Structure Determination from Powder Diffraction Data

by David, W. I. F.; Shankland, K.; McCusker, L.B.; Baerlocher, Ch.

• ISBN13: 9780198500919
• ISBN10: 0198500912
• Format: Hardcover
• Copyright: 2002-06-20
• Publisher: Oxford University Press

Summary

The art of solving a structure from powder diffraction data has developed rapidly over the last ten years to the point where numerous crystal structures, both organic and inorganic, have been solved directly from powder data. However, it is still an art and, in contrast to its single crystalequivalent, is far from routine. The art lies not only in the correct application of a specific experimental technique or computer program, but also in the selection of the optimal path for the problem at hand. Written and edited by experts active in the field, and covering both the fundamental andapplied aspects of structure solution from powder diffraction data, this book guides both novices and experienced practitioners alike through the maze of possibilities.

Table of Contents

List of contributors	xv
Introduction	1	(12)
William I. F. David
Kenneth Shankland
Lynne B. McCusker
Christian Baerlocher
Crystal structures from powder diffraction data	1	(3)
The structure determination process	4	(3)
Adapting single-crystal structure solution methods to powder diffraction data	7	(1)
Direct-space methods that exploit chemical knowledge	8	(1)
Hybrid approaches	9	(1)
Outlook	10	(3)
Acknowledgements	11	(1)
References	11	(2)
Structure determination from powder diffraction data: an overview	13	(16)
Anthony K. Cheetham
Introduction	13	(1)
Early history of powder diffraction	14	(1)
Early ab initio approaches	15	(1)
Pre-Rietveld refinement methods	15	(1)
Rietveld refinement	16	(3)
Solving unknown structures from powder data	19	(2)
Trial-and-error and simulation methods	21	(1)
Some examples of structure determination from powder data	22	(2)
Conclusions	24	(5)
References	26	(3)
Laboratory X-ray powder diffraction	29	(20)
Daniel Louer
Introduction	29	(1)
The reflection overlap problem	29	(4)
Instrumental broadening-g(2θ)	30	(2)
Sample broadening-fhkl(2θ)	32	(1)
H(x) profiles	33	(1)
Instrumentation and experimental considerations	33	(7)
Diffractometer geometries	34	(1)
Monochromatic radiation	35	(3)
Data quality	38	(2)
Examples of crystal structure solution	40	(5)
Bragg-Brentano powder diffraction data	40	(1)
Debye-Scherrer powder diffraction data	41	(4)
Conclusions	45	(4)
Acknowledgements	46	(1)
References	46	(3)
Synchrotron radiation powder diffraction	49	(39)
Peter W. Stephens
David E. Cox
Andrew N. Fitch
Introduction	49	(2)
Synchrotron powder diffraction instruments in use for ab initio structure determination	51	(3)
Angular resolution, lineshape and choice of wavelength	54	(5)
Data preparation and indexing	59	(2)
Pattern decomposition and intensity extraction	61	(3)
Systematic errors	64	(2)
Particle statistics	64	(1)
Preferred orientation	65	(1)
Absorption	65	(1)
Extinction	66	(1)
Examples of structure solution	66	(17)
Pioneering studies	66	(4)
Organic compounds	70	(5)
Microporous materials	75	(3)
Organometallics	78	(2)
More difficult problems	80	(3)
Conclusions	83	(5)
Acknowledgements	84	(1)
References	84	(4)
Neutron powder diffraction	88	(10)
Richard M. Ibberson
William I. F. David
Introduction	88	(1)
Instrumentation	89	(1)
Autoindexing and space group assignment	89	(2)
Patterson methods	91	(1)
Direct methods	91	(1)
X-n structure solution	92	(1)
Future possibilities	93	(5)
References	97	(1)
Sample preparation, instrument selection and data collection	98	(20)
Roderick J. Hill
Ian C. Madsen
Introduction	98	(1)
Issues and early decisions-experimental design	99	(1)
Multiple datasets	100	(1)
The sample	101	(4)
Sources of sample-related errors	101	(1)
Number of crystallites contributing to the diffraction process	101	(2)
Increasing the number of crystallites examined	103	(2)
Generating random orientation	105	(1)
Removing extinction	105	(1)
The instrument	105	(7)
What radiation to use-X-rays or neutrons?	106	(1)
What wavelength to use?	106	(1)
Number of `independent' observations (integrated intensities)	106	(2)
What geometry to use?	108	(3)
Sources of instrument-related error	111	(1)
Data collection	112	(4)
Step time and width recommendations	113	(1)
Variable counting time data collection	114	(2)
Conclusions	116	(2)
References	116	(2)
Autoindexing	118	(18)
Per-Erik Werner
Introduction	118	(1)
Basic relations	118	(2)
The indexing problem	120	(2)
The dominant zone problem	122	(1)
Geometrical ambiguities-derivative lattices	122	(1)
Errors in measurements	123	(2)
Indexing programs	125	(5)
ITO	125	(1)
DICVOL91	126	(2)
TREOR90	128	(1)
Why more than one indexing program?	129	(1)
Computing times	130	(1)
The PDF 2 database	131	(1)
Comments	132	(4)
Appendix: (Most likely) unit-cell dimensions for selected PDF-2 powder patterns	133	(1)
References	134	(2)
Extracting integrated intensities from powder diffraction patterns	136	(26)
William I. F. David
Devinderjit S. Sivia
Introduction	136	(2)
The Le Bail method	138	(5)
The origins of the Le Bail method	138	(2)
The iterative Le Bail algorithm	140	(3)
The Pawley method	143	(5)
Introduction	143	(1)
Mathematical background	144	(4)
Space group determination	148	(3)
Overcoming Bragg peak overlap	151	(3)
Incorporating crystallographic information	154	(6)
Conclusions	160	(2)
Acknowledgements	160	(1)
References	161	(1)
Experimental methods for estimating the relative intensities of overlapping reflections	162	(17)
Thomas Wessels
Christian Baerlocher
Lynne B. McCusker
William I. F. David
Introduction	162	(1)
Anisotropic thermal expansion	162	(6)
A simple two-peak analysis	163	(1)
Mathematical aspects of the analysis of integrated intensities collected at more than one temperature	164	(1)
An example of differential thermal expansion-chlorothiazide	165	(3)
Texture	168	(9)
Concept	168	(1)
Sample preparation	169	(1)
Texture description	170	(1)
Instrumentation	171	(2)
Data collection	173	(1)
Data analysis	173	(2)
Example	175	(2)
Conclusions	177	(2)
References	177	(2)
Direct methods in powder diffraction---basic concepts	179	(11)
Rene Peschar
Anke Etz
Jouk Jansen
Hendrick Schenk
Introduction	179	(1)
Basics of Direct methods	179	(2)
Direct methods in practice	181	(2)
Normalization and setting up phase relations	181	(1)
Selection of starting-set phases	182	(1)
Active phase extension	182	(1)
Selection of most likely numerical starting set (criteria)	183	(1)
Whole-pattern fitting	183	(2)
The Pawley whole-pattern refinement	184	(1)
The two-step LSQPROF whole-pattern fitting procedure	184	(1)
Estimation of the intensity of completely overlapping reflections: the DOREES program	185	(1)
Direct methods for powder data in practice: the POWSIM package	186	(4)
References	188	(2)
Direct methods in powder diffraction-applications	190	(12)
Carmelo Giacovazzo
Angela Altomare
Maria Cristina Burla
Benedetta Carrozzini
Giovanni Luca Cascarano
Antonietta Guagliardi
Anna Grazia G. Moliterni
Giampiero Polidori
Rosanna Rizzi
Introduction	190	(1)
A set of test structures	191	(1)
Performance of extraction algorithms	191	(4)
Some warnings about the use of powder data	195	(1)
Powder pattern decomposition using supplementary prior information	196	(4)
Pseudo-translational symmetry	197	(1)
Expected positivity of the Patterson function in reciprocal space	198	(1)
The expected positivity of the Patterson function in direct space	198	(1)
A located molecular fragment	198	(2)
Applications	200	(2)
References	200	(2)
Patterson methods in powder diffraction: maximum entropy and symmetry minimum function techniques	202	(17)
Michael A. Estermann
William I. F. David
Introduction	202	(1)
The crystal structure and its Patterson function	203	(2)
Patterson maps calculated from X-ray powder diffraction data	204	(1)
Patterson maps calculated from neutron powder diffraction data	204	(1)
Conventional methods for improving the interpretability of the Patterson map	205	(1)
Maximum entropy Patterson maps	205	(2)
Decomposition of overlapping Bragg peaks using the Patterson function	207	(1)
Solving a crystal structure directly from a powder Patterson map	208	(2)
Automatic location of atomic positions with the symmetry minimum function	210	(2)
Examples of structure solution using automated Patterson superposition techniques	212	(7)
Bismuth nitride fluoride Bi3NF6	212	(2)
Synthetic CaTisi5	214	(2)
Acknowledgements	216	(1)
References	217	(2)
Solution of Patterson-type syntheses with the Direct methods sum function	219	(14)
Jordi Rius
Introduction	219	(1)
Definition of the modulus sum function	220	(3)
The modulus sum function in reciprocal space	223	(3)
The sum function tangent formula, S' - TF	226	(1)
Application of the sum function tangent formula to powder diffraction data	227	(6)
Acknowledgements	232	(1)
References	232	(1)
A maximum entropy approach to structure solution	233	(19)
Christopher J. Gilmore
Kenneth Shankland
Wei Dong
Introduction	233	(1)
Data collection, range and overlap	233	(2)
Starting set choices: defining the origin and enantiomorph	235	(1)
Basis set expansion and the phasing tree	236	(1)
Log-likelihood gain	237	(4)
Centroid maps	241	(1)
Fragments and partial structures	241	(1)
Using likelihood to partition overlapped reflections	242	(5)
The overlap problem defined in terms of hyperphases and pseudophases	242	(1)
Duncan's procedure for multiple significance tests	243	(2)
The determination of pseudophases using the maximum entropy-likelihood method and Duncan's procedure	245	(2)
The maximum entropy method and the need for experimental designs	247	(2)
Error correcting codes and their use in MICE	247	(2)
Conclusions and other possibilities	249	(3)
Acknowledgements	250	(1)
References	250	(2)
Global optimization strategies	252	(34)
Kenneth Shankland
William I. F. David
Introduction	252	(1)
Background	253	(3)
Describing a crystal structure	256	(2)
Calculating the odds	258	(3)
Beating the odds-global optimization algorithms	261	(9)
A search method with a physical basis-simulated annealing	262	(1)
A search method with a biological basis-genetic algorithms	263	(3)
Search methods with a social basis-the swarm	266	(1)
The downhill simplex algorithm-a `semi-global' optimizer	267	(1)
Other approaches	268	(1)
Which algorithm is best?	268	(1)
Use of molecular envelope information	269	(1)
Hybrid DM-Global optimization approaches	269	(1)
Structure evaluation-the cost function	270	(2)
Efficiency of function evaluations	270	(2)
Multi-objective optimization	272	(1)
Examples	272	(3)
Influence of crystallographic factors	275	(3)
Caveats and pitfalls	278	(3)
Conclusions	281	(5)
Acknowledgements	282	(1)
References	282	(4)
Solution of flexible molecular structures by simulated annealing	286	(21)
Peter G. Bruce
Yuri G. Andreev
Introduction	286	(2)
Simulated annealing	288	(1)
Constraints and restraints	289	(4)
Non-structural constraints	290	(1)
Structural restraints	290	(1)
Molecular crystals	291	(2)
Examples	293	(10)
(PEO)3:LiN(SO2CF3)2	294	(4)
PEO:NaCF3SO3	298	(4)
PEO6:LiAsF6	302	(1)
Discussion	303	(4)
Acknowledgements	305	(1)
References	305	(2)
Chemical information and intuition in solving crystal structures	307	(18)
Lynne B. McCusker
Christian Baerlocher
Introduction	307	(1)
Data collection	308	(1)
Indexing and choice of space group	308	(1)
Model building	309	(5)
Computer generation of structural models	314	(1)
Using chemical information actively in an automated structure determination process	314	(2)
Recognizing a structure solution	316	(1)
Interpretation of Fourier maps	317	(3)
Elucidation of refinement difficulties	320	(1)
Evaluation of the final structure	321	(1)
Conclusion	321	(4)
References	322	(3)
Index of symbols	325	(2)
Index of abbreviations	327	(1)
Computer programs	328	(3)
Index	331