Modern X-Ray Analysis on Single Crystals

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