$The Basics of Crystallography and Diffraction : Fourth Edition$

The Basics of Crystallography and Diffraction : Fourth Edition

Name: The Basics of Crystallography and Diffraction : Fourth Edition
Author: Christopher Hammond
ISBN: 9780198738688

by Christopher Hammond

an item in the International Union of Crystallography Texts on Crystallography Series

Not Applicable

The Basics of Crystallography and Diffraction : Fourth Edition

by Christopher Hammond

an item in the International Union of Crystallography Texts on Crystallography Series

$The Basics of Crystallography and Diffraction : Fourth Edition$

Not Applicable

Overview

This book provides a clear and very broadly based introduction to crystallography, light, X-ray and electron diffraction - a knowledge which is essential to students in a wide range of scientific disciplines but which is otherwise generally covered in subject-specific and more mathematically detailed texts. The text is also designed to appeal to the more general reader since it shows, by historical and biographical references, how the subject has developed from the work and insights of successive generations of crystallographers and scientists. The book shows how an understanding of crystal structures, both inorganic and organic may be built up from simple ideas of atomic and molecular packing. Beginning with (two dimensional) examples of patterns and tilings, the concepts of lattices, symmetry point and space groups are developed. 'Penrose' tilings and quasiperiodic structures are also included. The reciprocal lattice and its importance in understanding the geometry of light, X-ray and electron diffraction patterns is explained in simple terms, leading to Fourier analysis in diffraction, crystal structure determination, image formation and the diffraction-limited resolution in these techniques. Practical X-ray and electron diffraction techniques and their applications are described. A recurring theme is the common principles: the techniques are not treated in isolation. The fourth edition has been revised throughout, and includes new sections on Fourier analysis, Patterson maps, direct methods, charge flipping, group theory in crystallography, and a new chapter on the description of physical properties of crystals by tensors (Chapter 14).

FormatNot Applicable

LanguageEnglish

PublisherOxford University Press, Incorporated

Publication DateJul. 28th, 2015

ISBN-139780198738688

Dimensions6.14 x 9.21 x 1.12 inches

ISBN-100198738684

Shipping Weight2.21 lbs

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Professional Reviews

"This updated, clearly written edition of a highly successful book is nearly 100 pages longer than its predecessor... Overall, a complete and valuable resource for any practicing crystallographer or upper-level student in crystallography. Highly recommended."
-- CHOICE

X-ray photograph of zinc blende (Friedrich, Knipping, and von Laue. 1912)	p. xvi
X-ray photograph of deoxyribonucleic acid (Franklin and Gosling, 1952)	p. xvii
Crystals and crystal structures	p. 1
The nature of the crystalline state	p. 1
Constructing crystals from close-packed hexagonal layers of atoms	p. 5
Unit cells of the hep and ccp structures	p. 6
Constructing crystals from square layers of atoms	p. 9
Constructing body-centred cubic crystals	p. 9
Interstitial structures	p. 11
Some simple ionic and covalent structures	p. 18
Representing crystals in projection: crystal plans	p. 20
Stacking faults and twins	p. 20
The crystal chemistry of inorganic compounds	p. 27
Bonding in inorganic crystals	p. 28
Representing crystals in terms of coordination polyhedra	p. 30
Introduction to some more complex crystal structures	p. 32
Perovskite (CaTiO3), barium titanate (BaTiO3) and related structures	p. 32
Tetrahedral and octahedral structures-silicon carbide and alumina	p. 34
The oxides and oxy-hydroxides of iron	p. 36
Silicate structures	p. 38
The structures of silica, ice and water	p. 44
The structures of carbon	p. 48
Exercises	p. 54
Two-dimensional patterns, lattices and symmetry	p. 56
Approaches to the study of crystal structures	p. 56
Two-dimensional patterns and lattices	p. 57
Two-dimensional symmetry elements	p. 59
The five plane lattices	p. 62
The seventeen plane groups	p. 65
One-dimensional symmetry: border or frieze patterns	p. 66
Symmetry in art and design: counterchange patterns	p. 66
Layer (two-sided) symmetry and examples in woven textiles	p. 74
Non-periodic patterns and tilings	p. 78
Exercises	p. 83
Bravais lattices and crystal systems	p. 86
Introduction	p. 86
The fourteen space (Bravais) lattices	p. 86
The symmetry of the fourteen Bravais lattices: crystal systems	p. 90
The coordination or environments of Bravais lattice points: space-filling polyhedra	p. 92
Exercises	p. 97
Crystal symmetry: point groups, space groups, symmetry-related properties and quasiperiodic crystals	p. 99
Symmetry and crystal habit	p. 99
The thirty-two crystal classes	p. 101
Centres and inversion axes of symmetry	p. 102
Crystal symmetry and properties	p. 106
Translational symmetry elements	p. 110
Space groups	p. 113
Bravais lattices, space groups and crystal structures	p. 120
The crystal structures and space groups of organic compounds	p. 123
The close packing of organic molecules	p. 124
Long-chain polymer molecules	p. 127
Quasicrystals (quasiperiodic crystals or crystalloids)	p. 129
Exercises	p. 134
Describing lattice planes and directions in crystals: Miller indices and zone axis symbols	p. 135
Introduction	p. 135
Indexing lattice directions-zone axis symbols	p. 136
Indexing lattice planes-Miller indices	p. 137
Miller indices and zone axis symbols in cubic crystals	p. 140
Lattice plane spacings, Miller indices and Laue indices	p. 141
Zones, zone axes and the zone law, the addition rule	p. 143
The Weiss zone law or zone equation	p. 143
Zone axis at the intersection of two planes	p. 143
Plane parallel to two directions	p. 144
The addition rule	p. 144
Indexing in the trigonal and hexagonal systems: Weber symbols and Miller-Bravais indices	p. 145
Transforming Miller indices, and zone axis symbols	p. 148
Transformation matrices for trigonal crystals with rhombohedral lattices	p. 151
A simple method for inverting a 3 x 3 matrix	p. 152
Exercises	p. 153
The reciprocal lattice	p. 155
Introduction	p. 155
Reciprocal lattice vectors	p. 155
Reciprocal lattice unit cells	p. 157
Reciprocal lattice cells for cubic crystals	p. 161
Proofs of some geometrical relationships using reciprocal lattice vectors	p. 163
Relationships between a, b, c and a, b, c*	p. 163
The addition rule	p. 164
The Weiss zone law or zone equation	p. 164
D-spacing of lattice planes (hkl)	p. 165
Angle p between plane normals (h1k1l1) and (h2k2l2)	p. 165
Definition of a, b, c* in terms of a, b, c	p. 166
Zone axis at intersection of planes (h1k1l1) and (h2k2l2)	p. 166
A plane containing two directions [u1v1w1] and [U2V2W2]	p. 166
Lattice planes and reciprocal lattice planes	p. 166
Summary	p. 169
Exercises	p. 169
The diffraction of light	p. 170
Introduction	p. 170
Simple observations of the diffraction of light	p. 172
The nature of light: coherence, scattering and interference	p. 177
Analysis of the geometry of diffraction patterns from gratings and nets	p. 180
The resolving power of optical instruments: the telescope, camera, microscope and the eye	p. 187
Exercises	p. 197
X-ray diffraction: the contributions of Max von Laue, W. H. and W. L. Bragg and P. P. Ewald	p. 198
Introduction	p. 198
Laue's analysis of X-ray diffraction: the three Laue equations	p. 199
Bragg's analysis of X-ray diffraction: Bragg's law	p. 202
Ewald's synthesis: the reflecting sphere construction	p. 204
Exercises	p. 209
The diffraction of X-rays	p. 210
Introduction	p. 210
The intensities of X-ray diffracted beams: the structure factor equation and its applications	p. 214
The broadening of diffracted beams: reciprocal lattice points and nodes	p. 223
The Scherrer equation: reciprocal lattice points and nodes	p. 223
Integrated intensity and its importance	p. 227
Crystal size and perfection: mosaic structure and coherence length	p. 227
Fixed ¿, varying ¿ X-ray techniques: the Lane method	p. 228
Fixed ¿, varying ¿ X-ray techniques: oscillation, rotation and precession methods	p. 231
The oscillation method	p. 232
The rotation method	p. 234
The precession method	p. 235
X-ray diffraction from single crystal thin films and multilayers	p. 239
X-ray (and neutron) diffraction from ordered crystals	p. 243
Practical considerations: X-ray sources and recording techniques	p. 246
The generation of X-rays in X-ray tubes	p. 247
Synchrotron X-ray generation	p. 248
X-ray recording techniques	p. 249
Exercises	p. 249
X-ray diffraction of polycrystalline materials	p. 252
Introduction	p. 252
The geometrical basis of polycrystalline (powder) X-ray diffraction techniques	p. 253
Intensity measurement in the X-ray diffractometer	p. 258
Back reflection and Debye-Scherrer powder techniques	p. 260
Some applications of X-ray diffraction techniques in polycrystalline materials	p. 262
Accurate lattice parameter measurements	p. 262
Identification of unknown phases	p. 263
Measurement of crystal (grain) size	p. 266
Measurement of internal elastic strains	p. 266
Preferred orientation (texture, fabric) and its measurement	p. 267
Fibre textures	p. 268
Sheet textures	p. 269
X-ray diffraction of DNA: simulation by light diffraction	p. 272
The Rietveld method for structure refinement	p. 277
Exercises	p. 280
Electron diffraction and its applications	p. 283
Introduction	p. 283
The Ewald reflecting sphere construction for electron diffraction	p. 284
The analysis of electron diffraction patterns	p. 288
Applications of electron diffraction	p. 290
Determining orientation relationships between crystals	p. 290
Identification of polycrystalline materials	p. 292
Identification of quasiperiodic crystals (quasicrystals)	p. 292
Kikuchi and electron backscattered diffraction (EBSD) patterns	p. 294
Kikuchi patterns in the TEM	p. 294
Electron backscattered diffraction (EBSD) patterns in the SEM	p. 298
Image formation and resolution in the TEM	p. 300
Exercises	p. 304
The stereographic projection and its uses	p. 308
Introduction	p. 308
Construction of the stereographic projection of a cubic crystal	p. 311
Manipulation of the stereographic projection: use of the Wulff net	p. 314
Stereographic projections of non-cubic crystals	p. 317
Applications of the stereographic projection	p. 320
Representation of point group symmetry	p. 320
Representation of orientation relationships	p. 322
Representation of preferred orientation (texture or fabric)	p. 323
Trace analysis	p. 325
Exercises	p. 328
Fourier analysis in diffraction and image formation	p. 329
Introduction-Fourier series and Fourier transforms	p. 329
Fourier analysis in crystallography	p. 332
X-ray resolution of a crystal structure	p. 337
The structural analysis of crystals and molecules	p. 338
Trial and error methods	p. 339
The Patterson function: Patterson or vector maps	p. 340
Interpretation of Patterson maps: heavy atom and isomorphous replacement techniques	p. 346
Direct methods	p. 348
Charge flipping	p. 349
Analysis of the Fraunhofer diffraction pattern from a grating	p. 350
Abbe theory of image formation	p. 356
The physical properties of crystals and their description by tensors	p. 362
Introduction	p. 362
Second rank tensor properties	p. 363
General expression for a second rank tensor relating two vectors	p. 363
Simplification of second rank tensor equations: principal axes	p. 366
Representation of second rank tensor properties: the representation quadric	p. 366
Neumann's principle	p. 368
Pyroelectricity and ferroelectricity	p. 369
Second rank tensors that describe stress and strain	p. 369
The stress tensor: principal axes (eigenvectors) and principal values (eigenvalues)	p. 369
The strain tensor, Neumann's principle, and thermal expansion	p. 372
Atomic displacement parameters (ADPs)	p. 374
The optical properties of crystals	p. 374
Third rank tensors: piezoelectricity	p. 379
Fourth rank tensor properties: elasticity	p. 380
Exercises	p. 382
Computer programs, models and model-building in crystallography	p. 385
Polyhedra in crystallography	p. 393
Biographical notes on crystallographers and scientists mentioned in the text	p. 403
Some useful crystallographic relationships	p. 449
A simple introduction to vectors and complex numbers and their use in crystallography	p. 452
Systematic absences (extinctions) in X-ray diffraction and double diffraction in electron diffraction patterns	p. 459
Group theory in crystallography	p. 469
Answers to exercises	p. 481
Further Reading	p. 497
Index	p. 507
Table of Contents provided by Ingram. All Rights Reserved.

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Overview

Product Details

FormatNot Applicable

LanguageEnglish

PublisherOxford University Press, Incorporated

Publication DateJul. 28th, 2015

ISBN-139780198738688

Dimensions6.14 x 9.21 x 1.12 inches

ISBN-100198738684

Shipping Weight2.21 lbs

Professional Reviews

X-ray photograph of zinc blende (Friedrich, Knipping, and von Laue. 1912)	p. xvi
X-ray photograph of deoxyribonucleic acid (Franklin and Gosling, 1952)	p. xvii
Crystals and crystal structures	p. 1
The nature of the crystalline state	p. 1
Constructing crystals from close-packed hexagonal layers of atoms	p. 5
Unit cells of the hep and ccp structures	p. 6
Constructing crystals from square layers of atoms	p. 9
Constructing body-centred cubic crystals	p. 9
Interstitial structures	p. 11
Some simple ionic and covalent structures	p. 18
Representing crystals in projection: crystal plans	p. 20
Stacking faults and twins	p. 20
The crystal chemistry of inorganic compounds	p. 27
Bonding in inorganic crystals	p. 28
Representing crystals in terms of coordination polyhedra	p. 30
Introduction to some more complex crystal structures	p. 32
Perovskite (CaTiO3), barium titanate (BaTiO3) and related structures	p. 32
Tetrahedral and octahedral structures-silicon carbide and alumina	p. 34
The oxides and oxy-hydroxides of iron	p. 36
Silicate structures	p. 38
The structures of silica, ice and water	p. 44
The structures of carbon	p. 48
Exercises	p. 54
Two-dimensional patterns, lattices and symmetry	p. 56
Approaches to the study of crystal structures	p. 56
Two-dimensional patterns and lattices	p. 57
Two-dimensional symmetry elements	p. 59
The five plane lattices	p. 62
The seventeen plane groups	p. 65
One-dimensional symmetry: border or frieze patterns	p. 66
Symmetry in art and design: counterchange patterns	p. 66
Layer (two-sided) symmetry and examples in woven textiles	p. 74
Non-periodic patterns and tilings	p. 78
Exercises	p. 83
Bravais lattices and crystal systems	p. 86
Introduction	p. 86
The fourteen space (Bravais) lattices	p. 86
The symmetry of the fourteen Bravais lattices: crystal systems	p. 90
The coordination or environments of Bravais lattice points: space-filling polyhedra	p. 92
Exercises	p. 97
Crystal symmetry: point groups, space groups, symmetry-related properties and quasiperiodic crystals	p. 99
Symmetry and crystal habit	p. 99
The thirty-two crystal classes	p. 101
Centres and inversion axes of symmetry	p. 102
Crystal symmetry and properties	p. 106
Translational symmetry elements	p. 110
Space groups	p. 113
Bravais lattices, space groups and crystal structures	p. 120
The crystal structures and space groups of organic compounds	p. 123
The close packing of organic molecules	p. 124
Long-chain polymer molecules	p. 127
Quasicrystals (quasiperiodic crystals or crystalloids)	p. 129
Exercises	p. 134
Describing lattice planes and directions in crystals: Miller indices and zone axis symbols	p. 135
Introduction	p. 135
Indexing lattice directions-zone axis symbols	p. 136
Indexing lattice planes-Miller indices	p. 137
Miller indices and zone axis symbols in cubic crystals	p. 140
Lattice plane spacings, Miller indices and Laue indices	p. 141
Zones, zone axes and the zone law, the addition rule	p. 143
The Weiss zone law or zone equation	p. 143
Zone axis at the intersection of two planes	p. 143
Plane parallel to two directions	p. 144
The addition rule	p. 144
Indexing in the trigonal and hexagonal systems: Weber symbols and Miller-Bravais indices	p. 145
Transforming Miller indices, and zone axis symbols	p. 148
Transformation matrices for trigonal crystals with rhombohedral lattices	p. 151
A simple method for inverting a 3 x 3 matrix	p. 152
Exercises	p. 153
The reciprocal lattice	p. 155
Introduction	p. 155
Reciprocal lattice vectors	p. 155
Reciprocal lattice unit cells	p. 157
Reciprocal lattice cells for cubic crystals	p. 161
Proofs of some geometrical relationships using reciprocal lattice vectors	p. 163
Relationships between a, b, c and a, b, c*	p. 163
The addition rule	p. 164
The Weiss zone law or zone equation	p. 164
D-spacing of lattice planes (hkl)	p. 165
Angle p between plane normals (h1k1l1) and (h2k2l2)	p. 165
Definition of a, b, c* in terms of a, b, c	p. 166
Zone axis at intersection of planes (h1k1l1) and (h2k2l2)	p. 166
A plane containing two directions [u1v1w1] and [U2V2W2]	p. 166
Lattice planes and reciprocal lattice planes	p. 166
Summary	p. 169
Exercises	p. 169
The diffraction of light	p. 170
Introduction	p. 170
Simple observations of the diffraction of light	p. 172
The nature of light: coherence, scattering and interference	p. 177
Analysis of the geometry of diffraction patterns from gratings and nets	p. 180
The resolving power of optical instruments: the telescope, camera, microscope and the eye	p. 187
Exercises	p. 197
X-ray diffraction: the contributions of Max von Laue, W. H. and W. L. Bragg and P. P. Ewald	p. 198
Introduction	p. 198
Laue's analysis of X-ray diffraction: the three Laue equations	p. 199
Bragg's analysis of X-ray diffraction: Bragg's law	p. 202
Ewald's synthesis: the reflecting sphere construction	p. 204
Exercises	p. 209
The diffraction of X-rays	p. 210
Introduction	p. 210
The intensities of X-ray diffracted beams: the structure factor equation and its applications	p. 214
The broadening of diffracted beams: reciprocal lattice points and nodes	p. 223
The Scherrer equation: reciprocal lattice points and nodes	p. 223
Integrated intensity and its importance	p. 227
Crystal size and perfection: mosaic structure and coherence length	p. 227
Fixed ¿, varying ¿ X-ray techniques: the Lane method	p. 228
Fixed ¿, varying ¿ X-ray techniques: oscillation, rotation and precession methods	p. 231
The oscillation method	p. 232
The rotation method	p. 234
The precession method	p. 235
X-ray diffraction from single crystal thin films and multilayers	p. 239
X-ray (and neutron) diffraction from ordered crystals	p. 243
Practical considerations: X-ray sources and recording techniques	p. 246
The generation of X-rays in X-ray tubes	p. 247
Synchrotron X-ray generation	p. 248
X-ray recording techniques	p. 249
Exercises	p. 249
X-ray diffraction of polycrystalline materials	p. 252
Introduction	p. 252
The geometrical basis of polycrystalline (powder) X-ray diffraction techniques	p. 253
Intensity measurement in the X-ray diffractometer	p. 258
Back reflection and Debye-Scherrer powder techniques	p. 260
Some applications of X-ray diffraction techniques in polycrystalline materials	p. 262
Accurate lattice parameter measurements	p. 262
Identification of unknown phases	p. 263
Measurement of crystal (grain) size	p. 266
Measurement of internal elastic strains	p. 266
Preferred orientation (texture, fabric) and its measurement	p. 267
Fibre textures	p. 268
Sheet textures	p. 269
X-ray diffraction of DNA: simulation by light diffraction	p. 272
The Rietveld method for structure refinement	p. 277
Exercises	p. 280
Electron diffraction and its applications	p. 283
Introduction	p. 283
The Ewald reflecting sphere construction for electron diffraction	p. 284
The analysis of electron diffraction patterns	p. 288
Applications of electron diffraction	p. 290
Determining orientation relationships between crystals	p. 290
Identification of polycrystalline materials	p. 292
Identification of quasiperiodic crystals (quasicrystals)	p. 292
Kikuchi and electron backscattered diffraction (EBSD) patterns	p. 294
Kikuchi patterns in the TEM	p. 294
Electron backscattered diffraction (EBSD) patterns in the SEM	p. 298
Image formation and resolution in the TEM	p. 300
Exercises	p. 304
The stereographic projection and its uses	p. 308
Introduction	p. 308
Construction of the stereographic projection of a cubic crystal	p. 311
Manipulation of the stereographic projection: use of the Wulff net	p. 314
Stereographic projections of non-cubic crystals	p. 317
Applications of the stereographic projection	p. 320
Representation of point group symmetry	p. 320
Representation of orientation relationships	p. 322
Representation of preferred orientation (texture or fabric)	p. 323
Trace analysis	p. 325
Exercises	p. 328
Fourier analysis in diffraction and image formation	p. 329
Introduction-Fourier series and Fourier transforms	p. 329
Fourier analysis in crystallography	p. 332
X-ray resolution of a crystal structure	p. 337
The structural analysis of crystals and molecules	p. 338
Trial and error methods	p. 339
The Patterson function: Patterson or vector maps	p. 340
Interpretation of Patterson maps: heavy atom and isomorphous replacement techniques	p. 346
Direct methods	p. 348
Charge flipping	p. 349
Analysis of the Fraunhofer diffraction pattern from a grating	p. 350
Abbe theory of image formation	p. 356
The physical properties of crystals and their description by tensors	p. 362
Introduction	p. 362
Second rank tensor properties	p. 363
General expression for a second rank tensor relating two vectors	p. 363
Simplification of second rank tensor equations: principal axes	p. 366
Representation of second rank tensor properties: the representation quadric	p. 366
Neumann's principle	p. 368
Pyroelectricity and ferroelectricity	p. 369
Second rank tensors that describe stress and strain	p. 369
The stress tensor: principal axes (eigenvectors) and principal values (eigenvalues)	p. 369
The strain tensor, Neumann's principle, and thermal expansion	p. 372
Atomic displacement parameters (ADPs)	p. 374
The optical properties of crystals	p. 374
Third rank tensors: piezoelectricity	p. 379
Fourth rank tensor properties: elasticity	p. 380
Exercises	p. 382
Computer programs, models and model-building in crystallography	p. 385
Polyhedra in crystallography	p. 393
Biographical notes on crystallographers and scientists mentioned in the text	p. 403
Some useful crystallographic relationships	p. 449
A simple introduction to vectors and complex numbers and their use in crystallography	p. 452
Systematic absences (extinctions) in X-ray diffraction and double diffraction in electron diffraction patterns	p. 459
Group theory in crystallography	p. 469
Answers to exercises	p. 481
Further Reading	p. 497
Index	p. 507
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