Introduction to Crystallography

Preface Chapter 1 Crystals and lattices 1-1 Definition of a crystal 1-2 Lattice points 1-3 Unit cells 1-4 Fractional coordinates 1-5 Unit cell calculations 1-6 Primitive and centered cells Chapter 2 Symmetry 2-1 Introduction 2-2 Definition of symmetry 2-3 Symmetry operations and elements of symmetry 2-4 Rotation axes 2-5 Mirror planes 2-6 Identity 2-7 Center of symmetry 2-8 Improper rotation axes 2-9 Point symmetry 2-10 Combinations of symmetry elements 2-11 Point groups 2-12 Group multiplication table 2-13 Point group nomenclature 2-14 Determination of point groups 2-15 Limitation on combinations of symmetry elements Chapter 3 Crystal systems and geometry 3-1 Classification of unit cells 3-2 Restrictions imposed by symmetry on unit cell dimensions 3-3 Crystal systems 3-4 Limitations on symmetry in crystals 3-5 Hermann-Mauguin notation 3-6 Bravais lattices 3-7 Distinction between trigonal and hexagonal systems 3-8 Crystal planes and indices 3-9 Law of rational indices 3-10 Interplanar spacings Chapter 4 Space groups and equivalent positions 4-1 Translational symmetry 4-2 Screw axes 4-3 Glide planes 4-4 Space groups 4-5 "Relationship between space groups, point groups, and physical properties" 4-6 Equivalent positions 4-7 Special positions 4-8 Space group tables in International Tables for X-ray Crystallography 4-9 Examples of the use of space group tables 4-10 Equivalent positions and the choice or origin Chapter 5 X-ray diffraction 5-1 Periodicity and structural information 5-2 The diffraction grating 5-3 Diffraction of X rays by crystals 5-4 The Laue equations 5-5 Rotating crystal method 5-6 Bragg's law 5-7 Generalization of Miller indices 5-8 Weissenberg camera 5-9 Buerger precession techniques 5-10 Comparison of Weissenberg and precession techniques 5-11 Information obtained from diffraction patterns 5-12 Electron density function 5-13 Fourier series 5-14 Fourier expansion of electron density 5-15 Intensities of diffraction spots 5-16 The phase problem 5-17 Calculation of structure factors 5-18 Effect of thermal vibration 5-19 Structure factors of centrosymmetric crystals 5-20 Friedel's law 5-21 Laue groups 5-22 Structure factors of sodium chloride 5-23 Extinctions due to glide planes 5-24 Extinctions due to screw axes Chapter 6 Determination of atomic positions 6-1 Solutions of structure factor equations 6-2 The Patterson function 6-3 Heavy-atom methods 6-4 Isomorphous replacement 6-5 Superposition methods 6-6 Inequalities 6-7 Sayre-Cochran-Zachariasen relationship 6-8 Hauptman-Karle methods 6-9 Summary of phase-determining methods 6-10 Refinement Chapter 7 Some simple structures 7-1 Close packing 7-2 Cubic close packing 7-3 Hexagonal close-packed structure 7-4 Body-centered cubic 7-5 Diamond structure 7-6 Graphite structure 7-7 Other elements 7-8 Sodium chloride structure 7-9 Cesium chloride structure 7-10 Fluorite structure 7-11 Rutile structure 7-12 Zinc sulfide structure 7-13 Zincite structure 7-14 Other structures Appendix 1 The 230 space groups Appendix 2 The reciprocal lattice Appendix 3 The powder method Solutions to exercises Index