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Contents
Page
1. Introduction 135
2. Basic principles 137
2.1. Characteristics of powder diffraction patterns 137
2.2. Diffraction line profiles 139
2.3. Convolution and deconvolution 140
2.4. Structural imperfections 142
3. Modelling of powder diffraction data 145
3.1. General considerations 145
3.2. Line-profile functions 146
3.3. Total pattern fitting 148
3.4. Reliability, precision and accuracy 152
4. Instrumentation and experimental considerations 154
4.1. Sources of radiation 154
4.2. Diffractometers and cameras 159
4.3. Detectors 160
4.4. Non-ambient diffraction 163
4.5. Sample preparation and experimental strategy 165
4.6. Instrument characterization and Standard Reference Materials 166
5. Databases and phase identification 169
5.1. Databases 169
5.2. Phase identification (Search/Match) 172
6. Crystal structure refinement from powder data 177
6.1. Factors affecting precision and accuracy 177
6.2. Current practices with the Rietveld method 182
6.3. Some applications of the Rietveld method 182
6.4. Pattern decomposition and structure refinement 188
7. Ab initio structure determination 188
7.1. Historical overview 188
7.2. Powder pattern indexing 189
7.3. Extraction of integrated intensities 192
7.4. Structure solution 193
7.5. Combined X-ray and neutron diffraction 196
7.6. Noteworthy examples of ab initio structure determination 197
7.7. Integrated software 197
8. Resonant diffraction (anomalous dispersion) 198
9. Quantitative phase analysis 199
9.1. Introduction 199
9.2. The internal-standard and the reference-intensity-ratio methods 200
9.3. Quantitative phase analysis by the Rietveld method 201
10. Line-profile analysis and microstructural properties 202
134 J I Langford and D Lou¡§er
10.1.Microstructure of materials 202
10.2.Analysis of microstructure based on Fourier series 202
10.3.Integral-breadth methods 209
11. Dynamic and non-ambient diffraction 211
11.1.Time- and temperature-dependent powder diffraction 211
11.2.High pressure diffraction 216
11.3.Magnetic X-ray powder diffraction 219
12. Concluding remarks 220
Appendix. Analytical functions commonly used to model powder diffraction line
profiles 221
References 223
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