ISBN: 3-540-67474-8
TITLE: Structure of Crystals
AUTHOR: Vainshtein, Boris K.; Fridkin, Vladimir M.; Indenbom, Vladimir L.
TOC:

1. Principles of Formation of the Atomic Structure of Crystals 1
1.1 The Structure of Atoms 1
1.1.1 A Crystal as an Assembly of Atoms 1
1.1.2 Electrons in an Atom 3
1.1.3 Multielectron Atoms and the Periodic System 7
1.2 Chemical Bonding Between Atoms 15
1.2.1 Types of Chemical Bonding 15
1.2.2 Ionic Bond 18
1.2.3 Covalent Bond. Valence-Bond Method 25
1.2.4 Hybridization. Conjugation 28
1.2.5 Molecular-Orbital (MO) Method 32
1.2.6 Covalent Bond in Crystals 37
1.2.7 Electron Density in a Covalent Bond 43
1.2.8 Metallic Bond 48
1.2.9 Weak (van der Waals) Bonds 51
1.2.10 Hydrogen Bonds 53
1.2.11 Magnetic Ordering 56
1.3 Energy of the Crystal Lattice 59
1.3.1 Experimental Determination of the Crystal Energy 59
1.3.2 Calculation of the Potential Energy 60
1.3.3 Organic Structures 65
1.4 Crystallochemical Radii Systems 67
1.4.1 Interatomic Distances 67
1.4.2 Atomic Radii 67
1.4.3 Ionic Radii 71
1.4.4 The System of Atomic-Ionic Radii of a Strong Bond 80
1.4.5 System of Intermolecular Radii 83
1.4.6 Weak- and Strong-Bond Radii 85
1.5 Geometric Regularities in the Atomic Structure of Crystals 87
1.5.1 The Physical and the Geometric Model of a Crystal 87
1.5.2 Structural Units of a Crystal 87
1.5.3 Maximum-Filling Principle 88
1.5.4 Relationship Between the Symmetry of Structural Units and Crystal Symmetry 90
1.5.5 Statistics of the Occurrence of Space Groups 94
1.5.6 Coordination 95
1.5.7 Classification of Structures According to the Dimensionality of Structural Groupings 96
1.5.8 Coordination Structures 98
1.5.9 Relationship Between Coordination and Atomic Sizes 98
1.5.10 Closest Packings 100
1.5.11 Structures of Compounds Based on Close Packing of Spheres 104
1.5.12 Insular, Chain and Layer Structures 106
1.6 Solid Solutions and Isomorphism 110
1.6.1 Isostructural Crystals 110
1.6.2 Isomorphism 111
1.6.3 Substitutional Solid Solutions 111
1.6.4 Interstitial Solid Solutions 116
1.6.5 Modulated and Incommensurate Structures 120
1.6.6 Composite Ultrastructures 122
2. Principal Types of Crystal Structures 124
2.1 Crystal Structures of Elements 124
2.1.1 Principal Types of Structures of Elements 124
2.1.2 Cystallochemical Properties of Elements 132
2.2 Intermetallic Structures 134
2.2.1 Solid Solutions and Their Ordering 134
2.2.2 Electron Compounds 136
2.2.3 Intermetallic Compounds 138
2.3 Structures with Bonds of Ionic Nature 140
2.3.1 Structures of Halides, Oxides, and Salts 140
2.3.2 Silicates 144
2.3.3 Superionic Conductors 153
2.4 Covalent Structures 155
2.5 Structure of Complex and Related Compounds 161
2.5.1 Complex Compounds 161
2.5.2 Compounds with Metal Atom Clusters 165
2.5.3 Metal-Molecular Bonds (pi Complexes of Transition Metals) 167
2.5.4 Compounds of Inert Elements168
2.6 Principles of Organic Crystal Chemistry 169
2.6.1 The Structure of Organic Molecules 169
2.6.2 Symmetry of Molecules 174
2.6.3 Packing of Molecules in a Crystal 176
2.6.4 Crystals with Hydrogen Bonds 182
2.6.5 Clathrate and Molecular Compounds 185
2.7 Structure of High-Polymer Substances 187
2.7.1 Noncrystallographic Ordering 187
2.7.2 Structure of Chain Molecules of High Polymers 187
2.7.3 Structure of a Polymer Substance 192
2.7.4 Polymer Crystals 193
2.7.5 Disordering in Polymer Structures 196
2.8 Structure of Liquid Crystals 200
2.8.1 Molecule Packing in Liquid Crystals 200
2.8.2 Types of Liquid-Crystal Ordering 201
2.9 Structures of Substances of Biological Origin 210
2.9.1 Types of Biological Molecules 210
2.9.2 Principles of Protein Structure 212
2.9.3 Fibrous Proteins 220
2.9.4 Globular Proteins 222
2.9.5 Structure of Nucleic Acids 250
2.9.6 Structure of Viruses 258
3. Band Energy Structure of Crystals 271
3.1 Electron Motion in the Ideal Crystal 271
3.1.1 Schrdinger Equation and Born-Karman Boundary Conditions 271
3.1.2 Energy Spectrum of an Electron 276
3.2 Brillouin Zones 278
3.2.1 Energy Spectrum of an Electron in the Weak-Bond Approximation 278
3.2.2 Faces of Brillouin Zones and the Laue Condition 281
3.2.3 Band Boundaries and the Structure Factor 283
3.3 Isoenergetic Surfaces. Fermi Surface and Band Structure 284
3.3.1 Energy Spectrum of an Electron in the Strong-Bond Approximation 284
3.3.2 Fermi Surfaces 286
4. Lattice Dynamics and Phase Transitions 289
4.1 Atomic Vibrations in a Crystal 289
4.1.1 Vibrations of a Linear Atomic Chain 289
4.1.2 Vibration Branches 290
4.1.3 Phonons 292
4.2 Heat Capacity, Thermal Expansion, and Thermal Conductivity of Crystals 293
4.2.1 Heat Capacity 293
4.2.2 Linear Thermal Expansion 294
4.2.3 Thermal Conductivity 295
4.3 Polymorphism. Phase Transitions 296
4.3.1 Phase Transitions of the First and Second Order 298
4.3.2 Phase Transitions and the Structure 299
4.4 Atomic Vibrations and Polymorphous Transitions 302
4.5 Ordering-Type Phase Transitions 306
4.6 Phase Transitions and ElectronPhonon Interaction 309
4.6.1 Contribution of Electrons to the Free Energy of the Crystal 309
4.6.2 Interband ElectronPhonon Interaction 310
4.6.3 Photostimulated Phase Transitions 314
4.6.4 Curie Temperature and the Energy Gap Width 315
4.7 Debye's Equation of State and Grneisen's Formula 316
4.8 Phase Transitions and Crystal Symmetry 318
4.8.1 Second-Order Phase Transitions 318
4.8.2 Description of Second-Order Transitions with an Allowance for the Symmetry 321
4.8.3 Phase Transitions Without Changing the Number of Atoms in the Unit Cell of a Crystal 323
4.8.4 Changes in Crystal Properties on Phase Transitions 326
4.8.5 Properties of Twins (Domains) Forming on Phase Transformations 327
4.8.6 Stability of the Homogeneous State of the Low-Symmetry Phase 328
5. The Structure of Real Crystals 330
5.1 Classification of Crystal Lattice Defects 330
5.2 Point Defects of the Crystal Lattice 331
5.2.1 Vacancies and Interstitial Atoms 331
5.2.2 Role of Impurities, Electrons, and Holes 337
5.2.3 Effect of External Influences 339
5.3 Dislocations 341
5.3.1 Burgers Circuit and Vector 341
5.3.2 Elastic Field of Straight Dislocation 344
5.3.3 Dislocation Reactions 349
5.3.4 Polygonal Dislocations 350
5.3.5 Curved Dislocations 355
5.4 Stacking Faults and Partial Dislocations 357
5.5 Continuum Description of Dislocations 364
5.5.1 Dislocation-Density Tensor 364
5.5.2 Example: A Dislocation Row 366
5.5.3 Scalar Dislocation Density 367
5.6 Subgrain Boundaries (Mosaic Structures) in Crystals 367
5.6.1 Examples of Subgrain Boundaries: A Tilt Boundary and a Twist Boundary 367
5.6.2 The Dislocation Structure of the Subgrain Boundry in General 369
5.6.3 Subgrain Boundary Energy 372
5.6.4 Incoherent Boundaries 373
5.7 Twins 375
5.7.1 Twinning Operations 376
5.7.2 Twinning with a Change in Crystal Shape 378
5.7.3 Twinning Without a Change in Shape 382
5.8 Direct Observation of Lattice Defects 384
5.8.1 Ionic Microscopy 385
5.8.2 Electron Microscopy 385
5.8.3 X-Ray Topography 340
5.8.4 Photoelasticity Method 396
5.8.5 Selective Etching Method 347
5.8.6 Investigation of the Crystal Surface 398
6. Advances in Structural Crystallography 400
6.1 Development of Structure Analysis. Data Banks 400
6.2 Fullerenes and Fullerides 402
6.2.1 Fullerenes 402
6.2.2 C_60 Crystals 405
6.3 Crystal Chemistry of Silicates and Related Compounds 404
6.3.1 Main Features of the Silicate Structures 404
6.3.2 Insular Anionic Tetrahedron Complexes in Silicates 410
6.3.3 Anionic Tetrahedron Complexes in the Form of Rings and Chains 411
6.3.4 Framework Silicates 413
6.3.5 Theoretical Methods for the Calculation of Silicate Structures 414
6.4 Structure of Superconductors 416
6.4.1 Superconductivity 416
6.4.2 High-Temperature Superconductors (HTSCs) 419
6.4.3 Structure of MeCuO_4 High-Tc Superconductors 421
6.4.4 Atomic Structure of YBaCu Phases 422
6.4.5 Atomic Structure of Tl-Phases of High-T_c Superconductors 423
6.4.6 Specific Features of the Structure of HTSCs 428
6.5 Modular Structures, Blocks, and Fragments 429
6.5.1 The Notion of Modular Structures (MS) 429
6.5.2 Relationship Between Different Types of Modular Structures 431
6.5.3 Symbolic Notations of MS 434
6.5.4 Structure-Property Relations for MS 435
6.6 X-Ray Analysis for Studying Chemical Bonding 435
6.7 Organic Crystal Chemistry 442
6.7.1 Organic Structures 442
6.7.2 Large Organic Molecules 442
6.7.3 Secondary Bonds 445
6.8 Structure Investigation of Biomolecular Crystals 447
6.8.1 Progress in the Methods of X-Ray Macromolecular Crystallography 447
6.8.2 Investigation of Protein Structure by the Nuclear Magnetic Resonance (NMR) Method 451
6.8.3 Dynamics of Protein Molecules 453
6.8.4 Data on the Structure of Large Proteins 457
6.8.5 X-Ray Investigation of Ribosomes 462
6.8.6 Virus Structures 462
6.9 Ordering in Liquid Crystals 467
6.9.1 Smectic A Polymorphism in Liquid Crystals (LC) Containing Polar Molecules 468
6.9.2 Smectic Lamellar Crystalline Phases and Hexatics 470
6.9.3 Freely Suspended Smectic Films 472
6.9.4 Cholesteric Blue Phases 472
6.9.5 Ohter Liquid Crystalline Phases 473
6.10 Langmuir-Blodgett Films 475
6.10.1 Principles of Formation 475
6.10.2 Chemical Composition, Properties and Applications of LB Films 475
6.10.3 Structure of LB Films 477
6.10.4 Multicomponent Langmuir-Blodgett Films. Superlattices 482
6.11 Photo- and Thermostimulated Phase Transitions in Ferroelectrics 485
6.11.1 Photostimulated Phase Transitions in Ferroelectrics 485
6.11.2 Thermostimulated Phase Transitions in Ferroelectrics 490
References 493
Bibliography 509
Subject Index 515
END
