International Tables for Crystallography (2010). Vol. B, ch. 2.1, pp. 195-214   | 1 | 2 |
doi: 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 |
      • 2.1.2.1. Mathematical background  (pp. 195-196) | html | pdf |
      • 2.1.2.2. Physical background  (p. 196) | html | pdf |
      • 2.1.2.3. An approximation for organic compounds  (p. 196) | html | pdf |
      • 2.1.2.4. Effect of centring  (p. 196) | html | pdf |
    • 2.1.3. The average intensity of zones and rows  (pp. 196-197) | html | pdf |
      • 2.1.3.1. Symmetry elements producing systematic absences  (p. 196) | html | pdf |
      • 2.1.3.2. Symmetry elements not producing systematic absences  (pp. 196-197) | html | pdf |
      • 2.1.3.3. More than one symmetry element  (p. 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 |
      • 2.1.6.1. Distributions of sums and averages  (p. 202) | html | pdf |
      • 2.1.6.2. Distribution of ratios  (pp. 202-203) | html | pdf |
      • 2.1.6.3. Intensities scaled to the local average  (p. 203) | html | pdf |
      • 2.1.6.4. The use of normal approximations  (p. 203) | html | pdf |
    • 2.1.7. Non-ideal distributions: the correction-factor approach  (pp. 203-207) | html | pdf |
      • 2.1.7.1. Introduction  (pp. 203-204) | html | pdf |
      • 2.1.7.2. Mathematical background  (p. 204) | html | pdf |
      • 2.1.7.3. Application to centric and acentric distributions  (pp. 204-205) | html | pdf |
      • 2.1.7.4. Fourier versus Hermite approximations  (pp. 205-207) | 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 [|E|] 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
      • Fig. 2.1.7.1. Atomic heterogeneity and intensity statistics  (p. 204) | html | pdf |
      • Fig. 2.1.8.1. The same recalculated histogram as in Fig. 2.1.7.1 along with the centric correction-factor p.d.f  (p. 212) | html | pdf |
    • 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 [\gamma_{2k}] [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 [p(|E|)]   (pp. 210-211) | html | pdf |