Massa Crystal Structure Determination

3. Auflage 2016
ISBN: 978-3-7412-3076-9
Verlag: BoD - Books on Demand
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 280 Seiten

This textbook gives a concise introduction to modern crystal structure determination, emphasising both its theoretical background and the way it actually occurs. The theoretical and experimental sections are supported by many illustrations, and lay emphasis on a good understanding rather than rigorous mathematics. The actual data collection techniques, and the methods of data reduction, structure solution and refinement are discussed from a practical point of view. Many tips and insigths help readers to recognise and avoid possible errors and traps, and to judge the quality of results. In the third English edition, based on the German eighth edition (Springer 2015), treatment of film methods, now extinct, and of the nearly extinct four-circle diffractometers has been omitted. Instead, the methods of obtaining and interpreting area detector data have been expanded, and e.g. actual alternative direct methods and time-resolved crystallography are included.

WERNER MASSA is retired Professor of Inorganic Chemistry and former Head of the Central Laboratory for X-ray Structure Analysis in the Department of Chemistry at the University of Marburg (Germany). This book, now in its third English Edition, is based on many years of teaching practical crystallography at Tübingen and Marburg.

Autoren/Hrsg.

Massa, Werner

Inhaltsverzeichnis

1;Dedication;2
2;Title Page;3
3;Copyright;4
4;Preface to the Third English Edition;5
5;Table of Contents;7
6;Commonly used symbols;12
7;1 Introduction;13
8;2 Crystal Lattices;14
8.1;2.1 The Lattice;14
8.1.1;2.1.1 The unit cell;15
8.1.2;2.1.2 Atom Parameters;16
8.1.3;2.1.3 The Seven Crystal Systems;17
8.2;2.2 The 14 Bravais Lattices;19
8.2.1;2.2.1 The Hexagonal, Trigonal and Rhombohedral Systems;20
8.2.2;2.2.2 The Reduced Cell;23
9;3 The Geometry of X-Ray Diffraction;25
9.1;3.1 X-Rays;25
9.2;3.2 Interference by a One-Dimensional Lattice;30
9.3;3.3 The Laue Equations;32
9.4;3.4 Lattice Planes and hkl-Indices;36
9.5;3.5 The Bragg Equation;38
9.6;3.6 Higher Orders of Diffraction;39
9.7;3.7 The Quadratic Form of the Bragg Equation;40
10;4 The Reciprocal Lattice;43
10.1;4.1 From the Direct to the Reciprocal Lattice;43
10.2;4.2 The Ewald Construction;46
11;5 Structure Factors;50
11.1;5.1 Atom Formfactors;50
11.2;5.2 Atom Displacement Factors;52
11.3;5.3 Structure Factors;56
12;6 Crystal Symmetry;61
12.1;6.1 Simple Symmetry Elements;61
12.1.1;6.1.1 Coupling of Symmetry Elements;63
12.1.2;6.1.2 Combination of Symmetry Elements;63
12.2;6.2 Symmetry Directions;65
12.3;6.3 Symmetry Elements Involving Translation;68
12.3.1;6.3.1 Combination of Translation with Other Symmetry Elements;68
12.3.2;6.3.2 Coupling of Translation with Other Symmetry Elements;68
12.4;6.4 The 230 Space Groups;71
12.4.1;6.4.1 Space-group Notation in International Tables for Crystallography;71
12.4.2;6.4.2 Centrosymmetric Crystal Structures;78
12.4.3;6.4.3 The Asymmetric Unit;79
12.4.4;6.4.4 Space Group Types;80
12.4.5;6.4.5 Group-Subgroup Relationships;81
12.5;6.5 Visible Effects of Symmetry;83
12.5.1;6.5.1 Microscopic Structure;83
12.5.2;6.5.2 Macroscopic Properties and Crystal Classes;83
12.5.3;6.5.3 Symmetry of the Lattice;84
12.5.4;6.5.4 Symmetry of the Diffraction Pattern – The Laue Groups;84
12.6;6.6 Determination of the Space Group;87
12.6.1;6.6.1 Determination of the Laue Group;87
12.6.2;6.6.2 Systematic absences;88
12.7;6.7 Transformations;94
13;7 Experimental Methods;97
13.1;7.1 Growth, Choice and Mounting of a Single Crystal;97
13.2;7.2 Measuring the Diffraction Pattern of Single Crystals;103
13.3;7.3 Area Detector Systems;104
13.4;7.4 Data collection on an area detector system;110
13.5;7.5 Lp–correction;119
13.6;7.6 Standard Uncertainty;120
13.7;7.7 Absorption correction;121
13.8;7.8 Other Diffraction Methods;125
13.8.1;7.8.1 Neutron Scattering;125
13.8.2;7.8.2 Electron Scattering;126
13.9;7.9 Time–resolved Crystallography;127
14;8 Structure Solution;129
14.1;8.1 Fourier Transforms;129
14.2;8.2 Patterson Methods;132
14.2.1;8.2.1 Symmetry in Patterson Space;134
14.2.2;8.2.2 Structure Solution Using Harker Peaks;134
14.2.3;8.2.3 Image-Seeking Methods;137
14.3;8.3 Direct Methods;138
14.3.1;8.3.1 Harker–Kasper Inequalities;138
14.3.2;8.3.2 Normalized Structure Factors;139
14.3.3;8.3.3 The Sayre Equation;141
14.3.4;8.3.4 The Triplet Relationship;142
14.3.5;8.3.5 Origin Fixation;145
14.3.6;8.3.6 Strategies of Phase Determination;147
14.3.7;8.3.7 Alternative Direct Methods;150
15;9 Structure Refinement;152
15.1;9.1 The Method of Least Squares;152
15.1.1;9.1.1 Refinement Based on F[sub(o)] or F[sup(2)][sub(o)] Data;157
15.2;9.2 Weights;158
15.3;9.3 Crystallographic R-Values;160
15.4;9.4 Refinement Techniques;162
15.4.1;9.4.1 Location and Treatment of Hydrogen Atoms;163
15.4.2;9.4.2 Restricted Refinement;165
15.4.3;9.4.3 Damping;166
15.4.4;9.4.4 Symmetry Restrictions;167
15.4.5;9.4.5 Residual Electron Density;167
15.5;9.5 Rietveld Refinement;168
16;10 Additional Topics;172
16.1;10.1 Disorder;172
16.1.1;10.1.1 Site Occupancy Disorder;172
16.1.2;10.1.2 Positional and Orientational Disorder;173
16.1.3;10.1.3 One– and Two–Dimensional Disorder;176
16.2;10.2 Modulated Structures;177
16.3;10.3 Quasicrystals;178
16.4;10.4 Anomalous Dispersion and “Absolute Structure”;179
16.4.1;10.4.1 Chirality and “Absolute Structure”;185
16.5;10.5 Extinction;189
16.6;10.6 The Renninger Effect;191
16.7;10.7 The ./2–Effect;192
16.8;10.8 Thermal Diffuse Scattering (TDS);193
17;11 Errors and Pitfalls;195
17.1;11.1 Wrong Atom–Types;195
17.2;11.2 Twinning;197
17.2.1;11.2.1 Classification by the Twin–Element;198
17.2.2;11.2.2 Classification According to Macroscopic Appearance;198
17.2.3;11.2.3 Classification According to Origin;199
17.2.4;11.2.4 Diffraction Patterns of Twinned Crystals and their Interpretation;200
17.2.5;11.2.5 Twinning or Disorder?;208
17.3;11.3 False Unit Cells;209
17.4;11.4 Space Group Errors;210
17.5;11.5 Misplaced Origins;212
17.6;11.6 Poor Atom Displacement Parameters;213
18;12 Interpretation of Results;215
18.1;12.1 Bond Lengths and Bond Angles;215
18.2;12.2 Best Planes and Torsion Angles;216
18.3;12.3 Structural Geometry and Symmetry;218
18.4;12.4 Structural Diagrams;220
18.5;12.5 Electron density;225
19;13 Crystallographic Databases;227
19.1;13.1 The Inorganic Crystal Structure Database ICSD;227
19.2;13.2 Metals Crystallographic Data File CRYSTMET;227
19.3;13.3 Pearson’s Crystal Data PCD;229
19.4;13.4 Cambridge Structural Database CSD;229
19.5;13.5 Protein–Database (PDB);229
19.6;13.6 Crystallography Open Database COD;232
19.7;13.7 Other Collections of Crystal Structure Data;232
19.8;13.8 Deposition of Structural Data in Data Bases;232
19.9;13.9 Crystallography on the Internet;233
20;14 Outline of a Structure Determination;234
21;15 Worked Example;237
22;16 Appendix;261
22.1;16.1 Selection of crystallographic texts;261
22.2;16.2 Selection of important crystallographic programs;262
23;References;267
24;Index;271