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ОбложкаHammond C. The basics of crystallography and diffraction. - 4th ed. - Oxford; New York: Oxford university press, 2015. - xiv, 519 p.: ill., tab. - (IUCr texts on crystallography / International union of crystallography; 21). - Bibliogr.: p.497-505. - Ind.: p.507-519. - ISBN 978-0-19-873868-8
Шифр: (И/В37-Н20) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
X-ray photograph of zinc blende (Friedrich, Knipping, and
von Laue, 1912) ............................................... xvi
X-ray photograph of deoxyribonucleic acid (Franklin and
Gosling, 1952) ............................................... xvii

1  Crystals and crystal structures .............................. 1
   1.1  The nature of the crystalline state ..................... 1
   1.2  Constructing crystals from close-packed hexagonal
        layers of atoms ......................................... 5
   1.3  Unit cells of the hep and ccp structures ................ 6
   1.4  Constructing crystals from square layers of atoms ....... 9
   1.5  Constructing body-centred cubic crystals ................ 9
   1.6  Interstitial structures ................................ 11
   1.7  Some simple ionic and covalent structures .............. 18
   1.8  Representing crystals in projection: crystal plans ..... 20
   1.9  Stacking faults and twins .............................. 20
   1.10 The crystal chemistry of inorganic compounds ........... 27
        1.10.1 Bonding in inorganic crystals ................... 28
        1.10.2 Representing crystals in terms of coordination
               polyhedra ....................................... 30
   1.11 Introduction to some more complex crystal structures ... 32
        1.11.1 Perovskite (СаТiO3), barium titanate (BaТiO3)
               and related structures .......................... 32
        1.11.2 Tetrahedral and octahedral structures - silicon
               carbide and alumina ............................. 34
        1.11.3 The oxides and oxy-hydroxides of iron ........... 36
        1.11.4 Silicate structures ............................. 38
        1.11.5 The structures of silica, ice and water ......... 44
        1.11.6 The structures of carbon ........................ 48
   Exercises ................................................... 54

2  Two-dimensional patterns, lattices and symmetry ............. 56
   2.1  Approaches to the study of crystal structures .......... 56
   2.2  Two-dimensional patterns and lattices .................. 57
   2.3  Two-dimensional symmetry elements ...................... 59
   2.4  The five plane lattices ................................ 62
   2.5  The seventeen plane groups ............................. 65
   2.6  One-dimensional symmetry: border or frieze patterns .... 66
   2.7  Symmetry in art and design: counterchange patterns ..... 66
   2.8  Layer (two-sided) symmetry and examples in woven
        textiles ............................................... 74
   2.9  Non-periodic patterns and tilings ...................... 78
   Exercises ................................................... 83
3  Bravais lattices and crystal systems ........................ 86
   3.1  Introduction ........................................... 86
   3.2  The fourteen space (Bravais) lattices .................. 86
   3.3  The symmetry of the fourteen Bravais lattices:
        crystal systems ........................................ 90
   3.4  The coordination or environments of Bravais lattice
        points: space-filling polyhedra ........................ 92
   Exercises ................................................... 97
4  Crystal symmetry: point groups, space groups, symmetry-
   related properties and quasiperiodic crystals ............... 99
   4.1  Symmetry and crystal habit ............................. 99
   4.2  The thirty-two crystal classes ........................ 101
   4.3  Centres and inversion axes of symmetry ................ 102
   4.4  Crystal symmetry and properties ....................... 106
   4.5  Translational symmetry elements ....................... 110
   4.6  Space groups .......................................... 113
   4.7  Bravais lattices, space groups and crystal
        structures ............................................ 120
   4.8  The crystal structures and space groups of organic
        compounds ............................................. 123
        4.8.1  The close packing of organic molecules ......... 124
        4.8.2  Long-chain polymer molecules ................... 127
   4.9  Quasicrystals (quasiperiodic crystals or
        crystalloids) ......................................... 129
   Exercises .................................................. 134
5  Describing lattice planes and directions in crystals:
   Miller indices and zone axis symbols ....................... 135
   5.1  Introduction .......................................... 135
   5.2  Indexing lattice directions—zone axis symbols ......... 136
   5.3  Indexing lattice planes—Miller indices ................ 137
   5.4  Miller indices and zone axis symbols in cubic
        crystals .............................................. 140
   5.5  Lattice plane spacings, Miller indices and Laue
        indices ............................................... 141
   5.6  Zones, zone axes and the zone law, the addition rule .. 143
        5.6.1  The Weiss zone law or zone equation ............ 143
        5.6.2  Zone axis at the intersection of two planes .... 143
        5.6.3  Plane parallel to two directions ............... 144
        5.6.4  The addition rule .............................. 144
   5.7  Indexing in the trigonal and hexagonal systems:
        Weber symbols and Miller-Bravais indices .............. 145
   5.8  Transforming Miller indices and zone axis symbols ..... 148
   5.9  Transformation matrices for trigonal crystals with
        rhombohedral lattices ................................. 151
   5.10 A simple method for inverting a 3 × 3 matrix .......... 152
   Exercises .................................................. 153
6  The reciprocal lattice ..................................... 155
   6.1  Introduction .......................................... 155
   6.2  Reciprocal lattice vectors ............................ 155
   6.3  Reciprocal lattice unit cells ......................... 157
   6.4  Reciprocal lattice cells for cubic crystals ........... 161
   6.5  Proofs of some geometrical relationships using
        reciprocal lattice vectors ............................ 163
        6.5.1  Relationships between a, b, с and a*, b*, c* ... 163
        6.5.2  The addition rule .............................. 164
        6.5.3  The Weiss zone law or zone equation ............ 164
        6.5.4  d-spacing of lattice planes (hkl) .............. 165
        6.5.5  Angle p between plane normals (h1k1l1) and
               {h2k2l2) ........................................ 165
        6.5.6  Definition of a*, b*, с* in terms of a, b, с ... 166
        6.5.7  Zone axis at intersection of planes (h1k1l1)
               and (h2k2l2) .................................... 166
        6.5.8  A plane containing two directions [u1v1w1]
               and [U2V2W2] ................................... 166
   6.6  Lattice planes and reciprocal lattice planes .......... 166
   6.7  Summary ............................................... 169
   Exercises .................................................. 169
7  The diffraction of light ................................... 170
   7.1  Introduction .......................................... 170
   7.2  Simple observations of the diffraction of light ....... 172
   7.3  The nature of light: coherence, scattering and
        interference .......................................... 177
   7.4  Analysis of the geometry of diffraction patterns
        from gratings and nets ................................ 180
   7.5  The resolving power of optical instruments: the
        telescope, camera, microscope and the eye ............. 187
   Exercises .................................................. 197
8  X-ray diffraction: the contributions of Max von
   Laue, W.H. and W.L. Bragg and P.P. Ewald ................... 198
   8.1  Introduction .......................................... 198
   8.2  Laue's analysis of X-ray diffraction: the three Laue
        equations ............................................. 199
   8.3  Bragg's analysis of X-ray diffraction: Bragg's law .... 202
   8.4  Ewald's synthesis: the reflecting sphere
        construction .......................................... 204
   Exercises .................................................. 209
9  The diffraction of X-rays .................................. 210
   9.1  Introduction .......................................... 210
   9.2  The intensities of X-ray diffracted beams: the
        structure factor equation and its applications ........ 214
   9.3  The broadening of diffracted beams: reciprocal
        lattice points and nodes .............................. 223
        9.3.1  The Scherrer equation: reciprocal lattice
               points and nodes ............................... 223
        9.3.2  Integrated intensity and its importance ........ 227
        9.3.3  Crystal size and perfection: mosaic structure
               and coherence length ........................... 227
   9.4  Fixed θ, varying λ X-ray techniques: the Laue method .. 228
   9.5  Fixed λ, varying θ X-ray techniques: oscillation,
        rotation and precession methods ....................... 231
        9.5.1  The oscillation method ......................... 232
        9.5.2  The rotation method ............................ 234
        9.5.3  The precession method .......................... 235
   9.6  X-ray diffraction from single crystal thin films and
        multilayers ........................................... 239
   9.7  X-ray (and neutron) diffraction from ordered
        crystals .............................................. 243
   9.8  Practical considerations: X-ray sources and
        recording techniques .................................. 246
        9.8.1  The generation of X-rays in X-ray tubes ........ 247
        9.8.2  Synchrotron X-ray generation ................... 248
        9.8.3  X-ray recording techniques ..................... 249
   Exercises .................................................. 249
10 X-ray diffraction of polycrystalline materials ............. 252
   10.1 Introduction .......................................... 252
   10.2 The geometrical basis of polycrystalline (powder)
        X-ray diffraction techniques .......................... 253
        10.2.1 Intensity measurement in the X-ray
               diffractometer ................................. 258
        10.2.2 Back reflection and Debye-Scherrer powder
               techniques ..................................... 260
   10.3 Some applications of X-ray diffraction techniques in
        polycrystalline materials ............................. 262
        10.3.1 Accurate lattice parameter measurements ........ 262
        10.3.2 Identification of unknown phases ............... 263
        10.3.3 Measurement of crystal (grain) size ............ 266
        10.3.4 Measurement of internal elastic strains ........ 266
   10.4 Preferred orientation (texture, fabric) and its
        measurement ........................................... 267
        10.4.1 Fibre textures ................................. 268
        10.4.2 Sheet textures ................................. 269
   10.5 X-ray diffraction of DNA: simulation by light
        diffraction ........................................... 272
   10.6 The Rietveld method for structure refinement .......... 277
   Exercises .................................................. 280
11 Electron diffraction and its applications .................. 283
   11.1 Introduction .......................................... 283
   11.2 The Ewald reflecting sphere construction for
        electron diffraction .................................. 284
   11.3 The analysis of electron diffraction patterns ......... 288
   11.4 Applications of electron diffraction .................. 290
        11.4.1 Determining orientation relationships between
               crystals ....................................... 290
        11.4.2 Identification of polycrystalline materials .... 292
        11.4.3 Identification of quasiperiodic crystals
               (quasicrystals) ................................ 292
   11.5 Kikuchi and electron backscattered diffraction
        (EBSD) patterns ....................................... 294
        11.5.1 Kikuchi patterns in the ТЕМ .................... 294
        11.5.2 Electron backscattered diffraction (EBSD)
               patterns in the SEM ............................ 298
   11.6 Image formation and resolution in the ТЕМ ............. 300
   Exercises .................................................. 304
12 The stereographic projection and its uses .................. 308
   12.1 Introduction .......................................... 308
   12.2 Construction of the stereographic projection of
        a cubic crystal ....................................... 311
   12.3 Manipulation of the stereographic projection: use
        of the Wulff net ...................................... 314
   12.4 Stereographic projections of non-cubic crystals ....... 317
   12.5 Applications of the stereographic projection .......... 320
        12.5.1 Representation of point group symmetry ......... 320
        12.5.2 Representation of orientation relationships .... 322
        12.5.3 Representation of preferred orientation
               (texture or fabric) ............................ 323
        12.5.4 Trace analysis ................................. 325
   Exercises .................................................. 328
13 Fourier analysis in diffraction and image formation ........ 329
   13.1 Introduction—Fourier series and Fourier transforms .... 329
   13.2 Fourier analysis in crystallography ................... 332
        13.2.1  X-ray resolution of a crystal structure ....... 337
   13.3 The structural analysis of crystals and molecules ..... 338
        13.3.1 Trial and error methods ........................ 339
        13.3.2 The Patterson function: Patterson or vector
               maps ........................................... 340
        13.3.3 Interpretation of Patterson maps: heavy atom
               and isomorphous replacement techniques ......... 346
        13.3.4 Direct methods ................................. 348
        13.3.5 Charge flipping ................................ 349
   13.4 Analysis of the Fraunhofer diffraction pattern from
        a grating ............................................. 350
   13.5 Abbe theory of image formation ........................ 356
14 The physical properties of crystals and their
   description by tensors ..................................... 362
   14.1 Introduction .......................................... 362
   14.2 Second rank tensor properties ......................... 363
        14.2.1 General expression for a second rank tensor
               relating two vectors ........................... 363
        14.2.2 Simplification of second rank tensor
               equations: principal axes ...................... 366
        14.2.3 Representation of second rank tensor
               properties: the representation quadric ......... 366
   14.3 Neumann's principle ................................... 368
        14.3.1 Pyroelectricity and ferroelectricity ........... 369
   14.4 Second rank tensors that describe stress and strain ... 369
        14.4.1 The stress tensor: principal axes
               (eigenvectors) and principal values
               (eigenvalues) .................................. 369
        14.4.2 The strain tensor, Neumann's principle, and
               thermal expansion .............................. 372
        14.4.3 Atomic displacement parameters (ADPs) ..........
   14.5 The optical properties of crystals .................... 374
   14.6 Third rank tensors: piezoelectricity .................. 379
   14.7 Fourth rank tensor properties: elasticity ............. 380
Exercises ..................................................... 382
Appendix 1  Computer programs, models and model-building in
   crystallography ............................................ 385
Appendix 2  Polyhedra in crystallography ...................... 393
Appendix 3  Biographical notes on crystallographers and
   scientists mentioned in the text ........................... 403
Appendix 4  Some useful crystallographic relationships ........ 449
Appendix 5  A simple introduction to vectors and complex
   numbers and their use in crystallography ................... 452
Appendix 6  Systematic absences (extinctions) in X-ray
   diffraction and double diffraction in electron
   diffraction patterns ....................................... 459
Appendix 7  Group theory in crystallography ................... 469
Answers to exercises .......................................... 481
Further Reading ............................................... 497
Index ......................................................... 507

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