Crystallography

CRYSTALLOGRAPHY......Page 1
Title Page......Page 3
Copyright Page......Page 4
Contents......Page 6
Foreword......Page 8
Technical Remarks......Page 9
1.1 Introduction......Page 12
1.2.2 Reciprocal Coordinate System......Page 13
1.2.3 Metric Tensor......Page 16
1.2.4 Covariant and Contravariant Transformations......Page 17
1.3.1 Law of Constant Dihedral Angles......Page 18
1.3.2 The Law of Ratlonal Indices......Page 19
1.3.4 Stereographic Projection......Page 21
1.4.1 Translational Lattice......Page 22
1.4.2 Edges, Faces and Lattlce......Page 26
1.4.3 Reciprocal Latice......Page 28
1.5.1 Quasi-periodic and Aperiodic Structures......Page 29
1.5.2 Real Structures, Order and Disorder......Page 31
2.1 Introduction......Page 34
2.2.1 Affine Transformations......Page 35
2.2.2 Groups......Page 36
2.2.3 Rotation, Rotoreflection, Rotoinversion......Page 37
2.3.1 Fixed Point, Rotation Axis, Mirror Plane......Page 40
2.3.2 Glide Planes and Screw Axes......Page 43
2.4.1 Symmetry Elements Compatible with Translations......Page 47
2.4.2 Metric Imposed by the Symmetry......Page 50
2.4.3 Point Groups and Space Groups......Page 51
2.5.2 Group Generators......Page 53
2.5.3 Generation of Point Groups......Page 55
2.5.4 The 32 Crystal Classes: Axial Groups......Page 58
2.5.5 The 23 Crystal Classes: Tetrahedral and Octahedral Groups......Page 59
2.5.6 Non-Crystallographic Point Groups......Page 60
2.5.7 The 11 Laue Classes......Page 61
2.5.8 The Seven Crystal Systems......Page 67
2.5.9 International Symbols for the Point Groups......Page 69
2.5.10 Schoenflies Symbols......Page 71
2.5.11 Abstract Groups......Page 72
2.6.7 The 14 Bravais Lattices......Page 73
2.6.2 Holohedry and Merohedry......Page 78
2.7.1 The 17 Plane Groups......Page 79
2.7.2 Equivalent Positions......Page 82
2.7.3 The 230 Space Groups......Page 84
2.7.4 Examples of Some Pages from the International Tables......Page 87
2.7.5 Classification of Crystals According to Their Symmetry......Page 91
2.8 Crystal Structures......Page 95
2.9 Miller–Bravais Indices for Hexagonal Coordinate Systems......Page 97
3.1.1 X-Ray Microscope......Page 100
3.1.2 Interference of Plane Waves......Page 103
3.1.3 The Optical Grating......Page 104
3.2.1 Classical Electron According to Thompson......Page 110
3.2.2 Polarization Factor......Page 111
3.3.1 Fourier Transform, the Phase Problem......Page 113
3.3.2 Primary and Secondary Extinction......Page 115
3.3.3 Atomistic Model: The Form Factor......Page 116
3.3.4 Atomistic Model: Thermal Vibrations in a Crystal......Page 119
3.4.1 Laue Equations......Page 122
3.4.2 Bragg's Law......Page 125
3.4.3 Ewald Construction......Page 127
3.4.4 One- and Two-Dimensional Structures......Page 129
3.5.1 Laue Method......Page 131
3.5.2 Rotating Crystal Method......Page 136
3.5.3 Powder Method......Page 138
3.6.1 Production of X-Rays......Page 140
3.6.2 Monochromatization of X-Rays, Absorption......Page 144
3.6.3 Synchrotron Radiation......Page 147
3.7.1 Structure Factor......Page 148
3.7.2 Integrated Intensity, Lorentz Factor......Page 150
3.7.3 Friedel's Law......Page 152
3.8.1 Determination of the Crystal System and of The Laue Class......Page 153
3.8.2 Integral Absences, Centered Cells......Page 154
3.8.3 Zonal Absences, Glide Planes......Page 156
3.8.5 Rotations and Rotoinversions......Page 157
3.8.6 Formal Derivation of the Systematic Absences......Page 158
3.8.7 Examples......Page 159
3.9.1 Fourier Series......Page 160
3.9.2 Patterson Function......Page 161
4.1 Anisotropy And Symmetry......Page 168
4.2.1 Cause and Effect......Page 169
4.2.2 Invariance with Respect to the Choice of Coordinate System......Page 171
4.2.3 Neumann Principle......Page 173
4.2.4 Polar Vectors and Axial Vectors......Page 175
4.2.5 Tensors of Rank 2: Reference Surface......Page 176
4.3.1 Mechanical Stress Tensor......Page 181
4.3.2 Strain Tensor......Page 183
4.4.1 Electric Polarization: Tensor of Rank 2......Page 187
4.4.2 Elasticity: Tensor of Rank 4......Page 191
4.4.3 Elastic Waves in a Crystal......Page 198
4.4.4 Pyroelectricity: Tensor of Rank 1......Page 201
4.4.5 Piezoelectricity: Tensor of Rank 3......Page 202
4.4.6 General Description of Equilibrium Properties......Page 208
4.5.1 Birefringence......Page 211
4.5.2 Wave Normal and Light Ray......Page 212
4.5.3 Snell's Law......Page 215
4.5.4 Fletcher Indicatrix......Page 217
4.5.5 Optical Axes......Page 220
4.5.6 Polarizing Microscope......Page 223
5.1 Exercises Relating to Chapter 1......Page 228
5.2 Exercises Relating to Chapter 2......Page 233
5.3 Exercises Relating to Chapter 3......Page 238
5.4 Exercises Relating to Chapter 4......Page 243
Index......Page 248
Back Cover......Page 253