Structure from Diffraction Methods - Inorganic Materials Series

Inorganic Materials Series Preface xi Preface xiii List of Contributors xv 1 Powder Diffraction 1 Kenneth D. M. Harris and Andrew Williams 1.1 Introduction 1 1.2 The Similarities and Differences Between Single-Crystal nd Powder XRD 2 1.3 Qualitative Aspects of Powder XRD: 'Fingerprinting' of Crystalline Phases 6 1.4 Quantitative Aspects of Powder XRD: Some reliminaries Relevant to Crystal Structure Determination 8 1.4.1 Relationship between a Crystal Structure and its Diffraction Pattern 8 1.4.2 Comparison of Experimental and Calculated Powder XRD Patterns 10 1.5 Structure Determination from Powder XRD Data 12 1.5.1 Overview 12 1.5.2 Unit Cell Determination (Indexing) 14 1.5.3 Preparing the Intensity Data for Structure Solution: Profile Fitting 15 1.5.4 Structure Solution 16 1.5.5 Structure Refinement 21 1.6 Some Experimental Considerations in Powder XRD 22 1.6.1 Synchrotron versus Laboratory Powder XRD Data 22 1.6.2 Preferred Orientation 24 1.6.3 Phase Purity of the Powder Sample 25 1.6.4 Analysis of Peak Widths in Powder XRD Data 26 1.6.5 Applications of Powder XRD for In Situ Studies of Structural Transformations and Chemical Processes 28 1.7 Powder Neutron Diffraction versus Powder XRD 30 1.8 Validation of Procedures and Results in Structure Determination from Powder XRD Data 33 1.8.1 Overview 33 1.8.2 Validation before Direct-Space Structure Solution 34 1.8.3 Aspects of Validation following Structure Refinement 36 1.9 A more Detailed Consideration of the Application of Powder XRD as a 'Fingerprint' of Crystalline Phases 40 1.10 Examples of the Application of Powder XRD in Chemical Contexts 45 1.10.1 Overview 45 1.10.2 Structure Determination of Zeolites and Other Framework Materials 46 1.10.3 In Situ Powder XRD Studies of Materials Synthesis 48 1.10.4 Structure Determination of New Materials Produced by Solid-State Mechanochemistry 50 1.10.5 In Situ Powder XRD Studies of Solid-State Mechanochemical Processes 53 1.10.6 In Situ Powder XRD Studies of a Polymorphic Transformation 55 1.10.7 In Situ Powder XRD Studies of a Solid-State Reaction 58 1.10.8 Establishing Details of a Hydrogen-Bonding Arrangement by Powder Neutron Diffraction 58 1.10.9 Structure Determination of a Material Produced by Rapid Precipitation from Solution 60 1.10.10 Structure Determination of Intermediates in a Solid-State Reaction 62 1.10.11 Structure Determination of a Novel Aluminium Methylphosphonate 62 1.10.12 Structure Determination of Materials Prepared by Solid-State Dehydration/Desolvation Processes 63 1.10.13 Structure Determination of the Product Material from a Solid-State Photopolymerisation Reaction 66 1.10.14 Exploiting Anisotropic Thermal Expansion in Structure Determination 68 1.10.15 Rationalisation of a Solid-State Reaction 69 1.10.16 Structure Determination of Organometallic Complexes 71 1.10.17 Examples of Structure Determination of Some Polymeric Materials 72 1.10.18 Structure Determination of Pigment Materials 73 1.11 Conclusion 74 References 75 2 X-Ray and Neutron Single-Crystal Diffraction 83 William Clegg 2.1 Introduction 83 2.2 Solid-State Fundamentals 86 2.2.1 Translation Symmetry 87 2.2.2 Other Symmetry 91 2.2.3 An Introduction to Non-Ideal Behaviour 98 2.3 Scattering and Diffraction 101 2.3.1 Fundamentals of Radiation and Scattering 102 2.3.2 Diffraction of Monochromatic X-Rays 103 2.3.3 Diffraction of Polychromatic X-Rays 110 2.3.4 Diffraction of Neutrons 111 2.3.5 Some Competing and Complicating Effects 114 2.4 Experimental Methods 119 2.4.1 Radiation Sources 119 2.4.2 Single Crystals 124 2.4.3 Measuring the Diffraction Pattern 126 2.4.4 Correcting for Systematic Errors 127 2.5 Structure Solution 128 2.5.1 Direct Methods 130 2.5.2 Patterson Synthesis 131 2.5.3 Symmetry Arguments 132 2.5.4 Charge Flipping 133 2.5.5 Completing a Partial Structure Model 134 2.6 Structure Refinement 138 2.6.1 Minimisation and Weights 139 2.6.2 Parameters, Constraints and Restraints 139 2.6.3 Refinement Results 140 2.6.4 Computer Programs for Structure Solution and Refinement 141 2.7 Problem Structures, Special Topics, Validation and Interpretation 142 2.7.1 Disorder 142 2.7.2 Twinning 143 2.7.3 Pseudosymmetry, Superstructures and Incommensurate Structures 145 2.7.4 Absolute Structure 147 2.7.5 Distinguishing Element Types, Oxidation States and Spin States 148 2.7.6 Valence Effects 149 2.7.7 Diffraction Experiments under Non-Ambient Conditions 150 2.7.8 Issues of Interpretation and Validation 151 Software Acknowledgements 153 References 153 3 PDF Analysis of Nanoparticles 155 Reinhard B. Neder 3.1 Introduction 155 3.2 Pair Distribution Function 160 3.3 Data Collection Strategies 168 3.4 Data Treatment 170 3.4.1 Calculation of G(r) from a Structural Model 175 3.4.2 Data Modelling 183 3.5 Examples 184 3.5.1 Local Disorder versus Long-Range Average Order 185 3.5.2 ZnSe Nanoparticle 189 3.5.3 Decorated ZnO Nanoparticle 194 3.6 Complementary Techniques 197 References 199 4 Electron Crystallography 201 Lu Han, Keiichi Miyasaka and Osamu Terasaki 4.1 Introduction 201 4.2 Crystal Description 203 4.2.1 Fourier Transformation and Related Functions 203 4.2.2 Lattices 204 4.2.3 Crystals and Crystal Structure Factors 205 4.2.4 Simple Description of Babinet's Principle 206 4.3 Electron Microscopy 208 4.3.1 Interaction between Electrons and Matter 208 4.3.2 Scanning Electron Microscopy 209 4.3.3 Transmission Electron Microscopy 214 4.4 Electron Diffraction 216 4.4.1 X-Rays (Photons) versus Electrons 216 4.4.2 Scattering Power of an Atom 217 4.4.3 Crystal Structure and Electron Diffraction 219 4.4.4 Relationship between Real and Reciprocal Space 221 4.4.5 Friedel's Law and Phase Restriction 223 4.4.6 Information on the 0th, 1st and Higher-Order Laue Zone 224 4.4.7 Determining Unit Cell Dimensions and Crystal Symmetry 226 4.4.8 Convergent Beam Electron Diffraction 227 4.5 Imaging 229 4.5.1 Crystal Structure and TEM Images 229 4.5.2 Image Resolution 230 4.5.3 Limitation of Structural Resolution 231 4.5.4 Electrostatic Potential and Structure Factors 232 4.5.5 Image Simulation 235 4.6 The EC Method of Solving Crystal Structures 235 4.6.1 1D Structures 236 4.6.2 2D Structures 239 4.6.3 3D Structures 240 4.7 Other TEM Techniques 249 4.7.1 STEM and HAADF 249 4.7.2 Electron Tomography 249 4.7.3 3D Electron Diffraction 252 4.8 Conclusion 255 Acknowledgment 256 References 256 5 Small-Angle Scattering 259 Theyencheri Narayanan 5.1 Introduction 259 5.2 General Principles of SAS 261 5.2.1 Momentum Transfer 261 5.2.2 Differential Scattering Cross-Section 262 5.2.3 Non-Interacting Systems 264 5.2.4 Influence of Polydispersity 266 5.2.5 Asymptotic Forms of I(q) 268 5.2.6 Multilevel Structures 269 5.2.7 Non-Particulate Systems 272 5.2.8 Structure Factor of Interactions 273 5.2.9 Highly Ordered Structures 275 5.3 Instrumental Set-Up for SAXS 279 5.3.1 Synchrotron Source 280 5.3.2 X-Ray Optics 281 5.3.3 X-Ray Detectors 283 5.3.4 SAXS Instrument Layout 284 5.4 Instrumental Set-Up for SANS 285 5.4.1 Neutron Sources 286 5.4.2 Neutron Optics 287 5.4.3 Neutron Detectors 288 5.4.4 SANS Instrument Layout 289 5.4.5 Combination with Wide-Angle Scattering 290 5.4.6 Instrumental Smearing Effects 292 5.4.7 Sample Environments 293 5.5 Application of SAS Methods 294 5.5.1 Real-Time and In Situ Studies 295 5.5.2 Ultra Small-Angle Scattering 303 5.5.3 Contrast Variation in SAS 308 5.5.4 Grazing-Incidence SAS 314 5.6 Conclusion 318 Acknowledgements 318 References 319 Index 325