Crystallography and the World of Symmetry (eBook)

Preface 7
Contents 9
1 Pattern 12
1.1 Pattern: An Introduction 12
1.2 Summary 18
References 18
2 Lattices 19
2.1 Plane Lattice 19
2.2 Space Lattice 22
2.3 Lattice Planes and Miller Indices 22
2.4 Lattice Directions 23
2.5 Summary 24
References 24
3 Symmetry in Lattices 25
3.1 Symmetry Operations in Plane Lattices 25
3.2 Symmetry Operation in Space Lattices 29
3.3 Summary 31
References 31
4 Crystal Symmetry (Crystal Pattern): I 32
4.1 Macroscopic Symmetry Elements 32
4.2 Thirty-Two Point Groups of Symmetries in Hermann – Mauguin Notations 33
4.3 Crystal Systems 36
4.4 Bravais Lattices 37
4.5 Summary 42
References 42
5 Crystal Symmetry (Crystal Pattern): II 43
5.1 Microscopic Symmetry Elements in Crystals 43
5.2 Space Groups 48
5.3 Constitution of Space Groups 50
5.4 Summary 50
References 50
6 Crystals and X-Ray 51
6.1 Production and Properties of X-Ray 51
6.2 Laue Equations 53
6.3 Bragg’s Law 55
6.4 Reciprocal Lattice 55
6.5 Geometry of X-Ray Di.raction: Use of Reciprocal Lattice 58
6.6 The Interplanar Distance (d-Spacing) of Di.erent Crystal Systems 61
6.7 Weighted Reciprocal Lattice 63
6.8 Summary 64
References 64
7 Experimental Methods for Structure Analysis: X- Ray Diffraction Techniques 65
7.1 Experimental Techniques for Single Crystal 65
7.2 Experimental Techniques for Polycrystals 78
7.3 Debye–Scherrer Cylindrical Powder Camera: The Plan View 80
7.4 Indexing of the Debye–Scherrer Pattern 81
7.5 Summary 83
References 83
8 Determination of Space Group and Crystal Structure 84
8.1 Determination of Space Group from Data Obtained from Moving Film 84
8.2 Determination of Crystal Structure 86
8.3 Summary 90
References 91
9 The World of Symmetry 92
9.1 Symmetry in Living Bodies 93
9.2 Symmetry in Patterns, Snow Flakes, and Gems 96
9.3 Symmetry in Architecture 98
9.4 Symmetry in Fundamental Particles 98
9.5 Symmetry (Invariance) of Physical Laws 102
9.6 Summary 105
References 106
10 Asymmetry in Otherwise Symmetrical Matter 107
10.1 Single Crystals, Poly Crystals, and Asymmetry – Symmetry 107
10.2 A Symmetry in Asymmetry I: Quasi Crystalline State of Matter 112
10.3 A Symmetry in Asymmetry II: Liquid Crystalline Phase 117
10.4 Symmetry Down to the Bottom: The Nanostructures 122
10.5 Summary 132
References 132
Epilogue 133
A An Outline of the Di.raction Theory of Periodic and Aperiodic Structures 135
Scattering by an Isolated Electron 135
Diffraction by Periodic Perfect Small Crystal 136
Diffraction by Modulated Structures 140
References 141
B Solved Problems 142
Further Reading 149
Index 151