Crystal structure determination / Werner Massa ; translated into English by Robert O. Gould.

Format:

Book

Author/Creator:

Massa, Werner, 1944-

Standardized Title:

Kristallstrukturbestimmung. English

Language:

English

German

Subjects (All):

X-ray crystallography.

Physical Description:

xi, 210 pages : illustrations ; 25 cm

Edition:

Second completely updated edition.

Place of Publication:

Berlin ; New York : Springer, [2004]

Summary:

This textbook gives a concise introduction to modern crystal structure determination, emphasising both its theoretical background and the way it actually occurs. The theoretical sections are supported by many illustrations, and lay emphasis on a good understanding rather than rigorous mathematics. The most important data collection techniques, and the methods of data reduction, structure solution and refinement are discussed from a practical point of view. Many tips and insights help readers to recognise and avoid possible errors and traps, and to judge the quality of results. The second edition has been considerably updated, especially the chapter on experimental methods, which is now mainly concerned with modern data collection using area-detectors.

Contents:

2 Crystal Lattices 3

2.1 The Lattice 3

2.1.1 The Unit Cell 4

2.1.2 Atom Parameters 5

2.1.3 The Seven Crystal Systems 6

2.2 The Fourteen Bravais Lattices 7

2.2.1 The Hexagonal, Trigonal and Rhombohedral Systems 8

2.2.2 The Reduced Cell 9

3 The Geometry of X-Ray Diffraction 13

3.1 X-Rays 13

3.2 Interference by a One-Dimensional Lattice 16

3.3 The Laue Equations 18

3.4 Lattice Planes and hkl-Indices 20

3.5 The Bragg Equation 22

3.6 Higher Orders of Diffraction 23

3.7 The Quadratic Form of the Bragg Equation 23

4 The Reciprocal Lattice 27

4.1 From the Direct to the Reciprocal Lattice 27

4.2 The Ewald Construction 30

5 Structure Factors 33

5.1 Atom Formfactors 33

5.2 Atom Displacement Factors 35

5.3 Structure Factors 37

6 Crystal Symmetry 41

6.1 Simple Symmetry Elements 41

6.1.1 Coupling of Symmetry Elements 42

6.1.2 Combination of Symmetry Elements 44

6.2 Symmetry Directions 44

6.3 Symmetry Elements Involving Translation 46

6.3.1 Combination of Translation with Other Symmetry Elements 46

6.3.2 Coupling of Translation with Other Symmetry Elements 46

6.4 The 230 Space Groups 52

6.4.1 Space-group Notation in International Tables for Crystallography 52

6.4.2 Centrosymmetric Crystal Structures 55

6.4.3 The Asymmetric Unit 56

6.4.4 Space Group Types 57

6.4.5 Group-Subgroup Relationships 57

6.5 Visible Effects of Symmetry 58

6.5.1 Microscopic Structure 58

6.5.2 Macroscopic Properties and Crystal Classes 59

6.5.3 Symmetry of the Lattice 59

6.5.4 Symmetry of the Diffraction Pattern

The Laue Groups 59

6.6 Determination of the Space Group 61

6.6.1 Determination of the Laue Group 61

6.6.2 Systematic Absences 62

6.7 Transformations 65

7 Experimental Methods 67

7.1 Growth, Choice and Mounting of a Single Crystal 67

7.2 Measuring the Diffraction Pattern of Single Crystals 71

7.2.1 Film Methods 71

7.2.2 The Four-circle (serial) Diffractometer 74

7.2.3 Reflection profile and scan type 78

7.3 Area Detector Systems 81

7.4 Data Reduction 86

7.4.1 Lp correction 86

7.4.2 Standard Uncertainty 87

7.4.3 Absorption Correction 89

7.5 Other Diffraction Methods 91

7.5.1 Neutron Scattering 91

7.5.2 Electron Scattering 92

8 Structure Solution 93

8.1 Fourier Transforms 93

8.2 Patterson Methods 95

8.2.1 Symmetry in Patterson Space 97

8.2.2 Structure Solution Using Harker Peaks 97

8.2.3 Patterson shift methods 99

8.3 Direct Methods 100

8.3.1 Harker-Kasper Inequalities 100

8.3.2 Normalized Structure Factors 101

8.3.3 The Sayre Equation 102

8.3.4 The Triplet Relationship 103

8.3.5 Origin Fixation 105

8.3.6 Strategies of Phase Determination 106

9 Structure Refinement 111

9.1 The Method of Least Squares 111

9.1.1 Refinement Based on F[subscript o] or F[superscript 2 subscript o] Data 115

9.2 Weights 116

9.3 Crystallographic R-Values 118

9.4 Refinement Techniques 119

9.4.1 Location and Treatment of Hydrogen Atoms 120

9.4.2 Restricted Refinement 121

9.4.3 Damping 122

9.4.4 Symmetry Restrictions 122

9.4.5 Residual Electron Density 123

9.5 Rietveld Refinement 124

10.1 Disorder 127

10.1.1 Site Occupancy Disorder 127

10.1.2 Positional and Orientational Disorder 128

10.1.3 One- and Two-Dimensional Disorder 130

10.1.4 Modulated Structures 131

10.1.5 Quasicrystals 131

10.2 Anomalous Dispersion and "Absolute Structure" 132

10.2.1 Chiral and Polar Space Groups 137

10.3 Extinction 139

10.4 The Renninger Effect 141

10.5 The [lambda]/2-Effect 142

10.6 Thermal Diffuse Scattering (TDS) 143

11 Errors and Pitfalls 145

11.1 Wrong Atom-Types 145

11.2 Twinning 146

11.2.1 Classification by the Twin-Element 147

11.2.2 Classification According to Macroscopic Appearance 147

11.2.3 Classification According to Origin 148

11.2.4 Diffraction Patterns of Twinned Crystals and their Interpretation 149

11.2.5 Twinning or Disorder? 155

11.3 False Unit Cells 155

11.4 Space Group Errors 156

11.5 Misplaced Origins 158

11.6 Poor Atom Displacement Parameters 159

12 Interpretation and Presentation of Results 161

12.1 Bond Lengths and Bond Angles 161

12.2 Best Planes and Torsion Angles 162

12.3 Structural Geometry and Symmetry 163

12.4 Structural Diagrams 165

12.5 Electron Density 169

13 Crystallographic Databases 171

13.1 The Inorganic Crystal Structure Database (ICSD) 171

13.2 The Cambridge Structural Database (CSD) 171

13.3 The Metals Crystallographic Data File (CRYST-MET) 175

13.4 Other Collections of Crystal Structure Data 175

13.5 Deposition of Structural Data in Data Bases 175

13.6 Crystallography on the Internet 176

14 Outline of a Crystal Structure Determination 177.

Notes:

Includes bibliographical references (pages [199]-203) and index.

ISBN:

3540206442

OCLC:

53972127