Crystal Structure Determination

by Werner Massa, Robert O. Gould (Translator)

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:	9783662064313
Publisher:	Springer-Verlag New York, LLC
Publication date:	03/09/2013
Sold by:	Barnes & Noble
Format:	eBook
File size:	14 MB
Note:	This product may take a few minutes to download.

Table of Contents

1	Introduction	1
2	Crystal Lattices	3
2.1	The Lattice	3
2.1.1	The Unit Cell	4
2.1.2	Atom Parameters	5
2.1.3	The Seven Crystal Systems	6
2.2	The Fourteen Bravais Lattices	7
2.2.1	The Hexagonal, Trigonal and Rhombohedral Systems	8
2.2.2	The Reduced Cell	9
3	The Geometry of X-Ray Diffraction	13
3.1	X-Rays	13
3.2	Interference by a One-Dimensional Lattice	16
3.3	The Laue Equations	18
3.4	Lattice Planes and hkl-Indices	20
3.5	The Bragg Equation	22
3.6	Higher Orders of Diffraction	23
3.7	The Quadratic Form of the Bragg Equation	23
4	The Reciprocal Lattice	27
4.1	From the Direct to the Reciprocal Lattice	27
4.2	The Ewald Construction	30
5	Structure Factors	33
5.1	Atom Formfactors	33
5.2	Atom Displacement Factors	35
5.3	Structure Factors	37
6	Crystal Symmetry	41
6.1	Simple Symmetry Elements	41
6.1.1	Coupling of Symmetry Elements	42
6.1.2	Combination of Symmetry Elements	44
6.2	Symmetry Directions	44
6.3	Symmetry Elements Involving Translation	46
6.3.1	Combination of Translation with Other Symmetry Elements	46
6.3.2	Coupling of Translation with Other Symmetry Elements	46
6.4	The 230 Space Groups	52
6.4.1	Space-group Notation in International Tables for Crystallography	52
6.4.2	Centrosymmetric Crystal Structures	55
6.4.3	The Asymmetric Unit	56
6.4.4	Space Group Types	57
6.4.5	Group-Subgroup Relationships	57
6.5	Visible Effects of Symmetry	58
6.5.1	Microscopic Structure	58
6.5.2	Macroscopic Properties and Crystal Classes	59
6.5.3	Symmetry of the Lattice	59
6.5.4	Symmetry of the Diffraction Pattern--The Laue Groups	59
6.6	Determination of the Space Group	61
6.6.1	Determination of the Laue Group	61
6.6.2	Systematic Absences	62
6.7	Transformations	65
7	Experimental Methods	67
7.1	Growth, Choice and Mounting of a Single Crystal	67
7.2	Measuring the Diffraction Pattern of Single Crystals	71
7.2.1	Film Methods	71
7.2.2	The Four-circle (serial) Diffractometer	74
7.2.3	Reflection profile and scan type	78
7.3	Area Detector Systems	81
7.4	Data Reduction	86
7.4.1	Lp correction	86
7.4.2	Standard Uncertainty	87
7.4.3	Absorption Correction	89
7.5	Other Diffraction Methods	91
7.5.1	Neutron Scattering	91
7.5.2	Electron Scattering	92
8	Structure Solution	93
8.1	Fourier Transforms	93
8.2	Patterson Methods	95
8.2.1	Symmetry in Patterson Space	97
8.2.2	Structure Solution Using Harker Peaks	97
8.2.3	Patterson shift methods	99
8.3	Direct Methods	100
8.3.1	Harker-Kasper Inequalities	100
8.3.2	Normalized Structure Factors	101
8.3.3	The Sayre Equation	102
8.3.4	The Triplet Relationship	103
8.3.5	Origin Fixation	105
8.3.6	Strategies of Phase Determination	106
9	Structure Refinement	111
9.1	The Method of Least Squares	111
9.1.1	Refinement Based on F[subscript o] or F[superscript 2 subscript o] Data	115
9.2	Weights	116
9.3	Crystallographic R-Values	118
9.4	Refinement Techniques	119
9.4.1	Location and Treatment of Hydrogen Atoms	120
9.4.2	Restricted Refinement	121
9.4.3	Damping	122
9.4.4	Symmetry Restrictions	122
9.4.5	Residual Electron Density	123
9.5	Rietveld Refinement	124
10	Additional Topics	127
10.1	Disorder	127
10.1.1	Site Occupancy Disorder	127
10.1.2	Positional and Orientational Disorder	128
10.1.3	One- and Two-Dimensional Disorder	130
10.1.4	Modulated Structures	131
10.1.5	Quasicrystals	131
10.2	Anomalous Dispersion and "Absolute Structure"	132
10.2.1	Chiral and Polar Space Groups	137
10.3	Extinction	139
10.4	The Renninger Effect	141
10.5	The [lambda]/2-Effect	142
10.6	Thermal Diffuse Scattering (TDS)	143
11	Errors and Pitfalls	145
11.1	Wrong Atom-Types	145
11.2	Twinning	146
11.2.1	Classification by the Twin-Element	147
11.2.2	Classification According to Macroscopic Appearance	147
11.2.3	Classification According to Origin	148
11.2.4	Diffraction Patterns of Twinned Crystals and their Interpretation	149
11.2.5	Twinning or Disorder?	155
11.3	False Unit Cells	155
11.4	Space Group Errors	156
11.5	Misplaced Origins	158
11.6	Poor Atom Displacement Parameters	159
12	Interpretation and Presentation of Results	161
12.1	Bond Lengths and Bond Angles	161
12.2	Best Planes and Torsion Angles	162
12.3	Structural Geometry and Symmetry	163
12.4	Structural Diagrams	165
12.5	Electron Density	169
13	Crystallographic Databases	171
13.1	The Inorganic Crystal Structure Database (ICSD)	171
13.2	The Cambridge Structural Database (CSD)	171
13.3	The Metals Crystallographic Data File (CRYST-MET)	175
13.4	Other Collections of Crystal Structure Data	175
13.5	Deposition of Structural Data in Data Bases	175
13.6	Crystallography on the Internet	176
14	Outline of a Crystal Structure Determination	177
15	Worked Example of a Structure Determination	181
	Bibliography	199
	Index	205

Editorial Reviews

From the reviews:

"Distinguished by its attention to the practicalities of working with real crystals…a lucid and relatively concise account of modern crystal structure solution …valuable to anyone who has an interest in crystal structure refinement." The Geological Journal

"The book provides a nice balance between describing the mathematical fundamentals and offering practical advice on how to solve a crystal structure… appropriate for an undergraduate audience (particularly in chemistry) and for graduate students or researchers who find they need a better grasp of the subject… a very helpful addition to the collection of introductory texts in X-ray crystallography. Especially for its treatment of common errors in the collection of intensity data and in the interpretation of results."

Acta Crystallographica

"Details at great length the inherent pitfalls and errors that one may encounter when calculating crystal structures using new software programs. The author does an excellent job of describing these errors and ways to recognize them when they appear in your calculations." Mineralium Deposita

From the reviews of the second edition:

"This textbook gives a concise introduction to modern crystal structure determination … . The theoretical sections are supported by many illustrations, and lay emphasis on a good understanding … . The most important data collection techniques … 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." (Chimie Nouvelle Societe Royale de Chimie, Vol. 23 (89), juin, 2005)

“‘Crystal Structure Determination’ gives a concise introduction to the subject, with particular emphasis placed on the manner in which contemporary analysis actually occurs. … The strengths of this book are numerous. The presentation is excellent: the diagrams are plentiful and oftenimpressive, and the formatting of the text is very pleasing to the eye. … the research chemist with a desire to appreciate more fully a technique that they are likely to use with increasing frequency – the book should be a helpful companion.” (Andrew Bond, Crystallography News, June, 2004)

From the Publisher