International Tables for Crystallography (2006). Vol. B. ch. 2.1, pp. 190-209
https://doi.org/10.1107/97809553602060000554 |
Chapter 2.1. Statistical properties of the weighted reciprocal lattice
Contents
- 2.1. Statistical properties of the weighted reciprocal lattice (pp. 190-209) | html | pdf | chapter contents |
- 2.1.1. Introduction (p. 190) | html | pdf |
- 2.1.2. The average intensity of general reflections (pp. 190-191) | html | pdf |
- 2.1.3. The average intensity of zones and rows (pp. 191-192) | html | pdf |
- 2.1.4. Probability density distributions – mathematical preliminaries (pp. 192-195) | html | pdf |
- 2.1.4.1. Characteristic functions (pp. 192-193) | html | pdf |
- 2.1.4.2. The cumulant-generating function (pp. 193-194) | html | pdf |
- 2.1.4.3. The central-limit theorem (pp. 194-195) | html | pdf |
- 2.1.4.4. Conditions of validity (p. 195) | html | pdf |
- 2.1.4.5. Non-independent variables (p. 195) | html | pdf |
- 2.1.5. Ideal probability density distributions (pp. 195-197) | html | pdf |
- 2.1.5.1. Ideal acentric distributions (pp. 195-196) | html | pdf |
- 2.1.5.2. Ideal centric distributions (p. 196) | html | pdf |
- 2.1.5.3. Effect of other symmetry elements on the ideal acentric and centric distributions (p. 196) | html | pdf |
- 2.1.5.4. Other ideal distributions (p. 196) | html | pdf |
- 2.1.5.5. Relation to distributions of I (p. 196) | html | pdf |
- 2.1.5.6. Cumulative distribution functions (pp. 196-197) | html | pdf |
- 2.1.6. Distributions of sums, averages and ratios (pp. 197-199) | html | pdf |
- 2.1.7. Non-ideal distributions: the correction-factor approach (pp. 199-203) | html | pdf |
- 2.1.8. Non-ideal distributions: the Fourier method (pp. 203-209) | html | pdf |
- 2.1.8.1. General representations of p.d.f.'s of by Fourier series (pp. 203-204) | html | pdf |
- 2.1.8.2. Fourier–Bessel series (pp. 204-205) | html | pdf |
- 2.1.8.3. Simple examples (p. 205) | html | pdf |
- 2.1.8.4. A more complicated example (pp. 205-206) | html | pdf |
- 2.1.8.5. Atomic characteristic functions (pp. 206-208) | html | pdf |
- 2.1.8.6. Other non-ideal Fourier p.d.f.'s (p. 208) | html | pdf |
- 2.1.8.7. Comparison of the correction-factor and Fourier approaches (pp. 208-209) | html | pdf |
- References | html | pdf |
- Figures
- Tables
- Table 2.1.3.1. Intensity-distribution effects of symmetry elements causing systematic absences (p. 191) | html | pdf |
- Table 2.1.3.2. Intensity-distribution effects of symmetry elements not causing systematic absences (p. 192) | html | pdf |
- Table 2.1.3.3. Average multiples for the 32 point groups (modified from Rogers, 1950). (p. 193) | html | pdf |
- Table 2.1.5.1. Some properties of gamma and beta distributions (p. 197) | html | pdf |
- Table 2.1.7.1. Some even absolute moments of the trigonometric structure factor (pp. 201-202) | html | pdf |
- Table 2.1.7.2. Closed expressions for [equation (2.1.7.11)] for space groups of low symmetry (p. 203) | html | pdf |
- Table 2.1.8.1. Atomic contributions to characteristic functions for (pp. 207-208) | html | pdf |