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Fundamentals Of Crystal Physics by Yu.I. Sirotin; M.P. Shaskolskaya

Over the past 15-20 years, experimental crystal physics has expanded beyond research laboratories and into practical applications in fields like quantum electronics, optics, semiconductor production, and piezotechnology. These advancements have highlighted the need for comprehensive textbooks on crystal physics. This book aims to fill that gap, offering a more detailed work to complement Nye’s 1967 textbook. It focuses on combining general physical principles with the symmetry approach characteristic of the Soviet crystal physics school founded by A.V. Shubnikov. The content is based on lectures and courses delivered at the Moscow Institute of Steel and Alloys and Moscow State University.

The book focuses on the anisotropy of crystal properties, particularly in areas such as diffusion, dielectric permittivity, magnetostriction, and piezooptical effects. It includes illustrations like representation surfaces and stereographic projections to explain the anisotropy of physical properties. The authors also provide a novel description of phase transitions with a double change of symmetry, illustrating how crystal properties change during phase transitions. The appendices include reference data, enhancing the book’s practical utility.

Translated from the Russian by Valentina Snigirevskaya.
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You can get the book here and here

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Contents

Preface to the Second Russian Edition 9
Excerpts from the Preface to the First Russian Edition 10
List of Notation 13

Chapter I. Basic Information on Crystallography 17

Crystal Structure and Space Lattice 17

Crystallographic Projections 23

Simple Finite Elements of the Symmetry of Crystals 27

Crystallographic Categories and Systems 42

Point Groups of Crystal Symmetry (Symmetry Classes) 47

Derivation and Description of 32 Classes of Crystal Symmetry (32 Point Groups of Symmetry) 55

Limit Groups of Symmetry (Curie Groups) 68

Symmetry of Crystal Structure 71

Combinations of the Symmetry Elements of Structures. Bravais Lattices. Generation of New Symmetry Elements 74

230 Space Groups of Symmetry 84

Mutual Vectors Basis and Reciprocal Lattice 88

Indexing of Directions and Planes in Crystals 92

Transformation of Indices with a Change of the System of Coordinates 101

Symmetrically Equivalent Sets of Planes and Directions. Simple Crystal Forms 114

Some Problems of Geometric Crystallography 125

Chapter II. Coordinate Systems, Vectors and Tensors 134

16. Cartesian Coordinate Systems 134
17. Orthogonal Transformations 137
18. Second-Rank Tensors 144
19. Eigenvectors and Eigenvalues of a Symmetric Second-Rank Tensors 147
20. Small Changes of a Symmetric Second-Rank Tensor 152
21. Normal and Tangential Components of a Second-Rank Symmetric Tensor 155
22. External Symmetry and Representation of Vectors and Second-Rank Symmetric Tensors 159
23. Axial Vectors 165

Chapter III. Introduction to Crystal Physics. Electrical and Thermal Properties of Crystals 174
24. Anisotropic Continuous Media 174
25. The Symmetry Principle in Crystal Physics 182
26. Fundamental Equations of Electrostatics of Crystals 188
27. Symmetry of the Dielectric Properties of Crystals 191
28. Crystals in a Uniform Electric Field 196
29. The Field in a Spherical Gap in an Anisotropic Medium 201
30. Fields of a Point Charge and a Dipole in an Anisotropic Medium 204
31. Pyroelectrics 207
32. Direct Electric Current in Crystals 210
33. Thermal Conductivity of Crystals 212

Chapter IV. Optical Properties of Crystals 216
34. Electromagnetic Waves in Transparent Crystals 216
35. Optical Indicatrix 220
36. Waves and Rays. Principle of Duality. Fresnel’s Ellipsoid 227
37. Solution of the Problem of Light Propagation in a Crystal in an Arbitrary System of Coordinates 232
38. Fresnel’s Equation. Wave and Ray Surfaces 236
39. Interconnection Between the Optical Surfaces in Crystals. Conical Refraction 240
40. Observation of the Optical Anisotropy of Crystals in Polarized Light 245

Chapter V. Symmetry of Higher-Rank Tensors 253
41. Tensors and Pseudotensors of Higher Ranks 253
42. Internal Symmetry of Tensors and Duality Relations 257
43. Non-Coordinate Notation of Tensors. Invariant Differential Operations on Tensors 263
44. External Symmetry and Representation of Tensors and Pseudotensors 266
45. Method of Direct Verification 275
46. Cyclic Coordinates. Hermann’s Theorem 281
47. Application of the Theory of Group Representation to the Problems of Tensor Symmetry 287
48. The Isotropic and Gyrotropic Tensors 301

Chapter VI. Elasticity of Crystals 308
49. Small Strains of a Continuous Medium 308
50. Stress Tensor 314
51. Generalized Hooke’s Law 319
52. Symmetry of the Elastic Properties of Crystals 324
53. Simple States of Stress 330
54. Bending and Twisting of Crystals 339
55. Temperature Stresses in Crystals 350
56. Elastic Waves in Crystals 358

Chapter VII. Thermodynamics of Crystals
57. Internal Energy and Thermodynamic Potential of a Crystal 380
58. Piezoelectric Effect and Its Symmetry 386
59. Simultaneous Solution of the Equations of the Electro- and Elastostatics of Crystals 396
60. Invariant and Non-Invariant Thermodynamic Potentials and Their Matrices 406
61. Dependence of Thermodynamic Coefficients on Conditions of Measurement 411
62. Elastic Waves in Piezoelectric Crystals 416
63. Thermodynamic Inequalities 419
64. Alterations of Crystal Symmetry in Phase Transitions of the Second Kind 423
65. Changes of the Physical Properties of Crystals Under Phase Transitions of the Second Kind 430
66. Mathematical Methods of the Theory of Phase Transitions 445

Chapter VIII. Magnetic Symmetry in Crystal Physics
67. Time Reversal and Antisymmetry 456
68. Point Groups of Magnetic Symmetry 460
69. Space Groups of Magnetic Symmetry—Shubnikov’s Groups 466
70. Magnetic Symmetry of Crystals 470
71. Geometric Realization of the Expanded Orthogonal Group 476
72. Tensors Defined on an Expanded Orthogonal Group 479
73. Piezomagnetic and Magnetoelectric Effects 485

Chapter IX. Effects of the Higher Orders
74. Thermodynamic Consideration of Non-Linear Effects 488
75. Piezoresistive Effect 491
76. Onsager Reciprocal Relations and Thermogalvanomagnetic Effects 493
77. Electrooptical and Piezooptical Effects 503
78. Artificial Optical Anisotropy of Crystals 508
79. Non-Linear Polarization in Case of Propagation of Electromagnetic Intense Waves 515
80. Generation of Light Harmonics. Directions of Synchronism 519
81. Optical Activity of Crystals 525
82. Artificial Optical Activity 540
83. Acoustic Activity of Crystals 545

Chapter X. Some General Problems of Crystal Physics
84. Extreme-Value Problems of Crystal Physics 551
85. The Problem of Comparing Tensor Properties of Crystals 535
86. The Problem of Choosing Standard Crystallographic and Crystal-Physical Systems of Coordinates 561
87. Functional Relations in Crystal Physics 556

Appendices
A. Crystallographic and Crystal-Physical Systems of Coordinates 581
B. Bravais Lattices and Crystallographic Matrices 581
C. Properties of Directions in Crystals 590
D. Analytical Proof of Theorems on the Multiplication of Symmetry Operations 597
E. Tensors Invariant with Respect to Crystallographic and Limit Groups 627
F. Contracted Notation of Tensors 627

References 637
Index 646