The Basics of Crystallography and Diffraction: Third Edition (International Lunion of Crystallography Texts on Crystallography)

Contents......Page 10
X-ray photograph of zinc blende (Friedrich, Knipping and von Laue, 1912)......Page 15
X-ray photograph of deoxyribonucleic acid (Franklin and Gosling, 1952)......Page 16
1.1 The nature of the crystalline state......Page 18
1.2 Constructing crystals from close-packed hexagonal layers of atoms......Page 22
1.3 Unit cells of the hcp and ccp structures......Page 23
1.4 Constructing crystals from square layers of atoms......Page 26
1.5 Constructing body-centred cubic crystals......Page 27
1.6 Interstitial structures......Page 28
1.7 Some simple ionic and covalent structures......Page 35
1.8 Representing crystals in projection: crystal plans......Page 36
1.9 Stacking faults and twins......Page 38
1.10 The crystal chemistry of inorganic compounds......Page 43
1.10.1 Bonding in inorganic crystals......Page 44
1.10.2 Representing crystals in terms of coordination polyhedra......Page 46
1.11.1 Perovskite (CaTiO3), barium titanate (BaTiO3) and related structures......Page 48
1.11.2 Tetrahedral and octahedral structures—silicon carbide and alumina......Page 50
1.11.3 The oxides and oxy-hydroxides of iron......Page 52
1.11.4 Silicate structures......Page 54
1.11.5 The structures of silica, ice and water......Page 60
1.11.6 The structures of carbon......Page 63
Exercises......Page 70
2.1 Approaches to the study of crystal structures......Page 72
2.2 Two-dimensional patterns and lattices......Page 73
2.3 Two-dimensional symmetry elements......Page 75
2.4 The five plane lattices......Page 78
2.5 The seventeen plane groups......Page 81
2.7 Symmetry in art and design: counterchange patterns......Page 82
2.8 Layer (two-sided) symmetry and examples in woven textiles......Page 90
2.9 Non-periodic patterns and tilings......Page 94
Exercises......Page 97
3.2 The fourteen space (Bravais) lattices......Page 101
3.3 The symmetry of the fourteen Bravais lattices: crystal systems......Page 105
3.4 The coordination or environments of Bravais lattice points: space-filling polyhedra......Page 107
Exercises......Page 112
4.1 Symmetry and crystal habit......Page 114
4.2 The thirty-two crystal classes......Page 116
4.3 Centres and inversion axes of symmetry......Page 117
4.4 Crystal symmetry and properties......Page 121
4.5 Translational symmetry elements......Page 124
4.6 Space groups......Page 128
4.7 Bravais lattices, space groups and crystal structures......Page 135
4.8 The crystal structures and space groups of organic compounds......Page 138
4.8.1 The close packing of organic molecules......Page 139
4.8.2 Long-chain polymer molecules......Page 141
4.9 Quasiperiodic crystals or crystalloids......Page 143
Exercises......Page 147
5.1 Introduction......Page 148
5.2 Indexing lattice directions—zone axis symbols......Page 149
5.3 Indexing lattice planes—Miller indices......Page 150
5.4 Miller indices and zone axis symbols in cubic crystals......Page 153
5.5 Lattice plane spacings, Miller indices and Laue indices......Page 154
5.6.2 Zone axis at the intersection of two planes......Page 156
5.6.4 The addition rule......Page 157
5.7 Indexing in the trigonal and hexagonal systems: Weber symbols and Miller-Bravais indices......Page 158
5.8 Transforming Miller indices and zone axis symbols......Page 160
5.9 Transformation matrices for trigonal crystals with rhombohedral lattices......Page 163
5.10 A simple method for inverting a 3 × 3 matrix......Page 164
Exercises......Page 166
6.2 Reciprocal lattice vectors......Page 167
6.3 Reciprocal lattice unit cells......Page 169
6.4 Reciprocal lattice cells for cubic crystals......Page 173
6.5.1 Relationships between a, b, c and a*, b*, c*......Page 175
6.5.3 The Weiss zone law or zone equation......Page 176
6.5.5 Angle Ρ between plane normals (h1k1l1) and (h2k2l2)......Page 177
6.6 Lattice planes and reciprocal lattice planes......Page 178
6.7 Summary......Page 180
Exercises......Page 181
7.1 Introduction......Page 182
7.2 Simple observations of the diffraction of light......Page 184
7.3 The nature of light: coherence, scattering and interference......Page 189
7.4 Analysis of the geometry of diffraction patterns from gratings and nets......Page 191
7.5 The resolving power of optical instruments: the telescope, camera, microscope and the eye......Page 198
Exercises......Page 207
8.1 Introduction......Page 209
8.2 Laue’s analysis of X-ray diffraction: the three Laue equations......Page 210
8.3 Bragg’s analysis of X-ray diffraction: Bragg’s law......Page 213
8.4 Ewald’s synthesis: the reflecting sphere construction......Page 215
Exercises......Page 219
9.1 Introduction......Page 220
9.2 The intensities of X-ray diffracted beams: the structure factor equation and its applications......Page 224
9.3 The broadening of diffracted beams: reciprocal lattice points and nodes......Page 232
9.3.1 The Scherrer equation: reciprocal lattice points and nodes......Page 233
9.3.3 Crystal size and perfection: mosaic structure and coherence length......Page 237
9.4 Fixed Θ, varying λ X-ray techniques: the Laue method......Page 238
9.5.1 The oscillation method......Page 240
9.5.2 The rotation method......Page 242
9.5.3 The precession method......Page 243
9.6 X-ray diffraction from single crystal thin films and multilayers......Page 246
9.7 X-ray (and neutron) diffraction from ordered crystals......Page 250
9.8 Practical considerations: X-ray sources and recording techniques......Page 254
9.8.1 The generation of X-rays in X-ray tubes......Page 255
9.8.2 Synchrotron X-ray generation......Page 256
Exercises......Page 257
10.1 Introduction......Page 260
10.2 The geometrical basis of polycrystalline (powder) X-ray diffraction techniques......Page 261
10.3.1 Accurate lattice parameter measurements......Page 269
10.3.2 Identification of unknown phases......Page 270
10.3.4 Measurement of internal elastic strains......Page 273
10.4 Preferred orientation (texture, fabric) and its measurement......Page 274
10.4.1 Fibre textures......Page 275
10.4.2 Sheet textures......Page 276
10.5 X-ray diffraction of DNA: simulation by light diffraction......Page 279
10.6 The Rietveld method for structure refinement......Page 284
Exercises......Page 286
11.1 Introduction......Page 290
11.2 The Ewald reflecting sphere construction for electron diffraction......Page 291
11.3 The analysis of electron diffraction patterns......Page 294
11.4.1 Determining orientation relationships between crystals......Page 297
11.4.2 Identification of polycrystalline materials......Page 298
11.4.3 Identification of quasiperiodic crystals......Page 299
11.5.1 Kikuchi patterns in the TEM......Page 300
11.5.2 Electron backscattered diffraction (EBSD) patterns in the SEM......Page 304
11.6 Image formation and resolution in the TEM......Page 305
Exercises......Page 309
12.1 Introduction......Page 313
12.2 Construction of the stereographic projection of a cubic crystal......Page 316
12.3 Manipulation of the stereographic projection: use of theWulff net......Page 319
12.4 Stereographic projections of non-cubic crystals......Page 322
12.5.1 Representation of point group symmetry......Page 325
12.5.2 Representation of orientation relationships......Page 327
12.5.3 Representation of preferred orientation (texture or fabric)......Page 328
Exercises......Page 331
13.1 Introduction—Fourier series and Fourier transforms......Page 332
13.2 Fourier analysis in crystallography......Page 335
13.3 Analysis of the Fraunhofer diffraction pattern from a grating......Page 340
13.4 Abbe theory of image formation......Page 345
Appendix 1 Computer programs, models and model-building in crystallography......Page 350
Appendix 2 Polyhedra in crystallography......Page 356
Appendix 3 Biographical notes on crystallographers and scientists mentioned in the text......Page 366
Appendix 4 Some useful crystallographic relationships......Page 399
Appendix 5 A simple introduction to vectors and complex numbers and their use in crystallography......Page 402
Appendix 6 Systematic absences (extinctions) in X-ray diffraction and double diffraction in electron diffraction patterns......Page 409
Answers to Exercises......Page 418
Further Reading......Page 431
B......Page 438
C......Page 439
E......Page 440
H......Page 441
K......Page 442
M......Page 443
P......Page 444
R......Page 445
S......Page 446
T......Page 447
Y......Page 448
Z......Page 449