Keywords:
X-ray crystallography.
;
Crystals -- Structure.
;
Powders -- Optical properties -- Measurement.
;
Electronic books.
Description / Table of Contents:
Our understanding of the properties of materials, from drugs and proteins to catalysts and ceramics, is almost always based on structural information. This book describes the new developments in powder diffraction which make it possible for scientists to obtain such information. This book guides both novices and experienced practitioners through the maze of possibilities.
Type of Medium:
Online Resource
Pages:
1 online resource (358 pages)
Edition:
1st ed.
ISBN:
9780191525568
Series Statement:
International Union of Crystallography Monographs on Crystallography Series ; v.13
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=430271
DDC:
548.9
Language:
English
Note:
Intro -- Contents -- List of contributors -- 1 Introduction -- 1.1 Crystal structures from powder diffraction data -- 1.2 The structure determination process -- 1.3 Adapting single-crystal structure solution methods to powder diffraction data -- 1.4 Direct-space methods that exploit chemical knowledge -- 1.5 Hybrid approaches -- 1.6 Outlook -- Acknowledgements -- References -- 2 Structure determination from powder diffraction data: an overview -- 2.1 Introduction -- 2.2 Early history of powder diffraction -- 2.3 Early ab initio approaches -- 2.4 Pre-Rietveld refinement methods -- 2.5 Rietveld refinement -- 2.6 Solving unknown structures from powder data -- 2.7 Trial-and-error and simulation methods -- 2.8 Some examples of structure determination from powder data -- 2.9 Conclusions -- References -- 3 Laboratory X-ray powder diffraction -- 3.1 Introduction -- 3.2 The reflection overlap problem -- 3.2.1 Instrumental broadening-g(2& -- #952 -- ) -- 3.2.2 Sample broadening-f[sub(hkl)](2& -- #952 -- ) -- 3.2.3 H(x) profiles -- 3.3 Instrumentation and experimental considerations -- 3.3.1 Diffractometer geometries -- 3.3.2 Monochromatic radiation -- 3.3.3 Data quality -- 3.4 Examples of crystal structure solution -- 3.4.1 Bragg-Brentano powder diffraction data -- 3.4.2 Debye-Scherrer powder diffraction data -- 3.5 Conclusions -- Acknowledgements -- References -- 4 Synchrotron radiation powder diffraction -- 4.1 Introduction -- 4.2 Synchrotron powder diffraction instruments in use for ab initio structure determination -- 4.3 Angular resolution, lineshape and choice of wavelength -- 4.4 Data preparation and indexing -- 4.5 Pattern decomposition and intensity extraction -- 4.6 Systematic errors -- 4.6.1 Particle statistics -- 4.6.2 Preferred orientation -- 4.6.3 Absorption -- 4.6.4 Extinction -- 4.7 Examples of structure solution.
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4.7.1 Pioneering studies -- 4.7.2 Organic compounds -- 4.7.3 Microporous materials -- 4.7.4 Organometallics -- 4.7.5 More difficult problems -- 4.8 Conclusions -- Acknowledgements -- References -- 5 Neutron powder diffraction -- 5.1 Introduction -- 5.2 Instrumentation -- 5.3 Autoindexing and space group assignment -- 5.4 Patterson methods -- 5.5 Direct methods -- 5.6 X-n structure solution -- 5.7 Future possibilities -- References -- 6 Sample preparation, instrument selection and data collection -- 6.1 Introduction -- 6.2 Issues and early decisions-experimental design -- 6.3 Multiple datasets -- 6.4 The sample -- 6.4.1 Sources of sample-related errors -- 6.4.2 Number of crystallites contributing to the diffraction process -- 6.4.3 Increasing the number of crystallites examined -- 6.4.4 Generating random orientation -- 6.4.5 Removing extinction -- 6.5 The instrument -- 6.5.1 What radiation to use-X-rays or neutrons? -- 6.5.2 What wavelength to use? -- 6.5.3 Number of 'independent' observations (integrated intensities) -- 6.5.4 What geometry to use? -- 6.5.5 Sources of instrument-related error -- 6.6 Data collection -- 6.6.1 Step time and width recommendations -- 6.6.2 Variable counting time data collection -- 6.7 Conclusions -- References -- 7 Autoindexing -- 7.1 Introduction -- 7.2 Basic relations -- 7.3 The indexing problem -- 7.4 The dominant zone problem -- 7.5 Geometrical ambiguities-derivative lattices -- 7.6 Errors in measurements -- 7.7 Indexing programs -- 7.7.1 ITO -- 7.7.2 DICVOL91 -- 7.7.3 TREOR90 -- 7.7.4 Why more than one indexing program? -- 7.8 Computing times -- 7.9 The PDF 2 database -- 7.10 Comments -- Appendix: (Most likely) unit-cell dimensions for selected PDF-2 powder patterns -- References -- 8 Extracting integrated intensities from powder diffraction patterns -- 8.1 Introduction -- 8.2 The Le Bail method.
,
8.2.1 The origins of the Le Bail method -- 8.2.2 The iterative Le Bail algorithm -- 8.3 The Pawley method -- 8.3.1 Introduction -- 8.3.2 Mathematical background -- 8.4 Space group determination -- 8.5 Overcoming Bragg peak overlap -- 8.6 Incorporating crystallographic information -- 8.7 Conclusions -- Acknowledgements -- References -- 9 Experimental methods for estimating the relative intensities of overlapping reflections -- 9.1 Introduction -- 9.2 Anisotropic thermal expansion -- 9.2.1 A simple two-peak analysis -- 9.2.2 Mathematical aspects of the analysis of integrated intensities collected at more than one temperature -- 9.2.3 An example of differential thermal expansion-chlorothiazide -- 9.3 Texture -- 9.3.1 Concept -- 9.3.2 Sample preparation -- 9.3.3 Texture description -- 9.3.4 Instrumentation -- 9.3.5 Data collection -- 9.3.6 Data analysis -- 9.3.7 Example -- 9.4 Conclusions -- References -- 10 Direct methods in powder diffraction-basic concepts -- 10.1 Introduction -- 10.2 Basics of Direct methods -- 10.3 Direct methods in practice -- 10.3.1 Normalization and setting up phase relations -- 10.3.2 Selection of starting-set phases -- 10.3.3 Active phase extension -- 10.3.4 Selection of most likely numerical starting set (criteria) -- 10.4 Whole-pattern fitting -- 10.4.1 The Pawley whole-pattern refinement -- 10.4.2 The two-step LSQPROF whole-pattern fitting procedure -- 10.5 Estimation of the intensity of completely overlapping reflections: the DOREES program -- 10.6 Direct methods for powder data in practice: the POWSIM package -- References -- 11 Direct methods in powder diffraction-applications -- 11.1 Introduction -- 11.2 A set of test structures -- 11.3 Performance of extraction algorithms -- 11.4 Some warnings about the use of powder data -- 11.5 Powder pattern decomposition using supplementary prior information.
,
11.5.1 Pseudo-translational symmetry -- 11.5.2 Expected positivity of the Patterson function in reciprocal space -- 11.5.3 The expected positivity of the Patterson function in direct space -- 11.5.4 A located molecular fragment -- 11.6 Applications -- References -- 12 Patterson methods in powder diffraction: maximum entropy and symmetry minimum function techniques -- 12.1 Introduction -- 12.2 The crystal structure and its Patterson function -- 12.2.1 Patterson maps calculated from X-ray powder diffraction data -- 12.2.2 Patterson maps calculated from neutron powder diffraction data -- 12.3 Conventional methods for improving the interpretability of the Patterson map -- 12.4 Maximum entropy Patterson maps -- 12.5 Decomposition of overlapping Bragg peaks using the Patterson function -- 12.6 Solving a crystal structure directly from a powder Patterson map -- 12.7 Automatic location of atomic positions with the symmetry minimum function -- 12.8 Examples of structure solution using automated Patterson superposition techniques -- 12.8.1 Bismuth nitride fluoride Bi[sub(3)]NF[(sub(6)] -- 12.8.2 Synthetic CaTiSiO[(sub(5)] -- Acknowledgements -- References -- 13 Solution of Patterson-type syntheses with the Direct methods sum function -- 13.1 Introduction -- 13.2 Definition of the modulus sum function -- 13.3 The modulus sum function in reciprocal space -- 13.4 The sum function tangent formula, S' - TF -- 13.5 Application of the sum function tangent formula to powder diffraction data -- Acknowledgements -- References -- 14 A maximum entropy approach to structure solution -- 14.1 Introduction -- 14.2 Data collection, range and overlap -- 14.3 Starting set choices: defining the origin and enantiomorph -- 14.4 Basis set expansion and the phasing tree -- 14.5 Log-likelihood gain -- 14.6 Centroid maps -- 14.7 Fragments and partial structures.
,
14.8 Using likelihood to partition overlapped reflections -- 14.8.1 The overlap problem defined in terms of hyperphases and pseudophases -- 14.8.2 Duncan's procedure for multiple significance tests -- 14.8.3 The determination of pseudophases using the maximum entropy-likelihood method and Duncan's procedure -- 14.9 The maximum entropy method and the need for experimental designs -- 14.9.1 Error correcting codes and their use in MICE -- 14.10 Conclusions and other possibilities -- Acknowledgements -- References -- 15 Global optimization strategies -- 15.1 Introduction -- 15.2 Background -- 15.3 Describing a crystal structure -- 15.4 Calculating the odds -- 15.5 Beating the odds-global optimization algorithms -- 15.5.1 A search method with a physical basis-simulated annealing -- 15.5.2 A search method with a biological basis-genetic algorithms -- 15.5.3 Search methods with a social basis-the swarm -- 15.5.4 The downhill simplex algorithm-a 'semi-global' optimizer -- 15.5.5 Other approaches -- 15.5.6 Which algorithm is best? -- 15.5.7 Use of molecular envelope information -- 15.5.8 Hybrid DM-global optimization approaches -- 15.6 Structure evaluation-the cost function -- 15.6.1 Efficiency of function evaluations -- 15.6.2 Multi-objective optimization -- 15.6.3 Maximum likelihood -- 15.7 Examples -- 15.8 Influence of crystallographic factors -- 15.9 Caveats and pitfalls -- 15.10 Conclusions -- Acknowledgements -- References -- 16 Solution of flexible molecular structures by simulated annealing -- 16.1 Introduction -- 16.2 Simulated annealing -- 16.3 Constraints and restraints -- 16.3.1 Non-structural constraints -- 16.3.2 Structural restraints -- 16.3.3 Molecular crystals -- 16.4 Examples -- 16.4.1 (PEO)[sub(3)]:LiN(SO[sub(2)]CF[sub(3)])[sub(2)] -- 16.4.2 PEO:NaCF[sub(3)]SO[sub(3)] -- 16.4.3 PEO[sub(6)]:LiAsF[sub(6)] -- 16.5 Discussion.
,
Acknowledgements.
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