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. , 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.