Vainshtein / Hargittai Crystal Symmetries

Shubnikov Centennial Papers
1. Auflage 2017
ISBN: 978-1-4832-9910-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 17, 321 Seiten, Web PDF

Reihe: International Series in Modern Applied Mathematics and Computer Science

Crystal Symmetries is a timely account of the progress in the most diverse fields of crystallography. It presents a broad overview of the theory of symmetry and contains state of the art reports of its modern directions and applications to crystal physics and crystal properties. Geometry takes a special place in this treatise. Structural aspects of phase transitions, correlation of structure and properties, polytypism, modulated structures, and other topics are discussed. Applications of important techniques, such as X-ray crystallography, biophysical studies, EPR spectroscopy, crystal optics, and nuclear solid state physics, are represented. Contains 30 research and review papers.

Autoren/Hrsg.

Vainshtein, B. K.

Hargittai, I.

Inhaltsverzeichnis

1;Front Cover;1
2;Crystal Symmetries: Shubnikov Centennial Papers;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;CHAPTER 1. A. V. SHUBNIKOV AND HIS IDEAS IN
MODERN CRYSTALLOGRAPHY;12
6.1;REFERENCES;16
7;CHAPTER
2. ON THE WORKS OF PIERRE CURIE ON SYMMETRY;18
8;CHAPTER
3. SYMMETRY OF SIMILARITY;26
8.1;HISTORICAL BACKGROUND;26
8.2;OPERATIONS IN THE SYMMETRY OF SIMILARITY;26
8.3;SIMILARITY SYMMETRY GROUPS;29
8.4;SUMMARY;31
8.5;REFERENCES;32
9;CHAPTER
4. ANTISYMMETRY OF TEXTURES ;34
9.1;REFERENCES;38
10;CHAPTER
5. SPACE AND TIME SYMMETRY;40
10.1;1. INTRODUCTION;40
10.2;2. SYMMETRY OF SCALAR AND VECTORS;40
10.3;3. THE KINETIC COEFFICIENT SYMMETRY PRINCIPLE (THE ONSAGER PRINCIPLE);41
10.4;4. GEOMETRICAL IMAGE REFLECTING SYMMETRY OF SPACE AND TIME;42
10.5;REFERENCES;45
11;CHAPTER
6. THE ROLE OF CRYSTALLOGRAPHIC SYMMETRY IN THE DIRECT METHODS OF X-RAY CRYSTALLOGRAPHY;46
11.1;1. SUMMARY;46
11.2;2. OVERVIEW;47
11.3;3. THE STRUCTURE INVARIANTS;48
11.4;4. THE STRUCTURE SEMINVARIANTS;48
11.5;5. THE ALGEBRAIC APPROACH;50
11.6;6. THE FUNDAMENTAL PRINCIPLE OF DIRECT METHODS;50
11.7;7. THE NEIGHBORHOOD PRINCIPLE;50
11.8;8. THE PROBABILISTIC APPROACH;51
11.9;9. CONCLUDING REMARKS;56
11.10;REFERENCES;57
12;CHAPTER
7. ORIGIN SPECIFICATION BY USE OF PHASES;58
12.1;1. INTRODUCTION;58
12.2;2. CENTROSYMMETRIC SPACE GROUPS;58
12.3;3. NON-CENTROSYMMETRIC SPACE GROUPS;61
12.4;4. APPLICATION;66
12.5;REFERENCES;67
13;CHAPTER
8. GENERALIZED SYMMETRY IN CRYSTAL PHYSICS;68
13.1;1. CONTRIBUTION OF A.V. SHUBNIKOV TO THE THEORY OF SYMMETRY;68
13.2;2. ORTHOGONAL-PERMUTATION SYMMETRY GROUPS IN CLASSICAL CRYSTAL PHYSICS;68
13.3;3. ANTISYMMETYU, COLOUR SYMMETRY AND THEIR MAGNETIC INTERPRETATIONS;69
13.4;4. MAGNETIC, COMPLEX AND PHASE SYMMETRY IN CRYSTAL PHYSICS AND IN STRUCTURE ANALYSIS OF CRYSTALS;72
13.5;5. SUPERSPACE SYMMETRY OF MOLECULARLY MODULATED POLYSYSTEM CRYSTALS;80
13.6;6. THE PROBLEM OF INCOMMENSURABILITY IN CRYSTAL PHYSICS;81
13.7;7. THE PROBLEM OF ICOSAHEDRIC QUASICRYSTALS [51-55];84
13.8;REFERENCES;84
14;CHAPTER
9. MATHEMATICAL PROBLEMS IN MODERN CRYSTALLOGRAPHY;86
14.1;1. INTRODUCTION;86
14.2;2. THE ASSESSMENT OF THE UNIQUENESS OF THE CRYSTAL STRUCTURE ANALYSIS;86
14.3;3. THE REGULARITY CONDITION OF A (r, R)-SYSTEM;87
14.4;4. DENSEST PACKING OF REGULAR POLYTOPES;88
14.5;5. PACKINGS OF RIGID BALLS;89
14.6;6. SUBGROUPS OF THE ORTHOGONAL GROUP O(n);89
14.7;7. DERIVATION OF SPACE GROUPS;90
14.8;8. AN UPPER BOUND FOR THE NUMBER OF FACES OF A DIRICHLET DOMAIN;91
14.9;9. CHARACTERIZATION OF Z-REDUCED QUADRATIC FORMS;92
14.10;10. CHARACTERIZATION OF THE TYPES OF MAXIMAL PARALLELOTOPES;93
14.11;11. A PROGRAM LIBRARY FOR MATHEMATICAL CRYSTALLOGRAPHY;96
14.12;REFERENCES;96
15;CHAPTER
10. FRUITFUL PARTNERSHIP COOPERATION WITH THE SHUBNIKOV INSTITUTE OF THE SOVIET ACADEMY OF SCIENCES;98
15.1;REFERENCES;101
16;CHAPTER
11. CRYSTAL SYMMETRY AND ATOMIC INTERACTIONS;104
16.1;INTRODUCTION;104
16.2;DESCRIPTION OF THE MODEL;104
16.3;ANALYSIS OF CRYSTAL STRUCTURE;107
16.4;DISCUSSION;111
16.5;REFERENCES;112
17;CHAPTER
12. SYMMETRY METHODS AND SPACE GROUP REPRESENTATIONS IN THE THEORY OF PHASE TRANSITIONS;114
17.1;1. INTRODUCTION;114
17.2;2. AGEOMETRICAL METHOD FOR OBTAINING THE LOW-SYMMETRY PHASES ARISING UPON PHASE TRANSITIONS;115
17.3;3. THERMODYNAMIC DESCRIPTION OF PHASE TRANSITIONS;116
17.4;4. THE PHASE DIAGRAMS WITH INCOMMENSURATE PHASES TAKEN INTO ACCOUNT;118
17.5;5. PHYSICAL FIELDS LOWERING THE SYMMETRY;121
17.6;6. COMPLETE CONDENSATE OF NORMAL MODES;123
17.7;REFERENCES;124
18;CHAPTER
13. SYMMETRY IN AN EQUILIBRIUM POSITION;126
18.1;REFERENCES;128
19;CHAPTER 14. ORDER–DISORDER STRUCTURES;130
19.1;1. THE NOTION OF OD STRUCTURES;130
19.2;2. BASIC IDEAS OF OD THEORY;130
19.3;3. OD STRUCTURES AND POLYTYPES;135
19.4;4. DATABASE OF OD STRUCTURES;137
19.5;5. CONCLUDING REMARKS;137
19.6;REFERENCES;137
20;CHAPTER
15. THEORY OF CRYSTAL SYMMETRY UPON THE DERIVATION OF THE 230 SPACE GROUPS;140
20.1;REFERENCES;145
21;CHAPTER
16. DEFINITION OF NIGGLI'S LATTICE CHARACTERS;148
21.1;1. INTRODUCTION;148
21.2;2. NIGGLI'S CRITERION;148
21.3;3. DEFINITION OF THE 44 CHARACTERS;149
21.4;4. NIGGLI AND THE CELL - TYPE CRITERION;150
21.5;REFERENCES;152
22;CHAPTER
17. TOWARDS A SYSTEM IN SPACE GROUP REPRESENTATIONS;154
22.1;1. INTRODUCTION;154
22.2;2. REMEMBRANCE OF THE THINGS KNOWN;154
22.3;3. CORRELATION OF REPRESENTATIONS WITH SUBGROUPS;155
22.4;4. LATTICES OF NORMAL SUBGROUPS OF IRREDUCIBLE SPACE GROUPS;156
22.5;5. REDUCIBLE SPACE GROUPS;158
22.6;6. A BRIEF REMARK ON ORIGIN CHOICES;161
22.7;7. LATTICES OF NORMAL SUBGROUPS OF LAYER AND ROD GROUPS AND THEIR RELATION TO LATTICES OF NORMAL SUBGROUPS OF SPACE GROUPS;161
22.8; 8. VIEWS FOR THE FUTURE;165
22.9;REFERENCES;165
23;CHAPTER
18. MINIMAL PRESENTATION OF CRYSTALLOGRAPHIC GROUPS BY FUNDAMENTAL POLYHEDRA;168
23.1;1. INTRODUCTION;168
23.2;2. RESULTS;169
23.3;3. DISCUSSION;180
23.4;REFERENCES;181
24;CHAPTER
19. RELATION BETWEEN MULTIDIMENSIONAL REPRESENTATIONS OF THE FEDOROV GROUPS AND THE GROUPS OF COLOR SYMMETRY;182
24.1;1. INTRODUCTION;182
24.2;2. THE GROUPS OF COLOR SYMMETRY;182
24.3;3. PHASE TRANSITIONS AND COMPLETE CONDENSATE OF THE STATIONARY VECTORS;183
24.4;4. EXAMPLES OF CONSTRUCTION OF THE COMPLETE CONDENSATE OF STATIONARY VECTORS;185
24.5;5. SUBGROUPS OF THE G-GROUP AND THE IRREDUCIBLE REPRESENTATIONS OF G;187
24.6;6. GROUPS OF THE COLOR P-SYMMETRY ASSOCIATED WITH MULTIDIMENSIONAL IR's;191
24.7;7. W-SYMMETRY GROUPS ASSOCIATED WITH MULTIDIMENSIONAL IR's;192
24.8;8. CONCLUSION;194
24.9;REFERENCES;195
25;CHAPTER
20. n-DIMENSIONAL SPACE GROUPS AND REGULAR POINT SYSTEMS;198
25.1;REFERENCES;203
26;CHAPTER
21. COLOR SYMMETRY;206
26.1;1. INTRODUCTION;206
26.2;2. COLOR GROUPS;207
26.3;3. FURTHER DEVELOPMENTS;209
26.4;4. COLORED PATTERNS;211
26.5;5. COLOR SYMMETRY AND SYMMETRY THEORY;213
26.6;REFERENCES;214
27;CHAPTER
22. GENERALIZED ANTISYMMETRY;216
27.1;SECTION 1;216
27.2;SECTION 2;216
27.3;SECTION 3;217
27.4;SECTION 4;220
27.5;SECTION 5;221
27.6;SECTION 6;222
27.7;REFERENCES;222
28;CHAPTER
23. FUNDAMENTAL LAW OF CRYSTAL CHEMISTRY BY SHUBNIKOV, ITS APPLICATIONS AND RESTRICTIONS;224
28.1;REFERENCES;227
29;CHAPTER
24. POLYTYPISM OF CRYSTAL STRUCTURES;230
29.1;1 INTRODUCTION;230
29.2;2. THE NOTION OF POLYTYPISM AND THE POSITION OF POLYTYPES IN THE STRUCTURAL SYSTEMATICS OF CRYSTALLINE SUBSTANCES;230
29.3;3. POLYTYPE STRUCTURES;233
29.4;4. POLYTYPE SYMBOLIC NOTATIONS;245
29.5;5. THE SCIENTIFIC SIGNIFICANCE OF CRYSTAL STRUCTURE POLYTYPISM;249
29.6;REFERENCES;250
30;CHAPTER
25. THE LAW OF CORRELATION OF SYMMETRY AND STATISTICS IN THE MINERAL WORLD;254
30.1;REFERENCES;257
31;CHAPTER
26. APPLICATION OF ELLIPTIC RIEMANNIAN GEOMETRY TO PROBLEMS OF CRYSTALLOGRAPHY;258
31.1;REFERENCES;277
32;CHAPTER
27. SYMMETRY AND STRUCTURE OF BACTERIOPHAGE T7;278
32.1;INTRODUCTION;278
32.2;GENERAL GEOMETRIC AND WEIGHT PARAMETERS;279
32.3;STRUCTURE ORGANIZATION OF DNA;281
32.4;DIRECT RESTORATION OF THE PHAGE STRUCTURE;284
32.5;TEMPERATURE TRANSITIONS IN PHAGE T7;285
32.6;INFLUENCE OF THE IONIC STRENGTH;286
32.7;CONCLUSION;288
32.8;REFERENCES;288
33;CHAPTER
28. INVARIANCE AND THE UNCERTAINTY PRINCIPLE IN EPR SPECTROSCOPY OF CRYSTALS AND LIQUIDS;290
33.1;INTRODUCTION;290
33.2;SPIN HAMILTONIAN FORMALISM;290
33.3;MOLECULAR MOTIONS;291
33.4;EPR TIME-SCALE;291
33.5;MAGNETIC RELAXATION;292
33.6;SPIN HAMILTONIAN INVARIANTS IN SINGLE CRYSTALS;293
33.7;SPIN HAMILTONIAN INVARIANTS IN ISOTROPIC LIQUIDS;294
33.8;INVARIANCE RELATIONS BETWEEN CRYSTALS AND LIQUIDS;295
33.9;CONCLUSIONS;296
33.10;REFERENCES;296
34;CHAPTER
29. CRYSTAL OPTICS OF ABSORBING AND GYROTROPIC MEDIA;298
34.1;1. INTRODUCTION;298
34.2;2. PROPER WAVES IN CRYSTALS;298
34.3;3. BOUNDARY PROBLEMS IN CRYSTAL OPTICS;302
34.4;4. THE DETERMINATION OF OPTICAL PARAMETERS OF CRYSTALS;307
34.5;5. CONCLUSION;314
34.6;REFERENCES;314
35;CHAPTER
30. SYMMETRY IN THE NUCLEAR SOLID STATE PHYSICS;318
35.1;REFERENCES;321
36;CHAPTER
31. SYMMETRIES IN MOSCOW AND LENINGRAD;324
36.1;REFERENCES;330