Lattice Dynamics (eBook)

Proceedings of the International Conference Held at Copenhagen, Denmark, August 5-9, 1963

R. F. Wallis (Herausgeber)

eBook Download: PDF

2013 | 1. Auflage
746 Seiten
Elsevier Science (Verlag)
978-1-4832-2341-4 (ISBN)

Infos

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.

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Lattice Dynamics covers the proceedings of the 1963 International Conference on Lattice Dynamics, held at the H.C. orsted 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.

Inhalt

Front Cover 1
Lattice Dynamics 4
Copyright Page 5
Table of Contents 10
CONFERENCE ORGANIZATION 6
FOREWORD 8
INTRODUCTORY REMARKS 16
REMINISCENCES OF MY WORK ON THE DYNAMICS OF CRYSTAL LATTICES 18
POSTSCIPT WRITTEN 
23 
THE EARLY DAYS OF LATTICE DYNAMICS 26
1. 
26 
2. SPECIFIC HEAT 27
3. THE WOLFSKEHL CONFERENCES 29
PART A: PHONON DISPERSION CURVES 32
CHAPTER A1. A STUDY OF THE CRYSTAL DYNAMICS OF ZINC 34
Abstract 34
CHAPTER A2. NORMAL VIBRATIONS IN GALLIUM ARSENIDE 36
Abstract 36
1. INTRODUCTION 36
2. EXPERIMENTAL METHODS AND RESULTS 37
3. THEORETICAL MODELS 42
4. CONCLUDING REMARKS 47
Acknowledgements 48
REFERENCES 48
CHAPTER A3. LATTICE DYNAMICS OF ZINC 50
Abstract 50
1. INTRODUCTION 50
2. CALCULATION OF PHONON DISPERSION RELATIONS IN ZINC 50
3. EXPERIMENTS 51
4. DISCUSSION 52
REFERENCES 54
CHAPTER A4. LATTICE DYNAMICS OF NIOBIUM 56
Abstract 56
1. INTRODUCTION 56
2. EXPERIMENTAL DETAILS 57
3. RESULTS 57
4. DISCUSSION 60
5. CONCLUSIONS 64
Acknowledgements 65
REFERENCES 65
CHAPTER A5. PHONON DISPERSION RELATIONS IN MAGNESIUM OXIDE 66
Abstract 66
Acknowledgements 68
REFERENCES 68
CHAPTER A6. THE FREQUENCIES OF THE NORMAL MODES OF COPPER 70
Abstract 70
1. INTRODUCTION 70
2. DESCRIPTION OF EXPERIMENT 70
3. RESULTS AND DISCUSSION 70
Acknowledgements 73
REFERENCES 73
CHAPTER A7. EXPERIMENTAL DISPERSION CURVES FOR PHONONS IN ALUMINUM 74
Abstract 74
1. INTRODUCTION 74
2. THE EXPERIMENT 75
3. RESULTS AND DISCUSSION 76
REFERENCES 78
CHAPTER 
80 
Abstract 80
1. INTRODUCTION 80
2. EQUIPMENT 81
3. EXPERIMENTAL RESULTS 81
4. DATA ANALYSIS AND DISCUSSION 83
APPENDIX 86
REFERENCES 86
CHAPTER A9. DETERMINATION OF DISPERSION CURVES OF PHONONS WITH THE AID OF DIFFUSE SCATTERING OF X-RAYS AND INELASTIC SCATTERING OF 
88 
Abstract 88
REFERENCES 88
CHAPTER A10. THE THERMAL SCATTERING OF X-RAYS IN ROCK SALT 90
Abstract 90
REFERENCE 90
CHAPTER A11. INTERPRETATION OF PHONON DISPERSION CURVES 92
Abstract 92
1. INTRODUCTION 92
2. IONIC AND COVALENT CRYSTALS 93
3. METALLIC CRYSTALS 96
Acknowledgements 100
REFERENCES 100
CHAPTER A12. THEORY OF PHONON DISPERSION IN METALS 102
Abstract 102
REFERENCES 107
NOTES ADDED IN PROOF 107
CHAPTER A13. LATTICE DYNAMICS OF LEAD 108
Abstract 108
1. INTRODUCTION 108
2. THE CHANGE OF ELECTRON DISTRIBUTION BY LATTICE VIBRATION 109
3. SELF-CONSISTENT SOLUTION FOR MONOVALENT METALS 110
4. THE CHANGE OF ELECTRON DISTRIBUTION FOR MULTIVALENT METALS 111
5. EFFECTIVE MATRIX ELEMENT FOR MULTIVALENT METALS 113
6. DISPERSION RELATION FOR MULTIVALENT METALS 114
7. DISPERSION RELATION FOR LEAD 114
Acknowledgements 116
REFERENCES 116
CHAPTER A14. STUDIES IN LATTICE DYNAMICS OF METALS USING THE 
118 
Abstract 118
1. INTRODUCTION 118
2. THEORETICAL FOUNDATION OF THE A-S MODEL 118
3. LATTICE STABILITY 120
4. CORRELATION OF ELASTIC CONSTANTS WITH VIBRATIONAL SPECTRA OF HEXAGONAL CLOSEPACKED METALS 120
5. COMPUTATION OF SPECIFIC HEAT AND DEBYE-WALLER FACTOR 123
REFERENCES 124
CHAPTER A15. LATTICE VIBRATIONS OF LaCl3 126
Abstract 126
INTRODUCTION 126
THE CRYSTAL STRUCTURE OF LaCl3 126
THE MODEL 127
INFRARED DATA 128
CALCULATIONS 129
DISCUSSION 134
REFERENCES 134
CHAPTER A16. DYNAMIQUE DES RESEAUX HEXAGONAUX COMPACTS SPECTRES DES FREQUENCES DE VIBRATION 136
Résumé 136
INTRODUCTION 136
DYNAMIQUE DU RESEAU 137
HYPOTHESE UTILISEE 138
COMPARAISON AVEC LES RESULTATS OBTENUS PAR DIFFRACTION DES RAYONS X ET DES NEUTRONS LENTS 140
SPECTRES DES FREQUENCES DE VIBRATION: CHALEURS SPECIFIQUES 141
CONCLUSION 143
BIBLIOGRAPHIE 143
CHAPTER A17. ON THE LATTICE DYNAMICS AND SPECIFIC HEAT OF THE RARE-GAS SOLIDS 146
Abstract 146
1. INTRODUCTION 146
2. SECULAR EQUATION 146
3. DEBYE T 147
4. ACCURACY 150
5. ARGON AND KRYPTON 150
Acknowledgement 151
REFERENCES 151
CHAPTER A18. LATTICE DYNAMICS OF TELLURIUM 152
Abstract 152
1. INTRODUCTION 152
2. THE MICROSCOPIC MODEL 152
3. COMPARISON OF EXPERIMENTAL AND THEORETICAL VALUES OF Cij 154
4. PREDICTED VALUES OF DYNAMICAL AND ELASTIC PROPERTIES OF Te LATTICES 155
5. CONCLUSION 157
Acknowledgement 157
REFERENCES 157
CHAPTER A19. A COMPARISON OF THE THERMODYNAMIC PROPERTIES AND SPECTRA OF THE F.C.C. AND H.C.P. LATTICES 158
Abstract 158
INTRODUCTION 158
THE LATTICE STRUCTURE 159
THE SPECTRUM 159
THE SPECIFIC HEAT DIFFERENCE 160
THE CHANGE IN THE ZERO POINT ENERGY 161
CONCLUSIONS 161
Acknowledgements 161
REFERENCES 161
CHAPTER A20. LATTICE VIBRATION OF MgO (PERICLASE) 162
Abstract 162
CHAPTER A21. THE FORCE CONSTANTS OF GERMANIUM 164
Abstract 164
1. INTRODUCTION 164
2. THE BORN-VON KÄRMÄN THEORY OF THE DIAMOND STRUCTURE 165
3. DETERMINATION OF THE FORCE CONSTANTS BY LEAST SQUARES FITTING 169
4. DETERMINATION OF THE FORCE CONSTANTS BY FOURIER ANALYSIS 171
5. CONCLUSION 173
Acknowledgements 174
REFERENCES 174
CHAPTER A22. SHELL AND EXCHANGE CHARGE MODELS OF INTERATOMIC INTERACTIONS IN SOLIDS 176
Abstract 176
1. INTRODUCTION 176
2. A SIMPLE SHELL MODEL 178
3. A GENERALIZED SHELL MODEL AND LATTICE DYNAMICS OF IONIC CRYSTALS 180
4. APPLICATIONS TO OTHER CRYSTALS 184
5. FOUNDATIONS 187
6. EXCHANGE CHARGE MODEL 188
Acknowledgements 190
REFERENCES 190
CHAPTER A23. APPLICABILITY OF THE "SHELL MODEL" TO THE LATTICE VIBRATIONS OF 
192 
Abstract 192
Acknowledgement 194
REFERENCES 194
CHAPTER A24. COMMENTS ON THE SHELL MODEL 
196 
Abstract 196
1. COMPARISON BETWEEN MODELS 196
2. THE QUADRUPOLE MODEL 196
3. RANGE OF FORCES IN THE SHELL MODEL 199
4. THE EFFECTIVE FIELD PROBLEM 201
5. ROTATIONAL INVARIANCE 201
6. DE LAUNAY'S METHOD 201
7. LATTICE VIBRATIONS IN METALS 202
REFERENCES 203
CHAPTER A25. LATTICE DYNAMICAL MODELS FOR GREY AND WHITE TIN AND THEIR RELEVANCE TO TRANSITIONS AT HIGH PRESSURE 206
Abstract 206
INTRODUCTION 206
ESTIMATION OF PHYSICAL PARAMETERS 206
RESULTS 208
Acknowledgement 209
REFERENCES 209
CHAPTER A26. ATOMIC MODEL FOR PHASE TRANSITIONS IN KH2P04 LIKE CRYSTALS 210
Abstract 210
CHAPTER A27. LATTICE DYNAMICS OF RUBIDIUM IODIDE IN RELATION TO THE NaCl-CsCl PHASE TRANSITION 212
Abstract 212
INTRODUCTION 212
THEORY 213
APPLICATION TO Rbl 215
Acknowledgements 217
REFERENCES 217
CHAPTER A28. ON THE EFFECTIVE CHARGE OF IONS AND THE DEVIATION FROM ADDITIVITY OF POLARIZABILITY AND DIAMAGNETIC SUSCEPTIBILITY OF IONIC CRYSTALS 220
Abstract 220
CHAPTER A29. APPLICATION OF A SUM RULE TO THE STUDY OF INTERATOMIC FORCES 222
Abstract 222
1. STATEMENT OF THE SUM RULE 222
2. GENERAL FORM OF TRACE 223
3. SPECIAL MODIFICATIONS FOR MONATONIC (BRAVAIS) LATTICES 225
4. APPLICATIONS 228
Acknowledgements 230
REFERENCES 230
CHAPTER A30. POLARIZATION OF ATOMIC VIBRATIONS IN CRYSTALS 232
Abstract 232
CHAPTER A31. ONDES DE LIBRATION DANS UN MODELE DE CRISTAL MOLÉCULAIRE 234
Résumé 234
CALCUL DE LA DISTRIBUTION DES FREQUENCES DE LIBRATION DANS LE CAS OU LINTERACTION EST DIPOLAIRE 236
REMARQUES 237
CONCLUSION 238
Remerciements 238
BIBLIOGRAPHIE 239
CHAPTER A 32. DISPERSION RELATIONS FOR PHONONS IN MAGNESIUM 240
Abstract 240
Acknowledgement 248
APPENDIX 248
REFERENCES 249
DISCUSSION 250
PART B: ANHARMONIC EFFECTS 252
CHAPTER B1. ANHARMONIC EFFECTS 254
Abstract 254
1. INTRODUCTION 254
2. EXPANSION OF THE POTENTIAL ENERGY 254
3. THERMODYNAMICS 256
4. DYNAMICAL EFFECTS 259
REFERENCES 261
CHAPTER B2. THERMODYNAMIC PROPERTIES AND EFFECTIVE VIBRATIONAL SPECTRA OF AN ANHARMONIC CRYSTAL 264
Abstract 264
1. INTRODUCTION 264
2. EFFECTIVE FREQUENCY SHIFTS FOR THERMODYNAMIC PROPERTIES 265
3. THE EFFECTIVE SPECTRUM AT LOW TEMPERATURES 267
4. INFLUENCE OF ANHARMONICITY UPON EQUIVALENT DEBYE TEMPERATURES 268
5. SOME SPECULATIVE REMARKS 270
REFERENCES 271
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
Abstract 272
1. INTRODUCTION 272
2. DEVIATIONS OF THE SPECIFIC HEATS OF THE ALKALI METALS FROM HARMONIC BEHAVIOUR 272
3. A POSSIBLE DEPENDENCE ON ISOTOPIC COMPOSITION OF THE ANHARMONIC CONTRIBUTION TO SPECIFIC HEAT 274
APPENDIX 277
REFERENCES 277
NOTES ADDED IN PROOF 277
CHAPTER B4. INELASTIC SCATTERING OF NEUTRONS BY ANHARMONIC CRYSTALS 278
Abstract 278
1. INTRODUCTION 278
2. GENERAL FORMULATION 280
3. ONE PHONON, MULTIPHONON AND INTERFERENCE EFFECTS 283
4. SUM RULES 284
5. CRUDE NUMERICAL ESTIMATE 286
Acknowledgements 287
REFERENCES 287
CHAPTER B5. PAPER WITHDRAWN 288
CHAPTER B6. THE PRESSURE DERIVATIVES OF ELASTIC CONSTANTS: MICROSCOPIC GRÜNEISEN PARAMETERS 290
Abstract 290
INTRODUCTION 290
SLATERS GAMMA 291
GENERAL ACOUSTIC CONTINUUM GAMMAS 292
DISCUSSION 294
GAMMAS OF DISPERSIVE MODES 296
Acknowledgements 296
REFERENCES 297
CHAPTER B7. EQUATION OF STATE AND THERMODYNAMIC FUNCTIONS OF NON-METALLIC CRYSTALS 298
Abstract 298
1. INTRODUCTION 298
2. EQUATION OF STATE OF CUBIC NON-METALS UNDER HYDROSTATIC PRESSURE 299
3. THERMAL THERMODYNAMIC FUNCTIONS 300
REFERENCES 301
CHAPTER B8. ANHARMONIC SPECIFIC HEAT AT INTERMEDIATE TEMPERATURES 304
Abstract 304
INTRODUCTION 304
ANHARMONIC DEVIATION SPECTRUM 306
SPECIFIC HEAT DEVIATION 307
ANHARMONIC OSCILLATIONS 308
REFERENCES 309
B9. ON THE TEMPERATURE VARIATION OF VOLUME AND COMPRESSIBILITY OF SOLIDS 310
Abstract 310
CHAPTER BI0. ANHARMONIC EFFECTS IN IONIC CRYSTALS 312
Abstract 312
1. INTRODUCTION 312
2. THE THERMAL EXPANSION 314
3. THE SHAPE OF INELASTIC NEUTRON SCATTERING GROUPS 315
4. THE DIELECTRIC PROPERTIES 316
Acknowledgements 320
REFERENCES 320
CHAPTER B11. A VARIATIONAL APPROACH TO THE ANHARMONIC LATTICE PROBLEM (WITH AN APPLICATION TO THE THEORY OF FERROELECTRIC TRANSITIONS) 322
Abstract 322
1. VARIATIONAL PRINCIPLE WITH APPLICATION TO AN ANHARMONIC EINSTEIN MODEL 322
2. VARIATIONAL PRINCIPLE EXTENDED TO INCLUDE PHONON DAMPING 323
3. EVALUATION OF THE VARIATIONAL PRINCIPLE IN TERMS OF TRIAL GREEN FUNCTIONS 324
4. APPLICATION TO THE THEORY OF FERROELECTRIC TRANSITIONS 326
Acknowledgement 327
REFERENCES 327
DISCUSSION 328
PART C: OPTICAL AND DIELECTRIC EFFECTS 330
CHAPTER C1. THE INTRINSIC INFRARED AND RAMAN LATTICE VIBRATION SPECTRA OF CUBIC DIATOMIC CRYSTALS 332
Abstract 332
1. INTRODUCTION 333
2. INFRARED LATTICE VIBRATION ABSORPTION SPECTRA 333
3. RAMAN LATTICE VIBRATION SPECTRA 344
4. CONCLUDING REMARKS 350
Acknowledgements 352
REFERENCES 352
CHAPTER C2. SPECTRE DE RAMAN D'UN CRISTAL DE WURTZITE 354
Résumé 354
1. INTRODUCTION 354
2. ANALYSE DANS LE GROUPE FACTEUR 354
3. RESULTATS EXPERIMENTAUX 355
4. MODELE DYNAMIQUE 356
5. SUR LES CONSTANTES DE FORCE 358
6. CONCLUSIONS 358
REFERENCES 358
CHAPTER C3. REPRÉSENTATION DES PROPRIÉTÉS DYNAMIQUES DE LA GLACE PAR DES MODÉLES SIMPLES. RÔLE DE LA LIAISON HYDROGÉNE 360
Résumé 360
RÉFÉRENCES 361
CHAPTER C4. INTERACTION DU CHAMP DE RAYONNEMENT AVEC DES PHONONS SIMPLES ET MULTIPLES DANS LES STRUCTURES DU TYPE WURTZITE ET BLENDE 362
Résumé 362
CHAPTER C5. CRITICAL POINTS OF THE FREQUENCY SURFACES IN THE SILICON CRYSTAL 364
Abstract 364
1. INTRODUCTION 364
2. PHONON-PHOTON INTERACTION IN HOMOPOLAR CRYSTALS 365
3. CRITICAL POINTS IN THE LATTICE OF SILICON 366
4. EXPERIMENTAL PART 368
5. CONCLUSION 370
Acknowledgement 370
REFERENCES 370
CHAPTER C6. LATTICE VIBRATIONS AND INFRARED ABSORPTION OF GERMANIUM, SILICON AND DIAMOND 372
Abstract 372
1. INTRODUCTION 372
2. THEORY OF ABSORPTION 373
3. ANALYSIS OF THE INFRARED-SPECTRA OF SILICON AND GERMANIUM 375
4. INFRARED AND RAMAN SPECTRA OF DIAMOND AND ITS DISPERSION CURVES 381
5. CONCLUSION 384
Acknowledgments 384
REFERENCES 385
CHAPTER C7. THE ABSORPTION OF SUB-MILLIMETRE RADIATION BY SOLID ARGON 386
Abstract 386
1. INTRODUCTION 386
2. THE ELECTRIC MOMENT INDUCED BY SIMULTANEOUS DISPLACEMENT OF NEAREST NEIGHBOURS 386
3. THE LATTICE ABSORPTION 388
4. SINGULARITIES IN THE ABSORPTION SPECTRUM 390
5. CONCLUSION 391
REFERENCES 392
CHAPTER C8. LATTICE BANDS IN CALCIUM FLUORIDE 394
Abstract 394
INTRODUCTION 394
EXPERIMENTAL 394
DISCUSSION 394
Acknowledgements 396
REFERENCES 396
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
Résumé 398
Abstract 398
1. MODIFICATION DES SPECTRES D'AB SORPTIONDES COMPOSES CRISTALLINS AU VOISINAGE DE LA TEMPERATURE L'HELIUM LIQUIDE 398
2. CAS DE L'ETAT VITREUX 400
3. ESSAI 
401 
4. APPLICATIONS 402
5. CRISTAUX IONIQUES ET MOLÉCULAIRES 402
CONCLUSIONS 403
RÉFÉRENCES 403
CHAPTER C10. TWO-PHONON INFRARED ABSORPTION OF NaCl STRUCTURE IONIC CRYSTALS 404
Abstract 404
EXPERIMENTAL 405
CHLORIDES 407
FLUORIDES 408
REFERENCES 409
CHAPTER C11. VARIATION DES FRÉQUENCES PRINCIPALES D'ÉMISSION INFRAROUGE DES CRISTAUX AVEC LA 
410 
Résumé 410
INTRODUCTION 410
DISPOSITIF EXPÉRIMENTAL 410
MESURES 412
RÉFÉRENCES 413
CHAPTER C12. INFRARED ABSORPTION BANDS AT POLAR LONGITUDINAL OPTIC MODE FREQUENCIES IN CUBIC CRYSTAL FILMS 414
Abstract 414
INTRODUCTION 414
MATHEMATICS OF THE EXPERIMENT 415
EXPERIMENTAL METHOD 416
RESULTS OF THE EXPERIMENTS 417
Acknowledgment 419
REFERENCES 419
CHAPTER C13. LATTICE VIBRATIONS OF LaCl3 AND LaBr3 FROM VIBRONIC SPECTRA 420
Abstract 420
REFERENCE 420
CHAPTER C14. SECOND-ORDER DIPOLE ABSORPTION IN IONIC CRYSTALS 422
Abstract 422
1. INTRODUCTION 422
2. GENERAL CONSIDERATIONS BASED ON THE FORMULA FOR THE ABSORPTION COEFFICIENT 423
3. COMPARISON OF THE SECOND-ORDER MOMENT IN VARIOUS SOLIDS 425
REFERENCES 427
CHAPTER C15. ON THE INTERACTION BETWEEN CUBIC ANHARMONICITY 
428 
Abstract 428
1. INTRODUCTION 428
2. ANHARMONIC COEFFICIENTS AND HIGHER ORDER ELECTRIC DIPOLE MOMENTS FOR THE SHELL MODEL 429
3. FORMAL EXPRESSION FOR THE ABSORPTION COEFFICIENT 430
4. OPTICAL ABSORPTION BY CRYSTALS WITH A SECOND-ORDER MOMENT 432
REFERENCES 436
CHAPTER C16. ON THEORY OF DIELECTRIC LOSSES AT SUPERHIGH FREQUENCIES IN IONIC CRYSTALS WITH NON0-IDEAL 
438 
Abstract 438
REFERENCES 442
CHAPTER C17. QUANTUM RELAXATION, THE SHAPE OF LATTICE ABSORPTION AND INELASTIC NEUTRON SCATTERING LINES 444
Abstract 444
CHAPTER C18. RAMAN SPECTRA OF ALKALI HALIDES 446
REFERENCES 447
DISCUSSION 450
PART D: DEFECTS AND LATTICE VIBRATIONS 452
CHAPTER D1. INFLUENCE OF DEFECTS ON LATTICE VIBRATIONS 454
CHAPTER D2. LOCALIZED MODES AT EXTENDED DEFECTS IN CRYSTALS 456
Abstract 456
1. MODEL 456
2. EQUATION OF MOTION AND SOLUTION 458
3. DISCUSSION 462
REFERENCES 467
CHAPTER D3. LOCALIZED VIBRATIONS AT A VACANCY IN A FACE-CENTERED CUBIC METAL 468
Abstract 468
1. INTRODUCTION 468
2. NEED FOR RELAXATION OF FORCES 468
3. MODELS FOR FACE-CENTERED CUBIC METAL 469
4. MOLECULAR TYPE CALCULATIONS 470
5. THE EFFECTIVE MODULUS APPROXIMATION 471
6. DISCUSSION 474
REFERENCES 474
CHAPTER D4. OPTICAL ABSORPTION DUE TO THE VIBRATIONS OF DEFECTS 476
1. INTRODUCTION 476
2. THEORY 476
3. EXEPRIMENTAL RESULTS 478
4. CONCLUSION 482
Acknowledgment 482
REFERENCES 482
CHAPTER D5. DEFECT AND IMPURITY VIBRATIONAL ABSORPTION IN DIAMOND, SILICON AND GERMANIUM 484
Abstract 484
1. INTRODUCTION 484
2. SILICON 485
3. DIAMOND 488
4. GERMANIUM 490
5. DISCUSSION 490
Acknowledgements 491
REFERENCES 491
CHAPTER D6. INFRARED ABSORPTION OF HYDROGEN AND DEUTERIUM IONS IN CALCIUM FLUORIDE 492
Abstract 492
REFERENCES 494
CHAPTER D7. THEORY OF OPTICAL ABSORPTION BY VIBRATION OF DEFECTS IN DIAMOND 496
Abstract 496
1. INTRODUCTION 496
2. MODEL 496
3. CALCULATIONS 498
4. RESULTS 499
REFERENCES 501
CHAPTER D8.ANHARM0NIC INTERACTION BETWEEN LOCALIZED MODES AND LATTICE MODES IN ALKALI HALIDES 502
Abstract 502
Acknowledgment 506
REFERENCES 506
CHAPTER D9. EFFECT OF ISOTOPIC COMPOSITION ON LATTICE VIBRATIONABSORPTION OF INFRARED RADIATION IN IONIC CRYSTALS 508
Abstract 508
EFFECT OF ISOTOPIC MASS IN ISOTOPICALLY-PURE SUBSTANCES 508
EFFECT OF ISOTOPIC COMPOSITION IN ISOTOPICALLY-IMPURE SUBSTANCES 509
THEORETICAL INTERPRETATION 509
REFERENCES 512
CHAPTER D10. VIBRATION OF A DIATOMIC SIMPLE CUBIC LATTICE WITH A HOLE 514
Abstract 514
1. INTRODUCTION 514
2. METHOD OF CALCULATIONS 514
3. CRITERION FOR THE APPEARANCE OF LOCALIZED MODES 516
4. SCATTERING OF LATTICE WAVES 519
REFERENCES 520
CHAPTER D11. DIRECT CALCULATION OF MODES MODIFIED BY A POINT IMPERFECTION 522
Abstract 522
1. INTRODUCTION 522
2. COMPARISON WITH GREEN'S 
523 
3. METHODS OF CALCULATION 523
4. APPLICATIONS TO ALKALI HALIDES 524
5. APPLICATIONS TO DIAMOND 525
6. CONCLUSION 528
REFERENCES 528
CHAPTER D 12. THE DYNAMICAL BEHAVIOR OF IMPURITY ATOMS IN CRYSTALS 530
Abstract 530
CHAPTER D13. LOCALIZED VIBRATIONAL MODES NEAR SUBSTITUTIONAL IMPURITIES IN ALKALI HALIDE CRYSTALS: THE U-CENTER 532
Abstract 532
REFERENCES 532
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
Abstract 534
REFERENCES 538
CHAPTER D15. THE SCATTERING OF LATTICE VIBRATIONS BY VACANCY TYPE DEFECTS 540
Abstract 540
1. INTRODUCTION 540
2. RELATION OF DEFECTS IN LATTICES TO FIELD THEORY 541
3. THE FREE PHONON FIELD AND APPROXIMATIONS TO THE GREEN'S FUNCTIONS 544
4. PARTICLE MODELS 545
5. SOLUTIONS WITH INTERACTIONS PRESENT 547
6. DISCUSSION OF VACANCY AND F-CENTER SCATTERING: OTHER POSSIBLE APPLICATIONS 550
Acknowledgment 551
APPENDIX A 551
REFERENCES 552
CHAPTER D16. SURFACE EFFECTS ON LATTICE VIBRATIONS 554
Abstract 554
1. INTRODUCTION 554
2. CONTINUUM THEORY 554
3. LATTICE THEORY FOR MONATOMIC SOLIDS 557
4. LATTICE THEORY FOR DIATOMIC SOLIDS 560
5. MEAN SQUARE DISPLACEMENT AND MEAN SQUARE VELOCITY 561
REFERENCES 564
CHAPTER D17. EINIGE FRAGEN DER THEORIE VON SCHWINGUNGEN 
566 
Zusammenfassung 566
EINLEITUNG 566
1. LOKALSCHWINGUNGEN IN GITTERN MIT ISOTOPISCHEM EFFEKT 567
2. DER CHARAKTER DER ENTSTELLUNG DER KRISTALLISCHEN SCHWINGUNGEN UND IHRE AUSWIRKUNG IN DEN ELEKTRONENSCHWINGUNGSSPEKTREN 570
3. SCHWINGUNGSRELAXATION IN 
572 
REFERENZEN 573
CHAPTER D18. THEORY OF VIBRATIONS OF DEFECTS USING GREEN'S FUNCTIONS 576
Abstract 576
REFERENCES 576
CHAPTER D19. DYNAMICS OF DISORDERED LATTICES 578
Abstract 578
1. INTRODUCTION 578
2. HISTORICAL SURVEY 579
3. SUMMARY, AND REVIEW OF THE PRESENT POSITION 584
Acknowledgment 585
REFERENCES 586
NOTES ADDED 
586 
CHAPTER D20. SOME APPLICATIONS OF THE METHOD OF TRANSFER-MATRIX TO THE VIBRATION OF LATTICES WITH FREE BOUNDARIES 588
Abstract 588
1. INTRODUCTION 588
2. ONE-DIMENSIONAL MONATOMIC LATTICES WITH FREE ENDS 588
3. TWO-DIMENSIONAL REGULAR LATTICE WITH FREE EDGES 590
4. TWO-DIMENSIONAL LATTICES WITH ISOTOPIC IMPURITIES ON ONE OF ITS EDGES 592
5. DISCUSSIONS 595
REFERENCES 595
DISCUSSION 596
PART E: ELASTICITY 598
CHAPTER El. THE RELATION BETWEEN MICROSCOPIC AND MACROSCOPIC THEORIES OF ELASTICITY 600
Abstract 600
1. INTRODUCTION 600
2. MACROSCOPIC STATIC CASE 602
3. EQUATIONS OF MOTION 602
4. SOUND WAVE MEASUREMENTS 604
5. STRAINED GIANT MOLECULES: ROTATIONAL INVARIANCE CONDITIONS 605
6. THE MICROSCOPIC STRAIN ENERGY 606
7. NONPRIMITIVE LATTICES 608
8. THE METHOD OF LONG WAVES 609
9. A ONE-DIMENSIONAL EXAMPLE 610
APPENDIX A 612
APPENDIXB 612
REFERENCES 613
CHAPTER E2. SURFACE EFFECTS AND INITIAL STRESS IN CONTINUUM AND LATTICE MODELS OF ELASTIC CRYSTALS 614
Abstract 614
1. INTRODUCTION 614
2. THE CONTINUUM MODEL 614
3. A SPECIAL FORM FOR THE ELASTIC ENERGY DENSITY 616
4. DEFORMATION OF A FREE SURFACE OF A CRYSTAL CAUSED BY INITIAL HYPERSTRESS 617
5. THE LATTICE MODEL 618
REFERENCES 622
CHAPTER E3.THE THIRD-ORDER ELASTIC MODULI OF GERMANIUM AND SILICON 624
Abstract 624
1. INTRODUCTION 624
2. THE SING-AROUND SYSTEM 625
3. MEASUREMENTS OF THE THIRD-ORDER ELASTIC MODULI OF GERMANIUM 627
4. MEASUREMENTS OF THE THIRD-ORDER CONSTANTS OF SILICON 628
5. DISCUSSION 628
Acknowledgements 629
REFERENCES 630
CHAPTER E4. APPROACHES TO PIEZOELECTRICITY AND ELASTICITY IN MIXED IONIC COVALENT COMPOUNDS 632
Abstract 632
INTRODUCTION 632
THEORIES: INTUITIVE 633
THEORIES: LATTICE DYNAMICAL (SPHALERITE) 634
THEORIES: LATTICE DYNAMICAL (WURTZITE) 637
THEORIES: LATTICE DYNAMICAL (DISCUSSION) 638
THEORIES: QUANTUM MECHANICAL 638
REFERENCES 641
CHAPTER E5. ELASTIC PROPERTIES OF MANGANESE FLUORIDE 642
Abstract 642
CHAPTER E 6. GENERALIZED CONTINUUM FIELD REPRESEN-TATIONS 
644 
Abstract 644
1. INTRODUCTION 644
2. REPRESENTATIONS OF LATTICE FIELDS 644
3. GENERALIZED CONTINUUM REPRESENTATION OF LATTICE DISPLACEMENT FIELDS IN THE HARMONIC APPROXIMATION 646
4. APPROXIMATION LEADING TO CONVENTIONAL ELASTICITY AND COUPLE STRESS THEORY 647
5. ATOMIC MODELS FOR TWISTING AND BENDING ENERGIES IN COUPLESTRESS ENERGY 648
6. AN "EFFECTIVE MODULUS" APPROXIMATION– GENERALIZATION OF THE METHOD OF LONG 
649 
Acknowledgments 651
APPENDIX A 651
REFERENCES 651
CHAPTER E7. THE TEMPERATURE VARIATION OF THE ELASTIC CONSTANTS OF CALCITE 652
Abstract 652
CHAPTER E8. ETUDE DES CONSTANTES ÉLASTIQUES DE LA BLENDE ET DE LEUR VARIATION AVEC LA TEMPÉRATURE 654
Abstract 654
DISCUSSION 656
PART F: RECENT DEVELOPMENTS 658
CHAPTER Fl. THE MÖSSBAUER EFFECT AND ITS RELATION TO LATTICE DYNAMICS IN SIMPLE LATTICES 660
Abstract 660
1. INTRODUCTION 660
2. SIMPLE CUBIC MODEL 662
3. ANHARMONICITIES 665
4. SURFACE EFFECTS 666
5. EXPERIMENTAL COMPARISONS 668
Acknowledgements 669
REFERENCES 669
CHAPTER F2. EXPERIMENTAL STUDY OF LATTICE PROPERTIES WITH THE MÖSSBAUER EFFECT 670
Abstract 670
REFERENCES 670
CHAPTER F3. RESONANT PHONON-ELECTRON PROCESSES IN SUPERCONDUCTORS 672
Abstract 672
REFERENCES 672
CHAPTER F4. PHONON SPECTRA AND DENSITY OF STATES IN SUPERCONDUCTORS 674
Abstract 674
REFERENCES 674
CHAPTER F5. SOME RESULTS OF THE MANY-BODY THEORY OF INTERACTING PHONONS IN A CRYSTAL 676
Abstract 676
1. INTRODUCTION 676
2. THE HAMILTONIAN OF THE PHONON SYSTEM 677
3. CORRELATION FUNCTIONS 678
4. SCATTERING OF NEUTRONS 680
4. LATTICE THERMAL CONDUCTIVITY 683
Acknowledgments 684
REFERENCES 684
CHAPTER F6. SPACE GROUP THEORY AND LATTICE DYNAMICS 686
Abstract 686
1. INTRODUCTION 686
2. CONSTRUCTION OF CHARACTER TABLES 686
3. CRYSTAL INVARIANTS AND COVARIANTS 690
REFERENCES 697
CHAPTER F7. MULTIPLE PHONON NUCLEAR SPIN EXCITATION IN GaAs 698
Abstract 698
Acknowledgement 703
REFERENCES 704
NOTE ADDED IN PROOF 704
CHAPTER F8. LATTICE DYNAMICS AND SPIN-LATTICE INTERACTION IN SOLID HYDROGEN 706
Abstract 706
1. CRYSTAL STRUCTURE, LATTICE VIBRATIONAL SPECTRUM, AND STABILITY 706
2. INFRARED ACTIVITY OF THE LATTICE VIBRATIONS. ZERO AND MULTIPLE PHONON PROCESSES 707
3. COUPLING BETWEEN THE LATTICE VIBRATIONS AND THE ROTATIONAL MOTION OF THE MOLECULES 707
REFERENCES 709
CHAPTER F9. PHONON BROADENING OF IMPURITY SPECTRAL LINES 710
Abstract 710
REFERENCES 712
CHAPTER FI0. AUTO-CORRELATION OF FLUCTUATIONS AND SCATTERING OF RADIATION 714
Abstract 714
REFERENCES 714
CHAPTER F 11. PSEUDO-PHONONS AND THE RELAXATION SPECTRA OF CRYSTALS AND LIQUIDS 716
Abstract 716
1. INTRODUCTION 716
2. SCATTERING CROSS-SECTION FOR ONE-PHONON PROCESS 717
3. PHONON LINE WIDTH FOR ANHARMONIC DEBYE CRYSTAL 718
4. PHONON LINE WIDTH FOR AN IDEAL FLUID 722
5. SIMPLE MODEL FOR HIGH-TEMPERATURE SOLID 722
6. DISCUSSION AND CONCLUSIONS 724
Acknowledgments 725
REFERENCES 725
DISCUSSION 728
PART G: SUMMARY 732
CHAPTER G1. CONFERENCE SUMMARY: MAINLY EXPERIMENTAL 734
CHAPTER G2. CONFERENCE SUMMARY: MAINLY THEORETICAL 740
AUTHOR INDEX 746

Produkt-Details

• Erscheint lt. Verlag: 3.9.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Chemie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Mineralogie / Paläontologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• ISBN-10: 1-4832-2341-8 / 1483223418
• ISBN-13: 978-1-4832-2341-4 / 9781483223414