Crystals and Crystal Structures

Chapter 1 Crystals and crystal structures 1.1 Crystal families and crystal systems 1.2 Unit cells and Miller indices 1.3 The determination of crystal structures 1.4 The description of crystal structures 1.5 Crystal structures: metals 1.5.1 The cubic close-packed (A1) structure of copper 1.5.2 The body-centred cubic (A2) structure of tungsten 1.5.3 The hexagonal (A3) structure of magnesium 1.6 Crystal structures: binary compounds 1.6.1 The halite (rock salt, NaCl) structure 1.6.2 The rutile structure 1.6.3 The fluorite structure 1.7 The cubic perovskite structure 1.8 The structure of urea 1.9 The density of a crystal Answers to introductory questions Problems and Exercises Chapter 2 Lattices, planes and directions 2.1 Two-dimensional lattices 2.2 Unit cells 2.3 The reciprocal lattice in two dimensions 2.4 Three-dimensional lattices 2.5 Rhombohedral, hexagonal and cubic lattices 2.6 Alternative unit cells 2.7 The reciprocal lattice in three dimensions 2.8 Lattice planes and Miller indices 2.9 Hexagonal lattices and Miller-Bravais indices 2.10 Miller indices and planes in crystals 2.11 Directions 2.12 Lattice geometry Answers to introductory questions Problems and Exercises Chapter 3 Two-dimensional patterns and tiling 3.1 The symmetry of an isolated shape: point symmetry 3.2 Rotation symmetry of a plane lattice 3.3 The symmetry of the plane lattices 3.4 The ten plane crystallographic point symmetry groups 3.5 The symmetry of patterns: the 17 plane groups 3.6 Two-dimensional "crystal structures" 3.7 General and special positions 3.8 Tesselations Answers to introductory questions Problems and Exercises Chapter 4 Symmetry in three dimensions 4.1 The symmetry of an object: point symmetry 4.2 Axes of inversion: rotoinversion 4.3 Axes of inversion: rotoreflection 4.4 The Hermann-Mauguin symbols for point groups 4.5 The symmetry of the Bravais lattices 4.6 The crystallographic point groups Answers to introductory questions Problems and Exercises Chapter 5 Symmetry and physical properties 5.1 Properties and symmetry 5.2 Point groups and physical properties 5.3 Specification of physical properties 5.4 Refractive index 5.5 Optical activity 5.5.1 Specific rotation 5.5.2 Optical activity in crystals 5.5.3 Optical activity in homogeneous crystals 5.5.4 Optical activity in crystals containing molecules 5.5.5 Optical activity and chiral molecules 5.5.6 Optical activity, chemical reactivity and symmetry 5.6 The pyroelectric effect 5.6.1 Pyroelectric and ferroelectric crystals 5.6.2 Crystallographic aspects of pyro- and ferroelectric behaviour 5.7 Dielectric properties 5.7.1 Dielectrics 5.7.2 Isotropic materials 5.7.3 Non-isotropic materials 5.9 Magnetic point groups and colour symmetry Answers to introductory questions Problems and exercises Chapter 6 Building crystal structures from lattices and space groups 6.1 Symmetry of three-dimensional patterns: space groups 6.2 The crystallographic space groups 6.3 Space group symmetry symbols 6.4 The graphical representation of the space groups 6.5 Building a structure from a space group: Cs3P7 6.6 The structure of diopside, MgCaSi2O6 6.7 The structure of alanine, C3H7NO2 Answers to introductory questions Problems and exercises Chapter 7 Diffraction and crystal structure determination 7.1 The occurrence of diffracted beams: Bragg's law 7.2 The geometry of the diffraction pattern 7.3 Particle size 7.4 The intensities of diffracted beams 7.5 The atomic scattering factor 7.6 The structure factor 7.7 Structure factors and intensities 7.8 Numerical evaluation of structure factors 7.9 Symmetry and reflection intensities 7.10 The temperature factor 7.11 Powder X-ray diffraction 7.12 Neutron diffraction 7.13 Structure determination using X-ray diffraction 7.14 Solving the phase problem 7.15 Electron microscopy 7.15.1 Diffraction patterns and structure images 7.15.2 Diffraction and Fourier transforms 7.16 Protein crystallography 7.16.1 The phase problem 7.16.2 The crystallinity problem: SFX 7.16.3 The crystallinity problem: single particle cryo-EM Answers to introductory questions Problems and Exercises Chapter 8 The depiction of crystal structures 8.1 The size of atoms 8.2 Sphere packing 8.3 Metallic radii 8.4 Ionic radii 8.5 Covalent radii 8.6 Van der Waals radii 8.7 Ionic structures and structure building rules 8.8 The bond valence model 8.9 Structures in terms of non-metal (anion) packing 8.10 Structures in terms of metal (cation) packing 8.11 Cation-centred polyhedral representations of crystals 8.12 Polyhedral representations of crystals and diffusion paths 8.13 Structures as nets 8.14 Organic structures 8.15 Protein structures 8.15.1 Proteins: primary structure 8.15.2 Proteins: secondary, tertiary and quaternary structure Answers to introductory questions Problems and Exercises Chapter 9 Defects, modulated structures and quasicrystals 9.1 Defects and occupancy factors 9.2 Defects and unit cell parameters 9.3 Defects and density 9.4 Modular structures 9.5 Polytypes 9.6 Crystallographic shear (CS) phases 9.7 Planar intergrowths and polysomes 9.8 Incommensurately modulated structures 9.9 Quasicrystals Answers to introductory questions Problems and Exercises Appendices Appendix 1 Vector addition and subtraction Appendix 2 Crystallographic data for some inorganic crystal structures Appendix 3 Schoenflies symbols Appendix 4 The 230 space groups Appendix 5 Complex numbers Appendix 6 Complex amplitudes Answers to problems and exercises Bibliography Formula Index Subject index