From glass to crystal: Nucleation, growth and phase separation: from research to applications 9782759819973, 9782759817832

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FROM GLASS TO CRYSTAL Nucleation, growth and phase ­separation, from research to applications

FROM GLASS TO CRYSTAL Nucleation, growth and phase ­separation, from research to applications

Editors Daniel R. Neuville, Laurent Cormier, Daniel Caurant, Lionel Montagne

EDP SCIENCES EDP Sciences Ltd Hamilton House, Mabledon Place, Bloomsbury, London WC1H 9BB, UK EDP Sciences SA 17, Avenue du Hoggar, PA de Courtabœuf, F-91940 Les Ulis, France Published in France by EDP Sciences SA, Les Ulis www.edpsciences.org

© EDP Sciences 2017 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad-casting, reproduction on microfilms or in other ways, and storage in data bank. Duplication of this publication or parts thereof is only permitted under the provisions of the French Copyright law of March 11, 1957. Violations fall under the prosecution act of the French Copyright law. Printed in France. ISBN 978-2-7598-1783-2

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Foreword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main symbols and physical constants. . . . . . . . . . . . . Abbreviations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main crystalline phases considered in this book.

1 5 7 9 13 15 17

Chapter 1: The classical nucleation theory. . . 19 1.1. From devitrification… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. … to the origins of CNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. Homogeneous nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1. Thermodynamic considerations. . . . . . . . . . . . . . . . . . . . . . . 1.3.2. Kinetic considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3. Nucleation rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4. Examples of glasses with homogeneous nucleation . . . . . . . . . 1.4. Heterogeneous nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5. Induction time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6. Crystal growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.1. Crystal growth rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.2. Crystalline morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.3. Constraints on crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.4. Ostwald ripening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6.5. TTT diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7. CNT facing experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20 21 22 22 25 26 27 29 31 33 33 35 38 38 39 40

II

From Glass to Crystal

1.8. Ostwald’s rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 1.9. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Chapter 2: Beyond the classical nucleation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Cluster dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density functional theory (DFT) . . . . . . . . . . . . . . . . . . . . . . . . . . Validity of the Stokes-Einstein equation? . . . . . . . . . . . . . . . . . . . . Models of non-classical nucleus . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. Introduction of a fractal surface . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Diffuse interface theory (DIT) . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3. Experimental observations of the critical nucleus? . . . . . . . . . . 2.5. Non-homogeneous disordered system . . . . . . . . . . . . . . . . . . . . . . 2.5.1. Nucleation theory in systems with static local disorder . . . . . . . 2.5.2. Recent experimental observations . . . . . . . . . . . . . . . . . . . . . 2.6. Generalized Gibbs’s approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1. Simplified theoretical description . . . . . . . . . . . . . . . . . . . . . . 2.6.2. Implications for nucleation/growth . . . . . . . . . . . . . . . . . . . . 2.6.3. Experimental observations of metastable nucleation . . . . . . . . 2.7. Two-step model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.1. Description of the two-step model . . . . . . . . . . . . . . . . . . . . . . 2.7.2. Experimental observations . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. 2.2. 2.3. 2.4.

43 45 47 47 48 49 50 51 51 53 54 54 57 60 62 62 64 65

Chapter 3: Thermodynamics of the glassy and the crystalline states– General kinetics of return to equilibrium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.1. Stability and instability: application to oxide glasses . . . . . . . . . . . 3.1.1. Stability and postulates of thermodynamics. . . . . . . . . . . . . . . 3.1.2. The stability condition – Back to equilibrium . . . . . . . . . . . . . 3.1.3. Application to the specific case of the spinodal decomposition (cf. also chapter 4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.4. Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Experimental methods for the determination of thermodynamic quantities at the equilibrium of a stable or metastable oxide glass or crystal . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Overview of thermodynamic measurable quantities . . . . . . . . .

68 68 71 73 75 77 77

Contents

III

3.2.2.

Measurement of enthalpy increment, heat capacity and transition enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.2.3. Measurement of the formation or mixing functions . . . . . . . . . 91 3.2.4. Measurement of free enthalpy and derivative quantities by Knudsen Effusion Mass Spectrometry (KEMS) . . . . . . . . . . . . 98 3.2.5. Importance of coupling the methods . . . . . . . . . . . . . . . . . . . . 101 3.3. Parameters characterizing the metastable vitreous state . . . . . . . . 103 3.3.1. Thermodynamical description of the glass transition . . . . . . . . 103 3.3.2. The fictive temperature and its measurement . . . . . . . . . . . . . . 106 3.3.3. Configurational entropy at 0 K and its measurement . . . . . . . . 108 3.3.4. Kinetic approach of the glassy transition – order parameter . . . . 109 3.4. Phenomenological approach of recrystallisation kinetics – Return to equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.4.1. Transformation by nucleation and growth - constant rate . . . . . 115 3.4.2. Transformation by nucleation and growth – constant growth rate, time-dependent germination rate . . . . . . . . . . . . . . . . . . 118 3.4.3. General form of the kinetic equation . . . . . . . . . . . . . . . . . . . 119 3.4.4. In practice… . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 3.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Chapter 4: Phase separation processes in glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.2. Thermodynamic description of phase separation . . . . . . . . . . . . . 126 4.2.1. Solubility in ideal solutions . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.2.2. Immiscibility in regular solutions . . . . . . . . . . . . . . . . . . . . . 127 4.2.3. Description of immiscibility regions in glass . . . . . . . . . . . . . . 130 4.3. Kinetics of phase separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.3.1. Effect of diffusion mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.3.2. Kinetics of phase separation by nucleation and growth . . . . . . . 137 4.3.3. Spinodal decomposition: Approach adopted by Cahn and Hilliard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.4. Influence of structure on the phase separation tendency of glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.4.1. Structural models: binary silicate and borate systems . . . . . . . . 140 4.4.2. Effect of the addition of elements on phase separation. . . . . . . . 144 4.4.3. Structural characterisation tools . . . . . . . . . . . . . . . . . . . . . . 146 4.5. Characterisation of phase separation . . . . . . . . . . . . . . . . . . . . . . . 146 4.5.1. Metastable phase separation . . . . . . . . . . . . . . . . . . . . . . . . . 146

IV

From Glass to Crystal

4.5.2. 4.5.3.

Stable phase separation extending into the metastable range . . . 148 Example of phase separation mode . . . . . . . . . . . . . . . . . . . . 150

Chapter 5: Solid-state chemistry approach of the main crystallinephases in glass-ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.2. Silicate crystalline phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.2.1. General features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.2.2. The six silicate families . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 5.2.3. Silica polymorphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 5.3. Phosphates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 5.3.1. Consequence of phosphorus pentavalency . . . . . . . . . . . . . . . . 171 5.3.2. Phosphate families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 5.3.3. Formation of non-phosphate crystals in phosphate based glass matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 5.4. Other crystalline phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 5.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Chapter 6: Elaboration and control of glass-ceramic microstructures . . . . . . . . . . . . . . . 185 6.1. Interest of controlling glass-ceramic microstructure . . . . . . . . . . . 185 6.2. Controllable parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6.2.1. Parent glass composition . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6.2.2. Nucleation/growth mechanism . . . . . . . . . . . . . . . . . . . . . . . 186 6.2.3. Thermal treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 6.3. Elaboration processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6.3.1. Classic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6.3.2. New glass-ceramic elaboration processes . . . . . . . . . . . . . . . . . 190 6.4. Characterisation methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 6.5. Microstructure types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 6.5.1. Spheroid microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 6.5.2. Needle-like microstructures . . . . . . . . . . . . . . . . . . . . . . . . . . 195 6.6. Designing glass-ceramics with desired properties by controlling the crystallisation process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 6.6.1. Volume nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Contents

V

6.6.2. Surface nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 6.6.3. Double nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 6.7. Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

Chapter 7: X-ray diffraction and glass-ceramic materials

. . . . . . . . . . . . . . . . . . . . . 201 7.1. Reminder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 7.1.1. X-ray/matter interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 7.1.2. Scattering by a single atom . . . . . . . . . . . . . . . . . . . . . . . . . . 203 7.1.3. The Bragg law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 7.1.4. Reciprocal space and diffraction . . . . . . . . . . . . . . . . . . . . . . 207 7.1.5. Diffracted intensity and correction terms . . . . . . . . . . . . . . . . 208 7.1.6. Bragg peak profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 7.2. Sample preparation and acquisition geometry . . . . . . . . . . . . . . . . 218 7.2.1. Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 7.2.2. Acquisition geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.3. Quantitative analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 7.3.1. Samples with low absorption contrast. . . . . . . . . . . . . . . . . . . 220 7.3.2. Samples with intermediate absorption contrast . . . . . . . . . . . . 220 7.3.3. Quantification for an “amorphous” phase‑containing compound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 7.3.4. Example of phase quantification in a nuclear glass . . . . . . . . . 223 7.4. Beyond conventional XRD analysis . . . . . . . . . . . . . . . . . . . . . . . . 225 7.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

Chapter 8: Glass and crystallisation: mechanical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 8.1. Effective elastic properties of glass-ceramics . . . . . . . . . . . . . . . . . 229 8.2. Hardness of glass-ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 8.3. Strength and toughness of glass-ceramics . . . . . . . . . . . . . . . . . . . 233 8.3.1. Theoretical and experimental considerations . . . . . . . . . . . . . . 233 8.3.2. Role of the microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 8.4. Residual stresses and cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 8.4.1. Modelling residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . 239 8.4.2. Residual stresses and microcracking . . . . . . . . . . . . . . . . . . . 241 8.4.3. Residual stress measurements . . . . . . . . . . . . . . . . . . . . . . . . 244

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From Glass to Crystal

8.5. Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 8.6. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Chapter 9: Electron microscopy applied to the study of nucleation and crystallisation in glasses . . . . . . . . . . . . . . . . . . . . . 249 9.1. Scanning Electron Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 9.2. Transmission Electron Microscopy . . . . . . . . . . . . . . . . . . . . . . . . 250 9.2.1. Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 9.2.2. TEM imaging techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 9.2.3. STEM-HAADF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 9.2.4. EELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 9.2.5. Chemical imaging: Energy Filtered TEM - EFTEM . . . . . . . . . 262 9.2.6. Aberration correction in HRTEM and STEM . . . . . . . . . . . . 263 9.2.7. Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 9.3. Nucleation/growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 9.3.1. Observation and nature of initial crystals . . . . . . . . . . . . . . . 264 9.3.2. Mechanisms of nucleation and role of nucleating agents . . . . . 265 9.3.3. Secondary crystallisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 9.4. Heterogeneities and phase separation . . . . . . . . . . . . . . . . . . . . . . 268 9.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

Chapter 10: X-ray and neutron small-angle scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 10.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 10.2. X-ray and neutron scattering: Specificities and complementarities . . . . . . . . . . . . . . . . . . . . . . . . 271 10.3. Distances and phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 10.3.1. Thermal density fluctuations . . . . . . . . . . . . . . . . . . . . . . . . 272 10.3.2. Chemical concentration fluctuations . . . . . . . . . . . . . . . . . . 273 10.3.3. Supercritical fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 10.4. Basic notions for small-angle scattering . . . . . . . . . . . . . . . . . . . . . 273 10.5. Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 10.6. Examples of applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 10.6.1. Detailed example of a liquid-liquid phase separation in a glass containing molybdenum . . . . . . . . . . . . . . . . . . . . . . 278 10.6.2. Other examples of study of phase separation . . . . . . . . . . . . . . 281

Contents

VII

10.6.3. 10.6.4. 10.6.5.

Nucleation study by SANS and SAXS . . . . . . . . . . . . . . . . . . 283 Example of nucleation and crystallisation in a glass by SANS . 283 Example of nucleation and crystallisation in a cordierite glass by SAXS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284 10.7. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

Chapter 11: Nuclear Magnetic Resonance: deciphering disorderand crystallisation phenomena in glassy materials . . . . . . . . . . . . . . . . . . 291 11.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 11.2. Basic principles of NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 11.2.1. NMR interactions: a fingerprint of the local environment . . . . . 294 11.2.2. The solid-state NMR toolkit . . . . . . . . . . . . . . . . . . . . . . . . . 295 11.3. Spectral signature of disorder in NMR and its resolution . . . . . . . 299 11.3.1. NMR of disordered systems . . . . . . . . . . . . . . . . . . . . . . . . . . 300 11.3.2. Combining NMR with atomistic modelling. . . . . . . . . . . . . . . 303 11.4. Application to crystallisation studies . . . . . . . . . . . . . . . . . . . . . . . 305 11.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

Chapter 12: Raman spectroscopy: a valuable tool to improveour understanding of nucleation and growth mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 12.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 12.2. Principle of Raman spectrometry . . . . . . . . . . . . . . . . . . . . . . . . . 320 12.3. Instrumentation and Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 12.3.1. HOLOLAB 5000 spectrometer . . . . . . . . . . . . . . . . . . . . . . . 322 12.3.2. T64000 spectrometer and the confocal system . . . . . . . . . . . . . 323 12.3.3. Sampling volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 12.3.4. Raman spectra intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 12.3.5. Black body emission and limitation to performing in situ measurements at high temperature . . . . . . . . . . . . . . . . . . . . . 325 12.3.6. Correction of the temperature effect and excitation wavelength . . 327 12.4. Various experimental studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 12.4.1. Nucleation and phase identification in the CaO-Al2O3-SiO2 system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 12.4.2. Ex situ measurements of silicate apatite crystallisation in a borosilicate matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330

VIII

From Glass to Crystal

12.4.3.

In situ study of silico apatite crystallisation in a borosilicate matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 12.4.4. Induced crystallisation by laser impact in GeO2 glass . . . . . . . . 335 12.4.5. Molybdenum demixion in a borosilicate glass . . . . . . . . . . . . . 337 12.5. Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

Chapter 13: In situ crystallisation investigations using large scale facilities . . . . . . . . . . . . . . . . . . . . . . . . . 345 13.1. X-ray absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 13.1.1. Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 13.1.2. Applications and results . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 13.2. X-ray and neutron scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 13.3. Non-conventional furnaces on high facilities . . . . . . . . . . . . . . . . . 352 13.3.1. Aerodynamic levitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 13.3.2. Micro heating device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 13.4. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

Chapter 14: Commercial applications of glass-ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 14.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 14.2. Microstructure and formation of glass-ceramics . . . . . . . . . . . . . . 361 14.2.1. Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 14.2.2. Glass-ceramic formation by crystal nucleation and growth . . . . 362 14.3. Glass-ceramic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 14.4. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 14.4.1. Transparent low-expansion glass-ceramics . . . . . . . . . . . . . . . 367 14.4.2. Other transparent glass-ceramics . . . . . . . . . . . . . . . . . . . . . . 370 14.4.3. Machinable glass-ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . 370 14.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

Chapter 15: Glass and glass-ceramic biomaterials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 15.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 15.2. Dental applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376 15.2.1. Materials for structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376

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15.2.2. Materials for aesthetics (cosmetics) . . . . . . . . . . . . . . . . . . . . 378 15.2.3. Bone reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 15.2.4. Bioactive coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 15.3. Orthopaedic applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 15.3.1. Monolithic glasses and glass-ceramics . . . . . . . . . . . . . . . . . . 380 15.3.2. Polymer-matrix composites . . . . . . . . . . . . . . . . . . . . . . . . . . 383 15.4. Biocidal glasses and glass-ceramics . . . . . . . . . . . . . . . . . . . . . . . . 385 15.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

Chapter 16: Colouring by metallic nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 16.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 16.2. Surface plasmons in metal colloids . . . . . . . . . . . . . . . . . . . . . . . . 388 16.3. Gold ruby glass and copper red glazes. . . . . . . . . . . . . . . . . . . . . . 392 16.3.1. Gold ruby glass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 16.3.2. Copper red glazes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 16.4. Luster ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 16.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400

Chapter 17: Transparent glass-ceramics

. . . . . . 407 17.1. Interest of transparent glass-ceramics . . . . . . . . . . . . . . . . . . . . . . 407 17.2. Transparency in glass-ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 17.2.1. General principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 17.2.2. Light scattering in transparent glass-ceramics . . . . . . . . . . . . . 408 17.2.3. Transparent glass-ceramic synthesis . . . . . . . . . . . . . . . . . . . . 410 17.2.4. Opalescence: a particular case . . . . . . . . . . . . . . . . . . . . . . . 411 17.3. Properties and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 17.3.1. Transparent glass-ceramics based on oxide compositions . . . . . . 413 17.3.2. Transparent glass-ceramics based on fluoride/oxyfluoride compositions . . . . . . . . . . . . . . . . . . . 417 17.3.3. Transparent glass-ceramics based on chalcogenides . . . . . . . . . 419 17.4. Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

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Chapter 18: Luminescence properties of rare earth ions dopedin insulating nanoparticles embedded in glassy hosts . . . . . . 423 18.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 18.2. Optical properties of rare earth ions in bulk materials . . . . . . . . . 425 18.2.1. Energy level structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 18.2.2. Transition intensities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 18.2.3. Homogeneous and inhomogeneous broadening of transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 18.2.4. Radiative and non-radiative lifetimes . . . . . . . . . . . . . . . . . . 428 18.2.5. Energy transfers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 18.3. Luminescence of rare earth ion doped nanoparticles . . . . . . . . . . 429 18.3.1. Phonon spectrum modification . . . . . . . . . . . . . . . . . . . . . . . 429 18.3.2. Structural effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 18.3.3. Surface effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 18.3.4. Quantum confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 18.4. RE doped nanoparticles luminescence and influence of the host matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 18.4.1. Dependence of the radiative lifetime on the refractive index of the surrounding host . . . . . . . . . . . . . . . . . . . . . . . 434 18.4.2. Two-level system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436 18.4.3. Interaction with “phonons” of the glassy environment . . . . . . . 437 18.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

Chapter 19: Glass-ceramics for engineering optical propertiesand nonlinear optics for engineering glass ceramics . . . . . . . . . . . . . . . . . . 441 19.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 19.2. Units and nonlinear optical phenomena . . . . . . . . . . . . . . . . . . . . 442 19.2.1. Second order nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . 442 19.2.2. Third order nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 19.3. Glass ceramic for nonlinear optics . . . . . . . . . . . . . . . . . . . . . . . . 444 19.3.1. Second order nonlinearity and second harmonic generation . . . 444 19.3.2. Third order nonlinearity and saturable absorption . . . . . . . . . 448 19.4. Laser induced phase separation and crystallisation . . . . . . . . . . . . 449 19.4.1. Laser-assisted crystallisation and second order nonlinearity . . . 450 19.4.2. Nonlinear optics and fabrication of glass ceramics. . . . . . . . . . 451 19.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

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Chapter 20: Oxyfluoride glass-ceramics . . . . . . . 459 20.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 20.2. Synthesis of oxyfluoride glass-ceramics . . . . . . . . . . . . . . . . . . . . . 460 20.3. Genesis, size and morphologies of fluoride particles inside a glassy matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 20.4. Crystallinity and size of the fluoride particles as function of the duration of the thermal treatment . . . . . . . . . . . . . . . . . . . . 466 20.5. Constraints induced by the glassy matrix and lattice parameters of the crystallized phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 20.6. Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 20.7. Conclusion and future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . 470

Chapter 21: Nucleation, crystallisation and phase separationin chalcogenide glasses . . . . 473 21.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 21.2. Chalcogenide glass-ceramics for infrared optics . . . . . . . . . . . . . . 474 21.2.1. Chalcogenide glass-ceramics for non-linear optics . . . . . . . . . . 475 21.2.2. Chalcogenide glass-ceramics with improved mechanical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 21.2.3. Increase of up-conversion luminescence . . . . . . . . . . . . . . . . . 478 21.3. Phase change tellurides: outstanding materials for information storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 21.4. Ion conductive chalcogenide glasses: effects of phase separation and partial crystallisation on electrical properties . . . . 483 21.4.1. Chalcogenide glass-ceramics for electrochemical energy storage . . 483 21.4.2. Photosensitive chalcogenide glasses, potential resins for submicronic resolution lithography . . . . . . . . . . . . . . . . . . 485 21.4.3. Chalcogenide glasses: promising materials for the development of ionic memories. . . . . . . . . . . . . . . . . . . 486 21.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

Chapter 22: Glass-ceramics for waste immobilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 22.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 22.2. Glass-ceramics for the immobilization of highly radioactive wastes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 22.2.1. Nature and origin of highly radioactive wastes. Aims of containment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494

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22.2.2. Glass-ceramic matrices to immobilize non‑separated wastes . . . . 496 22.2.3. Glass-ceramics to immobilize separated long‑life wastes . . . . . . . 509 22.3. Glass-ceramics for the immobilization of toxic or hazardous non-radioactive wastes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 22.3.1. Toxic or hazardous non-radioactive wastes: various origins and compositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 22.3.2. Vitrification and glass-ceramization of non‑radioactive wastes . 518 22.4. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

Chapter 23: Crystalline glazes

. . . . . . . . . . . . . . . . . . . 527 23.1. From traditional ceramics to glaze formulation . . . . . . . . . . . . . . . 527 23.2. The discovery of the role of zinc in crystalline glazes . . . . . . . . . . 529 23.3. Other crystal-glaze compositions: matte glazes . . . . . . . . . . . . . . . 536 23.4. Other examples of controlled crystallisations . . . . . . . . . . . . . . . . 537 23.5. Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figures Rights & Permissions . . . . . . . . . . . . . . . . . . . . . .

541 627 637

Preface

The glass research community agrees that the first reported attempt to control glass crystallisation was made by a French chemist René-Antoine Ferchault de Réaumur in 1736, who heat-treated a glass bottle in a bed of sand and gypsum, hoping to produce a porcelain vase… I am therefore delighted with this new undertaking by a group of Réaumur’s fellow countrymen, distinguished scientists who have written and compiled a particularly well-organized collection of chapters on a plethora of relevant scientific and technological problems pertaining to glass crystallisation processes; my favourite research topic! The first version, published in 2013, was written in French (which explains why all the authors are French). In the following paragraphs, I elucidate why I’m convinced of the keen interest and enthusiasm with which the international community will receive this new, English version. Glass has been a key material to mankind since the dawn of civilization. In his famous monograph “The Properties of Glass” published in 1938 and 1954, George W. Morey emphasized that “Devitrification is the chief factor which limits the composition range of practical glasses, it is an ever-present danger in all glass manufacture and working, and takes place promptly with any error in composition or technique.” On the other hand, by virtue of their exotic properties and uses, glass-ceramics are very important derivatives of glass. These polycrystalline materials are obtained via the controlled crystallisation of certain glasses that contain one or more crystalline phases dispersed in a residual glass matrix. The distinct chemical nature of these phases and their nano- or microstructures has given rise to various unusual combinations of properties and to exotic applications. In a recent article entitled “Two Centuries of Glass Research: Historical Trends, Current Status, and Grand Challenges for the Future“ – International Journal of Applied Glass Science 07/2014 – John C. Mauro and I demonstrate that “glass crystallisation, nucleation, and growth” are the keywords most frequently encountered in the history of scientific glass literature. Hence, crystallisation must be a relevant phenomenon! Unfortunately, Réaumur did not succeed in producing his porcelain vase due to the uncontrolled surface crystallisation and sagging of his bottle (we now know that soda-lime-silica glasses crystallize only from the surface). Two

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From Glass to Crystal

centuries after Réamur’s experiments, the process of controlled internal crystallisation in certain glasses, which is the basis of glass-ceramic development, was discovered accidentally in 1953 by a great American inventor, S. Donald Stookey, a scientist with Corning Glass Works (sadly, Stookey passed away on November 4, 2014, a few months before reaching his 100th birthday). Since Stookey’s ‘serendipitous’ discovery, many other researchers have made advances in the basic understanding of crystallisation processes and produced numerous patents and scientific articles on this subject. For a recent overview, I invite the reader to browse through the article “A Statistical Overview of GlassCeramic Science and Technology” – Am. Ceram. Soc. Bull. May 2015. In that paper, we demonstrate that the last 60 years have seen very significant progress in glass-ceramics research and development, with an exponential growth in the number of scientific articles and patents. New applications are being proposed and tested continuously. Recent advances in electrical, dental, biomedical and optical functions are evident. The current applications of glass-ceramics range from kitchenware and artificial stones for architecture to sophisticated uses, such as dental and medical implants, magnetic materials for the treatment of cancer with hyperthermia, telescope mirrors, radomes, waste containment matrices, tough, transparent polycrystalline materials, phase change materials for permanent storage of digital information, hard-disc substrates, etc. Technologists consider glass-ceramics promising materials for different applications, e.g., in the fields of space, defence, health, electronics, architecture, energy and waste management. Since the discovery of glass-ceramics 60 years ago, investigative techniques have become more powerful and scientists have delved deeper in their attempts to understand the evolution of the structural organisation of amorphous materials and have researched and developed new properties for novel applications. I concur with the editors that this book describes the latest advances in the field of glass crystallisation: the evolution of theories of nucleation, new methods for structural and microstructural development characterisation, and new applications. The book has about 600 pages and more than 1 300 references! In the first two chapters, Laurent Cormier sets forth the scientific background in a comprehensive account of the theory of homogeneous and heterogeneous nucleation and growth, describing the underlying hypothesis of CNT (classical nucleation theory) and several other sophisticated nucleation models. This is followed by other all-inclusive chapters on the thermodynamics of the glassy state (Jacques Rogez, Sophie Papin, Pierre Benigni, Cécile Jousseaume), liquid-liquid phase separation (Sophie Schuller), solid-state chemistry of the main crystal phases occurring in current glass-ceramics (Lionel Montagne, François O. Méar, Pascal Roussel, Grégory Tricot), and the preparation and control of glass‐ceramics microstructures (Mathieu Allix). The next set of chapters discuss micro-nano structural characterisation strategies, with insightful lessons on X‐ray diffraction (Philippe Deniard), mechanical properties (Jean-Christophe Sangleboeuf), electron microscopy

Preface

3

(Nicolas Menguy, Olivier Dargaud, Laurent Cormier), SANS and SAXS (Claire Levelut), NMR (Thibault Charpentier and Dominique Massiot) and Raman (Dominique de Ligny and Daniel R. Neuville), which are rounded out with several novel high-temperature crystallisation studies using XAS and XRD and Neutron Scattering (Daniel R. Neuville and Laurent Cormier). These in situ high-temperature studies, which were pioneered by this team of scientists, reveal interesting details about the structural reorganisation processes that precede crystal nucleation in glasses. The final set of chapters describe the main commercial glass-ceramics currently available and several proposed glass-ceramics applications, including machinable, low expansion glass-ceramics (Monique Comte), new classes of bioactive glass-ceramics (Laurent Gremillard, Marlin Magallanes-Pedromo, Sylvain Meille, Jérôme Chevalier, Leila Lefèbvre), glass-ceramics coloured with nanoparticles (Jacques Lafait, Serge Berthier, Christine Andraud, Vincent Reillon, Julie Boulenguez), transparent glass-ceramics (Mathieu Allix), luminescent glass-ceramics (Wilfred Blanc), glass-ceramics for non-linear optics (Thierry Cardinal, Mathieu Lancry, Evelyne Fargin, Yannick Petit, Marc Dussauze, Vincent Rodriguez, Nicolas Marquestaut, Bertrand Poumellec, Lionel Canioni), oxyfluoride glass ceramics (Patrick Gredin and Michel Mortier), chalcogenide glass-ceramics (Annie Pradel), waste immobilization in glass-ceramics (Daniel Caurant), and lastly, glass-ceramic glazes (Olivier Dargaud). From the preceding paragraphs, it is quite clear that glass-ceramics are indeed superb materials with a glorious past, exciting current applications and a very bright future! However, their future will be strongly dependent on the application of (existing and new) scientific knowledge and modern characterisation techniques. I believe the reader will find this book abounds in original ideas that will expand his knowledge about glass crystallisation and characterisation of glass-ceramics and enable him/her to envision new areas of application. On behalf of the international glass community, I heartily congratulate the editors Daniel Neuville, Laurent Cormier, Daniel Caurant and Lionel Montagne for their efficient compilation of this marvellous monograph, which I staunchly recommend for students, researchers, engineers and professors interested in glasses and glass-ceramics. I, for one, can’t wait to get hold of a signed copy! Prof. Edgar Dutra Zanotto Director Centre for Research, Technology and Education in Vitreous Materials CeRTEV (www.certev.ufscar.br) Federal University of São Carlos, São Paulo, Brazil

Foreword

This book arose through a very broad collaboration between academic and industrial research teams, initiated by two organisations: the GDR CNRS 3338 ‘Glasses’ and the ‘Union pour la Science et Technologie Verrières’ (USTV), the French glass society. GDR Glasses brings together 250 participants from 45 research teams. It was designed to be a body of multidisciplinary scientific animation, with inputs from scientific specialist institutions in the fields of chemistry, physics, engineering sciences and earth sciences, also with the French Alternative Energies and Atomic Energy Commission (CEA) and some major industry players: SaintGobain, Corning, Arc-International, Draka-Comtech, Baccarat. Its mission is to ensure the organisation of scientific meetings (seminars, workshops, thematic schools) for which 3 interdisciplinary themes have been defined: (i) properties, structure and modeling, (ii) heterogeneity, nucleation, growth, and (iii) energy efficiency, high glass temperature, surfaces and interfaces. The USTV is the French glass society whose purpose is to ensure a link between the industrial and academic teams working in the field of glass. It represents the community in international forums (International Commission on Glass, European Society of Glass). It organizes annual meetings on glass, and thematic meetings on issues related to industrial, scientific or regulatory concerns (rare earths, colours, REACH, Redox, irradiation, …). Lionel Montagne, Director of GDR-Glasses Daniel R. Neuville, President of the USTV

Introduction

Glass-ceramics were discovered accidentally by S. Donald Stookey in 1953 in the United States due to a failure of a heat treatment oven. Despite the attempts by the frenchman René-Antoine Ferchault de Réaumur in the 18th century for the manufacture of porcelain by crystallisation of glasses, this aspect was considered to be a defect for a long time, with the exception of a few decorative objects of art surface treatments. Since the discovery of glass-ceramics, control of nucleation and crystal growth processes has led to an impressive amount of materials produced for many industrial applications (and protected by some 2 400 patents in the US and 1 500 in Europe): cooking glass-ceramics, windows, fireplace doors, kitchen ware… Other applications are more confidential, but no less important: dental implants, mirrors for telescopes, radome for missile, matrices for waste management, colorful glass-ceramics, glass-ceramics for optical applications… In parallel, using more efficient investigation techniques, scientists are analyzing and doing research into these materials at the interface between glass science and crystallography to advance our understanding of the evolution of the atomic arrangements with the disordered environments as well as to search for new properties potentially to lead to new applications. An impressive number of scientific publications have been produced: some 10 000 papers were listed in the Scopus base for 2011! The French community is active in this field since nearly 1,000 articles and papers have been published since the 1960s. Many industrial and academic research teams are working in this area, as shown by 50 participants in the workshop on “nucleation” organized by the GDR and the USTV in September 2011. To follow it was decided to organize, in May 2013, a CNRS school on glass-ceramics, accompanied by publication of the French edition of this book incorporating elements from the course-work. One might be surprised by another book on glasses? But it presents recent advances in the field of glass-ceramics: evolution of the theories of nucleation, new structural and microstructural characterisation methods, and new methods of forming or controlling the microstructure and new applications. We do not doubt that the reader will find in this book of original ideas that will allow deepen knowledge of the crystallisation of glasses and the characterisation of glass ceramics while discovering unsuspected application domains for these hybrid materials, and

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From Glass to Crystal

why possible new research projects! Glass-ceramics are a superb example of a recent and promising material yet to have a very bright future as shown by the many chapters in this book related to their current or potential applications. For example transparent glass ceramics (oxides or chalcogenide), glass-ceramics phase change materials for the permanent storage of digital information, magnetic glass-ceramics for the treatment of cancer, applying a hyperthermia protocol… We greatly thank Edgar Zanotto for having agreed to write a preface for the English version of the original French. Publishers deeply thank all the authors who have developed their competence at the service of a book that will serve as a reference for the whole of the academic and industrial community. Daniel Caurant, Laurent Cormier, Lionel Montagne, Daniel R. Neuville

Contributors

Mathieu Allix (Chapter 6, 17) CEMHTI, CNRS UPR 3079, 1D Avenue de la Recherche Scientifique, 45071 Orléans Cedex 2, France Christine Andraud (Chapter 16) INSP, CNRS UMR 7588, Université Pierre et Marie Curie, 4 place Jussieu, boîte courrier 840, 75252 Paris Cedex 05, France Pierre Benigni (Chapter 3) IM2NP-CNRS, Aix-Marseille University, Campus de St Jérôme, case 251, Avenue de l’Escadrille Normandie-Niemen, 13397 Marseille, France Serge Berthier (Chapter 16) INSP, CNRS UMR 7588, Université Pierre et Marie Curie, 4 place Jussieu, boîte courrier 840, 75252 Paris Cedex 05, France Wilfried Blanc (Chapter 17) LPMC, Université de Nice-Sophia Antipolis, CNRS UMR7336, Parc Valrose, 06108 Nice, Cedex 2, France Julie Boulenguez (Chapter 16) INSP, CNRS UMR 7588, Université Pierre et Marie Curie, 4 place Jussieu, boîte courrier 840, 75252 Paris cedex 05, France Lionel Canioni (Chapter 19) LOMA, Université de Bordeaux 351 cours de la Liberation, 33405 Talence Cedex. France Thierry Cardinal (Chapter 19) ICMCB, CNRS, Université de Bordeaux 1, Pessac, France Daniel Caurant (Chapter 22) Institut de Recherche de Chimie Paris, CNRS UMR 8247, Chimie ParisTech, 11, rue Pierre et Marie Curie, 75005 Paris, France

10

From Glass to Crystal

Thibault Charpentier (Chapter 11) NIMBE, CEA, CNRS, Université Paris-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France Jerome Chevalier (Chapter 15) Laboratoire MATEIS, Université de Lyon, INSA-Lyon, UMR CNRS 5510, 20 avenue Einstein, F-69621 Villeurbanne, France Monique Comte (Chapter 14) Corning SAS, 77210 Avon, France Laurent Cormier (Chapters 1, 2, 9, 13) Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Paris-Sorbonne, CNRS UMR 7590, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France Olivier Dargaud (Chapters 9, 23) Sèvres - Cité de la céramique, 2 Place de la Manufacture , 92310 Sèvres, France Dominique de Ligny (Chapter 12) Universität Erlangen-Nürnberg, Department Werkstoffwissenschaften, Lehrstuhl für Glas und Keramik, Martensstr. 5, D-91058 Erlangen, Deutchland Philippe Deniard (Chapter 7) Institut des Matériaux Jean Rouxel, 2 rue de la Houssinière, BP 32229, 44322 Nantes cedex 3, France Marc Dussauze (Chapter 19) ISM, CNRS, Université de Bordeaux 1, Talence, France Evelyne Fargin (Chapter 19) ICMCB, CNRS, Université de Bordeaux 1, Pessac, France Patrick Gredin (Chapter 20) Université Pierre et Marie Curie et Institut de Recherche de Chimie Paris, UMR 8247, Chimie Paristech, 11, rue Pierre et Marie Curie, 75005 Paris, France Laurent Gremillard (Chapter 15) Université de Lyon, INSA-Lyon, Laboratoire MATEIS, CNRS UMR 5510, 20 avenue Einstein, 69621 Villeurbanne, France Cécile Jousseaume (Chapter 3) Saint-Gobain Recherche, 39, quai Lucien Lefranc, B. P. 135, 93303 Aubervilliers Cedex, France Jacques Lafait (Chapter 16) INSP, CNRS UMR 7588, Université Pierre et Marie Curie, 4 place Jussieu, boîte courrier 840, 75252 Paris cedex 05, France

Contributors

11

Mathieu Lancry (Chapter 19) Institut de Chimie Moléculaire et des Matériaux d’Orsay (ICMMO), UMR CNRS UPS 8182, Université de Paris Sud, 91405 Orsay Cedex, France Leila Lefebvre (Chapter 15) Laboratoire MATEIS, Université de Lyon, INSA-Lyon, CNRS UMR 5510, 20 avenue Einstein, F-69621 Villeurbanne, France Claire Levelut (Chapter 10) Laboratoire Charles Coulomb, CNRS UMR 5221, Université Montpellier II, Place Eugène Bataillon, CC069, 34095 Montpellier Cedex 5, France Marlin Magallanes-Pedromo (Chapter 15) Laboratoire MATEIS, Université de Lyon, INSA-Lyon, UMR CNRS 5510, 20 avenue Einstein, F-69621 Villeurbanne, France Nicolas Maquestaut (Chapters 19) LOMA, Université de Bordeaux 351 cours de la Liberation, 33405 Talence Cedex. France Dominique Massiot (Chapter 10) CEMHTI, CNRS UPR 3079, 1D Avenue de la Recherche Scientifique, 45071 Orléans cedex 2, France François Méar (Chapter 5) Unité de catalyse et Chimie du Solide, UCCS, CNRS UMR 8181, Université de Lille1 Sciences et Technologies, 59655 Villeneuve d’Ascq, France Sylvain Meille (Chapter 15) Laboratoire MATEIS, Université de Lyon, INSA-Lyon, CNRS UMR 5510, 20 avenue Einstein, 69621 Villeurbanne, France Nicolas Menguy (Chapters 9) Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Paris-Sorbonne, CNRS UMR 7590, Université Pierre et Marie Curie, 4 place Jussieu, 75005 Paris, France Lionel Montagne (Chapter 5) Unité de catalyse et Chimie du Solide, UCCS, CNRS UMR 8181, Université de Lille1 Sciences et Technologies, 59655 Villeneuve d’Ascq, France Michel Mortier (Chapter 20) Institut de Recherche de Chimie Paris, UMR 8247, Chimie Paristech, 11, rue Pierre et Marie Curie, 75005 Paris, France Daniel R. Neuville (Chapter 12, 13) Géomatériaux, CNRS, Institut de Physique du Globe de Paris, Sorbonne Paris Cité, Université Paris Denis Diderot, 1 rue Jussieu, 75005 Paris, France

12

From Glass to Crystal

Sophie Papin (Chapter 3) Saint-Gobain Recherche, 39, quai Lucien Lefranc, B. P. 135, 93303 Aubervilliers Cedex, France Yannick Petit (Chapter 19) ICMCB, CNRS, Université de Bordeaux 1, Pessac, France Bertrand Poumellec (Chapter 19) Institut de Chimie Moléculaire et des Matériaux d’Orsay (ICMMO), UMR CNRS UPS 8182, Université de Paris Sud, 91405 Orsay Cedex, France Annie Pradel (Chapter 21) Institut Charles Gerhardt, CNRS UMR 5253, Université Montpellier 2, Montpellier, France Vincent Reillon (Chapter 16) INSP, CNRS UMR 7588, Université Pierre et Marie Curie, 4 place Jussieu, boîte courrier 840, 75252 Paris Cedex 05, France Vincent Rodriguez (Chapter 19) ISM, CNRS, Université de Bordeaux 1, Talence, France Jacques Rogez (Chapter 3) IM2NP-CNRS, Aix-Marseille University, Campus de St Jérôme, case 251, Avenue de l’Escadrille Normandie-Niemen, 13397 MARSEILLE Pascal Roussel (Chapter 5) Unité de catalyse et Chimie du Solide, UCCS, CNRS UMR 8181, Université de Lille1 Sciences et Technologies, 59655 Villeneuve d’Ascq, France Jean-Christophe Sangleboeuf (Chapter 8) Institut de Physique de Rennes, CNRS UMR 6251, Université de Rennes 1, Bât. 10B, Campus de Beaulieu, 35042 Rennes Cedex, France Sophie Schuller (Chapter 4) CEA-Marcoule, CEA/SECM/LDMC, Bagnols sur Céze, France Grégory Tricot (Chapter 5) Unité de catalyse et Chimie du Solide, UCCS, CNRS UMR 8181, Université de Lille1 Sciences et Technologies, 59655 Villeneuve d’Ascq, France

Main symbols and physical constants

B0 c

Cp D dl eo h F G H K kB n NA Q Q R = kBNA S TC TCb Tg Tf TN DT W

magnetic field speed of light in vacuum (3.0×108 m s-1) calorific capacity (J kg-1 K-1) diffusion coefficient (m2 s-1) jump distance (~twice the ionic radius) electron charge (1.6 ×10-19 C) Planck’s constant (6.626×10-34 J s) Helmholtz free energy Gibbs free energy or free enthalpy enthalpy Scherrer’s constant Boltzmann’s constant (1.381×10-23 J K-1) refraction index Avogradro constant (6.022×1023 mol-1) heat (J) magnitude of the scattering vector (Å-1) universal constant of ideal gas (8.314 J mol-1 K-1) entropy crystallisation temperature critical temperature of phase separation (consolution) glass transition temperature fusion temperature nucleation temperature supercooling degree, temperature difference work of formation

14

g e0 h l n F

From Glass to Crystal

interfacial energy or tension surface permittivity of vacuum (8.85×10-12 F m-1) viscosity wave length frequency of lattive vibration heat flow

Abbreviations

ADF AFM ASAXS BSE CAS CNT DSC EBSD EDS, EDX EELS EFTEM ELNES EXAFS FIB GGA HAADF HRTEM IR LAS LED MAS MAS NMR MCVD MQMAS NMR PCM

Annular Dark Field Atomic Force Microscopy Anomalous Small-Angle X-ray Scattering Back Scattered Electrons Calcium aluminosilicate Classical Nucleation Theory Differential Scanning Calorimetry Electron Back Scattered Diffraction Energy Dispersive X-ray Spectroscopy Electron Energy Loss Spectroscopy Energy Filtered TEM Energy Loss Near Edge Structure Extended X-ray Absorption Fine Structure Focused Ion Beam Generalized Gibbs’s Approach High Angle Annular Dark Field High Resolution TEM Infra-Red Lithium aluminosilicate Light-Emitting Diode Magnesium aluminosilicate Magic Angle Spinning NMR Modified Chemical Vapor Deposition Multi-quanta Magic Ancle Spinning Nuclear Magnetic Resonance Phase Change Materials

16

PMC SAED SANS SAXS SEM SHG STEM TDA TEM THG XANES WAXS XRD YAG ZAS

From Glass to Crystal

Programmable Metallization Cell Selected Area Electron Diffraction Small Angle Neutron Scattering Small Angle X-ray Scattering Scanning Electron Microscopy Second Harmonic Generation Scanning Transmission Electron Microscopy Differential thermal analysis Transmission Electron Microscopy Third Harmonic Generation X-ray Absorption Near-Edge Structure Wide Angle X-ray Scattering X-ray diffraction Yttrium Aluminium Garnet Zinc aluminosilicate

Main crystalline phases considered in this book

Anorthite Apatite Aragonite Berlinite Beryl Biotite Boron phosphide Brookite Calcium metaphosphate

CaAl2Si2O8 Ca5(PO4)3(OH, Cl, F) (general formula, A5(XO4)3Zq) CaCO3 AlPO4 Be3Al2Si6O18 K(Mg,Fe)3(AlSi3)O10(OH)2 BPO4 TiO2 Ca(PO3)2

Calcium molybdate Calcium pyrophosphate Canasite fluorated Carnegieite Ca-Tschermak Chlorapatite Celsiane Cordierite Diopside Enstatite Eucryptite-b Ferrite Fluorapatite Fluorine Fluorophlogopite Forsterite Fresnoite Gahnite Gehlenite

CaMoO4 CaP2O7-β Na4K2Ca5Si12O30F4 NaAlSiO4 CaAl2SiO6 Ca5(PO4)3Cl BaAl2Si2O8 Mg2Al4Si5O18 CaMgSi2O6 MgSiO3 LiAlSiO4 AFe2O4 Ca5(PO4)3F CaF2 KMg3AlSi3O10F2 Mg2SiO4 Ba2TiSi2O8 ZnAl2O4 Ca2Al2SiO7

18

Hemimorphite Hydroxyapatite Ilmenite Kalsilite KTP Leucite LiSICON Lithium disilicate Lithium metasilicate Lithium niobate Lithium orthophosphate Mullite NaSICON Nepheline Norbergite Olivine Opal Powellite Pollucite Rutile Scheelite Silicorhenanite Sodium cyclotriphosphate Sodium molybdate Sodium niobate Spinel Spodumene-b Titanite (Sphene) Tremolite Tricalcic phosphate (TCP) Willemite Wollastonite YAG Yoshiokaite Zircon Zirconia Zirconolite

From Glass to Crystal

Zn4Si2O7(OH).H2O Ca5(PO4)3(OH) FeTiO3 (general formula ABO3) KAlSiO4 KTiOPO4 KAlSi2O6 LiTi2(PO4)3 Li2Si2O5 Li2SiO3 LiNbO3 Li3PO4 Al6Si2O13 A2(PO4)3 NaAlSiO4 or Na3KAl4Si4O16 Mg3SiO4(F,OH)2 Fe2SiO4 SiO2, nH2O CaMoO4 (Cs,Na)2Al2Si4O12·2H2O TiO2 BaMoO4 Na2Ca4(PO4)2SiO4 Na3P3O9 Na2MoO4 NaNbO3 MgAl2O4 (general formula AM2O4) LiAlSi2O6 CaTiSiO5 Ca2Mg5Si8O22(OH)2 Ca3(PO4)2 Zn2SiO4 CaSiO3 Y3Al5O12 Ca8-(x/2)[ ] (x/2)Al16-xSixO32 ZrSiO4 ZrO2 CaZrTi2O7

1

The classical nucleation theory

2

Laurent Cormier

“I viewed that my annealing had operated in the glass a composition or, if you prefer, a very singular decomposition” René-Antoine Ferchault de Réaumur

Preamble Crystallisation is described as a two-step process: nucleation at low temperatures and growth at higher temperatures. Both depend on temperature and can display a greater or lesser overlap in temperature. During the glass elaboration, we wish to avoid the persistence of crystalline phases (existing in the batches prior to melting or formed during heating by reaction between components) or their formation during the quenching, these phases being generally regarded as harmful for the glass properties (transparency…). In the case of glass-ceramics, the appearance of these crystalline phases will give them specific properties. It is therefore essential to understand the crystallisation phenomenon to be able to control the size, the distribution and the nature of the crystalline phases. We shall consider the general case of crystallisation of glass by successive heat treatment steps, formation of crystalline phases settling above the glass transition temperature (Tg), i.e., in a supercooled (metastable) liquid. Crystallisation may also take place by cooling the liquid, an especially important aspect for geologists to understand the cooling and the texturing of volcanic igneous rocks [1, 2] and during the cooling of nuclear waste to form glasses for disposal (chapter 22). Crystallisation can be understood simply by using Classical Nucleation Theory or CNT which, although imperfect as we shall discover, allows a physical approach to understand easily the main processes. Its great attractiveness results from its adaptation to a large number of nucleation processes: from a liquid, a vapour or a solution, thus covering the crystallisation of proteins [3-6], colloids and polymers [5, 7] or atmospheric nucleation [8]. Crystal nucleation in supercooled liquids is the object of this chapter and can also be addressed in details in several reference books [9-12].

20

From Glass to Crystal

In this chapter, we shall present the homogeneous and heterogeneous nucleation, specifying the hypothesis involved in the CNT. The basics of crystal growth will be addressed (§1.6) and developed in a separate chapter (chapter 6.1).

1.1. From devitrification… In the 1730s, Réaumur was the first to look at the devitrification of glasses with the goal to form porcelain [13]. During his work, in order to not misshape the glass pieces, the latter were placed in a refractory environment that did not stick, composed of a mixture of calcined gypsum and sand. Réaumur attributed the devitrification phenomenon to the medium in which he was “cementing” the glass (sic), an explanation which was latter rebutted. The 18th and 19th Centuries were mainly a period for optical observations, which showed that the devitrification results from the glass crystallisation and were not an extrinsic phenomenon (Fig. 1.1). These observations have led to understand that during a long softening at a red-hot temperature, atoms change their relative environment which induces the formation of a crystalline structure (cf. Ch. 5).

Fig. 1.1.  –  Reproduction of crystals observed in glasses by Bontemps (left) and Péligot (right) [14, 15].

In the process used by Réaumur, the crystallisation was not controlled. As Bontemps, Director of the Saint-Gobain glass factory at Choisy-le-Roi (France) [14], said “it is easier to get a complete devitrification, a Réaumur porcelain, than to stop this devitrification work in that state which presents well-formed crystals, showing that this devitrification phenomenon is due to the glass crystallisation.” So, already at that time arose the dreaded question of the observation of the early crystals. The importance of catalyzers had also been noted: “crystallisation was first manifested in the points of contact with the brick” [14]. It also appeared to this glass worker that “it is the surface that, cooling faster, is devitrifying and solidifying first.” Crystal growth was observed: “as the operation is prolonged, crystals … become more abundant, larger”. However, the rise of chemical analysis did not allow, at that time, to understand correctly the crystallisation process. Some have proposed that the crystallisation is due to the formation of defined, infusible compounds, resulting either from the volatilization of alkali or from a partition of the elements in the glass, the alkalis going to the glassy part [15]. This is especially the opinion of

Chapter 1 – The classical nucleation theory

21

Dumas who wrote in its Chemistry applied to arts [16]: “during the slow solidification of a glass, a partition of the elements takes place by means of which a defined silicate crystallizes and thus separates from the remaining mass.” The alternative hypothesis is crystallisation of a glass without alteration of the proportions of each of its constituents [14, 17, 18]. The pioneering Réaumur’s work immediately interested industrials, due to the new properties conferred to the material, such as a greater hardness. We can cite, for example, Jean Darcet, former Director of the Manufacture de Sèvres (France) at the end of the 18th century, who manufactured with “devitrified glass bottles, cameos, ornamental tiles, porphyries, mortars and colored stones for mosaic, whose valuable properties will be appreciated sooner or later” [16]. However, the cost and the potential deformation of the pieces which were manufactured by these uncontrolled processes were a long-lasting obstacle to the early development of glassceramics (chapter 23). Therefore, we shall have to wait for the beginning of the 1950s (cf. Ch. 14) and the discovery of nucleating agents to be able to control crystallisation. Since then, glass-ceramics have an important impetus that revolutionizes our daily life, with applications in building, aeronautics, medical treatments or energy [19].

1.2. … to the origins of CNT In addition to his experimental studies, Gibbs (Fig. 1.2) published in 1876 a seminal paper on the thermodynamic description of equilibria between phases [20]. The kinetics aspect of the transformations was still very poorly understood until Arrhenius formulated the notion of activation energy in 1889. The concepts of capillarity and thermodynamic equilibrium were followed by Volmer in 1926 leading to the foundations of the Classical Nucleation Theory (CNT) [21]. In 1935, Becker and Doring gave the theory is current form [22]. Historical notes can be found in various books [11, 23].

Fig. 1.2.  –  (Left) Portrait of René-Antoine Ferchault de Réaumur (1683-1757). (Right) Josiah Willard Gibbs (1839-1903).

22

From Glass to Crystal

CNT is based on some fundamental assumptions that delimit the theory: – It is considered that a nucleus (or a germ), regardless of its size, can be considered with the macroscopic variables of the stable crystalline phase that will be formed. This means the same properties (including thermodynamic), the same structure, the same composition and the same density; – The initial seed is spherical with a radius r and a finite, flat-type interface, to minimize the surface energy. These assumptions are known as the capillary approximation, which is the essential hypothesis of the CNT.

1.3. Homogeneous nucleation Homogeneous nucleation is a stochastic event: there is an identical probability of forming a crystalline seed in any volume or surface element. This spontaneous formation derives from fluctuations in density, composition, or entropy, all thermally activated.

1.3.1.

Thermodynamic considerations

A phase transformation is accompanied by a change in the Gibbs free energy (G or free enthalpy) to minimize it. Above the melting temperature, Tf (Tf for a pure body, Tliquidus for a mixture) the equilibrium phase corresponds to the liquid state, having the lowest free energy, and the crystalline state is not stable (Fig. 1.3). When T  0

(T  0 with LV the latent heat of melting, and the associated change in entropy, DSV = Sl – Sc > 0 (Fig. 1.3b):

ΔGV = ΔHV – TΔSV(1.2) Considering that ΔHV is a constant corresponding to the heat release during crystallisation, the free energy change comes only from the temperature dependence of the second term in equation (1.2) associated with the entropy term. Therefore, an increase in supercooling leads to an increase in the entropic difference term between the liquid and the crystal, DSV, which favors the formation of the latter. At Tf, the free energy difference is zero because the crystal and liquid have the same free energy (Fig. 1.3a) :

(ΔGV )T = Δ H V − T ΔSV = 0 (1.3) f

ΔSV =

ΔH V ΔH V  T f − T  (1.4) and ΔGV = ΔH V − T = Tf Tf  T f 

hence

ΔGV = ΔH V

ΔT (1.5) Tf

The change in free energy during nucleation will depend on three thermodynamic factors: – the decrease in the volumic free energy, – the increase in the surface energy, – the increase in the elastic energy (or strain energy). This last aspect is neglected in the context of a solid-liquid transformation. For a volume of material transformed from a liquid into a nucleus of the thermodynamically favoured crystal, the decrease in free energy corresponds to DGV multiplied by the volume of the spherical crystalline nucleus (4πr3/3) (Fig. 1.4a). The thermodynamic barrier to overcome the nucleation is the product of the nucleus/liquid surface tension (γ) by the surface area of the spherical nucleus (4πr2). This gives the work of formation of the critical nucleus, W,

24

From Glass to Crystal

corresponding to the energy released (where W  is positive) by the formation of a nucleus with a radius r: 4 W = 4π r 2γ − π r 3 ΔGV (1.6) 3 W  corresponds to a balance between the interfacial term, which is a thermodynamic barrier to surmount, and the volumic term, which favours nucleation (Fig. 1.4).

Fig. 1.4.  –  (a) Energy diagram illustrating the transition from the supercooled liquid state to the nucleus at a temperature T  G0(ν). If G″  lC. The critical wavelength is of the order of one nanometer. In the case of non-uniform fluctuations, the stability condition G″ > 0 is thus sufficient but not necessary.

λf < k

3.2. Experimental methods for the determination of thermodynamic quantities at the equilibrium of a stable or metastable oxide glass or crystal In order to measure the thermodynamic properties of the phases in equilibrium, it is naturally recommended to use good experimental devices. The behaviour of the selected device must be well known in order to reduce random errors and detect possible systematic errors. However, it is equally recommended to work with very well characterized samples. A very good measurement on a poorly characterized sample will inevitably be mediocre.

3.2.1.

Overview of thermodynamic measurable quantities

An exhaustive review of experimental methods for the determination of thermodynamic functions can be found in Kubaschewski et al. [121] and in Komarek [122]. Various classifications have been proposed in the literature. Overall, the methods can be classified into two main types: the calorimetric methods and the heterogeneous equilibrium methods. The calorimetric methods are based on the direct or indirect measurement of the heat quantity released or absorbed by a sample undergoing a temperature change, a structural transition or a chemical reaction. A classification of the various types of calorimeters has been proposed by Hemminger and Höhne [123] relying on their measuring principle, their mode of operation

78

From Glass to Crystal

and their construction principle. The most frequently used sensors are thermocouples and thermopiles for respectively temperature and heat flow measurements. Contact temperature measurement using a thermocouple requires the insertion of the sensor inside the part of the experimental device the temperature of which is to be measured. This disturbance of the thermal field may bias the result and hence special care must be taken in the positioning of the sensor to insure that the recorded value correctly represents the temperature to be measured, in particular under steep thermal gradients resulting in large heat flows [124]. Heat flow is one of the physical quantities that is the most difficult to measure, especially at high temperatures, for which the heat transfer conditions change over time. In this temperature range, ageing of materials used in the experimental devices, changes in the thermal contact resistances between the different parts of the device and changes in the surface conditions of radiating objects cannot be avoided due to enhanced interdiffusion of chemical elements, recrystallisation, oxidation… A thermopile, a sensor invented by Professor A. Tian, is made of hundreds of differential thermocouples connected in series [125]. This meticulous assembly, arranged in order to almost completely surround the sample cell, allows the measurement of a sum of elementary heat fluxes flowing between the sample cell and the thermostat. As it progresses, the heat flow is spatially integrated. Such thermopile can be very sensitive (10 µW/µV) depending on the nature and on the number of thermocouples. A calibration is needed to convert the recorded voltage (V) delivered by the thermopile to a thermal power (W). For each series of measurements, the calibration must be conducted under the same heat transfer conditions as those prevailing during the measurement. As the signal of the thermopile is recorded vs time, the heat flow is also time-integrated. In the differential calorimeter design, two thermopiles are connected in opposition in such a manner that all thermal disturbances affecting the calorimeter are evenly distributed between the thermopiles generating electric voltages of equal magnitudes and opposite signs. As a result, the differential signal of the two thermopiles is not affected by the disturbance. This differential design due to E. Calvet, increases the detection limit of the apparatus. Both thermopiles must be as similar as possible. The heterogeneous equilibrium methods include the Electro-Motive Force (EMF) and the vapour pressure measurement methods. A very recent and comprehensive overview of the EMF method is given by Ipser et al. [126]. The method requires (i) finding a suitable electrolyte and (ii) identifying the single electrode process that occurs reversibly at each electrode [121]. Among the different vapour pressure techniques, the Knudsen Effusion Mass Spectrometry (KEMS), alternatively named High Temperature Mass Spectrometry (HTMS), is the most versatile and powerful, which can deal with complex vapors in large pressure (from 10-12 up to 10-4 atm) and temperature (up to 2 500-3 000 K) intervals. A third method consists in equilibrating a phase to be studied with one phase, the thermodynamic properties of which are known, and then measuring the chemical composition. The equality of

Chapter 3 – Thermodynamics of the glassy and the crystalline states

79

the chemical potentials allows the calculus of the thermodynamical quantities in the phase under investigation. The measurement methods for the thermal and the formation or mixing functions of a given phase, which can be a crystal, a liquid or a vitreous phase, are summarized in Table 3.1. Table 3.1.  –  Functions relative to a single phase. Thermal functions Quantity

Method • Isothermal drop calorimetry • Inverse drop calorimetry for glasses

DH TT12

DtrsH

• Isothermal drop calorimetry • Adiabatic calorimetry • DSC or qDTA

Cp

• Derivative of DH with respect to T • Adiabatic calorimetry • DSC or qDTA

DS

T2 T1

∫

T2

T1

D H CP dT + ∑ trs T Ttrs

Formation or mixing functions Quantity

DfH or DmixH

DfG or DmixG

DfS or DmixS

Method • Direct reaction calorimetry • Solution calorimetry • Temperature coefficient in heterogeneous equilibrium (2nd law) • 3rd law knowing the absolute entropy of all the products and reactants • Equilibrium constant of heterogeneous equilibrium: DG = RT lnK • Equilibrium constant of heterogeneous equilibrium: DH − DG DS = T

The enthalpy increment DH TT12 between the two temperatures T1 and T2 is measured by isothermal drop calorimetry. For glasses, the inverse drop calorimetry, in which a sample held in a high temperature furnace is dropped into a room temperature calorimeter, is most frequently used [127]. The transition enthalpy DtrsH can also be measured by the same technique if the drops are repeated from two temperatures slightly below (Ttrs – DT) and slightly above (Ttrs + DT) the transition temperature Ttrs or by temperature scanning techniques such as adiabatic calorimetry or Differential Scanning Calorimetry (DSC). The heat capacity CP can be indirectly determined as the derivative of the enthalpy curve vs temperature obtained by drop calorimetry experiments performed at different temperatures. However, this method is very time consuming. Moreover if the heat capacity undergoes large changes within a small temperature range, DSC and adiabatic calorimetric operating

80

From Glass to Crystal

in scanning mode are more accurate at low scanning rates. The absolute entropy can be derived by temperature integration of the heat capacity over temperature ratio if the heat capacity is measured from a temperature of few degrees Kelvin up to the temperature of interest. For example, this approach has been successfully implemented by Gailhanou et al. [128] on a series of clay minerals by using low temperature adiabatic calorimetry in conjunction with DSC above room temperature. The variations with temperature of the enthalpy and of the Gibbs energy are of course easily derived from the complete Cp curve. The enthalpy of formation or of mixing can be accurately measured by solution calorimetry or by direct reaction calorimetry if the reactivity between the reactants and the temperature are high enough for complete reaction. These enthalpies can also be experimentally determined using heterogeneous equilibrium techniques provided that the measurements are performed as a function of temperature over a sufficiently large temperature range. For example, raw vapour pressure data are processed according to the 2nd law of thermodynamics and possibly the 3rd law if the thermal functions of all the individual components of the reaction are known [129]. Gibbs energy of formation is only measured by heterogeneous equilibrium techniques. The experimental methods for measuring partial functions relative to a solution are summarized in Table 3.2. The partial Gibbs energy is only measured by heterogeneous equilibrium techniques such as Knudsen effusion in which a condensed phase is equilibrated with its vapour or by the EMF method. The most accurate methods for partial enthalpy determination are the direct reaction or solution calorimetry. An example of the latter approach can be found in the work of Linard et al. who measured the enthalpies of solution of La2O3, TiO2, HfO2, NiO and CuO by high-temperature drop calorimetry in a sodium silicate solvent [130]. Table 3.2.  –  Partial functions relative to a solution. Quantity

Method

DG i

• Equilibrium between a gaseous and a condensed phase: Knudsen effusion • Electrochemical equilibrium: EMF method • Equilibrating a phase to be studied with one phase the properties of which are known

DH i

• Direct reaction calorimetry • Solution calorimetry

The subsequent parts of the paper are focused on techniques devoted to obtaining thermodynamic quantities of oxide glasses and crystals and which are available in industrial or academic research laboratories. For each quantity several methods are generally available.

Chapter 3 – Thermodynamics of the glassy and the crystalline states

3.2.2.

81

Measurement of enthalpy increment, heat capacity and transition enthalpy

3.2.2.1. DSTT12 , Cp and DtrsH measurements by drop methods In drop calorimetry, the measurement consists of quantifying the enthalpy change of a sample between two well-defined states at constant temperatures. For that reason, this calorimetry is also named “isothermal calorimetry”. Two variations of the method are used. In the direct method, the sample initially thermalized at ambient temperature is dropped in the calorimeter maintained at a higher temperature. The advantages of the technique are (i) the final high temperature where the thermal and chemical equilibrium is rapidly attained, (ii) the initial state which can be very well characterized at room temperature by various methods. Up to 1 300 K, calorimeters of the Tian-Calvet type, the sensor of which is a very sensitive differential heat flow meter [131], can be used and the method is very accurate. Above 1 300 K, the rugged sensors of high temperature calorimeters are less sensitive, the accuracy of the direct method is lower and the method faces the competition of the inverse method. In the inverse method, the sample thermalized at high temperature is dropped in a room temperature calorimeter. Technology available at room temperature enables us to build very sensitive and reliable calorimetric devices that can be of the Tian-Calvet or of the phase transition types. In the latter type, the sample releases its heat to a mantle of a substance maintained in a diphasic state, e.g., melting ice [132] or melting diphenyl ether. The volume of molten solid is measured very precisely by weighing a displaced volume of mercury. The main difficulty in the inverse method is that, due to the rapid sample cooling involved, an undefined end state of the sample is obtained. In particular, for glass samples the cooling rate in the glass transition region must be known or its fictive temperature evaluated a posteriori. By differentiation of the enthalpy with respect to temperature, these drop techniques allow us to measure the heat capacity CP(T) with a low uncertainty even at high temperature (e.g., 0.5% between 673 °C and 1 873 °C [133]). Drop calorimetry is also used to assess the precise values of transition enthalpy by repeating the enthalpy measurements below and above the transition temperature. An uncertainty of about 0.5% can be achieved [133]. However, these techniques require experienced and skilled operators and cannot easily be transferred to application laboratories. Unfortunately, the commercial versions of the high temperature calorimeters are not yet adapted to the study of glasses. Because the sensitivity coefficient of these calorimeters varies with the filling of the measurement cell, it is necessary to alternate drops of samples and of standard reference material during the experiments. Furthermore, the partial dissolution of the α-Al2O3 standard reference material in the melts makes the measurement on this type impossible. Pure platinum, the thermodynamic properties of which are well-known, becomes, despite its metallic nature, the preferred calibration material in this case.

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3.2.2.2. Cp and DtrsH measurements by scanning methods Two types of Differential Scanning Calorimeters (DSC) must be distinguished as explained in the circular ISO 11357 [134]. The first is the power compensation DSC originally developed by the Perkin Elmer® company [135]. The standard material and the sample are placed in two identical microfurnaces mounted in a thermostatic metallic block. During the linear increase of the controlled block temperature, the microfurnaces compensate for the thermal asymmetry resulting from the difference in thermal inertia of the sample and the standard material. Equality of the temperatures of the sample and of the standard material is thereby ensured, whatever the thermal events occurring in the sample cell. This technology has not been applied at very high temperatures and hence is not suitable for glassy materials. The second is the heat flux DSC in which a classical flux meter technology is used in a temperature scanning mode. Compared to isothermal heat flux calorimeters, the main difference in the design lies in the low thermal inertia of the furnace and of the calorimetric block. Heat flux DSC and quantitative Differential Thermal Analysis (qDTA) are methods that are very similar. In both methods, a differential setup is used, the sample and the reference cells follow a common and usually linear heating or cooling program versus time. If the sensor used to detect the thermal asymmetry between the sample and the reference cells is a thermopile, the apparatus may be referred to as a heat flux DSC. If the sensor is reduced to two or few thermocouples, the apparatus will be called a DTA. In either case, the sensor only detects a fraction of the thermal energy exchanged. This fraction is larger in DSC than in qDTA and consequently its sensitivity is also higher. These two technologies are commercialized. The efforts of manufacturers to overcome the difficulties encountered in the early DTA setup resulted in fact in DSC [136]. DSC can be used to measure Cp with a good precision but in a restricted temperature range, typically up to maximum 800 °C or 1 000 °C. The characterisations of liquid and glassy samples are very stringent because of the necessity to perform the measurements in situ at high temperature: the reusable crucible undergoes progressive deformation, overflowing of a liquid phase from the crucible may stick to the sensing elements… Hence, the useful life of the measuring head is drastically reduced. Many efforts continue to be undertaken by manufacturers both technologically, with, for example, the development of planar or 3D geometries, series of thermocouples or semiconductor, and in the modeling of the heat transfer in the measurement cell. At present, the available technology does not allow to characterize the behaviour of glasses at very high temperature by DSC. In this temperature range, it is necessary to simplify the setup, mainly in regard to the reduced choice of available materials. qDTA remains the preferred technique for the measurement of Cp and transition enthalpy in temperature scanning from ambient temperature up to 1 600 °C and even 2 400 °C, even if a relative error of 10% in the measurement is sometimes recorded. It can be

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83

conveniently used, provided there is a prior energy calibration complying with a protocol similar to that used in the DSC method. As a good calibration must be made under thermal conditions as close as possible to those prevailing during the measurement itself, the reproducibility of the base line between successive runs is an essential quality feature of the apparatus. Small thermal effects such as the glass transition or the crystallisation temperatures can be measured with both DSC and qDTA techniques. Moriya and Navrotsky [137] discuss the values of zirconia heat capacity measured by qDTA between 800 °C and 1 400 °C and compare the results to those obtained by drop enthalpimetry on a multi HTC model of the SETARAM® Company. In the following, a similar comparison will be shown for a CaO-Na2O-SiO2 glass.

3.2.2.3. Quantitative DTA The measuring head (Fig. 3.4a) consists of two symmetrical housings for the reference material and the sample. The sample can be encapsulated in a sealed or open crucible depending on its chemical nature and on the gas atmosphere inside the apparatus. The symmetrical housing receives the reference crucible which can contain a mass of a thermally inert compound in the studied temperature range (e.g., calcined alumina) or in some cases simply be kept empty.

Fig. 3.4.  –  Principle of differential thermal analysis (DTA).

Both housings are equipped with a variable number of thermocouples, depending on each specific setup, which are connected in a differential/series arrangement, in order to monitor any temperature difference between the sample and the reference. The measuring head is inserted in the isothermal zone of a high temperature furnace. The whole assembly must be made perfectly thermally symmetric, so that the sample and the reference receive the same amount

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of thermal energy per unit time. The temperature/time program is generally a constant heating or cooling rate but some instruments use a periodically modulated heating or cooling rate. The differential design allows the changes in the sample, either exothermic (e.g., crystallisation or oxidation) or endothermic (e.g. dehydration, fusion), to be detected relative to the inert reference. To maximize the heat transfer between the sample or the reference and the sensors, it is necessary to use metallic crucibles and more specifically platinum for oxide systems. For glass compositions that react with platinum, the solution is (i) to use an alumina liner despite the risk of enrichment of the liquid phase in aluminum at high temperatures and (ii) to cover the crucible with a perforated platinum lid. After an experiment, the crucibles must be cleaned in order to remove any residual glass, then, a delicate operation of reshaping of the crucibles is necessary. However, run after run, the crucibles are progressively damaged and the thermal symmetry is lost. Fig. 3.4b schematically shows the evolution of the temperature versus time for both the sample and the reference in the case of the melting of a pure substance. The temperature of the chemically inert reference follows the linear heating program of the furnace. A thermal arrest is recorded on the sample temperature-time curve, corresponding to the invariant melting of the pure substance. After the completion of the melting reaction, the sample temperature progressively returns to the linear baseline imposed by the furnace. Fig. 3.4c shows the corresponding evolution of the differential signal during the melting reaction. The melting enthalpy is proportional to the area under the peak. The proportionality factor is the calibration coefficient Equations 3.22 and 3.23. The small difference in heat capacity of solid and liquid leads to a small offset of the baseline before and after melting. Cp =

( ∂∂HT )

= P

dQ P dQ P dt = (3.22) dT dt dT

dQ P = dQ a + dQ e if dQe ≫ dQa then

dQ P

dt = K S (TS − TT ) (3.23)

with dQP, the total heat quantity released or absorbed by the phenomenon under study dQP/dt, the heat flux resulting from it dQa, the heat quantity absorbed or released by the measuring cell dQe, the heat quantity exchanged between the measuring cell and the calorimetric chamber Ks, the coefficient of heat transfer between the measuring cell and the calorimetric chamber Ts, the temperature of the measuring cell containing the sample TT, the temperature of the calorimetric chamber

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3.2.2.4. Temperature and enthalpy calibrations As stated previously, DTA is not the preferred method for quantitative Cp measurement. The default factory settings and procedures of the equipment are not sufficient to obtain accurate results. It is thus necessary to apply a specific experimental protocol and a rigorous data processing to get a correct estimate of the Cp values. The necessary calibration protocols are based on those described for DSC in the literature [138-142] and in the ASTM [143-145] and the ISO [134] standards. Notwithstanding, it is impossible to strictly follow these standard methods because they are suitable for only very restricted temperature ranges (about 100 °C). One of the recommendations requires that the runs corresponding to the baseline experiment (empty crucible), the calibration (crucible + reference material) and the measurement (crucible + sample) are performed consecutively in an as short as possible time frame. This becomes problematic when the measurements spread over a wide temperature range. The thermocouple is located close to the sample but not inside it and hence does not exactly measure the sample temperature. Measurements are conducted under dynamic thermal conditions. As in all thermal analysis methods, it is absolutely mandatory to perform a temperature calibration. This temperature correction is carried out through a series of measurements of the melting temperatures of 4-5 different metals within the appropriate temperature range (Table 3.3) on heating. In practice, platinum crucibles are protected by an alumina liner to avoid any contact and possible reaction of platinum with the metal and the amount of metal used remains small when the fusion enthalpy is high. Table 3.3.  –  Recommended fusion temperatures and fusion enthalpies of pure metals [141]. Metal

In

Sn

Zn

Al

Ag

Au

Ni

Tf (°C)

156.6

231.9

419.5

660.3

961.8

1064.2

1455

DfH (J/g)

28.6

59.2

112.0

397.0

104.7

63.7

297.8

According to the ASTM E967 [144], the melting temperature is associated to the extrapolated onset temperature (Fig. 3.4c) defined as the intersection between the straight line extension of the baseline and the linear portion of the endothermic peak. Fig. 3.5 shows that this onset temperature is weakly affected by a change in the heating rate or the mass of the sample. To determine the true melting temperature at equilibrium, the measurements must be repeated at different heating and cooling rates and the measured values extrapolated at zero rate. If the value extrapolated at zero rate from the heating experiments is the same as the one obtained from the cooling experiments, we can conclude that the sample solidifies without any significant supercooling and that the heating and cooling experiments are consistent. It is recommended to calibrate the instrument in the same range

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From Glass to Crystal

of heating and cooling rates as the one that will be used to characterize the samples under study. In commercial instruments, the calibration results are generally stored in the form of a polynomial expression of the temperature and the rate.

Fig. 3.5.  –  Endotherm of melting aluminum according to the mass of the sample under N2 flow and to the heating rate. The recommended enthalpy is 397 J/g.

The enthalpy calibration consists of evaluating the energy fraction not detected by the differential sensor during the measurement. This fraction depends on the dynamic thermal conditions of the system and hence the calibration is only valid for the rate with which it was established. If the differential sensor gives a linear response, the calibration coefficient (in W/V) expresses the proportionality between the heat flux value (in W) and the voltage measured by the differential sensor (in V). Likewise, knowing the sample mass, the area (in V.s) of endothermic and exothermic peaks on the thermogram can be converted to enthalpy values (J/g). The calibration can be performed in two ways: – from measurements of melting enthalpies of well-known products such as pure metallic elements; – from Cp measurements on a standard reference material such as a a-Al2O3 sample in powder or single crystal form1, or a pure platinum sample, materials for which heat capacities are certified to ±1% over the whole temperature range [142, 145].

1   Note that the thermal conductivity of glasses differs from that of corundum. The calibration will be performed using alumina in the same physical form, powder or bulk, as the samples, in order to ensure that similar thermal gradient conditions prevail during the calibration and the measurement.

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However, both calibration methods cannot be applied equally. The choice should be guided by a reflection on the reproducibility of the heat transfer during the measurement and the calibration processes. The first method is based on a solid/liquid first order transition for which a high quantity of latent heat is released or absorbed at a constant temperature. This calibration is suitable for quantifying the enthalpies associated to similar transitions. The second method is especially suited for Cp measurements or for measuring the enthalpy of the transitions which span over a temperature range like second order transitions. The calibration coefficients obtained by the two methods are of the same order of magnitude but generally different. It is what differentiates quantitative DTA from true calorimetry.

3.2.2.5. Heat capacity measurement The Cp measurement follows a three-step technique, (Fig. 3.6): – A blank experiment (baseline or zero-line run) in which the sample crucible is kept empty. As this crucible has undergone many previous cleaning and reforming operations, this measurement is doubled to ensure that the crucible is thermally stable. Note that, for reasons of symmetry, an empty crucible of equal weight is inserted in the reference side of the instrument during this and the two subsequent steps;

Fig. 3.6.  –  Temperature difference (converted to heat flow) recorded versus time [141]. Three successive experiments are required for heat capacity measurement: a blank experiment, a calibration run on a standard reference material and a sample run.

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From Glass to Crystal

– A calibration (or reference) run in which the sample crucible contains a standard material; – The sample run in which the sample crucible is filled with a quantity of sample. The thermal diffusivities of sample and reference materials being de facto different, it is recommended to adjust their quantities to obtain thermal masses as close as possible to each other. This principle will minimize any errors due to non-strictly equal thermal conditions. The crucibles and lids and the applied thermal cycles must be the identical for the three successive steps. To achieve a satisfactory estimate of Cp values, it is recommended to calibrate each measurement against the corundum reference. The repetition of the calibration steps is made easier as a single crystal corundum disk is used. Even if alumina in powder form would be preferable if the glass sample is also powdered, the cleaning of the crucible after a high temperature cycle may become more difficult because alumina grains tend to stick to rhodium/platinum crucibles. At each instant, the Cp value is obtained by assuming that the offset of the baseline is proportional to the thermal mass m.Cp of the crucible + sample or reference equipment. As the Cp of the reference material e.g. a-Al2O3 is well known throughout the entire temperature range [134, 139, 142-145], it is easy to calculate the Cp of the sample according to: C P sample (T ) =

m reference Φ sample (T ) − Φ baseline (T ) (T )(3.24) C m sample Φ reference (T ) − Φ baseline (T ) P reference

Commercial software packages directly display the calculated Cp values. It is recommended to consider carefully how these data are calculated and in particular what corrections and approximations are made. It is also obviously understood that such an analysis is meaningless if a first order transition (Fig. 3.5) occurs within the temperature range of the measurements. By subtracting the blank experiment, the unavoidable reference/sample asymmetry is partially corrected. However, geometries and weights of the samples, produce an additional and different offset for each acquisition. Gmelin and Sarge [139] and Della Gatta et al. [142] consider as a first approximation that this offset is linear and propose also a standard procedure to correct it. The three measurement steps must include, before and after the heating or cooling period, some temperature plateau, the duration of which is sufficient to ensure that quasi stationary isothermal conditions are well-established (Fig. 3.7). During both isothermal stabilizations, a residual thermal flow is measured. This residual flow would be zero for a setup that is perfectly symmetric at any temperature, but in real experiments, the residual isothermal heat flows recorded at two different temperatures differ by a certain amount. Moreover this amount is different for the baseline, the reference and the measurement steps. Consequently the offset of the isothermal levels must be corrected to a common level before the CP calculation by equation 3.24.

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For each step, the heat flow is corrected by linear interpolation between the two isothermal heat flows. This method is illustrated by (Fig. 3.7) and Equation 3.25 for a thermogram recorded during the reference run:

Φ iso , end , ref − Φ iso , start , ref   Φ corr , ref (T ) = Φ meas , ref (T ) − Φ iso , start , ref + (t − t start ) (3.25) t end − t start  

Fig. 3.7.  –  Illustration of the correction method by linear interpolation of the residual flow offsets in the case of the standard material. This correction must be applied to each acquisition needed to calculate the CP. Adapted from [139] and [142].

This protocol is now routinely implemented in the data processing software, with more or less freedom left to the user to set these experimental corrections. It is thus necessary to well understand what kind of corrections are applied and possibly, following Dargaud [146], select the appropriate duration of the thermal equilibration periods, which depend on the thermal cycle and on the sample studied, and finally process the signal to ensure a proper correction of the residual flow (Fig. 3.8). Well-calibrated, this method allows exploring a large number of compositions over a wide temperature range, with a sufficient sensitivity in the heat capacity measurement to detect the exothermic events occurring in the supercooled liquid. In the discontinuous or incremental method (ISO 11357-4), the overall temperature range to be analyzed is divided into small temperature segments. A three-step sequence (Fig. 3.6) is repeated for each individual small temperature segment. For each small temperature interval, the heat quantity involved is obtained by integrating the heat flow curve and the mean Cp is calculated by dividing the heat quantity by the temperature increase. The objective of this

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From Glass to Crystal

Fig. 3.8.  –  Correction of the isothermal heat flows on a parent vitroceramic glass in the system MgO-Al2O3-SiO2 with ZrO2 addition. [146] a) standard material, b) blank, c) sample. Uncorrected signals are shown in blue, the linear corrections in dashed blue line and the corrected signals in pink/green.

more time consuming method is to reduce experimental uncertainty. Indeed, the correction method by linear interpolation of the isothermal heat flows is more accurate for small temperature intervals. DTA experiments are generally carried out on heating because the temperature can be controlled with a greater precision than on cooling. However, a thermogram recorded on cooling remains useful for the study of a glass composition because it provides information about the ability of the liquid to crystallize at a given temperature rate.

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More rarely, DTA is used with a scanning modulated temperature. The aim [136, 147] is to separate (in the response of the sample), the temperature-dependent contribution from the rate-dependent one. The temperature is periodically modulated around an average value which may itself be kept constant or varied at constant heating or cooling rate. The coupling of a heating or cooling stage with an isothermal holding is a valuable tool to investigate issues such as the physical ageing in the glass transition domain and the crystallisation.

3.2.2.6. Some practical tips Powdered samples must have a homogeneous granulometry, i.e., particles of uniform size, for kinetic study and be compacted at the bottom of the crucible to improve the thermal contact between the sample and the crucible. For high temperatures experiments, it is a good practice to assess the risk of chemical reaction between the metal alloy of the crucible and the sample, and also to check if the sample is subject to significant foaming. The thermal cycle that will be applied during the measurement can be simulated in a separate furnace: weighing and careful a posteriori examination of the crucible allows to conclude on the feasibility of the measurement without damaging the sensor. If the glass sample partially crystallizes during the measurement, the CP values will obviously not be a characteristic of the glass alone. After the measurement, careful observation of the sample is recommended. Particular attention should be paid to crucibles and lids. They must be identified and referenced: their masses must be checked after each cleaning cycle which includes a HF attack of the residual glass, a HCl dissolution of the fluorides formed and finally a rinsing step in boiling water. Note that the cleaning of glass-ceramic samples is particularly difficult when the sample is highly crystallized after the thermal analysis cycle. Depending on the nature of the crystals, it may become necessary to increase the number of HF attacks to dissolve the crystals. Crucibles must be reshaped to improve thermal contact with the sensor. Compared to conventional sensors that are constituted by a flat bottom on which the crucible is placed, a 3D sensor minimizes this problem. In this setup, as in true calorimetry, the thermocouples are arranged around the lateral walls of the crucible and the amount of glass analysed is larger.

3.2.3.

Measurement of the formation or mixing functions

Inasmuch as it is not possible, given its metastable nature, to form a glass or an oxide compound in general by direct reaction of its various constitutive simple oxides inside the calorimeter, solution calorimetry is the generally preferred method in order to determine the enthalpy of formation of a glass. In this method, prior elaboration of the glass is required then, in a second step, the glass and each of its constitutive reference oxides are dissolved

92

From Glass to Crystal

separately in various batches of the same liquid solvent S at the temperature T. For example, for a ternary glass xSiO2-yAl2O3-zNa2O, the individual separate solution reactions are written: Glass + 3S ® ((xSiO2, yAl2O3, zNa2O))3S(3.26) xSiO2 + S ® ((xSiO2))S(3.27) yAl2O3 + S ® ((yAl2O3))S(3.28) zNa2O + S ® ((zNa2O))S(3.29) where “Glass” in equation 3.26 represents one mole of a ternary glass xSiO2yAl2O3-zNa2O and “(( ))S” means that the species between the double parentheses are dissolved in the quantity S of the solvent. The formation reaction of the glass is written as follows: xSiO2 + yAl2O3 + zNa2O ® Glass

(3.30)

According to the reaction 3.30, the enthalpy of formation of the glass is simply obtained from the difference between the algebraic sum of the enthalpies of solution of the reference oxides and the solution enthalpy of the glass: DfH(Glass) = DsolH(3.27) + DsolH(3.28) + DsolH(3.29) – DsolH(3.26)(3.31) where the enthalpy of reaction (i) is noted DsolH(i). However equation 3.31 holds true only if the sum of the final states of the reactions 3.27, 3.28 and 3.29 is the same as the final state of reaction 3.26 requiring that there are no interactions between SiO2, Na2O and Al2O3 in the final bath of reaction 3.26. This condition is fulfilled if the DsolH of all the reactions are measured at infinite dilution. In practice, the solution enthalpies are measured versus the concentration in the solvent and the values are extrapolated to zero concentration. In the cases where the DsolH at high dilution are not concentration-dependent, extrapolation to infinite dilution is not necessary. The solvent must meet several requirements: – It must dissolve the substance to be studied and all the references in order to attain a final equilibrium state in a reasonable time compatible with the thermal stability of the calorimeter; – DsolH for the glass and for all references (i = 1,…n) must have the same order of magnitude DfH in order to obtain a good precision on DfH, because DfH is calculated by a difference through equation 3.31.

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The dissolution process depends on the nature of the chemical bonding in the solute, on the nature of the solvent and on the temperature. It involves the destruction of the solid lattice of the substance to be dissolved, the dissolution effect in the solvent (e.g., ionization of a metal in an acid aqueous solution) and potential side reactions with the solvent like the precipitation of a compound (e.g., CaF2 after dissolving a CaO containing glass in a HF aqueous solution if Ca2+ concentration exceeds the solubility limit) or the formation of a complex by solvatation. Solution calorimetry on nuclear glasses can be performed both at room temperature using mixtures of aqueous acids as the solvent or at higher temperature in molten oxide bathes.

3.2.3.1. Room temperature solution calorimetry An example is given by the special swinging Tian-Calvet microcalorimeter named CALSOL. This prototype constructed in the “Centre de Thermodynamique et Microcalorimétrie de Marseille” by Ganteaume and his co-workers is described in details in Ganteaume et al. [148]. The apparatus (Fig. 3.9a) is a heat flow meter based on a differential twin cell design. It is used in isothermal mode. To promote good mixing of the solute and the solvent, the whole calorimeter is able to rotate around the horizontal axis (Fig. 3.9a). The calorimeter is itself located in a temperature-controlled (± 0.5 K) room. The reaction cell is shown in Fig. 3.9b. In the starting position, the solute and the solvent are housed in separate containers. During the first rotation, the cell is turned upside down and the lid covering the solute container falls and the solvent comes into contact with the solute. Periodic rocking of the calorimeter is continued for the entire duration of the dissolution reaction. The differential voltage of the two copper/constantan thermopiles surrounding respectively the sample and the reference cells is recorded versus time. This voltage is proportional to the instantaneous heat flow. The calibration, which is needed to convert the recorded voltage in watt, can be performed using the calibration resistance embedded in the cell (Fig. 3.9b) or preferably by the endoor exothermic effect resulting from the dissolution of a reference material in a well-defined solvent [148]. The heat quantity is obtained by time integration of the instantaneous heat flow over the whole duration of the dissolution. The calorimeter has a time constant of 45 min and combines a high sensitivity of 0.05 mW/cm3 with a very steady response. It has been checked that the calibration constant does not change appreciably over several years. The baseline is very stable over several days. For compounds containing silica and silicate glasses, the usual solvent is a mixture of acids involving hydrofluoric acid: e.g., HF(13M) – HNO3(6M) for a beidellite clay mineral. The thermal effect induced by stirring the solvent must be measured and subtracted from the overall effect. In Fig. 3.10 the return of the calorimetric signal to its initial baseline, as soon as the stirring is stopped, is evidence of the

94

a) A, calorimeter block; B, thick thermoregulated vessel; C, outer vessel; D, temperature sensor of the controller; E, double coil heating resistance; G, electronic control board; I, thermal insulator; K, cones for even distribution of outer thermal disturbances; L and T, thermopiles M, thermistor for calorimeter temperature control; N, cell blocking rods; P and Q, housings of the reaction and reference cells; R et S, top et bottom outer vessel lids.

From Glass to Crystal

b) A, cell body; B, immersion sleeve; C, calibration electrical resistance; D, solute container; E, platinum lid; F, Viton O-ring; G, screwed lid of the cell; H, electrical leads of the calibration resistance; I, Solute; J, liquid seal; K, solvent; ab, height of the cell which is inserted in the thermopile

Fig. 3.9. – a) Section of the CALSOL calorimeter. b) Section of the reaction cell, adapted from [148].

completion of the dissolution reaction. Practically, the dissolution is considered finished when the heat flow becomes lower than 10-4 of its peak recorded value. The scale displayed on the vertical axis also shows that the baseline has a better stability than ± 4 µW allowing very small heat effects to be accurately measured. Despite this, the return of the calorimetric signal to the baseline may become difficult to assess when the dissolution kinetics is slow and lasts several days. It represents the main measuring error in this case. The CALSOL calorimeter has been recently used in an unconventional way to investigate the solubility of molybdenum oxide in a ternary model glass containing silica, sodium and boron oxides. In Fig. 3.11, the solution enthalpy is

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95

plotted against the atomic percent of molybdenum oxide. The curve presents a slope change around 1.5% which is a signature of the precipitation of a crystalline phase inside the glass. Beyond this solubility limit, dissolution enthalpy is a linear function of the atomic percentage of molybdenum oxide typical of a two-phased region. Moreover, if the crystalline phase is well identified and its dissolution enthalpy is separately measured, then the precipitated phase fraction can be determined.

Fig. 3.10.  –  Calorimetric signal recorded during a dissolution.

Fig. 3.11. – Solution enthalpy of a ternary model glass against molar percentage of molybdenum oxide.

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From Glass to Crystal

3.2.3.2. High temperature solution calorimetry in molten oxide solvent This technique is described in details by Kleppa [149] and in two subsequent reviews by Navrotsky [150, 151]. High temperature Tian-Calvet calorimeters are mainly used. The principle of these calorimeters, which operate up to 1 300 K, is identical to their room temperature version but their technology is obviously different. Refractory materials, capable of withstanding long-term stay at high temperature, are required. For example, the thermopiles are made of platinum/rhodium wires. Among the different oxides mixtures used as solvents in the literature, lead metaborate 2PbO-B2O3 is the most largely utilized [150] because of its excellent ability to dissolve both acidic (e.g., SiO2, Al2O3) and basic (e.g., CaO or MgO) oxides. Moreover, this specific solvent acts as a buffer avoiding significant change of the dissolution enthalpy within slight variations of the melt composition. Lead metaborate is also easy to elaborate and to store because it is vitreous and weakly hygroscopic at room temperature. Its eutectic composition is fully liquid at the relatively low temperature of 773 K. However, in the temperature range of the calorimetric experiments, the viscosity of lead metaborate and oxide melts in general is sufficiently high to render stirring of the melt mandatory in order to enhance dissolution of the samples. In practice, solvent stirring is performed by vertical translation of the platinum sample holder inside the bath. In the operating mode of [149] and [150], after thermal equilibration of the sample holder at the calorimeter temperature, the dissolution reaction is initiated by lowering the sample cup into the melt, performing a quick stirring and then returning the sample holder to its original position. This procedure is repeated several times during the dissolution. After completion of the dissolution, the heat effect induced by the intermittent stirring is evaluated by a blank experiment. Even if a standard length of time and a number of up and down movements are applied for each stirring, the procedure remains manual. Another difficulty can arise if the sample is not totally washed out of the cup during the first immersion. In order to increase the reproducibility of such experiments and enhance the sample dissolution, Brousse et al. [152, 153] from the Centre de Thermodynamique et Microcalorimétrie de Marseille have developed an automated stirring device equipped with synchronous motors to provide periodic vertical translation of the sample holder. The experiments follow a five-step operating mode (Fig. 3.12): – Step 1: the filled sample cup is thermally equilibrated at the calorimeter temperature few millimeters above the solvent bath, – Step 2: the dissolution is started by lowering the sample holder into the melt. Stirring is performed for the entire duration of the dissolution. At the end of this step, a baseline shift of the calorimetric signal is observed due to the increased heat loss by conduction through the immersed sample holder.

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– Step 3: the sample holder is moved upwards, the baseline returns to its initial value. – Step 4: A blank stirring experiment is performed by lowering the now empty sample cup inside the melt and agitating the melt in the same way as in step 2. – Step 5: again, the sample is moved upwards and the baseline returns to its initial value.

Fig. 3.12.  –  Five-step operating mode for oxide melt solution calorimetry.

The net heat effect corresponding to the sample dissolution is obtained by the difference between the heat effects recorded during steps 2 and 4 and represented by the hatched area in Fig. 3.12. Due to the differential nature of the calorimetric signal delivered by Tian-Calvet calorimeters, the magnitude of the blank stirring effect can be minimized by fine-tuning the relative immersion depths of the calorimetric devices in the reference and in the sample thermopiles. Example of results obtained with this experimental setup are given in Brousse et al. [153], in Rogez and Mathieu [154] and in the more recent study of Linard et al. [155] for a simplified ternary SiO2-B2O3-Na2O nuclear glass composition.

3.2.3.3. Room temperature vs. high temperature solution calorimetry A detailed comparison of the two techniques is given by Navrotsky [150]. The main advantage of oxide melt solution calorimetry lies in the fact that it is possible to handle refractory oxides such as Al2O3, MgO, Cr2O3 which is not possible with room temperature solution calorimetry in HF mixtures. Moreover, the acidic solvents used in room temperature solution calorimetry do not act as a buffer and hence significant evolution of the thermal effect due to side

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reactions (redox, acid-base reactions, solvatation, precipitation...) are observed when the solvent concentration changes. However, room temperature has several interesting features. The room temperature calorimeters have a precision which is ten times higher than the high temperature ones. The working temperature of the calorimeter is well below the glass transition temperature range of silicate melts. Hence, the state of a glass sample will not be altered during the thermal equilibration of the sample inside the calorimeter before the dissolution. Conversely, depending of the sample composition, stabilization of a glass sample may occur in the 700-1 000 °C operating range of oxide solution calorimetry changing the initial thermodynamic state of the sample.

3.2.4.

Measurement of free enthalpy and derivative quantities by Knudsen Effusion Mass Spectrometry (KEMS)

In this quantitative technique, a condensed phase is equilibrated with its vapour inside a Knudsen cell heated at high temperature for example up to 2 500 K and under vacuum. The vapor phase is sampled under molecular regime and analyzed by mass spectrometry. The technique allows identifying all the molecules simultaneously present in a complex vapour and determining their individual partial pressure which can be measured in the range 10-12 up to 10-4 atm. A high level overview of this technique can be found in Drowart et al. [156]. The schematic of a KEMS apparatus is presented in Fig. 3.13.

Fig. 3.13.  –  Principle of the multiple cell Knudsen Effusion Mass Spectrometry.

Chapter 3 – Thermodynamics of the glassy and the crystalline states

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The molecular beam (in blue) effusing from one Knudsen cell crosses an electron beam (in red) inside an ion source. Neutral molecules of the vapor are ionized, extracted and accelerated by an ion optics to form an ion beam (in green) before entering a mass filter, which can be a quadripole, a magnetic sector, or a double focusing spectrometer composed of a magnetic sector and an electrostatic sector. The ionic current is measured using a Faraday cup and/or an electron multiplier to increase the sensitivity. The fundamental relation of the spectrometer links the partial pressure pi of a species i in the Knudsen cell to the ionic current Ii which is detected for this species: pi = S

Ii T (3.32) σ i βi

Obviously, the pressure is proportional to the temperature T of the Knudsen cell (perfect gas law). The quantities at the denominator of equation 3.32 are the ionization cross section (σi) and the relative detector sensitivity (βi), they depend on the species. The S factor is a device constant which includes geometric factors of the apparatus. The S factor cannot be calculated and, in the most general case, a calibration of the apparatus is needed to convert ionic intensities to vapour pressures. This calibration can be performed by using a reference sample of known vapour pressure or, when relevant, by weighing the cell before and after the experiment in order to determine the total mass loss. Inside a Knudsen cell, the thermodynamic equilibrium imposes that the activity in the condensed phase ai equals the activity in the gas phase: ai = γ i X i =

pi (3.33) pi0

where ai and Xi are respectively the activity coefficient and the molar fraction of i in the condensed phase, pi is the partial pressure of i above the melt or glass and p°i the partial pressure of i above a condensed reference state (e.g., pure oxide). Using monocell effusion, two successive experimental runs are required for activity determination: the first for the solution sample and the second for the reference. The activity can then be written as a function of the ion intensities: SI T  σ i βi  ai =  i   σ i βi  run 1  SI i0T 

(3.34) run 2

However, S cannot be kept strictly constant between these two runs because venting of the spectrometer is needed to exchange samples and, in general, the ion source has also to be stopped. Different methods can be found in the literature to overcome this problem. They are based on simultaneous measurements of ion intensities for different

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species i and j using additional relations to eliminate or evaluate the remaining unknown quantities [157]. Among these methods, the dual or multiple cell effusion, alternately named differential mass spectrometry, has been strongly developed by C. Chatillon and its co-workers from 1975 up to now in Grenoble [158]. A minimum of 2 up to 6 cells are used and this comparative method has many advantages: – One cell filled with a reference sample acts as an internal standard allowing a continuous calibration of the mass spectrometer for each species considered and at a strictly identical ionization energy. – Several chemical compositions can be studied and compared in a single run. – Different dimensions and shapes of the effusion orifice for each cell can be used simultaneously during a single run to estimate the equilibrium pressure when the evaporation coefficients are low. – Activity is measured directly in a single run, provided that the multicell block is isothermal and S remains the same when the cells are switched. The data treatment is straightforward and easily extended to ternary or multicomponent systems. – Only one component needs to be volatile. This feature is very interesting in oxide systems because vapour pressures of the components are low and sometimes measurable only for one vapour component preventing the use of the classical ratio methods in monocell effusion. – Measurement over a large composition range is not mandatory to obtain an activity value: any single measurement for any composition gives one activity value. – The possibility to perform internal consistency check; for example, in a binary system, measurements of two volatile components give a GibbsDuhem check. The price to pay for these increased capabilities is that part of the spectrometer has to be rebuilt because, in general, vacuum chambers of conventional spectrometers are not large enough to house a multicell furnace. It is worth noting that isothermicity of the multicell block is harder to achieve and can be an issue at T  Al2O3 in mol%), adding aluminum reduced the solubility of lanthanide ions and the crystallization tendency of Ca2Ln8(SiO4)6O2 increases (Fig. 22.2d,e,f and Fig. 22.10a). This is interesting for formulating apatite-based glass-ceramics by allowing crystallization to change from surface crystallization (Fig. 22.2d) to strong crystallization in the bulk (Fig. 22.2f) [1236]. However, when the composition of the glass becomes peraluminous (i.e., when (Na2O + CaO)