The basics of crystallography and diffraction / Christopher Hammond.

Format:

Book

Author/Creator:

Hammond, C. (Christopher), 1942-

Series:

International Union of Crystallography texts on crystallography ; 5.

International Union of Crystallography texts on crystallography ; 5

Language:

English

Subjects (All):

Crystallography.

X-ray crystallography.

Physical Description:

xiii, 331 pages : illustrations ; 25 cm.

Edition:

Second edition.

Place of Publication:

New York : Oxford University Press, 2001.

Summary:

This is a clear and comprehensive introduction to the topics of crystallography and diffraction for undergraduate and beginning graduate students and lecturers in physics, chemistry, materials, and earth sciences. It shows how crystal structures may be built up from simple ideas of atomic packing and co-ordination, and develops the concepts of crystal symmetry, point and space groups by way of two-dimensional examples of patterns and tilings. The concept of the reciprocal lattice is explained in simple terms and its importance in an understanding o light, x-ray and electron diffraction. Finally, the book covers practical examples of the applications of these techniques and describes the importance of diffraction in the performance of optical instruments.

Contents:

X-ray photograph of zinc blende (Friedrich, Knipping and von Laue, 1912) xiv

X-ray photograph of deoxyribonucleic acid (Franklin and Gosling, 1952) xv

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 hcp 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 10

1.7 Some simple ionic and covalent structures 18

1.8 Representing crystals in projection: crystal plans 18

1.9 Stacking faults and twins 20

1.10 Introduction to some more complex crystal structures 26

1.10.1 Tetrahedral and octahedral structures

silicon carbide and alumina 26

1.10.2 Silicate structures 28

1.10.3 The structures of carbon 33

2 Two-dimensional patterns, lattices and symmetry 41

2.1 Approaches to the study of crystal structures 41

2.2 Two-dimensional patterns and lattices 42

2.3 Two-dimensional symmetry elements 44

2.4 The five plane lattices 47

2.5 The seventeen plane groups 50

2.6 One-dimensional symmetry: border or frieze patterns 55

2.7 Symmetry in art and design: counterchange patterns 55

2.8 Non-periodic patterns and tilings 59

3 Bravais lattices and crystal systems 67

3.2 The fourteen space (Bravais) lattices 67

3.3 The symmetry of the fourteen Bravais lattices: crystal systems 71

3.4 The coordination or environments of Bravais lattice points: space-filling polyhedra 74

4 Crystal symmetry: point groups, space groups, symmetry-related properties and quasiperiodic crystals 79

4.1 Symmetry and crystal habit 79

4.2 The thirty-two crystal classes 80

4.3 Centres and inversion axes of symmetry 81

4.4 Crystal symmetry and properties 85

4.5 Translational symmetry elements 89

4.6 Space groups 92

4.7 Bravais lattices, space groups and crystal structures 95

4.8 Quasiperiodic crystals or crystalloids 100

5 Describing lattice planes and directions in crystals: Miller indices and zone axis symbols 104

5.2 Indexing lattice directions

zone axis symbols 105

5.3 Indexing lattice planes

Miller indices 106

5.4 Miller indices and zone axis symbols in cubic crystals 109

5.5 Lattice plane spacings, Miller indices and Laue indices 110

5.6 Zones, zone axes and the zone law, the addition rule 112

5.6.1 The Weiss zone law or zone equation 112

5.6.2 Zone axis at the intersection of two planes 112

5.6.3 Plane parallel to two directions 112

5.6.4 The addition rule 113

5.7 Indexing in the trigonal and hexagonal systems: Weber symbols and Miller-Bravais indices 113

5.8 Transforming Miller indices and zone axis symbols 115

5.9 Transformation matrices for trigonal crystals with rhombohedral lattices 118

5.10 A simple method for inverting a 3 x 3 matrix 119

6 The reciprocal lattice 122

6.2 Reciprocal lattice vectors 122

6.3 Reciprocal lattice unit cells 125

6.4 Reciprocal lattice cells for cubic crystals 128

6.5 Proofs of some geometrical relationships using reciprocal lattice vectors 130

6.5.1 Relationships between a, b, c and a*, b*, c* 130

6.5.2 The addition rule 130

6.5.3 The Weiss zone law or zone equation 131

6.5.4 d-spacing of lattice planes (hkl) 132

6.5.5 Angle [rho] between plane normals (h[subscript 1]k[subscript 1]l[subscript 1] and (h[subscript 2]k[subscript 2]l[subscript 2]) 132

6.5.6 Definition of a*, b*, c*, in terms of a, b, c 132

6.5.7 Zone axis at intersection of planes (h[subscript 1]k[subscript 1]l[subscript 1]) and (h[subscript 2]k[subscript 2]l[subscript 2]) 133

6.5.8 A plane containing two directions [u[subscript 1]v[subscript 1]w[subscript 1] and [u[subscript 2]v[subscript 2]w[subscript 2] 133

7 The diffraction of light 134

7.2 Simple observations of the diffraction of light 136

7.3 The nature of light: coherence, scattering and interference 140

7.4 Analysis of the geometry of diffraction patterns from gratings and nets 143

7.5 The resolving power of optical instruments, the telescope, camera, microscope and the eye 150

8 X-ray diffraction: the contributions of Max von Laue, W. H. and W. L. Bragg and P. P. Ewald 160

8.2 Laue's analysis of X-ray diffraction: the three Laue equations 161

8.3 Bragg's analysis of X-ray diffraction: Bragg's law 163

8.4 Ewald's synthesis: the reflecting sphere construction 166

9 The diffraction of X-rays 170

9.2 The intensities of X-ray diffracted beams: the structure factor equation and its applications 174

9.3 The broadening of diffracted beams: reciprocal lattice points and nodes 180

9.4 Fixed [theta], varying [lambda] X-ray techniques: the Laue method 183

9.5 Fixed [lambda], varying [theta] X-ray techniques: oscillation, rotation and precession methods 185

9.5.1 The oscillation method 185

9.5.2 The rotation method 188

9.5.3 The precession method 188

9.6 X-ray diffraction from single crystal thin films and multilayers 192

9.7 X-ray (and neutron) diffraction from ordered crystals 196

10 X-ray diffraction of polycrystalline materials 200

10.2 The geometrical basis of polycrystalline (powder) X-ray diffraction techniques 201

10.3 Some applications of X-ray techniques in polycrystalline materials 210

10.3.1 Accurate lattice parameter measurements 210

10.3.2 Identification of unknown phases 211

10.3.3 Measurement of crystal (grain) size 213

10.3.4 Measurement of internal elastic strains 214

10.4 Preferred orientation (texture, fabric) and its measurement 214

10.4.1 Fibre textures 215

10.4.2 Sheet textures 216

10.5 X-ray diffraction pattern of DNA: simulation by light diffraction 219

11 Electron diffraction and its applications 228

11.2 The Ewald reflecting sphere construction for electron diffraction 229

11.3 The analysis of electron diffraction patterns 231

11.4 Applications of electron diffraction 234

11.4.1 Determining orientation relationships between crystals 234

11.4.2 Identification of polycrystalline materials 236

11.4.3 Identification of quasiperiodic crystals 237

12 The stereographic projection and its uses 242

12.2 Construction of the stereographic projection of a cubic crystal 246

12.3 Manipulation of the stereographic projection: use of the Wulff net 249

12.4 Stereographic projections of non-cubic crystals 251

12.5 Applications of the stereographic projection 254

12.5.1 Representation of point group symmetry 254

12.5.2 Representation of orientation relationships 255

12.5.3 Representation of preferred orientation (texture or fabric) 257

Appendix 1 Useful components for crystallography model-building and suppliers 261

Appendix 2 Computer programs in crystallography 263

Appendix 3 Biographical notes on crystallographers and scientists mentioned in the text 267

Appendix 4 Some useful crystallographic relationships 287

Appendix 5 A simple introduction to vectors and complex numbers and their use in crystallography 290

Appendix 6 Systematic absences (extinctions) in X-ray diffraction and double diffraction in electron diffraction patterns 297.

Notes:

Includes bibliographical references (pages [317]-322) and index.

ISBN:

0198505531

OCLC:

52265064