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The basics of crystallography and diffraction
Hammond, C
اطلاعات کتابشناختی
The basics of crystallography and diffraction
Author :
Hammond, C
Publisher :
Oxford University Press,
Pub. Year :
2015
Subjects :
Crystallography. X-ray crystallography.
Call Number :
QD 905 .2 .H355 2015
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Cover
(1)
Preface to the First Edition (1997)
(6)
Preface to the Fourth Edition (2015)
(7)
Acknowledgements
(8)
Contents
(10)
X-ray photograph of zinc blende (Friedrich, Knipping, and von Laue, 1912)
(17)
X-ray photograph of deoxyribonucleic acid (Franklin and Gosling, 1952)
(18)
1 Crystals and crystal structures
(20)
1.1 The nature of the crystalline state
(20)
1.2 Constructing crystals from close-packed hexagonal layers of atoms
(24)
1.3 Unit cells of the hcp and ccp structures
(25)
1.4 Constructing crystals from square layers of atoms
(28)
1.5 Constructing body-centred cubic crystals
(28)
1.6 Interstitial structures
(30)
1.7 Some simple ionic and covalent structures
(37)
1.8 Representing crystals in projection: crystal plans
(39)
1.9 Stacking faults and twins
(39)
1.10 The crystal chemistry of inorganic compounds
(46)
1.10.1 Bonding in inorganic crystals
(47)
1.10.2 Representing crystals in terms of coordination polyhedra
(49)
1.11 Introduction to some more complex crystal structures
(51)
1.11.1 Perovskite (CaTiO3), barium titanate (BaTiO3) and related structures
(51)
1.11.2 Tetrahedral and octahedral structures—silicon carbide and alumina
(53)
1.11.3 The oxides and oxy-hydroxides of iron
(55)
1.11.4 Silicate structures
(57)
1.11.5 The structures of silica, ice and water
(63)
1.11.6 The structures of carbon
(67)
Exercises
(73)
2 Two-dimensional patterns, lattices and symmetry
(75)
2.1 Approaches to the study of crystal structures
(75)
2.2 Two-dimensional patterns and lattices
(76)
2.3 Two-dimensional symmetry elements
(78)
2.4 The five plane lattices
(81)
2.5 The seventeen plane groups
(84)
2.6 One-dimensional symmetry: border or frieze patterns
(85)
2.7 Symmetry in art and design: counterchange patterns
(85)
2.8 Layer (two-sided) symmetry and examples in woven textiles
(93)
2.9 Non-periodic patterns and tilings
(97)
Exercises
(102)
3 Bravais lattices and crystal systems
(105)
3.1 Introduction
(105)
3.2 The fourteen space (Bravais) lattices
(105)
3.3 The symmetry of the fourteen Bravais lattices: crystal systems
(109)
3.4 The coordination or environments of Bravais lattice points: space-filling polyhedra
(111)
Exercises
(116)
4 Crystal symmetry: point groups, space groups, symmetry-related properties and quasiperiodic crystals
(118)
4.1 Symmetry and crystal habit
(118)
4.2 The thirty-two crystal classes
(120)
4.3 Centres and inversion axes of symmetry
(121)
4.4 Crystal symmetry and properties
(125)
4.5 Translational symmetry elements
(129)
4.6 Space groups
(132)
4.7 Bravais lattices, space groups and crystal structures
(139)
4.8 The crystal structures and space groups of organic compounds
(142)
4.8.1 The close packing of organic molecules
(143)
4.8.2 Long-chain polymer molecules
(146)
4.9 Quasicrystals (quasiperiodic crystals or crystalloids)
(148)
Exercises
(153)
5 Describing lattice planes and directions in crystals: Miller indices and zone axis symbols
(154)
5.1 Introduction
(154)
5.2 Indexing lattice directions—zone axis symbols
(155)
5.3 Indexing lattice planes—Miller indices
(156)
5.4 Miller indices and zone axis symbols in cubic crystals
(159)
5.5 Lattice plane spacings, Miller indices and Laue indices
(160)
5.6 Zones, zone axes and the zone law, the addition rule
(162)
5.6.1 The Weiss zone law or zone equation
(162)
5.6.2 Zone axis at the intersection of two planes
(162)
5.6.3 Plane parallel to two directions
(163)
5.6.4 The addition rule
(163)
5.7 Indexing in the trigonal and hexagonal systems: Weber symbols and Miller-Bravais indices
(164)
5.8 Transforming Miller indices and zone axis symbols
(167)
5.9 Transformation matrices for trigonal crystals with rhombohedral lattices
(170)
5.10 A simple method for inverting a 3 × 3 matrix
(171)
Exercises
(172)
6 The reciprocal lattice
(174)
6.1 Introduction
(174)
6.2 Reciprocal lattice vectors
(174)
6.3 Reciprocal lattice unit cells
(176)
6.4 Reciprocal lattice cells for cubic crystals
(180)
6.5 Proofs of some geometrical relationships using reciprocal lattice vectors
(182)
6.5.1 Relationships between a, b, c and a*, b*, c*
(182)
6.5.2 The addition rule
(183)
6.5.3 The Weiss zone law or zone equation
(183)
6.5.4 d-spacing of lattice planes (hkl)
(184)
6.5.5 Angle ρ between plane normals (h1k1l1) and (h2k2l2)
(184)
6.5.6 Definition of a*, b*, c* in terms of a, b, c
(185)
6.5.7 Zone axis at intersection of planes (h1k1l1) and (h2k2l2)
(185)
6.5.8 A plane containing two directions [u1v1w1] and [u2v2w2]
(185)
6.6 Lattice planes and reciprocal lattice planes
(185)
6.7 Summary
(188)
Exercises
(188)
7 The diffraction of light
(189)
7.1 Introduction
(189)
7.2 Simple observations of the diffraction of light
(191)
7.3 The nature of light: coherence, scattering and interference
(196)
7.4 Analysis of the geometry of diffraction patterns from gratings and nets
(199)
7.5 The resolving power of optical instruments: the telescope, camera, microscope and the eye
(206)
Exercises
(216)
8 X-ray diffraction: the contributions of Max von Laue, W. H. and W. L. Bragg and P. P. Ewald
(217)
8.1 Introduction
(217)
8.2 Laue's analysis of X-ray diffraction: the three Laue equations
(218)
8.3 Bragg's analysis of X-ray diffraction: Bragg's law
(221)
8.4 Ewald's synthesis: the reflecting sphere construction
(223)
Exercises
(228)
9 The diffraction of X-rays
(229)
9.1 Introduction
(229)
9.2 The intensities of X-ray diffracted beams: the structure factor equation and its applications
(233)
9.3 The broadening of diffracted beams: reciprocal lattice points and nodes
(242)
9.3.1 The Scherrer equation: reciprocal lattice points and nodes
(242)
9.3.2 Integrated intensity and its importance
(246)
9.3.3 Crystal size and perfection: mosaic structure and coherence length
(246)
9.4 Fixed θ, varying λ X-ray techniques: the Laue method
(247)
9.5 Fixed λ, varying θ X-ray techniques: oscillation, rotation and precession methods
(250)
9.5.1 The oscillation method
(251)
9.5.2 The rotation method
(253)
9.5.3 The precession method
(254)
9.6 X-ray diffraction from single crystal thin films and multilayers
(258)
9.7 X-ray (and neutron) diffraction from ordered crystals
(262)
9.8 Practical considerations: X-ray sources and recording techniques
(265)
9.8.1 The generation of X-rays in X-ray tubes
(266)
9.8.2 Synchrotron X-ray generation
(267)
9.8.3 X-ray recording techniques
(268)
Exercises
(268)
10 X-ray diffraction of polycrystalline materials
(271)
10.1 Introduction
(271)
10.2 The geometrical basis of polycrystalline (powder) X-ray diffraction techniques
(272)
10.2.1 Intensity measurement in the X-ray diffractometer
(277)
10.2.2 Back reflection and Debye–Scherrer powder techniques
(279)
10.3 Some applications of X-ray diffraction techniques in polycrystalline materials
(281)
10.3.1 Accurate lattice parameter measurements
(281)
10.3.2 Identification of unknown phases
(282)
10.3.3 Measurement of crystal (grain) size
(285)
10.3.4 Measurement of internal elastic strains
(285)
10.4 Preferred orientation (texture, fabric) and its measurement
(286)
10.4.1 Fibre textures
(287)
10.4.2 Sheet textures
(288)
10.5 X-ray diffraction of DNA: simulation by light diffraction
(291)
10.6 The Rietveld method for structure refinement
(296)
Exercises
(299)
11 Electron diffraction and its applications
(302)
11.1 Introduction
(302)
11.2 The Ewald reflecting sphere construction for electron diffraction
(303)
11.3 The analysis of electron diffraction patterns
(307)
11.4 Applications of electron diffraction
(309)
11.4.1 Determining orientation relationships between crystals
(309)
11.4.2 Identification of polycrystalline materials
(311)
11.4.3 Identification of quasiperiodic crystals (quasicrystals)
(311)
11.5 Kikuchi and electron backscattered diffraction (EBSD) patterns
(313)
11.5.1 Kikuchi patterns in the TEM
(313)
11.5.2 Electron backscattered diffraction (EBSD) patterns in the SEM
(317)
11.6 Image formation and resolution in the TEM
(319)
Exercises
(323)
12 The stereographic projection and its uses
(327)
12.1 Introduction
(327)
12.2 Construction of the stereographic projection of a cubic crystal
(330)
12.3 Manipulation of the stereographic projection: use of the Wulff net
(333)
12.4 Stereographic projections of non-cubic crystals
(336)
12.5 Applications of the stereographic projection
(339)
12.5.1 Representation of point group symmetry
(339)
12.5.2 Representation of orientation relationships
(341)
12.5.3 Representation of preferred orientation (texture or fabric)
(342)
12.5.4 Trace analysis
(344)
Exercises
(347)
13 Fourier analysis in diffraction and image formation
(348)
13.1 Introduction—Fourier series and Fourier transforms
(348)
13.2 Fourier analysis in crystallography
(351)
13.2.1 X-ray resolution of a crystal structure
(356)
13.3 The structural analysis of crystals and molecules
(357)
13.3.1 Trial and error methods
(358)
13.3.2 The Patterson function: Patterson or vector maps
(359)
13.3.3 Interpretation of Patterson maps: heavy atom and isomorphous replacement techniques
(365)
13.3.4 Direct methods
(367)
13.3.5 Charge flipping
(368)
13.4 Analysis of the Fraunhofer diffraction pattern from a grating
(369)
13.5 Abbe theory of image formation
(375)
14 The physical properties of crystals and their description by tensors
(381)
14.1 Introduction
(381)
14.2 Second rank tensor properties
(382)
14.2.1 General expression for a second rank tensor relating two vectors
(382)
14.2.2 Simplification of second rank tensor equations: principal axes
(385)
14.2.3 Representation of second rank tensor properties: the representation quadric
(385)
14.3 Neumann's principle
(387)
14.3.1 Pyroelectricity and ferroelectricity
(388)
14.4 Second rank tensors that describe stress and strain
(388)
14.4.1 The stress tensor: principal axes (eigenvectors) and principal values (eigenvalues)
(388)
14.4.2 The strain tensor, Neumann's principle, and thermal expansion
(391)
14.4.3 Atomic displacement parameters (ADPs)
(393)
14.5 The optical properties of crystals
(393)
14.6 Third rank tensors: piezoelectricity
(398)
14.7 Fourth rank tensor properties: elasticity
(399)
Exercises
(401)
Appendix 1 Computer programs, models and model-building in crystallography
(404)
Appendix 2 Polyhedra in crystallography
(412)
Appendix 3 Biographical notes on crystallographers and scientists mentioned in the text
(422)
Appendix 4 Some useful crystallographic relationships
(468)
Appendix 5 A simple introduction to vectors and complex numbers and their use in crystallography
(471)
Appendix 6 Systematic absences (extinctions) in X-ray diffraction and double diffraction in electron diffraction patterns
(478)
Appendix 7 Group theory in crystallography
(488)
Answers to exercises
(500)
Further Reading
(516)
Index
(526)
