Crystal structure analysis : principles and practice

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Title:

Publication Information:

Oxford : Oxford Science Publications, 2001

ISBN:

9780198506188

Subject Term:

X-ray crystallography

Crystals -- Structure

Added Author:

Clegg, W.

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010025915	QD945 C79 2001	Open Access Book	Book	Searching... Unknown

This text focuses on the practical aspects of crystal structure analysis, and provides the necessary conceptual framework for understanding and applying the technique. By choosing an approach that avoids undue emphasis on the mathematics involved, the book gives practical advice on topics such as growing crystals, solving and refining structures, and understanding and using the results. The technique described is a core experimental method in modern structural chemistry, and plays an ever more important role in the careers of final-year undergraduates, graduate students, postdoctoral and academic staff in chemistry.

Author Notes

Alexander J. Blake is at the School of Chemistry, The University of Nottingham. Robert O. Gould is in the Structural Biochemistry Unit, University of Edinburgh. Peter Main is in the Department of Physics, University of York. William Clegg is in the Department of Chemistry, University of Newcastle.

1 A basic introduction to X-ray crystallography	p. 1
1.1 X-ray scattering from electrons	p. 1
1.2 X-ray scattering from atoms	p. 1
1.3 X-ray scattering from the contents of a unit cell	p. 3
1.4 The effects of the crystal lattice	p. 3
1.5 X-ray scattering from the crystal	p. 4
1.6 The structure factor equation	p. 4
1.7 The electron density equation	p. 5
1.8 A mathematical relationship	p. 6
1.9 Bragg's law	p. 6
1.10 Resolution	p. 7
1.11 The phase problem	p. 8
1.12 A flowchart for crystal structure determination	p. 9
2 Crystal growth, evaluation and mounting	p. 10
2.1 Crystal growth	p. 10
2.2 Survey of methods	p. 10
2.2.1 Solution methods	p. 10
2.2.2 Sublimation	p. 15
2.2.3 Fluid phase growth	p. 15
2.2.4 Solid-state synthesis	p. 16
2.2.5 General comments	p. 16
2.3 Sample evaluation	p. 17
2.3.1 Microscopy	p. 17
2.3.2 X-ray photography	p. 18
2.3.3 Diffractometry	p. 18
2.4 Crystal mounting	p. 18
2.4.1 Standard procedures	p. 18
2.4.2 Air-sensitive crystals	p. 20
References	p. 21
Some references on crystal growth and handling	p. 21
Exercises	p. 22
3 Symmetry and space group determination	p. 24
3.1 Introduction	p. 24
3.2 Basic operations and point groups	p. 25
3.3 External morphology	p. 26
3.4 Diffraction symmetry and the amount of independent data	p. 29
3.5 Internal symmetry and translational symmetry operations	p. 29
3.6 Detection of symmetry elements from intensity statistics	p. 32
3.7 Further notes on space group symbols	p. 34
3.8 Symmetry restrictions on atoms in special positions	p. 37
Exercises	p. 38
4 Background theory for data collection	p. 42
4.1 Introduction	p. 42
4.2 The geometry of X-ray diffraction	p. 42
4.3 The reciprocal lattice	p. 44
4.4 Unit cell and orientation matrix on a diffractometer	p. 45
4.5 Obtaining a matrix and cell from initially found reflections	p. 47
4.6 Symmetry aspects of the diffraction pattern	p. 48
References	p. 49
Exercises	p. 49
5 Data collection using four-circle diffractometers	p. 51
5.1 Introduction	p. 51
5.2 Experimental conditions	p. 51
5.2.1 Radiation	p. 51
5.2.2 Temperature	p. 52
5.2.3 Other conditions	p. 52
5.3 Getting started	p. 53
5.3.1 Reflection searching	p. 53
5.3.2 Indexing, orientation matrix and cell determination	p. 55
5.3.3 Finding the correct cell	p. 56
5.3.4 Obtaining a good orientation matrix	p. 57
5.3.5 Obtaining the best unit cell dimensions	p. 58
5.4 Preparing for data collection	p. 58
5.4.1 Introduction	p. 58
5.4.2 Parameters	p. 59
5.5 Data collection	p. 62
5.6 Gross systematic errors	p. 63
5.7 Correction of intensity data	p. 63
5.7.1 Absorption corrections	p. 63
5.7.2 Decay corrections	p. 65
5.7.3 Other possible corrections	p. 65
Exercises	p. 66
6 Area detectors	p. 69
6.1 Introduction	p. 69
6.2 Types of area detectors	p. 69
6.3 Some characteristics of CCD area detector systems	p. 72
6.4 A typical experiment	p. 74
6.4.1 Crystal screening	p. 74
6.4.2 Unit cell and orientation matrix determination	p. 74
6.4.3 Data collection	p. 76
6.4.4 Data reduction and corrections	p. 76
7 Fourier syntheses	p. 77
7.1 Fourier synthesis in 1D	p. 77
7.2 A 1D example--iron pyrites	p. 78
7.3 The 2D synthesis	p. 80
7.4 The 3D synthesis	p. 84
7.5 Uses of Fouriers	p. 84
7.6 Weighted Fouriers	p. 85
Exercises	p. 87
8 Structure determination by Patterson methods	p. 90
8.1 The heavy atom method	p. 93
8.2 Patterson search techniques	p. 96
8.2.1 Rotation search	p. 97
8.2.2 Translation search	p. 97
Exercises	p. 100
9 Direct methods of crystal structure determination	p. 102
9.1 Amplitudes and phases	p. 102
9.2 The physical basis of direct methods	p. 103
9.3 Constraints on the electron density	p. 103
9.3.1 Discrete atoms	p. 104
9.3.2 Non-negative electron density	p. 104
9.3.3 Random atomic distribution	p. 106
9.3.4 Maximum value of [function of] [rho superscript 3] (x) dV	p. 107
9.3.5 Equal atoms	p. 108
9.3.6 Maximum entropy	p. 108
9.3.7 Equal molecules and [rho] (x) = constant	p. 109
9.4 Structure invariants	p. 109
9.5 Structure determination	p. 109
9.5.1 Calculation of E values	p. 110
9.5.2 Setting up phase relationships	p. 111
9.5.3 Finding reflections for phase determination	p. 111
9.5.4 Assignment of starting phases	p. 112
9.5.5 Phase determination and refinement	p. 112
9.5.6 Figures of merit	p. 113
9.5.7 Interpretation of maps	p. 114
9.5.8 Completion of the structure	p. 114
References	p. 114
Exercises	p. 114
General bibliography	p. 117
10 An introduction to maximum entropy	p. 119
10.1 Entropy	p. 119
10.2 Maximum entropy	p. 119
10.3 Calculations with incomplete data	p. 120
10.4 Forming images	p. 122
10.5 Entropy and probability	p. 122
10.6 Electron density maps	p. 123
11 Least-squares fitting of parameters	p. 125
11.1 Weighted mean	p. 125
11.2 Linear regression	p. 126
11.3 Variances and covariances	p. 127
11.4 Restraints	p. 128
11.5 Constraints	p. 129
11.6 Non-linear least squares	p. 131
11.7 Ill-conditioning	p. 133
11.8 Computing time	p. 134
Exercises	p. 134
12 Practical aspects of structure refinement	p. 135
12.1 Introduction	p. 135
12.2 Data	p. 136
12.3 Parameters	p. 138
12.4 Constraints	p. 140
12.5 Restraints	p. 141
12.6 Refinement procedures	p. 142
12.7 Disorder	p. 144
12.8 Twinning	p. 144
12.9 Absolute structure	p. 145
12.10 Other problems	p. 146
Exercises	p. 147
13 The derivation of results	p. 148
13.1 Introduction	p. 148
13.2 Statistical background	p. 149
13.2.1 Some basic mathematics and statistics	p. 149
13.2.2 Errors, precision and accuracy	p. 153
13.2.3 Estimated standard deviations/standard uncertainties in crystallographic results	p. 154
13.3 Analysis of the agreement between observed and calculated data	p. 156
13.3.1 Observed and calculated data	p. 157
13.3.2 Significance testing	p. 159
13.4 Geometry	p. 159
13.4.1 Bond lengths, bond angles and torsion angles	p. 160
13.4.2 Least-squares planes and dihedral angles	p. 162
13.4.3 Conformations of rings and other molecular features	p. 163
13.4.4 Hydrogen atoms and hydrogen bonding	p. 163
13.5 Thermal motion	p. 164
13.5.1 [beta], B and U parameters	p. 164
13.5.2 'The equivalent isotropic displacement parameter'	p. 165
13.5.3 Models of thermal motion and geometrical corrections: rigid body motion	p. 166
13.5.4 Temperature and atomic displacement parameters	p. 167
References	p. 167
Exercises	p. 167
14 The interpretation of results	p. 169
14.1 Introduction	p. 169
14.2 Averages, comparisons and differences	p. 169
14.2.1 Comparison of geometrical parameters	p. 169
14.2.2 Averaging geometrical parameters	p. 171
14.2.3 When is a set of atoms genuinely planar?	p. 172
14.2.4 Comparing different structures	p. 173
14.3 Interpretation of interatomic distances and bonds	p. 175
14.4 The effects of errors on structural results	p. 176
14.4.1 Systematic errors in the data	p. 177
14.4.2 Data thresholds and weighting	p. 178
14.4.3 Errors and limitations of the model	p. 178
14.5 Assessment of a structure determination	p. 181
References	p. 182
Exercises	p. 183
15 The presentation of results	p. 184
15.1 Introduction	p. 184
15.2 Graphics	p. 184
15.2.1 Graphics programs	p. 185
15.2.2 Underlying concepts	p. 185
15.2.3 Drawing styles	p. 187
15.3 Creating three-dimensional illusions	p. 192
15.4 The use of colour	p. 193
15.5 Textual information in drawings	p. 194
15.6 Some hints for effective drawings	p. 194
15.7 Tables of results	p. 196
15.8 The content of tables	p. 196
15.9 The format of tables	p. 198
15.10 Hints on presentation	p. 198
15.11 Archiving of results	p. 201
References	p. 202
Exercises	p. 203
16 The Crystallographic Information File	p. 205
16.1 Introduction	p. 205
16.2 Basics	p. 205
16.3 Uses of CIF	p. 207
16.4 Some properties of the CIF format	p. 207
16.5 Some practicalities	p. 209
16.5.1 Strings	p. 209
16.5.2 Text	p. 209
16.5.3 Checking the CIF	p. 210
References	p. 210
Exercises	p. 211
17 Crystallographic databases	p. 214
17.1 Available structural databases	p. 214
17.2 Contents of the Cambridge Structural Database	p. 215
17.3 Searching the CSD	p. 216
18 Other topics	p. 218
18.1 Twinning	p. 218
18.2 Anomalous dispersion	p. 220
18.3 Sources of X-rays	p. 223
References	p. 226
Appendix 1 Useful mathematics and formulae	p. 227
Appendix 2 A short crystallographic dictionary	p. 237
Appendix 3 Answers to exercises	p. 245
Index	p. 263

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