Luger Modern X-Ray Analysis on Single Crystals

A Practical Guide
2. fully revidierte and extended ed
ISBN: 978-3-11-030828-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 345 Seiten

An excellent book for professional crystallographers! In 2012 the crystallographic community celebrated 100 years of X-ray diffraction in honour of the pioneering experiment in 1912 by Max von Laue, Friedrich and Knipping. Experimental developments e.g. brilliant X-ray sources, area detection, and developments in computer hardware and software have led to increasing applications in X-ray analysis. This completely revised edition is a guide for practical work in X-ray analysis. An introduction to basic crystallography moves quickly to a practical and experimental treatment of structure analysis. Emphasis is placed on understanding results and avoiding pitfalls. Essential reading for researchers from the student to the professional level interested in understanding the structure of molecules.

Zielgruppe

Students and researchers in chemistry, biochemistry, solid state

Autoren/Hrsg.

Luger, Peter

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Geowissenschaften Geologie Petrologie, Mineralogie
• Naturwissenschaften Chemie Physikalische Chemie Chemische Kristallographie
• Naturwissenschaften Chemie Analytische Chemie

Inhaltsverzeichnis

1;1 Introduction;13
1.1;1.1 Historical remarks;13
1.2;1.2 The crystal lattice: Basic definitions;14
1.2.1;1.2.1 Periodicity, lattice constants;14
1.2.2;1.2.2 Lattice points, lattice planes, reciprocal lattice;17
1.3;1.3 Sample structures;25
2;2 Fundamental results of diffraction theory, X-radiation;26
2.1;2.1 Electron density and related functions;26
2.2;2.2 Diffraction conditions for single crystals;29
2.3;2.3 X-rays;33
2.3.1;2.3.1 Generation of X-rays;33
2.3.2;2.3.2 Absorption;38
2.3.3;2.3.3 Filters, monochromators;43
2.3.4;2.3.4 X-ray tubes;46
2.3.5;2.3.5 Synchrotron radiation;51
3;3 Preliminary experiments;54
3.1;3.1 Film methods;54
3.1.1;3.1.1 The rotation method;54
3.1.2;3.1.2 Zero level Weissenberg method;58
3.1.3;3.1.3 Upper level Weissenberg – normal beam and equi-inclination method;62
3.1.4;3.1.4 Precession technique;66
3.2;3.2 Practicing film techniques;73
3.2.1;3.2.1 Choice of experimental conditions;73
3.2.2;3.2.2 Rotation and Weissenberg photographs of KAMTRA and SUCROS;75
4;4 Crystal symmetry;80
4.1;4.1 Symmetry operations in a crystal lattice;80
4.1.1;4.1.1 Introduction;80
4.1.2;4.1.2 Basic symmetry operations;81
4.1.3;4.1.3 Crystal classes and related coordinate systems;85
4.1.4;4.1.4 Translational symmetry, lattice types and space groups;94
4.2;4.2 Crystal symmetry and related intensity symmetry;106
4.2.1;4.2.1 Representation of ? and F as Fourier series;106
4.2.2;4.2.2 Thermal motion, displacement parameters;110
4.2.3;4.2.3 Intensity symmetry, asymmetric unit;115
4.2.4;4.2.4 Systematic extinctions;122
4.2.5;4.2.5 Quasicrystals;124
4.3;4.3 Space group determination;127
4.3.1;4.3.1 General considerations, practical aspects;127
4.3.2;4.3.2 Space groups of KAMTRA and SUCROS from film exposures;132
5;5 Diffractometer measurements;138
5.1;5.1 Point detector data collection on a four-circle diffractometer;138
5.1.1;5.1.1 Eulerian cradle geometry;139
5.1.2;5.1.2 Choice of experimental conditions;143
5.1.3;5.1.3 Precise determination of lattice constants;146
5.1.4;5.1.4 Intensity measurements;147
5.2;5.2 Area detector diffractometers;153
5.2.1;5.2.1 Imaging plates;154
5.2.2;5.2.2 CCD diffractometers;156
5.2.3;5.2.3 Data processing for area detector measurements;158
5.2.4;5.2.4 Data collections for B12 and C60F18;159
6;6 Computer programs;162
7;7 Solution of the phase problem;166
7.1;7.1 Data reduction;166
7.2;7.2 Fourier methods;171
7.2.1;7.2.1 Interpretation of the Patterson function;171
7.2.2;7.2.2 Heavy atom methods, principle of difference electron density;173
7.2.3;7.2.3 Harker sections, applications to KAMTRA;177
7.2.4;7.2.4 Numerical calculation of Fourier syntheses;182
7.3;7.3 Direct methods;184
7.3.1;7.3.1 Normalization;184
7.3.2;7.3.2 Fundamental formulae;192
7.3.3;7.3.3 Origin definition, choice of starting set;199
7.3.4;7.3.4 Application of direct methods, the examples of SUCROS and C60F18;207
7.4;7.4 Phase determination for macromolecules;209
8;8 Refinements;215
8.1;8.1 Theoretical aspects;215
8.1.1;8.1.1 Model versus experiment, R-value;215
8.1.2;8.1.2 Theory of least-squares refinement;216
8.2;8.2 Practicing least-squares methods;224
8.2.1;8.2.1 Aspects of numerical calculations;224
8.2.2;8.2.2 Execution of a complete refinement process;224
8.2.3;8.2.3 Corrections to be applied during refinement;226
8.3;8.3 Analysis and representation of results;234
8.3.1;8.3.1 Geometrical data;234
8.3.2;8.3.2 Graphical representations;236
8.3.3;8.3.3 Archiving data, crystallographic information file (CIF);238
8.4;8.4 Applications to the test structures;241
8.4.1;8.4.1 KAMTRA and SUCROS: Completion and refinement;241
8.4.2;8.4.2 Refinement of C60F18;247
8.4.3;8.4.3 Structure solution and refinement of B12;248
9;9 Structure analysis at non-routine conditions;252
9.1;9.1 Low temperature X-ray diffraction experiments;252
9.2;9.2 Neutron diffraction;256
9.3;9.3 Structure analysis at high pressures;259
9.4;9.4 Electron density;261
9.4.1;9.4.1 Multipole model, experimental conditions;261
9.4.2;9.4.2 Topological analysis using QTAIM;265
9.4.3;9.4.3 Examples in the Life Sciences;274
10;10 Concluding remarks and outlook;282
11;Appendix: Mathematics;284
11.1;A.1 Matrices, vectors;284
11.1.1;A.1.1 Introduction;284
11.1.2;A.1.2 Matrices, determinants, linear equations;284
11.1.3;A.1.3 Vector algebra;293
11.1.4;A.1.4 Linear independency, bases, reciprocal bases;300
11.1.5;A.1.5 Basis transformations;308
11.1.6;A.1.6 Lines and planes;312
11.2;A.2 Fourier transforms and convolution operations;317
11.3;A.3 Counter statistics, mean value, standard deviation;322
12;Bibliography;327
13;Index;335

Über Autor(innen)

Peter Luger, Free University Berlin, Germany