The crystal lattice: phonons, solitons, dislocations, superlattices
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| Format: | Electronic eBook |
|---|---|
| Language: | English |
| Published: |
Weinheim
Wiley-VCH-Verl.
2005
|
| Edition: | 2., rev. and updated ed. |
| Subjects: | |
| Online Access: | FRO01 UBR01 Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 3527405089 9783527405084 9783527606672 |
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| adam_text | Contents
Prefaces IX
Part 1 Introduction 1
0 Geometry of Crystal Lattice 3
0.1 Translational Symmetry 3
0.2 Bravais Lattice 5
0.3 The Reciprocal Lattice 7
0.4 Use of Penetrating Radiation to Determine Crystal Structure 10
0.4.1 Problems 12
Part 2 Classical Dynamics of a Crystal Lattice 15
1 Mechanics of a One Dimensional Crystal 17
1.1 Equations of Motion and Dispersion Law 17
1.1.1 Problems 23
1.2 Motion of a Localized Excitation in a Monatomic Chain 24
1.3 Transverse Vibrations of a Linear Chain 29
1.4 Solitons of Bending Vibrations of a Linear Chain 33
1.5 Dynamics of Biatomic ID Crystals 36
1.6 Frenkel Kontorova Model and sine Gordon Equation 39
1.7 Soliton as a Particle in ID Crystals 43
1.8 Harmonic Vibrations in a ID Crystal Containing a Crowdion (Kink) 46
1.9 Motion of the Crowdion in a Discrete Chain 49
1.10 Point Defect in the 1D Crystal 51
111 Heavy Defects and ID Superlattice 54
2 General Analysis of Vibrations of Monatomic Lattices 59
2.1 Equation of Small Vibrations of 3D Lattice 59
The Crystal Lattice: Phonons, Solitons, Dislocations, Superlattices, Second Edition. Arnold M. Kosevich
Copyright © 2005 WILEY VCH Verlag GmbH Co. KGaA, Weinheim
ISBN: 3 527^0508 9
VII Contents
2.2 The Dispersion Law of Stationary Vibrations 63
2.3 Normal Modes of Vibrations 66
2.4 Analysis of the Dispersion Law 67
2.5 Spectrum of Quasi Wave Vector Values 70
2.6 Normal Coordinates of Crystal Vibrations 72
2.7 The Crystal as a Violation of Space Symmetry 74
2.8 Long Wave Approximation and Macroscopic Equations for the
Displacements Field 75
2.9 The Theory of Elasticity 77
2.10 Vibrations of a Strongly Anisotropic Crystal (Scalar Model) SO
2.11 Bending Waves in a Strongly Anisotropic Crystal S3
2.11.1 Problem 88
3 Vibrations of Polyatomic Lattices 89
3.1 Optical Vibrations 89
3.2 General Analysis of Vibrations of Polyatomic Lattice 94
3.3 Molecular Crystals 98
3.4 Two Dimensional Dipole Lattice 101
3.5 Optical Vibrations of a 2D Lattice of Bubbles 105
3.6 Long Wave Librational Vibrations of a 2D Dipole Lattice 109
3.7 Longitudinal Vibrations of 2D Electron Crystal 112
3.8 Long Wave Vibrations of an Ion Crystal 117
3.8.1 Problems 123
4 Frequency Spectrum and Its Connection with the Green Function 125
4.1 Constant Frequency Surface 125
4.2 Frequency Spectrum of Vibrations 129
4.3 Analysis of Vibrational Frequency Distribution 132
4.4 Dependence of Frequency Distribution on Crystal Dimensionality 136
4.5 Green Function for the Vibration Equation 141
4.6 Retarding and Advancing Green Functions 145
A.I Relation Between Density of States and Green Function 147
4.8 The Spectrum of Eigenfrequencies and the Green Function of a Deformed
Crystal 149
4.8.1 Problems 151
5 Acoustics of Elastic Superlattices: Phonon Crystals 153
5.1 Forbidden Areas of Frequencies and Specific Dynamic States in such
Areas 153
5.2 Acoustics of Elastic Superlattices 155
5.3 Dispersion Relation for a Simple Superlattice Model 159
5.3.1 Problem 162
Contents I VII
Part 3 Quantum Mechanics of Crystals 163
6 Quantization of Crystal Vibrations 165
6.1 Occupation Number Representation 165
6.2 Phonons 170
6.3 Quantum Mechanical Definition of the Green Function 172
6.4 Displacement Correlator and the Mean Square of Atomic
Displacement 174
6.5 Atomic Localization near the Crystal Lattice Site 776
6.6 Quantization of Elastic Deformation Field 178
7 Interaction of Excitations in a Crystal 183
1.1 Anharmonicity of Crystal Vibrations and Phonon Interaction 183
7.2 The Effective Hamiltonian for Phonon Interaction and Decay
Processes 186
7.3 Inelastic Diffraction on a Crystal and Reproduction of the Vibration
Dispersion Law 191
7.4 Effect of Thermal Atomic Motion on Elastic 7 Quantum Scattering 196
7.5 Equation of Phonon Motion in a Deformed Crystal 198
8 Quantum Crystals 203
8.1 Stability Condition of a Crystal State 203
8.2 The Ground State of Quantum Crystal 206
8.3 Equations for Small Vibrations of a Quantum Crystal 207
8.4 The Long Wave Vibration Spectrum 211
Part 4 Crystal Lattice Defects 213
9 Point Defects 215
9.1 Point Defect Models in the Crystal Lattice 215
9.2 Defects in Quantum Crystals 218
9.3 Mechanisms of Classical Diffusion and Quantum Diffusion of
Defectons 222
9.4 Quantum Crowdion Motion 225
9.5 Point Defect in Elasticity Theory 227
9.5.1 Problem 232
10 Linear Crystal Defects 233
10.1 Dislocations 233
10.2 Dislocations in Elasticity Theory 235
10.3 Glide and Climb of a Dislocation 238
10.4 Disclinations 241
10.5 Disclinations and Dislocations 244
10.5.1 Problems 246
Mill Contents
11 Localization of Vibrations 247
11.1 Localization of Vibrations near an Isolated Isotope Defect 247
11.2 Elastic Wave Scattering by Point Defects 253
11.3 Green Function for a Crystal with Point Defects 259
11.4 Influence of Defects on the Density of Vibrational States in a Crystal 264
11.5 Quasi Local Vibrations 267
11.6 Collective Excitations in a Crystal with Heavy Impurities 271
11.7 Possible Rearrangement of the Spectrum of Long Wave Crystal
Vibrations 274
11.7.1 Problems 277
12 Localization of Vibrations Near Extended Defects 279
12.1 Crystal Vibrations with ID Local Inhomogeneity 279
12.2 Quasi Local Vibrations Near a Dislocation 283
12.3 Localization of Small Vibrations in the Elastic Field of a Screw
Dislocation 285
12.4 Frequency of Local Vibrations in the Presence of a Two Dimensional
(Planar) Defect 288
13 Elastic Field of Dislocations in a Crystal 297
13.1 Equilibrium Equation for an Elastic Medium Containing Dislocations 297
13.2 Stress Field Action on Dislocation 299
13.3 Fields and the Interaction of Straight Dislocations 303
13.4 The Peierls Model 309
13.5 Dislocation Field in a Sample of Finite Dimensions 312
13.6 Long Range Order in a Dislocated Crystal 314
13.6.1 Problems 319
14 Dislocation Dynamics 321
14.1 Elastic Field of Moving Dislocations 321
14.2 Dislocations as Plasticity Carriers 325
14.3 Energy and Effective Mass of a Moving Dislocation 327
14.4 Equation for Dislocation Motion 331
14.5 Vibrations of a Lattice of Screw Dislocations 336
Bibliography 341
Index 343
|
| adam_txt |
Contents
Prefaces IX
Part 1 Introduction 1
0 Geometry of Crystal Lattice 3
0.1 Translational Symmetry 3
0.2 Bravais Lattice 5
0.3 The Reciprocal Lattice 7
0.4 Use of Penetrating Radiation to Determine Crystal Structure 10
0.4.1 Problems 12
Part 2 Classical Dynamics of a Crystal Lattice 15
1 Mechanics of a One Dimensional Crystal 17
1.1 Equations of Motion and Dispersion Law 17
1.1.1 Problems 23
1.2 Motion of a Localized Excitation in a Monatomic Chain 24
1.3 Transverse Vibrations of a Linear Chain 29
1.4 Solitons of Bending Vibrations of a Linear Chain 33
1.5 Dynamics of Biatomic ID Crystals 36
1.6 Frenkel Kontorova Model and sine Gordon Equation 39
1.7 Soliton as a Particle in ID Crystals 43
1.8 Harmonic Vibrations in a ID Crystal Containing a Crowdion (Kink) 46
1.9 Motion of the Crowdion in a Discrete Chain 49
1.10 Point Defect in the 1D Crystal 51
111 Heavy Defects and ID Superlattice 54
2 General Analysis of Vibrations of Monatomic Lattices 59
2.1 Equation of Small Vibrations of 3D Lattice 59
The Crystal Lattice: Phonons, Solitons, Dislocations, Superlattices, Second Edition. Arnold M. Kosevich
Copyright © 2005 WILEY VCH Verlag GmbH Co. KGaA, Weinheim
ISBN: 3 527^0508 9
VII Contents
2.2 The Dispersion Law of Stationary Vibrations 63
2.3 Normal Modes of Vibrations 66
2.4 Analysis of the Dispersion Law 67
2.5 Spectrum of Quasi Wave Vector Values 70
2.6 Normal Coordinates of Crystal Vibrations 72
2.7 The Crystal as a Violation of Space Symmetry 74
2.8 Long Wave Approximation and Macroscopic Equations for the
Displacements Field 75
2.9 The Theory of Elasticity 77
2.10 Vibrations of a Strongly Anisotropic Crystal (Scalar Model) SO
2.11 "Bending" Waves in a Strongly Anisotropic Crystal S3
2.11.1 Problem 88
3 Vibrations of Polyatomic Lattices 89
3.1 Optical Vibrations 89
3.2 General Analysis of Vibrations of Polyatomic Lattice 94
3.3 Molecular Crystals 98
3.4 Two Dimensional Dipole Lattice 101
3.5 Optical Vibrations of a 2D Lattice of Bubbles 105
3.6 Long Wave Librational Vibrations of a 2D Dipole Lattice 109
3.7 Longitudinal Vibrations of 2D Electron Crystal 112
3.8 Long Wave Vibrations of an Ion Crystal 117
3.8.1 Problems 123
4 Frequency Spectrum and Its Connection with the Green Function 125
4.1 Constant Frequency Surface 125
4.2 Frequency Spectrum of Vibrations 129
4.3 Analysis of Vibrational Frequency Distribution 132
4.4 Dependence of Frequency Distribution on Crystal Dimensionality 136
4.5 Green Function for the Vibration Equation 141
4.6 Retarding and Advancing Green Functions 145
A.I Relation Between Density of States and Green Function 147
4.8 The Spectrum of Eigenfrequencies and the Green Function of a Deformed
Crystal 149
4.8.1 Problems 151
5 Acoustics of Elastic Superlattices: Phonon Crystals 153
5.1 Forbidden Areas of Frequencies and Specific Dynamic States in such
Areas 153
5.2 Acoustics of Elastic Superlattices 155
5.3 Dispersion Relation for a Simple Superlattice Model 159
5.3.1 Problem 162
Contents I VII
Part 3 Quantum Mechanics of Crystals 163
6 Quantization of Crystal Vibrations 165
6.1 Occupation Number Representation 165
6.2 Phonons 170
6.3 Quantum Mechanical Definition of the Green Function 172
6.4 Displacement Correlator and the Mean Square of Atomic
Displacement 174
6.5 Atomic Localization near the Crystal Lattice Site 776
6.6 Quantization of Elastic Deformation Field 178
7 Interaction of Excitations in a Crystal 183
1.1 Anharmonicity of Crystal Vibrations and Phonon Interaction 183
7.2 The Effective Hamiltonian for Phonon Interaction and Decay
Processes 186
7.3 Inelastic Diffraction on a Crystal and Reproduction of the Vibration
Dispersion Law 191
7.4 Effect of Thermal Atomic Motion on Elastic 7 Quantum Scattering 196
7.5 Equation of Phonon Motion in a Deformed Crystal 198
8 Quantum Crystals 203
8.1 Stability Condition of a Crystal State 203
8.2 The Ground State of Quantum Crystal 206
8.3 Equations for Small Vibrations of a Quantum Crystal 207
8.4 The Long Wave Vibration Spectrum 211
Part 4 Crystal Lattice Defects 213
9 Point Defects 215
9.1 Point Defect Models in the Crystal Lattice 215
9.2 Defects in Quantum Crystals 218
9.3 Mechanisms of Classical Diffusion and Quantum Diffusion of
Defectons 222
9.4 Quantum Crowdion Motion 225
9.5 Point Defect in Elasticity Theory 227
9.5.1 Problem 232
10 Linear Crystal Defects 233
10.1 Dislocations 233
10.2 Dislocations in Elasticity Theory 235
10.3 Glide and Climb of a Dislocation 238
10.4 Disclinations 241
10.5 Disclinations and Dislocations 244
10.5.1 Problems 246
Mill Contents
11 Localization of Vibrations 247
11.1 Localization of Vibrations near an Isolated Isotope Defect 247
11.2 Elastic Wave Scattering by Point Defects 253
11.3 Green Function for a Crystal with Point Defects 259
11.4 Influence of Defects on the Density of Vibrational States in a Crystal 264
11.5 Quasi Local Vibrations 267
11.6 Collective Excitations in a Crystal with Heavy Impurities 271
11.7 Possible Rearrangement of the Spectrum of Long Wave Crystal
Vibrations 274
11.7.1 Problems 277
12 Localization of Vibrations Near Extended Defects 279
12.1 Crystal Vibrations with ID Local Inhomogeneity 279
12.2 Quasi Local Vibrations Near a Dislocation 283
12.3 Localization of Small Vibrations in the Elastic Field of a Screw
Dislocation 285
12.4 Frequency of Local Vibrations in the Presence of a Two Dimensional
(Planar) Defect 288
13 Elastic Field of Dislocations in a Crystal 297
13.1 Equilibrium Equation for an Elastic Medium Containing Dislocations 297
13.2 Stress Field Action on Dislocation 299
13.3 Fields and the Interaction of Straight Dislocations 303
13.4 The Peierls Model 309
13.5 Dislocation Field in a Sample of Finite Dimensions 312
13.6 Long Range Order in a Dislocated Crystal 314
13.6.1 Problems 319
14 Dislocation Dynamics 321
14.1 Elastic Field of Moving Dislocations 321
14.2 Dislocations as Plasticity Carriers 325
14.3 Energy and Effective Mass of a Moving Dislocation 327
14.4 Equation for Dislocation Motion 331
14.5 Vibrations of a Lattice of Screw Dislocations 336
Bibliography 341
Index 343 |
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| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2., rev. and updated ed. |
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| id | DE-604.BV022422636 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:26:13Z |
| indexdate | 2024-07-09T20:57:15Z |
| institution | BVB |
| isbn | 3527405089 9783527405084 9783527606672 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015630932 |
| oclc_num | 633736335 |
| open_access_boolean | |
| owner | DE-83 DE-355 DE-BY-UBR DE-861 |
| owner_facet | DE-83 DE-355 DE-BY-UBR DE-861 |
| physical | 1 Online-Ressource |
| psigel | ZDB-35-WIC ebook FHR_PDA_WIC UBG_PDA_WIC ZDB-35-WIC FRO_PDA_WIC |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Wiley-VCH-Verl. |
| record_format | marc |
| spelling | The crystal lattice phonons, solitons, dislocations, superlattices Arnold M. Kosevich 2., rev. and updated ed. Weinheim Wiley-VCH-Verl. 2005 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Kristallgitter (DE-588)4139853-1 gnd rswk-swf Phonon (DE-588)4129373-3 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Gitterdynamik (DE-588)4157376-6 gnd rswk-swf Gitterbaufehler (DE-588)4125030-8 gnd rswk-swf Gitterdynamik (DE-588)4157376-6 s DE-604 Kristallgitter (DE-588)4139853-1 s Phonon (DE-588)4129373-3 s Soliton (DE-588)4135213-0 s Gitterbaufehler (DE-588)4125030-8 s Kosevič, Arnolʹd Markovič 1928-2006 Sonstige (DE-588)11204512X oth https://onlinelibrary.wiley.com/doi/book/10.1002/352760667X Verlag Volltext http://www3.interscience.wiley.com/cgi-bin/homepage/?isbn=9783527606672 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015630932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The crystal lattice phonons, solitons, dislocations, superlattices Kristallgitter (DE-588)4139853-1 gnd Phonon (DE-588)4129373-3 gnd Soliton (DE-588)4135213-0 gnd Gitterdynamik (DE-588)4157376-6 gnd Gitterbaufehler (DE-588)4125030-8 gnd |
| subject_GND | (DE-588)4139853-1 (DE-588)4129373-3 (DE-588)4135213-0 (DE-588)4157376-6 (DE-588)4125030-8 |
| title | The crystal lattice phonons, solitons, dislocations, superlattices |
| title_auth | The crystal lattice phonons, solitons, dislocations, superlattices |
| title_exact_search | The crystal lattice phonons, solitons, dislocations, superlattices |
| title_exact_search_txtP | The crystal lattice phonons, solitons, dislocations, superlattices |
| title_full | The crystal lattice phonons, solitons, dislocations, superlattices Arnold M. Kosevich |
| title_fullStr | The crystal lattice phonons, solitons, dislocations, superlattices Arnold M. Kosevich |
| title_full_unstemmed | The crystal lattice phonons, solitons, dislocations, superlattices Arnold M. Kosevich |
| title_short | The crystal lattice |
| title_sort | the crystal lattice phonons solitons dislocations superlattices |
| title_sub | phonons, solitons, dislocations, superlattices |
| topic | Kristallgitter (DE-588)4139853-1 gnd Phonon (DE-588)4129373-3 gnd Soliton (DE-588)4135213-0 gnd Gitterdynamik (DE-588)4157376-6 gnd Gitterbaufehler (DE-588)4125030-8 gnd |
| topic_facet | Kristallgitter Phonon Soliton Gitterdynamik Gitterbaufehler |
| url | https://onlinelibrary.wiley.com/doi/book/10.1002/352760667X http://www3.interscience.wiley.com/cgi-bin/homepage/?isbn=9783527606672 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015630932&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kosevicarnolʹdmarkovic thecrystallatticephononssolitonsdislocationssuperlattices |