International Tables for Crystallography (2006). Vol. C, ch. 2.6, pp. 89-112
doi: 10.1107/97809553602060000581

Chapter 2.6. Small-angle techniques

Contents

  • 2.6. Small-angle techniques  (pp. 89-112) | html | pdf | chapter contents |
    • 2.6.1. X-ray techniques  (pp. 89-104) | html | pdf |
      • 2.6.1.1. Introduction  (pp. 89-90) | html | pdf |
      • 2.6.1.2. General principles  (pp. 90-91) | html | pdf |
      • 2.6.1.3. Monodisperse systems  (pp. 91-99) | html | pdf |
        • 2.6.1.3.1. Parameters of a particle  (pp. 91-93) | html | pdf |
        • 2.6.1.3.2. Shape and structure of particles  (pp. 93-97) | html | pdf |
          • 2.6.1.3.2.1. Homogeneous particles  (pp. 93-96) | html | pdf |
          • 2.6.1.3.2.2. Hollow and inhomogeneous particles  (pp. 96-97) | html | pdf |
        • 2.6.1.3.3. Interparticle interference, concentration effects  (pp. 97-99) | html | pdf |
      • 2.6.1.4. Polydisperse systems  (p. 99) | html | pdf |
      • 2.6.1.5. Instrumentation  (pp. 99-100) | html | pdf |
        • 2.6.1.5.1. Small-angle cameras  (pp. 99-100) | html | pdf |
        • 2.6.1.5.2. Detectors  (p. 100) | html | pdf |
      • 2.6.1.6. Data evaluation and interpretation  (pp. 100-103) | html | pdf |
        • 2.6.1.6.1. Primary data handling  (pp. 100-101) | html | pdf |
        • 2.6.1.6.2. Instrumental broadening – smearing  (p. 101) | html | pdf |
        • 2.6.1.6.3. Smoothing, desmearing, and Fourier transformation  (pp. 101-103) | html | pdf |
        • 2.6.1.6.4. Direct structure analysis  (p. 103) | html | pdf |
        • 2.6.1.6.5. Interpretation of results  (p. 103) | html | pdf |
      • 2.6.1.7. Simulations and model calculations  (pp. 103-104) | html | pdf |
        • 2.6.1.7.1. Simulations  (p. 103) | html | pdf |
        • 2.6.1.7.2. Model calculation  (p. 104) | html | pdf |
        • 2.6.1.7.3. Calculation of scattering intensities  (p. 104) | html | pdf |
        • 2.6.1.7.4. Method of finite elements  (p. 104) | html | pdf |
        • 2.6.1.7.5. Calculation of distance-distribution functions  (p. 104) | html | pdf |
      • 2.6.1.8. Suggestions for further reading  (p. 104) | html | pdf |
    • 2.6.2. Neutron techniques  (pp. 105-112) | html | pdf |
      • 2.6.2.1. Relation of X-ray and neutron small-angle scattering  (pp. 105-106) | html | pdf |
        • 2.6.2.1.1. Wavelength  (pp. 105-106) | html | pdf |
        • 2.6.2.1.2. Geometry  (p. 106) | html | pdf |
        • 2.6.2.1.3. Correction of wavelength, slit, and detector-element effects  (p. 106) | html | pdf |
      • 2.6.2.2. Isotopic composition of the sample  (pp. 106-107) | html | pdf |
        • 2.6.2.2.1. Contrast variation  (p. 107) | html | pdf |
        • 2.6.2.2.2. Specific isotopic labelling  (p. 107) | html | pdf |
      • 2.6.2.3. Magnetic properties of the neutron  (pp. 107-108) | html | pdf |
        • 2.6.2.3.1. Spin-contrast variation  (p. 108) | html | pdf |
      • 2.6.2.4. Long wavelengths  (p. 108) | html | pdf |
      • 2.6.2.5. Sample environment  (p. 108) | html | pdf |
      • 2.6.2.6. Incoherent scattering  (pp. 108-110) | html | pdf |
        • 2.6.2.6.1. Absolute scaling  (pp. 108-109) | html | pdf |
        • 2.6.2.6.2. Detector-response correction  (p. 109) | html | pdf |
        • 2.6.2.6.3. Estimation of the incoherent scattering level  (p. 109) | html | pdf |
        • 2.6.2.6.4. Inner surface area  (pp. 109-110) | html | pdf |
      • 2.6.2.7. Single-particle scattering  (pp. 110-112) | html | pdf |
        • 2.6.2.7.1. Particle shape  (p. 110) | html | pdf |
        • 2.6.2.7.2. Particle mass  (p. 110) | html | pdf |
        • 2.6.2.7.3. Real-space considerations  (pp. 110-111) | html | pdf |
        • 2.6.2.7.4. Particle-size distribution  (p. 111) | html | pdf |
        • 2.6.2.7.5. Model fitting  (p. 111) | html | pdf |
        • 2.6.2.7.6. Label triangulation  (p. 111) | html | pdf |
        • 2.6.2.7.7. Triple isotropic replacement  (pp. 111-112) | html | pdf |
      • 2.6.2.8. Dense systems  (p. 112) | html | pdf |
    • References | html | pdf |
    • Figures
      • Fig. 2.6.1.1. The height of the p ( r ) function for a certain value of r is proportional to the number of lines with a length between r and r + d r within the particle  (p. 91) | html | pdf |
      • Fig. 2.6.1.2. Comparison of the scattering functions of a sphere (dashed line) and a cube (continuous line) with same radius of gyration  (p. 94) | html | pdf |
      • Fig. 2.6.1.3. Distance distribution function of a sphere (dashed line) and a cube (continuous line) with the same radius of gyration and the same scattering intensity at zero angle  (p. 94) | html | pdf |
      • Fig. 2.6.1.4. Comparison of the p ( r ) function of a sphere (continuous line), a prolate ellipsoid of revolution 1:1:3 (dash-dotted line), and an oblate ellipsoid of revolution 1:1:0.2 (dashed line) with the same radius of gyration  (p. 94) | html | pdf |
      • Fig. 2.6.1.5. Comparison of the I ( h ) functions of a sphere, a prolate, and an oblate ellipsoid (see legend to Fig  (p. 94) | html | pdf |
      • Fig. 2.6.1.6. Distance distributions from homogeneous parallelepipeds with edge lengths of: ( a ) 50 × 50 × 500 Å; ( b ) 50 × 50 × 250 Å; ( c ) 50 × 50 × 150 Å  (p. 95) | html | pdf |
      • Fig. 2.6.1.7. Three parallelepipeds with constant length L (400 Å) and a constant cross section but varying length of the edges: continuous line 40 × 40 Å; dash-dotted line 80 × 20 Å; dashed line 160 × 10 Å  (p. 95) | html | pdf |
      • Fig. 2.6.1.8. Circular cylinder with a constant length of 480 Å and an outer diameter of 48 Å  (p. 96) | html | pdf |
      • Fig. 2.6.1.9. Inhomogeneous circular cylinder with periodical changes of the electron density along the cylinder axis compared with a homogeneous cylinder with the same mean electron density  (p. 97) | html | pdf |
      • Fig. 2.6.1.10. p ( r ) function of a lamellar particle  (p. 97) | html | pdf |
      • Fig. 2.6.1.11. Characteristic types of scattering functions: ( a ) gas type; ( b ) particle scattering; ( c ) liquid type  (p. 98) | html | pdf |
      • Fig. 2.6.1.12. Distance distribution – hard-sphere interference model  (p. 98) | html | pdf |
      • Fig. 2.6.1.13. Schematic drawing of the block collimation (Kratky camera): E edge; B 1 centre piece; B 2 bridge; P primary-beam profile; PS primary-beam stop; PR plane of registration  (p. 99) | html | pdf |
      • Fig. 2.6.1.14. Function systems ϕ v ( r ); Ψ v ( h ); and χ v ( h ) used for the approximation of the scattering data in the indirect transformation method  (p. 102) | html | pdf |
    • Tables
      • Table 2.6.1.1. Formulae for the various parameters for h (left) and m (right) scales  (p. 92) | html | pdf |