Crystal Structure Determination / Edition 2

Crystal Structure Determination / Edition 2

by Werner Massa
     
 

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ISBN-10: 3540206442

ISBN-13: 9783540206446

Pub. Date: 11/30/2011

Publisher: Springer Berlin Heidelberg

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

Overview

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.

Product Details

ISBN-13:
9783540206446
Publisher:
Springer Berlin Heidelberg
Publication date:
11/30/2011
Edition description:
2nd ed. 2004, Corr. 5th printing 2010
Pages:
222
Product dimensions:
9.20(w) x 6.40(h) x 1.20(d)

Related Subjects

Table of Contents

1Introduction1
2Crystal Lattices3
2.1The Lattice3
2.1.1The Unit Cell4
2.1.2Atom Parameters5
2.1.3The Seven Crystal Systems6
2.2The Fourteen Bravais Lattices7
2.2.1The Hexagonal, Trigonal and Rhombohedral Systems8
2.2.2The Reduced Cell9
3The Geometry of X-Ray Diffraction13
3.1X-Rays13
3.2Interference by a One-Dimensional Lattice16
3.3The Laue Equations18
3.4Lattice Planes and hkl-Indices20
3.5The Bragg Equation22
3.6Higher Orders of Diffraction23
3.7The Quadratic Form of the Bragg Equation23
4The Reciprocal Lattice27
4.1From the Direct to the Reciprocal Lattice27
4.2The Ewald Construction30
5Structure Factors33
5.1Atom Formfactors33
5.2Atom Displacement Factors35
5.3Structure Factors37
6Crystal Symmetry41
6.1Simple Symmetry Elements41
6.1.1Coupling of Symmetry Elements42
6.1.2Combination of Symmetry Elements44
6.2Symmetry Directions44
6.3Symmetry Elements Involving Translation46
6.3.1Combination of Translation with Other Symmetry Elements46
6.3.2Coupling of Translation with Other Symmetry Elements46
6.4The 230 Space Groups52
6.4.1Space-group Notation in International Tables for Crystallography52
6.4.2Centrosymmetric Crystal Structures55
6.4.3The Asymmetric Unit56
6.4.4Space Group Types57
6.4.5Group-Subgroup Relationships57
6.5Visible Effects of Symmetry58
6.5.1Microscopic Structure58
6.5.2Macroscopic Properties and Crystal Classes59
6.5.3Symmetry of the Lattice59
6.5.4Symmetry of the Diffraction Pattern--The Laue Groups59
6.6Determination of the Space Group61
6.6.1Determination of the Laue Group61
6.6.2Systematic Absences62
6.7Transformations65
7Experimental Methods67
7.1Growth, Choice and Mounting of a Single Crystal67
7.2Measuring the Diffraction Pattern of Single Crystals71
7.2.1Film Methods71
7.2.2The Four-circle (serial) Diffractometer74
7.2.3Reflection profile and scan type78
7.3Area Detector Systems81
7.4Data Reduction86
7.4.1Lp correction86
7.4.2Standard Uncertainty87
7.4.3Absorption Correction89
7.5Other Diffraction Methods91
7.5.1Neutron Scattering91
7.5.2Electron Scattering92
8Structure Solution93
8.1Fourier Transforms93
8.2Patterson Methods95
8.2.1Symmetry in Patterson Space97
8.2.2Structure Solution Using Harker Peaks97
8.2.3Patterson shift methods99
8.3Direct Methods100
8.3.1Harker-Kasper Inequalities100
8.3.2Normalized Structure Factors101
8.3.3The Sayre Equation102
8.3.4The Triplet Relationship103
8.3.5Origin Fixation105
8.3.6Strategies of Phase Determination106
9Structure Refinement111
9.1The Method of Least Squares111
9.1.1Refinement Based on F[subscript o] or F[superscript 2 subscript o] Data115
9.2Weights116
9.3Crystallographic R-Values118
9.4Refinement Techniques119
9.4.1Location and Treatment of Hydrogen Atoms120
9.4.2Restricted Refinement121
9.4.3Damping122
9.4.4Symmetry Restrictions122
9.4.5Residual Electron Density123
9.5Rietveld Refinement124
10Additional Topics127
10.1Disorder127
10.1.1Site Occupancy Disorder127
10.1.2Positional and Orientational Disorder128
10.1.3One- and Two-Dimensional Disorder130
10.1.4Modulated Structures131
10.1.5Quasicrystals131
10.2Anomalous Dispersion and "Absolute Structure"132
10.2.1Chiral and Polar Space Groups137
10.3Extinction139
10.4The Renninger Effect141
10.5The [lambda]/2-Effect142
10.6Thermal Diffuse Scattering (TDS)143
11Errors and Pitfalls145
11.1Wrong Atom-Types145
11.2Twinning146
11.2.1Classification by the Twin-Element147
11.2.2Classification According to Macroscopic Appearance147
11.2.3Classification According to Origin148
11.2.4Diffraction Patterns of Twinned Crystals and their Interpretation149
11.2.5Twinning or Disorder?155
11.3False Unit Cells155
11.4Space Group Errors156
11.5Misplaced Origins158
11.6Poor Atom Displacement Parameters159
12Interpretation and Presentation of Results161
12.1Bond Lengths and Bond Angles161
12.2Best Planes and Torsion Angles162
12.3Structural Geometry and Symmetry163
12.4Structural Diagrams165
12.5Electron Density169
13Crystallographic Databases171
13.1The Inorganic Crystal Structure Database (ICSD)171
13.2The Cambridge Structural Database (CSD)171
13.3The Metals Crystallographic Data File (CRYST-MET)175
13.4Other Collections of Crystal Structure Data175
13.5Deposition of Structural Data in Data Bases175
13.6Crystallography on the Internet176
14Outline of a Crystal Structure Determination177
15Worked Example of a Structure Determination181
Bibliography199
Index205

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