Crystallography (eBook)

Front Cover 1
Crystallography: An Introduction for Earth Science 
4 
Copyright Page 5
Table of Contents 10
Preface 6
Acknowledgements 8
Introduction 13
Part I: 14
Chapter 1. External Form and Cell Structure of Crystals 16
Conventions regarding angles 23
Problems 24
Chapter 2. Repeating Patterns and Lattices 25
Problems 29
Chapter 3. Crystal Symmetry 30
Symmetry of unit cells in two dimensions 32
Symmetry of unit cells in three dimensions 33
The minimum symmetry characterising a crystal system 36
Instructions for viewing stereoscopic drawings 40
Problems 41
Chapter 4. Notation for Crystallographic Faces, Forms and Zones 42
Crystallographic axes 42
Miller indices 43
Forms and form indices 43
Symbols for zones and zone axes 45
Calculations using indices and zone symbols 45
Reformulation of the process of finding axial ratios 47
Problems 48
Chapter 5. Use of the Stereographic Projection 49
Well-formed crystals 49
The spherical projection of a crystal 50
The stereographic projection and its properties 51
The stereographic net 55
Projection of the lower hemisphere to the north pole 57
Plotting the stereogram of a crystal 57
Use of the stereogram for visualising symmetry 59
Use of the stereogram of a crystal to find axial ratios 60
Accurate calculations from the stereogram 61
Problems 64
Chapter 6. Morphology of the Seven Crystal Systems 66
The orthorhombic system (holosymmetric class) 66
The tetragonal system (holosymmetric class) 69
The cubic system (holosymmetric class) 71
The monoclinic system (holosymmetric class) 79
The triclinic system (holosymmetric class) 84
The hexagonal system (holosymmetric class) 86
The trigonal system (holosymmetric class) 90
Problems 94
Chapter 7. The Thirty-two Crystal Classes 95
Nomenclature 97
Representation of symmetry and derivation of forms 98
The triclinic system 99
The monoclinic system 100
The orthorhombic system 102
The tetragonal system 104
The cubic system 109
The hexagonal system 113
The trigonal system 119
Determination of crystal class 123
Appendix on the properties of axes of rotation–inversion 128
Problems 130
Part II: 132
Chapter 8. The Basis of X-ray Crystallography 134
Problem 142
Chapter 9. X-ray Powder Diffraction 143
The Debye-Scherrer powder camera 143
Transmission and back-reflection cameras 146
The Gandolfi camera 147
The powder diffractometer 149
Uses of powder diffraction 152
Problems 157
Chapter 10. Intensities of X-ray Reflections 158
The atomic scattering factor 158
Amplitude of reflection from a crystal slice 160
Other factors affecting intensities 163
Problems 167
Chapter 11. The Fourteen Bravais Lattices 168
Monoclinic system 168
Orthorhombic system 170
Tetragonal system 173
Cubic system 176
Hexagonal and trigonal systems 176
The effect of non-primitive cells in X-ray crystallography 176
Rhombohedral and hexagonal cells in the trigonal system 178
Problems 179
Chapter 12. Interpretation of Powder Photographs 181
Powder patterns of cubic substances 182
Powder patterns of non-cubic substances 186
Ambiguities in indexing powder reflections 189
Problems 189
Chapter 13. X-ray Diffraction by Single Crystals 191
Difficulties associated with powder photographs 191
Rotation photographs 192
Oscillation photographs 197
Non-zero layer lines 199
Problems 206
Chapter 14. Symmetry in Repeating Patterns 207
Space-group determination 211
The representation of space-group symmetry 213
The recognition of space-group symmetry 215
Problems 218
Chapter 15. The Determination of Crystal Structures 219
Determination of the structure of rutile 220
Refinement of the structure of solid solutions 226
Problems 229
Chapter 16. Electron Diffraction in the Electron Microscope 230
Principles of the method 230
Some practical details 232
The interpretation of the diffraction pattern 233
Problems 237
Chapter 17. Irregularities in Crystals 238
External form 238
Cleavage and parting 238
Twinned crystals 239
Polytypes and stacking disorder 245
Irregularities of composition 248
Crystal defects 249
Chapter 18. Morphology Revisited 253
Glossary of Terms Used in Crystallography 257
Answers to Problems 259
Further Reading 262
Index 264