Preface xiii
Part I Perfect Crystals 1
1 Lattice Geometry 3
1.1 The Unit Cell 3
1.2 Lattice Plane and Directions 7
1.3 The Weiss Zone Law 11
1.4 Symmetry Elements 14
1.5 Restrictions on Symmetry Elements 16
1.6 Possible Combinations of Rotational Symmetries 21
1.7 Crystal Systems 26
1.8 Space Lattices (Bravais Lattices) 26
Problems 37
Suggestions for Further Reading 40
References 41
2 Point Groups and Space Groups 43
2.1 Macroscopic Symmetry Elements 43
2.2 Orthorhombic System 49
2.3 Tetragonal System 52
2.4 Cubic System 53
2.5 Hexagonal System 56
2.6 Trigonal System 59
2.7 Monoclinic System 63
2.8 Triclinic System 65
2.9 Special Forms in the Crystal Classes 67
2.10 Enantiomorphous Crystal Classes 68
2.11 Laue Groups 69
2.12 Space Groups 69
2.13 Nomenclature for Point Groups and Space Groups 78
2.14 Groups, Subgroups and Supergroups 79
2.15 An Example of a Three-Dimensional Space Group 79
Problems 82
Suggestions for Further Reading 84
References 84
3 Crystal Structures 85
3.1 Introduction 85
3.2 Common Metallic Structures 86
3.3 Related Metallic Structures 93
3.4 Other Elements and Related Compounds 95
3.5 Simple MX and MX2 Compounds 98
3.6 Other Inorganic Compounds 104
3.7 Interatomic Distances 110
3.8 Solid Solutions 110
3.9 Polymers 113
3.10 Additional Crystal Structures and their Designation 116
Problems 119
Suggestions for Further Reading 121
References 122
4 Amorphous Materials and Special Types of Crystal–Solid Aggregate 123
4.1 Introduction 123
4.2 Amorphous Materials 123
4.3 Liquid Crystals 126
4.4 Geometry of Polyhedra 129
4.5 Icosahedral Packing 134
4.6 Quasicrystals 135
4.7 Incommensurate Structures 137
4.8 Foams, Porous Materials and Cellular Materials 137
Problems 139
Suggestions for Further Reading 139
References 140
5 Tensors 141
5.1 Nature of a tensor 141
5.2 Transformation of components of a vector 142
5.3 Dummy Suffix Notation 145
5.4 Transformation of Components of a Second-Rank Tensor 146
5.5 Definition of a Tensor of the Second Rank 148
5.6 Tensor of the Second Rank Referred to Principal Axes 149
5.7 Limitations Imposed by Crystal Symmetry for Second-Rank Tensors 153
5.8 Representation Quadric 155
5.9 Radius–Normal Property of the Representation Quadric 159
5.10 Third- and Fourth-Rank Tensors 161
Problems 161
Suggestions for Further Reading 163
References 163
6 Strain, Stress, Piezoelectricity and Elasticity 165
6.1 Strain: Introduction 165
6.2 Infinitesimal Strain 166
6.3 Stress 170
6.4 Piezoelectricity 177
6.5 Elasticity of Crystals 181
Problems 193
Suggestions for Further Reading 196
References 196
Section II Imperfect Crystals 197
7 Glide and Texture 199
7.1 Translation Glide 199
7.2 Glide Elements 203
7.3 Independent Slip Systems 208
7.4 Large Strains of Single Crystals: The Choice of Glide System 218
7.5 Large Strains: The Change in the Orientation of the Lattice During Glide 222
7.6 Texture 228
Problems 235
Suggestions for Further Reading 237
References 237
8 Dislocations 241
8.1 Introduction 241
8.2 Dislocation Motion 247
8.3 The Force on a Dislocation 249
8.4 The Distortion in a Dislocated Crystal 253
8.5 Atom Positions Close to a Dislocation 258
8.6 The Interaction of Dislocations with One Another 261
Problems 265
Suggestions for Further Reading 266
References 267
9 Dislocations in Crystals 269
9.1 The Strain Energy of a Dislocation 269
9.2 Stacking Faults and Partial Dislocations 277
9.3 Dislocations in c.c.p. Metals 280
9.4 Dislocations in the Rock Salt Structure 288
9.5 Dislocations in Hexagonal Metals 290
9.6 Dislocations in b.c.c. Crystals 295
9.7 Dislocations in Some Covalent Solids 297
9.8 Dislocations in Other Crystal Structures 301
Problems 301
Suggestions for Further Reading 303
References 303
10 Point Defects 305
10.1 Introduction 305
10.2 Point Defects in Ionic Crystals 309
10.3 Point Defect Aggregates 310
10.4 Point Defect Configurations 312
10.5 Experiments on Point Defects in Equilibrium 317
10.6 Experiments on Quenched Metals 321
10.7 Radiation Damage 324
10.8 Anelasticity and Point Defect Symmetry 326
Problems 329
Suggestions for Further Reading 331
References 331
11 Twinning 335
11.1 Introduction 335
11.2 Description of Deformation Twinning 337
11.3 Examples of Twin Structures 342
11.4 Twinning Elements 350
11.5 The Morphology of Deformation Twinning 354
Problems 358
Suggestions for Further Reading 360
References 360
12 Martensitic Transformations 363
12.1 Introduction 363
12.2 General Crystallographic Features 364
12.3 Transformation in Cobalt 366
12.4 Transformation in Zirconium 369
12.5 Transformation of Indium–Thallium Alloys 374
12.6 Transformations in Steels 379
12.7 Transformations in Copper Alloys 382
12.8 Transformations in Ni–Ti-Based Alloys 383
12.9 Transformations in Nonmetals 384
12.10 Crystallographic Aspects of Nucleation and Growth 385
Problems 387
Suggestions for Further Reading 388
References 389
13 Crystal Interfaces 391
13.1 The Structure of Surfaces and Surface Free Energy 391
13.2 Structure and Energy of Grain Boundaries 397
13.3 Interface Junctions 409
13.4 The Shapes of Crystals and Grains 414
13.5 Boundaries between Different Phases 420
13.6 Strained Layer Epitaxy of Semiconductors 424
Problems 429
Suggestions for Further Reading 431
References 431
Appendix 1 Crystallographic Calculations 435
A1.1 Vector Algebra 435
A1.2 The Reciprocal Lattice 440
A1.3 Matrices 443
A1.4 Rotation Matrices and Unit Quaternions 448
References 449
Appendix 2 The Stereographic Projection 451
A2.1 Principles 451
A2.2 Constructions 455
A2.3 Constructions with the Wulff net 460
A2.4 Proof of the Properties of the Stereographic Projection 465
References 468
Appendix 3 Planar Spacings and Interplanar Angles 469
A3.1 Planar Spacings 469
A3.2 Interplanar Angles 472
Appendix 4 Transformation of Indices Following a Change of Unit Cell 473
A4.1 Change of Indices of Directions 473
A4.2 Change of Indices of Planes 475
A4.3 Example 1: Interchange of Hexagonal and Orthorhombic Indices for Hexagonal Crystals 476
A4.4 Example 2: Interchange of Rhombohedral and Hexagonal Indices 477
Appendix 5 Slip Systems in C.C.P. and B.C.C. Crystals 481
A5.1 Independent Glide Systems in C.C.P. Metals 481
A5.2 Diehl’s Rule and the OILS Rule 483
A5.3 Proof of Diehl’s Rule and the OILS Rule 485
References 486
Appendix 6 Homogeneous Strain 487
A6.1 Simple Extension 488
A6.2 Simple Shear 488
A6.3 Pure Shear 489
A6.4 The Relationship between Pure Shear and Simple Shear 489
Appendix 7 Crystal Structure Data 491
A7.1 Crystal structures of the Elements, Interatomic Distances and Ionic radii at Room Temperature 491
A7.2 Crystals with the Sodium Chloride Structure 495
A7.3 Crystals with the Caesium Chloride Structure 496
A7.4 Crystals with the Sphalerite Structure 497
A7.5 Crystals with the Wurtzite Structure 497
A7.6 Crystals with the Nickel Arsenide Structure 497
A7.7 Crystals with the Fluorite structure 498
A7.8 Crystals with the Rutile Structure 498
Appendix 8 Further Resources 499
A8.1 Useful Web Sites 499
A8.2 Computer Software Packages 499
Brief Solutions to Selected Problems 501
Index 509