Crystal Structure Determination

by Massa, Werner; Gould, Robert O.

• ISBN13: 9783540659709
• ISBN10: 3540659706
• Format: Paperback
• Copyright: 2000-05-01
• Publisher: Springer Verlag

Summary

Provides a concise introduction to modern crystal structure determination, emphasizing both the crystallographic background and the successive practical steps. Softcover. DLC: X-ray crystallography.

Author Biography

Werner Massa is Professor of Inorganic Chemistry and Director of Central Laboratory for X-Ray Structure Analysis in the Department of Chemistry at the University of Marburg (Germany).

Table of Contents

Introduction	1	(2)
Crystal Lattices	3	(10)
The Lattice	3	(4)
The Unit Cell	4	(1)
Atom Parameters	5	(1)
The Seven Crystal Systems	6	(1)
The Fourteen Bravais Lattices	7	(6)
The Hexagonal, Trigonal and Rhombohedral Systems	8	(1)
The Reduced Cell	9	(4)
The Geometry of X-Ray Diffraction	13	(14)
X-Rays	13	(3)
Interference by a One-Dimensional Lattice	16	(1)
The Laue Equations	17	(3)
Lattice Planes and hkl-Indices	20	(1)
The Bragg Equation	21	(1)
Higher Orders of Diffraction	22	(1)
The Quadratic Form of the Bragg Equation	23	(4)
The Reciprocal Lattice	27	(6)
From the Direct to the Reciprocal Lattice	27	(3)
The Ewald Construction	30	(3)
Structure Factors	33	(8)
Atom Formfactors	33	(2)
Atom Displacement Factors	35	(2)
Structure Factors	37	(4)
Crystal Symmetry	41	(26)
Simple Symmetry Elements	41	(3)
Coupling of Symmetry Elements	42	(2)
Combination of Symmetry Elements	44	(1)
Symmetry Directions	44	(2)
Symmetry Elements Involving Translation	46	(5)
Combination of Translation with Other Symmetry Elements	46	(1)
Coupling of Translation with Other Symmetry Elements	46	(5)
The 230 Space Groups	51	(7)
Space-group Notation in International Tables for Crystallography	52	(3)
Centrosymmetric Crystal Structures	55	(1)
The Asymmetric Unit	55	(2)
Space Group Types	57	(1)
Group-Subgroup Relationships	57	(1)
Visible Effects of Symmetry	58	(3)
Microscopic Structure	58	(1)
Macroscopic Properties and Crystal Classes	59	(1)
Symmetry of the Lattice	59	(1)
Symmetry of the Diffraction Pattern --- The Laue Groups	59	(2)
Determination of the Space Group	61	(4)
Determination of the Laue Group	61	(1)
Systematic Absences	62	(3)
Transformations	65	(2)
Experimental Methods	67	(32)
Growth, Choice and Mounting of a Single Crystal	67	(4)
Film Methods	71	(13)
Rotation and Weissenberg Methods	72	(6)
The Precession Method	78	(5)
Other Film Methods	83	(1)
The Single-Crystal Diffractometer	84	(7)
Types of Instruments	84	(2)
Determination of the Orientation Matrix	86	(2)
Reflection Profile and Scan Type	88	(2)
Selection of Data to be Measured	90	(1)
Area Detectors	91	(1)
Data Reduction	92	(5)
Lp Correction	93	(1)
Standard Uncertainty	93	(2)
Absorption Correction	95	(2)
Other Diffraction Methods	97	(2)
Synchrotron Radiation	97	(1)
Neutron Scattering	97	(1)
Electron Scattering	98	(1)
Structure Solution	99	(16)
Fourier Transforms	99	(2)
Patterson Methods	101	(5)
Symmetry in Patterson Space	103	(1)
Structure Solution Using Harker Peaks	103	(2)
Image-Seeking Methods	105	(1)
Direct Methods	106	(9)
Harker-Kasper Inequalities	106	(1)
Normalized Structure Factors	107	(1)
The Sayre Equation	108	(1)
The Triplet Relationship	108	(3)
Origin Fixation	111	(1)
Strategies of Phase Determination	112	(3)
Structure Refinement	115	(14)
The Method of Least Squares	115	(5)
Refinement Based on Fo or F2o Data	119	(1)
Weights	120	(2)
Crystallographic R-Values	122	(1)
Refinement Techniques	123	(4)
Location and Treatment of Hydrogen Atoms	124	(1)
Restricted Refinement	125	(1)
Damping	126	(1)
Symmetry Restrictions	126	(1)
Residual Electron Density	127	(1)
Rietveld Refinement	127	(2)
Additional Topics	129	(12)
Anomalous Dispersion and ``Absolute Structure''	129	(7)
Chiral and Polar Space Groups	133	(3)
Extinction	136	(1)
The Renninger Effect	137	(2)
The λ/2-Effect	139	(1)
Thermal Diffuse Scattering (TDS)	139	(2)
Errors and Pitfalls	141	(20)
Wrong Atom-Types	141	(1)
Disorder	142	(6)
Site Occupancy Disorder	143	(1)
Positional and Orientational Disorder	143	(2)
One- and Two-Dimensional Disorder	145	(1)
Modulated Structures	146	(1)
Quasicrystals	147	(1)
Twinning	148	(8)
Classification by the Twin-Element	148	(1)
Classification According to Macroscopic Appearance	148	(2)
Classification According to Origin	150	(1)
Diffraction Patterns of Twinned Crystals and their Interpretation	150	(6)
Twinning or Disorder?	156	(1)
False Unit Cells	156	(1)
Space Group Errors	157	(2)
Misplaced Origins	159	(1)
Poor Atom Displacement Parameters	160	(1)
Interpretation and Presentation of Results	161	(10)
Bond Lengths and Bond Angles	161	(1)
Best Planes and Torsion Angles	162	(1)
Structural Geometry and Symmetry	163	(2)
Structural Diagrams	165	(3)
Electron Density	168	(3)
Crystallographic Databases	171	(6)
The Inorganic Crystal Structure Database (ICSD)	171	(1)
The Cambridge Structural Database (CSD)	171	(1)
The Metals Crystallographic Data File (CRYST-MET)	172	(1)
Other Collections of Crystal Structure Data	173	(1)
Deposition of Structural Data in Data Bases	174	(1)
Crystallography on the Internet	175	(2)
Outline of a Crystal Structure Determination	177	(4)
Worked Example of a Structure Determination	181	(16)
Bibliography	197	(4)
Index	201