International Tables for Crystallography (2010). Vol. B. ch. 2.1, pp. 195-214
https://doi.org/10.1107/97809553602060000763 |
Chapter 2.1. Statistical properties of the weighted reciprocal lattice
Contents
- 2.1. Statistical properties of the weighted reciprocal lattice (pp. 195-214) | html | pdf | chapter contents |
- 2.1.1. Introduction (p. 195) | html | pdf |
- 2.1.2. The average intensity of general reflections (pp. 195-196) | html | pdf |
- 2.1.3. The average intensity of zones and rows (pp. 196-197) | html | pdf |
- 2.1.4. Probability density distributions – mathematical preliminaries (pp. 197-200) | html | pdf |
- 2.1.4.1. Characteristic functions (pp. 197-198) | html | pdf |
- 2.1.4.2. The cumulant-generating function (p. 198) | html | pdf |
- 2.1.4.3. The central-limit theorem (pp. 198-199) | html | pdf |
- 2.1.4.4. Conditions of validity (p. 199) | html | pdf |
- 2.1.4.5. Non-independent variables (pp. 199-200) | html | pdf |
- 2.1.5. Ideal probability density distributions (pp. 200-202) | html | pdf |
- 2.1.5.1. Ideal acentric distributions (p. 200) | html | pdf |
- 2.1.5.2. Ideal centric distributions (p. 200) | html | pdf |
- 2.1.5.3. Effect of other symmetry elements on the ideal acentric and centric distributions (pp. 200-201) | html | pdf |
- 2.1.5.4. Other ideal distributions (p. 201) | html | pdf |
- 2.1.5.5. Relation to distributions of I (p. 201) | html | pdf |
- 2.1.5.6. Cumulative distribution functions (pp. 201-202) | html | pdf |
- 2.1.6. Distributions of sums, averages and ratios (pp. 202-203) | html | pdf |
- 2.1.7. Non-ideal distributions: the correction-factor approach (pp. 203-207) | html | pdf |
- 2.1.8. Non-ideal distributions: the Fourier method (pp. 207-212) | html | pdf |
- 2.1.8.1. General representations of p.d.f.'s of by Fourier series (p. 208) | html | pdf |
- 2.1.8.2. Fourier–Bessel series (pp. 208-209) | html | pdf |
- 2.1.8.3. Simple examples (p. 209) | html | pdf |
- 2.1.8.4. A more complicated example (pp. 209-211) | html | pdf |
- 2.1.8.5. Atomic characteristic functions (pp. 211-212) | html | pdf |
- 2.1.8.6. Other non-ideal Fourier p.d.f.'s (p. 212) | html | pdf |
- 2.1.8.7. Comparison of the correction-factor and Fourier approaches (p. 212) | html | pdf |
- References | html | pdf |
- Figures
- Tables
- Table 2.1.3.1. Intensity-distribution effects of symmetry elements and centred lattices causing systematic absences (p. 196) | html | pdf |
- Table 2.1.3.2. Intensity-distribution effects of symmetry elements not causing systematic absences (p. 197) | html | pdf |
- Table 2.1.3.3. Average multiples for the 32 point groups (modified from Rogers, 1950) (p. 197) | html | pdf |
- Table 2.1.5.1. Some properties of gamma and beta distributions (p. 201) | html | pdf |
- Table 2.1.7.1. Some even absolute moments of the trigonometric structure factor (pp. 206-207) | html | pdf |
- Table 2.1.7.2. Closed expressions for [equation (2.1.7.11)] for space groups of low symmetry (p. 207) | html | pdf |
- Table 2.1.8.1. Atomic contributions to characteristic functions for (pp. 210-211) | html | pdf |