Structure from Diffraction Methods

Duncan Bruce is Professor of Liquid Crystals and Materials Chemistry at the University of York. Prior to this he was Professor of Inorganic Chemistry at the University of Exeter, and co-director of the Sheffield Centre for Molecular Materials. His current research interests include liquid crystals and nanoparticle-doped, nanostructured, mesoporous silicates.He is immediate Past President of the Royal Society of Chemistry Materials Chemistry Division and Chair of the British Liquid Crystal Society. His work has been recognized by various awards including the RSC Tilden Prize for 2010, the RSC's Sir Edward Frankland Fellowship and Corday-Morgan Medal and Prize.Dermot O'Hare is Professor in the Chemistry Research Laboratory at the University of Oxford. His interests are wide ranging, and include exploratory synthetic organometallic chemistry, intercalation chemistry, time-resolved, in situ diffraction studies and the synthesis of meso- and microporous solids.In 2010 he won the RSC Ludwig Mond award for outstanding research in Inorganic chemistry.Dr Richard Walton is Associate Professor in Inorganic Chemistry at the University of Warwick.  He was also formerly based in the Department of Chemistry at the University of Exeter. His research group works in the area of solid-state materials chemistry and has a number of projects focusing upon the synthesis, structural characterization and properties of inorganic materials.

• Inorganic Materials Series Preface xi Preface xiiiList of Contributors xv1 Powder Diffraction 1Kenneth D. M. Harris and Andrew Williams1.1 Introduction 11.2 The Similarities and Differences Between Single-Crystal nd Powder XRD 21.3 Qualitative Aspects of Powder XRD: 'Fingerprinting' of Crystalline Phases 61.4 Quantitative Aspects of Powder XRD: Some reliminaries Relevant to Crystal Structure Determination 81.4.1 Relationship between a Crystal Structure and its Diffraction Pattern 81.4.2 Comparison of Experimental and Calculated Powder XRD Patterns 101.5 Structure Determination from Powder XRD Data 121.5.1 Overview 121.5.2 Unit Cell Determination (Indexing) 141.5.3 Preparing the Intensity Data for Structure Solution: Profile Fitting 151.5.4 Structure Solution 161.5.5 Structure Refinement 211.6 Some Experimental Considerations in Powder XRD 221.6.1 Synchrotron versus Laboratory Powder XRD Data 22 1.6.2 Preferred Orientation 241.6.3 Phase Purity of the Powder Sample 251.6.4 Analysis of Peak Widths in Powder XRD Data 261.6.5 Applications of Powder XRD for In Situ Studies of Structural Transformations and Chemical Processes 281.7 Powder Neutron Diffraction versus Powder XRD 301.8 Validation of Procedures and Results in Structure Determination from Powder XRD Data 331.8.1 Overview 331.8.2 Validation before Direct-Space Structure Solution 341.8.3 Aspects of Validation following Structure Refinement 361.9 A more Detailed Consideration of the Application of Powder XRD as a 'Fingerprint' of Crystalline Phases 401.10 Examples of the Application of Powder XRD in Chemical Contexts 451.10.1 Overview 451.10.2 Structure Determination of Zeolites and Other Framework Materials 461.10.3 In Situ Powder XRD Studies of Materials Synthesis 481.10.4 Structure Determination of New Materials Produced by Solid-State Mechanochemistry 501.10.5 In Situ Powder XRD Studies of Solid-State Mechanochemical Processes 531.10.6 In Situ Powder XRD Studies of a Polymorphic Transformation 551.10.7 In Situ Powder XRD Studies of a Solid-State Reaction 581.10.8 Establishing Details of a Hydrogen-Bonding Arrangement by Powder Neutron Diffraction 581.10.9 Structure Determination of a Material Produced by Rapid Precipitation from Solution 601.10.10 Structure Determination of Intermediates in a Solid-State Reaction 621.10.11 Structure Determination of a Novel Aluminium Methylphosphonate 621.10.12 Structure Determination of Materials Prepared by Solid-State Dehydration/Desolvation Processes 631.10.13 Structure Determination of the Product Material from a Solid-State Photopolymerisation Reaction 661.10.14 Exploiting Anisotropic Thermal Expansion in Structure Determination 681.10.15 Rationalisation of a Solid-State Reaction 691.10.16 Structure Determination of Organometallic Complexes 711.10.17 Examples of Structure Determination of Some Polymeric Materials 721.10.18 Structure Determination of Pigment Materials 731.11 Conclusion 74References 752 X-Ray and Neutron Single-Crystal Diffraction 83William Clegg2.1 Introduction 832.2 Solid-State Fundamentals 862.2.1 Translation Symmetry 872.2.2 Other Symmetry 912.2.3 An Introduction to Non-Ideal Behaviour 982.3 Scattering and Diffraction 1012.3.1 Fundamentals of Radiation and Scattering 1022.3.2 Diffraction of Monochromatic X-Rays 1032.3.3 Diffraction of Polychromatic X-Rays 1102.3.4 Diffraction of Neutrons 1112.3.5 Some Competing and Complicating Effects 1142.4 Experimental Methods 1192.4.1 Radiation Sources 1192.4.2 Single Crystals 1242.4.3 Measuring the Diffraction Pattern 1262.4.4 Correcting for Systematic Errors 1272.5 Structure Solution 1282.5.1 Direct Methods 1302.5.2 Patterson Synthesis 1312.5.3 Symmetry Arguments 1322.5.4 Charge Flipping 1332.5.5 Completing a Partial Structure Model 1342.6 Structure Refinement 1382.6.1 Minimisation and Weights 1392.6.2 Parameters, Constraints and Restraints 1392.6.3 Refinement Results 1402.6.4 Computer Programs for Structure Solution and Refinement 1412.7 Problem Structures, Special Topics, Validation and Interpretation 1422.7.1 Disorder 1422.7.2 Twinning 1432.7.3 Pseudosymmetry, Superstructures and Incommensurate Structures 1452.7.4 Absolute Structure 1472.7.5 Distinguishing Element Types, Oxidation States and Spin States 1482.7.6 Valence Effects 1492.7.7 Diffraction Experiments under Non-Ambient Conditions 1502.7.8 Issues of Interpretation and Validation 151Software Acknowledgements 153References 1533 PDF Analysis of Nanoparticles 155Reinhard B. Neder3.1 Introduction 1553.2 Pair Distribution Function 1603.3 Data Collection Strategies 1683.4 Data Treatment 1703.4.1 Calculation of G(r) from a Structural Model 1753.4.2 Data Modelling 1833.5 Examples 1843.5.1 Local Disorder versus Long-Range Average Order 1853.5.2 ZnSe Nanoparticle 1893.5.3 Decorated ZnO Nanoparticle 1943.6 Complementary Techniques 197References 1994 Electron Crystallography 201Lu Han, Keiichi Miyasaka and Osamu Terasaki4.1 Introduction 2014.2 Crystal Description 2034.2.1 Fourier Transformation and Related Functions 2034.2.2 Lattices 2044.2.3 Crystals and Crystal Structure Factors 2054.2.4 Simple Description of Babinet's Principle 2064.3 Electron Microscopy 2084.3.1 Interaction between Electrons and Matter 2084.3.2 Scanning Electron Microscopy 2094.3.3 Transmission Electron Microscopy 2144.4 Electron Diffraction 2164.4.1 X-Rays (Photons) versus Electrons 2164.4.2 Scattering Power of an Atom 2174.4.3 Crystal Structure and Electron Diffraction 2194.4.4 Relationship between Real and Reciprocal Space 2214.4.5 Friedel's Law and Phase Restriction 2234.4.6 Information on the 0th, 1st and Higher-Order Laue Zone 2244.4.7 Determining Unit Cell Dimensions and Crystal Symmetry 2264.4.8 Convergent Beam Electron Diffraction 2274.5 Imaging 2294.5.1 Crystal Structure and TEM Images 2294.5.2 Image Resolution 2304.5.3 Limitation of Structural Resolution 2314.5.4 Electrostatic Potential and Structure Factors 2324.5.5 Image Simulation 2354.6 The EC Method of Solving Crystal Structures 2354.6.1 1D Structures 2364.6.2 2D Structures 2394.6.3 3D Structures 2404.7 Other TEM Techniques 2494.7.1 STEM and HAADF 2494.7.2 Electron Tomography 2494.7.3 3D Electron Diffraction 2524.8 Conclusion 255Acknowledgment 256References 2565 Small-Angle Scattering 259Theyencheri Narayanan5.1 Introduction 2595.2 General Principles of SAS 2615.2.1 Momentum Transfer 2615.2.2 Differential Scattering Cross-Section 2625.2.3 Non-Interacting Systems 2645.2.4 Influence of Polydispersity 2665.2.5 Asymptotic Forms of I(q) 2685.2.6 Multilevel Structures 2695.2.7 Non-Particulate Systems 2725.2.8 Structure Factor of Interactions 2735.2.9 Highly Ordered Structures 2755.3 Instrumental Set-Up for SAXS 2795.3.1 Synchrotron Source 2805.3.2 X-Ray Optics 2815.3.3 X-Ray Detectors 2835.3.4 SAXS Instrument Layout 2845.4 Instrumental Set-Up for SANS 2855.4.1 Neutron Sources 2865.4.2 Neutron Optics 2875.4.3 Neutron Detectors 2885.4.4 SANS Instrument Layout 2895.4.5 Combination with Wide-Angle Scattering 2905.4.6 Instrumental Smearing Effects 2925.4.7 Sample Environments 2935.5 Application of SAS Methods 2945.5.1 Real-Time and In Situ Studies 2955.5.2 Ultra Small-Angle Scattering 3035.5.3 Contrast Variation in SAS 3085.5.4 Grazing-Incidence SAS 3145.6 Conclusion 318Acknowledgements 318References 319Index 325