Wallis Lattice Dynamics

Proceedings of the International Conference Held at Copenhagen, Denmark, August 5-9, 1963
1. Auflage 2013
ISBN: 978-1-4832-2341-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 746 Seiten, Web PDF

Lattice Dynamics covers the proceedings of the 1963 International Conference on Lattice Dynamics, held at the H.C. Ørsted Institute of the University of Copenhagen on August 5-9. This book is composed of seven parts that focus on a better fundamental understanding of the interactions between atoms in solids and their role in lattice dynamics. The major topics covered include phonon dispersion curves, anharmonic effects, optical and dielectric effects, influence of defects on lattice vibrations, elasticity, and developments. Papers on the study of vibrational spectra by infrared absorption, X-ray and neutron scattering and the electron tunneling effects as well as papers on the influence of defects and on a variety of other problems in lattice dynamics are included. This book will prove useful to applied physicists and researchers in the field and related fields of lattice dynamics.

Autoren/Hrsg.

Wallis, R. F.

Inhaltsverzeichnis

1;Front Cover;1
2;Lattice Dynamics;4
3;Copyright Page;5
4;Table of Contents;10
5;CONFERENCE ORGANIZATION;6
6;FOREWORD;8
7;INTRODUCTORY REMARKS;16
8;REMINISCENCES OF MY WORK ON THE DYNAMICS OF CRYSTAL LATTICES;18
9;POSTSCIPT WRITTEN
AFTER THE CONFERENCE;23
10;THE EARLY DAYS OF LATTICE DYNAMICS;26
10.1;1.
BACKGROUND;26
10.2;2. SPECIFIC HEAT;27
10.3;3. THE WOLFSKEHL CONFERENCES;29
11;PART A: PHONON DISPERSION CURVES;32
11.1;CHAPTER A1. A STUDY OF THE CRYSTAL DYNAMICS OF ZINC;34
11.1.1;Abstract;34
11.2;CHAPTER A2. NORMAL VIBRATIONS IN GALLIUM ARSENIDE;36
11.2.1;Abstract;36
11.2.2;1. INTRODUCTION;36
11.2.3;2. EXPERIMENTAL METHODS AND RESULTS;37
11.2.4;3. THEORETICAL MODELS;42
11.2.5;4. CONCLUDING REMARKS;47
11.2.6;Acknowledgements;48
11.2.7;REFERENCES;48
11.3;CHAPTER A3. LATTICE DYNAMICS OF ZINC;50
11.3.1;Abstract;50
11.3.2;1. INTRODUCTION;50
11.3.3;2. CALCULATION OF PHONON DISPERSION RELATIONS IN ZINC;50
11.3.4;3. EXPERIMENTS;51
11.3.5;4. DISCUSSION;52
11.3.6;REFERENCES;54
11.4;CHAPTER A4. LATTICE DYNAMICS OF NIOBIUM;56
11.4.1;Abstract;56
11.4.2;1. INTRODUCTION;56
11.4.3;2. EXPERIMENTAL DETAILS;57
11.4.4;3. RESULTS;57
11.4.5;4. DISCUSSION;60
11.4.6;5. CONCLUSIONS;64
11.4.7;Acknowledgements;65
11.4.8;REFERENCES;65
11.5;CHAPTER A5. PHONON DISPERSION RELATIONS IN MAGNESIUM OXIDE;66
11.5.1;Abstract;66
11.5.2;Acknowledgements;68
11.5.3;REFERENCES;68
11.6;CHAPTER A6. THE FREQUENCIES OF THE NORMAL MODES OF COPPER;70
11.6.1;Abstract;70
11.6.2;1. INTRODUCTION;70
11.6.3;2. DESCRIPTION OF EXPERIMENT;70
11.6.4;3. RESULTS AND DISCUSSION;70
11.6.5;Acknowledgements;73
11.6.6;REFERENCES;73
11.7;CHAPTER A7. EXPERIMENTAL DISPERSION CURVES FOR PHONONS IN ALUMINUM;74
11.7.1;Abstract;74
11.7.2;1. INTRODUCTION;74
11.7.3;2. THE EXPERIMENT;75
11.7.4;3. RESULTS AND DISCUSSION;76
11.7.5;REFERENCES;78
11.8;CHAPTER
A8. MEASURED VIBRATIONAL FREQUENCY DISTRIBUTIONS OF Ni, V, Ti, AND Ti67Zr33;80
11.8.1;Abstract;80
11.8.2;1. INTRODUCTION;80
11.8.3;2. EQUIPMENT;81
11.8.4;3. EXPERIMENTAL RESULTS;81
11.8.5;4. DATA ANALYSIS AND DISCUSSION;83
11.8.6;APPENDIX;86
11.8.7;REFERENCES;86
11.9;CHAPTER A9. DETERMINATION OF DISPERSION CURVES OF PHONONS WITH THE AID OF DIFFUSE SCATTERING OF X-RAYS AND INELASTIC SCATTERING OF
NEUTRONS;88
11.9.1;Abstract;88
11.9.2;REFERENCES;88
11.10;CHAPTER A10. THE THERMAL SCATTERING OF X-RAYS IN ROCK SALT;90
11.10.1;Abstract;90
11.10.2;REFERENCE;90
11.11;CHAPTER A11. INTERPRETATION OF PHONON DISPERSION CURVES;92
11.11.1;Abstract;92
11.11.2;1. INTRODUCTION;92
11.11.3;2. IONIC AND COVALENT CRYSTALS;93
11.11.4;3. METALLIC CRYSTALS;96
11.11.5;Acknowledgements;100
11.11.6;REFERENCES;100
11.12;CHAPTER A12. THEORY OF PHONON DISPERSION IN METALS;102
11.12.1;Abstract;102
11.12.2;REFERENCES;107
11.12.3;NOTES ADDED IN PROOF;107
11.13;CHAPTER A13. LATTICE DYNAMICS OF LEAD;108
11.13.1;Abstract;108
11.13.2;1. INTRODUCTION;108
11.13.3;2. THE CHANGE OF ELECTRON DISTRIBUTION BY LATTICE VIBRATION;109
11.13.4;3. SELF-CONSISTENT SOLUTION FOR MONOVALENT METALS;110
11.13.5;4. THE CHANGE OF ELECTRON DISTRIBUTION FOR MULTIVALENT METALS;111
11.13.6;5. EFFECTIVE MATRIX ELEMENT FOR MULTIVALENT METALS;113
11.13.7;6. DISPERSION RELATION FOR MULTIVALENT METALS;114
11.13.8;7. DISPERSION RELATION FOR LEAD;114
11.13.9;Acknowledgements;116
11.13.10;REFERENCES;116
11.14;CHAPTER A14. STUDIES IN LATTICE DYNAMICS OF METALS USING THE
A–S MODEL;118
11.14.1;Abstract;118
11.14.2;1. INTRODUCTION;118
11.14.3;2. THEORETICAL FOUNDATION OF THE A-S MODEL;118
11.14.4;3. LATTICE STABILITY;120
11.14.5;4. CORRELATION OF ELASTIC CONSTANTS WITH VIBRATIONAL SPECTRA OF HEXAGONAL CLOSEPACKED METALS;120
11.14.6;5. COMPUTATION OF SPECIFIC HEAT AND DEBYE-WALLER FACTOR;123
11.14.7;REFERENCES;124
11.15;CHAPTER A15. LATTICE VIBRATIONS OF LaCl3;126
11.15.1;Abstract;126
11.15.2;INTRODUCTION;126
11.15.3;THE CRYSTAL STRUCTURE OF LaCl3;126
11.15.4;THE MODEL;127
11.15.5;INFRARED DATA;128
11.15.6;CALCULATIONS;129
11.15.7;DISCUSSION;134
11.15.8;REFERENCES;134
11.16;CHAPTER A16. DYNAMIQUE DES RESEAUX HEXAGONAUX COMPACTS SPECTRES DES FREQUENCES DE VIBRATION;136
11.16.1;Résumé;136
11.16.2;INTRODUCTION;136
11.16.3;DYNAMIQUE DU RESEAU;137
11.16.4;HYPOTHESE UTILISEE;138
11.16.5;COMPARAISON AVEC LES RESULTATS OBTENUS PAR DIFFRACTION DES RAYONS X ET DES NEUTRONS LENTS;140
11.16.6;SPECTRES DES FREQUENCES DE VIBRATION: CHALEURS SPECIFIQUES;141
11.16.7;CONCLUSION;143
11.16.8;BIBLIOGRAPHIE;143
11.17;CHAPTER A17. ON THE LATTICE DYNAMICS AND SPECIFIC HEAT OF THE RARE-GAS SOLIDS;146
11.17.1;Abstract;146
11.17.2;1. INTRODUCTION;146
11.17.3;2. SECULAR EQUATION;146
11.17.4;3. DEBYE T;147
11.17.5;4. ACCURACY;150
11.17.6;5. ARGON AND KRYPTON;150
11.17.7;Acknowledgement;151
11.17.8;REFERENCES;151
11.18;CHAPTER A18. LATTICE DYNAMICS OF TELLURIUM;152
11.18.1;Abstract;152
11.18.2;1. INTRODUCTION;152
11.18.3;2. THE MICROSCOPIC MODEL;152
11.18.4;3. COMPARISON OF EXPERIMENTAL AND THEORETICAL VALUES OF Cij;154
11.18.5;4. PREDICTED VALUES OF DYNAMICAL AND ELASTIC PROPERTIES OF Te LATTICES;155
11.18.6;5. CONCLUSION;157
11.18.7;Acknowledgement;157
11.18.8;REFERENCES;157
11.19;CHAPTER A19. A COMPARISON OF THE THERMODYNAMIC PROPERTIES AND SPECTRA OF THE F.C.C. AND H.C.P. LATTICES;158
11.19.1;Abstract;158
11.19.2;INTRODUCTION;158
11.19.3;THE LATTICE STRUCTURE;159
11.19.4;THE SPECTRUM;159
11.19.5;THE SPECIFIC HEAT DIFFERENCE;160
11.19.6;THE CHANGE IN THE ZERO POINT ENERGY;161
11.19.7;CONCLUSIONS;161
11.19.8;Acknowledgements;161
11.19.9;REFERENCES;161
11.20;CHAPTER A20. LATTICE VIBRATION OF MgO (PERICLASE);162
11.20.1;Abstract;162
11.21;CHAPTER A21. THE FORCE CONSTANTS OF GERMANIUM;164
11.21.1;Abstract;164
11.21.2;1. INTRODUCTION;164
11.21.3;2. THE BORN-VON KÄRMÄN THEORY OF THE DIAMOND STRUCTURE;165
11.21.4;3. DETERMINATION OF THE FORCE CONSTANTS BY LEAST SQUARES FITTING;169
11.21.5;4. DETERMINATION OF THE FORCE CONSTANTS BY FOURIER ANALYSIS;171
11.21.6;5. CONCLUSION;173
11.21.7;Acknowledgements;174
11.21.8;REFERENCES;174
11.22;CHAPTER A22. SHELL AND EXCHANGE CHARGE MODELS OF INTERATOMIC INTERACTIONS IN SOLIDS;176
11.22.1;Abstract;176
11.22.2;1. INTRODUCTION;176
11.22.3;2. A SIMPLE SHELL MODEL;178
11.22.4;3. A GENERALIZED SHELL MODEL AND LATTICE DYNAMICS OF IONIC CRYSTALS;180
11.22.5;4. APPLICATIONS TO OTHER CRYSTALS;184
11.22.6;5. FOUNDATIONS;187
11.22.7;6. EXCHANGE CHARGE MODEL;188
11.22.8;Acknowledgements;190
11.22.9;REFERENCES;190
11.23;CHAPTER A23. APPLICABILITY OF THE "SHELL MODEL" TO THE LATTICE VIBRATIONS OF
LiH;192
11.23.1;Abstract;192
11.23.2;Acknowledgement;194
11.23.3;REFERENCES;194
11.24;CHAPTER A24. COMMENTS ON THE SHELL MODEL
FOR LATTICE VIBRATIONS;196
11.24.1;Abstract;196
11.24.2;1. COMPARISON BETWEEN MODELS;196
11.24.3;2. THE QUADRUPOLE MODEL;196
11.24.4;3. RANGE OF FORCES IN THE SHELL MODEL;199
11.24.5;4. THE EFFECTIVE FIELD PROBLEM;201
11.24.6;5. ROTATIONAL INVARIANCE;201
11.24.7;6. DE LAUNAY'S METHOD;201
11.24.8;7. LATTICE VIBRATIONS IN METALS;202
11.24.9;REFERENCES;203
11.25;CHAPTER A25. LATTICE DYNAMICAL MODELS FOR GREY AND WHITE TIN AND THEIR RELEVANCE TO TRANSITIONS AT HIGH PRESSURE;206
11.25.1;Abstract;206
11.25.2;INTRODUCTION;206
11.25.3;ESTIMATION OF PHYSICAL PARAMETERS;206
11.25.4;RESULTS;208
11.25.5;Acknowledgement;209
11.25.6;REFERENCES;209
11.26;CHAPTER A26. ATOMIC MODEL FOR PHASE TRANSITIONS IN KH2P04 LIKE CRYSTALS;210
11.26.1;Abstract;210
11.27;CHAPTER A27. LATTICE DYNAMICS OF RUBIDIUM IODIDE IN RELATION TO THE NaCl-CsCl PHASE TRANSITION;212
11.27.1;Abstract;212
11.27.2;INTRODUCTION;212
11.27.3;THEORY;213
11.27.4;APPLICATION TO Rbl;215
11.27.5;Acknowledgements;217
11.27.6;REFERENCES;217
11.28;CHAPTER A28. ON THE EFFECTIVE CHARGE OF IONS AND THE DEVIATION FROM ADDITIVITY OF POLARIZABILITY AND DIAMAGNETIC SUSCEPTIBILITY OF IONIC CRYSTALS;220
11.28.1;Abstract;220
11.29;CHAPTER A29. APPLICATION OF A SUM RULE TO THE STUDY OF INTERATOMIC FORCES;222
11.29.1;Abstract;222
11.29.2;1. STATEMENT OF THE SUM RULE;222
11.29.3;2. GENERAL FORM OF TRACE;223
11.29.4;3. SPECIAL MODIFICATIONS FOR MONATONIC (BRAVAIS) LATTICES;225
11.29.5;4. APPLICATIONS;228
11.29.6;Acknowledgements;230
11.29.7;REFERENCES;230
11.30;CHAPTER A30. POLARIZATION OF ATOMIC VIBRATIONS IN CRYSTALS;232
11.30.1;Abstract;232
11.31;CHAPTER A31. ONDES DE LIBRATION DANS UN MODELE DE CRISTAL MOLÉCULAIRE;234
11.31.1;Résumé;234
11.31.2;CALCUL DE LA DISTRIBUTION DES FREQUENCES DE LIBRATION DANS LE CAS OU LINTERACTION EST DIPOLAIRE;236
11.31.3;REMARQUES;237
11.31.4;CONCLUSION;238
11.31.5;Remerciements;238
11.31.6;BIBLIOGRAPHIE;239
11.32;CHAPTER A 32. DISPERSION RELATIONS FOR PHONONS IN MAGNESIUM;240
11.32.1;Abstract;240
11.32.2;Acknowledgement;248
11.32.3;APPENDIX;248
11.32.4;REFERENCES;249
11.33;DISCUSSION;250
12;PART B: ANHARMONIC EFFECTS;252
12.1;CHAPTER B1. ANHARMONIC EFFECTS;254
12.1.1;Abstract;254
12.1.2;1. INTRODUCTION;254
12.1.3;2. EXPANSION OF THE POTENTIAL ENERGY;254
12.1.4;3. THERMODYNAMICS;256
12.1.5;4. DYNAMICAL EFFECTS;259
12.1.6;REFERENCES;261
12.2;CHAPTER B2. THERMODYNAMIC PROPERTIES AND EFFECTIVE VIBRATIONAL SPECTRA OF AN ANHARMONIC CRYSTAL;264
12.2.1;Abstract;264
12.2.2;1. INTRODUCTION;264
12.2.3;2. EFFECTIVE FREQUENCY SHIFTS FOR THERMODYNAMIC PROPERTIES;265
12.2.4;3. THE EFFECTIVE SPECTRUM AT LOW TEMPERATURES;267
12.2.5;4. INFLUENCE OF ANHARMONICITY UPON EQUIVALENT DEBYE TEMPERATURES;268
12.2.6;5. SOME SPECULATIVE REMARKS;270
12.2.7;REFERENCES;271
12.3;CHAPTER B3. DEVIATIONS OF THE SPECIFIC HEATS OF THE ALKALI METALS FROM HARMONIC BEHAVIOUR. A POSSIBLE DEPENDENCE ON ISOTOPIC COMPOSITION OF THE ANHARMONIC CONTRIBUTION TO SPECIFIC HEAT;272
12.3.1;Abstract;272
12.3.2;1. INTRODUCTION;272
12.3.3;2. DEVIATIONS OF THE SPECIFIC HEATS OF THE ALKALI METALS FROM HARMONIC BEHAVIOUR;272
12.3.4;3. A POSSIBLE DEPENDENCE ON ISOTOPIC COMPOSITION OF THE ANHARMONIC CONTRIBUTION TO SPECIFIC HEAT;274
12.3.5;APPENDIX;277
12.3.6;REFERENCES;277
12.3.7;NOTES ADDED IN PROOF;277
12.4;CHAPTER B4. INELASTIC SCATTERING OF NEUTRONS BY ANHARMONIC CRYSTALS;278
12.4.1;Abstract;278
12.4.2;1. INTRODUCTION;278
12.4.3;2. GENERAL FORMULATION;280
12.4.4;3. ONE PHONON, MULTIPHONON AND INTERFERENCE EFFECTS;283
12.4.5;4. SUM RULES;284
12.4.6;5. CRUDE NUMERICAL ESTIMATE;286
12.4.7;Acknowledgements;287
12.4.8;REFERENCES;287
12.5;CHAPTER B5. PAPER WITHDRAWN;288
12.6;CHAPTER B6. THE PRESSURE DERIVATIVES OF ELASTIC CONSTANTS: MICROSCOPIC GRÜNEISEN PARAMETERS;290
12.6.1;Abstract;290
12.6.2;INTRODUCTION;290
12.6.3;SLATERS GAMMA;291
12.6.4;GENERAL ACOUSTIC CONTINUUM GAMMAS;292
12.6.5;DISCUSSION;294
12.6.6;GAMMAS OF DISPERSIVE MODES;296
12.6.7;Acknowledgements;296
12.6.8;REFERENCES;297
12.7;CHAPTER B7. EQUATION OF STATE AND THERMODYNAMIC FUNCTIONS OF NON-METALLIC CRYSTALS;298
12.7.1;Abstract;298
12.7.2;1. INTRODUCTION;298
12.7.3;2. EQUATION OF STATE OF CUBIC NON-METALS UNDER HYDROSTATIC PRESSURE;299
12.7.4;3. THERMAL THERMODYNAMIC FUNCTIONS;300
12.7.5;REFERENCES;301
12.8;CHAPTER B8. ANHARMONIC SPECIFIC HEAT AT INTERMEDIATE TEMPERATURES;304
12.8.1;Abstract;304
12.8.2;INTRODUCTION;304
12.8.3;ANHARMONIC DEVIATION SPECTRUM;306
12.8.4;SPECIFIC HEAT DEVIATION;307
12.8.5;ANHARMONIC OSCILLATIONS;308
12.8.6;REFERENCES;309
12.9;B9. ON THE TEMPERATURE VARIATION OF VOLUME AND COMPRESSIBILITY OF SOLIDS;310
12.9.1;Abstract;310
12.10;CHAPTER BI0. ANHARMONIC EFFECTS IN IONIC CRYSTALS;312
12.10.1;Abstract;312
12.10.2;1. INTRODUCTION;312
12.10.3;2. THE THERMAL EXPANSION;314
12.10.4;3. THE SHAPE OF INELASTIC NEUTRON SCATTERING GROUPS;315
12.10.5;4. THE DIELECTRIC PROPERTIES;316
12.10.6;Acknowledgements;320
12.10.7;REFERENCES;320
12.11;CHAPTER B11. A VARIATIONAL APPROACH TO THE ANHARMONIC LATTICE PROBLEM (WITH AN APPLICATION TO THE THEORY OF FERROELECTRIC TRANSITIONS);322
12.11.1;Abstract;322
12.11.2;1. VARIATIONAL PRINCIPLE WITH APPLICATION TO AN ANHARMONIC EINSTEIN MODEL;322
12.11.3;2. VARIATIONAL PRINCIPLE EXTENDED TO INCLUDE PHONON DAMPING;323
12.11.4;3. EVALUATION OF THE VARIATIONAL PRINCIPLE IN TERMS OF TRIAL GREEN FUNCTIONS;324
12.11.5;4. APPLICATION TO THE THEORY OF FERROELECTRIC TRANSITIONS;326
12.11.6;Acknowledgement;327
12.11.7;REFERENCES;327
12.12;DISCUSSION;328
13;PART C: OPTICAL AND DIELECTRIC EFFECTS;330
13.1;CHAPTER C1. THE INTRINSIC INFRARED AND RAMAN LATTICE VIBRATION SPECTRA OF CUBIC DIATOMIC CRYSTALS;332
13.1.1;Abstract;332
13.1.2;1. INTRODUCTION;333
13.1.3;2. INFRARED LATTICE VIBRATION ABSORPTION SPECTRA;333
13.1.4;3. RAMAN LATTICE VIBRATION SPECTRA;344
13.1.5;4. CONCLUDING REMARKS;350
13.1.6;Acknowledgements;352
13.1.7;REFERENCES;352
13.2;CHAPTER C2. SPECTRE DE RAMAN D'UN CRISTAL DE WURTZITE;354
13.2.1;Résumé;354
13.2.2;1. INTRODUCTION;354
13.2.3;2. ANALYSE DANS LE GROUPE FACTEUR;354
13.2.4;3. RESULTATS EXPERIMENTAUX;355
13.2.5;4. MODELE DYNAMIQUE;356
13.2.6;5. SUR LES CONSTANTES DE FORCE;358
13.2.7;6. CONCLUSIONS;358
13.2.8;REFERENCES;358
13.3;CHAPTER C3. REPRÉSENTATION DES PROPRIÉTÉS DYNAMIQUES DE LA GLACE PAR DES MODÉLES SIMPLES. RÔLE DE LA LIAISON HYDROGÉNE;360
13.3.1;Résumé;360
13.3.2;RÉFÉRENCES;361
13.4;CHAPTER C4. INTERACTION DU CHAMP DE RAYONNEMENT AVEC DES PHONONS SIMPLES ET MULTIPLES DANS LES STRUCTURES DU TYPE WURTZITE ET BLENDE;362
13.4.1;Résumé;362
13.5;CHAPTER C5. CRITICAL POINTS OF THE FREQUENCY SURFACES IN THE SILICON CRYSTAL;364
13.5.1;Abstract;364
13.5.2;1. INTRODUCTION;364
13.5.3;2. PHONON-PHOTON INTERACTION IN HOMOPOLAR CRYSTALS;365
13.5.4;3. CRITICAL POINTS IN THE LATTICE OF SILICON;366
13.5.5;4. EXPERIMENTAL PART;368
13.5.6;5. CONCLUSION;370
13.5.7;Acknowledgement;370
13.5.8;REFERENCES;370
13.6;CHAPTER C6. LATTICE VIBRATIONS AND INFRARED ABSORPTION OF GERMANIUM, SILICON AND DIAMOND;372
13.6.1;Abstract;372
13.6.2;1. INTRODUCTION;372
13.6.3;2. THEORY OF ABSORPTION;373
13.6.4;3. ANALYSIS OF THE INFRARED-SPECTRA OF SILICON AND GERMANIUM;375
13.6.5;4. INFRARED AND RAMAN SPECTRA OF DIAMOND AND ITS DISPERSION CURVES;381
13.6.6;5. CONCLUSION;384
13.6.7;Acknowledgments;384
13.6.8;REFERENCES;385
13.7;CHAPTER C7. THE ABSORPTION OF SUB-MILLIMETRE RADIATION BY SOLID ARGON;386
13.7.1;Abstract;386
13.7.2;1. INTRODUCTION;386
13.7.3;2. THE ELECTRIC MOMENT INDUCED BY SIMULTANEOUS DISPLACEMENT OF NEAREST NEIGHBOURS;386
13.7.4;3. THE LATTICE ABSORPTION;388
13.7.5;4. SINGULARITIES IN THE ABSORPTION SPECTRUM;390
13.7.6;5. CONCLUSION;391
13.7.7;REFERENCES;392
13.8;CHAPTER C8. LATTICE BANDS IN CALCIUM FLUORIDE;394
13.8.1;Abstract;394
13.8.2;INTRODUCTION;394
13.8.3;EXPERIMENTAL;394
13.8.4;DISCUSSION;394
13.8.5;Acknowledgements;396
13.8.6;REFERENCES;396
13.9;CHAPTER C9. SPECTRES D'ABSORPTION DE COMPOSÉS Á L'ÉTAT CRISTALLIN ET VITREUX DANS L'INFRAROUGE LOINTAIN(40-1600 MICRONS) ENTRE 4 ET 300°K;398
13.9.1;Résumé;398
13.9.2;Abstract;398
13.9.3;1. MODIFICATION DES SPECTRES D'AB SORPTIONDES COMPOSES CRISTALLINS AU VOISINAGE DE LA TEMPERATURE L'HELIUM LIQUIDE;398
13.9.4;2. CAS DE L'ETAT VITREUX;400
13.9.5;3. ESSAI
D'INTERPRÉTATION;401
13.9.6;4. APPLICATIONS;402
13.9.7;5. CRISTAUX IONIQUES ET MOLÉCULAIRES;402
13.9.8;CONCLUSIONS;403
13.9.9;RÉFÉRENCES;403
13.10;CHAPTER C10. TWO-PHONON INFRARED ABSORPTION OF NaCl STRUCTURE IONIC CRYSTALS;404
13.10.1;Abstract;404
13.10.2;EXPERIMENTAL;405
13.10.3;CHLORIDES;407
13.10.4;FLUORIDES;408
13.10.5;REFERENCES;409
13.11;CHAPTER C11. VARIATION DES FRÉQUENCES PRINCIPALES D'ÉMISSION INFRAROUGE DES CRISTAUX AVEC LA
TEMPERATURE;410
13.11.1;Résumé;410
13.11.2;INTRODUCTION;410
13.11.3;DISPOSITIF EXPÉRIMENTAL;410
13.11.4;MESURES;412
13.11.5;RÉFÉRENCES;413
13.12;CHAPTER C12. INFRARED ABSORPTION BANDS AT POLAR LONGITUDINAL OPTIC MODE FREQUENCIES IN CUBIC CRYSTAL FILMS;414
13.12.1;Abstract;414
13.12.2;INTRODUCTION;414
13.12.3;MATHEMATICS OF THE EXPERIMENT;415
13.12.4;EXPERIMENTAL METHOD;416
13.12.5;RESULTS OF THE EXPERIMENTS;417
13.12.6;Acknowledgment;419
13.12.7;REFERENCES;419
13.13;CHAPTER C13. LATTICE VIBRATIONS OF LaCl3 AND LaBr3 FROM VIBRONIC SPECTRA;420
13.13.1;Abstract;420
13.13.2;REFERENCE;420
13.14;CHAPTER C14. SECOND-ORDER DIPOLE ABSORPTION IN IONIC CRYSTALS;422
13.14.1;Abstract;422
13.14.2;1. INTRODUCTION;422
13.14.3;2. GENERAL CONSIDERATIONS BASED ON THE FORMULA FOR THE ABSORPTION COEFFICIENT;423
13.14.4;3. COMPARISON OF THE SECOND-ORDER MOMENT IN VARIOUS SOLIDS;425
13.14.5;REFERENCES;427
13.15;CHAPTER C15. ON THE INTERACTION BETWEEN CUBIC ANHARMONICITY
AND A SECOND-ORDER ELECTRIC MOMENT IN THE OPTICAL ABSORPTION OF CRYSTALS;428
13.15.1;Abstract;428
13.15.2;1. INTRODUCTION;428
13.15.3;2. ANHARMONIC COEFFICIENTS AND HIGHER ORDER ELECTRIC DIPOLE MOMENTS FOR THE SHELL MODEL;429
13.15.4;3. FORMAL EXPRESSION FOR THE ABSORPTION COEFFICIENT;430
13.15.5;4. OPTICAL ABSORPTION BY CRYSTALS WITH A SECOND-ORDER MOMENT;432
13.15.6;REFERENCES;436
13.16;CHAPTER C16. ON THEORY OF DIELECTRIC LOSSES AT SUPERHIGH FREQUENCIES IN IONIC CRYSTALS WITH NON0-IDEAL
LATTICE;438
13.16.1;Abstract;438
13.16.2;REFERENCES;442
13.17;CHAPTER C17. QUANTUM RELAXATION, THE SHAPE OF LATTICE ABSORPTION AND INELASTIC NEUTRON SCATTERING LINES;444
13.17.1;Abstract;444
13.18;CHAPTER C18. RAMAN SPECTRA OF ALKALI HALIDES;446
13.18.1;REFERENCES;447
13.19;DISCUSSION;450
14;PART D: DEFECTS AND LATTICE VIBRATIONS;452
14.1;CHAPTER D1. INFLUENCE OF DEFECTS ON LATTICE VIBRATIONS;454
14.2;CHAPTER D2. LOCALIZED MODES AT EXTENDED DEFECTS IN CRYSTALS;456
14.2.1;Abstract;456
14.2.2;1. MODEL;456
14.2.3;2. EQUATION OF MOTION AND SOLUTION;458
14.2.4;3. DISCUSSION;462
14.2.5;REFERENCES;467
14.3;CHAPTER D3. LOCALIZED VIBRATIONS AT A VACANCY IN A FACE-CENTERED CUBIC METAL;468
14.3.1;Abstract;468
14.3.2;1. INTRODUCTION;468
14.3.3;2. NEED FOR RELAXATION OF FORCES;468
14.3.4;3. MODELS FOR FACE-CENTERED CUBIC METAL;469
14.3.5;4. MOLECULAR TYPE CALCULATIONS;470
14.3.6;5. THE EFFECTIVE MODULUS APPROXIMATION;471
14.3.7;6. DISCUSSION;474
14.3.8;REFERENCES;474
14.4;CHAPTER D4. OPTICAL ABSORPTION DUE TO THE VIBRATIONS OF DEFECTS;476
14.4.1;1. INTRODUCTION;476
14.4.2;2. THEORY;476
14.4.3;3. EXEPRIMENTAL RESULTS;478
14.4.4;4. CONCLUSION;482
14.4.5;Acknowledgment;482
14.4.6;REFERENCES;482
14.5;CHAPTER D5. DEFECT AND IMPURITY VIBRATIONAL ABSORPTION IN DIAMOND, SILICON AND GERMANIUM;484
14.5.1;Abstract;484
14.5.2;1. INTRODUCTION;484
14.5.3;2. SILICON;485
14.5.4;3. DIAMOND;488
14.5.5;4. GERMANIUM;490
14.5.6;5. DISCUSSION;490
14.5.7;Acknowledgements;491
14.5.8;REFERENCES;491
14.6;CHAPTER D6. INFRARED ABSORPTION OF HYDROGEN AND DEUTERIUM IONS IN CALCIUM FLUORIDE;492
14.6.1;Abstract;492
14.6.2;REFERENCES;494
14.7;CHAPTER D7. THEORY OF OPTICAL ABSORPTION BY VIBRATION OF DEFECTS IN DIAMOND;496
14.7.1;Abstract;496
14.7.2;1. INTRODUCTION;496
14.7.3;2. MODEL;496
14.7.4;3. CALCULATIONS;498
14.7.5;4. RESULTS;499
14.7.6;REFERENCES;501
14.8;CHAPTER D8.ANHARM0NIC INTERACTION BETWEEN LOCALIZED MODES AND LATTICE MODES IN ALKALI HALIDES;502
14.8.1;Abstract;502
14.8.2;Acknowledgment;506
14.8.3;REFERENCES;506
14.9;CHAPTER D9. EFFECT OF ISOTOPIC COMPOSITION ON LATTICE VIBRATIONABSORPTION OF INFRARED RADIATION IN IONIC CRYSTALS;508
14.9.1;Abstract;508
14.9.2;EFFECT OF ISOTOPIC MASS IN ISOTOPICALLY-PURE SUBSTANCES;508
14.9.3;EFFECT OF ISOTOPIC COMPOSITION IN ISOTOPICALLY-IMPURE SUBSTANCES;509
14.9.4;THEORETICAL INTERPRETATION;509
14.9.5;REFERENCES;512
14.10;CHAPTER D10. VIBRATION OF A DIATOMIC SIMPLE CUBIC LATTICE WITH A HOLE;514
14.10.1;Abstract;514
14.10.2;1. INTRODUCTION;514
14.10.3;2. METHOD OF CALCULATIONS;514
14.10.4;3. CRITERION FOR THE APPEARANCE OF LOCALIZED MODES;516
14.10.5;4. SCATTERING OF LATTICE WAVES;519
14.10.6;REFERENCES;520
14.11;CHAPTER D11. DIRECT CALCULATION OF MODES MODIFIED BY A POINT IMPERFECTION;522
14.11.1;Abstract;522
14.11.2;1. INTRODUCTION;522
14.11.3;2. COMPARISON WITH GREEN'S
FUNCTION METHODS;523
14.11.4;3. METHODS OF CALCULATION;523
14.11.5;4. APPLICATIONS TO ALKALI HALIDES;524
14.11.6;5. APPLICATIONS TO DIAMOND;525
14.11.7;6. CONCLUSION;528
14.11.8;REFERENCES;528
14.12;CHAPTER D 12. THE DYNAMICAL BEHAVIOR OF IMPURITY ATOMS IN CRYSTALS;530
14.12.1;Abstract;530
14.13;CHAPTER D13. LOCALIZED VIBRATIONAL MODES NEAR SUBSTITUTIONAL IMPURITIES IN ALKALI HALIDE CRYSTALS: THE U-CENTER;532
14.13.1;Abstract;532
14.13.2;REFERENCES;532
14.14;CHAPTER D14. ON THE ELASTIC AND INELASTIC MÖSSBAUER EFFECT FOR IMPURITY ATOMS IN A CRYSTAL AND THE EFFECT OF SUCH ATOMS ON NEUTRON SCATTERING;534
14.14.1;Abstract;534
14.14.2;REFERENCES;538
14.15;CHAPTER D15. THE SCATTERING OF LATTICE VIBRATIONS BY VACANCY TYPE DEFECTS;540
14.15.1;Abstract;540
14.15.2;1. INTRODUCTION;540
14.15.3;2. RELATION OF DEFECTS IN LATTICES TO FIELD THEORY;541
14.15.4;3. THE FREE PHONON FIELD AND APPROXIMATIONS TO THE GREEN'S FUNCTIONS;544
14.15.5;4. PARTICLE MODELS;545
14.15.6;5. SOLUTIONS WITH INTERACTIONS PRESENT;547
14.15.7;6. DISCUSSION OF VACANCY AND F-CENTER SCATTERING: OTHER POSSIBLE APPLICATIONS;550
14.15.8;Acknowledgment;551
14.15.9;APPENDIX A;551
14.15.10;REFERENCES;552
14.16;CHAPTER D16. SURFACE EFFECTS ON LATTICE VIBRATIONS;554
14.16.1;Abstract;554
14.16.2;1. INTRODUCTION;554
14.16.3;2. CONTINUUM THEORY;554
14.16.4;3. LATTICE THEORY FOR MONATOMIC SOLIDS;557
14.16.5;4. LATTICE THEORY FOR DIATOMIC SOLIDS;560
14.16.6;5. MEAN SQUARE DISPLACEMENT AND MEAN SQUARE VELOCITY;561
14.16.7;REFERENCES;564
14.17;CHAPTER D17. EINIGE FRAGEN DER THEORIE VON SCHWINGUNGEN
IN FREMDIONEN ENTHALTENDEN IONENKRISTALLEN;566
14.17.1;Zusammenfassung;566
14.17.2;EINLEITUNG;566
14.17.3;1. LOKALSCHWINGUNGEN IN GITTERN MIT ISOTOPISCHEM EFFEKT;567
14.17.4;2. DER CHARAKTER DER ENTSTELLUNG DER KRISTALLISCHEN SCHWINGUNGEN UND IHRE AUSWIRKUNG IN DEN ELEKTRONENSCHWINGUNGSSPEKTREN;570
14.17.5;3. SCHWINGUNGSRELAXATION IN
NICH-TIDEALEM GITTER;572
14.17.6;REFERENZEN;573
14.18;CHAPTER D18. THEORY OF VIBRATIONS OF DEFECTS USING GREEN'S FUNCTIONS;576
14.18.1;Abstract;576
14.18.2;REFERENCES;576
14.19;CHAPTER D19. DYNAMICS OF DISORDERED LATTICES;578
14.19.1;Abstract;578
14.19.2;1. INTRODUCTION;578
14.19.3;2. HISTORICAL SURVEY;579
14.19.4;3. SUMMARY, AND REVIEW OF THE PRESENT POSITION;584
14.19.5;Acknowledgment;585
14.19.6;REFERENCES;586
14.19.7;NOTES ADDED
IN PROOF;586
14.20;CHAPTER D20. SOME APPLICATIONS OF THE METHOD OF TRANSFER-MATRIX TO THE VIBRATION OF LATTICES WITH FREE BOUNDARIES;588
14.20.1;Abstract;588
14.20.2;1. INTRODUCTION;588
14.20.3;2. ONE-DIMENSIONAL MONATOMIC LATTICES WITH FREE ENDS;588
14.20.4;3. TWO-DIMENSIONAL REGULAR LATTICE WITH FREE EDGES;590
14.20.5;4. TWO-DIMENSIONAL LATTICES WITH ISOTOPIC IMPURITIES ON ONE OF ITS EDGES;592
14.20.6;5. DISCUSSIONS;595
14.20.7;REFERENCES;595
14.21;DISCUSSION;596
15;PART E: ELASTICITY;598
15.1;CHAPTER El. THE RELATION BETWEEN MICROSCOPIC AND MACROSCOPIC THEORIES OF ELASTICITY;600
15.1.1;Abstract;600
15.1.2;1. INTRODUCTION;600
15.1.3;2. MACROSCOPIC STATIC CASE;602
15.1.4;3. EQUATIONS OF MOTION;602
15.1.5;4. SOUND WAVE MEASUREMENTS;604
15.1.6;5. STRAINED GIANT MOLECULES: ROTATIONAL INVARIANCE CONDITIONS;605
15.1.7;6. THE MICROSCOPIC STRAIN ENERGY;606
15.1.8;7. NONPRIMITIVE LATTICES;608
15.1.9;8. THE METHOD OF LONG WAVES;609
15.1.10;9. A ONE-DIMENSIONAL EXAMPLE;610
15.1.11;APPENDIX A;612
15.1.12;APPENDIXB;612
15.1.13;REFERENCES;613
15.2;CHAPTER E2. SURFACE EFFECTS AND INITIAL STRESS IN CONTINUUM AND LATTICE MODELS OF ELASTIC CRYSTALS;614
15.2.1;Abstract;614
15.2.2;1. INTRODUCTION;614
15.2.3;2. THE CONTINUUM MODEL;614
15.2.4;3. A SPECIAL FORM FOR THE ELASTIC ENERGY DENSITY;616
15.2.5;4. DEFORMATION OF A FREE SURFACE OF A CRYSTAL CAUSED BY INITIAL HYPERSTRESS;617
15.2.6;5. THE LATTICE MODEL;618
15.2.7;REFERENCES;622
15.3;CHAPTER E3.THE THIRD-ORDER ELASTIC MODULI OF GERMANIUM AND SILICON;624
15.3.1;Abstract;624
15.3.2;1. INTRODUCTION;624
15.3.3;2. THE SING-AROUND SYSTEM;625
15.3.4;3. MEASUREMENTS OF THE THIRD-ORDER ELASTIC MODULI OF GERMANIUM;627
15.3.5;4. MEASUREMENTS OF THE THIRD-ORDER CONSTANTS OF SILICON;628
15.3.6;5. DISCUSSION;628
15.3.7;Acknowledgements;629
15.3.8;REFERENCES;630
15.4;CHAPTER E4. APPROACHES TO PIEZOELECTRICITY AND ELASTICITY IN MIXED IONIC COVALENT COMPOUNDS;632
15.4.1;Abstract;632
15.4.2;INTRODUCTION;632
15.4.3;THEORIES: INTUITIVE;633
15.4.4;THEORIES: LATTICE DYNAMICAL (SPHALERITE);634
15.4.5;THEORIES: LATTICE DYNAMICAL (WURTZITE);637
15.4.6;THEORIES: LATTICE DYNAMICAL (DISCUSSION);638
15.4.7;THEORIES: QUANTUM MECHANICAL;638
15.4.8;REFERENCES;641
15.5;CHAPTER E5. ELASTIC PROPERTIES OF MANGANESE FLUORIDE;642
15.5.1;Abstract;642
15.6;CHAPTER E 6. GENERALIZED CONTINUUM FIELD REPRESEN-TATIONS
FOR LATTICE VIBRATIONS;644
15.6.1;Abstract;644
15.6.2;1. INTRODUCTION;644
15.6.3;2. REPRESENTATIONS OF LATTICE FIELDS;644
15.6.4;3. GENERALIZED CONTINUUM REPRESENTATION OF LATTICE DISPLACEMENT FIELDS IN THE HARMONIC APPROXIMATION;646
15.6.5;4. APPROXIMATION LEADING TO CONVENTIONAL ELASTICITY AND COUPLE STRESS THEORY;647
15.6.6;5. ATOMIC MODELS FOR TWISTING AND BENDING ENERGIES IN COUPLESTRESS ENERGY;648
15.6.7;6. AN "EFFECTIVE MODULUS" APPROXIMATION– GENERALIZATION OF THE METHOD OF LONG
WAVES;649
15.6.8;Acknowledgments;651
15.6.9;APPENDIX A;651
15.6.10;REFERENCES;651
15.7;CHAPTER E7. THE TEMPERATURE VARIATION OF THE ELASTIC CONSTANTS OF CALCITE;652
15.7.1;Abstract;652
15.8;CHAPTER E8. ETUDE DES CONSTANTES ÉLASTIQUES DE LA BLENDE ET DE LEUR VARIATION AVEC LA TEMPÉRATURE;654
15.8.1;Abstract;654
15.9;DISCUSSION;656
16;PART F: RECENT DEVELOPMENTS;658
16.1;CHAPTER Fl. THE MÖSSBAUER EFFECT AND ITS RELATION TO LATTICE DYNAMICS IN SIMPLE LATTICES;660
16.1.1;Abstract;660
16.1.2;1. INTRODUCTION;660
16.1.3;2. SIMPLE CUBIC MODEL;662
16.1.4;3. ANHARMONICITIES;665
16.1.5;4. SURFACE EFFECTS;666
16.1.6;5. EXPERIMENTAL COMPARISONS;668
16.1.7;Acknowledgements;669
16.1.8;REFERENCES;669
16.2;CHAPTER F2. EXPERIMENTAL STUDY OF LATTICE PROPERTIES WITH THE MÖSSBAUER EFFECT;670
16.2.1;Abstract;670
16.2.2;REFERENCES;670
16.3;CHAPTER F3. RESONANT PHONON-ELECTRON PROCESSES IN SUPERCONDUCTORS;672
16.3.1;Abstract;672
16.3.2;REFERENCES;672
16.4;CHAPTER F4. PHONON SPECTRA AND DENSITY OF STATES IN SUPERCONDUCTORS;674
16.4.1;Abstract;674
16.4.2;REFERENCES;674
16.5;CHAPTER F5. SOME RESULTS OF THE MANY-BODY THEORY OF INTERACTING PHONONS IN A CRYSTAL;676
16.5.1;Abstract;676
16.5.2;1. INTRODUCTION;676
16.5.3;2. THE HAMILTONIAN OF THE PHONON SYSTEM;677
16.5.4;3. CORRELATION FUNCTIONS;678
16.5.5;4. SCATTERING OF NEUTRONS;680
16.5.6;4. LATTICE THERMAL CONDUCTIVITY;683
16.5.7;Acknowledgments;684
16.5.8;REFERENCES;684
16.6;CHAPTER F6. SPACE GROUP THEORY AND LATTICE DYNAMICS;686
16.6.1;Abstract;686
16.6.2;1. INTRODUCTION;686
16.6.3;2. CONSTRUCTION OF CHARACTER TABLES;686
16.6.4;3. CRYSTAL INVARIANTS AND COVARIANTS;690
16.6.5;REFERENCES;697
16.7;CHAPTER F7. MULTIPLE PHONON NUCLEAR SPIN EXCITATION IN GaAs;698
16.7.1;Abstract;698
16.7.2;Acknowledgement;703
16.7.3;REFERENCES;704
16.7.4;NOTE ADDED IN PROOF;704
16.8;CHAPTER F8. LATTICE DYNAMICS AND SPIN-LATTICE INTERACTION IN SOLID HYDROGEN;706
16.8.1;Abstract;706
16.8.2;1. CRYSTAL STRUCTURE, LATTICE VIBRATIONAL SPECTRUM, AND STABILITY;706
16.8.3;2. INFRARED ACTIVITY OF THE LATTICE VIBRATIONS. ZERO AND MULTIPLE PHONON PROCESSES;707
16.8.4;3. COUPLING BETWEEN THE LATTICE VIBRATIONS AND THE ROTATIONAL MOTION OF THE MOLECULES;707
16.8.5;REFERENCES;709
16.9;CHAPTER F9. PHONON BROADENING OF IMPURITY SPECTRAL LINES;710
16.9.1;Abstract;710
16.9.2;REFERENCES;712
16.10;CHAPTER FI0. AUTO-CORRELATION OF FLUCTUATIONS AND SCATTERING OF RADIATION;714
16.10.1;Abstract;714
16.10.2;REFERENCES;714
16.11;CHAPTER F 11. PSEUDO-PHONONS AND THE RELAXATION SPECTRA OF CRYSTALS AND LIQUIDS;716
16.11.1;Abstract;716
16.11.2;1. INTRODUCTION;716
16.11.3;2. SCATTERING CROSS-SECTION FOR ONE-PHONON PROCESS;717
16.11.4;3. PHONON LINE WIDTH FOR ANHARMONIC DEBYE CRYSTAL;718
16.11.5;4. PHONON LINE WIDTH FOR AN IDEAL FLUID;722
16.11.6;5. SIMPLE MODEL FOR HIGH-TEMPERATURE SOLID;722
16.11.7;6. DISCUSSION AND CONCLUSIONS;724
16.11.8;Acknowledgments;725
16.11.9;REFERENCES;725
16.12;DISCUSSION;728
17;PART G: SUMMARY;732
17.1;CHAPTER G1. CONFERENCE SUMMARY: MAINLY EXPERIMENTAL;734
17.2;CHAPTER G2. CONFERENCE SUMMARY: MAINLY THEORETICAL;740
18;AUTHOR INDEX;746