Fundamentals of Powder Diffraction and Structural Characterization of Materials

Preface. 1: Fundamentals of Crystalline State. 1.1. Introduction. 1.2. Crystalline state. 1.3. Crystal lattice and crystal structure. 1.4. Symmetry operations and symmetry elements. 1.5. Finite symmetry elements. 1.6. Interaction of symmetry elements. 1.7. Fundamentals of group theory. 1.8. Crystal systems. 1.9. Stereographic projections. 1.10. Crystallographic point groups. 1.11. Laue classes. 1.12. Selection of a unit cell and Bravais lattices. 1.13. Infinite symmetry elements. 1.14. Crystallographic planes, directions and indices. 1.15. Reciprocal lattice. 1.16. Crystallographic space groups. 1.17. International Tables for Crystallography. 1.18. Equivalent positions. 1.19. Symbolic description of symmetry operations. 1.20. Algebraic treatment of symmetry operations. 1.21. Non-conventional symmetry. 1.22. Additional reading. 1.23. Problems. 2: Fundamentals of Diffraction. 2.1. Introduction. 2.2. Properties and sources of radiation. 2.3. Collimation and monochromatization. 2.4. Detection of x-rays. 2.5. Scattering by electrons, atoms and lattices. 2.6. Geometry of diffraction by lattices. 2.7. Origin of the powder diffraction pattern. 2.8. Positions of powder diffraction peaks. 2.9. Shapes of powder diffraction peaks. 2.10. Intensity of powder diffraction peaks. 2.11. Structure factor. 2.12. Effects of symmetry on the structure amplitude. 2.13. Fourier transformation. 2.14. Phase problem. 2.15. Additional reading. 2.16. Problems. 3: Experimental Techniques. 3.1. Introduction. 3.2. Brief history of the powder diffraction method. 3.3. Powder diffractometers. 3.4. Safety. 3.5. Sample preparation. 3.6. Data acquisition. 3.7. Quality of experimental data. 3.8. Additional reading. 3.9. Problems. 4: Preliminary Data Processing and Phase Analysis. 4.1. Introduction. 4.2. Interpretation of powder diffraction data. 4.3. Preliminary data processing. 4.4. Phase identification and analysis. 4.5. Additional reading. 4.6. Problems. 5: Unit Cell Determination and Refinement. 5.1. Introduction. 5.2. The indexing problem. 5.3. Known versus unknown unit cell dimensions. 5.4. Indexing: known unit cell. 5.5. Reliability of indexing. 5.6. Introduction to ab initio indexing. 5.7. Cubic crystal system. 5.8. Tetragonal and hexagonal crystal systems. 5.9. Automatic ab initio indexing algorithms. 5.10. Unit cell reduction algorithms. 5.11. Automatic ab initio indexing: computer codes. 5.12. Ab initio indexing examples. 5.13. Precise lattice parameters and linear least squares. 5.14. Epilogue. 5.15. Additional reading. 5.16. Problems. 6: Crystal Structure Determination. 6.1. Introduction. 6.2. A