current calculations of pseudotachylyte formation conditions tend to rest on thermochronology (e.g., Kirkpatrick et al. 2012), though volcanic environments with their high ambient temperatures are not ideal settings for such approaches.

Frictional Melting in Magma and Lava

947

Elevated ambient temperature We have little data on the influence of elevated starting temperature (such as seen in volcanoes) on fault slip, as such this section has been kept separate in order to briefly examine preliminary experimental observations and speculate as to the cause and consequence of these results in light of our observations of natural systems. The technological challenge of performing experiments at high slip rates over long slip distances at elevated starting temperatures means there is a scarcity of data in this regime. Noda et al. (2011) performed rotary shear friction experiments on dolerite at temperatures up to 1,000 °C, yet they used a slip rate of 0.010 m.s-1 at 1 MPa normal stress to isolate the effect of temperature from other weakening mechanisms under stable slip conditions, suggesting that rate weakening observed in the absence of melt may be due in part to temperature increase. Here we will explore the rheological response, temperature profile and textures of a glass-bearing dacite from Mount Unzen (Japan) deformed in a rotary shear apparatus at an ambient temperature of 600 oC (from here-on termed HT) at high velocity (1 m.s-1), a normal stress of 2 MPa over a slip distance of 17 m, generated in Wallace et al. (2019a) in comparison to a room-temperature (RT) equivalent generated in Hornby et al. (2015), neither of which have been previously examined in this light. Figure 13 shows the shear stress response of both experiments. The RT experiment progressed via the typical stages of fault slip (depicted in Fig. 3), with an initial peak (P1) during rock–rock contact, a weakening phase to lubricated sliding by comminution and flash heating (SS1), a strengthening phase where melt patches initiate, increasing in shear stress to a second peak (P2) that is followed by weakening as the melt zone thickens and stable sliding (SS2) as the melt generation and melt expulsion rate equilibrate. The HT experiment however showed no initial peak (P1), initial weakening, or stable sliding (SS1) of the rock–rock contact, and instead moved directly into strengthening initiated by molten patches forming and potentially viscous remobilization of the interstitial glass of the lava. This strengthening period is followed by a broad and unstable peak (P2) and subsequently a less pronounced weakening phase than the RT equivalent. Stable sliding (SS2) ensues for a brief time, but after ~8 m of slip shear stress begins to increase and becomes markedly higher than in the RT experiment. Until this point the shortening curves are relatively similar despite the differences in shear stress, but at this point they diverge as shortening rate accelerates in the sample at HT. The temperature profiles (dashed lines, Fig. 13) are however disparate from the start. The RT experiment follows a non-linear heating profile (similar to that in Fig. 3), which depicts the progression from comminution and grain size reduction, flash heating and decrepitation that further enhances grain size reduction (Spray 2010), to the initiating of melting of small grains and asperities and their rapid coalescence to form a frictional melt layer (e.g., Hirose and Shimamoto 2005b). In the HT example, heating is near linear. This may reflect the diminished effect of flash heating at elevated starting temperature (e.g., Passelègue et al. 2014), and also the less effective grain size reduction by comminution and by thermal fracturing, since decrepitation can be attributed in part to differential thermal expansion of minerals (Spray 2010), which here would already be equilibrated to the ambient condition of 600 oC. An absence of smaller grains, which preferentially melt (e.g., Lee et al. 2017), would mean that melting progresses more gradually (though, beginning at conditions closer to melting). A closer examination of the evolution of temperature across the shear zones in the RT and HT experiments (Fig. 14) reveals that not only does peak temperature increase throughout slip, but the width of the high temperature zone increases, meaning that increasing portions of the rock are at temperatures above the glass transition and above the onset of melting (Tmo) of the mineral assemblage (In Fig. 14 denoted as dg for width above Tg and dmo for width above Tmo). In the RT example dg and dmo widen but achieve relatively stable width after around 8 m (8 s) of slip, which corresponds to the attainment of steady state slip (SS2) and a steady shortening rate. On the other hand, in the HT experiment dg and dmo continue to increase throughout slip (to

948

Kendrick & Lavallée

Figure 13. Friction experiments performed on dacite samples at room temperature (RT) and an elevated ambient starting temperature of 600 oC (HT) using a rotary shear apparatus. The results show that the RT experiment follows the conventional progression from P1 to SS1, to P2 and eventually SS2 similar to the example in Figure 3, and that shortening accelerates from the creation of the melt layer until it achieves steady state, beyond which it follows a linear relationship. However, the HT experiment exhibits no discernible P1 and SS1 phases, instead moving directly to melting, shown by the broad peak in shear stress from 0–2 m slip distance; it is followed by a less pronounced weakening stage as the melt zone thickens, a shortening rate that continues to accelerate throughout slip, and a shear stress that also gradually increases throughout the nominal SS2 phase. These observations are complemented by temperature measurements (showing the maximum temperature on a representative transect perpendicular to the slip surface) of the sample surface which indicate a steady increase from the onset of sliding for the HT sample, compared to a more typical heating profile of the RT sample where temperature ramps rapidly after a few m’s slip as melt patches begin to form. In the HT example, melting onset was likely near-instantaneous, and increasing shear stress through SS2 may represent viscous remobilization of the glass phase and partial melting of mineral phases in the host rock. RT data from Hornby et al. (2015) and HT data from Wallace et al. (2019a).

Figure 14. Sample surface temperature perpendicular to the slip surface over a 6 mm wide thermal profile measured every 1m slip in dacite samples using a thermographic camera, for the mechanical data shown in Figure 13 (at 1 m.s-1 and normal stress of 2 MPa). The glass transition temperature Tg ≅ 790 oC and the melting onset temperature Tmo ≅ 900 oC are marked against the temperature profiles for (A) the experiment starting at room-temperature (RT) and (B) an experiment starting at 600 oC (HT). Both show how the peak temperature increases through time and eventually stabilizes (after ~7 m at RT and ~6 m at HT); the data show that the hot zone thickens to a relatively stable width in the RT example, but continues to thicken throughout slip (17m) in the HT example. We further characterize dg as the thickness of the area able to viscously remobilize as the interstitial glass exceeds Tg, and dmo, the thickness of the area where partial melting can occur above Tmo, both of which are nearly doubled in width in the HT sample. Reprocessing of RT data from Hornby et al. (2015) and HT data from Wallace et al. (2019a).

17 m), which may account for the increasing shear stress during what ought to be steadystate sliding (SS2) and to the continuously accelerating shortening rate observed during slip (Fig. 13). In the HT experiment dg (the portion above Tg) widens near-linearly throughout the experiment, whereas dmo (the portion above Tmo) potentially approaches stabilization beyond 15 m slip. Thermal conductivity theory dictates that temperatures should eventually stabilize, but evidence suggests this may be after a longer slip distance at elevated starting temperature. This observation perhaps indicates that slip in volcanic settings, particularly in magmas, would

Frictional Melting in Magma and Lava

949

struggle to achieve steady-state sliding, and that shear stress may continue to increase during slip until the resistance is eventually so high that the viscous brake comes into effect, which could halt slip or cause failure by localizing strain elsewhere. The absolute values of dg (width above Tg) are almost twice as large in the HT example, indicating that a much larger area is able to viscously mobilize (Fig. 14). The wider zone of viscous remobilization could explain the higher shear stress in the HT as compared to RT experiment (Fig. 13) as viscous remobilization is postulated to be the cause of higher steadystate shear stress during slip in glass-bearing lavas (cf. Violay et al. 2014). In nature, large areas of viscous remobilization caused by shear localization and heating were invoked to explain the rotation and deformation of phenocrysts and microlites in the upper few 100 m’s of the conduit at Mount Unzen (Fig. 1; Wallace et al. 2019a). The zone of viscous remobilization would also have a thermally insulating effect in nature and the experiments, impacting conduction of heat away from the slip zone, and accordingly, the growth of the molten zone (Fig. 1) described by the Stefan problem. We see evidence of this in the thickness of the melt zone itself, dmo is also almost twice as wide in the HT compared to the RT example (Fig. 14), suggesting that mineral breakdown and partial melting can occur over a wider area in initially-HT shear zones. In the aforementioned natural example at Mount Unzen, the shear zone revealed a systematic variation in thermallyinduced breakdown textures in amphiboles which were observed as much as 2 m from the primary slip surface (Wallace et al. 2019a). The width of the areas that exceeded Tg and Tmo (Fig. 14) are compared to the dissected HT sample in thin section in Fig. 15. The >250 mm thick melt layer in the HT experiment compares to a ~150 mm layer in the RT experiment (Hornby et al. 2015). The visible impact of viscous remobilization is seen in the microlite alignment in the zone adjacent to the frictional melt (Fig. 15A,C) as well as the compaction of pore space in this region (Fig. 15B). Viscous remobilization has been shown to result in more effective pore closure than brittle deformation (Heap et al. 2017), resulting in densification and anisotropy development, which in natural shear zones would impact the percolation of fluids. In the experimental sample, we see that suspended survivor clasts are primarily highermelting temperature plagioclase crystals, with some Fe–Ti oxides (Fig. 15C). Decrepitation of minerals adjacent to the slip zone is evident (Fig. 15D), and these directly feed into the melt zone as suspended particles. The onset of mineral breakdown is seen in the rims of plagioclase phenocrysts adjacent to the slip zone (which exceeded Tmo), whilst those further away have none (Fig. 15A). Biotite, containing water in its structure, shows vesicular reaction rims adjacent to the melt (Fig. 15E), and microlites adjacent to the slip zone are extensively molten, contributing to heterogeneous schlieren and melts that infiltrate fractures in phenocrysts (Fig. 15D–F). Many of the textures seen in the HT experimental sample reflect those seen in nature, especially those within volcanic pseudotachylytes (Kendrick et al. 2012, 2014b; Lavallée et al. 2015b). Finally, the onset of crystallization is captured in Fig. 15E. Typically, experimentally generated pseudotachylytes cool very rapidly when slip is halted and the thermal input drops due to cool ambient conditions, but in the HT example the sample was left to cool within the furnace (at ~10 oC.min-1), which provided time for crystallization. Such cooling timescales are rapid compared to that envisaged for pseudotachylytes that form in active volcanic complexes (Kendrick et al. 2014b). This brings an important consideration for the evidence of frictional melting in volcanic environments, as potentially the presence of elevated temperatures after the formation of a pseudotachylyte enables complete crystallization of frictional melt layers and obscures their occurrence. Even if the frictional melt represented only selective melting, and was more mafic than the host rock, then recrystallisation of mafic minerals such as hornblende, pyroxene or magnetite (e.g., Lin 2008) would still surround equant survivor clasts of plagioclase and other minerals with high melting temperatures. Thus, finer grained or more mafic bands may represent historic fault slip and frictional melting in volcanic materials at elevated temperature (Kendrick et al. 2012, 2014b; Plail et al. 2014).

950

Kendrick & Lavallée

Figure 15. Examination of a frictional melt zone in a dacitic lava, formed during a rotary shear experiment at 600 oC (mechanical data shown in Fig. 13 and temperature evolution in Fig. 14b). The frictional melt zone is shown in (A) plane-polarized light using an optical microscope, (B) as solid (white) and porosity (black) binary images generated from (C) mineralogical distribution map resolved by QEMSCAN, highlighting embayments of the frictional melt into neighboring phenocrysts (especially biotite), densification of the host rock in areas neighboring the melt, potentially due to partial melting at >Tmo and viscous remobilization of interstitial glass >Tg. Textures are examined in detail in backscattered electron images of the frictional melt zone (FMZ) in D–F. (D) Frictional melt zone sandwiched between a plagioclase [Pl] and biotite [B] phenocryst showing the interaction with both; the plagioclase is fractured, and small fragments are suspended in the frictional melt. Angular embayments are filled by filaments (or schlieren) of protomelts, whereas the biotite has an undulating contact with the melt and has a rim of vesiculation adjacent to the FMZ; the area in the blue box is shown in greater detail in (E) where the biotite is directly bordered by protomelts which crystallized during post-experiment cooling (which takes place more slowly following HT experiments due to elevated ambient temperature conditions); note an oxide [Ox] next to the biotite is shown to be stable at the conditions locally experienced. (F) Area of viscous remobilization, showing elongate schlierens of partial melt, observed in the host adjacent to the FMZ. The partial melts occupy fractures in phenocrysts of plagioclase to the left of the slip zone and variably rounded survivor clasts of plagioclase are suspended in the melt. Sample from Wallace et al. (2019a).

Frictional Melting in Magma and Lava

951

Fault healing and cyclic rupture One of the largest unknowns in the study of fault rupture concerns fault healing through time (e.g., Copley 2018). In tectonic settings, sealing, healing and strength recovery of faults has often been considered as time-dependent, occurring over timescales of decades to centuries (e.g., Scholz 2019). In active volcanoes the processes driving healing may differ to tectonic faulting due to their distinct temperature conditions above those typical of the Earth’s geotherm. Even in faulting conditions starting from ambient temperatures, recent experimental work has shown that fault strengthening can be a near-instantaneous process upon frictional melting (e.g., Hirose and Shimamoto 2005b; Mitchell et al. 2016; Proctor and Lockner 2016; Hayward and Cox 2017). Field examination of eruptive products reveals that magma failure in the conduit is a common process (Tuffen et al. 2003; Cashman et al. 2008; Kendrick et al. 2012; Pallister et al. 2013; Lavallée et al. 2015b; Wallace et al. 2019a), influencing the explosivity of ongoing activity (Tuffen and Dingwell 2005; Lensky et al. 2008; De Angelis and Henton 2011; Costa et al. 2012; Okumura and Kozono 2017). Frequently observed cyclic/ repetitive seismic signals at many volcanoes worldwide have been attributed to repeated magma failure or slip on a fault plane at the conduit margin at shallow depth (Fig. 1; Denlinger and Hoblitt 1999; Neuberg et al. 2006; Lensky et al. 2008; Costa et al. 2012; Hornby et al. 2015; Lamb et al. 2015). Evidence for comminution, brecciation (Rust et al. 2004; Goto et al. 2008; Castro et al. 2012), cataclasis (Tuffen and Dingwell 2005; Kennedy et al. 2009; Pallister et al. 2013), frictional melting (Kendrick et al. 2012, 2014b; Plail et al. 2014), and enhanced viscous remobilization of magma near the conduit margin (Wallace et al. 2019a) supports the view that, in viscous magmatic systems, the bulk of the magma is able to ascend as a plug, due to strain localization at the conduit margin (Fig. 1; e.g., Costa et al. 2007b). The consequences of this strain localization at the conduit margin are complex and numerous. Temporal and spatial evolution of fault zone products results from fluctuations in temperature (e.g., Heap et al. 2017) and variation of local stresses, caused by e.g., changing ascent rate, decreasing normal stress during shallowing, changes in conduit width or geometry or influx of fluids. Once formed, frictional melt can be lubricating, or can act as a viscous brake, and can dynamically shift from one to another. How fault slip occurs will impact how the shear zone evolves, how shear heating is developed, how heat is dissipated (Fig. 1) and how subsequent episodes of slip proceed. These changes act as feedbacks to the ongoing magma ascent, enhancing instability and contributing to the cyclicity of fault slip (e.g., Kendrick et al. 2014a). Fault strengthening occurs at the onset of melting (e.g., Tsutsumi and Shimamoto 1997; Hirose and Shimamoto 2005b; Kendrick et al. 2014a). Where the rocks or magma contain interstitial glass or melt, frictional melt can viscously heal to the host rock on a rapid timescale (~seconds, depending on viscosity), as indicated by the healing timescale of melt (Yoshimura and Nakamura 2010; Lamur et al. 2019). Even without interstitial glass, welding of the frictional melt can activate almost immediately, even during ongoing fault displacement (Hayward and Cox 2017). Depending on the timescale of healing, this could serve to either: (1) if inefficient, allow strain to remain localized on a defined slip plane, requiring overcoming of resistance imposed by the healing surfaces for further slip (Lockner et al. 2017), which in a conduit could accentuate stick slip cycles (Kendrick et al. 2014a); or; (2) if efficient, result in slip zones that are stronger than the rock or magma from which they formed (e.g., Mitchell et al. 2016; Proctor and Lockner 2016; Lee et al. 2020), which would dissipate damage during slip and encourage subsequent fractures to occur in the neighboring areas (e.g., Hayward and Cox 2017), generating multiple slip planes of pseudotachylyte (Kendrick et al. 2014b). Scenario 1 may be most relevant to high viscosity magmatic systems, for example more silicic melts or magmas with higher crystal contents, or cooler settings, which heals comparatively slowly (cf. Lamur et al. 2019), whereas scenario 2 may be most applicable to lower viscosity melts, and highly vesicular magmas in which compaction is efficient (Shields et al. 2016) or porous rocks subjected to melting.

952

Kendrick & Lavallée

Fault slip and healing will also impact permeability of the fault and adjacent areas, which will impact the drainage conditions of the fault plane (Beeler et al. 2016), which in turn impacts the stress conditions experienced (see Eqn. 2). In viscous systems, e.g., in the presence of melt, this evolution may be particularly dynamic as fracture zones shut, seal and heal, reducing the permeability of the system (Tuffen et al. 2003; Yoshimura and Nakamura 2010; Cabrera et al. 2011; Okumura and Sasaki 2014; Lamur et al. 2019). The effective stress coefficient a (introduced in Eqns. 2–3, which weights the geometric fault area and the real contact area) may shift rapidly due to wetting of the fault interface (e.g., Lamur et al. 2019), thus the area over which pressurized fluids counteract normal stress may be transient in meltbearing fault zones. The area accessible to fluids defines the ability for the volcano to outgas and alleviate pressure. If the shear zone developed is sufficiently permeable, outgassing may release excess pressure, favoring effusive activity, however, if permeability is lower and pressure can accumulate, it may drive an explosive episode (e.g., Lavallée and Kendrick 2020). In combination with seismicity and ground deformation measurements, gas flux measurements during volcanic crises allude to the percolation of gases through the permeable subsurface (e.g., Edmonds 2008), which can provide clues as to the state of unrest of a volcanic system, though most inferences of conduit processes originate from the examination and experimental interrogation of eruptive products. Fracture system longevity controls both strength recovery, and the extent to which the magma can outgas before the pathways close and heal, allowing the system to pressurize again in a quasi-continuous cycle (Okumura and Sasaki 2014). A full understanding of the timescale of strength recovery, and thus the ability to build and release stress during cyclic magma ascent remains elusive, yet paramount, for the development of a comprehensive model addressing shifts in eruptive behavior.

SUMMARY AND CONCLUDING REMARKS Whilst this chapter is by no means a comprehensive overview of frictional melting, it should serve as a starting point, briefly overviewing the occurrence of frictional melting, distinguishing features and approaches used to interrogate pseudotachylyte formation, before moving to focus exclusively on frictional melting in volcanic materials, specifically during the ascent of viscous magma. The ensuing summary briefly encapsulates the observations that have shaped our view of frictional melting in volcanic conduits, rather than attempting to recover ground covered earlier in the chapter. In volcanic environments, the transition from endogenous to exogenous growth can be attributed to a shift in magma rheology into the brittle regime (Hale and Wadge 2008), and thus the ascent of high-viscosity magma can form discrete shear zones along conduit margins. The conduit margin may then be considered analogous to a fault zone, owing to the elastic response of a highly viscous magma subjected to stress variations shorter than the structural relaxation timescale. It has become increasingly recognized, via theoretical models (Costa et al. 2007a; Hale and Muhlhaus 2007; Gonnermann and Manga 2013), experimentation (Lavallée et al. 2012a, 2015a) and detailed petrological constraints (Tuffen and Dingwell 2005; Wright and Weinberg 2009; Wallace et al. 2019a), that strain localization may locally raise magmatic temperatures. The plug-like flow that characterizes high viscosity magma ascent enhances these systems susceptibility to frictional heating, contributing to shifts in rheology that in-part dictate eruption style. To our benefit a plethora of work has explored the occurrence of pseudotachylytes (e.g., Sibson 1975), their distinguishing features (e.g., Kirkpatrick and Rowe 2013) and the process of formation (e.g., Spray 1992) in a wide range of materials. Rotary shear experiments, were first introduced to the geological community in the early 1990’s (Shimamoto and Tsutsumi 1994), spurring an influx of experimental data on frictional melting (Tsutsumi and Shimamoto 1997; Lin and Shimamoto 1998; Nakamura et al. 2002; Hirose and Shimamoto 2005a; Niemeijer et

Frictional Melting in Magma and Lava

953

al. 2011). Experiments on volcanic rocks have shown that fault friction localized on narrow planes can generate temperature rises of >1000 oC per second, resulting in melting (Lavallée et al. 2012a, 2015a; Kendrick et al. 2014a,b; Hornby et al. 2015). Frictional melting can alter the physical and chemical properties of the magma: driving mineral reactions; melting crystalline phases; triggering devolatilisation and vesiculation; inducing fragmentation; lowering interstitial melt viscosity; altering magnetic properties; redistributing or closing-off porosity that alters degassing pathways and efficiently healing fractures. Volcanic rocks demonstrate a propensity for frictional melting in as little as a few centimeters of slip, and fewer from high ambient volcanic temperatures (the distinct mineralogy, presence of interstitial glass that allows viscous remobilization and larger surface area afforded by high porosities facilitates rapid melting as compared to many other lithologies), and show that even from room temperature, enough heat is generated to induce frictional melting at as little as 0.1 m.s−1—a rate commonly achieved during magma ascent. Frictional melts have been proposed as one of the major dynamic weakening mechanisms that reduce shear resistance during co-seismic slip, and at high normal stresses melt has a lubricating effect on fault slip. However, during the onset of melting and throughout slip at low normal stresses, particularly in more silicic melts, melt-bearing slip surfaces show exceptionally high shear stresses (compared with a solid rock–rock contact or gouge-hosting shear zone), revealing frictional melt’s role as a viscous brake in many scenarios. While recent experimental efforts have helped define the fault slip processes occurring in volcanic material (Moore et al. 2008; Kennedy et al. 2009; Lavallée et al. 2012a; Kendrick et al. 2014a,b; Hornby et al. 2015; Wallace et al. 2019a,b) the new model of fault-controlled viscous magma ascent lacks a solid mechanical description of dynamic slip processes at the high temperature conditions extant in volcanic conduits. Preliminary results indicate that: (1) comminution and grain size reduction may be less effective at elevated starting temperature; (2) flash heating becomes less effective with increasing ambient temperature; (3) heating may be more linear due to efficiency of heat dissipation from the slip zone and lack of smaller particles; (4) shear zones are likely to be wider at high ambient temperatures (due to thermal insulation and the presence of interstitial glass that allows strain to be distributed over a wider area); (5) shear resistance is likely to be higher in slip zones at higher temperature (potentially due to adjacent viscous remobilization, and wider, more thermally insulated shear zones; Fig. 1); (6) the attainment of steady-state slip will take longer slip distances due to sluggish temperature equilibration; (7) post-slip healing efficiency may be enhanced. All of which sums to point to enhanced instability of fault slip at elevated temperatures. Understanding the conduit margin processes that regulate magma ascent is vital to understanding the style and timescale of an eruption, as well as establishing links to monitored geophysical signals. These recent developments have compelled the volcanological community to begin reassessing the driving forces of eruption dynamics, marking the beginning of a new chapter in volcanological investigations.

ACKNOWLEDGEMENTS J.E. Kendrick acknowledges the support of an Early Career Fellowship of the Leverhulme Trust. Yan Lavallée was supported by the Natural Environment Research Council (grant no. NE/T007796/1) and a Research Fellowship of the Leverhulme Trust. Both authors were additionally supported by a Starting Grant of the European Research Council (grant no. 306488).

REFERENCES Abe S, Dieterich JH, Mora P, Place D (2002) Simulation of the influence of rate- and state-dependent friction on the macroscopic behavior of complex fault zones with the lattice solid model. Pure Appl Geophys 159:1967–1983 Acocella V (2021) Volcano flank instability and collapse. In: Volcano-Tectonic Processes. Acocella V, (ed) Springer International Publishing, Cham, p 205–244

954

Kendrick & Lavallée

Alatorre-Ibargüengoitia MA, Scheu B, Dingwell DB, Delgado-Granados H, Taddeucci J (2010) Energy consumption by magmatic fragmentation and pyroclast ejection during Vulcanian eruptions. Earth Planet Sci Lett 291:60–69 Albino F, Pinel V, Massol H, Collombet M (2011) Conditions for detection of ground deformation induced by conduit flow and evolution. J Geophys Res: Solid Earth 116 Alidibirov M, Dingwell DB (2000) Three fragmentation mechanisms for highly viscous magma under rapid decompression. J Volcanol Geotherm Res 100:413–421 Allen AR (1979) Mechanism of frictional fusion in fault zones. J Struct Geol 1:231–243 Andersen TB, Mair K, Austrheim H, Podladchikov YY, Vrijmoed JC ­­ (2008) Stress release in exhumed intermediate and deep earthquakes determined from ultramafic pseudotachylyte. Geology 36:995–998 Arciniega-Ceballos A, Alatorre-Ibargüengoitia M, Scheu B, Dingwell D (2015) Analysis of source characteristics of experimental gas burst and fragmentation explosions generated by rapid decompression of volcanic rocks. J Geophys Res: Solid Earth 120:5104–5116 Bain AA, Kendrick JE, Lamur A, Lavallée Y, Calder ES, Cortés JA, Cortés GP, Gómez Martinez D, Torres RA (2021) Micro-textural controls on magma rheology and vulcanian explosion cyclicity. Front Earth Sci 8 Barker SLL (2005) Pseudotachylyte-generating faults in Central Otago, New Zealand. Tectonophysics 397:211–223 Beeler NM, Tullis TE, Goldsby DL (2008) Constitutive relationships and physical basis of fault strength due to flash heating. J Geophys Res: Solid Earth 113:B01401 Beeler NM, Hirth G, Thomas A, Bürgmann R (2016) Effective stress, friction, and deep crustal faulting. J Geophys Res: Solid Earth 121:1040–1059 Behera BM, Thirukumaran V, Soni A, Mishra PK, Biswal TK (2017) Size distribution and roundness of clasts within pseudotachylytes of the Gangavalli Shear Zone, Salem, Tamil Nadu: An insight into its origin and tectonic significance. J Earth Syst Sci 126:46 Ben-Zion Y, Sammis CG (2003) Characterization of Fault Zones. Pure Appl Geophys 160:677–715 Berlo K, Tuffen H, Smith VC, Castro JM, Pyle DM, Mather TA, Geraki K (2013) Element variations in rhyolitic magma resulting from gas transport. Geochim Cosmochim Acta 121:436–451 Bernard K, van Wyk de Vries B (2017) Volcanic avalanche fault zone with pseudotachylite and gouge in French Massif Central. J Volcanol Geotherm Res 347:112–135 Biek RF, Rowley PD, Hacker DB (2019) The Gigantic Markagunt and Sevier Gravity Slides resulting from MidCenozoic catastrophic mega-scale failure of the Marysvale Volcanic Field, Utah, USA. GSA Field Guide 56, Geological Society of America Biot MA, Willis DG (1957) The elastic coefficients of the theory of consolidation. J Appl Mech 24:594–601 Blundy J, Cashman K, Humphreys M (2006) Magma heating by decompression-driven crystallization beneath andesite volcanoes. Nature 443:76–80 Boulton C, Yao L, Faulkner DR, Townend J, Toy VG, Sutherland R, Ma S, Shimamoto T (2017) High-velocity frictional properties of Alpine Fault rocks: Mechanical data, microstructural analysis, and implications for rupture propagation. J Struct Geol 97:71–92 Bowden FP, Tabor D (1950) The Friction and Lubrication of Solids, Pt 2. Oxford University Press Brace WF, Byerlee JD (1966) Stick-slip as a mechanism for earthquakes. Science 153:990–992 Brace WF, Martin RJ (1968) A test of the law of effective stress for crystalline rocks of low porosity. Int J Rock Mech Min Sci Geomech Abstr 5:415–426 Brace WF, Paulding B, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71:3939–3953 Brodsky EE, Kanamori H (2001) Elastohydrodynamic lubrication of faults. J Geophys Res 106:16357–16374 Burgisser A, Degruyter W (2015) Magma ascent and degassing at shallow levels. Chapter 11 In: The Encyclopedia of Volcanoes (Second Edition). Sigurdsson H (ed) Academic Press, Amsterdam, p 225–236 Burton MR, Mader HM, Polacci M (2007) The role of gas percolation in quiescent degassing of persistently active basaltic volcanoes. Earth Planet Sci Lett 264:46–60 Byerlee JD (1967) Frictional characteristics of granite under high confining pressure. J Geophys Res 72:3639–3648 Byerlee J (1978) Friction of rocks. Pure Appl Geophys 116:615–626 Cabrera A, Weinberg RF, Wright HMN, Zlotnik S, Cas RAF (2011) Melt fracturing and healing: A mechanism for degassing and origin of silicic obsidian. Geology 39:67–70 Calder ES, Lavallée Y, Kendrick JE, Bernstein M (2015) Lava dome eruptions. Chapter 18 In: The Encyclopedia of Volcanoes (Second Edition). Sigurdsson H, (ed) Academic Press, Amsterdam, p 343–362 Camacho A, Vernon RH, Fitz Gerald JD (1995) Large volumes of anhydrous pseudotachylyte in the Woodroffe Thrust, eastern Musgrave Ranges, Australia. J Struct Geol 17:371–383 Caricchi L, Burlini L, Ulmer P, Gerya T, Vassalli M, Papale P (2007) Non-Newtonian rheology of crystal-bearing magmas and implications for magma ascent dynamics. Earth Planet Sci Lett 264:402–419 Carslaw HS, Jaeger JC (1959) Conduction of Heat in Solids. Oxford University Press Cashman K, Blundy J (2000) Degassing and crystallization of ascending andesite and dacite. Philos Trans R Soc London 358:1487–1513 Cashman C, Scheu B (2015) Magmatic fragmentation. Chaper 25 In: Encyclopedia of Volcanoes. 2nd Edition. Sigurdsson H, Houghton B, Rymer H, Stix J, McNutt S (eds). Elsevier, p 459–471

Frictional Melting in Magma and Lava

955

Cashman KV, Thornber CR, Pallister JS (2008) From dome to dust: shallow crystallization and fragmentation of conduit magma during the 2004–2006 dome extrusion of Mount St. Helens, Washington. In: A Volcano Rekindled: The Renewed Eruption of Mount St Helens, 2004–2006. Sherrod DR, Scott WE, Stauffer PH, (eds). U.S. Geological Survey Professionnal Paper 1750, p 387–413 Cassidy M, Manga M, Cashman K, Bachmann O (2018) Controls on explosive–effusive volcanic eruption styles. Nat Commun 9:2839 Castro JM, Cordonnier B, Tuffen H, Tobin MJ, Puskar L, Martin MC, Bechtel HA (2012) The role of melt–fracture degassing in defusing explosive rhyolite eruptions at volcán Chaitén. Earth Planet Sci Lett 333–334:63–69 Chadwick Jr WW, Archuleta RJ, Swanson DA (1988) The mechanics of ground deformation precursory to domebuilding extrusions at Mount St. Helens 1981–1982. J Geophys Res: Solid Earth 93:4351–4366 Chen J, Rempel AW (2014) Progressive flash heating and the evolution of high-velocity rock friction. J Geophys Res: Solid Earth 119:3182–3200 Chen X, Elwood Madden AS, Reches Ze (2017) Friction evolution of granitic faults: heating controlled transition from powder lubrication to frictional melt. J Geophys Res: Solid Earth 122:9275–9289 Chester FM, Chester JS (1998) Ultracataclasite structure and friction processes of the Punchbowl fault, San Andreas system, California. Tectonophysics 295:199–221 Chiodini G, Paonita A, Aiuppa A, Costa A, Caliro S, De Martino P, Acocella V, Vandemeulebrouck J (2016) Magmas near the critical degassing pressure drive volcanic unrest towards a critical state. Nat Commun 7:13712 Chouet BA, Matoza RS (2013) A multi-decadal view of seismic methods for detecting precursors of magma movement and eruption. J Volcanol Geotherm Res 252:108–175 Christie JM, Griggs DT, Heuer AH, Nord GL, Jr., Radcliffe SV, Lally JS, Fisher RM (1973) Electron petrography of Apollo 14 and 15 breccias and shock-produced analogs. Lunar Planet Sci Confer Proc 4:365 Cimarelli C, Costa A, Mueller S, Mader HM (2011) Rheology of magmas with bimodal crystal size and shape distributions: Insights from analog experiments. Geochem Geophys Geosyst 12:Q07024 Coats R, Kendrick JE, Wallace PA, Miwa T, Hornby AJ, Ashworth JD, Matsushima T, Lavallée Y (2018) Failure criteria for porous dome rocks and lavas: a study of Mt. Unzen, Japan. Solid Earth Discuss 2018:1–42 Copley A (2018) The strength of earthquake-generating faults. J Geol Soc 175:1–12 Cordonnier B, Caricchi L, Pistone M, Castro J, Hess K-U, Gottschaller S, Manga M, Dingwell DB, Burlini L (2012) The viscous–brittle transition of crystal-bearing silicic melt: Direct observation of magma rupture and healing. Geology 40:611–614 Costa A, Macedonio G (2002) Nonlinear phenomena in fluids with temperature-dependent viscosity: An hysteresis model for magma flow in conduits. Geophys Res Lett 29:1402 Costa A, Macedonio G (2005) Viscous heating effects in fluids with temperature-dependent viscosity: triggering of secondary flows. J Fluid Mech 540:21–38 Cowie PA, Scholz CH (1992) Displacement-length scaling relationship for faults: data synthesis and discussion. J Struct Geol 14:1149–1156 Costa A, Melnik O, Vedeneeva E (2007a) Thermal effects during magma ascent in conduits. J Geophys Res: Solid Earth 112:B12205 Costa A, Melnik O, Sparks RSJ, Voight B (2007b) Control of magma flow in dykes on cyclic lava dome extrusion. Geophys Res Lett 34: L02303 Costa A, Caricchi L, Bagdassarov N (2009) A model for the rheology of particle-bearing suspensions and partially molten rocks. Geochemistry, Geophysics, Geosystems 10:Q03010 Costa A, Wadge G, Melnik O (2012) Cyclic extrusion of a lava dome based on a stick-slip mechanism. Earth Planet Sci Lett 337–338:39–46 Curewitz D, Karson JA (1999) Ultracataclasis, sintering, and frictional melting in pseudotachylytes from East Greenland. J Struct Geol 21:1693–1713 De Angelis S, Henton SM (2011) On the feasibility of magma fracture within volcanic conduits: Constraints from earthquake data and empirical modelling of magma viscosity. Geophys Res Lett 38:L19310 De Angelis S, Lamb OD, Lamur A, Hornby AJ, von Aulock F, Chigna G, Lavallée Y, Rietbrock A (2016) Characterization of moderate ash-and-gas explosions at Santiaguito volcano, Guatemala, from infrasound waveform inversion and thermal infrared measurements. Geophys Res Lett 43:6220–6227 De Blasio FV, Elverhøi A (2008) A model for frictional melt production beneath large rock avalanches. J Geophys Res: Earth Surface 113:F02014 De Blasio FV, Medici L (2017) Microscopic model of rock melting beneath landslides calibrated on the mineralogical analysis of the Köfels frictionite. Landslides 14:337–350 de’ Michieli Vitturi M, Clarke AB, Neri A, Voight B (2008) Effects of conduit geometry on magma ascent dynamics in dome-forming eruptions. Earth Planet Sci Lett 272:567–578 Del Gaudio P, Di Toro G, Han R, Hirose T, Nielsen S, Shimamoto T, Cavallo A (2009) Frictional melting of peridotite and seismic slip. J Geophys Res: Solid Earth 114:B06306 Denlinger RP, Hoblitt RP (1999) Cyclic eruptive behavior of silicic volcanoes. Geology 27:459–462 Deseta N, Andersen TB, Ashwal LD (2014) A weakening mechanism for intermediate-depth seismicity? Detailed petrographic and microtextural observations from blueschist facies pseudotachylytes, Cape Corse, Corsica. Tectonophysics 610:138–149

956

Kendrick & Lavallée

Deubelbeiss Y, Kaus BJP, Connolly JAD, Caricchi L (2011) Potential causes for the non-Newtonian rheology of crystal-bearing magmas. Geochem Geophys Geosyst 12:Q05007 Di Toro G, Pennacchioni G (2005) Fault plane processes and mesoscopic structure of a strong-type seismogenic fault in tonalites (Adamello batholith, Southern Alps). Tectonophysics 402:55–80 Di Toro G, Goldsby DL, Tullis TE (2004) Friction falls towards zero in quartz rock as slip velocity approaches seismic rates. Nature 427:436–439 Di Toro G, Hirose T, Nielsen S, Pennacchioni G, Shimamoto T (2006) Natural and experimental evidence of melt lubrication of faults during earthquakes. Science 311:647–649 Di Toro G, Pennacchioni G, Nielsen S (2008) Pseudotachylytes and earthquake source mechanics. Chapter 5 In: International Geophysics. Vol. 94 (Eiichi F ed.) Academic Press, p 87–133 Di Toro G, Han R, Hirose T, De Paola N, Nielsen S, Mizoguchi K, Ferri F, Cocco M, Shimamoto T (2011) Fault lubrication during earthquakes. Nature 471:494–498 Dieterich JH (1972) Time-dependent friction in rocks. J Geophys Res (1896–1977) 77:3690–3697 Dieterich JH (1979) Modeling of rock friction: 1. Experimental results and constitutive equations. J Geophys Res: Solid Earth 84:2161–2168 Dieterich JH (1992) Earthquake nucleation on faults with rate-and state-dependent strength. Tectonophysics 211:115–134 Dieterich JH, Kilgore BD (1994) Direct observation of frictional contacts: New insights for state-dependent properties. Pure Appl Geophys 143:283–302 Diller K, Clarke AB, Voight B, Neri A (2006) Mechanisms of conduit plug formation: Implications for vulcanian explosions. Geophys Res Lett 33:L20302 Dingwell DB (1996) Volcanic dilemma: Flow or blow? Science 273:1054–1055 Dingwell D, Webb SL (1989) Structural relaxation in silicate melts and Non-Newtonian melt rheology in geologic processes. Phys Chem Mineral 16:508–516 Edmonds M (2008) New geochemical insights into volcanic degassing. Philos Trans R Soc A 366:4559–4579 Edmonds M, Herd RA (2007) A volcanic degassing event at the explosive–effusive transition. Geophys Res Lett 34:L21310 Evans JP, Forster CB, Goddard JV (1997) Permeability of fault-related rocks, and implications for hydraulic structure of fault zones. J Struct Geol 19:1393–1404 Faulkner DR, Mitchell TM, Jensen E, Cembrano J (2011) Scaling of fault damage zones with displacement and the implications for fault growth processes. J Geophys Res 116:B05403 Ferrand TP, Nielsen S, Labrousse L, Schubnel A (2021) Scaling seismic fault thickness from the laboratory to the field. J Geophys Res: Solid Earth 126:e2020JB020694 Ferré EC, Zechmeister MS, Geissman JW, MathanaSekaran N, Kocak K (2005) The origin of high magnetic remanence in fault pseudotachylites: Theoretical considerations and implication for coseismic electrical currents. Tectonophysics 402:125–139 Ferré EC, Geissman JW, Zechmeister MS (2012) Magnetic properties of fault pseudotachylytes in granites. J Geophys Res: Solid Earth 117:B01106 Fialko Y, Khazan Y (2005) Fusion by earthquake fault friction: Stick or slip? J Geophys Res: Solid Earth 110:B12407 Freund F, Salgueiro da Silva MA, Lau BWS, Takeuchi A, Jones HH (2007) Electric currents along earthquake faults and the magnetization of pseudotachylite veins. Tectonophysics 431:131–141 Fukuchi T (2003) Strong ferrimagnetic resonance signal and magnetic susceptibility of the Nojima pseudotachylyte in Japan and their implication for coseismic electromagnetic changes. J Geophys Res: Solid Earth 108: 2312 Gaunt HE, Sammonds PR, Meredith PG, Smith R, Pallister JS (2014) Pathways for degassing during the lava dome eruption of Mount St. Helens 2004–2008. Geology 42:947–950 Giordano D, Mangiacapra A, Potuzak M, Russell JK, Romano C, Dingwell DB, Di Muro A (2006) An expanded non-Arrhenian model for silicate melt viscosity: A treatment for metaluminous, peraluminous and peralkaline liquids. Chem Geol 229:42–56 Giordano D, Russell JK, Dingwell DB (2008) Viscosity of magmatic liquids: A model. Earth Planet Sci Lett 271:123–134 Gonnermann HM, Manga M (2007) The fluid mechanics inside a volcano. Annu Rev Fluid Mech 39:321–356 Gonnermann HM, Manga M (2013) Dynamics of magma ascent in the volcanic conduit. In: Modeling Volcanic Processes: The Physics and Mathematics of Volcanism. Lopes RMC, Fagents SA, Gregg TKP, (eds). Cambridge University Press, Cambridge, p 55–84 Goodwin LB (1999) Controls on pseudotachylyte formation during tectonic exhumation in the South Mountains metamorphic core complex, Arizona. Geol Soc London Spec Publ 154:325–342 Goto Y, Nakada S, Kurokawa M, Shimano T, Sugimoto T, Sakuma S, Hoshizumi H, Yoshimoto M, Uto K (2008) Character and origin of lithofacies in the conduit of Unzen volcano, Japan. J Volcanol Geotherm Res 175:45–59 Gottsmann J, Dingwell DB (2001) Cooling dynamics of spatter-fed phonolite obsidian flows on Tenerife, Canary Islands. J Volcanol Geotherm Res 105:323–342 Gottsmann J, Lavallée Y, Martí J, Aguirre-Díaz G (2009) Magma–tectonic interaction and the eruption of silicic batholiths. Earth Planet Sci Lett 284:426–434 Green DN, Neuberg J (2006) Waveform classification of volcanic low-frequency earthquake swarms and its implication at Soufrière Hills Volcano, Montserrat. J Volcanol Geotherm Res 153:51–63

Frictional Melting in Magma and Lava

957

Green DN, Neuberg J, Cayol V (2006) Shear stress along the conduit wall as a plausible source of tilt at Soufriere Hills volcano, Montserrat. Geophys Res Lett 33:L10306 Grunewald U, Sparks RSJ, Kearns S, Komorowski JC (2000) Friction marks on blocks from pyroclastic flows at the Soufriere Hills volcano, Montserrat: Implications for flow mechanisms. Geology 28:827–830 Guo Y, Morgan JK (2006) The frictional and micromechanical effects of grain comminution in fault gouge from distinct element simulations. J Geophys Res: Solid Earth 111:B12406 Hacker DB, Biek RF, Rowley PD (2014) Catastrophic emplacement of the gigantic Markagunt gravity slide, southwest Utah (USA): Implications for hazards associated with sector collapse of volcanic fields. Geology 42:943–946 Hale AJ, Muhlhaus HB (2007) Modelling shear bands in a volcanic conduit: Implications for over-pressures and extrusion-rates. Earth Planet Sci Lett 263:74–87 Hale AJ, Wadge G (2008) The transition from endogenous to exogenous growth of lava domes with the development of shear bands. J Volcanol Geotherm Res 171:237–257 Hale AJ, Wadge G, Muhlhaus HB (2007) The influence of viscous and latent heating on crystal-rich magma flow in a conduit. Geophys J Int 171:1406–1429 Han R, Shimamoto T, Hirose T, Ree J-H, Ando J-i (2007) Ultralow friction of carbonate faults caused by thermal decomposition. Science 316:878–881 Hayward KS, Cox SF (2017) Melt welding and its role in fault reactivation and localization of fracture damage in seismically active faults. J Geophys Res: Solid Earth 122:9689–9713 Heap MJ, Violay M, Wadsworth FB, Vasseur J (2017) From rock to magma and back again: The evolution of temperature and deformation mechanism in conduit margin zones. Earth Planet Sci Lett 463:92–100 Hess KU, Dingwell DB (1996) Viscosities of hydrous leucogranitic melts: A non-Arrhenian model. Am Mineral 81:1297–1300 Hetzel R, Altenberger U, Strecker MR (1996) Structural and chemical evolution of pseudotachylytes during seismic events. Mineral Petrol 58:33–50 Hirose T, Bystricky M (2007) Extreme dynamic weakening of faults during dehydration by coseismic shear heating. Geophys Res Lett 34:L14311 Hirose T, Shimamoto T (2003) Fractal dimension of molten surfaces as a possible parameter to infer the slipweakening distance of faults from natural pseudotachylytes. J Struct Geol 25:1569–1574 Hirose T, Shimamoto T (2005a) Slip-weakening distance of faults during frictional melting as inferred from experimental and natural pseudotachylytes. Bull Seismol Soc Am 95:1666–1673 Hirose T, Shimamoto T (2005b) Growth of molten zone as a mechanism of slip weakening of simulated faults in gabbro during frictional melting. J Geophys Res: Solid Earth 110:B05202 Holland TH (1900) The Charnockite Series, A group of Archean hypersthenic rocks in peninsular India. Mem Geol Surv India 28:119–249 Hornby AJ, Kendrick JE, Lamb OD, Hirose T, De Angelis S, von Aulock FW, Umakoshi K, Miwa T, Henton De Angelis S, Wadsworth FB, Hess KU (2015) Spine growth and seismogenic faulting at Mt. Unzen, Japan. J Geophys Res: Solid Earth 20:4034–4054 Hughes A, Kendrick JE, Salas G, Wallace PA, Legros F, Di Toro G, Lavallée Y (2020) Shear localisation, strain partitioning and frictional melting in a debris avalanche generated by volcanic flank collapse. J Struct Geol 140:104132 Ishikawa T, Ujiie K (2019) Geochemical analysis unveils frictional melting processes in a subduction zone fault. Geology 47:343–346 Jiang H, Lee C-TA, Morgan JK, Ross CH (2015) Geochemistry and thermodynamics of an earthquake: A case study of pseudotachylites within mylonitic granitoid. Earth Planet Sci Lett 430:235–248 Kendrick JE, Lavallée Y, Ferk A, Perugini D, Leonhardt R, Dingwell DB (2012) Extreme frictional processes in the volcanic conduit of Mount St. Helens (USA) during the 2004–2008 eruption. J Struct Geol 38:61–76 Kendrick JE, Lavallée Y, Hess KU, Heap MJ, Gaunt HE, Meredith PG, Dingwell DB (2013) Tracking the permeable porous network during strain-dependent magmatic flow. J Volcanol Geotherm Res 260:117–126 Kendrick JE, Lavallée Y, Hirose T, Di Toro G, Hornby AJ, De Angelis S, Dingwell DB (2014a) Volcanic drumbeat seismicity caused by stick-slip motion and magmatic frictional melting. Nature Geosci 7:438–442 Kendrick JE, Lavallée Y, Hess KU, De Angelis S, Ferk A, Gaunt HE, Meredith PG, Dingwell DB, Leonhardt R (2014b) Seismogenic frictional melting in the magmatic column. Solid Earth 5:199–208 Kendrick JE, Lavallée Y, Mariani E, Dingwell DB, Wheeler J, Varley NR (2017) Crystal plasticity as an indicator of the viscous-brittle transition in magmas. Nat Commun 8:1926 Kennedy FE (2000) Frictional heating and contact temperatures. In: Modern Tribology Handbook. Bhushan B (ed) CRC Press Kennedy LA, Russell JK (2012) Cataclastic production of volcanic ash at Mount Saint Helens. Phys Chem Earth, Parts A/B/C 45–46:40–49 Kennedy LA, Russell JK, Nelles E (2009) Origins of Mount St. Helens cataclasites: Experimental insights. Am Mineral 94:995–1004 Killick AM (1990) Pseudotachylite generated as a result of a drilling “burn-in”. Tectonophysics 171:221–227 Killick AM (1994) The geochemistry of pseudotachylyte and its host rocks from the West Rand Goldfield, Witwatersrand Basin, South Africa: implications for pseudotachylyte genesis. Lithos 32:193–205

958

Kendrick & Lavallée

Kim JW, Ree JH, Han R, Shimamoto T (2010) Experimental evidence for the simultaneous formation of pseudotachylyte and mylonite in the brittle regime. Geology 38:1143–1146 Kirkpatrick JD, Rowe CD (2013) Disappearing ink: How pseudotachylytes are lost from the rock record. J Struct Geol 52:183–198 Kirkpatrick JD, Shipton ZK, Persano C (2009) Pseudotachylytes: rarely generated, rarely preserved, or rarely reported? Bull Seismol Soc Am 99:382–388 Kirkpatrick JD, Dobson KJ, Mark DF, Shipton ZK, Brodsky EE, Stuart FM (2012) The depth of pseudotachylyte formation from detailed thermochronology and constraints on coseismic stress drop variability. J Geophys Res: Solid Earth 117:B06406 Kirkpatrick JD, Rowe CD, White JC, Brodsky EE (2013) Silica gel formation during fault slip: Evidence from the rock record. Geology 41:1015–1018 Kitajima H, Chester JS, Chester FM, Shimamoto T (2010) High-speed friction of disaggregated ultracataclasite in rotary shear: Characterization of frictional heating, mechanical behavior, and microstructure evolution. J Geophys Res: Solid Earth 115:B08408 Kokelaar P (2007) Friction melting, catastrophic dilation and breccia formation along caldera superfaults. J Geol Soc 164:751–754 Lamb OD, Varley NR, Mather TA, Pyle DM, Smith PJ, Liu EJ (2014) Multiple timescales of cyclical behaviour observed at two dome-forming eruptions. J Volcanol Geotherm Res 284:106–121 Lamb OD, De Angelis S, Umakoshi K, Hornby AJ, Kendrick JE, Lavallée Y (2015) Repetitive fracturing during spine extrusion at Unzen volcano, Japan. Solid Earth 6:1277–1293 Lamur A, Kendrick JE, Wadsworth FB, Lavallée Y (2019) Fracture healing and strength recovery in magmatic liquids. Geology 47:195–198 Landman U, Luedtke WD, Gao J (1996) Atomic-scale issues in tribology: interfacial junctions and nanoelastohydrodynamics. Langmuir 12:4514–4528 Lavallée Y, Kendrick JE (2020) A review of the physical and mechanical properties of volcanic rocks and magmas in the brittle and ductile fields. In: Forecasting and planning for volcanic hazards, risks, and disasters. Papale P, (ed) Elsevier Lavallée Y, Kendrick JE (2022) Strain localization in magmas. Rev Mineral Geochem 87:721-765 Lavallée Y, Hess KU, Cordonnier B, Dingwell DB (2007) Non-Newtonian rheological law for highly crystalline dome lavas. Geology 35:843–846 Lavallée Y, Mitchell TM, Heap MJ, Vasseur J, Hess K-U, Hirose T, Dingwell DB (2012a) Experimental generation of volcanic pseudotachylytes: Constraining rheology. J Struct Geol 38:222–233 Lavallée Y, Varley N, Alatorre-Ibargüengoitia M, Hess KU, Kueppers U, Mueller S, Richard D, Scheu B, Spieler O, Dingwell D (2012b) Magmatic architecture of dome-building eruptions at Volcán de Colima, Mexico. Bull Volcanol 74:249–260 LavalléeY, Benson PM, Heap MJ, Hess KU, Flaws A, Schillinger B, Meredith PG, Dingwell DB (2013) Reconstructing magma failure and the degassing network of dome-building eruptions. Geology 41:515–518 Lavallée Y, Hirose T, Kendrick JE, Hess K-U, Dingwell DB (2015a) Fault rheology beyond frictional melting. PNAS 112:9276 Lavallée Y, Dingwell DB, Johnson JB, Cimarelli C, Hornby AJ, Kendrick JE, Von Aulock FW, Kennedy BM, Andrews BJ, Wadsworth FB, Rhodes E (2015b) Thermal vesiculation during volcanic eruptions. Nature 528:544–547 Lee SK, Han R, Kim EJ, Jeong GY, Khim H, Hirose T (2017) Quasi-equilibrium melting of quartzite upon extreme friction. Nat Geosci 10:436–441 Lee AL, Lloyd GE, Torvela T, Walker AM (2020) Evolution of a shear zone before, during and after melting. J Geol Soc 177:738–751 Legros F, Cantagrel JM, Devouard B (2000) Pseudotachylyte (frictionite) at the base of the Arequipa volcanic landslide deposit (Peru): Implications for emplacement mechanisms. J Geol 108:601–611 Lejeune AM, Richet P (1995) Rheology of crystal-bearing silicate melts—an experimental study at high viscosities. J Geophys Res 100:4215–4229 Lensky NG, Sparks RSJ, Navon O, Lyakhovsky V (2008) Cyclic activity at Soufrière Hills Volcano, Montserrat: degassing-induced pressurization and stick-slip extrusion. Geol Soc London Spec Publ 307:169–188 Lesher CE, Spera FJ (2015) Thermodynamic and transport properties of silicate melts and magma. Chapter 5 In: The Encyclopedia of Volcanoes (Second Edition). Sigurdsson H, (ed) Academic Press, Amsterdam, p 113–141 Lin A (1994a) Microlite morphology and chemistry in pseudotachylite, from the Fuyun Fault Zone, China. J Geol 102:317–329 Lin A (1994b) Glassy pseudotachylyte veins from the Fuyun fault zone, northwest China. J Struct Geol 16:71–83 Lin AM (1999) Roundness of clasts in pseudotachylytes and cataclastic rocks as an indicator of frictional melting. J Struct Geol 21:473–478 Lin A (2007) Fossil earthquakes: The Formation and Preservation of Pseudotachylytes. Lecture Notes in Earth Sciences. Springer Berlin Heidelberg, Berlin, Heidelberg Lin A (2008) Chemical composition and melting processes of pseudotachylyte. In: Fossil Earthquakes: The Formation and Preservation of Pseudotachylytes. Lin A (ed) Springer Berlin Heidelberg, Berlin, Heidelberg, p 159–176

Frictional Melting in Magma and Lava

959

Lin A, Shimamoto T (1998) Selective melting processes as inferred from experimentally generated pseudotachylytes. J Asian Earth Sci 16:533–545 Lin A, Chen A, Liau C-F, Lee C-T, Lin C-C, Lin P-S, Wen S-C, Ouchi T (2001) Frictional fusion due to coseismic landsliding during the 1999 Chi-Chi (Taiwan) ML 7.3 Earthquake. Geophys Res Lett 28:4011–4014 Linker MF, Dieterich JH (1992) Effects of variable normal stress on rock friction: observations and constitutive equations. J Geophys Res 97:4923–4940 Liu Y, Zhang Y, Behrens H (2005) Solubility of H2O in rhyolitic melts at low pressures and a new empirical model for mixed H2O–CO2 solubility in rhyolitic melts. J Volcanol Geotherm Res 143:219–235 Llewellin EW, Mader HM, Wilson SDR (2002) The constitutive equation and flow dynamics of bubbly magmas. Geophys Res Lett 29:2170 Lockner DA, Kilgore BD, Beeler NM, Moore DE (2017) The transition from frictional sliding to shear melting in laboratory stick-slip experiments. In: Fault Zone Dynamic Processes: Evolution of Fault Properties during Seismic Rupture. Wiley, p 105–130 Luhr JF, Carmichael ISE (1990) Petrological monitoring of cyclical eruptive activity at Volcán Colima, Mexico. J Volcanol Geotherm Res 42:235–260 Lyakhovsky V, Ben-Zion Y (2008) Scaling relations of earthquakes and aseismic deformation in a damage rheology model. Geophys J Int 172:651–662 Ma S, Shimamoto T, Yao L, Togo T, Kitajima H (2014) A rotary-shear low to high-velocity friction apparatus in Beijing to study rock friction at plate to seismic slip rates. Earthquake Sci 27:469–497 Maddock RH (1986) Frictional melting in landslide-generated frictionites (hyalomylonites) and fault-generated pseudotachylytes-discussion. Tectonophysics 128:151–153 Maddock RH (1992) Effects of lithology, cataclasis and melting on the composition of fault-generated pseudotachylytes in Lewisian gneiss, Scotland. Tectonophysics 204:261–278 Maddock RH, Grocott J, Van Nes M (1987) Vesicles, amygdales and similar structures in fault-generated pseudotachylytes. Lithos 20:419–432 Mader H, Llewellin E, Mueller S (2013) The rheology of two-phase magmas: A review and analysis. J Volcanol Geotherm Res 257:135–158 Magloughlin JF (1989) The nature and significance of pseudotachylite from the Nason terrane, North Cascade Mountains, Washington. J Struct Geol 11:907–917 Magloughlin JF (2005) Immiscible sulfide droplets in pseudotachylyte: Evidence for high temperature (>1200 °C) melts. Tectonophysics 402:81–91 Magloughlin JF (2011) Bubble collapse structure: a microstructural record of fluids, bubble formation and collapse, and mineralization in pseudotachylyte. J Geol 119:351–371 Magloughlin JF, Spray JG (1992) Frictional melting processes and products in geological materials. Tectonophysics 204:197–204 Manga M, Castro J, Cashman KV, Loewenberg M (1998) Rheology of bubble-bearing magmas. J Volcanol Geotherm Res 87:15–28 Marone C, Richardson E (2010) Learning to read fault-slip behavior from fault-zone structure. Geology 38:767–768 Masch L, Wenk HR, Preuss E (1985) Electron microscopy study of hyalomylonites—evidence for frictional melting in landslides. Tectonophysics 115:131–160 McGarr A (1999) On relating apparent stress to the stress causing earthquake fault slip. J Geophys Res: Solid Earth 104:3003–3011 McKenzie D, Brune JN (1972) Melting on fault planes during large earthquakes. Geophys J R Astronom Soc 29:65–78 McNulty BA (1995) Pseudotachylyte generated in the semi-brittle and brittle regimes, Bench Canyon shear zone, central Sierra Nevada. J Struct Geol 17:1507–1521 McNutt SR (1996) Seismic monitoring and eruption forecasting of volcanoes: a review of the state-of-the-art and case histories. In: Monitoring and Mitigation of Volcano Hazards. Scarpa R, Tilling RI, (eds). Springer-Verlag, Berlin, p 99–146 McNutt SR (2005) Volcanic seismology. Annu Rev Earth Planet Sci 33:461–491 Melnik O, Sparks RSJ (2002) Dynamics of magma ascent and lava extrusion at Soufrière Hills Volcano, Montserrat. Geol Soc London Memoirs 21:153–171 Melnik OE, Sparks RSJ (2005) Controls on conduit magma flow dynamics during lava dome building eruptions. J Geophys Res 110:B02209 Melosh HJ (2005) The mechanics of pseudotachylite formation in impact events. In: Impact Tectonics. Koeberl C, Henkel H (eds). Springer Berlin Heidelberg, Berlin, Heidelberg, p 55–80 Mitchell TM, Toy V, Di Toro G, Renner J, Sibson RH (2016) Fault welding by pseudotachylyte formation. Geology 44:1059–1062 Mittempergher S, Dallai L, Pennacchioni G, Renard F, Di Toro G (2014) Origin of hydrous fluids at seismogenic depth: Constraints from natural and experimental fault rocks. Earth Planet Sci Lett 385:97–109 Miwa T, Okumura S, Matsushima T, Shimizu H (2013) Asymmetric deformation structure of lava spine in Unzen Volcano Japan. In Book Asymmetric deformation structure of lava spine in Unzen Volcano Japan. 2013 Fall Meeting, AGU, San Francisco, Abst. V14A-03

960

Kendrick & Lavallée

Molina Garza RS, Geissman J, Wawrzyniec T, Weber B, Martínez ML, Aranda-Gómez J (2009) An integrated magnetic and geological study of cataclasite-dominated pseudotachylytes in the Chiapas Massif, Mexico: a snapshot of stress orientation following slip. Geophys J Int 177:891–912 Monzawa N, Otsuki K (2003) Comminution and fluidization of granular fault materials: implications for fault slip behavior. Tectonophysics 367:127–143 Moore PL, Iverson NR, Iverson RM (2008) Frictional properties of the Mount St. Helens gouge. In: A Volcano Rekindled: The Renewed Eruption of Mount St Helens, 2004–2006. Sherrod DR, Scott WE, Stauffer PH (eds). U.S. Geological Survey Professionnal Paper 1750, p 415–424 Moran SC, Malone S, Qamar A, Thelen W, Waite G, Horton S, LaHusen R, Major JJ (2005) Overview of seismicity associated with the 2004–2005 eruption of Mount St. Helens. AGU Fall Meeting Abstr: V52B-02 Mueller S, Llewellin EW, Mader HM (2011) The effect of particle shape on suspension viscosity and implications for magmatic flows. Geophys Res Lett 38:L13316 Nakada S, Shimizu H, Ohta K (1999) Overview of the 1990–1995 eruption at Unzen Volcano. J Volcanol Geotherm Res 89:1–22 Nakamura N, Hirose T, Borradaile GJ (2002) Laboratory verification of submicron magnetite production in pseudotachylytes: relevance for paleointensity studies. Earth Planet Sci Lett 201:13–18 Neuberg J (2000) Characteristics and causes of shallow seismicity in andesite volcanoes. Philos Transactions R Soc London 358:533–1546 Neuberg JW, Tuffen H, Collier L, Green D, Powell T, Dingwell D (2006) The trigger mechanism of low-frequency earthquakes on Montserrat. J Volcanol Geotherm Res 153:37–50 Neuberg JW, Collinson ASD, Mothes PA, Ruiz CM, Aguaiza S (2018) Understanding cyclic seismicity and ground deformation patterns at volcanoes: Intriguing lessons from Tungurahua volcano, Ecuador. Earth Planet Sci Lett 482:193–200 Nielsen SB, Carlson JM, Olsen KB (2000) Influence of friction and fault geometry on earthquake rupture. J Geophys Res 105:6069–6088 Nielsen S, Di Toro G, Hirose T, Shimamoto T (2008) Frictional melt and seismic slip. J Geophys Res: Solid Earth 113:B01308 Nielsen S, Toro GD, Griffith WA (2010a) Friction and roughness of a melting rock surface. Geophys J Int 182:299–310 Nielsen S, Mosca P, Giberti G, Di Toro G, Hirose T, Shimamoto T (2010b) On the transient behavior of frictional melt during seismic slip. J Geophys Res-Solid Earth 115:B10301 Niemeijer AR, Di Toro G, Nielsen S, Di Felice F (2011) Frictional melting of gabbro under extreme experimental conditions of normal stress, acceleration and sliding velocity. J Geophys Res: Solid Earth 116:B07404 Niemeijer A, Di Toro G, Griffith WA, Bistacchi A, Smith SAF, Nielsen S (2012) Inferring earthquake physics and chemistry using an integrated field and laboratory approach. J Struct Geol 39:2–36 Noda H, Kanagawa K, Hirose T, Inoue A (2011) Frictional experiments of dolerite at intermediate slip rates with controlled temperature: Rate weakening or temperature weakening? J Geophys Res: Solid Earth 116:B07306 O’Hara K (1992) Major- and trace-element constraints on the petrogenesis of a fault-related pseudotachylyte, western Blue Ridge province, North Carolina. Tectonophysics 204:279–288 O’Hara KD (2001) A pseudotachylyte geothermometer. J Struct Geol 23:1345–1357 Obata M, Karato S-i (1995) Ultramafic pseudotachylite from the Balmuccia peridotite, Ivrea-Verbano zone, northern Italy. Tectonophysics 242:313–328 Ohtomo Y, Shimamoto T (1994) Significance of thermal fracturing in the generation of fault gouge during rapid fault motion: An experimental verification. Struct Geol J Tectonic Res Group Jpn 39:135–144 Okumura S, Kozono T (2017) Silicic lava effusion controlled by the transition from viscous magma flow to friction controlled flow. Geophys Res Lett 44:3608–3614 Okumura S, Sasaki O (2014) Permeability reduction of fractured rhyolite in volcanic conduits and its control on eruption cyclicity. Geology 42:843–846 Okumura S, Uesugi K, Nakamura M, Sasaki O (2015) Rheological transitions in high-temperature volcanic fault zones. J Geophys Res: Solid Earth 120:2974–2987 Otsuki K, Monzawa N, Nagase T (2003) Fluidization and melting of fault gouge during seismic slip: Identification in the Nojima fault zone and implications for focal earthquake mechanisms. J Geophys Res-Solid Earth 108:2192 Ozawa K, Takizawa S (2007) Amorphous material formed by the mechanochemical effect in natural pseudotachylyte of crushing origin: A case study of the Iida-Matsukawa Fault, Nagano Prefecture, Central Japan. J Struct Geol 29:1855–1869 Paillat O, Elphick SC, Brown WL (1992) The solubility of water in NaAlSi3O8 melts: a re-examination of Ab−H2O phase relationships and critical behaviour at high pressures. Contrib Mineral Petrol 112:490–500 Pallister JS, Cashman KV, Hagstrum JT, Beeler NM, Moran SC, Denlinger RP (2013) Faulting within the Mount St. Helens conduit and implications for volcanic earthquakes. GSA Bull 125:359–376 Papale P (1999) Strain-induced magma fragmentation in explosive eruptions. Nature 397:425–428 Papale P (2001) Dynamics of magma flow in volcanic conduits with variable fragmentation efficiency and nonequilibrium pumice degassing. J Geophys Res: Solid Earth 106:11043–11065 Passelègue FX, Goldsby DL, Fabbri O (2014) The influence of ambient fault temperature on flash-heating phenomena. Geophys Res Lett 41:828–835

Frictional Melting in Magma and Lava

961

Pei J, Zhou Z, Dong S, Tang L (2014) Magnetic evidence revealing frictional heating from fault rocks in granites. Tectonophysics 637:207–217 Petrík I, Nabelek PI, Janák M, Plašienka D (2003) Conditions of formation and crystallization kinetics of highly oxidized pseudotachylytes from the High Tatras (Slovakia). J Petrol 44:901–927 Philpotts AR (1964) Origin of pseudotachylites. Am J Sci 262:1008–1035 Pittarello L, Pennacchioni G, Di Toro G (2012) Amphibolite-facies pseudotachylytes in Premosello metagabbro and felsic mylonites (Ivrea Zone, Italy). Tectonophysics 580:43–57 Plail M, Edmonds M, Humphreys MCS, Barclay J, Herd RA (2014) Geochemical evidence for relict degassing pathways preserved in andesite. Earth Planet Sci Lett 386:21–33 Preece K, Gertisser R, Barclay J, Charbonnier SJ, Komorowski J-C, Herd RA (2016) Transitions between explosive and effusive phases during the cataclysmic 2010 eruption of Merapi volcano, Java, Indonesia. Bull Volcanol 78:54 Price NA, Johnson SE, Gerbi CC, West DP (2012) Identifying deformed pseudotachylyte and its influence on the strength and evolution of a crustal shear zone at the base of the seismogenic zone. Tectonophysics 518–521:63–83 Proctor B, Lockner DA (2016) Pseudotachylyte increases the post-slip strength of faults. Geology 44:1003–1006 Rabinowicz E (1951) The nature of the static and kinetic coefficients of friction. J Appl Physics 22:1373–1379 Rabinowicz E (1958) The intrinsic variables affecting the stick-slip process. Proc Phys Soc 71:668–675 Ray SK (2004) Melt–clast interaction and power-law size distribution of clasts in pseudotachylytes. J Struct Geol 26:1831–1843 Reches Z, Lockner DA (2010) Fault weakening and earthquake instability by powder lubrication. Nature 467:452-U102 Reimold WU (1995) Pseudotachylite in impact structures—generation by friction melting and shock brecciation?: A review and discussion. Earth Sci Rev 39:247–265 Rempe M, Di Toro G, Mitchell TM, Smith SAF, Hirose T, Renner J (2020) Influence of effective stress and pore fluid pressure on fault strength and slip localization in carbonate slip zones. J Geophys Res: Solid Earth 125:e2020JB019805 Rempel AW (2006) The effects of flash-weakening and damage on the evolution of fault strength and temperature. In: Earthquakes: Radiated Energy and the Physics of Faulting. Vol 170. Abercrombie R, McGarr A, DiToro G, Kanamori H, (eds). Amer Geophysical Union, Washington, p 263–270 Rempel AW, Rice JR (2006) Thermal pressurization and onset of melting in fault zones. J Geophys Res: Solid Earth 111 Rice JR (2006) Heating and weakening of faults during earthquake slip. J Geophys Res 111:B05311 Rigney DA, Hirth JP (1979) Plastic deformation and sliding friction of metals. Wear 53:345–370 Rittinger V (1867) Lehrbuch der Aufbersitungskunde. Berlin Rosenberg CL, Handy MR (2005) Experimental deformation of partially melted granite revisited: implications for the continental crust. J Metamorph Petrol 23:19–28 Rowe CD, Moore JC, Meneghini F, McKeirnan AW (2005) Large-scale pseudotachylytes and fluidized cataclasites from an ancient subduction thrust fault. Geology 33:937–940 Ruina A (1983) Slip instability and state variable friction laws. J Geophys Res 88:10359–10370 Rust AC, Cashman KV, Wallace PJ (2004) Magma degassing buffered by vapor flow through brecciated conduit margins. Geology 32:349–352 Sammis C, King G, Biegel R (1987) The kinematics of gouge deformation. Pure Appl Geophys 125:777–812 Sarkar A, Chattopadhyay A, Singh T (2019) Roundness of survivor clasts as a discriminator for melting and crushing origin of fault rocks: A reappraisal. J Earth System Sci 128:51 Scheu B, Ichihara M, Spieler O, Dingwell DB (2008) A closer look at magmatic fragmentation. Scheu B, Ichihara M, Spieler O, Dingwell DB. A closer look at magmatic fragmentation. AGU Fall Meeting Abstr V43C-1813 Scholz CH (1998) Earthquakes and friction laws. Nature 391:37–42 Scholz CH (2019) The Mechanics of Earthquakes and Faulting. Cambridge University Press, Cambridge Scholz CH, Engelder JT (1976) The role of asperity indentation and ploughing in rock friction — I: Asperity creep and stick-slip. Int J Rock Mech Min Sci Geomech Abstracts 13:149–154 Scholz CH, Dawers NH, Yu JZ, Anders MH (1993) Fault growth and fault scaling laws—preliminary results. J Geophys Res-Solid Earth 98:21951–21961 Schwarzkopf, Schmincke, Troll (2001) Pseudotachylite on impact marks of block surfaces in block-and-ash flows at Merapi volcano, Central Java, Indonesia. Int J Earth Sci 90:769–775 Scott JS, Drever HI (1954) X. Frictional fusion along a Himalayan Thrust. Proc R Soc Edinburgh Sect B Biology 65:121–142 Scott JAJ, Pyle DM, Mather TA, Rose WI (2013) Geochemistry and evolution of the Santiaguito volcanic dome complex, Guatemala. J Volcanol Geotherm Res 252:92–107 Shand SJ (1916) The pseudotachylyte of Parijs (Orange Free State), and its relation to ‘Trap-Shotten Gneiss’ and ‘Flinty Crush-Rock’. Q J Geol Soc 72:198–221 Shields JK, Mader HM, Caricchi L, Tuffen H, Mueller S, Pistone M, Baumgartner L (2016) Unravelling textural heterogeneity in obsidian: Shear-induced outgassing in the Rocche Rosse flow. J Volcanol Geotherm Res 310:137–158 Shimamoto T, Lin AM (1994) Is frictional melting equilibrium or non-equilibrium melting? Struct Geol (J Tectonic Res Group Japan) 39:79–84 Shimamoto T, Tsutsumi A (1994) A new rotary-shear high-velocity frictional testing machine: Its basic design and scope of research. Struct Geol 39:65–78

962

Kendrick & Lavallée

Sibson RH (1973) Interactions between temperature and pore-fluid pressure during earthquake faulting and a mechanism for partial or total stress relief. Nat Phys Sci 243:66–68 Sibson RH (1975) Generation of pseudotachylyte by ancient seismic faulting. R Astronom Soc London J 43:775–794 Sibson RH (1977) Fault rocks and fault mechanisms. J Geol Soc 133:191–213 Sibson RH, Toy VG (2006) The habitat of fault-generated pseudotachylyte: presence vs. absence of friction-melt. In: Earthquakes: Radiated Energy and the Physics of Faulting. Abercrombie R, McGarr A, Di Toro G, Kanamori H (eds) AGU Geophysical Monograph 170:153–166 Smith DR, Leeman WP (1987) Petrogenesis of Mount St. Helens dacitic magmas. J Geophys Res: Solid Earth 92:10313–10334 Spagnuolo E, Nielsen S, Violay M, Di Toro G (2016) An empirically based steady state friction law and implications for fault stability. Geophys Res Lett 43:3263–3271 Sparks RSJ (1997) Causes and consequences of pressurisation in lava dome eruptions. Earth Planet Sci Lett 150:177–189 Spray JG (1987) Artificial generation of pseudotachylyte using friction welding apparatus: simulation of melting on a fault plane. J Struct Geol 9:49–60 Spray JG (1992) A physical basis for the frictional melting of some rock-forming minerals. Tectonophysics 204:205–221 Spray JG (1993) Viscosity determinations of some frictionally generated silicate melts: Implications for fault zone rheology at high strain rates. J Geophys Res: Solid Earth 98:8053–8068 Spray JG (1998) Localized shock- and friction-induced melting in response to hypervelocity impact. Geol Soc London, Spec Publ 140:195–204 Spray JG (2005) Evidence for melt lubrication during large earthquakes. Geophys Res Lett 32: L07301 Spray JG (2010) Frictional melting processes in planetary materials: from hypervelocity impact to earthquakes. Annu Rev Earth Planet Sci 38:221–254 Swanson MT (1992) Fault structure, wear mechanisms and rupture processes in pseudotachylyte generation. Tectonophysics 204:223–242 Tait S, Jaupart C, Vergniolle S (1989) Pressure, gas content and eruption periodicity of a shallow, crystallising magma chamber. Earth Planet Sci Lett 92:107–123 Takagi H, Arita K, Danhara T, Iwano H (2007) Timing of the Tsergo Ri landslide, Langtang Himal, determined by fission-track dating of pseudotachylyte. J Asian Earth Sci 29:466–472 Terzaghi K (1923) Die Berechnung der Durchlassigkeitsziffer des Tones aus Dem Verlauf der Hidrodynamichen. SpanNungserscheinungen Akademie der Wissenschaften in Wien; Mathematish-Naturwissen-SchaftilicheKlasse: Mainz, Germany, p 125–138 Thelen W, Malone S, West M (2011) Multiplets: Their behavior and utility at dacitic and andesitic volcanic centers. J Geophys Res:Solid Earth 116:B08210 Tromans D (2008) Mineral comminution: Energy efficiency considerations. Miner Eng 21:613–620 Truby JM, Mueller SP, Llewellin EW, Mader HM (2015) The rheology of three-phase suspensions at low bubble capillary number. Proc R Soc London A 471:20140557 Tsutsumi A, Shimamoto T (1997) High-velocity frictional properties of gabbro. Geophys Res Lett 24:699–702 Tuffen H, Dingwell D (2005) Fault textures in volcanic conduits: evidence for seismic trigger mechanisms during silicic eruptions. Bull Volcanol 67:370–387 Tuffen H, Dingwell DB, Pinkerton H (2003) Repeated fracture and healing of silicic magma generate flow banding and earthquakes? Geology 31:1089–1092 Umakoshi K, Takamura N, Shinzato N, Uchida K, Matsuwo N, Shimizu H (2008) Seismicity associated with the 1991–1995 dome growth at Unzen Volcano, Japan. J Volcanol Geotherm Res 175:91–99 van den Ende MPA, Chen J, Ampuero JP, Niemeijer AR (2018) A comparison between rate-and-state friction and microphysical models, based on numerical simulations of fault slip. Tectonophysics 733:273–295 Violay M, Di Toro G, Gibert B, Nielsen S, Spagnuolo E, Del Gaudio P, Azais P, Scarlato PG (2014) Effect of glass on the frictional behavior of basalts at seismic slip rates. Geophys Res Lett 41:348–355 Voight B, Hoblitt RP, Clarke AB, Lockhart AB, Miller AD, Lynch L, McMahon J (1998) Remarkable cyclic ground deformation monitored in real-time on Montserrat, and its use in eruption forecasting. Geophys Res Lett 25:3405–3408 Voight B, Sparks RS, Miller AD, Stewart RC, Hoblitt RP, Clarke A, Ewart J, Aspinall WP, Baptie B, Calder ES, Cole P (1999) Magma flow instability and cyclic activity at Soufriere Hills Volcano, Montserrat, British West Indies. Science 283:1138–1142 Wallace PA, Kendrick JE, Miwa T, Ashworth JD, Coats R, Utley JE, Henton De Angelis S, Mariani E, Biggin A, Kendrick R, Nakada S (2019a) Petrological architecture of a magmatic shear zone: a multidisciplinary investigation of strain localisation during magma ascent at Unzen Volcano, Japan. J Petrol 60:791–826 Wallace PA, De Angelis SH, Hornby AJ, Kendrick JE, Clesham S, von Aulock FW, Hughes A, Utley JE, Hirose T, Dingwell DB, Lavallée Y (2019b) Frictional melt homogenisation during fault slip: Geochemical, textural and rheological fingerprints. Geochim Cosmochim Acta 255:265–288 Wang C-y, Goodman RE, Sundaram PN (1975) Variations of VP and VS in granite premonitory to shear rupture and stick-slip sliding: Application to earthquake prediction. Geophys Res Lett 2:309–311

Frictional Melting in Magma and Lava

963

Webb SL, Dingwell DB (1990) Non-Newtonian rheology of igneous melts at high stresses and strain rates: experimental results for rhyolite, andesite, basalt and nephelinite. J Geophys Res 95:15695–15701 Weber B, Suhina T, Brouwer AM, Bonn D (2019) Frictional weakening of slip interfaces. Sci Adv 5:eaav7603 Wells DL, Coppersmith KJ (1994) New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull Seismol Soc Am 84:974–1002 Wong T-f, Gu Y, Yanagidani T, Zhao Y (1992) Chapter 5 Stabilization of Faulting by Cumulative Slip. In: International Geophysics. Vol Volume 51. Brian E, Teng-fong W, (eds). Academic Press, p 119–143 Wright HMN, Weinberg RF (2009) Strain localization in vesicular magma: Implications for rheology and fragmentation. Geology 37:1023–1026 Yamada K, Hanamuro T, Tagami T, Shimada K, Takagi H, Yamada R, Umeda K (2012) The first (U–Th)/He thermochronology of pseudotachylyte from the Median Tectonic Line, southwest Japan. J Asian Earth Sci 45:17–23 Yang T, Chou Y-M, Ferré EC, Dekkers MJ, Chen J, Yeh E-C, Tanikawa W (2020) Faulting Processes Unveiled by Magnetic Properties of Fault Rocks. Rev Geophys 58:e2019RG000690 Yoshimura S, Nakamura M (2010) Fracture healing in a magma: An experimental approach and implications for volcanic seismicity and degassing. J Geophys Res-Solid Earth 115:B09209 Zhang S, Tullis TE, Scruggs VJ (1999) Permeability anisotropy and pressure dependency of permeability in experimentally sheared gouge materials. J Struct Geol 21:795–806 Zhang L, Li H, Sun Z, Chou Y-M, Cao Y, Wang H (2018) Metallic iron formed by melting: A new mechanism for magnetic highs in pseudotachylyte. Geology 46:779–782 Zhu W, Allison KL, Dunham EM, Yang Y (2020) Fault valving and pore pressure evolution in simulations of earthquake sequences and aseismic slip. Nat Commun 11:4833

21

Reviews in Mineralogy & Geochemistry Vol. 87 pp. 965-1014, 2022 Copyright © Mineralogical Society of America

Non-Magmatic Glasses Maria Rita Cicconi1,*, John S. McCloy2, Daniel R. Neuville1 1

Université de Paris Insitut de Physique du Globe de Paris Géomatériaux, CNRS 1 rue Jussieu F-75005 Paris France [email protected] [email protected] 2

School of Mechanical and Materials Engineering Washington State University PO Box 642920 Pullman, WA 99164–2920 USA [email protected]

* Correspondence address: WW3—Friedrich-Alexander-Universität Erlangen-Nürnberg D-91058 Erlangen Germany

OVERVIEW On Earth, natural glasses are typically produced by rapid cooling of melts, and as in the case of minerals and rocks, natural glasses can provide key information on the evolution of the Earth. However, natural glasses are products not solely terrestrial, and different formation mechanisms give rise to a variety of natural amorphous materials. In this chapter, we provide an overview of the different natural glasses of non-magmatic origin and on their formation mechanisms. We focus on natural glasses formed by mechanisms other than magmatic activity and included are metamorphic glasses and glasses produced from highly energetic events (shock metamorphism). The study of these materials has strong repercussions on planetary surface processes, paleogeography/paleoecology, and even on the origin of life.

ACRONYMS AND GLOSSARY Hypervelocity impacts

Impacts, involving impacting bodies that are traveling at speed (generally greater than a few km/s) higher enough to generate shock waves upon impact.

K–Pg

Cretaceous–Paleogene (K–Pg) boundary (~66 million years ago)

KT

Cretaceous–Tertiary boundary (former name for K–Pg)

Lechatelierite

shock-fused SiO2 glass

LDG

Libyan Desert Glass

m-Tek or m-T

microtektites; Small distal ejecta with diameter less than 0.1 cm.

1529-6466/22/0087-0021$05.00 (print) 1943-2666/22/0087-0021$05.00 (online)

http://dx.doi.org/10.2138/rmg.2022.87.21

966

Cicconi et al.

MN

Muong Nong-type tektites

PDFs

Planar deformation features; microscopic parallel, isotropic features in minerals that originate from elevated shock metamorphism.

SF

tektite/mictotektites strewn fields

TAS

Total-Alkalis versus Silica diagram

Tektites

mm- to cm-scale, glassy particles of ballistically transported impact melt, formed by the impact of an extraterrestrial projectile.

Tg

Glass transition temperature

YD

Younger Dryas is a geological period from ~12,900 to ~11,700 BP

YDB

Younger Dryas boundary

XAS

X-ray Absorption Spectroscopy

INTRODUCTION This chapter aims to review natural glasses formed by mechanisms other than magmatic activity. After a brief description of the most common natural amorphous materials and of the different mechanisms of formation, we report some examples of metamorphic glasses and glasses from highly energetic events. In the end, we provide an overview of the properties of these natural amorphous materials. In the last decades, several reviews, for specific natural glasses, have been published (e.g., Glass 1990; Koeberl 1997; Eby et al. 2010 ; Pasek et al. 2012; Glass and Simonson 2013), with more recent general reviews on different natural glasses provided in Heide and Heide (2011), Glass (2016), Cicconi and Neuville (2019), McCloy (2019).

The composition and origin of natural glasses Natural glasses have different origins and chemical compositions, though their chemical variability matches the differentiation found in many common types of volcanic rocks. An overview of the enormous variability of natural glasses occurring on Earth and Lunar soil can be appreciated in the TAS diagram (total alkalis vs. silica; Fig. 1). These amorphous materials have SiO2 contents between ~33–99 wt.%, and alkali contents ranging between 0 and 15 wt.%, thus covering many common types of volcanic rocks. Despite glasses having differentiated chemically in similar ways to many common volcanic rocks, most of the time, non-magmatic glasses have experienced extreme conditions of formation, far from those of common igneous materials. Indeed, most of the glasses considered in this chapter have cooling rates orders of magnitude higher than volcanic terrestrial (or lunar) glasses, and/or have been subject to extremely elevated peak pressures. For instance, cooling rates may range from extremely high values, as in fulgurite formation (~1010 °C/min) and submarine basaltic eruptions (107 °C/min), to moderate values in tektites 104 –10−2 °C/min, to very slow rates in massive obsidian flows 10−2–10−4 °C /min (Switzer and Melson 1972; Weeks et al. 1984; Wilding et al. 1996a,b; Rietmeijer et al. 1999; Potuzak et al. 2008). By comparison, water, which is considered to be a very weak glass former, requires cooling rates on the order of 106 °C/s to form an amorphous solid (Debenedetti and Stanley 2003). Before describing non-magmatic glasses, we would like to provide an overview of all amorphous materials found on Earth (and on other terrestrial planets), and of the various mechanisms of formation. The most well-known natural amorphous materials are of magmatic origin and include basaltic glasses and obsidians. Basaltic glasses have an average composition of about (wt.%) 50–54% SiO2, 12–17% Al2O3, 8–12% FeOtot, 2–4% alkali (K2O + Na2O), 15–20% alkaline-earth (CaO + MgO) (Cicconi and Neuville 2019 and references therein) and their low viscosity favors crystallization (devitrification). Volcanic glasses produced upon rapid cooling of basaltic melts are called sideromelane, but they also occur as volcanic ash, fibers, and teardrops (i.e., Pele’s Hair and Pele’s Tears) and more rarely form solidified foam—reticulite.

Non-Magmatic Glasses

967

Figure 1. SiO2 vs. total alkali (wt.%) diagram for several natural non-magmatic glasses described in this chapter. Glasses deriving from magmatic processes are reported for comparison. Data compilation from Cicconi and Neuville (2019). Combustion glasses from Table 1. LDG = Libyan Desert Glass; mT = microtektites.

Obsidian glass was first described in Pliny The Elder’s Natural History with the name of “obsiana”, so-called because of its similarity to a very dark stone found in Ethiopia by Obsius. This glass has accompanied and influenced human evolution since prehistoric times, and nowadays it still enters the popular culture, even if with more fanciful names (i.e., dragonglass, after the fantasy drama television series Game of Thrones). Obsidians are generally subalkalic rhyolitic with an average composition of about (wt.%) 72–77% SiO2, 10–15% Al2O3, 1–2% FeOtot, 7–10% alkali (K2O + Na2O), 0.5–2% alkaline-earth (CaO + MgO) (Cicconi and Neuville 2019 and references therein). The glass-forming processes of obsidian melts are strongly influenced by the content, size, and shape of microlites, and by the contents of volatile components (such as water, fluorine, and chlorine, sulphur and carbon oxides), and small variations in volatile contents can cause important changes in the flow dynamics of obsidian melts (Carmichael 1979; Castro et al. 2002; Heide and Heide 2011 and references therein). Other natural amorphous materials are formed by metamorphic processes. For instance, the so-called pyrometamorphic glasses form due to burning of fossil fuels such as coal and natural gas or other organic material (McCloy 2019 and references therein). The term pyrometamorphism, which defines a type of contact metamorphism, was originally proposed in 1912 by Brauns (Brauns 1912; Grapes 2010 and references therein) to describe a hightemperature/low-pressure metamorphism observed in schist xenoliths in trachyte and phonolite magma of the East Eifel area (Germany). The term buchite is used to define those partially or completely melted materials as a consequence of pyrometamorphism. Glasses from highly energetic events are formed in a completely different way, and with a completely different timescale than magmatic and metamorphic ones. For instance, impact glass formation is related to the collision of an extraterrestrial body on the surface of the Earth. Thus, they derive from shock metamorphism of existing silicate rocks and sediments. Impacts or airbursts (shock melting caused by a cosmic object exploding in the atmosphere) can be either natural or artificial, and both provide shock markers due to the extreme high temperatures and pressures. Among natural glasses that experienced extremely high temperatures in a very short time, there are also the fulgurites, formed following lightning strikes.

968

Cicconi et al.

Finally, biomineralization processes can produce amorphous materials. These are considered eco-friendly, and thus they have captured the attention of organic-/inorganic chemists and materials scientists (Cicconi and Neuville 2019 and references therein). Several siliceous marine organisms exhibit discontinuous, three-dimensional frameworks of short chains of SiO4 tetrahedra, bonded with apical hydroxyls. The low-temperature hydrated variety of silica, opal (SiO2∙nH2O), is a biomineral and displays different arrangements of amorphous SiO2, water, and cristobalite, and/or tridymite (see Cicconi and Neuville 2019 and references therein). Depending on the arrangements, it is possible to distinguish three opal types: i) opal-C (cristobalite); ii) opal-CT (cristobalite and tridymite); iii) opal-A (X-ray-amorphous opal). The latter can be further divided in opal-AN (e.g., hyalite) and opal-AG with an amorphous silica gel structure. In a “maturation process” (Ostwald ripening) opals are transformed as follows: Opal-AG→Opal-CT→Opal-C→ microcrystalline quartz (Skinner and Jahren 2003 and references therein).

METAMORPHIC GLASSES Pyrometamorphic glasses General features of pyrometamorphism. Pyrometamorphic glasses are an important class of amorphous materials summarized by Grapes (2010). The term ‘pyrometamorphism’ was originally used by Brauns (1912) to describe changes in contact zones (i.e., aureoles) between magma intrusions and country rock, where high temperature and atmospheric pressure result in particular mineralogical and morphological changes. These high temperature changes are often observed in xenoliths within later igneous rocks, near shallow magmatic intrusions, and within tuffs and breccias. Brauns assumed that pyrometamorphism must create melting in the heataffected rocks and vitrification on cooling. Other terms have been introduced but have fallen out of favor, such as optalic metamorphism, emphasizing the transient, quickly dissipated heat such as used when ‘baking a brick.’ Pyrometamorphized rocks tend to lose all volatiles, and melts recrystallize with anhydrous mineral assemblages, mostly oxides and simple silicates, but at least 60 different minerals have been reported from this prograde metamorphic process (Sokol et al. 2007). Some characteristic evidence of such processes include bleaching of carbonate rocks, reddening of iron-containing rocks, fusion of mineral grains, hardening, and similar morphological and chemical changes to those observed in earthenware ceramic and clay brickmaking processes. Heat for pyrometamorphic transformations need not come from contact magmatic heat, but also from other sources, such as combustion of coal beds and organic-rich sediments or even lightning. The Subcommission on the Systematics of Metamorphic Rocks (SCMR) of the International Union of Geological Sciences (IUGS) categorizes these effects as subvariants of contact metamorphism, namely ‘burning/combustion metamorphism’ and ‘lightning metamorphism,’ i.e., fulgurites (Callegari and Pertsev 2007). While contact and lightning metamorphism are highly localized, high-temperature changes in rock due to coal bed combustion can be regionally extensive. Well documented examples in the USA occur in the Grimes Canyon area, Monterey Formation, California (Bentor et al. 1981); the Powder River Basin, Wyoming (Herring and Modreski 1986; Cosca et al. 1989; Clark and Peacor 1992); and various coal-bearing areas of Montana and Colorado (Rogers 1918). The phenomenon of combustion metamorphism has been found to be quite common (Bentor et al. 1981; Sokol et al. 2007; Grapes 2010), including examples in China (de Boer et al. 2001), Mongolia (Peretyazhko et al. 2018), Indonesia, India, Russia (e.g., Chelyabinsk brown coal basin) (Sokol et al. 1998), Iran, Iraq, Jordan (Khoury et al. 2015), Israel e.g., Hatrurim basin (Ron and Kolodny 1992; Vapnik et al. 2007; Sokol et al. 2014), Czechia, Germany, England, Italy (Melluso et al. 2004), Mali (Svensen et al. 2003), Canada (Mathews and Bustin 1984; Canil et al. 2018), Venezuela, Colombia, New Zealand (Tulloch and Campbell 1993), and Australia (Rattigan 1967).

Non-Magmatic Glasses

969

Some terms are commonly used for pyrometamorphic rocks as follows. Hornfels forms where clay-rich rocks contact a hot igneous body, and partially or entirely recrystallize after in-situ melting, resulting in baked and hardened silicate + oxide systems. Clinker originally referred to altered or burned coal, but now refers generally to burnt brick-like rock which ‘rings’ (‘clinks’) when struck. Note that clinker is also the high-temperature processed calcium aluminosilicate used as the reactive precursor for Portland cement. These same ‘clinker’ minerals, e.g., belite sulfoaluminate, have been found in Israel in natural pyrometamorphic contexts (Sokol et al. 2014). Buchite, in contrast to hornfels, is largely vitrified from high heat applied to sandstones or pelites, resulting in hard, fused, and glassy material; the term is not restricted to coal fire lithologies, so in that case, should be referred to as ‘buchite clinker.’ Finally, paralava resembles artificial slag or basalt, is generally vesicular and aphanitic, sometimes shows evidence of flow, and formed from burning and melting of sedimentary rocks (shale, sandstone, marl) by proximal combusting coal seams. The distinction among these is based on both protolith and peak temperature, which can be ~400 to >1600 °C locally, resulting in a continuum from baked/burnt rock to fused-grained rock (clinker) to partially melted buchite, to wholly melted and partially devitrified rock (paralava), often all in the same area. Terminology is not uniformly employed, and in certain localities clinker is still called ‘scoria’ despite the different volcanic origin assumed from that term. Use of the terms ‘buchite’ and ‘paralava’ imply the observable presence of glass resulting from a quenched rock melt (Grapes 2010). Table 1 lists the chemical composition of different combustion glasses. Coal fires and spontaneous combustion. Coals in the Western USA, known to spontaneous combust, are typically lignite or sub-bituminous grade (Rogers 1918; Heffern et al. 2007). Spontaneous combustion occurs due to a complex process involving absorption of oxygen, such as through cracks, and oxidation of unsaturated hydrocarbons (Stracher 2007). The main exothermic reaction is that of carbon reacting with oxygen gas to form CO2 (Grapes 2010). These early reactions take place at temperatures as low as 80 °C, but this oxidation further generates heat until about 200 °C, where autogenous oxidation occurs, followed by ignition at 350–400 °C. Fine dust lignite, however, which has typically absorbed a large amount of oxygen, can ignite at temperatures as low as 150 °C (Rogers 1918). Moisture is said to exacerbate this effect, with escaping hydrogen-containing gases also playing a role. Other factors influencing the combustion reaction include coal factors such as rank and pyrite content, reaction factors such as particle size and temperature, and macroscopic factors such as air flow, overbedding rock type, and thermal conduction (Grapes 2010). Often areas can burn in the absence of additional oxygen, producing highly reducing conditions and the creation of coal ash with evidence of metallic iron (de Boer et al. 2001; Grapes 2010). Combustion of coal beds has been observed in modern times on the coast of Dorset, England; in the ‘Smoking Hills’ of Canada (Mathews and Bustin 1984); and at the ‘Burning Mountain’ (Mt. Wingen) in New South Wales, Australia (Bentor et al. 1981). The Smoking Hills are thought to have been burning for at least 150 years, while the Burning Mountain has been combusting for at least 15,000 years. The Posidonia shales in Germany, though not currently combusting, are thought to have been active c. 1000–1500 CE (Bentor et al. 1981). Many other examples are known (Kuenzer and Stracher 2012). Examples of creation of pyrometamorphic materials in the historic past are known from burning of a wide range of fossil fuels, from spontaneous combustion but also other natural or anthropogenic ignition (Kuenzer and Stracher 2012). Combustion in coal mining ‘spoil heaps’ has resulted in recent pyrometamorphic processes in Russia (Chelyabinsk) (Sokol et al. 1998) and Italy (Ricetto) (Capitanio et al. 2004; Stoppa et al. 2005) (Fig. 2). One of the interesting features of the assemblage in Russia is the presence of pure glassy carbon, known as shungite (Beyssac et al. 2002; Melezhik et al. 2004 ; Kwiecinska et al. 2007; Golubev et al. 2016). Additionally, minerals have been observed which were crystallized from the gas phase in cracks, including pure oxide, sulfide, silicate, and carbide single crystals.

Glass in Paralava

Khazakstan

Ricetto, Italy

3.08

8.87

7.97

0.15

1.67

21.40

0.58

3.56

0.37

F e 2O 3 tot

MnO

MgO

CaO

Na2O

K2O

P2O5

1.00

0.66

[1]

[3]

[4]

[5]

[6]

99.01

0.31

2.59

0.10

1.27

2.23

0.12

11.40

[1]

98.99

0.83

3.08

7.45

12.76

4.78

0.09

3.03

7.91

0.34

0.91

97.54

5.06

2.66

1.07

0.31

0.14

2.71

15.07

0.60

101.4

4.55

2.31

3.60

1.48

0.08

4.75

16.65

0.35

[7]

[8]

[9]

97.96

0.60

0.10

4.34

2.39

1.44

0.18

0.04

2.32

12.20

0.43

[4]

99.57

0.19

7.97

0.41

1.81

0.32

1.47

13.13

0.60

9.80

3.24

3.62

0.21

3.76

25.22

[7]

93.36

[10]

98.83

4.89

4.25

4.29

2.04

0.43

7.13

15.31

0.74

59.76

[11]

98.55

1.58

7.15

2.64

0.85

2.83

0.35

17.65

65.495

[10]

98.22

9.11

4.91

3.68

1.06

0.16

7.75

17.28

1.10

53.17

[4]

99.02

0.14

2.47

0.30

4.78

2.56

0.04

3.41

16.14

0.74

68.46

Biomass slag

[12]

96.85

0.07

1.71

14.27

0.64

4.52

2.53

0.16

3.09

2.96

0.71

66.19

Footnotes: [1] Melluso et al. 2004; [2] Grapes et al. 2013; [3] Sokol et al. 1998; [4] Cosca et al. 1989; [5] Grapes et al. 2009; [6] Piepjohn et al. 2007; [7] Peretyazhko et al. 2018; [8] Capitanio et al. 2004; [9] Bentor 1984; [10] Canil et al. 2018; [11] Coombs et al. 2008; [12] Thy et al. 1995.

[2]

98.59

101.08

TOT

Ref.

100.12

0.31

1.00

0.02

9.62

4.59

0.45

13.71

1.71 20.43

0.16

0.42

SO3

100.82

0.61

18.35

46.48

SrO

0.35

1.48

0.01

7.57

1.96

0.26

22.51

16.54

73.86

0.28

99.83

1.43

0.10

15.13

5.15

0.24

14.36

17.59

74.00

BaO

1.48

3.88

8.96

0.14

2.62

7.78

Russia, Chelyabinsk

0.38

USA, PRB Wyom.

0.94

China

20.05

Silicate paralava Canada

Al2O3

Khazakstan

TiO2

Mongolia (1) 67.42

Italy, Ricetto

69.63

USA, Grimes, Calif.

58.73

USA, PRB WY

58.88

Mongolia (2)

51.47

Canada, Shrimpton

49.50

New Zealand

44.86

Canada, Tranquille

60.97

Clinker USA, PRB WY.

44.40

Glass Botswana

SiO2

Paralava

Table 1. Chemical composition (wt.%) of different combustion glasses.

970 Cicconi et al.

Non-Magmatic Glasses

971

Figure 2. Pyrometamorphic material at Ricetto (Italy). Modified from Figure 1, Stoppa et al. (2005). MSA copyright.

Other processes fueling pyrometamorphism. It should be noted that pyrometamorphic rocks and glasses can be produced by high temperature burning using any fuel, not just coal. Many examples have been described where the fuel was biomass or organic material covered by sediment. This organic material can be deposited naturally, and subsequently be covered to ignite and burn in the subsurface under dry conditions, such as examples in Chile (Roperch et al. 2017) and Africa (Melson and Potts 2002; Svensen et al. 2003). Alternatively, organic deposits can be a result of human activity, such as archaeologically observed middens (Thy et al. 1995) or modern-day haystacks (Baker and Baker 1964), the burning of which produces glassy material. Organic gases can be fuels for rock burning as well. One of the most studied areas of pyrometamorphic rocks, the Dead Sea region in Israel, has been interpreted as having a pyrometamorphic origin, from a mud volcano and associated methane and hydrocarbon gas combustion (Sokol et al. 2007, 2010). Gas seeps and their associated ‘eternal flames’ from spontaneous combustion have played important roles in human history, especially in religious and mythological traditions. For example, the methane seeps known as Chimera in southwest Turkey was the site of the first Olympic fire in the ancient Greek world, and the site of a temple of Hephaestus (Vulcan) the god of fire and metallurgy (Hosgormez et al. 2008; Etiope 2015), and it still burns today. All kerogens of various grades, from bitumen to oil, are potential sources of fuel for creation of pyrometamorphic rocks and glass. Pyrometamorphic melts are also known to be produced from oilfield fire. Characteristic glasses, known as tengizites after the Tengiz oildfield in Kazakhstan, formed in this inferno (Kokh et al. 2016). Tengizites, essentially a type of paralava/slag, contain 59–69 wt.% SiO2, 7.3–9.7 wt.% Al2O3, 12.8–17.9 wt.% CaO, 2.0–3.7 wt.% MgO, 2.0–3.0 wt.% Na2O, 1.3–1.9 wt.% K2O, 11 km s−1; French 1998), with the surface will create an impact crater after a very short sequence of complex events, which can be summarized into three main stages: contact and compression, excavation, and modifications (Melosh 2011). The generic term impactite refers to the large variety of materials (rocks, melts) formed by the hypervelocity impact(s) of a large extraterrestrial body. Distinct materials are generated by the forces of a hypervelocity impact, starting with a shock wave (compression stage) and followed by decompression from peak shock pressures, with associated heat generation and material transport (excavation stage) (Reimold and Jourdan 2012). The post-shock heat causes the solid-state deformation and/or melting of the target crustal rock and even its vaporization, and the original material is entirely altered by the extreme heat and pressure regimes. Simulations of impact processes have established that the timescale of crater formation is extremely short, compared to many other geological processes, and is in the order of seconds to minutes for craters ranging from 1 to 100 km. Thus impactites will present very distinctive characteristics (French 1998; Stöffler and Grieve 2007; Stöffler et al. 2018). Impactite is the commonly used (and misused) word for all shocked, melted or vaporized materials as a consequence of a hypervelocity impact, and because of the confusion, a study group proposed a classification and a nomenclature of these materials, based on geological

Non-Magmatic Glasses

975

setting, texture, composition, and degree of shock metamorphism (Stöffler and Grieve 2007; Stöffler et al. 2018). The first grouping is based on the location of the materials, and “proximal impactites” is used for materials found in the proximity of the impact crater, whereas the term “distal impactites” refers to materials that do not occur directly in or around a source crater (i.e., distal ejecta). Further sub-classifications have been applied to proximal impactites, and according to Stöffler and Grieve 2007, proximal can be further divided into three subgroups: shocked rocks, impact melt-rocks and impact breccias. Depending on the peak pressure and the post-shock temperatures, both minerals and original rocks texture will present shock effects that allow identifying progressive stages of shock metamorphism. For instance, by increasing shock pressure, there are i) Planar Fractures (PFs) and Planar Deformation Features (PDFs) in minerals such as quartz, zircon and feldspars; ii) high-pressure quartz polymorphs (coesite, stishovite); iii) diaplectic mineral glasses (produced without fusion); iv) fused mineral glasses (produced with fusion), and v) melts (see Fig. 3; Reimold and Jourdan 2012). For example, quartz grains exposed to shock compression develop planar microstructures depending on the pressure range: PFs for pressure range of 5–8 GPa, and PDFs over the pressure range of 5–10 GPa to ~35 GPa. Shockinduced deformation in zircon grains have been reported as well, indicating shock pressures higher than 20 GPa (Ferrière and Osinski 2012). Impact diamonds have been reported as well in many impact sites. The transition from carbon (graphite) to diamond and lonsdaleite is around 13–15 GPa, with temperature in the range of 1300–2000 K (French 1998; Pratesi 2009). Figure 3 clearly shows that the pressure conditions for normal crustal metamorphism (regional, contact) differs completely from shock metamorphism, resulting in the production of characteristic features and materials. In normal crustal metamorphism, the range of temperature and pressure is around ≤1000 °C and 1–3 GPa, respectively, and rocks and mineral transformations occur in very long times (>105 years), thus approaching equilibrium (French 1998). On the contrary, shock metamorphism is a relatively instantaneous process, with peak pressures that reach >100 GPa, and temperatures much higher than 2000 °C (French 1998). Because of the rapid process, particularly of cooling, quenched amorphous and crystalline metastable phases are characteristic. For a detailed description of all shocked materials, readers are referred to the comprehensive work of Stöffler and Langenhorst (1994) and to Osinski et al. (2012).

Figure 3. Pressure (P)–temperature (T) diagram for normal (crustal) and shock metamorphisms. Ranges for silica polymorphs and shock markers are reported. Figure from Reimold and Jourdan (2012). Copyright MSA.

976

Cicconi et al.

In the following, we will mainly discuss the most homogeneous glasses created by hypervelocity impact events, i.e., the distal ejecta tektites, but we will also provide a brief overview of some other distal ejecta and proximal glasses. To distinguish proximal impact glasses, volcanic glasses, and distal ejecta tektites, Koeberl (2013) provides some characteristics that are distinctive of the distal ejecta and enable their recognition. Tektites are: i) amorphous and fairly homogeneous (no crystallites); ii) contain lechatelierite (amorphous SiO2); iii) occur within definite areas, called strewn-fields (SF) and are associated with a single source impact crater; iv) do not occur directly in or around a source crater (they are distal ejecta). Moreover, tektites are depleted in water (0.002 to 0.02 wt.%, at least an order of magnitude lower than the H2O content of volcanic glasses) and are highly reduced (almost all iron occurs as Fe2+) (Fudali et al. 1987; Koeberl 1994, 2013; Beran and Koeberl 1997; Rossano et al. 1999; Melosh and Artemieva 2004; Giuli et al. 2010a, 2013a, 2014a; Giuli 2017). Distal Ejecta. As a consequence of a hypervelocity impact, the uppermost (200 m) surficial target rock is melted and ejected. A small portion of this molten ejected material will fly far away from the source crater, and the materials are called distal ejecta (according to Montanari and Koeberl 2000, ~90 % of the ejecta are proximal i.e., deposited within five crater radii from the impact site). The flying melts are quickly quenched to form fairly homogeneous amorphous materials with typical shapes (e.g., splash forms) like spheres, teardrops, disc-shaped form, and are known as tektites (Fig. 4). A partial crystallization of primary microlites/crystallites (e.g., clinopyroxene or Ni-rich spinel) upon cooling could occur, and the material formed is called microkrystite (Glass and Simonson 2013 and references therein). Distal ejecta deposits (or air-fall beds) are deposited far away from the source crater and can be divided into two types: i) tektites and microtektites, and ii) spherule beds (Osinski et al. 2012). A more enigmatic kind of distal ejecta found on Earth consists of glassy materials, not volcanic in origin, but not having spherical shapes and not classified as tektites. Examples of these enigmatic glasses are Libyan Desert Glass, and Darwin glass (Glass and Simonson 2013). The reasons behind the formation of spherules and tektites remain poorly understood, and no widely accepted model or evidence has been found to explain why just a few impacts form large amounts of high-speed ejected glasses and why only a few provide tektites (Howard 2011). Thus, tektite formation must require specific impact conditions (see below). On Earth, impact craters are not easily found (190 confirmed impact structure as of July 2019; Earth Impact Database 2019) because their morphologies have been modified by hydrothermal and chemical alteration and by tectonic processes. Thus, most of the impact craters which occurred on Earth have been subsequently destroyed or covered. For instance, the Chicxulub impact structure is located beneath ~1 km of sediment and half offshore of the Yucatan Peninsula. Until 1991, the year of the discovery, the only proof of a connection between end-Cretaceous mass extinction (K–Pg boundary layer) and a possible cataclysmic impact was the worldwide occurrence of distal ejecta horizons. Hence, sometimes, distal ejecta are the only remaining witnesses of large impact events, and they provide essential information regarding planetary processes when found in the stratigraphic record. The importance of air-fall beds has been compared to the importance of volcaniclastic layers (Glass 2016). When dealing with distal ejecta, or in general, with glass spherules, the most critical point is to gather enough evidence to rule out the volcanic origin. These pieces of evidence are usually called ‘impact markers’ and include chemical, isotopic, and mineralogical marks that indicate the involvement of a cosmic body. Examples of markers that indicate an extraterrestrial contribution

Non-Magmatic Glasses

977

Figure 4. Australasian tektites with various shapes; dumbbell, teardrop, and fragments. Dumbbells are formed by the rapid rotation of melt droplets ejected into the atmosphere. When the rotation is high enough, the dumbbell is broken to form teardrops.

are the elevated content of siderophile elements (Ir, platinum group elements, PGE), the occurrence of shocked minerals and/or Ni-rich spinels and/or impact diamonds, and atypical isotope ratios. The complete list of the well-established or new ‘impact markers’ is beyond the scope of this chapter, and the readers are referred to the exhaustive contribution of Goderis et al. (2012).

Tektites and microtektites Tektites are small, typically dark, glassy objects that have been transported through the atmosphere hundreds to thousands of kilometers from the impact site, and are found only in some regions of the Earth’s surface, called tektite strewn fields (SF). Tektites are generally chemically homogeneous, Si-rich glasses of various sizes (usually >1 cm), with typical aerodynamic shapes and very characteristic surface features (Fig. 4). Microtektites are microscopic tektites, with a diameter 10,000 km) from the hypothetical source crater. Microtektites, like tektites, show various morphologies, with oblate/prolate spheres, dumbbell- and teardrop-shaped, and may contain lechatelierite and vesicles. However, microtektites display a larger range of colors than tektites, with the majority being transparent, colorless, or greenish/yellowish. Trace elements and isotopic abundances confirm that microtektites are genetically related to tektites in the associated strewn field (Frey 1977). However, microtektites usually show a wider compositional range than tektites, even if generally they are similar to the tektites from the same strewn-field (Table 2). For example, it is possible to recognize IC and AA microtektites based on their alkaline earth ratios (MgO/CaO). There is a particular sub-group of AA microtektites that presents notably high Mg contents (denoted HMg; up to 24 wt.% MgO) and lower SiO2 contents than “normal” AA-microtektites, with a bottle-green color and highly eroded state (Glass and Simonson 2013). A detailed study of major and trace elements of >100 microtektites from the different strewn fields has been performed by Glass et al. (2004), who found, besides the HMg microtektites, some glasses with high Ni contents (denoted HNi; up to ~470 ppm). HMg microtektites have been found also in the IC strewn-field. The study of the trace elements in microtektites also confirmed that these small distal ejecta derive from the upper continental crust. Everything seemed to point to microtektites being just smaller tektites. However, lately, some differences have been found, namely on the Fe oxidation state of North American microtektites (Giuli et al. 2013a). These authors have shown that some North American microtektites present higher Fe3+/Fe2+ ratio (up to 0.61), compared to the respective tektites, implying that different formation mechanisms are involved for such small objects. Interestingly, for these microtektites, there is a positive correlation with the distance from the known source crater, and more oxidized conditions are reported for longer distances. This seems to be in contrast with the data available on other microtektites recovered at much further distances (i.e., AA microtektites). Because of the relatively limited information available on tektite/

Non-Magmatic Glasses

981

microtektite formation mechanisms (see below), it is difficult to provide an interpretation of those data. Do microtektites register another “path” of the ejecta, or perhaps a different timeframe? Do they have different cooling rates? Further experimental studies, along with modeling and further ejecta discoveries, will help to answer these questions, and probably the broader question of “how do distal ejecta form?”. Other distal ejecta. Besides tektites and microtektites, it is worth mentioning the occurrence of many other spherule-associated layers across the world. For example, a clinopyroxene-bearing spherule layer (cpx-spherules) has been traced in many locations on Earth. The cpx-spherules associated layer is enriched in Ir and is ~10–20 ka older than the North American microtektite one (Glass et al. 2004 and references therein). These spherules have been associated with the Popigai complex crater (Siberia, Russia), an extremely large structure (~100 km diameter) of 35.7 ± 0.2 Ma (Melosh 2011). As mentioned before, the most notorious and studied distal ejecta deposits are the K–Pg (formerly KT) spherule ones, associated with the 170–180 km Chicxulub crater (Yucatan, Mexico). The impact event responsible for this crater had enough energy to distribute ejecta worldwide. The small K–Pg spherules (100–500 mm), that resemble microtektites, were first detected in the Cretaceous–Paleogene K–Pg layer in Gubbio (Italy) (Alvarez et al. 1980). K–Pg distal impact ejecta horizons are associated with Ir enrichments, siderophile element anomalies, shocked minerals, and high-pressure polymorphs (shocked quartz grains, coesite and stishovite). K–Pg spherule layers have a global geographical extension with more than 350 sites identified, but because of the poor preservation of the claystone at the K–Pg boundary, in the early 80s there were some debates as to the origin of these spherules, with some authors supporting an impact hypothesis (e.g., Smit and Klaver 1981), and others attributing an authigenic origin for the spherules (e.g., Izett 1987). A few years later, many authors, by studying many K–Pg spherules, and in particular the Si-rich spherules preserved at the K–Pg layer at Beloc (Haiti), provided clear evidences of an impact origin, based on geochemical data, enrichment in platinum group elements, the presence of lechatelierite and shocked quartz grains (Bohor 1990; Sigurdsson et al. 1991; Koeberl 1992b; Koeberl and Sigurdsson 1992). Despite the alteration of some deposits, according to Morgan et al. (2006) there is a correlation between shock markers and paleodistances from the impact site, and in particular, the number and size of the spherules and shocked minerals are inversely proportional to their distance from Chicxulub. This evidence has been used to confirm the occurrence of a single highly energetic impact event related to the formation of the K–Pg spherule horizons, and to provide insights on the obliquity of the projectile. Among the proposed impact-related Cenozoic distal ejecta layers, there is one horizon related to a hypothesized impact event, that according to Firestone et al. (2007), may have occurred at the beginning of the Younger Dryas (YD ~12.8 ka). In this case, the impact event is not strictly related to a collision with the Earth’s surface, but (allegedly) to an airburst, that is a shock wave caused by the explosion of a cosmic object in the atmosphere (such as the wellknown 1908 Tunguska airburst, Siberia; e.g. Melosh 1989 and references therein). The Younger Dryas boundary is a 1900 K and pressure from 10 to >30 GPa (Pratesi et al. 2002; Gomez-Nubla et al., 2017; Cavoisie and Koeberl 2019). However, while high pressure occurred, most probably during melting and ejection, the quenching of the molten material happened quickly at atmospheric pressure (Greshake et al. 2018). The occurrence of a meteoritic component suggests the impact of an extraterrestrial object and not an airburst. This seems to be confirmed by recent work by Koeberl and Ferrière (2019) that reports the discovery of shock markers (e.g. PFs and PDFs on quartz grains) in bedrock samples recovered in the Libyan Desert Glass strewn-field, and the suggestion of a deeply eroded impact crater in the area. Moreover, the detection of reidite, a high pressure (>30 GPa) polymorph of zircon ZrSiO4, indicates that the pressure–temperature regimes are in line with a crater-forming impact (Cavoisie and Koeberl 2019).

984

Cicconi et al.

Another impact glass that cannot be referred to as tektite is found in a strewn-field of ~400 km2 in western Tasmania (Australia): the Darwin glass. The age of this glass, estimated by Ar–Ar methods, is 816 ± 7 ka (Lo et al. 2002), thus very close to the Australasian tektites, although their major and trace element compositions are very different, indicating that the temporal association is coincidental. The Darwin crater, a small (~1.2 km) simple impact crater formed in sedimentary target rocks, was discovered in 1972 and proposed as the source of Darwin glasses (Ford 1972; Fudali and Ford 1979). Howard and Haines (2007) carried out a detailed petrographic study of the crater-filling samples, but no conclusive shock markers have been found (e.g., PDFs in quartz grains). Nevertheless, the geochemistry of the target rocks and glasses, the location of the crater, and the glass distribution (Darwin strewn-field) all point to the Darwin crater as the source of the ejecta. Darwin glasses occur in an area larger than 400 km2, with distances of at least 20 km (Howard 2011) from the putative Darwin crater, thus belonging to the distal ejecta group. Glasses generally occur as irregular centimeter-sized fragments, or masses, even if small splash-forms (spheres and teardrops 70 wt.% SiO2), and glasses strongly depleted in silica ( Te, is due to the non-bonding electrons, which form an intermediate level between the bonding and antibonding levels.

Figure 7. Arsenic selenide glasses, inside the melting ampule and cut samples after melting at 600 ºC for 18 hours (Photo Topper).

Figure 8. UV–Vis–IR transmission range of a selection of different glass systems, modified after data from suprasil, SiO2, d = 10 mm (Heraeus Quarzglas GmbH & Co. KG 2016); ZBLAN, d = 2 mm (Ledemi et al. 2013), As2S3, d = ca. 2mm (Verger et al. 2012) and Ge10As15Te75, d = 1.4 mm (Yang et al. 2010).

The evolution of the structure in chalcogenide glasses is best understood by first considering the glass formed by Se alone. As a group VI element, selenium, like oxygen, has six outer electrons, of these, two are bonding, forming strong covalent sigma-bonds, while the other four electrons form two lone pairs (Lucas et al. 2018).The two bonds and two lone electron pairs can be viewed as a pseudo-tetrahedra, linking via corners to form a glass. Amorphous selenium forms thus a one-dimensional glass consisting of puckered chains with

Glass as a State of Matter

1051

some 8 member rings, interacting via van der Waals forces with one another, resulting in a bulk structure resembling a bowl of spaghetti (see Fig. 3; Lucas et al. 2018). Due to the lack of crosslinking and the rotational freedom of the sigma bonds, selenium and sulfur glasses are very soft and the Tg might lie below room temperature, leading to the claim of having formed the first inorganic flexible bulk glass (Yuan et al. 2018). The difficulty in forming a glass from tellurium alone is most probably due to the more metallic character of tellurium. This character leads to a delocalization of the electrons that form lone electrons pairs in sulfur or selenium and the formation of a metallic π-bond along the chains. The chains are more stringent, losing the rotational freedom, and instead of a structure that can be described by the random coil model, the material crystallizes. In ternary Ga–Ge– Te, the lone pair deficient Ga can trap the mobile electrons of the Te. Similarly, as shown by Lucas and Zhang (1990), addition of halogens (such as Cl, Br or I) can eliminate the π-bonding as the halogen ions “capture” the free electrons of the Te-chains. Thus, were born the TeX glasses, which show a transparency as low as 20 µm. These glasses are part of the appropriately named chalcohalide family (Sanghera et al. 1988). Two-dimensional chalcogenide networks consist of the higher coordination number group V elements, typically arsenic or antimony, and one or more of the chalcogen ions S, Se, or Te. These 2-dimensional chalcogenides possess higher glass transition temperatures making them more appropriate for technical applications. The divalent chalcogenides are usually linked to only two direct neighbors. Take As2Se3 as an example, the network is formed of pyramidal AsSe3 units with a lone pair of electrons on the As-atoms. The same structure would arise if S was substituted for Se. If the composition is chalcogen-rich, the pyramidal AsSe3 units are linked by Se chains. AsxSey can take on a more rigid structure when the arsenic content exceeds the stoichiometric quantity of As2Se3, leading to the formation of As4Se4 cage structures and the presence of As–As homopolar bonds (King et al. 1995). The addition of group IV elements, most frequently germanium, increases the connectivity of the network to 3-dimensions. GeSe2 forms a vitreous network of corner sharing GeSe4 tetrahedra analogous to the SiO4 tetrahedra in vitreous silica. The presence of the tetravalent element increases crosslinking further resulting in an increased glass transition temperature. These glasses display more suitable mechanical and thermal properties for various applications compared to their lower dimensional counterparts (Lucas et al. 2018). Of all combinations, binary sulfides and selenides of As and Ge have attracted the most attention on account of their large glass forming regions. The ternary Ge–As–Se system provides an illustrative example of the multi-dimensional bonding accessible to chalcogenides that allows great compositional flexibility. If the composition is selected to have excess chalcogen, the bonding consists of divalent Se atoms forming chains which are then crosslinked three-fold at the As atom sites and four-fold at the Ge atom sites (Zallen 1998). Given this flexibility in network formation, chalcogenide glass compositions can be readily tailored to have specific properties. Such as for example the glass Te20As30Se50 (TAS), was developed for the best combination of large IR transparency, durability and good mechanical properties for use in IR spectroscopy. TAS glass has been optimized to develop optical fibers for medical and biological applications (Lucas et al. 2018). Interesting are problems related to the structure of nonstoichiometric phases which, while well known for crystals, do not appear to be a significant problem in other glasses (Gaskell 1982) Manufacturing high purity chalcogenide glasses, free of impurities including oxygen and water, has received much attention for undisrupted infrared transmission (King et al. 1995; Seddon 1995; Danto et al. 2013). The melting of high-quality chalcogenide glasses is typically carried out by purifying the components, sealing them off in an ampoule under vacuum, melting in a rocking furnace to homogenize the melt, quenching the melt, and annealing the glass in the ampoule. Melting under a controlled atmosphere furnace is another preparation route. Once formed, the chemical durability of chalcogenide glasses is quite good (Lucas et al. 2018).

1052

Möncke et al.

Chalcogenide glasses can be formed by molding, extrusion and drawing into fibers from a preform (Lucas et al. 2018). The window of stability, ΔT = Tc − Tg, must also be carefully considered when processing these glasses for applications, which typically demands heating the system above the glass transition temperature in order to achieve the viscosity required for the particular forming process (Musgraves et al. 2014; Svoboda and Málek 2015). Chalcogenide glasses possess a relatively low glass transition temperature which presents additional challenges for implementation in devices and instruments (see also Table 3). Additionally, they have displayed structural relaxation below their glass transition leading to aging effects where the properties of the glass change with the passage of time (Jensen et al. 2012). A variety of photoinduced phenomena take place as a result of the lone electrons on the chalcogen atoms (Zakery and Elliott 2003). Indeed, this nature was first employed for use in Xerox machines and later DVDs (Zallen 1998; Wuttig and Yamada 2007).

4.2 Fluoride glasses Fluoride glasses challenge some traditional concepts of glass formation. Fluoride glasses—like metallic glasses—possess high crystallization tendencies, this time due to their strong ionic bonds and the very low viscosity of their melts (Ehrt 2015). Coming from oxide glasses, it was natural to describe glass formation in fluoride glasses based on structural criteria, that is, by defined polyhedra and their connectivities resulting in a random threedimensional network (Poulain et al. 1992). In this scheme, glass forming ability is correlated to the possibility of shaping a disordered network of relatively small polyhedra (trigonal or tetrahedral). Applying the same approach to fluoride glasses is challenging, since the network forming polyhedra may be much larger, such as AlF6 octahedra (Ehrt 2015), ZrF7 or HfF8 polyhedra. Thus, a contrary approach was to describe glass formation in fluoride systems as random ionic packing (Poulain et al. 1992). In this description, lager cations (Pb2+, Ba2+, Na+ etc.) take the place of an anion in a random packing (Poulain and Maze 1988). The authors of this study emphasize that the atoms are not fully ionized, and binding electrons are located in the molecular orbitals that link neighboring atoms. In fact, the minimization of electrostatic energy leads, in most cases, to the minimization of the interatomic distances and is consistent with a very dense packing. In these conditions, the two models (i) random packing and (ii) network, reflect the different and complementary aspects of the same material. It appears that glass formation in fluoride systems requires at least one cation of mediate field strength (e.g. Al3+, Be2+, Zn2+, Zr4+, Hf4+ or La3+) and that multicomponent glasses are often more stable than binary glasses, following the well-known confusion principle as it has been formulated for metallic glasses (see Section 3; Poulain and Maze 1988). The transparency window of fluoride glasses depends naturally on the cations within the glass, high field strengths ions such as Be2+ or Al3+ provide in combination with fluorides a very high transparency in the UV, at even highe energies than pure SiO2 (Ehrt 2018), while heavier, more polarizable cations such as Hf4+, Zr4+ or Pb2+ will lower the intrinsic absorption edge. The wide transmission window is even more pronounced on the IR side of the spectrum, as the vibrational stretching modes of ZrF4 are much lower in energy than of Si–O (Möncke and Eckert 2019; see Fig. 8). Depending on the sample thickness and composition, heavy metal fluoride glasses can be transparent beyond 7 µm in the IR. The presence of lighter cations can reduce the infrared window. The IR edge shifts to higher energies in the series: AlF3 < ZrF4 < HfF4 < ScF3 < GaF3 < InF3 (Poulain et al. 1992). The transition temperature is relatively low, starting around 200 °C for alkali free glasses but reaching 500 °C in some alkali and barium containing glasses (see also Table 3), while the thermal expansion is relatively high, ranging for most fluoride glasses between 140 to 200  10−7 K−1 (Poulain et al. 1992). In fluoride glasses, the melting temperature Tm and transition temperature Tg can often be correlated by the 2/3 rule (Poulain et al. 1992).

Glass as a State of Matter

1053

For most fluoride glasses, atmospheric moisture is far less detrimental than exposure to liquid water. Some fluoride glasses such as certain fluoroaluminate and fluoro–indate glasses are even relatively stable when immersed in water (Poulain et al. 1992). BeF2 glasses have very low refractive indices and high partial dispersion (see Fig. 9).

nD  1 ) of various glass nF  nC systems modified after Vogel and Hartmann (Vogel 1992, Hartmann, Jedamzik et al. 2010). Figure 9. Refractive index nD and dispersion coefficient or Abbe number νD ( D 

4.2.1 BeF2 glasses as a weak model of SiO2. Interestingly, Goldstein’s condition of glass formation is also fulfilled for BeF2 (Vogel 1992), which was therefore studied for a while as a model compound for isomorphous crystalline and glassy SiO2. Exploiting the weaker binding forces in the fluoride compared to the oxide compound, and the divalent Be compared to tetravalent Si, many properties were more easily accessible, including the viscosity and melting temperature, as well as other transport related processes such as crystallization or diffusion, which are subsequently accelerated in Be–fluoride glasses. For example, BeF2glasses have 21% homopolar bonding which is less than half the value than the 50% expected in the bonds of silicate glasses (Mackenzie 1960). Just as BeF2 can be seen as a weak bonding model of SiO2, alkali–beryllium fluoride glasses can be seen as doubly weakened models of the respective alkaline earth silicate melts (Vogel 1992). BeF4 tetrahedra form the main glass building units, just as SiO4 tetrahedra do in silicate glasses (Wright et al. 1989). See for comparison the schematic in Figure 12. Befluoride glasses show similar regions of immiscibility, with asymmetrical immiscibility gaps as binary alkali or alkaline earth silicate glasses, but the extent of phase separation is much more pronounced, by up to an order in magnitude for the fluoride systems, thus starting the research in phase separation of glasses (Vogel 1992). Fluoro–beryllate glasses are known for their low refractive index and low dispersion. The big drawback of this glass system however is the toxicity of beryllium ions. Therefore, much research focused on the development of other, Be-free, fluoride glasses.

1054

Möncke et al.

4.2.2 Fluoroaluminate glasses. The earliest reports we found on fluoroaluminate glasses based on AlF3 and MF2 (M = Mg, Ca, Ba) were written by Videau et al. (1979) and by Ehrt et al. (1982). A chain-like structure based on AlF6 octahedra was suggested, based on results from NMR and vibrational techniques. According to Poulain and Maze (1988), only very few AlF3-based glass systems can be prepared in bulk with a thickness exceeding several mm or and only few systems even allow the drawing of fibers. The few fluoride compositions that allow processing include: AlF3–BaF2–YF3–CaF2 (Y– ABC), (Kanamori et al. 1981); AlF3–BaF2–YF3–ThF4 (BATY) (Poulain et al. 1981); CdF2–LiF–AlF3–PbF2 (CLAP) (Tick 1985); AlF3–NaF–MgF2–YF3–ZrF4 (Izumitani et al. 1987) and CaF2–AlF3–MgF2–BaF2–YF3–SrF2 (CAMBYS) (Kucuk and Clare 1999). As already realized by Ehrt et al. in the early 1980s (Ehrt et al. 1982, 1983; Ehrt and Vogel 1983; Ehrt 2015), the very high crystallization tendency of pure fluoroaluminate glasses can be drastically decreased by adding small amounts of phosphates (1–2 mol%). Fluoroaluminate glasses with 3–15 mol% phosphates can be produced in large scales for applications in high performance optics, and as active laser and amplifier glasses. Contrary to fluoride–phosphate or fluoro–phosphate glasses with higher phosphate content, these fluoride rich glasses are dominated by a fluoroaluminate glass structure and properties (Ehrt et al. 1982, 1983; Ehrt and Vogel 1983; Ehrt 2015). The low phosphate content helps to stabilize the glasses and prevents crystallization, while asserting only a marginal impact on the optical properties. See Section 5.1.7.3 for more details on FP glasses. 4.2.3 Zr–Ba–La–Na–fluoride glasses (ZBLAN). The more accidental discovery of the first fluoro–zirconate glasses around 1974 lead to increased research into heavy metal fluoride glasses (HMFG) and the development of the first industrially produced and traded vitreous fluoride glasses and fibers. Most fluoride glasses require fast cooling or quenching during preparation and therefore offer limited potential for applications. One system that can be processed and that allows fiber drawing are the ZBLAN type glasses (Poulain and Maze 1988). Like HfF4 or ThF4 based glasses, systems based on ZrF4 were studied for their use in infrared optical materials. ZBLAN stands for a complex composition such as 60ZrF4–20BaF2–4LaF3–6AlF3–10NaF (Poulain 1981). Zirconium fluoride does not exist in the vitreous form, however, together with LaF3, ThF4, BaF2 or SrF2, binary glass can be prepared by fast quenching of the melt (Poulain et al. 1992). In ZBLAN, ZrF7–8, AlF6 and LaF8 are the glass-forming polyhedra, whereas Ba2+ and Na+ are classical modifier cations. LaF3 can be substituted by other, optically active, RE elements allowing the preparation of optical amplifiers or fiber lasers which show more emission lines than silica glass (Miyajima et al. 1994; Lucas et al. 2018). In order to minimize devitrification on reheating, the composition has to be adjusted, and an increasing number of glass components are added, according to the already mentioned “confusion principle” (Poulain et al. 1992). Hafnium can substitute for zirconium, but despite many similarities, there are some differences in the optimized glass composition seen between fluoro–zirconate and fluoro– hafnate glasses (Poulain et al. 1992). It can be shown, that some glass forming principles such as the similarity between the structure in the melt and the glass, as postulated in the definition by Zanotto and Mauro (2017), is also valid for fluoride glasses. The coordination number and bond length of the crystalline phases are close to those observed in the glassy phase of many fluoride systems that contain the same cations, thus retaining the same short-range order between the glass and the crystal. For example in fluoro–zirconate glasses, zirconium cations are usually coordinated to eight F atoms while the coordination number of Ba2+ varies between 10 and 12 depending on composition (Poulain et al. 1992).

Glass as a State of Matter

1055

While one viewpoint describes the glass structure as a random network of ZrF8, AlF6 and LnFn polyhedra, that share corners and edges, trapping large cations, e.g. Na+ or Ba2+ between them, another viewpoint focuses on a random packing of large F− ions and Ba2+ ions, between which the smaller cations Zr4+, AI3+ or Zn2+ are randomly inserted. This approach was especially successful when discussing mixed fluoride–phosphate glasses as laid out in the review paper by Möncke and Eckert (2019). For more on mixed fluoro–phosphate and fluoride–phosphate glasses see Section 5.1.7.3.

4.3 Other ionic and molecular glasses Fluoride glasses are the most important of the halogen glasses, though other systems with high fractions of chloride (Chen et al. 2018) or iodide (Lefterova et al. 1997) have been prepared successfully. While some simple systems form glasses (Mackenzie 1987), mixed components are studied more often for ion conduction, e.g. in phosphate, borate or tellurite halogen glass systems (Lefterova et al. 1997). Other salt-like glass systems include mixed alkaline earth nitrates (Duffy and Ingram 1968; Ingram and Lewis 1974) or sulphates (Thieme et al. 2015; Nienhuis et al. 2019) which can be formed by relatively slow quenching from the melt (Gaskell 1982). The ZnSO4– K2SO4–NaCl system for example has been studied in the context of immobilization of salt rich nuclear waste (Nienhuis et al. 2019). Contrary to fluoride glasses, no strong anion-cation complexes are formed. The large ions Cl− or I−, like multiatomic anions such as SO42−, NO3− or acetate (H3C–COO−) are charge balanced and crosslinked to cations without forming a threedimensional glass network, thus coining the term “molecular” glass (Gaskell 1982; Thieme et al. 2015; Nienhuis et al. 2019).

4.4 Nitride glasses In nitride glasses, oxygens ions are replaced by nitrogen ions, which form similarly strong covalent bonds. However, nitrogen ions are in group V of the periodic table and can form three bonds, resulting in a higher degree of crosslinking and thus a stronger glass network when compared to the two bonds oxygen can provide. This extra bond results in a higher Tg, and higher mechanical strength in nitridified glasses compared to the respective oxide glasses (Larson and Day 1986; Loehman 1987; Becher et al. 2011). For each nitrogen bond, the maximal linkages of silicate tetrahedra can increase by +1, and nitridification of SiO2 can give rise to previously unknown QSi4+m units—even though the silicate tetrahedron retains its four-fold coordination (see Figs. 10 and 11). The factor, +m, describes the additional nitrogenbridged silicate units that form at the fully linked nitrogen atoms. Koroglu et al. (2011) shows evidence for some SiON3 and possibly SiN4 species in nitrogen-rich Y–Si–Al–O–N glasses. Due to the increased crosslinking of nitrogen ions compared to lower valent anions, high melting temperatures are often needed in the preparation. For example, the melting temperature of Si3N4 is Tm = 1900 °C, which poses a significant strain on the crucible material, which in turn might dissolve into the glass or react with the nitridification agent (Wójcik et al. 2018a,b). Refractive index and polarizability are also higher for nitride than for oxide glasses (Möncke et al. 2019). In the review by Becher et al. (2011), several studies are cited that indicate that DC conductivity and electrical constants increase in nitride containing systems, a fact, that was also discussed by Mascaraque et al. (2013) and Wójcik et al. (2018a,b). 4.4.1 Alumo-silicate based oxynitride systems SiAlON. The most studies of oxynitride glasses are based on silicate and alumo-silicate systems (Loehman 1987; Becher et al. 2011; Ali et al. 2015; Garcia et al. 2016). The early research was driven by Si3N4 and other nitridebased ceramics, and glassy phases within the grain boundaries of Si3N4 (Jack 1976). Typical systems include MSiON and MSiAlON where M stands for any alkaline earth or rare earth element, though yttrium can be found in these glasses as well.

1056

Möncke et al.

Figure 10. Depiction of basic glass forming units in silica–oxynitride glasses, after Becher et al. (2011). (a) bridging nitrogen linking three silicate tetrahedra; (b) charge balanced bridging nitrogen linking two silicate tetrahedra—being essentially a mix of the bridging and a non-bridging oxygen atom; (c) a double bonded two fold coordinated nitrogen, having a higher bond equivalent unit than a single bond, but connecting only two silicate tetrahedra and having no need for charge balance; (d) a classical Q3 unit with three bridging and one non-bridging oxygen ion; (e) the corresponding Q3O(N1) unit with three bridging oxygen and one bridging nitrogen ion that also has one non-bridging site at the nitrogen ion that need to be charge balanced by one modifier cation; (f) Q3O(N2) unit with three bridging oxygen and one doubly bridging nitrogen ion which effectively has the connectivity of a Q5 unit, linking 5 silicate tetrahedra to the central silicate unit.

Figure 11. Depiction of oxynitride phosphate glasses (Larson and Day 1986; Bunker et al. 1987; Muñoz et al. 2013).

Good results have been obtained by dissolving nitride components Si3N4, and / or AIN in a silicate melt. The first prepared oxynitride glass was made by Mulfinger et al, who studied the dissolution of nitrogen through bubbling N2, H2/N2 or NH3 in silicate and borate melts (Mulfinger 1966). However, using this method, he was only able to retain less than 1 wt. % of nitrogen in the glasses. As has been shown since, other methods give much better results, for example, when an oxide glass is re-melted with the addition of Si3N4 or other metallic nitrides. Another method would be the addition of powdered metallic alkaline earth elements while maintaining an N2 or NH3 atmosphere. N0 or N3+ are reduced in a redox reaction, oxidizing the metals to the corresponding nitrides, which in turn will result in an oxynitride glass that sustains a significant nitride fraction (Loehman 1987; Becher et al. 2011, Ali et al. 2015; Garcia et al. 2016). Addition of Si can also help with nitrogen retention and prevents foaming from the melt, as it helps to retain reducing conditions in the melt (Baik and Raj 1985; Loehman 1987). While alkaline earth, rare earth, and lithium oxide are stable in silicate based oxynitride glass, heavier alkali oxides may decompose in nitride melts according to the following example of the reaction of potassium oxide in an oxy-nitride silicate melt (Loehman 1987): 12 K2O(glass) + Si3N4 → 3 SiO2(glass) + 2 N2 + 12 K(g) (g): gaseous, AG (1923 °C) = −733 kJ

Glass as a State of Matter

1057

In contrast to most other glass systems, the concept of corresponding salt pairs is used for the description of MSiON glasses. A four-component system such as Si–Al–O–N, is represented as a square plane with the corners represented by the two metal ions (Al and Si) and two anions (N and O). For multicomponent systems with three cations, the five-component system can be represented by a 3D Jänecke prism, where the oxide ternary is plotted at one end, and the corresponding nitride ternary on the other end of the prism (Hampshire 2003). Instead of mol % the components are given in at% or as equivalent fractions, e O/N. Other techniques for the preparation of oxynitride silicate glasses with high nitrogen levels include hot isostatic pressure for bubble-free YSiAlON glasses, or sol–gel preparation (Loehman 1987). 4.4.2 Phosphate based oxynitride systems. The phosphate oxynitride system behaves quite differently from the silicate system. This is partially because of the high chemical solubility of nitrogen in phosphate melts. This effect causes the often unwanted re-boil effect, when in seemingly homogenous phosphate melts, suddenly myriads of tiny bubbles form during cooling, since the chemical solubility of nitrogen is so much higher at melting temperatures than at lower temperatures (Von Jebsen-Marwedel 2011). Preparation of P-based oxynitride glasses differs from alumina-silicate oxynitride glasses in several aspects. For one, thermal ammonolysis at relative low temperatures is the preferred preparation method (Bunker et al. 1987; Muñoz 2011). NH3 is bubbled through the melt at temperatures below 800 °C, resulting in oxynitride phosphate glasses with up to 20 at% nitrogen. In order for this technique to work, it is important to control the viscosity of the melt, e.g. by selecting compositions chosen to be close to the eutectic of the respective metal oxidephosphorus pentoxide, and having low field strength cations, such as alkali metals (Loehman 1987; Muñoz 2011). The following liquid–gas chemical reaction was postulated by Munoz: MPO3 + xNH3 → 3 MPO3-3x/2Nx + 3x/2 Nx+ 3x/2 H2O Early reviews on nitrogen rich oxynitride systems appear in the 1980s. Marchand et al. (1983) describes alkali P–O–N systems prepared by the reaction between alkaline polyphosphates with ammonia at 700 °C. Up to 25 % nitrogen was retained in the glasses. The use of ammonia however leads to a water rich glassy phase, that can be ascribed to the H–P–O–N system. Isotopic substitution of 17O-NMR studies on NaPON glasses allowed to distinguish non-bridging oxygen atoms on PO4 and PO3N or PO2N2 sides (Muñoz et al. 2013). Elemental analysis is important since nitrogen incorporation can vary significantly, depending on composition and preparation technique. 4.4.3 Mixed anionic systems. Recently, Mascaraque et al. (2015) studied fluoride containing LiOPN glasses, 30 years after earlier attempts to introduce nitride into fluoride (oxide) systems by Vaughn and Risbud (1984) and Fletcher et al. (1990). Mascaraque et al. (2014) also prepared a thio-phosphorus oxynitride glass electrolyte, showing the versatility of glass formation on the anion side. 4.4.4 Applications of oxynitride glasses. In contrast to chalcogenide and fluoride glasses, which found their niche for high specialty applications in optics and photonics, such applications for bulk oxynitride glasses are still not fully developed. Preparation of larger batch sizes and processing of the melts is difficult and so far, improving mechanical properties in silicate glasses is often easier. However, applications that show promise are the fusing of high strength high temperature ceramics, exploiting the natural tendency of Si3N4 to occur in grain boundaries (Loehman 1987). Another application might be protective or active coatings on thin films (Ali et al. 2015).

Möncke et al.

1058

5. SIMPLE INORGANIC OXIDE GLASSES Non-silicate oxide glasses are technologically very important, as they provide a combination of properties that are hard to derive when using only silicate glasses. This is not only supported by the early systematic studies by Otto Schott (Kühnert 2012; Chopinet 2019), but also by the prominent role non silicate glasses have in the general understanding of glass formation (Zachariasen 1932). Many of today’s products are based on all type of oxide glasses, covering applications that range from lasers, to ion conducting, or biomedical materials, as well as nuclear waste vitrification (Musgraves et al. 2019). Classically, a glass former has been defined as an oxide that can form a glass without additional components, for example B2O3, P2O5, GeO2, TeO2, As2O3/As2O5, or Sb2O3. The first two, B2O3 and P2O5, are probably the most important of this series, with GeO2 and TeO2 fostering more interest for their optical properties and various special applications. Contrary to SiO2, B2O3 and P2O5 are very hygroscopic and the simple vitreous oxides are only of academic interest. However, both borates and phosphates react readily with many oxides of the periodic table and have large glass forming regions (Vogel 1992). Both result in a wide range of binary glasses (not counting the oxide as third component), andd many of these glasses are quite stable—depending of course on the second component and the exact composition. Both borates and phosphates can form glasses with each other, resulting in boro–phosphate glasses, or with other glass formers, such as SiO2 or Sb2O3, as well as with intermediate oxides such as Al2O3, rare earth oxides or transition metal and post transition metal oxides (though regions of immiscibility or high tendencies of crystallization occur for various compositions). This extensive flexibility in the glass composition allows the design of glasses with distinct combination of desired properties, from optical to mechanical properties, to dopant solubility, and chemical stability to name just a few. In the following we will give an overview on phosphates, then borate glasses and afterwards briefly on the less common germanate, tellurite and antimonate glasses. Both phosphate and borate glasses, as typical network former oxide glasses, show many similarities, but also many distinct differences from silicate glass systems. One is the lower network connectivity of the pure oxides B2O3 and P2O5 compared to SiO2 (see Fig. 12), as both elements in fully polymerized pure systems are only connected via three bridging oxygen atoms.

Figure 12. Basic structural units in (a) phosphates, (b) silicates and (c) borate glasses. The top species is found in the fully polymerized simple oxides P2O5, SiO2, and B2O3.

5.1 Phosphate glasses Pure SiO2 is made of silicate tetrahedra that are connected via all four corners (Q4). Phosphorus is in the 5th group of the periodic table and therefore has a higher charge than Si4+. In pure vitreous P2O5, P5+ is at the center of a phosphate tetrahedra with three oxygen atoms that are bridged via a shared corner to other tetrahedra, while the fourth oxygen atom consists 3 of a double bonded terminal oxygen (P=O) (see Fig. 12), resulting in QP as the uncharged fully 4 bonded unit (the QP+ unit is a special case, see Fig. 13)

Glass as a State of Matter

1059

As a consequence, transition temperature Tg and mechanical properties of P2O5 reflect the less connected network compared to SiO2 (see also Table 3 for comparison). Addition of network modifiers such as alkali oxides will depolymerize the network further, much as in the case of silicate glasses. 5.1.1 Delocalized double bond. A peculiarity of phosphate compared to silicate glasses is the delocalization of the double bond to all non-bridging oxygen atoms of the same phosphate tetrahedron. However, this is typical for phosphate compounds in general and not specific to glasses. Details can be found in any book of inorganic chemistry (Wiberg et al. 2007). Since the delocalization of the double bond strongly affects the P–O bond strength, we briefly review the basics in this paragraph. The P=O double bond can easily be identified in pure P2O5 by XPS or Raman spectroscopy as well as by other methods. However, in modified phosphate glasses, the P=O double bond cannot be distinguished from a P–O bond containing a non–bridging oxygen atom, as the electron of the second bond will be delocalized over all bonds that contain a non–bridging oxygen atom P–O– (Brow 2000). The bond strength, given as valence units, vu, increases therefore by the effect of this additional contribution of the delocalized electron (see Fig. 13). Thus, for phosphate glasses, it is more precise to distinguish bridging oxygen and terminal atoms, instead of trying to further discriminate the double bonded from a non-bridging oxygen atom. Having said this, there are rare cases in which a double bonded oxygen atom gives a separate signal from a nbO atom (e.g. by Raman), for example for the high field strength Zn2+ ion, which so much prefers bonding to a nbO, creating a Zn–O–P bonds, that the P=O bond can form on non-ligand sites (Brow 2000).

Figure 13. Delocalized electron on the basic phosphate units with increasing depolymerization (a) ultraphosphate, (b) metaphosphate, (c) pyrophosphate, (d) orthophosphate, and (e) the special case of the fourfold coordinated phosphate tetrahedra, bond strength values are given in valence units (vu) after Brow et al. (1995).

5.1.2 Chemical stability of phosphate glasses. Pure P2O5 is so hygroscopic, that it has long been used as a drying agent in chemistry (Wiberg et al. 2007). Not surprisingly, pure vitreous P2O5, as well as ultraphosphate glasses with a O:P ratio  1). For other mixed network glasses see borates, Section 5.2.9, tellurites Section 5.3.2, or germanates, Section 5.4.2. 5.1.7.2 Phosphate glasses with high amounts of intermediate oxides. Phosphate glasses form readily with many elements, and in many systems with intermediate network forming oxides like WO3 or Nb2O5 as exemplified by Šubčík et al. (2010) in their study on the glass forming range and glass characteristics. In the frame of this chapter we can only mention briefly a nonrepresentative arbitrary collection of interesting systems. Binary phospho–titanate glasses form only in the TiO2-rich region with 55–70 mol% TiO2, which corresponds to the orthophosphate stoichiometry (Hashimoto et al. 2006). Multicomponent titano–phosphates form on the other hand over wide compositional ranges, as reported by Hashimoto et al. (2006) who also studied multicomponent titano–phosphate glasses as ecologically sustainable optical glasses with a high refractive index around 1.9. AgO containing TiO2–P2O2 glasses were found as promising nonlinear optical glass and photocatalytic glasses with self-cleaning properties, the K2O–TiO2–P2O2 system excels in its athermal properties. Shen et al. looked into Na2O–WO3–P2O5 glass for photochromism under gamma-ray irradiation (Shen et al. 2015) while color bleaching and oxygen diffusion was studied by Ghussn et al. (2014) in a niobium phosphate glass of the composition 23K2O·40Nb2O5·37P2O2. Interestingly, the colorless d 0 ion Nb5+ could be reduced to blue d1 ion Nb4+ when heated close to Tg under a reducing atmosphere, and bleached under an oxygen atmosphere, the kinetics of the oxidation and reduction processes following diffusion laws. Recently, a multi-technical study of the structure and properties of xZnO–(67 − x)SnO– 33P2O2 glasses showed a change in the phosphate speciation as Zn2+ changes its role from modifier to a [ZnO4]2− glass former (Hoppe et al. 2018; Saitoh et al. 2018a,b). This in-depth study includes Raman, infrared and NMR spectroscopies, neutron and X-ray diffraction studies, as well as chromatography and the correlation with thermal, optical, mechanical and photo-elastic properties. See also Sections 5.2.7 to 5.2.9 for similar mixed boro–phosphate glasses.

Glass as a State of Matter

1065

Fluorophosphate and fluoride phosphate (FP) glasses. Fluoride phosphate (no P–F bond) and fluorophosphate (with F–P bond) glasses combine many favorable aspects of fluoride and phosphate glasses and are currently studied as matrices for applications in optics, photonics and for energy storage (Musgraves et al. 2019). For review papers on the structure and properties of FP glasses we refer to (Ehrt 2015; Möncke and Eckert 2019). Any of the fluoride systems discussed in Section 4.2 can be combined with phosphates. Even when batching fluoride components, fluoride is easily lost from the melt as either HF, POF3 or even SnF2. Maintaining a fluoride rich atmosphere, e.g. by the addition of NH4.HF2 to the batch, can reduce the otherwise inevitable losses of fluoride during melting. The ready reaction of fluoride with water introduced by the batch materials, ensures that FP glasses are not likely to contain significant water bands, which is important when foped for photoluminescence. For applications in laser glasses and photonics, the low phonon energies of the fluoride network increase radiative transitions and up-conversion efficiencies, while the phosphate content increases the solubility of active ions such as transition or rare earth elements (Seeber et al. 1995; Ehrt 2015). The ligand field can be tuned by variation of the fluoride versus phosphate components. The structure of FP glasses consists usually of phosphate monomers and dimers, that are connected via cations to the fluoride components such as fluoroaluminate Al(O,F)6 or fluoro– zirconate Zr(O,F)8. For example, in fluoroaluminate–phosphate glasses Al–O–P bridges link the fluoroaluminate units directly to the phosphate tetrahedra, while bridging fluoride atoms are only found in Al–F–Al bridges (Möncke and Eckert 2019). P–F bonds decompose at high melting temperatures and are therefore only found in lower melted FP glasses, such as the fluoro–stanno– phosphate system (Anma et al. 1991), or the model system NaPO3–AlF3 (Möncke et al. 2018a). Since the major application of FP glasses based on fluoro–aluminates with phosphates is in the area of optics and photonics and includes interaction of the glass with low- and highlevel irradiation, irradiation induced defect formation has garnered significant attention (Ehrt 2015; Möncke et al. 2018b). 5.1.7.4 Ionic glasses containing halides or sulfates. Phosphate glasses can also contain high halogen levels, such as in the ion conducting AgPO3–AgI system (Rodrigues et al. 2011; Palles et al. 2016). Here, silver iodide addition will not shorten the metaphosphate chains, but the large iodine ions act as spacers between the chains and also contribute additional mobile ions to the glass (see Fig. 17c for a schematic). In contrast to fluorine, heavier hadlides form no direct bonds with the phosphate network, but like orthophosphate or sulfate ions are ionically crosslinked to diverse cations. Following the confusion principle as discussed for metallic glasses (see Fig. 3), glasses might form even without the presence of a higher order network. Perhaps one of the better studied systems of such ionic invert glasses are the sulfate phosphate glasses (Mamoshin 1996; Thieme et al. 2015). Structurally, phosphate free sulfate chloride glasses fall in the same category of ionic glass systems (see Section 4.3). 5.1.7.5 Natural polyphosphates (Holm 2014). Zhang et al. (2007) describe residual phases of glassy phosphates from the Keluo area, Heilongjiang Province, China. Small samples of natural phosphate glass have been identified by Raman spectroscopy. The authors suggest a P- and F-rich melt/fluid played an important role in an upper-mantle metasomatism, where minerals can change their composition by slow dissolution and reprecipitation processes. The assumption was that glasses formed by rapid quenching of this mantle material, and that such samples are widely distributed in the lithospheric mantle. Similar phosphate rich glasses have been identified in France (Rosenbaum et al. 1997).

1066

Möncke et al.

5.2 Borate glasses Boron has an unusually small coordination number for a glass former. The basic glass forming entity of pure vitreous B2O3 is made of trigonal BØ3 units (Ø denotes bridging oxygen atoms), so the same network connectivity of three ensues for pure boron oxide as for pure phosphorus oxide glasses (Krogh-Moe 1969). Like P2O5, pure vitreous B2O3 is highly hygroscopic and readily forms boric acid, B(OH)3 (Ehrt 2000, 2013). The BØ3 trigonal unit is a strong Lewis base, and readily accepts a fourth ligand, forming borate tetrahedra (Wiberg et al. 2007). Thus, upon addition of modifier oxides, instead of the formation of non-bridging oxygen atoms at these borate trigonals, the coordination initially increases to four, as negatively charged [BØ4]− tetrahedra are generated. Fully bridged borate tetrahedra drastically improve the chemical stability of borate glasses. The cross-linking capability of the modifier cation contributes as well. Tetrahedral metaborate units [BØ4]− are in an equilibrium with the trigonal BØ2O− groups, the relative population depends strongly on the type of the charge compensating modifier cation (Möncke et al. 2016). Higher modifier oxide concentrations form significant numbers of nbO (Wright et al. 2014). 5.2.1 Vitreous B2O3. B2O3 readily forms a glass which might be explained by the multitude of crystalline polymorphs, and the competing restructuring of the melt upon cooling, not settling on one crystal form, thus resulting in an amorphous material without any long-range structure (Ferlat et al. 2012). Interestingly, the structure of pure vitreous B2O3 consists of 75% boroxol rings B3Ø6 (Hannon et al. 1994), and the remaining 25 % represent “isolated”, that is non-ring BØ3 groups that are connected to these rings and are therefore not actually “isolated” at all–even though this term is found frequently in the literature. The ring breathing mode of this boroxol ring can be easily identified by Raman spectroscopy through a sharp signal at ca. 805 cm−1 (Galeener and Geissberger 1982). B2O3 glasses possess some aspects of ‘sheet-like’ properties that are akin to graphite, such as partial π-bonding (Duffy 2008), with strong B–O–B bonds within boroxol rings, one of the many well-defined superstructural units, but weaker van der Waal’s bonding between the rings. The importance of the boroxol rings on the glass properties was also highlighted by an in-situ Raman study of borate melts by Yano et al. (2003a,b,c), who found that the low Tg of borate glasses correlates to the break-up of boroxol rings. 5.2.2 Boron oxide anomaly. As indicated in the beginning of this section, the initial increase in network connectivity with modifier oxide addition has an impact on many borate glass properties, from density to Tg to chemical stability, which often display an extrema around the maximum in network connectivity (Vogel 1992; Brauer and Möncke 2016). N4, the ratio of B4/(B3 + B4), with B3 and B4 the population of three and four fold coordinated borate respectively, is therefore an important parameter for borate containing glasses. Pyroborate (BØO22−) and orthoborate units (BO33−) are usually found as trigonal borate entities, though tetrahedral borate pyroborate (BØ3O−) and orthoborate units (BØ2O22−) are known to occur in crystals (Wright et al. 2014), and possibly in glasses (Winterstein-Beckmann et al. 2013, 2015). See the schematic in Figure 18 for a depiction of the various borate species. The N4 fraction depends not only on the molar ratio in binary xM2O–(1 − x)B2O3 glasses, but also on the type of modifier cation. High field strength cations such as Mg2+ and Zn2+ prefer the highly charged sites of non-bridging oxygen as found in BØ2O−, and even support disproportionation into BØO22−and BØ3 (Möncke et al. 2016). The small Li+ ion on the other side prefers [BØ4]− tetrahedra over BØ2O− trigonals for charge compensation (Kamitsos and Chryssikos 1991). A second anomaly was found for ortho-borate compositions in the SrO–MnO–B2O3 and the SrO–Eu2O3–B2O3 systems (Winterstein-Beckmann et al. 2013, 2015). Both glass systems

Glass as a State of Matter

1067

Figure 18. Depiction of the various borate species that are known to exist in glasses and crystals. While all trigonal species, as well as the tetrahedral metaborate in the bottom row, are typically found in alkali or alkaline earth borate glasses, the tetrahedral pyro- and ortho-species are less typical though they might occur in lead or bismuth metaborate glass for the pyroborate and in Mn- or Eu- containing orthoborate glasses for the orthoborate unit (see the text for more details).

had initially been selected for their high loads of optically active manganese and europium ions for possible Faraday rotator materials, which renders the glasses paramagnetic and prevented further NMR studies regarding the structure. However, Raman and IR spectra are consistent with the formation of tetrahedral orthoborate units at high modifier concentration and both systems show an increase in Tg for the lowest borate levels, both signs for the occurrence of a second boron anomaly (see Fig. 19). The tetrahedral orthoborate species (depicted on the lower right side in Fig. 18) can form rings of the type [B3O9]9− with three bridging oxygen in the ring, and 6 non-bridging oxygen atoms sticking out (see Fig. 19).

Figure 19. First and second boron anomaly for SrO–B2O3 glasses. Diamonds denote data from Ohta et al. (1982) for the binary system xB2O3 − (100 − x) sytem with light blue colored symbols for the Al-free system and blue and white split diamonds for the glasses conatining 3 mol% Al2O3, the maximum reflects on the equilibrium of trigonal and tetrahedral metaborate. The round symbols are from Winterstein et al. (2013) who found a second boron anomaly as trigoanl orthoborate is in equilibrium with tetrahedral orthoborate units in the ternary xB2O3–xSrO–(100 − 2x)MnO.

1068

Möncke et al.

5.2.3 Superstructural units. Borate glasses are fascinating for their variety in medium range order or superstructural units, including various chains and ring type modifications. Many of these superstructural units are known from borate crystals (Wright 2010). Structural analysis depends heavily on 11B-NMR, which can not only distinguish the coordination, but also the presence of ring and non-ring entities (Deters et al. 2011). Raman spectroscopy is further sensitive to even small numbers of boroxol rings with their sharp ring breathing mode near 805 cm−1. Even the substitution of one or two BØ3 units by tetrahedral [BØ4]−, is reflected in separate bands in the Raman spectra. The metaborate or orthoborate ring can further be identified by distinctive bands, as can larger super structural units with strained rings such as the penta-diborate (Kamitsos and Chryssikos 1991; Yiannopoulos et al. 2001; Möncke et al. 2016). Some crystals, such as lead borate or bismuth borate, are characterized by large superstructural units with well-defined structures, such as 20 atoms containing polyanions (Kamitsos and Chryssikos 1991; Wright et al. 2010; Wright 2014; Möncke 2017). Of the many relevant reviews on borate glasses, we suggest the in-depth review on the structural differences between borate and silicate glasses written by Wright et al. (2010). 5.2.4 Non-applicability of Loewenstein rule. The original Loewenstein rule from 1954 had often been wrongly applied to borate glasses where it was dubbed [BØ4]−-avoidance rule. Loewenstein (1954) explained the absence of directly linked [AlØ4]− tetrahedra in zeolites by the third Pauling rule: “anion bridges between polyhedra with lowest possible number of coordination, though formally possible according to the electrostatic valence rule, must be expected to be unstable whenever alternative structures with higher numbers of coordination in a part of the polyhedra are possible”. This means that alumina tetrahedra will prefer to bond to other glass forming units or take on a higher coordination number in order to avoid linking two [AlØ4]− tetrahedra directly. However, for borate glasses, the tetrahedron has the higher coordination number and therefore the analogy between [AlØ4]− and [BØ4]− does not apply (Möncke et al. 2017), as borne out by the many superstructural units in glasses and crystals that do contain linked [BØ4]− tetrahedra, the most charged one being the tetrahedral orthoborate ring (see Fig. 20). Loewenstein never applied his rule to glasses, nor to B-containing compounds and he did not rule out the tetrahedral linkage on electrostatic grounds or charge repulsion, as often wrongly referred to in the later literature. 5.2.5 Glass formation and phase separation in binary glasses. Like phosphates, borates have a tendency to react with many network former, intermediates and modifier oxides and readily form glasses (Ehrt 2006; Bengisu 2016; Möncke et al. 2016; Milanova et al. 2019). However, some metaborate glasses crystallize (Yiannopoulos et al. 2001) or clustering and phase separation (Ehrt 2013; Herrmann et al. 2019) might occur. ZnO or MnO-metaborate glasses actually display such a pronounced liquid–liquid phase separation, that the heavy MO–B2O3 (56:44) sinks to the bottom of the crucible, while the light B2O3 / H3BO3 phase swims above, preventing even the slightest oxidation of Mn2+ (Ehrt 2013). Lead and bismuth borate glasses form PbO and Bi2O3 pseudo phases embedded in a connective tissue, as described by Ingram for silicates (Ingram et al. 1991). Raman and XPS spectroscopy can distinguish these embedded micro phases from the surrounding phase of undermodified borate compositions (Möncke et al. 2016). The oxygen within the PbO and Bi2O3 regions would correspond to the free oxygen introduced by Henderson and Stebbins (2022, this volume) for silicate glasses. 5.2.6 Modifier cations in borate glasses. The strength of glass network depends not only on the degree of polymerization—and therefore the N4 value with N4 = B4 / (B4 + B3) with B4 and B3 being the fraction of tetrahedral and trigonal coordinated borate species—but also on the cross-linking capability of the modifier cations. In analogy to the discussion in Section 5.1.6, for phosphate glasses, the metal-oxide bonds in the far infrared can be used to calculate the force constant between the modifier cation and the oxygen atoms of the network. Since borate related bands are found at higher energies, more studies have been conducted on the far IR region of borate than most other glasses (Yiannopoulos et al. 2001). Figure 21 shows the correlation of

Glass as a State of Matter

1069

Figure 20. Depiction of typical superstructural units found in borate glasses and crystals (a) boroxol ring, (b) triborate ring, (c) di-triborate ring, (d) diborate unit, (e) pentaborate unit, (f) di-pentaborate unit, (g) tri-pentaborate, (h) metaborate chain, (i) metaborate ring, (j) pyroborate, (k) orthoborate, (l) orthoborate ring with three linked [BØ2O2]3− Td-orthoborate units; and finally two large polyanions, known from crystals and suggested to exist “(m) as di-pentaborate anion [B5O11]7− in bismuth-metaborate glass or (n) as bi-diborate polyanion [B10O21]12− in lead-metaborate glass (Kamitsos and Chryssikos 1991; Wright et al. 2010; Wright 2014; Möncke et al. 2015; Möncke 2017).

Figure 21. Dependence of transition temperature on the modifier cations in binary MO–B2O3 glasses. (a) shows the dependence on the force constant of the M–O bond as derived from far infrared measurements, and (b) the fraction of tetrahedral borate groups (N4) as different cations favor different sides of the metaborate equilibrium or disproportionation. Modified after Möncke et al. (2016).

1070

Möncke et al.

the transition temperature for a series of transition metal and post transition metal cations with the degree of polymerization (N4) and with the force constant. It is apparent that both factors are equally important. Not shown is the similar correlation with the hardness (Möncke, et al. 2016), results that were recently verified by a mechanical study of alkali and alkaline earth alumoborate glasses (Frederiksen et al. 2018). The dependence of the modifier cation on the optical properties or the viscosity of binary borate glasses is also discussed in (Ehrt 2006). 5.2.7 Multicomponent borate glasses. Borates readily form glasses with other glass formers, intermediate oxides, transition metals or rare earth elements. While some of the binary systems are prone to phase separation or crystallization, many compositions do form glasses, especially when combined with a third or more components (Vogel 1992; Musgraves et al. 2019). For example, the upper limit of glass formation in the SrO–B2O3 binary lies at 47SrO– 53B2O3 while the nominal metaborate 50:50 composition of SrO–B2O3 crystallizes. Adding a third component to SrO–B2O3 allows glass formation beyond the metaborate stoichiometry. As seen in Figure 19, the addition of 8 mol%–60 mol% MnO permits glass formation in the Sr–borate system well beyond the metaborate, into and beyond the orthoborate composition. The combination of B2O3 with modifier ions has been discussed above and the combination with the glass formers SiO2 and P2O5 will be briefly discussed in the following two sections. Doris Ehrt studied the effect of ZnO, La2O3,PbO and Bi2O3 on the properties of binary borate glasses and melts (Ehrt 2006), while Milanova et al. combined more intermediate glass former in borate glasses, such as in the B2O3–Bi2O3–La2O3–WO3 glass system with La2O3 varying from 0 to 10 mol% and WO3 levels from 0 to 40 mol% (Milanova et al. 2019). Heavy metal containing glasses are studied as materials for radiation shielding, while other applications focus on the low Tg, such as in sealing glasses. 5.2.8 Borosilicate glasses. Technologically the borosilicate glass system is the most important. These glasses are treated in detail in Youngman (2022, this volume). Applications include, but are not limited, to optics and photonics (Ehrt 2018), laboratory ware, display screens or nuclear waste immobilization. The presence of superstructural units, preferential bonding as well as sub-liquidus phase separation make these glasses fascinating to study (Bunker et al. 1990; Möncke et al. 2015, 2017; Herrmann et al. 2019). 5.2.9 Borophosphate glasses. Eckert et al. studied the structure and properties of different series of sodium borophosphate glasses with enhanced NMR in combination with other spectroscopic techniques (Raman, XPS), once with constant B:P ratio (Rinke and Eckert 2011), once with constant alkali levels but varying B:P ratios for the mixed network former effect (Larink et al. 2012). For the first case of the (Na2O)x(BPO4)1−x (0.25 < x < 0.55) system (Rinke and Eckert 2011), 11B MAS-NMR data reflects a dominance of [BØ4]− borate tetrahedra (Ø denotes bridging oxygen atoms) while 31P MAS NMR reveals the successive transformation of neutral QP3 into QP2 and further into QP1 units as the Na2O content increases. Initially, Na2O additions form [BØ4]− borate tetrahedra, while nbO on the phosphate units form only at higher Na2O additions (for x > 0.35). All spectroscopic techniques used revealed strong interactions between the two network formers B and P which are reflected in the preferred formation of B–O–P bonds. Variations in Tg were correlated to the overall network connectivity as expressed by the total number of bridging oxygen atoms per network former species (Rinke and Eckert 2011). Despite the known phase separation of binary borosilicate or phospho–silicate systems is glass formation reported for ternary and quaternary systems containing only network former oxides. The modifier free boro–phospho–silicate glass system, containing only the network forming oxides B2O3, P2O5 and SiO2. has been studied with multinuclear NMR Spectroscopy by Uesbeck et al. (2017). The quaternary, which also contains Al2O3, has been reported by Liu et al. (2018).

Glass as a State of Matter

1071

Borophosphate glasses containing transition metal and post-transition metal ions are studied for their large glass forming region, and their ability to stabilize high fractions of highly polarizable ions. Such glasses are of interest for their non-linear optical properties and electric field induced second harmonic generation (Dussauze et al. 2006). 5.2.10 Borate glasses applications. Applications of borate glasses range from shielding materials to sealing glasses to bio glasses (Bengisu 2016). Borate glass fibers are used in wound healing (Zhao et al. 2015), showing great potential for vascular regrowth. For the technologically so important field of borosilicate glasses, we refer once again to Youngman (2022, this volume).

5.3 Tellurite glasses Already in 1834, Berzelius (1834) reported on tellurite glasses consisting of TeO2 and BaO and similar oxides. Other authors followed up with studies on glass formation and since Stanworth (1952), with characterization of the properties (Vogel 1992). 5.3.1 Pure TeO2 glass. Pure TeO2 is not a good glass former and shows a great tendency towards crystallization when prepared in Pt-crucibles. However, dip quenching (Tagiara et al. 2017) allows the preparation of bulk samples of vitreous TeO2. Pure TeO2 is unusual in so far as it has asymmetric Te–O–Te bonds, a long and a short bond distance without charge distribution over these bridges (Barney et al. 2013). This is closest to g-TeO2, one of the three crystalline phases (McLaughlin et al. 2001). The basic glass forming unit is a pseudo-trigonal bipyramid, with the lone electron pair on tellurium at the 3rd axial corner, the 2 other axial corners are formed by the short Te–O bonds while the Te–O bonds on the z–axis are the long distant bonds. For tellurites, as for borates, the coordination has to be considered when using the Q-nomenclature, this is achieved by adding a 3 or 4 as subscript. The fully polymerized TeO2 glass consists of TeO4 units. The interest in tellurite glasses arises mostly for optical applications (El-Mallawany 2018). The low phonon side bands are of interest for fluorescing materials. The high polarizability induces a high third order susceptibility c3 and therefore makes tellurites interesting for their non-linear optical applications. In order to keep a high c3, combining TeO2 with another highly polarizable component, such as Tl2O or Nb2O5 (Bertrand et al. 2015; Carreaud et al. 2015; Kato et al. 2016) is most advantageous. 5.3.2 Structure of tellurite glasses. Contrary to silicate and the previously discussed oxide glass formers, tellurite units exhibit a lone electron pair that takes no part in bonding. Like tin or lead ions, the lone electron pair occupies one side of the basic polyhedra, and in terms of network bonding the lone electron pair can be seen as a non-bridging side at one corner of the pseudo-polyhedra and is one reason for the low Tg (Tagiara et al. 2017) (See Fig. 22). The basics of this structure has been confirmed by Raman (Tagiara et al. 2017), neutron diffraction (McLaughlin et al. 2001; Barney et al. 2013), and NMR spectroscopy (McLaughlin et al. 2001; Garaga et al. 2017). The lone electron pair at the tellurium ion distorts the fundamental TeOn polyhedral structure and some ambiguity exists on the nature of the shortest Te–O bonds (see Fig. 22 for a depiction of various tellurite species). Depending on the analytical method used, the short bond might be seen as Te=O double bond or as being weakly bonded to a neighboring tellurium ion as in a Te–O– –Te type of bond, as depicted in Figure 22b as TeO3+1 unit. Diffraction studies seem to indicate a significant fraction of such terminal units (Barney et al. 2013); however, Raman spectroscopy does not see a Te=O double bond with a signal at ca. 850 cm−1 for pure TeO2 (Tagiara et al. 2017). On the other hand, if the glass is melted in SiO2 crucibles, the tellurite network is modified and a Te=O bond is indeed observable in the Raman spectra (Tagiara et al. 2017).

1072

Möncke et al.

Crucible dissolution has been discussed for the case of phosphate glasses before, and as shown by Tagiara et al. (2017), melting pure TeO2 in Al2O3 crucibles will enhance glass formation through the dissolution and uptake of Al2O3 from the crucible. The uptake modifies the network significantly creating non-bridging oxygen atoms (see Fig. 22 for the tellurite species seen in depolymerized glasses) but increasing Tg through the strong cross-linking of Al3+ ions. Like in many other glasses, depolymerization occurs with the addition of modifier oxides to pure TeO2. From a CN = 4 fully polymerized tellurite network with four-fold coordinated entities, 4 th QTe 4 , modifier addition creates first TeO3+1 (trigonal bi-pyramid) units, where the 4 oxygen is loosely bound to another tellurite entity, while one oxygen atom is bridging and 2 oxygen atoms are terminal, sharing an excess electron and a double bond. Further modifier oxide addition creates three-fold TeO3 groups with 1 or two nbO (trigonal pyramid, with the lone electron pair at the apex), that are however delocalized with the double bond of the 3rd terminal oxygen atom. Figure 22 depicts the five tellurite polyhedra that are known from crystals and the TeO3+1 group that is an important intermediate species in glasses (McLaughlin et al. 2000). It is easy to follow these structural changes by IR and Raman spectroscopy. Interestingly, the change in the Raman spectra is very different for addition of the intermediate oxide Nb2O5 or when adding modifier oxides such as Tl2O, ZnO or Al2O3 e.g. (Tagiara et al. 2017). Thomas suggested that niobium ions have a similar bond strength to oxygen as tellurium ions and that therefore a solid solution forms between Te- and Nb-oxides. This is reflected for the (1 − x)TeO2−xNb2O5 series in almost unchanged Raman spectra as Nb2O5 is added to TeO2. This behavior is contrary to the (1 − x)TeO2−xTl2O series, where the weaker thallium ions act as network modifier, changing the connectivity and coordination of the tellurite polyhedra, which in turn is apparent in significant changes in the Raman spectra (Mirgorodsky et al. 2012) When TeO2 is combined with another compound that exhibits even stronger oxygen bonds than Te–O, TeO2 now acts as modifier oxide e.g. in (1 − x)TeO2 − xWO3 (Mirgorodsky et al. 2012) or when combined with borate as in the Li2O–x(2TeO2)–(1 − x)B2O3 glasses (Chatzipanagis et al. 2019). TeO2 reacts also readily with other typical glass former oxides, though the mixed B-, Ge- and Si-systems often show phase separation which is not described for phosphorus–tellurite glasses (Vogel 1992), but was for example reported for (1 − x)TeO2 − xWO3 (Mirgorodsky et al. 2012). Phase separation or a low degree of mixing is often the reason for a strong negative mixed network former effect, as for example observed for Li2O–x(2TeO2)–(1 − x)B2O3 glasses (de Oliveira et al. 2018).

4 Figure 22. Depiction of the tellurite polyhedra known from crystals and glasses, (a) TeØ4 or QTe 4 trigonal bipyramid (tbp), (b) TeØ3+1 an intermediate form between the four and three fold coordinated tellurite form 3 with long and short bonds, (c) TeØ3O− or QTe4 (tbp), the non-bridging oxygen can be the long or the short 0 1 2 bonded one, (d) TeØ2O or QTe3 trigonal pyramid (tp), (e) TeØO2− or QTe3(tp), (f) TeO32− or QTe3 (tp), after McLaughlin et al. (2000).

Glass as a State of Matter

1073

When studying the Raman spectra, it should be noted, that Raman spectroscopy has the highest sensitivity for highly polarizable ions such as Te4+, and if combined with low polarizable classical network former such as B, Si or P, those bands are therefore often hidden under the Te-related Raman bands (Chatzipanagis et al. 2019). For mixed tellurite–germanate glasses see Section 5.4. 5.3.3 Properties and applications. Applications of tellurite glasses are especially focused on optics and photonics for their high polarizability resulting in high refractive index and high third order susceptibility, which is of interest for non-linear optics (NLO) (Weber 2006; Barbosa et al. 2017). Tellurites have a high transparency in the IR, as can be seen from Figure 8, the highest for oxide glasses as low as 5 to 7 µm (Vogel 1992). On the other hand, the high polarizability of tellurium decreases the transparency in the UV-visible wavelength region, shifting the band gap to lower energies (same figure). The low energy phonon side bands are advantageous for fluorescence, as is the high solubility of rare earth ions in tellurite glasses (Wang et al. 1994). The same authors also include a detailed study on the formability of tellurite glasses including fiber drawing and extrusion. Other applications include laser materials and energy conversion, but also radiation shielding because of the high density and even biomedical applications (El-Mallawany 2018). Many publications can be found on the structures and properties of tellurite glasses, including The “Tellurite Glasses Handbook: Physical Properties and Data” by R. A. H. El-Mallawany (Vogel 1992; El-Mallawany 2012). The melting temperatures are low, between 700–900 °C, and as a consequence they also display a low Tg. Density and coefficient of thermal expansion are high while mechanical strength and hardness are relatively low compared with other oxide glasses (Stanworth 1952; Tagiara et al. 2017). The latter can be improved by crystallization, and transparent glass ceramics for optical applications have been successfully prepared e.g. by complete crystallization of the 75 TeO2–12.5 Nb2O5–12.5 Bi2O3 glasses (Bertrand et al. 2016). Researchers that have worked excessively with tellurium containing glasses might have experienced the typical garlic-odor breath, as the body converts any tellurium taken up, to dimethyl telluride (CH3)2Te (Chasteen and Bentley 2003). 5.3.4 Antiglass. The term “anti-glass” was defined by Burckhardt and Trömel (1983) when describing a very small group of oxide materials from the tellurite system. The definition of anti-glass refers to a solid, with cationic long-range order but lacking any anionic short-range order. This is exactly contrary to glasses with short-range order and a lack of long-range order, hence the name. Many reported anti-glass structures derive from tellurites and are based on a CaF2 fluorite structure with Te4+ and other metal ions such as for example Bi3+ or Sr2+, statistically distributed at the available cation positions while not all crystallographic anion positions are occupied by oxygen (Bertrand et al. 2015). Reported antiglass compositions include SrTe5O11 (Burckhardt and Trömel 1983) or glass ceramic from the TeO2−Nb2O5−Bi2O3 system (Bertrand et al. 2015).

5.4 Germanate glasses Germanium is an important element for chalcogenide glasses (see Section 4.1) but plays only a minor role in technological oxide glasses. GeO2 doped SiO2 fibers are used in telecommunication, mostly to increase the refractive index in the core of the fiber. GeCl4 is used as precursor in the preparation of preforms by vapor deposition in the same way as SiCl4 (Vogel 1992). However, since the glass formation of GeO2 was first suggested by Zachariasen (1932), oxide-germanate glasses garnered so far more academic interest—despite the wide glass forming range. Notwithstanding many analogies to silicate systems, the lower field strength of Ge4+ to the smaller Si4+ ion results in distinct differences, including a smaller tendency toward phase separation (Vogel 1992).

1074

Möncke et al.

5.4.1 Simple GeO2 glass. The structure of pure vitreous GeO2 glass is in good agreement with vitreous SiO2. The basic glass forming units are GeO4-tetrahedra, though the O−Ge−O intra tetrahedral angles seem to be more distorted in vitreous GeO2 compared to vitreous SiO2. This fact was attributed to the larger size of the germanium compared to the silicon ion and a higher number of smaller 3-membered rings in vitreous germania glass. A nice review on the structure of amorphous, crystalline and liquid GeO2 was conducted by Micoulaut et al. (2006). Of interest are also structural variations under high pressure, since GeO2 has a higher tendency than SiO2 to form higher coordinated polyhedra (Kono et al. 2016). Not only under pressure, but also in mixed component glasses are germanium ions found in five- and six-fold coordination in addition to GeO4 tetrahedra. Important differences between GeO2 and SiO2 glasses concern the mid-range order and the bond strength. Thus, the Tg of GeO2 glasses is with only 514 °C significantly lower than the Tg of SiO2 with 1203 °C, see also Table 3 (Shelby 1974). 5.4.2 Modifier free mixed network former germanate glasses. GeO2 easily forms glasses with many other glass formers, intermediates and modifier oxides (Haiyan et al. 1986). Shelby studied glass formation and properties of many GeO2-containing glasses, including the binary B2O3–GeO2 system (Shelby 1974; Vogel 1992). Germano–silicate glasses are widely used as low-attenuation optical fibers, yielding numerous studies on their physical (optical) properties (Fleming 1984). Studies that focus on the underlying structure are rare and the fundamental question on the homogeneity of germano–silicate glasses still has not been answered, e.g. if clustering or significant phase separation occurs (Micoulaut et al. 2006; Majérus et al. 2008). Germano–phosphate glasses were studied by X-ray and neutron diffraction and show better glass formation and less regions of phase separation than the corresponding phospho– silica glass (Hoppe et al. 2006). Germano–borate glasses exhibit a distinct mixed network former effect, displaying negative deviations from additivity for all intermediate glasses for properties related to ion mobility (e.g. viscosity, thermal expansion, but also for density) while a positive deviation from additivity was seen for the refractive index (Shelby 1974). There is no evidence of macroscopic phase separation in these glasses. Raman studies on the binary GeO2–B2O3 and the ternary GeO2– B2O3–SiO2 system have been performed, and Chakraborty and Condrate (1986a,b) looked into the connectivity and coordination of these glass former oxides in the mixed glass systems. Germano–tellurite glasses have been studied for their optical properties, especially fluorescence in glasses doped with Er3+ and Tm3+ ions (Mattarelli et al. 2005). 5.4.3 Modified germanate glasses. Various studies looked into the structure of modified germanate glasses, such as in regard to alkali sites and optical basicity (Kamitsos et al. 2002), including IR and Raman investigations exemplified in the xRb2O·(1 − x)GeO2 series (Kamitsos et al. 1996). Binary germanate systems such as TiO2–GeO2 (Khan and Mohamed–Osman 1986), GeO2–Bi2O3 (Kassab et al. 2019) and GeO2–PbO (Bahari et al. 2013) were studied for their structure and optical properties after addition of optically active elements such as rare earth ions and silver nano particles. 5.4.4 Multicomponent germanate glasses. Newer, in depth multi-technique structural studies on mixed network former glasses have been conducted by Eckert et al. including the (M2O)0.33[(Ge2O4)x(P2O5)1−x]0.67 system with M = Na and K (Behrends and Eckert 2014). The formula uses the term Ge2O4 to account for the fact that the same number of phosphate tetrahedra will be replaced by germanate polyhedra. Here, the authors used 31P and 23Na NMR, Raman, and O-1s XPS (X-ray photoelectron) spectroscopy. It was found that heteroatomic P−O−Ge linkages were overall preferred over homoatomic P−O−P and Ge−O−Ge linkages. Alkali ions tend to be always linked to more terminal oxygen atoms from phosphate rather than germanate polyhedra. The preferred association of sodium ions with QP1 groups results

Glass as a State of Matter

1075

partially in cation clusters. The authors deduced indirectly the formation of higher germanium coordination states in this glass system (Behrends and Eckert 2014). Multicomponent germanate glasses containing Bi2O3, Gd2O3, Ga2O3, WO3, TeO2 or even CoO as additional components have been successfully prepared and studied, e.g. by Jewell et al. (1994), Simon et al. (2000), Ardelean et al. (2001) ,Upender et al. (2011) and more recently by Tagiara et al. (2020) and Bradtmüller et al. (2021). Fluoride containing germanate systems were recently studied in detail, see for example Pereira et al. (2017, 2018).

5.5 Other glasses In the frame of the current publication we cannot cover the full range of non-metallic oxide glasses that exist in addition to the already mentioned glass forming system. However, we want to mention a couple more examples to show the variety and that even glasses lacking an accepted network former might form glasses in combination with other oxides. 5.5.1 Antimonite glasses. Miller and Cody (1982) successfully prepared vitreous Sb2O3 glasses by quenching in liquid nitrogen. Multicomponent antimonate glasses are studied as possible non-linear optical and laser materials. They are in many aspects similar to tellurite glasses (Baazouzi et al. 2013). Honma et al. studied the binary Sb2O3–B2O3 system by XPS and optical spectroscopy in order to understand the impact of different polarizability of the trivalent ions in this M2O3 systems (Honma et al. 2000). Montesso et al. looked into glass formation, structure and properties of a SbPO4–GeO2 glass system for possible applications exploiting its high polarizability (Montesso et al. 2018). Antimonates can be introduced into many glass systems, such as tungstates or molybdates see for example Kubliha et al. (2015), as well as germano–silicates (Zmojda et al. 2016). While most glasses contain trivalent Sb3+ in the form of antimonite, Mößbauer and photo electron spectroscopy can distinguish pentavalent Sb5+ (antimonate) in some samples (Schütz et al. 2004). This is contrary to arsenate glasses, which usually are found to contain arsenic in the form of As2O3–As2O5 mixtures (Vogel 1992). Binary As-containing compositions with alkali oxides or intermediate oxides can be prepared as well, though due to volatility and the intrinsic toxicity of arsenic and ensuing safety concerns caused de facto the termination of further studies into arsenite glasses. Moreover, arsenic oxide glasses do not offer any properties that are fundamentally different from other highly polarizable oxides or for that matter, arsenic chalcogenides. 5.5.2 Intermediate glass former (oxides of Pb, W, Mo, Nb, Ta, Al, Zn…). Interestingly, a typical glass former is not always required in order to get a glass. For example, binary glasses form in the CaO–Al2O3 system (Drewitt et al. 2012; Akola et al. 2013). For the 64CaO–36Al2O3 eutectic, the quenched glasses consist of a topologically disordered cage network with largesized rings. A coordination number of 4 has been found earlier for Al3+ in 50CaO–50Al2O3 glass, and generally if CaO 6. PNAS 113:3436 Kordes E (1939) Physikalisch-chemische Untersuchungen über den Feinbau von Gläsern. III Mitteilung. Binäre und pseudobinäre Gläser ohne nennenswerte Packungsdefekte Z Physikalische Chem B 43:173–190 Kordes E, Vogel W, Feterowsky R (1953) Physikalisch-chemische Untersuchungen über die Eigenschaften und den Feinbau von Phosphatgläsern. Z Elektrochem Ber Bunsen Phys Chem 57:282–289 Koroglu A, Thompson DP, Apperley DC, Harris RK (2011) 15N, 17O MAS NMR studies of yttrium oxynitride glasses. Phys Chem Glass—Euro J Glass Sci Technol Part B 52:175–180 Kosareva IA, Tkachenko KG, Karapetjan GO, Limbach IY, Karapetjan KG, Rozhdestvensky I (2006) Comparative analysis of impact of the complex vitreous fertilizers with microelements on the microflora of sod-podzolic, peat soils. J Plant Nutr 29:933–942 Krogh-Moe J (1969) The structure of vitreous and liquid boron oxide. J Non-Cryst Solids 1:269–284 Kruzic JJ (2016) Bulk metallic glasses as structural materials: A review. Adv Eng Mater 18:1308–1331 Kubliha M, Soltani MT, Trnovcová V, Legouera M, Labaš V, Kostka P, Le D Coq, Hamzaoui M (2015) Electrical, dielectric, and optical properties of Sb2O3–Li2O–MoO3 glasses. J Non-Cryst Solids 428:42–48 Kucuk A, Clare AG (1999) Optical properties of cerium, europium doped fluoroaluminate glasses. Opt Mater 13:279–287 Kühnert H (2012) Forschungen zur Geschichte des Jenaer Glaswerks Schott & Genossen.Wien Köln Weimar, Böhlau Verlag Kurkjian CR, Prindle WR (1998) Perspectives on the history of glass composition. J Am Ceram Soc 81:795–813 Lambert JB, Poinar GO (2002) Amber: the organic gemstone. Acc Chem Res 35:628–636 Larink D, Eckert H, Reichert M, Martin SW (2012) Mixed network former effect in ion-conducting alkali borophosphate glasses: structure/property correlations in the system [M2O]1/3[(B2O3)x(P2O5)1–x]2/3 (M = Li, K, Cs). J Phys Chem C 116:26162–26176 Larson RW, Day DE (1986) Preparation, characterization of lithium phosphorus oxynitride glass. J Non-Cryst Solids 88:97–113 Ledemi Y, El-Amraoui M, Calvez L, Zhang X-H, Bureau B, Messaddeq Y (2013) Colorless chalco-halide Ga2S3GeS2–CsCl glasses as new optical material, SPIE Lefterova ED, Angelov P, Dimitriev Y, Stoynov Z (1997) Silver ion conducting glasses. Analytical Laboratory 6(3) Leicester HM (1969) Mikhail Lomonosov, the manufacture of glass and mosaics. J Chem Educ 46:295 Liu H, Youngman RE, Kapoor S, Jensen LR, Smedskjaer MM, Yue Y (2018) Nano-phase separation, structural ordering in silica-rich mixed network former glasses. Phys Chem Chem Phys 20:15707–15717 Loehman RE (1987) Oxynitride glasses. MRS Bull 12:26–31 Loewenstein W (1954) The distribution of aluminum in the tetrahedra of silicates, aluminates. Am Mineral 92:92–96 Lucas J, Zhang XH (1990) The tellurium halide glasses. J Non-Cryst Solids 125:1–16

1084

Möncke et al.

Lucas J, Troles J, Zhang XH, Boussard-Pledel C, Poulain M, Bureau B (2018) Glasses to see beyond visible. C R Chimie 21:916–922 Lundquist PM, Wortmann R, Geletneky C, Twieg RJ, Jurich M, Lee VY, Moylan CR, Burland DM (1996) Organic glasses: A new class of photorefractive materials. Science 274:1182 Lupton DF, Merker J, Schölz F (1997) The correct use of platinum in the XRF laboratory. X-Ray Spectrom 26:132–140 Machida N, Shigematsu T, Nakanishi N, Tsuchida S, Minami T (1992) Glass formation, ion conduction in the CuCl– Cu2MoO4–Cu3PO4 system. J Chem Soc Faraday Trans 88:3059–3062 Mackenzie JD (1960) Modern Aspects of the Vitreous State. Butterworths, Co Ltd, London Mackenzie JD (1987) Chloride, bromide and iodide glasses. In: Halide Glasses for Infrared Fiberoptics. Almeida R.M. (ed) Dordrecht, Springer Netherlands: 357–366 Majérus O, Cormier L, Neuville DR, Galoisy L, Calas G (2008) The structure of SiO2–GeO2 glasses: A spectroscopic study. J Non-Cryst Solids 354:2004–2009 Mamoshin VL (1996) Theoretical estimation of the possibility of glass formation in sulfate, phosphate, sulfate– phosphate systems. Glass Ceram 53:104–106 Marchand R (1983) Nitrogen-containing phosphate glasses. J Non-Cryst Solids 56:173–178 Mascaraque N, Fierro JLG, Durán A, Muñoz F (2013) An interpretation for the increase of ionic conductivity by nitrogen incorporation in LiPON oxynitride glasses. Solid State Ionics 233:73–79 Mascaraque N, Takebe H, Tricot G, Fierro JLG, Durán A, Muñoz F (2014) Structure and electrical properties of a new thio-phosphorus oxynitride glass electrolyte. J Non-Cryst Solids 405:159–162 Mascaraque N, Durán A, Muñoz F (2015) Effect of fluorine, nitrogen on the chemical durability of lithium phosphate glasses. J Non-Cryst Solids 417(Suppl C):60–65 Masuno A, Inoue H, Arai Y, Yu J, Watanabe Y (2011) Structural-relaxation-induced high refractive indices of Ba1-xCaxTi2O5 glasses. J Mater Chem 21:17441–17447 Mattarelli M, Chiappini A, Montagna M, Martucci A, Ribaudo A, Guglielmi M, Ferrari M, Chiasera A (2005) Optical spectroscopy of TeO2–GeO2 glasses activated with Er3+, Tm3+ ions. J Non-Cryst Solids 351:1759–1763 Mazurin OV, Priven. A SciGlass Information System, version 6EPAM 7 Systems McLaughlin JC, Tagg SL, Zwanziger JW, Haeffner DR, Shastri SD (2000) The structure of tellurite glass: A combined NMR, neutron diffraction,, X-ray diffraction study. J Non-Cryst Solids 274:1–8 McLaughlin JC, Tagg SL, Zwanziger JW (2001) The structure of alkali tellurite glasses. J Phys Chem B 105:67–75 Meille SV, Allegra G, Geil PH, He J, Hess M, Jin JI, Kratochvíl P, Mormann W, Stepto R (2011) Definitions of terms relating to crystalline polymers (IUPAC Recommendations 2011). Pure Appl Chem 83:1831 Micoulaut M, Cormier L, Henderson GS (2006) The structure of amorphous, crystalline, liquid GeO2. J Phys Condens Matter 18:R753–R784 Milanova M, Iordanova R, Aleksandrov L, Hassan M, Dimitriev Y (2011) Glass formation, structure of glasses in the ZnO–Bi2O3–WO3–MoO3 system. J Non-Cryst Solids 357:2713–2718 Milanova M, Iordanova R, Kostov KL, Dimitriev Y (2014) X-ray photoelectron spectroscopic studies of glasses in the MoO3–Bi2O3, MoO3–Bi2O3–CuO systems. J Non-Cryst Solids 401:175–180 Milanova M, Kostov KL, Iordanova R, Aleksandrov L, Yordanova A, Mineva T (2019) Local structure, connectivity and physical properties of glasses in the B2O3–Bi2O3–La2O3–WO3 system. J Non-Cryst Solids 516:35–44 Miller PJ, Cody CA (1982) Infrared, Raman investigation of vitreous antimony trioxide. Spectrochim Acta Part A 38:555–559 Miller MK, Liaw P (2008) Bulk Metallic Glasses. Boston, MA, Springer US Miracle DB (2004) A structural model for metallic glasses. Nat Mater 3:697–702 Miracle DB (2012) A physical model for metallic glass structures: An introduction and update. JOM 64:846–855 Mirgorodsky A, Colas M, Smirnov M, Merle-Méjean T, El-Mallawany R, Thomas P (2012) Structural peculiarities and Raman spectra of TeO2/WO3-based glasses: A fresh look at the problem. J Solid State Chemi 190:45–51 Miyabe D, Takahashi M, Tokuda Y, Yoko T, Uchino T (2005) Structure, formation mechanism of six-fold coordinated silicon in phosphosilicate glasses. Phys Rev B 71:172202 Miyajima Y, Komukai T, Sugawa T, Yamamoto T (1994) Rare earth-doped fluoride fiber amplifiers, fiber lasers. Opt Fiber Technol 1:35–47 Möncke D (2017) Metal Ions and their Interactions in Covalent to Ionic Glass Systems—a Spectroscopic Study. Habilitation, Frierdich-Schiller-University Jena, Germany Möncke D, Eckert H (2019) Review on the structural analysis of fluoride–phosphate and fluoro–phosphate glasses. J Non-Cryst Solids: X 3:100026 Möncke D, Ehrt D, Velli L, Varsamis CPE, Kamitsos EI (2004) Structural investigation of fluoride phosphate glasses. XX Int Congr Glass, Kyoto, Japan Möncke D, Ehrt D, Velli LL, Varsamis CPE, Kamitsos EI (2005) Structure, properties of mixed phosphate and fluoride glasses. Phys Chem Glasses 46:67–71 Möncke D, Mountrichas G, Pispas S, Kamitsos EI (2011) Orientation phenomena in chromophore DR1-containing polymer films, their non-linear optical response. Mater Sci Eng B 176:515–520

Glass as a State of Matter

1085

Möncke D, Papageorgiou M, Winterstein-Beckmann A, Zacharias N (2014) Roman glasses coloured by dissolved transition metal ions: redox-reactions, optical spectroscopy, ligand field theory. J Archaeol Sci 46:23–36 Möncke D, Tricot G, Ehrt D, Kamitsos EI (2015) Connectivity of borate, silicate groups in a low-alkali borosilicate glass by vibrational and 2D NMR spectroscopy. J Chem Technol Metall 50:381–386 Möncke D, Kamitsos EI, Palles D, Limbach R, Winterstein A-Beckmann, Honma T, Yao Z, Rouxel T, Wondraczek L (2016) Transition, post-transition metal ions in borate glasses: Borate ligand speciation, cluster formation, and their effect on glass transition and mechanical properties. J Chem Phys 145:124501 Möncke D, Tricot G, Winterstein A, Ehrt D, Kamitsos EI (2017) Preferential bonding in low alkali borosilicate glasses. Phys Chem Glass—Euro J Glass Sci Technol Part B 58:171–179 Möncke D, da Cruz Barbosa Neto M, Bradtmüller H, de Souza GB, Rodrigues AM, Elkholy HS, Othman HA, Moulton BJ, Kamitsos EI, Rodrigues AC, Ehrt D (2018) NaPO3–AlF3 glasses: Fluorine evaporation during melting, the resulting variations in structure and properties. J Chem Technol Metall 53:1047–1060 Möncke D, Jiusti J, Silva LD, Rodrigues ACM (2018) Long-term stability of laser-induced defects in (fluoride-) phosphate glasses doped with W, Mo, Ta, Nb and Zr ions. J Non-Cryst Solids 498:401–414 Möncke D, Ali S, Jonson B, Kamitsos EI (2020) Anion polarizabilities in oxynitride glasses. Establishing a common optical basicity scale, Phys Chem Chem Phys 22:9543–9560 Montanari B, Barbosa AJ, Ribeiro SJL, Messaddeq Y, Poirier G, Li MS (2008) Structural study of thin films prepared from tungstate glass matrix by Raman, X-ray absorption spectroscopy. Appl Surf Sci 254:5552–5556 Montesso M, Manzani D, Donoso JP, Magon CJ, Silva IDA, Chiesa M, Morra E, Nalin M (2018) Synthesis and structural characterization of a new SbPO4–GeO2 glass system. J Non-Cryst Solids Mulfinger, H-O (1966) Physical, chemical solubility of nitrogen in glass melts. J Am Ceram Soc 49:462–467 Muñoz F (2011) Kinetic analysis of the substitution of nitrogen for oxygen in phosphate glasses. Phys Chem Glass— Euro J Glass Sci Technol Part B 52:181–186 Muñoz F, Delevoye L, Montagne L, Charpentier T (2013) New insights into the structure of oxynitride NaPON phosphate glasses by 17-oxygen NMR. J Non-Cryst Solids 363:134–139 Musgraves JD, Danto S, Richardson K (2014) Thermal properties of chalcogenide glasses. In: Chalcogenide Glasses Adam JL and Zhang X (eds) Woodhead Publishing, p 82–112 Musgraves JD, Hu J, Calvez L (2019) Springer Handbook of Glass, Springer Narasimhan LR, Littau KA, Pack DW, Bai YS, Elschner A, Fayer MD (1990) Probing organic glasses at low temperature with variable time scale optical dephasing measurements. Chem Rev 90:439–457 Nasikas NK, Chrissanthopoulos A, Bouropoulos N, Sen S, Papatheodorou GN (2011) Silicate glasses at the ionic limit: Alkaline-earth sub-orthosilicates. Chem Mater 23:3692–3697 Nasikas NK, Retsinas A, Papatheodorou GN (2014) Y3Al5O12–SiO2 glasses: Structure, polyamorphism. J Am Ceram Soc 97:2054–2060 Nienhuis ET, Saleh M, Marcial J, Kriegsman K, Lonergan J, Lipton AS, Guo X, McCloy JS (2019) Structural characterization of ZnSO4–K2SO4–NaCl glasses. J Non-Cryst Solids 524:119639 Ohta Y, Shimada M, Koizumi M (1982) Properties, structure of lithium borate and strontium borate glasses. J Am Ceram Soc 65:572–574 Ojovan MI, Lee WE (2011) Glassy wasteforms for nuclear waste immobilization. Metall Mater Trans A 42:837–851 Palles D, Konidakis I, Varsamis CPE, Kamitsos EI (2016) Vibrational spectroscopic, bond valence study of structure and bonding in Al2O3-containing AgI–AgPO3 glasses. RSC Advances 6:16697–16710 Pariafsai F (2016) A review of design considerations in glass buildings. Front Archit Res 5:171–193 Paul A (1990) Chemistry of Glasses. Netherlands, Springer Pereira C, Cassanjes FC, Barbosa JS, Gonçalves RR, Ribeiro SJL, Poirier G (2017) Structural and optical study of glasses in the TeO2–GeO2–PbF2 ternary system. J Non-Cryst Solids 463:158–162 Phillips JC (1979) Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys. J NonCryst Solids 34:153–181 Pisarska J, Sołtys M, Janek J, Górny A, Pietrasik E, Goryczka T, Pisarski WA (2018) Crystallization of lead-based and leadfree oxyfluoride germanate glasses doped with erbium during heat treatment process. J Non-Cryst Solids 501:121–125 Poulain M (1981) Glass formation in ionic systems. Nature 293:279–280 Poulain M, Maze G (1988) Chemistry of fluoride glasses. Chemtronics 3:77–85 Poulain M, Poulain M, Matecki M (1981) Verres fluores a large bande de transmission optique et a haute resistance chimique. Mater Res Bull 16:555–564 Poulain M, Soufiane A, Messaddeq Y, Aegerter MA (1992) Fluoride glasses: Synthesis, properties. Braz J Phys 22:205–217 Priven AI (2004) General method for calculating the properties of oxide glasses, glass forming melts from their composition and temperature. Glass Technol 45:244–254 Qiu H-H, Sakata H, Hirayama T (1996) Electrical conductivity of Fe2O3–PbO–Bi2O3 glasses. J Ceram Soc Jpn 104:1004–1007 Ràfols-Ribé J, Will P-A, Hänisch C, Gonzalez-Silveira M, Lenk S, Rodríguez-Viejo J, Reineke S (2018) Highperformance organic light-emitting diodes comprising ultrastable glass layers. Sci Adv 4:eaar8332 Ravaine D (1980) Glasses as solid electrolytes. J Non-Cryst Solids 38–39:353–358

1086

Möncke et al.

Richardson K, Krol D, Hirao K (2010) Glasses for photonic applications. Inter J Appl Glass Sci 1:74–86 Rinke MT, Eckert H (2011) The mixed network former effect in glasses: Solid state NMR, XPS structural studies of the glass system (Na2O)x(BPO4)1−x. Phys Chem Chem Phys 13:6552–6565 Rodrigues ACM, Nascimento MLF, Bragatto CB, Souquet J-L (2011) Charge carrier mobility, concentration as a function of composition in AgPO3–AgI glasses. J Chem Phys 135:234504 Rosenbaum JM, Wilson M, Condliffe E (1997) Partial melts of subducted phosphatic sediments in the mantle. Geology 25:77–80 Rouxel T (2007) Elastic properties, short-to medium-range order in glasses. J Am Ceram Soc 90:3019–3039 Rouxel T, Soraru G-D, Vicens J (2001) Creep viscosity, stress relaxation of gel-derived silicon oxycarbide glasses. J Am Ceram Soc 84:1052–1058 Saitoh A, Kitamura N, Ma L, Freudenberger P, Choudhury A, Takebe H, Brow RK (2017) Structural study of chemically durable BaO–FeOx–P2O5 glasses by Mössbauer spectroscopy and high performance liquid chromatography. J Non-Cryst Solids 460:106–112 Saitoh A, Brow RK, Hoppe U, Tricot G, Anan S, Takebe H (2018) The structure, properties of xZnO–(67 − x)SnO–P2O5 glasses: (I) optical and thermal properties, Raman and infrared spectroscopies. J Non-Cryst Solids 484:132–138 Saitoh A, Hoppe U, Brow RK, Tricot G, Hashida Y, Takebe H (2018) The structure, properties of xZnO–(67 − x) SnO–33P2O5 glasses: (III) Photoelastic behavior. J Non-Cryst Solids 498:173–176 Sanghera JS, Heo J, Mackenzie JD (1988) Chalcohalide glasses. J Non-Cryst Solids 103:155–178 Savage JA, Nielsen S (1965) Chalcogenide glasses transmitting in the infrared between 1, 20 μ — a state of the art review. Infrared Physics 5:195–204 Sawangboon N, Nizamutdinova A, Uesbeck T, Limbach R, Meechoowas E, Tapasa K, Möncke D, Wondraczek L, Kamitsos EI, van Wüllen L, Brauer DS (2019) Modification of silicophosphate glass composition, structure, properties via crucible material and melting conditions. Inter J Appl Glass Sci 11:46–57 Schaut RA, Weeks WP (2017) Historical review of glasses used for parenteral packaging. PDA J Pharm Sci Technol 71:279 SCHOTT Lithotec AG (2006) Synthetic Fused Silica Data Sheet Schütz A, Ehrt D, Dubiel M, Yang XC, Mosel B, Eckert H (2004) A multi-method characterization of borosilicate glasses doped with 1 up to 10 mol% of Fe, Ti, Sb. Glass Sci Technol 77:295–305 Schweizer F (2003) Glas des 2. Jahrtausends v. Chr. im Ostmittelmeerraum. BAG-Verlag Scully JR, Gebert A, Payer JH (2007) Corrosion, related mechanical properties of bulk metallic glasses. J Mater Res 22:302–313 Seddon AB (1995) Chalcogenide glasses: a review of their preparation, properties and applications. J Non-Cryst Solids 184:44–50 Seeber W, Downing EA, Hesselink L, Fejer MM, Ehrt D (1995) Pr3+-doped fluoride glasses. J Non-Cryst Solids 189:218–226 Sen P, DasMohapatra GK, Ghosh K, Sood N Biswas (2006) Aqueous durability of K2O–CaO–P2O5–SO3 glasses: Kinetics, mechanism. Phys Chem Glass Euro J Glass Sci Technol Part B 47:294–300 Sharmin N, Rudd CD (2017) Structure, thermal properties, dissolution behaviour, biomedical applications of phosphate glasses and fibres: A Review. J Mater Sci 52:8733–8760 Shelby JE (1974) Properties, structure of B2O3–GeO2 glasses. J Appl Phys 45:5272–5277 Shelby JE (2005) Introduction to Glass Science and Technology, Royal Society of Chemistry Shen W, Baccaro S, Cemmi A, Xu X, Chen G (2015) Gamma-ray irradiation induced bulk photochromism in WO3– P2O5 glass. Nucl Instrum Methods Phys Res Sect B 362:34–37 Shirosaki Y, Osaka A, Tsuru K, Hayakawa S (2012) Inorganic–Organic Sol–Gel Hybrids. Bio-Glasses, John Wiley & Sons, Ltd: 139–158 Simon S, Ardelean I, Filip S, Bratu I, Cosma I (2000) Structure, magnetic properties of Bi2O3–GeO2–Gd2O3 glasses. Solid State Commun 116:83–86 Skopak T, Serment B, Ledemi Y, Dussauze M, Cardinal T, Fargin E, Messaddeq Y (2018) Structure-properties relationship study in niobium oxide containing GaO3/2–LaO3/2–KO1/2 gallate glasses. Mater Res Bull Soltani MT, Haddad S, Möncke D, Kamitsos EI (2016) Structural investigations of binary glasses Sb2O3–Na2O by Raman, FTIR and optical spectroscopy using Co2+ as probe ion. Society of Glass Technology Centenary Conference and ESG, September 4–8, 2016 Sheffield, UK Stanworth JE (1952) Tellurite glasses. Nature 169:581–582 Stokes ME, Schreiber HD (2006) Copper as a structural probe for acetate glass. Phys Chem Glass Euro J Glass Sci Technol Part B 47:233–235 Šubčík J, Koudelka L, Mošner P, Montagne L, Tricot G, Delevoye L, Gregora I (2010) Glass-forming ability, structure of ZnO–MoO3–P2O5 glasses. J Non-Cryst Solids 356:2509–2516 Suryanarayana C, Inoue A (2017) Physical Properties of Bulk Metallic Glasses. Boca Raton, FL, CRC Press Svoboda R, Málek J (2015) Evaluation of glass-stability criteria for chalcogenide glasses: Effect of experimental conditions. J Non-Cryst Solids 413:39–45 Tagiara NS, Palles D, Simandiras ED, Psycharis V, Kyritsis A, Kamitsos EI (2017) Synthesis, thermal, structural properties of pure TeO2 glass and zinc–tellurite glasses. J Non-Cryst Solids 457(Suppl C):116–125

Glass as a State of Matter

1087

Tagiara NS, Chatzipanagis KI, Bradtmüller H, Rodrigues ACM, Möncke D, Kamitsos EI (2021) Network former mixing effects in alkali germanotellurite glasses: A vibrational spectroscopic study. J Alloy Compd 882:160782 Terashima K, Hashimoto T, Uchino T, S-Kim H, Yoko T (1996) Structure, nonlinear optical properties of Sb2O3-B2O3 binary glasses. J Ceram Soc Jpn 104:1008–1014 Thieme A, Möncke D, Limbach R, Fuhrmann S, Kamitsos EI, Wondraczek L (2015) Structure, properties of alkali and silver sulfophosphate glasses. J Non-Cryst Solids 410:142–150 Tick PA (1985) Glass forming in the cadmium fluoride–lithium fluoride–aluminium fluoride–lead fluoride system. Mater Sci Forum 5–6:165–165 Tite M, Shortland A, Paynter S (2002) The beginnings of vitreous materials in the Near East, Egypt. Acc Chem Res 35:585–593 Tsuchida JE, Ferri FA, Pizani PS, Martins AC Rodrigues, Kundu S, Schneider JF, Zanotto ED (2017) Ionic conductivity, mixed-ion effect in mixed alkali metaphosphate glasses. Phys Chem Chem Phys 19:6594–6600 Uesbeck T, Eckert H, Youngman R, Aitken B (2017) The structure of borophosphosilicate pure network former glasses studied by multinuclear NMR spectroscopy. J Phys Chem C 121:1838–1850 Upender G, Prasad M, Mouli VC (2011) Vibrational, EPR, optical spectroscopy of the Cu2+ doped glasses with (90–x)TeO2–10GeO2–xWO3 (75≤ x ≤30) composition. J Non-Cryst Solids 357:903–909 Uusitalo O (2010) Revisiting the case of float glass. Euro J Innovation Manage 13:24–45 Van Wazer JR, Holst KA (1950) Structure, properties of the condensed phosphate. I. Some general considerations about phosphoric acids. J Am Chem Soc 72:639–644 van Wüllen L, Eckert H, Schwering G (2000) Structure−property correlations in lithium phosphate glasses: New insights from 31P ↔ 7Li double-resonance NMR. Chem Mater 12:1840–1846 Varshneya AK (2013) Fundamentals of inorganic glasses. Sheffield, UK, Society of Glass Technology Vaughn WL, Risbud SH (1984) New fluoronitride glasses in zirconium–metal–F–N systems J Mater Sci Letters 3:162–164 Velli LL, Varsamis CP E, Kamitsos EI, Möncke D, Ehrt D (2005) Structural investigation of metaphosphate glasses. Phys Chem Glasses 46:178–181 Venkatachalam S, Schröder C, Wegner S, van Wüllen L(2014) The structure of a borosilicate, phosphosilicate glasses and its evolution at temperatures above the glass transition temperature: Lessons from in situ MAS NMR. Phys Chem Glasses—Euro J Glass Sci Technol Part B 55:280–287 Verger F, Pain T, Nazabal V, Boussard C-Plédel, Bureau B, Colas F, Rinnert E, Boukerma K, Compère C, Guilloux M-Viry, Deputier S, Perrin A, Guin JP (2012) Surface enhanced infrared absorption (SEIRA) spectroscopy using gold nanoparticles on As2S3 glass. Sensors Actuators B 175:142–148 Videau J-J, Portier J, Blanzat B, Barthou C (1979) Etude spectroscopique par la technique d’affinement de raie de fluorescence de verres fluorophosphates dopes a Eu3+. Mater Res Bull 14:1225–1229 Vogel W (1992) Glass Chemistry, Springer-Verlag Von Jebsen-Marwedel H (2011) Glastechnische Fabrikationsfehler, Einführung. Berlin, Heidelberg, Springer Berlin Heidelberg Walker B, Dharmawardhana CC, Dari N, Rulis P, Ching W-Y (2015) Electronic structure and optical properties of amorphous GeO2 in comparison to amorphous SiO2. J Non-Cryst Solids 428:176–183 Wang C, Zimmer J (2015) Aluminosilicate glass for touch screen. USA, SCHOTT GLASS TECHNOLOGIES (SUZHOU) CLTD O (Jiangsu, CN) Wang JS, Vogel EM, Snitzer E (1994) Tellurite glass: A new candidate for fiber devices. Optical Materials 3:187–203 Weber MJ (2006) Optical Properties of Glasses. Mater Sci Technol, Wiley-VCH Verlag GmbH & Co. KGaA Weber JKR, Rix JE, Hiera KJ, Tangeman JA, Benmore CJ, Hart RT, Siewenie JE, Santodonato LJ (2005) Neutron diffraction from levitated liquids—a technique for measurements under extreme conditions. Phys Chem Glass 46:487–491 Wiberg N, Wiberg E, Holleman A (2007) Lehrbuch der Anorganischen Chem, de Gruyter & Co, Berlin Wilk NR Jr, Schreiber HD (1997) Co2+ as a structural probe in acetate liquids, glasses. J Non-Cryst Solids 217: 189–198 Winterstein-Beckmann A, Möncke D, Palles D, Kamitsos EI, Wondraczek L (2013) Structure–property correlations in highly modified Sr, Mn-borate glasses. J Non-Cryst Solids 376:165–174 Winterstein-Beckmann A, Möncke D, Palles D, Kamitsos EI, Wondraczek L (2015) Structure, Properties of Orthoborate Glasses in the Eu2O3–(Sr,Eu)O–B2O3 Quaternary. J Phys Chem B 119:3259–3272 Wójcik NA, Jonson B, Barczyński RJ, Kupracz P, Möncke D, Ali S (2018a) Electrical properties of Na2O–CaO–P2O5 glasses doped with SiO2 and Si3N4. Solid State Ionics 325:157–162 Wójcik NA, Jonson B, Möncke D, Palles D, Kamitsos EI, Ghassemali E, Seifeddine S, Eriksson M, Ali S (2018b) Influence of synthesis conditions on glass formation, structure and thermal properties in the Na2O–CaO–P2O5 system doped with Si3N4 and Mg. J Non-Cryst Solids 494:66–77 Wright AC (2010) Borate structures: Crystalline and vitreous. Phys Chem Glass—Euro J Glass Sci Technol Part B 51:1–39 Wright AC (2014) The great crystallite versus random network controversy: A personal perspective. Inter J Appl Glass Sci 5:31–56 Wright AC, Hannon AC, Clare AG, Sinclair RN, Johnson WL, Atzmon M, Mangin P (1985) A neutron diffraction investigation of the atomic, magneticstructure of amorphous Dy7Ni3. J Phys Colloq 46:C8-299–C298-303

1088

Möncke et al.

Wright AC, Dalba G, Rocca F, Vedishcheva NM (2010) Borate versus silicate glasses: Why are they so different? Phys Chem Glass Euro J Glass Sci Technol Part B 51:233–265 Wright AC, Clare AG, Etherington G, Sinclair RN, Brawer SA, Weber MJ (1989) A neutron diffraction, molecular dynamics investigation of the structure of vitreous beryllium fluoride. J Non-Cryst Solids 111:139–152 Wright AC, Sinclair RN, Stone CE, Shaw JL, Feller SA, Williams RB, Fischer HE, Vedishcheva NM (2014) A neutron diffraction study of sodium, rubidium, caesium borate glasses. Phys Chem Glass Euro J Glass Sci Technol Part B 55:74–84 Wuttig M, Yamada N (2007) Phase-change materials for rewriteable data storage. Nat Mater 6:824–832 Yang Z, Wilhelm AA, Lucas P (2010) High-conductivity tellurium-based infrared transmitting glasses, their suitability for bio-optical detection. J Am Ceram Soc 93:1941–1944 Yano T, Kunimine N, Shibata S, Yamane M (2003a) Structural investigation of sodium borate glasses and melts by Raman spectroscopy.: I. Quantitative evaluation of structural units. J Non-Cryst Solids 321:137–146 Yano T, Kunimine N, Shibata S, Yamane M (2003b) Structural investigation of sodium borate glasses and melts by Raman spectroscopy. II. Conversion between BO4 and BO2O-units at high temperature. J Non-Cryst Solids.. J Non-Cryst Solids 321:157–168 Yano T, Kunimine N, Shibata S, Yamane M (2003c) Structural investigation of sodium borate glasses and melts by Raman spectroscopy. III. Relation between the rearrangement of super-structures and the properties of glass. J Non-Cryst Solids 321:147–156 Yiannopoulos YD, Chryssikos GD, Kamitsos EI (2001) Structure, properties of alkaline earth borate glasses. Phys Chem Glasses 42:164–172 Youngmann RE (2022) Silicate glasses and their impact on humanity. Rev Mineral Geochem 87:1015-1038 Yuan B, Zhu W, Hung I, Gan Z, Aitken B, Sen S (2018) Structure, chemical order in S–Se binary glasses. J Phys Chem B 122:12219–12226 Yue X, Inoue A, Liu C-T, Fan C (2017) The development of sructure model in metallic glasses. Materials Research 20:326–338 Zachariasen WH (1932) The atomic arrangement in glass. J Am Chem Soc 54:3841–3851 Zakery A, Elliott SR (2003) Optical properties, applications of chalcogenide glasses: a review. J Non-Cryst Solids 330:1–12 Zallen R (1998) The Physics of Amorphous Solids, Wiley-VCH Verlag GmbH & Co. KGaA Zanotto ED, Coutinho FAB (2004) How many non-crystalline solids can be made from all the elements of the periodic table? J Non-Cryst Solids 347:285–288 Zanotto ED, Mauro JC (2017) The glassy state of matter: Its definition and ultimate fate. J Non-Cryst Solids 471:490–495 Zhang L, Eckert H (2006) Short-, medium-range order in sodium aluminophosphate glasses: New insights from highresolution dipolar solid-state NMR spectroscopy. J Phys Chem B 110:8946–8958 Zhang W, Shao J, Xu X, Wang R, Chen L (2007) Mantle metasomatism by P-, F-rich melt/fluids: Evidence from phosphate glass in spinel lherzolite xenolith in Keluo, Heilongjiang Province. Chin Sci Bull 52:1827–1835 Zhang L, Hu L, Jiang S (2018) Progress in Nd3+, Er3+, Yb3+ doped laser glasses at Shanghai Institute of Optics and Fine Mechanics. Inter J Appl Glass Sci 9:90–98 Zhao J, Ragazzi E, McKenna GB (2013) Something about amber: Fictive temperature, glass transition temperature of extremely old glasses from copal to Triassic amber. Polymer 54:7041–7047 Zhao S, Li L, Wang H, Zhang Y, Cheng X, Zhou N, Rahaman MN, Liu Z, Huang W, Zhang C (2015) Wound dressings composed of copper-doped borate bioactive glass microfibers stimulate angiogenesis and heal full-thickness skin defects in a rodent model. Biomaterials 53:379–391 Zhou C, Longley L, Krajnc A, Smales GJ, Qiao A, Erucar I, Doherty CM, Thornton AW, Hill AJ, Ashling CW, Qazvini OT, Lee SJ, Chater PA, Terrill NJ, Smith AJ, Yue Y, Mali G, Keen DA, Telfer SG, Bennett TD (2018) Metal-organic framework glasses with permanent accessible porosity. Nat Commun 9:5042 Zmojda J, Kochanowicz M, Miluski P, Leśniak M, Sitarz M, Pisarski W, Pisarska J, Dorosz D (2016) Effect of GeO2 content on structural, spectroscopic properties of antimony glasses doped with Sm3+ ions. J Mol Struct 1126(Suppl C): 207–212 Zschimmer E, Cable MT (2013) Chemical Technology of Glass, Society of Glass Technology