(International Tables) Mathematical, physical and chemical tables

International Tables for Crystallography
Volume C: Mathematical, physical and chemical tables

First online edition (2006) ISBN: 978-1-4020-1900-5 doi: 10.1107/97809553602060000103

Edited by E. Prince

Preface to the third edition (p. xxxi) | html | pdf |
E. Prince

Crystal geometry and symmetry
- 1.1. Summary of general formulae (pp. 2-5) | html | pdf | chapter contents |
  E. Koch
  - 1.1.1. General relations between direct and reciprocal lattices (pp. 2-3) | html | pdf |
    - 1.1.1.1. Primitive crystallographic bases (pp. 2-3) | html | pdf |
    - 1.1.1.2. Non-primitive crystallographic bases (p. 3) | html | pdf |
  - 1.1.2. Lattice vectors, point rows, and net planes (pp. 3-4) | html | pdf |
  - 1.1.3. Angles in direct and reciprocal space (pp. 4-5) | html | pdf |
  - 1.1.4. The Miller formulae (p. 5) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.1.1.1. Direct and reciprocal lattices described with respect to conventional basis systems (p. 3) | html | pdf |
- 1.2. Application to the crystal systems (pp. 6-9) | html | pdf | chapter contents |
  E. Koch
  - 1.2.1. Triclinic crystal system (p. 6) | html | pdf |
  - 1.2.2. Monoclinic crystal system (p. 6) | html | pdf |
    - 1.2.2.1. Setting with `unique axis b' (p. 6) | html | pdf |
    - 1.2.2.2. Setting with `unique axis c' (p. 6) | html | pdf |
  - 1.2.3. Orthorhombic crystal system (pp. 6-7) | html | pdf |
  - 1.2.4. Tetragonal crystal system (p. 7) | html | pdf |
  - 1.2.5. Trigonal and hexagonal crystal system (pp. 7-9) | html | pdf |
    - 1.2.5.1. Description referred to hexagonal axes (pp. 7-8) | html | pdf |
    - 1.2.5.2. Description referred to rhombohedral axes (pp. 8-9) | html | pdf |
  - 1.2.6. Cubic crystal system (p. 9) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.2.4.1. Assignment of integers $[s\le 100]$ to pairs h, k with (p. 7) | html | pdf |
    - Table 1.2.5.1. Assignment of integers $[s\le100]$ to pairs h, k with (p. 8) | html | pdf |
    - Table 1.2.5.2. Assignment of integers $[s_1\le50]$ to triplets h, k, l with and to integers (p. 8) | html | pdf |
    - Table 1.2.6.1. Assignment of integers $[s\le 100]$ to triplets h, k, l with (p. 9) | html | pdf |
- 1.3. Twinning (pp. 10-14) | html | pdf | chapter contents |
  E. Koch
  - 1.3.1. General remarks (p. 10) | html | pdf |
  - 1.3.2. Twin lattices (pp. 10-12) | html | pdf |
    - 1.3.2.1. Examples (pp. 11-12) | html | pdf |
  - 1.3.3. Implication of twinning in reciprocal space (p. 12) | html | pdf |
  - 1.3.4. Twinning by merohedry (pp. 12-14) | html | pdf |
  - 1.3.5. Calculation of the twin element (p. 14) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.3.2.1. (a) Projection of the lattices of the twin components of a monoclinic twinned crystal (unique axis c, γ = 93°) with twin index 3 (p. 11) | html | pdf |
    - Fig. 1.3.2.2. Projection of the lattices of the twin components of an orthorhombic twinned crystal (oP, b = $[\sqrt3]$ a) with twin index 2 (p. 12) | html | pdf |
    - Fig. 1.3.2.3. Projection of the lattices of the twin components of an orthorhombic twinned crystal (oC, b = 2a) with twin index 4 (p. 12) | html | pdf |
  - Tables
    - Table 1.3.2.1. Lattice planes and rows that are perpendicular to each other independently of the metrical parameters (p. 11) | html | pdf |
    - Table 1.3.4.1. Possible twin operations for twins by merohedry (p. 13) | html | pdf |
    - Table 1.3.4.2. Simulated Laue classes, extinction symbols, simulated `possible space groups', and possible true space groups for crystals twinned by merohedry (type 2) (p. 13) | html | pdf |
- 1.4. Arithmetic crystal classes and symmorphic space groups (pp. 15-22) | html | pdf | chapter contents |
  A. J. C. Wilson
  - 1.4.1. Arithmetic crystal classes (pp. 15-19) | html | pdf |
    - 1.4.1.1. Arithmetic crystal classes in three dimensions (p. 15) | html | pdf |
    - 1.4.1.2. Arithmetic crystal classes in one, two and higher dimensions (p. 16) | html | pdf |
  - 1.4.2. Classification of space groups (pp. 20-21) | html | pdf |
    - 1.4.2.1. Symmorphic space groups (p. 21) | html | pdf |
  - 1.4.3. Effect of dispersion on diffraction symmetry (p. 21) | html | pdf |
    - 1.4.3.1. Symmetry of the Patterson function (p. 21) | html | pdf |
    - 1.4.3.2. `Laue' symmetry (p. 21) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 1.4.1.1. The two-dimensional arithmetic crystal classes (p. 15) | html | pdf |
    - Table 1.4.2.1. The three-dimensional space groups, arranged by arithmetic crystal class (pp. 16-19) | html | pdf |
    - Table 1.4.3.1. Arithmetic crystal classes classified by the number of space groups that they contain (p. 20) | html | pdf |

Diffraction geometry and its practical realization
- 2.1. Classification of experimental techniques (pp. 24-25) | html | pdf | chapter contents |
  J. R. Helliwell
  - References | html | pdf |
  - Tables
    - Table 2.1.1. Summary of main experimental techniques for structure analysis (p. 25) | html | pdf |
- 2.2. Single-crystal X-ray techniques (pp. 26-41) | html | pdf | chapter contents |
  J. R. Helliwell
  - 2.2.1. Laue geometry (pp. 26-29) | html | pdf |
    - 2.2.1.1. General (pp. 26-27) | html | pdf |
    - 2.2.1.2. Crystal setting (p. 27) | html | pdf |
    - 2.2.1.3. Single-order and multiple-order reflections (pp. 27-29) | html | pdf |
    - 2.2.1.4. Angular distribution of reflections in Laue diffraction (p. 29) | html | pdf |
    - 2.2.1.5. Gnomonic and stereographic transformations (p. 29) | html | pdf |
  - 2.2.2. Monochromatic methods (pp. 29-30) | html | pdf |
    - 2.2.2.1. Monochromatic still exposure (p. 30) | html | pdf |
    - 2.2.2.2. Crystal setting (p. 30) | html | pdf |
  - 2.2.3. Rotation/oscillation geometry (pp. 31-34) | html | pdf |
    - 2.2.3.1. General (p. 31) | html | pdf |
    - 2.2.3.2. Diffraction coordinates (pp. 31-33) | html | pdf |
    - 2.2.3.3. Relationship of reciprocal-lattice coordinates to crystal system parameters (p. 33) | html | pdf |
    - 2.2.3.4. Maximum oscillation angle without spot overlap (pp. 33-34) | html | pdf |
    - 2.2.3.5. Blind region (p. 34) | html | pdf |
  - 2.2.4. Weissenberg geometry (pp. 34-35) | html | pdf |
    - 2.2.4.1. General (p. 34) | html | pdf |
    - 2.2.4.2. Recording of zero layer (p. 34) | html | pdf |
    - 2.2.4.3. Recording of upper layers (pp. 34-35) | html | pdf |
  - 2.2.5. Precession geometry (pp. 35-36) | html | pdf |
    - 2.2.5.1. General (p. 35) | html | pdf |
    - 2.2.5.2. Crystal setting (p. 35) | html | pdf |
    - 2.2.5.3. Recording of zero-layer photograph (p. 35) | html | pdf |
    - 2.2.5.4. Recording of upper-layer photographs (pp. 35-36) | html | pdf |
    - 2.2.5.5. Recording of cone-axis photograph (p. 36) | html | pdf |
  - 2.2.6. Diffractometry (pp. 36-37) | html | pdf |
    - 2.2.6.1. General (p. 36) | html | pdf |
    - 2.2.6.2. Normal-beam equatorial geometry (pp. 36-37) | html | pdf |
    - 2.2.6.3. Fixed χ = 45° geometry with area detector (p. 37) | html | pdf |
  - 2.2.7. Practical realization of diffraction geometry: sources, optics, and detectors (pp. 37-41) | html | pdf |
    - 2.2.7.1. General (p. 37) | html | pdf |
    - 2.2.7.2. Conventional X-ray sources: spectral character, crystal rocking curve, and spot size (pp. 37-38) | html | pdf |
    - 2.2.7.3. Synchrotron X-ray sources (pp. 38-41) | html | pdf |
    - 2.2.7.4. Geometric effects and distortions associated with area detectors (p. 41) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.2.1.1. Laue geometry (p. 27) | html | pdf |
    - Fig. 2.2.1.2. A predicted Laue pattern of a protein crystal with a zone axis parallel to the incident, polychromatic X-ray beam (p. 27) | html | pdf |
    - Fig. 2.2.1.3. A multiple component spot in Laue geometry (p. 28) | html | pdf |
    - Fig. 2.2.1.4. The variation with M = λ_max/λ_min of the proportions of relp's lying on single, double, and triple rays for the case $[\lambda_{\rm max} \lt 2/d^*_{\rm max}]$ (p. 28) | html | pdf |
    - Fig. 2.2.1.5. Geometrical principles of the spherical, stereographic, gnomonic, and Laue projections (p. 29) | html | pdf |
    - Fig. 2.2.3.1. (a) Elevation of the sphere of reflection (p. 30) | html | pdf |
    - Fig. 2.2.3.2. Geometrical principles of recording the pattern on (a) a plane detector, (b) a V-shaped detector, (c) a cylindrical detector (p. 31) | html | pdf |
    - Fig. 2.2.3.3. The rotation method. Definition of coordinate systems (p. 32) | html | pdf |
    - Fig. 2.2.3.4. The rotation method. The blind region associated with a single rotation axis (p. 33) | html | pdf |
    - Fig. 2.2.5.1. The screenless precession setting photograph (schematic) and associated mis-setting angles for a typical orientation error when the crystal has been set previously by a monochromatic still or Laue (p. 35) | html | pdf |
    - Fig. 2.2.6.1. Normal-beam equatorial geometry: the angles ω, χ, φ, 2θ are drawn in the convention of Hamilton (1974) (p. 36) | html | pdf |
    - Fig. 2.2.6.2. Diffractometry with normal-beam equatorial geometry and angular motions ω, χ and φ (p. 36) | html | pdf |
    - Fig. 2.2.7.1. Reflection rocking width for a conventional X-ray source (p. 38) | html | pdf |
    - Fig. 2.2.7.2. Single-crystal monochromator illuminated by synchrotron radiation: (a) flat crystal, (b) Guinier setting, (c) overbent crystal, (d) effect of source size (shown at the Guinier setting for clarity) (p. 39) | html | pdf |
    - Fig. 2.2.7.3. Double-crystal monochromator illuminated by synchrotron radiation (p. 40) | html | pdf |
    - Fig. 2.2.7.4. The rocking width of an individual reflection for the case of Fig. 2.2.7.2(c) and a vertical rotation axis (p. 40) | html | pdf |
  - Tables
    - Table 2.2.3.1. Glossary of symbols used to specify quantities on diffraction patterns and in reciprocal space (p. 32) | html | pdf |
    - Table 2.2.5.1. The distance displacement (in mm) measured on the film versus angular setting error of the crystal for a screenless precession ( $[\bar\mu=5^\circ]$ ) setting photograph (p. 35) | html | pdf |
- 2.3. Powder and related techniques: X-ray techniques (pp. 42-79) | html | pdf | chapter contents |
  W. Parrish and J. I. Langford
  - 2.3.1. Focusing diffractometer geometries (pp. 43-54) | html | pdf |
    - 2.3.1.1. Conventional reflection specimen, θ–2θ scan (pp. 44-50) | html | pdf |
      - 2.3.1.1.1. Geometrical instrument parameters (pp. 44-46) | html | pdf |
      - 2.3.1.1.2. Use of monochromators (p. 46) | html | pdf |
      - 2.3.1.1.3. Alignment and angular calibration (pp. 46-47) | html | pdf |
      - 2.3.1.1.4. Instrument broadening and aberrations (pp. 47-48) | html | pdf |
      - 2.3.1.1.5. Focal line and receiving-slit widths (p. 48) | html | pdf |
      - 2.3.1.1.6. Aberrations related to the specimen (pp. 48-49) | html | pdf |
      - 2.3.1.1.7. Axial divergence (p. 50) | html | pdf |
      - 2.3.1.1.8. Combined aberrations (p. 50) | html | pdf |
    - 2.3.1.2. Transmission specimen, θ–2θ scan (pp. 50-52) | html | pdf |
    - 2.3.1.3. Seemann–Bohlin method (pp. 52-53) | html | pdf |
    - 2.3.1.4. Reflection specimen, θ–θ scan (p. 53) | html | pdf |
    - 2.3.1.5. Microdiffractometry (pp. 53-54) | html | pdf |
  - 2.3.2. Parallel-beam geometries, synchrotron radiation (pp. 54-60) | html | pdf |
    - 2.3.2.1. Monochromatic radiation, θ–2θ scan (pp. 55-57) | html | pdf |
    - 2.3.2.2. Cylindrical specimen, 2θ scan (pp. 57-58) | html | pdf |
    - 2.3.2.3. Grazing-incidence diffraction (p. 58) | html | pdf |
    - 2.3.2.4. High-resolution energy-dispersive diffraction (pp. 58-60) | html | pdf |
  - 2.3.3. Specimen factors, angle, intensity, and profile-shape measurement (pp. 60-69) | html | pdf |
    - 2.3.3.1. Specimen factors (pp. 60-62) | html | pdf |
      - 2.3.3.1.1. Preferred orientation (pp. 60-61) | html | pdf |
      - 2.3.3.1.2. Crystallite-size effects (p. 62) | html | pdf |
    - 2.3.3.2. Problems arising from the Kα doublet (pp. 62-63) | html | pdf |
    - 2.3.3.3. Use of peak or centroid for angle definition (p. 63) | html | pdf |
    - 2.3.3.4. Rate-meter/strip-chart recording (p. 63) | html | pdf |
    - 2.3.3.5. Computer-controlled automation (pp. 63-64) | html | pdf |
    - 2.3.3.6. Counting statistics (pp. 64-65) | html | pdf |
    - 2.3.3.7. Peak search (pp. 65-66) | html | pdf |
    - 2.3.3.8. Profile fitting (pp. 66-69) | html | pdf |
    - 2.3.3.9. Computer graphics for powder patterns (p. 69) | html | pdf |
  - 2.3.4. Powder cameras (pp. 70-71) | html | pdf |
    - 2.3.4.1. Cylindrical cameras (Debye–Scherrer) (p. 70) | html | pdf |
    - 2.3.4.2. Focusing cameras (Guinier) (pp. 70-71) | html | pdf |
    - 2.3.4.3. Miscellaneous camera types (p. 71) | html | pdf |
  - 2.3.5. Generation, modifications, and measurement of X-ray spectra (pp. 71-79) | html | pdf |
    - 2.3.5.1. X-ray tubes (pp. 71-74) | html | pdf |
      - 2.3.5.1.1. Stability (p. 72) | html | pdf |
      - 2.3.5.1.2. Spectral purity (p. 72) | html | pdf |
      - 2.3.5.1.3. Source intensity distribution and size (p. 73) | html | pdf |
      - 2.3.5.1.4. Air and window transmission (pp. 73-74) | html | pdf |
      - 2.3.5.1.5. Intensity variation with take-off angle (p. 74) | html | pdf |
    - 2.3.5.2. X-ray spectra (pp. 74-75) | html | pdf |
      - 2.3.5.2.1. Wavelength selection (p. 75) | html | pdf |
    - 2.3.5.3. Other X-ray sources (p. 75) | html | pdf |
    - 2.3.5.4. Methods for modifying the spectrum (pp. 75-79) | html | pdf |
      - 2.3.5.4.1. Crystal monochromators (pp. 76-78) | html | pdf |
      - 2.3.5.4.2. Single and balanced filters (pp. 78-79) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.3.1.1. Basic arrangements of focusing diffractometer methods (p. 43) | html | pdf |
    - Fig. 2.3.1.2. Specimen orientation for three diffractometer geometries (p. 44) | html | pdf |
    - Fig. 2.3.1.3. X-ray optics in the focusing plane of a `conventional' diffractometer with reflection specimen, diffracted-beam monochromator, and θ–2θ scanning (p. 44) | html | pdf |
    - Fig. 2.3.1.4. Length of specimen irradiated, S_l, as a function of 2θ for various angular apertures (p. 45) | html | pdf |
    - Fig. 2.3.1.5. Slit designs made with (a) rods, (b) bars, and (c) machined from single piece (p. 45) | html | pdf |
    - Fig. 2.3.1.6. Zero-angle calibration (p. 46) | html | pdf |
    - Fig. 2.3.1.7. (a) θ–2θ setting at 0° (p. 47) | html | pdf |
    - Fig. 2.3.1.8. Diffractometer profiles (p. 48) | html | pdf |
    - Fig. 2.3.1.9. (a) Effect of source size on profile shape, Cu Kα, α_ES 1°, α_RS 0.05°, Si(111) (p. 49) | html | pdf |
    - Fig. 2.3.1.10. (a) Origin of specimen-related aberrations in focusing plane of conventional reflection specimen diffractometer (Fig. 2.3.1.3) (p. 50) | html | pdf |
    - Fig. 2.3.1.11. Effect of axial divergence on profile shape (p. 50) | html | pdf |
    - Fig. 2.3.1.12. X-ray optics of the transmission specimen with asymmetric focusing monochromator and θ–2θ scanning (p. 51) | html | pdf |
    - Fig. 2.3.1.13. Seemann–Bohlin method (p. 52) | html | pdf |
    - Fig. 2.3.1.14. Optics of θ–θ scanning diffractometer (p. 53) | html | pdf |
    - Fig. 2.3.1.15. Rigaku microdiffractometer for microanalysis (p. 54) | html | pdf |
    - Fig. 2.3.2.1. Method to obtain parallel beam from X-ray tube for powder diffraction (p. 54) | html | pdf |
    - Fig. 2.3.2.2. Silicon powder pattern with 1 Å synchrotron radiation using method shown in Fig. 2.3.2.4(a) (p. 54) | html | pdf |
    - Fig. 2.3.2.3. Synchrotron-radiation patterns of a mixture of Ni and ZnO powders (p. 55) | html | pdf |
    - Fig. 2.3.2.4. (a) Optics of dispersive parallel-beam method for synchrotron X-rays (p. 56) | html | pdf |
    - Fig. 2.3.2.5. Comparison of patterns obtained with a conventional focusing diffractometer (a) and (c), and synchrotron parallel-beam method (b) and (d) (p. 57) | html | pdf |
    - Fig. 2.3.2.6. (a) and (c) Fourier maps of orthorhombic Mg₂GeO₄ calculated directly from profile-fitted synchrotron powder data (p. 57) | html | pdf |
    - Fig. 2.3.2.7. Penetration depth t' as a function of grazing-incidence angle α for γ-Fe₂O₃ thin film (p. 58) | html | pdf |
    - Fig. 2.3.2.8. Synchrotron diffraction patterns of annealed 5000 Å iron oxide film, λ = 1.75 Å (p. 58) | html | pdf |
    - Fig. 2.3.2.9. (a)–(d) High-resolution energy-dispersive diffraction patterns of quartz powder sample obtained with 2θ settings shown in upper left corners (p. 59) | html | pdf |
    - Fig. 2.3.2.10. Specimen orientation for symmetric reflection (a) from (hkl) planes and (b) specimen rotated θ_r for symmetric reflection from (pqr) planes (p. 59) | html | pdf |
    - Fig. 2.3.3.1. Differences in relative intensities due to preferred orientation as seen in synchrotron X-ray patterns of m-chlorobenzoic acid obtained with a specimen in reflection and transmission compared with calculated pattern (p. 61) | html | pdf |
    - Fig. 2.3.3.2. Effect of specimen rotation and particle size on Si powder intensity using a conventional diffractometer (Fig. 2.3.1.3) and Cu Kα (p. 62) | html | pdf |
    - Fig. 2.3.3.3. Various measures of profile (p. 62) | html | pdf |
    - Fig. 2.3.3.4. Rate-meter strip-chart recordings (p. 63) | html | pdf |
    - Fig. 2.3.3.5. Fig (p. 64) | html | pdf |
    - Fig. 2.3.3.6. Percentage error as a function of the total number of counts N for several confidence levels (p. 64) | html | pdf |
    - Fig. 2.3.3.7. Effect of 4σ maximum peak height (horizontal line) on dropping weak peaks from inclusion in computer calculation (p. 65) | html | pdf |
    - Fig. 2.3.3.8. (a) Si(220) Cu Kα reflection (p. 66) | html | pdf |
    - Fig. 2.3.3.9. (a) Computer-generated symmetrical Lorentzian profile L and Gaussian G with equal peak heights, 2θ and FWHM (p. 66) | html | pdf |
    - Fig. 2.3.3.10. Profile fitting with sum-of-Lorentzians method (p. 68) | html | pdf |
    - Fig. 2.3.3.11. Profile fitting of poor statistical data (p. 69) | html | pdf |
    - Fig. 2.3.3.12. Some examples of computer graphics of powder patterns (p. 69) | html | pdf |
    - Fig. 2.3.4.1. Powder-camera geometries (p. 70) | html | pdf |
    - Fig. 2.3.5.1. Sealed X-ray diffraction tube (Philips), dimensions are given in mm (p. 71) | html | pdf |
    - Fig. 2.3.5.2. (a) Transmission of Be, Al and air as a function of wavelength (p. 73) | html | pdf |
    - Fig. 2.3.5.3. X-ray spectrum of copper target tube with Be window, 50 kV constant potential, 12° take-off angle (p. 75) | html | pdf |
    - Fig. 2.3.5.4. (a) Continuous X-ray spectrum of tungsten target X-ray tube as a function of voltage and constant current (p. 76) | html | pdf |
    - Fig. 2.3.5.5. Portion of diffractometer pattern of topaz showing effect of increasing dispersion on separation of peaks (p. 76) | html | pdf |
    - Fig. 2.3.5.6. Crystal monochromators most frequently used in powder diffraction (p. 77) | html | pdf |
  - Tables
    - Table 2.3.3.1. Preferred-orientation data for silicon (p. 61) | html | pdf |
    - Table 2.3.3.2. R(Bragg) values obtained with different preferred-orientation formulae (p. 61) | html | pdf |
    - Table 2.3.5.1. X-ray tube maximum ratings (p. 72) | html | pdf |
    - Table 2.3.5.2. β filters for common target elements (p. 78) | html | pdf |
    - Table 2.3.5.3. Calculated thickness of balanced filters for common target elements (p. 79) | html | pdf |
- 2.4. Powder and related techniques: electron and neutron techniques (pp. 80-83) | html | pdf | chapter contents |
  J. M. Cowley and A. W. Hewat
  - 2.4.1. Electron techniques (pp. 80-82) | html | pdf |
    J. M. Cowley
    - 2.4.1.1. Powder-pattern geometry (p. 80) | html | pdf |
    - 2.4.1.2. Diffraction patterns in electron microscopes (p. 80) | html | pdf |
    - 2.4.1.3. Preferred orientations (p. 80) | html | pdf |
    - 2.4.1.4. Powder-pattern intensities (pp. 80-81) | html | pdf |
    - 2.4.1.5. Crystal-size analysis (p. 81) | html | pdf |
    - 2.4.1.6. Unknown-phase identification: databases (pp. 81-82) | html | pdf |
  - 2.4.2. Neutron techniques (pp. 82-83) | html | pdf |
    A. W. Hewat
  - References | html | pdf |
  - Figures
    - Fig. 2.4.2.1. Schematic drawing of the high-resolution neutron powder diffractometer D2B at ILL, Grenoble (p. 82) | html | pdf |
- 2.5. Energy-dispersive techniques (pp. 84-88) | html | pdf | chapter contents |
  B. Buras, W. I. F. David, L. Gerward, J. D. Jorgensen and B. T. M. Willis
  - 2.5.1. Techniques for X-rays (pp. 84-87) | html | pdf |
    B. Buras and L. Gerward
    - 2.5.1.1. Recording of powder diffraction spectra (p. 84) | html | pdf |
    - 2.5.1.2. Incident X-ray beam (p. 84) | html | pdf |
    - 2.5.1.3. Resolution (p. 85) | html | pdf |
    - 2.5.1.4. Integrated intensity for powder sample (pp. 85-86) | html | pdf |
    - 2.5.1.5. Corrections (p. 86) | html | pdf |
    - 2.5.1.6. The Rietveld method (p. 86) | html | pdf |
    - 2.5.1.7. Single-crystal diffraction (p. 86) | html | pdf |
    - 2.5.1.8. Applications (pp. 86-87) | html | pdf |
  - 2.5.2. White-beam and time-of-flight neutron diffraction (pp. 87-88) | html | pdf |
    J. D. Jorgensen, W. I. F. David and B. T. M. Willis
    - 2.5.2.1. Neutron single-crystal Laue diffraction (p. 87) | html | pdf |
    - 2.5.2.2. Neutron time-of-flight powder diffraction (pp. 87-88) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.5.1.1. Standard and conical diffraction geometries: 2θ₀ = fixed scattering angle (p. 84) | html | pdf |
    - Fig. 2.5.1.2. XED powder spectrum of BaTiO₃ recorded with synchrotron radiation from the electron storage ring DORIS at DESY-HASYLAB in Hamburg, Germany (p. 84) | html | pdf |
    - Fig. 2.5.1.3. Relative resolution, $[\delta E/E]$ , as function of Bragg angle, $[\theta_0]$ , for two values of the lattice plane spacing: (a) 1 Å and (b) 0.5 Å (p. 85) | html | pdf |
    - Fig. 2.5.2.1. Construction in reciprocal space to illustrate the use of multi-wavelength radiation in single-crystal diffraction (p. 87) | html | pdf |
- 2.6. Small-angle techniques (pp. 89-112) | html | pdf | chapter contents |
  O. Glatter and R. May
  - 2.6.1. X-ray techniques (pp. 89-104) | html | pdf |
    O. Glatter
    - 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 |
    R. May
    - 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 + dr 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; B₁ centre piece; B₂ 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 |
- 2.7. Topography (pp. 113-123) | html | pdf | chapter contents |
  A. R. Lang
  - 2.7.1. Principles (pp. 113-114) | html | pdf |
  - 2.7.2. Single-crystal techniques (pp. 114-117) | html | pdf |
    - 2.7.2.1. Reflection topographs (pp. 114-115) | html | pdf |
    - 2.7.2.2. Transmission topographs (pp. 115-117) | html | pdf |
  - 2.7.3. Double-crystal topography (pp. 117-119) | html | pdf |
  - 2.7.4. Developments with synchrotron radiation (pp. 119-121) | html | pdf |
    - 2.7.4.1. White-radiation topography (pp. 119-120) | html | pdf |
    - 2.7.4.2. Incident-beam monochromatization (pp. 120-121) | html | pdf |
  - 2.7.5. Some special techniques (pp. 121-123) | html | pdf |
    - 2.7.5.1. Moiré topography (pp. 121-122) | html | pdf |
    - 2.7.5.2. Real-time viewing of topograph images (pp. 122-123) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.7.1.1. Surface reflection topography with a point source of diverging continuous radiation (p. 113) | html | pdf |
    - Fig. 2.7.1.2. Transmission topography with a point source of diverging continuous radiation (p. 113) | html | pdf |
    - Fig. 2.7.1.3. Differentiation between orientation contrast and diffraction contrast in types of topograph images, (b)–(e), of a crystal surface (a) (p. 114) | html | pdf |
    - Fig. 2.7.2.1. Berg–Barrett arrangement for surface-reflection topographs (p. 114) | html | pdf |
    - Fig. 2.7.2.2. Arrangements for section topographs and projection topographs (p. 115) | html | pdf |
    - Fig. 2.7.2.3. Arrangements for limited projection topographs and direct-beam topographs (p. 116) | html | pdf |
    - Fig. 2.7.2.4. Topographic techniques using anomalous transmission (p. 117) | html | pdf |
    - Fig. 2.7.3.1. Double-crystal + + setting (p. 117) | html | pdf |
    - Fig. 2.7.3.2. Du Mond diagram for + + setting in Fig. 2.7.3.1 (p. 117) | html | pdf |
    - Fig. 2.7.3.3. Double-crystal topographic arrangement, + − setting (p. 118) | html | pdf |
    - Fig. 2.7.3.4. Du Mond diagrams for + − setting in Fig. 2.7.3.3 (p. 118) | html | pdf |
    - Fig. 2.7.3.5. Transmission double-crystal topography in + − setting with spatial limitation of beam leaving reference crystal (p. 119) | html | pdf |
    - Fig. 2.7.4.1. Monolithic multiply reflecting monochromator for plane-wave topography (p. 121) | html | pdf |
    - Fig. 2.7.5.1. Scanning arrangement for moiré topography with the Bonse–Hart interferometer (p. 122) | html | pdf |
    - Fig. 2.7.5.2. Superposition of crystals (1) and (2) for production of moiré topographs (p. 122) | html | pdf |
  - Tables
    - Table 2.7.4.1. Monolithic monochromator for plane-wave synchrotron-radiation topography (p. 121) | html | pdf |
- 2.8. Neutron diffraction topography (pp. 124-125) | html | pdf | chapter contents |
  M. Schlenker and J. Baruchel
  - 2.8.1. Introduction (p. 124) | html | pdf |
  - 2.8.2. Implementation (p. 124) | html | pdf |
  - 2.8.3. Application to investigations of heavy crystals (p. 124) | html | pdf |
  - 2.8.4. Investigation of magnetic domains and magnetic phase transitions (pp. 124-125) | html | pdf |
  - References | html | pdf |
- 2.9. Neutron reflectometry (pp. 126-146) | html | pdf | chapter contents |
  G. S. Smith and C. F. Majkrzak
  - 2.9.1. Introduction (p. 126) | html | pdf |
  - 2.9.2. Theory of elastic specular neutron reflection (pp. 126-127) | html | pdf |
  - 2.9.3. Polarized neutron reflectivity (p. 127) | html | pdf |
  - 2.9.4. Surface roughness (p. 128) | html | pdf |
  - 2.9.5. Experimental methodology (pp. 128-129) | html | pdf |
  - 2.9.6. Resolution in real space (p. 129) | html | pdf |
  - 2.9.7. Applications of neutron reflectometry (pp. 129-130) | html | pdf |
    - 2.9.7.1. Self-diffusion (pp. 129-130) | html | pdf |
    - 2.9.7.2. Magnetic multilayers (p. 130) | html | pdf |
    - 2.9.7.3. Hydrogenous materials (p. 130) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.9.2.1. Schematic diagram of reflection geometry (p. 126) | html | pdf |
    - Fig. 2.9.2.2. Arbitrary scattering density profile represented by slabs of uniform potential (p. 127) | html | pdf |
    - Fig. 2.9.2.3. Neutron reflectivities calculated for an infinite Si substrate (dashed line) and 1000 Å Ni film on an Si substrate (solid line) (p. 127) | html | pdf |
    - Fig. 2.9.6.1. Calculated neutron reflectivity curves corresponding to the three density profiles in the inset (p. 128) | html | pdf |
    - Fig. 2.9.7.1. Measured neutron reflectivities from boron bilayers (p. 128) | html | pdf |
    - Fig. 2.9.7.2. The fitted real part of the scattering density profiles for the measured reflectivities of Fig. 2.9.7.1 (p. 128) | html | pdf |
    - Fig. 2.9.7.3. Co/Cu(111) spin-dependent reflectivities (top) (p. 129) | html | pdf |
    - Fig. 2.9.7.4. (a) Measured neutron reflectivity for the Langmuir–Blodgett multilayer described in the text along with the fit (p. 129) | html | pdf |

Preparation and examination of specimens
- 3.1. Preparation, selection, and investigation of specimens (pp. 148-155) | html | pdf | chapter contents |
  P. F. Lindley
  - 3.1.1. Crystallization (pp. 148-151) | html | pdf |
    - 3.1.1.1. Introduction (p. 148) | html | pdf |
    - 3.1.1.2. Crystal growth (p. 148) | html | pdf |
    - 3.1.1.3. Methods of growing crystals (p. 148) | html | pdf |
    - 3.1.1.4. Factors affecting the solubility of biological macromolecules (pp. 148-150) | html | pdf |
    - 3.1.1.5. Screening procedures for the crystallization of biological macromolecules (p. 150) | html | pdf |
    - 3.1.1.6. Automated protein crystallization (p. 150) | html | pdf |
    - 3.1.1.7. Membrane proteins (pp. 150-151) | html | pdf |
  - 3.1.2. Selection of single crystals (pp. 151-155) | html | pdf |
    - 3.1.2.1. Introduction (p. 151) | html | pdf |
    - 3.1.2.2. Size, shape, and quality (pp. 151-154) | html | pdf |
    - 3.1.2.3. Optical examination [see IT A (2002), Section 10.2.4 ] (pp. 154-155) | html | pdf |
    - 3.1.2.4. Twinning (see Chapter 1.3 ) (p. 155) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 3.1.1.1. Survey of crystallization techniques suitable for the crystallization of low-molecular-weight organic compounds for X-ray crystallography (p. 149) | html | pdf |
    - Table 3.1.1.2. Commonly used ionic and organic precipitants (p. 150) | html | pdf |
    - Table 3.1.1.3. Crystallization matrix parameters for sparse-matrix sampling (p. 151) | html | pdf |
    - Table 3.1.1.4. Reservoir solutions for sparse-matrix sampling (p. 152) | html | pdf |
    - Table 3.1.2.1. Use of crystal properties for selection and preliminary study of crystals (pp. 153-154) | html | pdf |
- 3.2. Determination of the density of solids (pp. 156-159) | html | pdf | chapter contents |
  F. M. Richards and P. F. Lindley
  - 3.2.1. Introduction (p. 156) | html | pdf |
    P. F. Lindley
    - 3.2.1.1. General precautions (p. 156) | html | pdf |
  - 3.2.2. Description and discussion of techniques (pp. 156-159) | html | pdf |
    F. M. Richards
    - 3.2.2.1. Gradient tube (pp. 156-158) | html | pdf |
      - 3.2.2.1.1. Technique (pp. 156-157) | html | pdf |
      - 3.2.2.1.2. Suitable substances for columns (pp. 157-158) | html | pdf |
      - 3.2.2.1.3. Sensitivity (p. 158) | html | pdf |
    - 3.2.2.2. Flotation method (p. 158) | html | pdf |
    - 3.2.2.3. Pycnometry (p. 158) | html | pdf |
    - 3.2.2.4. Method of Archimedes (p. 158) | html | pdf |
    - 3.2.2.5. Immersion microbalance (p. 158) | html | pdf |
    - 3.2.2.6. Volumenometry (p. 158) | html | pdf |
    - 3.2.2.7. Other procedures (pp. 158-159) | html | pdf |
  - 3.2.3. Biological macromolecules (p. 159) | html | pdf |
    P. F. Lindley
  - References | html | pdf |
  - Figures
    - Fig. 3.2.2.1. Nomogram for the preparation of bromobenzene–xylene gradient column components at room temperature (p. 157) | html | pdf |
  - Tables
    - Table 3.2.2.1. Possible substances for use as gradient-column components (p. 157) | html | pdf |
    - Table 3.2.3.1. Typical calculations of the values of V_M and V_solv for proteins (p. 159) | html | pdf |
- 3.3. Measurement of refractive index (pp. 160-161) | html | pdf | chapter contents |
  E. S. Larsen Jr, R. Meyrowitz and A. J. C. Wilson
  - 3.3.1. Introduction (p. 160) | html | pdf |
  - 3.3.2. Media for general use (p. 160) | html | pdf |
  - 3.3.3. High-index media (pp. 160-161) | html | pdf |
  - 3.3.4. Media for organic substances (p. 161) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 3.3.2.1. Immersion media for general use in the measurement of index of refraction (p. 160) | html | pdf |
    - Table 3.3.4.1. Aqueous solutions for use as immersion media for organic crystals (p. 160) | html | pdf |
    - Table 3.3.4.2. Organic immersion media for use with organic crystals of low solubility (p. 160) | html | pdf |
- 3.4. Mounting and setting of specimens for X-ray crystallographic studies (pp. 162-170) | html | pdf | chapter contents |
  P. F. Lindley
  - 3.4.1. Mounting of specimens (pp. 162-167) | html | pdf |
    - 3.4.1.1. Introduction (p. 162) | html | pdf |
    - 3.4.1.2. Polycrystalline specimens (pp. 162-163) | html | pdf |
      - 3.4.1.2.1. General (p. 162) | html | pdf |
      - 3.4.1.2.2. Non-ambient conditions (pp. 162-163) | html | pdf |
    - 3.4.1.3. Single crystals (small molecules) (pp. 163-165) | html | pdf |
      - 3.4.1.3.1. General (pp. 163-164) | html | pdf |
      - 3.4.1.3.2. Non-ambient conditions (pp. 164-165) | html | pdf |
    - 3.4.1.4. Single crystals of biological macromolecules at ambient temperatures (pp. 165-166) | html | pdf |
    - 3.4.1.5. Cryogenic studies of biological macromolecules (pp. 166-167) | html | pdf |
      - 3.4.1.5.1. Radiation damage (p. 166) | html | pdf |
      - 3.4.1.5.2. Cryoprotectants (p. 166) | html | pdf |
      - 3.4.1.5.3. Crystal mounting and cooling (pp. 166-167) | html | pdf |
      - 3.4.1.5.4. Cooling devices (p. 167) | html | pdf |
      - 3.4.1.5.5. General (p. 167) | html | pdf |
  - 3.4.2. Setting of single crystals by X-rays (pp. 167-170) | html | pdf |
    - 3.4.2.1. Introduction (pp. 167-168) | html | pdf |
    - 3.4.2.2. Preliminary considerations (p. 168) | html | pdf |
    - 3.4.2.3. Equatorial setting using a rotation camera (p. 168) | html | pdf |
    - 3.4.2.4. Precession geometry setting with moving-crystal methods (p. 168) | html | pdf |
    - 3.4.2.5. Setting and orientation with stationary-crystal methods (p. 169) | html | pdf |
      - 3.4.2.5.1. Laue images – white radiation (p. 169) | html | pdf |
      - 3.4.2.5.2. `Still' images – monochromatic radiation (p. 169) | html | pdf |
    - 3.4.2.6. Setting and orientation for crystals with large unit cells using oscillation geometry (pp. 169-170) | html | pdf |
    - 3.4.2.7. Diffractometer-setting considerations (p. 170) | html | pdf |
    - 3.4.2.8. Crystal setting and data-collection efficiency (p. 170) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 3.4.2.1. A zero-layer reciprocal-lattice plane will record on a flat-plate detector placed at a distance D from the crystal C as an ellipsoid of maximum dimension S from the direct-beam position O′ (p. 169) | html | pdf |
  - Tables
    - Table 3.4.1.1. Single-crystal and powder mounting, capillary tubes and other containers (p. 163) | html | pdf |
    - Table 3.4.1.2. Single-crystal mounting – adhesives (p. 164) | html | pdf |
    - Table 3.4.1.3. Cryoprotectants commonly used for biological macromolecules (p. 166) | html | pdf |
- 3.5. Preparation of specimens for electron diffraction and electron microscopy (pp. 171-176) | html | pdf | chapter contents |
  N. J. Tighe, J. R. Fryer and H. M. Flower
  - 3.5.1. Ceramics and rock minerals (pp. 171-173) | html | pdf |
    - 3.5.1.1. Thin fragments, particles, and flakes (p. 171) | html | pdf |
    - 3.5.1.2. Thin-section preparation (pp. 171-172) | html | pdf |
    - 3.5.1.3. Final thinning by argon-ion etching (pp. 172-173) | html | pdf |
    - 3.5.1.4. Final thinning by chemical etching (p. 173) | html | pdf |
    - 3.5.1.5. Evaporated and sputtered thin films (p. 173) | html | pdf |
  - 3.5.2. Metals (pp. 173-176) | html | pdf |
    - 3.5.2.1. Thin sections (p. 174) | html | pdf |
    - 3.5.2.2. Final thinning methods (pp. 174-175) | html | pdf |
    - 3.5.2.3. Chemical and electrochemical thinning solutions (pp. 175-176) | html | pdf |
  - 3.5.3. Polymers and organic specimens (p. 176) | html | pdf |
    - 3.5.3.1. Cast films (p. 176) | html | pdf |
    - 3.5.3.2. Sublimed films (p. 176) | html | pdf |
    - 3.5.3.3. Oriented solidification (p. 176) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 3.5.1.1. The two types of arrangement for final thinning by argon-ion etching (p. 172) | html | pdf |
    - Fig. 3.5.1.2. Dependence of sputtering rate on the angle of tilt (p. 172) | html | pdf |
    - Fig. 3.5.3.1. Typical anode current/voltage relationship at fixed temperature under potentiostatic conditions (p. 175) | html | pdf |
  - Tables
    - Table 3.5.1.1. Chemical etchants used for preparing thin foils from single-crystal ceramic materials (p. 173) | html | pdf |
- 3.6. Specimens for neutron diffraction (pp. 177-184) | html | pdf | chapter contents |
  B. T. M. Willis

Production and properties of radiations
- 4.1. Radiations used in crystallography (pp. 186-190) | html | pdf | chapter contents |
  V. Valvoda
  - 4.1.1. Introduction (p. 186) | html | pdf |
  - 4.1.2. Electromagnetic waves and particles (pp. 186-187) | html | pdf |
  - 4.1.3. Most frequently used radiations (pp. 187-188) | html | pdf |
  - 4.1.4. Special applications of X-rays, electrons, and neutrons (p. 189) | html | pdf |
    - 4.1.4.1. X-rays, synchrotron radiation, and γ-rays (p. 189) | html | pdf |
    - 4.1.4.2. Electrons (p. 189) | html | pdf |
    - 4.1.4.3. Neutrons (p. 189) | html | pdf |
  - 4.1.5. Other radiations (pp. 189-190) | html | pdf |
    - 4.1.5.1. Atomic and molecular beams (p. 189) | html | pdf |
    - 4.1.5.2. Positrons and muons (p. 189) | html | pdf |
    - 4.1.5.3. Infrared, visible, and ultraviolet light (pp. 189-190) | html | pdf |
    - 4.1.5.4. Radiofrequency and microwaves (p. 190) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 4.1.1.1. Schematic diagram of the main types of radiation application in crystallography (dashed lines represent structure investigation on a larger than atomic scale) (p. 186) | html | pdf |
    - Fig. 4.1.2.1. Comparison of the energy, frequency, and wavelength of the electromagnetic waves used in crystallography (logarithmic scale) (p. 187) | html | pdf |
    - Fig. 4.1.3.1. Angular dependence of the atomic scattering amplitudes of lead for (1) electron, (2) X-ray, and (3) neutron scattering (in absolute values) (p. 188) | html | pdf |
    - Fig. 4.1.3.2. Relative dependence of the average atomic scattering amplitudes on the atomic number Z for X-rays (continuous line), electrons (dashed line), and neutrons (circles) (p. 188) | html | pdf |
  - Tables
    - Table 4.1.3.1. Average diffraction properties of X-rays, electrons, and neutrons (p. 187) | html | pdf |
- 4.2. X-rays (pp. 191-258) | html | pdf | chapter contents |
  U. W. Arndt, D. C. Creagh, R. D. Deslattes, J. H. Hubbell, P. Indelicato, E. G. Kessler Jr and E. Lindroth
  - 4.2.1. Generation of X-rays (pp. 191-200) | html | pdf |
    U. W. Arndt
    - 4.2.1.1. The characteristic line spectrum (pp. 191-192) | html | pdf |
      - 4.2.1.1.1. The intensity of characteristic lines (pp. 191-192) | html | pdf |
    - 4.2.1.2. The continuous spectrum (pp. 192-193) | html | pdf |
    - 4.2.1.3. X-ray tubes (pp. 193-195) | html | pdf |
      - 4.2.1.3.1. Power dissipation in the anode (p. 195) | html | pdf |
    - 4.2.1.4. Radioactive X-ray sources (pp. 195-196) | html | pdf |
    - 4.2.1.5. Synchrotron-radiation sources (pp. 196-198) | html | pdf |
    - 4.2.1.6. Plasma X-ray sources (pp. 198-199) | html | pdf |
    - 4.2.1.7. Other sources of X-rays (pp. 199-200) | html | pdf |
  - 4.2.2. X-ray wavelengths (pp. 200-212) | html | pdf |
    R. D. Deslattes, E. G. Kessler Jr, P. Indelicato and E. Lindroth
    - 4.2.2.1. Historical introduction (pp. 200-201) | html | pdf |
    - 4.2.2.2. Known problems (p. 201) | html | pdf |
    - 4.2.2.3. Alternative strategies (p. 201) | html | pdf |
    - 4.2.2.4. The X-ray wavelength scales, old and new (pp. 201-202) | html | pdf |
    - 4.2.2.5. K-series reference wavelengths (p. 202) | html | pdf |
    - 4.2.2.6. L-series reference wavelengths (p. 202) | html | pdf |
    - 4.2.2.7. Absorption-edge locations (pp. 202-204) | html | pdf |
    - 4.2.2.8. Outline of the theoretical procedures (pp. 204-205) | html | pdf |
    - 4.2.2.9. Evaluation of the uncorrelated energy with the Dirac–Fock method (p. 205) | html | pdf |
    - 4.2.2.10. Correlation and Auger shifts (p. 205) | html | pdf |
    - 4.2.2.11. QED corrections (pp. 205-208) | html | pdf |
    - 4.2.2.12. Structure and format of the summary tables (pp. 211-212) | html | pdf |
    - 4.2.2.13. Availability of a more complete X-ray wavelength table (p. 212) | html | pdf |
    - 4.2.2.14. Connection with scales used in previous literature (p. 212) | html | pdf |
  - 4.2.3. X-ray absorption spectra (pp. 213-220) | html | pdf |
    D. C. Creagh
    - 4.2.3.1. Introduction (pp. 213-214) | html | pdf |
      - 4.2.3.1.1. Definitions (p. 213) | html | pdf |
      - 4.2.3.1.2. Variation of X-ray attenuation coefficients with photon energy (p. 213) | html | pdf |
      - 4.2.3.1.3. Normal attenuation, XAFS, and XANES (pp. 213-214) | html | pdf |
    - 4.2.3.2. Techniques for the measurement of X-ray attenuation coefficients (pp. 214-215) | html | pdf |
      - 4.2.3.2.1. Experimental configurations (pp. 214-215) | html | pdf |
      - 4.2.3.2.2. Specimen selection (p. 215) | html | pdf |
      - 4.2.3.2.3. Requirements for the absolute measurement of μ_l or (μ/ρ) (p. 215) | html | pdf |
    - 4.2.3.3. Normal attenuation coefficients (p. 215) | html | pdf |
    - 4.2.3.4. Attenuation coefficients in the neighbourhood of an absorption edge (pp. 216-219) | html | pdf |
      - 4.2.3.4.1. XAFS  (pp. 216-219) | html | pdf |
        4.2.3.4.1.1. Theory  (pp. 216-217) | html | pdf |
        4.2.3.4.1.2. Techniques of data analysis  (pp. 217-218) | html | pdf |
        4.2.3.4.1.3. XAFS experiments  (pp. 218-219) | html | pdf |
      - 4.2.3.4.2. X-ray absorption near edge structure (XANES) (p. 219) | html | pdf |
    - 4.2.3.5. Comments (p. 220) | html | pdf |
  - 4.2.4. X-ray absorption (or attenuation) coefficients (pp. 220-229) | html | pdf |
    D. C. Creagh and J. H. Hubbell
    - 4.2.4.1. Introduction (pp. 220-221) | html | pdf |
    - 4.2.4.2. Sources of information (pp. 221-229) | html | pdf |
      - 4.2.4.2.1. Theoretical photo-effect data: σ_pe (p. 221) | html | pdf |
      - 4.2.4.2.2. Theoretical Rayleigh scattering data: σ_R (pp. 221-229) | html | pdf |
      - 4.2.4.2.3. Theoretical Compton scattering data: σ_C (p. 229) | html | pdf |
    - 4.2.4.3. Comparison between theoretical and experimental data sets (p. 229) | html | pdf |
    - 4.2.4.4. Uncertainty in the data tables (p. 229) | html | pdf |
  - 4.2.5. Filters and monochromators (pp. 229-241) | html | pdf |
    D. C. Creagh
    - 4.2.5.1. Introduction (pp. 229-236) | html | pdf |
    - 4.2.5.2. Mirrors and capillaries (pp. 236-238) | html | pdf |
      - 4.2.5.2.1. Mirrors (pp. 236-237) | html | pdf |
      - 4.2.5.2.2. Capillaries (p. 237) | html | pdf |
      - 4.2.5.2.3. Quasi-Bragg reflectors (pp. 237-238) | html | pdf |
    - 4.2.5.3. Filters (p. 238) | html | pdf |
    - 4.2.5.4. Monochromators (pp. 238-241) | html | pdf |
      - 4.2.5.4.1. Crystal monochromators (pp. 238-239) | html | pdf |
      - 4.2.5.4.2. Laboratory monochromator systems (p. 239) | html | pdf |
      - 4.2.5.4.3. Multiple-reflection monochromators for use with laboratory and synchrotron-radiation sources (pp. 239-240) | html | pdf |
      - 4.2.5.4.4. Polarization (pp. 240-241) | html | pdf |
  - 4.2.6. X-ray dispersion corrections (pp. 241-258) | html | pdf |
    D. C. Creagh
    - 4.2.6.1. Definitions (pp. 242-243) | html | pdf |
      - 4.2.6.1.1. Rayleigh scattering (p. 242) | html | pdf |
      - 4.2.6.1.2. Thomson scattering by a free electron (p. 242) | html | pdf |
      - 4.2.6.1.3. Elastic scattering from electrons bound to atoms: the atomic scattering factor, the atomic form factor, and the dispersion corrections (pp. 242-243) | html | pdf |
    - 4.2.6.2. Theoretical approaches for the calculation of the dispersion corrections (pp. 243-248) | html | pdf |
      - 4.2.6.2.1. The classical approach (pp. 243-244) | html | pdf |
      - 4.2.6.2.2. Non-relativistic theories (pp. 244-245) | html | pdf |
      - 4.2.6.2.3. Relativistic theories  (pp. 245-248) | html | pdf |
        4.2.6.2.3.1. Cromer and Liberman: relativistic dipole approach  (pp. 245-246) | html | pdf |
        4.2.6.2.3.2. The scattering matrix formalism  (pp. 246-248) | html | pdf |
      - 4.2.6.2.4. Intercomparison of theories (p. 248) | html | pdf |
    - 4.2.6.3. Modern experimental techniques (pp. 248-258) | html | pdf |
      - 4.2.6.3.1. Determination of the real part of the dispersion correction: $[f'(\omega,0)]$ (pp. 248-250) | html | pdf |
      - 4.2.6.3.2. Determination of the real part of the dispersion correction: $[f'(\omega,{\boldDelta})]$   (pp. 250-251) | html | pdf |
        4.2.6.3.2.1. Measurements using the dynamical theory of X-ray diffraction  (pp. 250-251) | html | pdf |
        4.2.6.3.2.2. Friedel- and Bijvoet-pair techniques  (p. 251) | html | pdf |
      - 4.2.6.3.3. Comparison of theory with experiment  (pp. 251-258) | html | pdf |
        4.2.6.3.3.1. Measurements in the high-energy limit $[(\omega/\omega_\kappa\rightarrow0)]$   (pp. 251-252) | html | pdf |
        4.2.6.3.3.2. Measurements in the vicinity of an absorption edge  (pp. 252-253) | html | pdf |
        4.2.6.3.3.3. Accuracy in the tables of dispersion corrections  (p. 253) | html | pdf |
        4.2.6.3.3.4. Towards a tensor formalism  (pp. 253-258) | html | pdf |
        4.2.6.3.3.5. Summary  (p. 258) | html | pdf |
    - 4.2.6.4. Table of wavelengths, energies, and linewidths used in compiling the tables of the dispersion corrections (p. 258) | html | pdf |
    - 4.2.6.5. Tables of the dispersion corrections for forward scattering, averaged polarization using the relativistic multipole approach (p. 258) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 4.2.1.1. f(χ) curves for Cu K-L₃ at a series of different accelerating voltages (in kV) (p. 192) | html | pdf |
    - Fig. 4.2.1.2. Experimental measurements of $[N_\varphi]$ for Cu K-L₃ as functions of the accelerating voltage for different take-off angles (p. 193) | html | pdf |
    - Fig. 4.2.1.3. Intensity per unit frequency interval versus frequency in the continuous spectrum from a thick target at different accelerating voltages (p. 193) | html | pdf |
    - Fig. 4.2.1.4. The function μ in Müller's equation (equation 4.2.1.12) as a function of the ratio of width to length of the focal spot (p. 195) | html | pdf |
    - Fig. 4.2.1.5. Synchrotron radiation emitted by a relativistic electron travelling in a curved trajectory (p. 197) | html | pdf |
    - Fig. 4.2.1.6. Synchrotron-radiation spectrum: percentage per unit wavelength interval (a) of power of total power and (b) of number of photons of total number of photons at wavelengths greater than λ versus λ/λ_c (p. 197) | html | pdf |
    - Fig. 4.2.1.7. Main components of a dedicated electron storage-ring synchrotron-radiation source (p. 198) | html | pdf |
    - Fig. 4.2.1.8. Electron trajectory within a multipole wiggler or undulator (p. 198) | html | pdf |
    - Fig. 4.2.1.9. Spectral distribution and critical wavelengths for (a) a dipole magnet, (b) a wavelength shifter, and (c) a multipole wiggler for the proposed ESRF (p. 198) | html | pdf |
    - Fig. 4.2.1.10. Comparison of the spectra from the storage ring SPEAR in photons s⁻¹ mA⁻¹ mrad⁻¹ per 1% passband (1978 performance) and a rotating-anode X-ray generator (p. 198) | html | pdf |
    - Fig. 4.2.1.11. The evolution of storage-ring synchrotron-radiation sources over the decades, as illustrated by their increasing number and range of machine energies (based on Suller, 1992) (p. 200) | html | pdf |
    - Fig. 4.2.1.12. X-ray emission from various laser-produced plasmas (p. 200) | html | pdf |
    - Fig. 4.2.2.1. Relative deviations between theoretical and experimental results for K-series spectra (p. 212) | html | pdf |
    - Fig. 4.2.2.2. Comparison of L-series data with experiment for the indicated range of Z (p. 212) | html | pdf |
    - Fig. 4.2.3.1. Theoretical cross sections for photon interactions with carbon showing the contributions of photoelectric, elastic (Rayleigh), inelastic (Compton), and pair-production cross sections to the total cross sections (p. 213) | html | pdf |
    - Fig. 4.2.3.2. The dependence of the X-ray attenuation coefficient on energy for a range of germanium compounds, taken in the neighbourhood of the germanium absorption edge (from IT IV, 1974) (p. 214) | html | pdf |
    - Fig. 4.2.3.3. Schematic representations of experimental apparatus used in the IUCr X-ray Attenuation Project (Creagh & Hubbell, 1987; Creagh, 1985) (p. 214) | html | pdf |
    - Fig. 4.2.3.4. Steps in the reduction of data from an XAFS experiment using the Fourier transform technique: (a) after the removal of background χ(k) versus k; (b) after multiplication by a weighting function (in this case k³); (c) after Fourier transformation to determine r′ (p. 217) | html | pdf |
    - Fig. 4.2.3.5. Schematic representations of the scattering processes undergone by the ejected photoelectron in the single-scattering (XAFS) case and the full multiple-scattering regime (XANES) (p. 219) | html | pdf |
    - Fig. 4.2.4.1. Agreement between theory and experiment for oxygen (Z = 8) in the `soft' X-ray region (p. 220) | html | pdf |
    - Fig. 4.2.4.2. The total cross section for silicon (Z = 14) compared with the unrenormalized Scofield values (p. 221) | html | pdf |
    - Fig. 4.2.4.3. The total cross section for uranium (Z = 92): The theoretical values (solid line) are partially obscured by the high density of available measurements (p. 222) | html | pdf |
    - Fig. 4.2.4.4. Comparison between this tabulation and experimental data contained in Saloman & Hubbell (1986) (p. 222) | html | pdf |
    - Fig. 4.2.5.1. The variation of specular reflectivity with incident photon energy is shown for materials of different atomic number and a constant angle of incidence of 0.2° (p. 236) | html | pdf |
    - Fig. 4.2.5.2. The use of mirrors in a typical synchrotron-radiation beamline (p. 237) | html | pdf |
    - Fig. 4.2.5.3. The reflectivity of a multiple-quantum-well device is shown (p. 238) | html | pdf |
    - Fig. 4.2.5.4. In (a), the schematic rocking curve for a silicon crystal in the neighbourhood of the 111 Bragg peak is shown (p. 239) | html | pdf |
    - Fig. 4.2.5.5. A schematic diagram of a beamline designed to produce circularly polarized light from initially linearly polarized light using Laue-case reflections (p. 240) | html | pdf |
    - Fig. 4.2.5.6. A schematic diagram of a Hart-type tuneable channel-cut monochromator is shown (p. 241) | html | pdf |
    - Fig. 4.2.5.7. A schematic diagram of the use of a Bragg–Fresnel lens to focus hard X-rays onto a high-pressure cell (p. 241) | html | pdf |
    - Fig. 4.2.6.1. The relativistic correction in electrons per atom for: (a) the modified form-factor approach; (b) the relativistic multipole approach; (c) the relativistic dipole approach (p. 247) | html | pdf |
    - Fig. 4.2.6.2. Measured values of f′(ω, 0) at the K-edge of Nb in LiNbO₃ and the Kramers–Kronig transformation of f′′(ω, 0) (p. 247) | html | pdf |
  - Tables
    - Table 4.2.1.1. Correspondence between X-ray diagram levels and electron configurations (p. 191) | html | pdf |
    - Table 4.2.1.2. Correspondence between IUPAC and Siegbahn notations for X-ray diagram lines (p. 191) | html | pdf |
    - Table 4.2.1.3. Copper-target X-ray tubes and their loading (p. 194) | html | pdf |
    - Table 4.2.1.4. Relative permissible loading for different target materials (p. 196) | html | pdf |
    - Table 4.2.1.5. Radionuclides decaying wholly by electron capture, and yielding little or no γ-radiation (p. 196) | html | pdf |
    - Table 4.2.1.6. Comparison of storage-ring synchrotron-radiation sources (p. 199) | html | pdf |
    - Table 4.2.1.7. Intensity gain with storage rings over conventional sources (p. 200) | html | pdf |
    - Table 4.2.2.1. K-series reference wavelengths in Å (p. 203) | html | pdf |
    - Table 4.2.2.2. Directly measured L-series reference wavelengths in Å (p. 204) | html | pdf |
    - Table 4.2.2.3. Directly measured and emission + binding energies (see text) K-absorption edges in Å (p. 205) | html | pdf |
    - Table 4.2.2.4. Wavelengths of K-emission lines and K-absorption edges in Å (pp. 206-208) | html | pdf |
    - Table 4.2.2.5. Wavelengths of L-emission lines and L-absorption edges in Å (pp. 209-211) | html | pdf |
    - Table 4.2.2.6. Wavelength conversion factors (p. 212) | html | pdf |
    - Table 4.2.3.1. Some synchrotron-radiation facilities providing XAFS databases and analysis utilities (p. 219) | html | pdf |
    - Table 4.2.4.1. Table of wavelengths and energies for the characteristic radiations used in Tables 4.2.4.2 and 4.2.4.3 (p. 221) | html | pdf |
    - Table 4.2.4.2. Total phonon interaction cross section (pp. 223-229) | html | pdf |
    - Table 4.2.4.3. Mass attenuation coefficients (pp. 230-236) | html | pdf |
    - Table 4.2.6.1. Values of E_tot/mc² listed as a function of atomic number Z (p. 246) | html | pdf |
    - Table 4.2.6.2. Comparison between the S-matrix calculations of Kissel (K) (1977) and the form-factor calculations of Cromer & Liberman (C & L) (1970, 1981, 1983) and Creagh & McAuley (C & M) for the noble gases and several common metals (p. 249) | html | pdf |
    - Table 4.2.6.3. A comparison of the forward-scattering amplitudes computed using different theoretical approaches (p. 250) | html | pdf |
    - Table 4.2.6.4. Comparison of measurements of the real part of the dispersion correction for LiF, Si, Al and Ge for characteristic wavelengths Ag Kα₁, Mo Kα₁ and Cu Kα₁ with theoretical predictions (p. 252) | html | pdf |
    - Table 4.2.6.5. Comparison of measurements of f′(ω, 0) for C, Si and Cu for characteristic wavelengths Ag Kα₁, Mo Kα₁ and Cu Kα₁ with theoretical predictions (p. 253) | html | pdf |
    - Table 4.2.6.6. Comparison of $[f'(\omega_A,0)]$ for copper, nickel, zirconium, and niobium for theoretical and experimental data sets (p. 254) | html | pdf |
    - Table 4.2.6.7. Lists of wavelengths, energies, and linewidths used in compiling the table of dispersion corrections (p. 254) | html | pdf |
    - Table 4.2.6.8. Dispersion corrections for forward scattering (pp. 255-257) | html | pdf |
- 4.3. Electron diffraction (pp. 259-429) | html | pdf | chapter contents |
  C. Colliex, J. M. Cowley, S. L. Dudarev, M. Fink, J. Gjønnes, R. Hilderbrandt, A. Howie, D. F. Lynch, L. M. Peng, G. Ren, A. W. Ross, V. H. Smith Jr, J. C. H. Spence, J. W. Steeds, J. Wang, M. J. Whelan and B. B. Zvyagin
  - 4.3.1. Scattering factors for the diffraction of electrons by crystalline solids (pp. 259-262) | html | pdf |
    J. M. Cowley
    - 4.3.1.1. Elastic scattering from a perfect crystal (p. 259) | html | pdf |
    - 4.3.1.2. Atomic scattering factors (pp. 259-260) | html | pdf |
    - 4.3.1.3. Approximations of restricted validity (p. 260) | html | pdf |
    - 4.3.1.4. Relativistic effects (pp. 260-261) | html | pdf |
    - 4.3.1.5. Absorption effects (p. 261) | html | pdf |
    - 4.3.1.6. Tables of atomic scattering amplitudes for electrons (p. 261) | html | pdf |
    - 4.3.1.7. Use of Tables 4.3.1.1 and 4.3.1.2 (pp. 261-262) | html | pdf |
  - 4.3.2. Parameterizations of electron atomic scattering factors (p. 262) | html | pdf |
    J. M. Cowley, L. M. Peng, G. Ren, S. L. Dudarev and M. J. Whelan
  - 4.3.3. Complex scattering factors for the diffraction of electrons by gases (pp. 262-391) | html | pdf |
    A. W. Ross, M. Fink, R. Hilderbrandt, J. Wang and V. H. Smith Jr
    - 4.3.3.1. Introduction (p. 262) | html | pdf |
    - 4.3.3.2. Complex atomic scattering factors for electrons (pp. 262-390) | html | pdf |
      - 4.3.3.2.1. Elastic scattering factors for atoms (pp. 262-389) | html | pdf |
      - 4.3.3.2.2. Total inelastic scattering factors (pp. 389-390) | html | pdf |
      - 4.3.3.2.3. Corrections for defects in the theory of atomic scattering (p. 390) | html | pdf |
    - 4.3.3.3. Molecular scattering factors for electrons (pp. 390-391) | html | pdf |
  - 4.3.4. Electron energy-loss spectroscopy on solids (pp. 391-412) | html | pdf |
    C. Colliex
    - 4.3.4.1. Definitions (pp. 391-394) | html | pdf |
      - 4.3.4.1.1. Use of electron beams (pp. 391-392) | html | pdf |
      - 4.3.4.1.2. Parameters involved in the description of a single inelastic scattering event (p. 392) | html | pdf |
      - 4.3.4.1.3. Problems associated with multiple scattering (pp. 392-393) | html | pdf |
      - 4.3.4.1.4. Classification of the different types of excitations contained in an electron energy-loss spectrum (pp. 393-394) | html | pdf |
    - 4.3.4.2. Instrumentation (pp. 394-397) | html | pdf |
      - 4.3.4.2.1. General instrumental considerations (pp. 394-395) | html | pdf |
      - 4.3.4.2.2. Spectrometers (pp. 395-397) | html | pdf |
      - 4.3.4.2.3. Detection systems (p. 397) | html | pdf |
    - 4.3.4.3. Excitation spectrum of valence electrons (pp. 397-404) | html | pdf |
      - 4.3.4.3.1. Volume plasmons (pp. 397-399) | html | pdf |
      - 4.3.4.3.2. Dielectric description (pp. 399-401) | html | pdf |
      - 4.3.4.3.3. Real solids (pp. 401-403) | html | pdf |
      - 4.3.4.3.4. Surface plasmons (pp. 403-404) | html | pdf |
    - 4.3.4.4. Excitation spectrum of core electrons (pp. 404-411) | html | pdf |
      - 4.3.4.4.1. Definition and classification of core edges (pp. 404-406) | html | pdf |
      - 4.3.4.4.2. Bethe theory for inelastic scattering by an isolated atom (Bethe, 1930; Inokuti, 1971; Inokuti, Itikawa & Turner, 1978, 1979) (pp. 406-408) | html | pdf |
      - 4.3.4.4.3. Solid-state effects (pp. 408-410) | html | pdf |
      - 4.3.4.4.4. Applications for core-loss spectroscopy (pp. 410-411) | html | pdf |
    - 4.3.4.5. Conclusions (pp. 411-412) | html | pdf |
  - 4.3.5. Oriented texture patterns (pp. 412-414) | html | pdf |
    B. B. Zvyagin
    - 4.3.5.1. Texture patterns (p. 412) | html | pdf |
    - 4.3.5.2. Lattice plane oriented perpendicular to a direction (lamellar texture) (pp. 412-413) | html | pdf |
    - 4.3.5.3. Lattice direction oriented parallel to a direction (fibre texture) (pp. 413-414) | html | pdf |
    - 4.3.5.4. Applications to metals and organic materials (p. 414) | html | pdf |
  - 4.3.6. Computation of dynamical wave amplitudes (pp. 414-416) | html | pdf |
    - 4.3.6.1. The multislice method (pp. 414-415) | html | pdf |
      D. F. Lynch
    - 4.3.6.2. The Bloch-wave method (pp. 415-416) | html | pdf |
      A. Howie
  - 4.3.7. Measurement of structure factors and determination of crystal thickness by electron diffraction (pp. 416-419) | html | pdf |
    J. Gjønnes and J. W. Steeds
  - 4.3.8. Crystal structure determination by high-resolution electron microscopy (pp. 419-429) | html | pdf |
    J. C. H. Spence and J. M. Cowley
    - 4.3.8.1. Introduction (pp. 419-421) | html | pdf |
    - 4.3.8.2. Lattice-fringe images (pp. 421-422) | html | pdf |
    - 4.3.8.3. Crystal structure images (pp. 422-424) | html | pdf |
    - 4.3.8.4. Parameters affecting HREM images (pp. 424-425) | html | pdf |
    - 4.3.8.5. Computing methods (pp. 425-427) | html | pdf |
    - 4.3.8.6. Resolution and hyper-resolution (p. 427) | html | pdf |
    - 4.3.8.7. Alternative methods (pp. 427-428) | html | pdf |
    - 4.3.8.8. Combined use of HREM and electron diffraction (pp. 428-429) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 4.3.4.1. Definition of the regions in (E, q) space that can be investigated with the different primary sources of particles available at present (p. 392) | html | pdf |
    - Fig. 4.3.4.2. A primary electron of energy E₀ and wavevector k is inelastically scattered into a state of energy E₀ − ΔE and wavevector k′ (p. 392) | html | pdf |
    - Fig. 4.3.4.3. Excitation spectrum of aluminium from 1 to 250 eV, investigated by EELS on 300 keV primary electrons (p. 393) | html | pdf |
    - Fig. 4.3.4.4. Complete electron energy-loss spectrum of a thin rhodizite crystal (thickness ~60 nm) (p. 393) | html | pdf |
    - Fig. 4.3.4.5. Schematic energy-level representation of the origin of a core-loss excitation (from a core level C at energy E_c to an unoccupied state U above the Fermi level E_f) and its general shape in EELS, as superimposed on a continuously decreasing background (p. 393) | html | pdf |
    - Fig. 4.3.4.6. Energy-loss spectrum, in the meV region, of an evaporated germanium film (thickness $[\simeq]$ 25 nm) (p. 394) | html | pdf |
    - Fig. 4.3.4.7. Schematic drawing of a uniform magnetic sector spectrometer with induction B normal to the plane of the figure (p. 395) | html | pdf |
    - Fig. 4.3.4.8. Different factors contributing to the energy resolution in the dispersion plane (p. 395) | html | pdf |
    - Fig. 4.3.4.9. Optical coupling of a magnetic sector spectrometer on a STEM column (p. 396) | html | pdf |
    - Fig. 4.3.4.10. Principle of the Wien filter used as an EELS spectrometer: the trajectories are shown in the two principal (dispersive and focusing) sections (p. 396) | html | pdf |
    - Fig. 4.3.4.11. Principle of the Castaing & Henry filter made from a magnetic prism and an electrostatic mirror (p. 396) | html | pdf |
    - Fig. 4.3.4.12. A commercial EELS spectrometer designed for parallel detection on a photodiode array (p. 397) | html | pdf |
    - Fig. 4.3.4.13. The dispersion curve for the excitation of a plasmon (curve 1) merges into the continuum of individual electron–hole excitations (between curves 2 and 4) for a critical wavevector q_c (p. 398) | html | pdf |
    - Fig. 4.3.4.14. Measured angular dependence of the differential cross section dσ/dΩ for the 15 eV plasmon loss in Al (dots) compared with a calculated curve by Ferrell (solid curve) and with a sharp cut-off approximation at θ_c (dashed curved) (p. 399) | html | pdf |
    - Fig. 4.3.4.15. Variation of plasmon excitation mean free path Λ_p as a function of accelerating voltage V in the case of carbon and aluminium (p. 399) | html | pdf |
    - Fig. 4.3.4.16. Dielectric and optical functions calculated in the Drude model of a free-electron gas with ħω_p = 16 eV and τ = 1.64 × 10⁻¹⁶ s (p. 400) | html | pdf |
    - Fig. 4.3.4.17. Same as previous figure, but for a Lorentz model with an oscillator of eigenfrequency ħω₀ = 10 eV and relaxation time τ₀ = 6.6 × 10⁻¹⁶ s superposed on the free-electron term (p. 401) | html | pdf |
    - Fig. 4.3.4.18. Dielectric coefficients $[\varepsilon_1]$ , $[\varepsilon_2]$ and $[{\rm Im}(-1/\varepsilon)]$ from a collection of typical real solids (p. 402) | html | pdf |
    - Fig. 4.3.4.19. Dielectric functions in graphite derived from energy losses for E ⊥ c (i.e. the electric field vector being in the layer plane) and for E||c (p. 403) | html | pdf |
    - Fig. 4.3.4.20. Geometric conditions for investigating the anisotropic energy-loss function (p. 404) | html | pdf |
    - Fig. 4.3.4.21. Definition of electron shells and transitions involved in core-loss spectroscopy (p. 404) | html | pdf |
    - Fig. 4.3.4.22. Chart of edges encountered in the 50 eV up to 3 keV energy-loss range with symbols identifying the types of shapes (p. 405) | html | pdf |
    - Fig. 4.3.4.23. A selection of typical profiles (K, L_2,3, M_4,5, and N_2,3) illustrating the most important behaviours encountered on major edges through the Periodic Table (p. 406) | html | pdf |
    - Fig. 4.3.4.24. Bethe surface for K-shell ionization, calculated using a hydrogenic model (p. 407) | html | pdf |
    - Fig. 4.3.4.25. A novel technique for simulating an energy-loss spectrum with two distinct edges as a superposition of theoretical contributions (hydrogenic saw-tooth for O K, Lorentzian white lines and delayed continuum for Fe L_2,3 calculated with the Hartree–Slater description) (p. 407) | html | pdf |
    - Fig. 4.3.4.26. Definition of the different fine structures visible on a core-loss edge (p. 408) | html | pdf |
    - Fig. 4.3.4.27. High-energy resolution spectra on the L_2,3 titanium edge from two phases (rutile and anatase) of TiO₂ (p. 408) | html | pdf |
    - Fig. 4.3.4.28. The dramatic change in near-edge fine structures on the L₃ and L₂ lines of Cu, from Cu metal to CuO (p. 409) | html | pdf |
    - Fig. 4.3.4.29. Illustration of the single and multiple scattering effects used to describe the final wavefunction on the excited site (p. 409) | html | pdf |
    - Fig. 4.3.4.30. Comparison of the experimental O K edge (solid line) with calculated profiles in the multiple scattering approach (p. 409) | html | pdf |
    - Fig. 4.3.4.31. The conventional method of background subtraction for the evaluation of the characteristic signals S_{O K} and S_{Fe L_2,3} used for quantitative elemental analysis (p. 410) | html | pdf |
    - Fig. 4.3.4.32. Values of n_eff for metallic aluminium based on composite optical data (p. 411) | html | pdf |
    - Fig. 4.3.5.1. The relative orientations of the direct and the reciprocal axes and their projections on the plane ab, with indication of the distances B_hk and D_hkl that define the positions of reflections in lamellar texture patterns (p. 412) | html | pdf |
    - Fig. 4.3.5.2. (a) Part of the OTED pattern of the clay mineral kaolinite and (b) the intensity profile of a characteristic quadruplet of reflections recorded with the electron diffractometry system (p. 413) | html | pdf |
    - Fig. 4.3.5.3. The projections of the reciprocal axes on the plane ab of the direct lattice, with indications of the distances B and D of the hk rows from the fibre-texture axes a or [hk] (p. 413) | html | pdf |
    - Fig. 4.3.7.1. (a) Dispersion-surface section for the symmetric four-beam case (0, g, g + h, m), γk is a function of k_x, referred to (b), where k_x = k_y = 0 corresponds to the exact Bragg condition for all three reflections (p. 418) | html | pdf |
    - Fig. 4.3.8.1. Atomic resolution image of a tantalum-doped tungsten trioxide crystal (pseudo-cubic structure) showing extended crystallographic shear-plane defects (C), pentagonal-column hexagonal-tunnel (PCHT) defects (T), and metallization of the surface due to oxygen desorption (JEOL 4000EX, crystal thickness less than 200 Å, 400 kV, C_s = 1 mm) (p. 419) | html | pdf |
    - Fig. 4.3.8.2. Imaging conditions for few-beam lattice images (p. 420) | html | pdf |
    - Fig. 4.3.8.3. A summary of three- (or five-) beam axial imaging conditions (p. 422) | html | pdf |
    - Fig. 4.3.8.4. The contrast of few-beam lattice images as a function of focus in the neighbourhood of the stationary-phase focus (p. 422) | html | pdf |
    - Fig. 4.3.8.5. (a) The transfer function for a 400 kV electron microscope with a point resolution of 1.7 Å at the Scherzer focus; the curve is based on equation (4.3.8.17) (p. 424) | html | pdf |
    - Fig. 4.3.8.6. Structure image of a thin lamella of the 6H polytype of SiC projected along [110] and recorded at 1.2 MeV (p. 426) | html | pdf |
  - Tables
    - Table 4.3.1.1. Atomic scattering amplitudes (Å) for electrons for neutral atoms (pp. 263-271) | html | pdf |
    - Table 4.3.1.2. Atomic scattering amplitudes (Å) for electrons for ionized atoms (pp. 272-281) | html | pdf |
    - Table 4.3.2.1. Parameters useful in electron diffraction as a function of accelerating voltage (p. 281) | html | pdf |
    - Table 4.3.2.2. Elastic atomic scattering factors of electrons for neutral atoms and s up to 2.0 Å⁻¹ (pp. 282-283) | html | pdf |
    - Table 4.3.2.3. Elastic atomic scattering factors of electrons for neutral atoms and s up to 6.0 Å⁻¹ (pp. 284-285) | html | pdf |
    - Table 4.3.3.1. Partial wave elastic scattering factors for neutral atomsinteractive version (pp. 286-377) | html | pdf |
    - Table 4.3.3.2. Inelastic scattering factors (pp. 378-388) | html | pdf |
    - Table 4.3.4.1. Different possibilities for using EELS information as a function of the different accessible parameters (r, $[\boldtheta]$ , ΔE) (p. 394) | html | pdf |
    - Table 4.3.4.2. Plasmon energies measured (and calculated) for a few simple metals (p. 397) | html | pdf |
    - Table 4.3.4.3. Experimental and theoretical values for the coefficient α in the plasmon dispersion curve together with estimates of the cut-off wavevector (p. 398) | html | pdf |
    - Table 4.3.4.4. Comparison of measured and calculated values for the halfwidth ΔE_1/2(0) of the plasmon line (p. 398) | html | pdf |
- 4.4. Neutron techniques (pp. 430-487) | html | pdf | chapter contents |
  I. S. Anderson, P. J. Brown, J. M. Carpenter, G. Lander, R. Pynn, J. M. Rowe, O. Schärpf, V. F. Sears and B. T. M. Willis
  - 4.4.1. Production of neutrons (pp. 430-431) | html | pdf |
    J. M. Carpenter and G. Lander
  - 4.4.2. Beam-definition devices (pp. 431-443) | html | pdf |
    I. S. Anderson and O. Schärpf
    - 4.4.2.1. Introduction (p. 431) | html | pdf |
    - 4.4.2.2. Collimators (pp. 431-432) | html | pdf |
    - 4.4.2.3. Crystal monochromators (pp. 432-435) | html | pdf |
    - 4.4.2.4. Mirror reflection devices (pp. 435-438) | html | pdf |
      - 4.4.2.4.1. Neutron guides (pp. 435-436) | html | pdf |
      - 4.4.2.4.2. Focusing mirrors (p. 436) | html | pdf |
      - 4.4.2.4.3. Multilayers (pp. 436-437) | html | pdf |
      - 4.4.2.4.4. Capillary optics (pp. 437-438) | html | pdf |
    - 4.4.2.5. Filters (p. 438) | html | pdf |
    - 4.4.2.6. Polarizers (pp. 438-442) | html | pdf |
      - 4.4.2.6.1. Single-crystal polarizers (pp. 438-439) | html | pdf |
      - 4.4.2.6.2. Polarizing mirrors (p. 440) | html | pdf |
      - 4.4.2.6.3. Polarizing filters (pp. 440-441) | html | pdf |
      - 4.4.2.6.4. Zeeman polarizer (p. 442) | html | pdf |
    - 4.4.2.7. Spin-orientation devices (pp. 442-443) | html | pdf |
      - 4.4.2.7.1. Maintaining the direction of polarization (p. 442) | html | pdf |
      - 4.4.2.7.2. Rotation of the polarization direction (p. 442) | html | pdf |
      - 4.4.2.7.3. Flipping of the polarization direction (pp. 442-443) | html | pdf |
    - 4.4.2.8. Mechanical choppers and selectors (p. 443) | html | pdf |
  - 4.4.3. Resolution functions (pp. 443-444) | html | pdf |
    R. Pynn and J. M. Rowe
  - 4.4.4. Scattering lengths for neutrons (pp. 444-454) | html | pdf |
    V. F. Sears
    - 4.4.4.1. Scattering lengths (p. 444) | html | pdf |
    - 4.4.4.2. Scattering and absorption cross sections (p. 452) | html | pdf |
    - 4.4.4.3. Isotope effects (pp. 452-453) | html | pdf |
    - 4.4.4.4. Correction for electromagnetic interactions (p. 453) | html | pdf |
    - 4.4.4.5. Measurement of scattering lengths (p. 453) | html | pdf |
    - 4.4.4.6. Compilation of scattering lengths and cross sections (pp. 453-454) | html | pdf |
  - 4.4.5. Magnetic form factors (pp. 454-461) | html | pdf |
    P. J. Brown
  - 4.4.6. Absorption coefficients for neutrons (p. 461) | html | pdf |
    B. T. M. Willis
  - References | html | pdf |
  - Figures
    - Fig. 4.4.1.1. A plane view of the installation at the Institut Laue–Langevin, Grenoble (p. 430) | html | pdf |
    - Fig. 4.4.1.2. Schematic diagram for performing diffraction experiments at steady-state and pulsed neutron sources (p. 431) | html | pdf |
    - Fig. 4.4.2.1. Two methods by which artificial mosaic monochromators can be constructed: (a) out of a stack of crystalline wafers, each with a mosaicity close to the global value (p. 434) | html | pdf |
    - Fig. 4.4.2.2. Reciprocal-lattice representation of the effect of a monochromator with reciprocal-lattice vector τ on the reciprocal-space element of a beam with divergence α (p. 434) | html | pdf |
    - Fig. 4.4.2.3. Momentum-space representation of Bragg scattering from a crystal moving (a) perpendicular and (b) parallel to the diffracting planes with a velocity v_k (p. 435) | html | pdf |
    - Fig. 4.4.2.4. In a curved neutron guide, the transmission becomes λ dependent: (a) the possible types of reflection (garland and zig-zag), the direct line-of-sight length, the critical angle θ*, which is related to the characteristic wavelength $[\lambda^*=\theta^*{\sqrt{\pi/Nb_{\rm coh}}}]$ ; (b) transmission across the exit of the guide for different wavelengths, normalized to unity at the outside edge; (c) total transmission of the guide as a function of λ (p. 436) | html | pdf |
    - Fig. 4.4.2.5. Illustration of how a variation in the bilayer period can be used to produce a monochromator, a broad-band device, or a supermirror (p. 437) | html | pdf |
    - Fig. 4.4.2.6. Typical applications of polycapillary devices: (a) lens used to refocus a divergent beam; (b) half-lens to produce a nearly parallel beam or to focus a nearly parallel beam; (c) a compact bender (p. 437) | html | pdf |
    - Fig. 4.4.2.7. Total cross section for beryllium in the energy range where it can be used as a filter for neutrons with energy below 5 meV (Freund, 1983) (p. 438) | html | pdf |
    - Fig. 4.4.2.8. Energy-dependent cross section for a neutron beam incident along the c axis of a pyrolytic graphite filter (p. 439) | html | pdf |
    - Fig. 4.4.2.9. Geometry of a polarizing monochromator showing the lattice planes (hkl) with |F_N| = |F_M|, the direction of P and $[\boldmu]$ , the expected spin direction and intensity (p. 439) | html | pdf |
    - Fig. 4.4.2.10. Measured reflectivity curve of an FeCoV/TiZr polarizing supermirror with an extended angular range of polarization of three times that of γ_c(Ni) for neutrons without spin flip, ↑↑, and with spin flip, ↑↓ (p. 440) | html | pdf |
  - Tables
    - Table 4.4.2.1. Some important properties of materials used for neutron monochromator crystals (p. 433) | html | pdf |
    - Table 4.4.2.2. Neutron scattering-length densities, Nb_coh, for some commonly used materials (p. 435) | html | pdf |
    - Table 4.4.2.3. Characteristics of some typical elements and isotopes used as neutron filters (p. 439) | html | pdf |
    - Table 4.4.2.4. Properties of polarizing crystal monochromators (p. 440) | html | pdf |
    - Table 4.4.2.5. Scattering-length densities for some typical materials used for polarizing multilayers (p. 441) | html | pdf |
    - Table 4.4.4.1. Bound scattering lengths, b, in fm and cross sections, σ, in barns (1 barn = 100 fm²) of the elements and their isotopesinteractive version (pp. 445-452) | html | pdf |
    - Table 4.4.5.1. 〈j₀〉 form factors for 3d transition elements and their ions (p. 454) | html | pdf |
    - Table 4.4.5.2. 〈j₀〉 form factors for 4d atoms and their ions (p. 455) | html | pdf |
    - Table 4.4.5.3. 〈j₀〉 form factors for rare-earth ions (p. 455) | html | pdf |
    - Table 4.4.5.4. 〈j₀〉 form factors for actinide ions (p. 455) | html | pdf |
    - Table 4.4.5.5. 〈j₂〉 form factors for 3d transition elements and their ions (p. 456) | html | pdf |
    - Table 4.4.5.6. 〈j₂〉 form factors for 4d atoms and their ions (p. 457) | html | pdf |
    - Table 4.4.5.7. 〈j₂〉 form factors for rare-earth ions (p. 457) | html | pdf |
    - Table 4.4.5.8. 〈j₂〉 form factors for actinide ions (p. 457) | html | pdf |
    - Table 4.4.5.9. 〈j₄〉 form factors for 3d atoms and their ions (p. 458) | html | pdf |
    - Table 4.4.5.10. 〈j₄〉 form factors for 4d atoms and their ions (p. 459) | html | pdf |
    - Table 4.4.5.11. 〈j₄〉 form factors for rare-earth ions (p. 459) | html | pdf |
    - Table 4.4.5.12. 〈j₄〉 form factors for actinide ions (p. 459) | html | pdf |
    - Table 4.4.5.13. 〈j₆〉 form factors for rare-earth ions (p. 460) | html | pdf |
    - Table 4.4.5.14. 〈j₆〉 form factors for actinide ions (p. 460) | html | pdf |
    - Table 4.4.6.1. Absorption of the elements for neutrons (p. 461) | html | pdf |

Determination of lattice parameters
- 5.1. Introduction (p. 490) | html | pdf | chapter contents |
  A. J. C. Wilson
- 5.2. X-ray diffraction methods: polycrystalline (pp. 491-504) | html | pdf | chapter contents |
  W. Parrish, A. J. C. Wilson and J. I. Langford
  - 5.2.1. Introduction (pp. 491-492) | html | pdf |
    - 5.2.1.1. The techniques available (p. 491) | html | pdf |
    - 5.2.1.2. Errors and aberrations: general discussion (p. 491) | html | pdf |
    - 5.2.1.3. Errors of the Bragg angle (p. 491) | html | pdf |
    - 5.2.1.4. Bragg angle: operational definitions (pp. 491-492) | html | pdf |
  - 5.2.2. Wavelength and related problems (pp. 492-493) | html | pdf |
    - 5.2.2.1. Errors and uncertainties in wavelength (p. 492) | html | pdf |
    - 5.2.2.2. Refraction (p. 492) | html | pdf |
    - 5.2.2.3. Statistical fluctuations (pp. 492-493) | html | pdf |
  - 5.2.3. Geometrical and physical aberrations (pp. 493-494) | html | pdf |
    - 5.2.3.1. Aberrations (p. 493) | html | pdf |
    - 5.2.3.2. Extrapolation, graphical and analytical (pp. 493-494) | html | pdf |
  - 5.2.4. Angle-dispersive diffractometer methods: conventional sources (p. 495) | html | pdf |
  - 5.2.5. Angle-dispersive diffractometer methods: synchrotron sources (pp. 495-496) | html | pdf |
  - 5.2.6. Whole-pattern methods (p. 496) | html | pdf |
  - 5.2.7. Energy-dispersive techniques (pp. 496-497) | html | pdf |
  - 5.2.8. Camera methods (pp. 497-498) | html | pdf |
  - 5.2.9. Testing for remanent systematic error (p. 498) | html | pdf |
  - 5.2.10. Powder-diffraction standards (pp. 498-499) | html | pdf |
  - 5.2.11. Intensity standards (p. 500) | html | pdf |
  - 5.2.12. Instrumental line-profile-shape standards (p. 501) | html | pdf |
  - 5.2.13. Factors determining accuracy (pp. 501-504) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 5.2.1.1. Functions of the cell angles in equation (5.2.1.3) for the possible unit cells (p. 492) | html | pdf |
    - Table 5.2.4.1. Centroid displacement 〈Δθ/θ〉 and variance W of certain aberrations of an angle-dispersive diffractometer (p. 494) | html | pdf |
    - Table 5.2.7.1. Centroid displacement $[\langle \Delta E/E\rangle]$ and variance W of certain aberrations of an energy-dispersive diffractometer (p. 497) | html | pdf |
    - Table 5.2.8.1. Some geometrical aberrations in the Debye–Scherrer method (p. 498) | html | pdf |
    - Table 5.2.10.1. NIST values for silicon standards (p. 499) | html | pdf |
    - Table 5.2.10.2. Reflection angles (°) for tungsten, silver, and silicon (p. 499) | html | pdf |
    - Table 5.2.10.3. Silicon standard reflection angles (°) (p. 500) | html | pdf |
    - Table 5.2.10.4. Silicon standard high reflection angles (°) (p. 501) | html | pdf |
    - Table 5.2.10.5. Tungsten reflection angles (°) (p. 502) | html | pdf |
    - Table 5.2.10.6. Fluorophlogopite 00l standard reflection angles (p. 503) | html | pdf |
    - Table 5.2.10.7. Silver behenate 00l standard reflection angles (p. 503) | html | pdf |
    - Table 5.2.11.1. NIST intensity standards, SRM 674 (p. 503) | html | pdf |
- 5.3. X-ray diffraction methods: single crystal (pp. 505-536) | html | pdf | chapter contents |
  E. Gałdecka
  - 5.3.1. Introduction (pp. 505-508) | html | pdf |
    - 5.3.1.1. General remarks (pp. 505-506) | html | pdf |
    - 5.3.1.2. Introduction to single-crystal methods (pp. 506-508) | html | pdf |
  - 5.3.2. Photographic methods (pp. 508-516) | html | pdf |
    - 5.3.2.1. Introduction (p. 508) | html | pdf |
    - 5.3.2.2. The Laue method (p. 508) | html | pdf |
    - 5.3.2.3. Moving-crystal methods (pp. 508-510) | html | pdf |
      - 5.3.2.3.1. Rotating-crystal method (pp. 508-509) | html | pdf |
      - 5.3.2.3.2. Moving-film methods (p. 509) | html | pdf |
      - 5.3.2.3.3. Combined methods (p. 509) | html | pdf |
      - 5.3.2.3.4. Accurate and precise lattice-parameter determinations (pp. 509-510) | html | pdf |
      - 5.3.2.3.5. Photographic cameras for investigation of small lattice-parameter changes (p. 510) | html | pdf |
    - 5.3.2.4. The Kossel method and divergent-beam techniques (pp. 510-516) | html | pdf |
      - 5.3.2.4.1. The principle (pp. 510-512) | html | pdf |
      - 5.3.2.4.2. Review of methods of accurate lattice-parameter determination (pp. 512-515) | html | pdf |
      - 5.3.2.4.3. Accuracy and precision (p. 515) | html | pdf |
      - 5.3.2.4.4. Applications (pp. 515-516) | html | pdf |
  - 5.3.3. Methods with counter recording (pp. 516-534) | html | pdf |
    - 5.3.3.1. Introduction (p. 516) | html | pdf |
    - 5.3.3.2. Standard diffractometers (pp. 516-517) | html | pdf |
      - 5.3.3.2.1. Four-circle diffractometer (pp. 516-517) | html | pdf |
      - 5.3.3.2.2. Two-circle diffractometer (p. 517) | html | pdf |
    - 5.3.3.3. Data processing and optimization of the experiment (pp. 517-520) | html | pdf |
      - 5.3.3.3.1. Models of the diffraction profile (pp. 517-519) | html | pdf |
      - 5.3.3.3.2. Precision and accuracy of the Bragg-angle determination; optimization of the experiment (pp. 519-520) | html | pdf |
    - 5.3.3.4. One-crystal spectrometers (pp. 521-526) | html | pdf |
      - 5.3.3.4.1. General characteristics (p. 521) | html | pdf |
      - 5.3.3.4.2. Development of methods based on an asymmetric arrangement and their applications (pp. 521-522) | html | pdf |
      - 5.3.3.4.3. The Bond method  (pp. 522-526) | html | pdf |
        5.3.3.4.3.1. Description of the method  (pp. 522-523) | html | pdf |
        5.3.3.4.3.2. Systematic errors  (pp. 523-524) | html | pdf |
        5.3.3.4.3.3. Development of the Bond method and its applications  (pp. 524-525) | html | pdf |
        5.3.3.4.3.4. Advantages and disadvantages of the Bond method  (p. 526) | html | pdf |
    - 5.3.3.5. Limitations of traditional methods (p. 526) | html | pdf |
    - 5.3.3.6. Multiple-diffraction methods (pp. 526-528) | html | pdf |
    - 5.3.3.7. Multiple-crystal – pseudo-non-dispersive techniques (pp. 528-533) | html | pdf |
      - 5.3.3.7.1. Double-crystal spectrometers (pp. 528-530) | html | pdf |
      - 5.3.3.7.2. Triple-crystal spectrometers (pp. 530-531) | html | pdf |
      - 5.3.3.7.3. Multiple-beam methods (p. 531) | html | pdf |
      - 5.3.3.7.4. Combined methods (pp. 531-533) | html | pdf |
    - 5.3.3.8. Optical and X-ray interferometry – a non-dispersive technique (pp. 533-534) | html | pdf |
    - 5.3.3.9. Lattice-parameter and wavelength standards (p. 534) | html | pdf |
  - 5.3.4. Final remarks (pp. 534-536) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 5.3.2.1. (a) Photographic recording of lattice-parameter changes (p. 511) | html | pdf |
    - Fig. 5.3.2.2. Schematic representation of the origin of the Kossel lines (p. 512) | html | pdf |
    - Fig. 5.3.2.3. (a) The Kossel pattern from iron and (b) the corresponding stereographic projection (Tixier & Waché, 1970) (p. 513) | html | pdf |
    - Fig. 5.3.2.4. Lens-shaped figures formed by pairs of intersecting conics (p. 514) | html | pdf |
    - Fig. 5.3.2.5. Schematic representation of the multiple-exposure technique (after Fischer & Harris, 1970) (p. 514) | html | pdf |
    - Fig. 5.3.3.1. Determination of reciprocal-lattice angles on the θ circle (after Luger, 1980) (p. 517) | html | pdf |
    - Fig. 5.3.3.2. The extrapolated-peak procedure (after Bearden, 1933) (p. 518) | html | pdf |
    - Fig. 5.3.3.3. Determination of the Bragg angle by means of the one-crystal spectrometer using (a) an asymmetric or (b) a symmetric arrangement (p. 521) | html | pdf |
    - Fig. 5.3.3.4. Schematic representation of the Bond (1960) method (p. 522) | html | pdf |
    - Fig. 5.3.3.5. Schematic representation of multiple diffraction in reciprocal space (after Post, 1975) (p. 526) | html | pdf |
    - Fig. 5.3.3.6. Schematic representation of the multiple-diffraction method (p. 527) | html | pdf |
    - Fig. 5.3.3.7. The multiple-diffraction pattern at the 222 position in germanium (Cole, Chambers & Dunn, 1962) (p. 527) | html | pdf |
    - Fig. 5.3.3.8. Schematic representation of the double-crystal spectrometer (p. 528) | html | pdf |
    - Fig. 5.3.3.9. Schematic representation of the double-crystal arrangement of Hart & Lloyd (1975) for the examination of epitaxic layers (p. 529) | html | pdf |
    - Fig. 5.3.3.10. Schematic representation of the double-crystal arrangement of Okazaki & Kawaminami (1973a); white incident X-rays are used (p. 529) | html | pdf |
    - Fig. 5.3.3.11. Schematic representation of the triple-crystal spectrometer developed by Buschert (1965) (after Hart, 1981) (p. 530) | html | pdf |
    - Fig. 5.3.3.12. Schematic representation of the double-beam comparator of Hart (1969) (p. 531) | html | pdf |
    - Fig. 5.3.3.13. The double-axis lattice-spacing comparator of Ando, Bailey & Hart (1978); a triple-diffracted beam is used (p. 532) | html | pdf |
    - Fig. 5.3.3.14. Schematic representation of the double-beam triple-crystal spectrometer of Buschert et al (p. 532) | html | pdf |
    - Fig. 5.3.3.15. The geometry of the diffractometer used by Fewster & Andrew (1995) (p. 533) | html | pdf |
    - Fig. 5.3.3.16. Optical and X-ray interferometry (p. 533) | html | pdf |
    - Fig. 5.3.3.17. Portion of a dual-channel recording of X-ray and optical fringes (Deslattes, 1969) (p. 533) | html | pdf |
    - Fig. 5.3.3.18. Synchrotron radiation, SR, from the bending magnet incident on the Si(111) double-crystal monochromator and, after four reflections from the monolithic monochromator (0.1410 nm), impinges on sample Si(444) (p. 534) | html | pdf |
    - Fig. 5.3.3.19. Synchrotron radiation, SR, from the bending magnet incident on the Si(111) double-crystal monochromator and, after four reflections from the monolithic monochromator (0.1612 nm), impinges on sample Si(153) (p. 535) | html | pdf |
    - Fig. 5.3.3.20. Experimental set-up for measuring lattice parameters (p. 535) | html | pdf |
- 5.4. Electron-diffraction methods (pp. 537-540) | html | pdf | chapter contents |
  A. W. S. Johnson and A. Olsen
  - 5.4.1. Determination of cell parameters from single-crystal patterns (pp. 537-538) | html | pdf |
    A. W. S. Johnson
    - 5.4.1.1. Introduction (pp. 537-538) | html | pdf |
    - 5.4.1.2. Zero-zone analysis (p. 538) | html | pdf |
    - 5.4.1.3. Non-zero-zone analysis (p. 538) | html | pdf |
  - 5.4.2. Kikuchi and HOLZ techniques (pp. 538-540) | html | pdf |
    A. Olsen
  - References | html | pdf |
  - Figures
    - Fig. 5.4.1.1. Diffraction geometry (p. 537) | html | pdf |
    - Fig. 5.4.1.2. A diffraction pattern with the crystal oriented at a zone axis (p. 538) | html | pdf |
    - Fig. 5.4.2.1. Schematic diagram showing the geometry of a Kikuchi pattern (p. 538) | html | pdf |
    - Fig. 5.4.2.2. Schematic diagram of three Kikuchi lines that nearly intersect at the same point (p. 539) | html | pdf |
    - Fig. 5.4.2.3. Schematic diagram showing the indexing of the most prominent lines in the selected-area channelling pattern near the [111] zone of Si (p. 540) | html | pdf |
  - Tables
    - Table 5.4.1.1. Unit-cell information available for photographic recording (p. 537) | html | pdf |
- 5.5. Neutron methods (pp. 541-551) | html | pdf | chapter contents |
  B. T. M. Willis

Interpretation of diffracted intensities
- 6.1. Intensity of diffracted intensities (pp. 554-595) | html | pdf | chapter contents |
  P. J. Brown, A. G. Fox, E. N. Maslen, M. A. O'Keefe and B. T. M. Willis
  - 6.1.1. X-ray scattering (pp. 554-590) | html | pdf |
    E. N. Maslen, A. G. Fox and M. A. O'Keefe
    - 6.1.1.1. Coherent (Rayleigh) scattering (p. 554) | html | pdf |
    - 6.1.1.2. Incoherent (Compton) scattering (p. 554) | html | pdf |
    - 6.1.1.3. Atomic scattering factor (pp. 554-565) | html | pdf |
      - 6.1.1.3.1. Scattering-factor interpolation (p. 565) | html | pdf |
    - 6.1.1.4. Generalized scattering factors (pp. 565-584) | html | pdf |
    - 6.1.1.5. The temperature factor (pp. 584-585) | html | pdf |
    - 6.1.1.6. The generalized temperature factor (pp. 585-590) | html | pdf |
      - 6.1.1.6.1. Gram–Charlier series (p. 586) | html | pdf |
      - 6.1.1.6.2. Fourier-invariant expansions (pp. 586-588) | html | pdf |
      - 6.1.1.6.3. Cumulant expansion (p. 588) | html | pdf |
      - 6.1.1.6.4. Curvilinear density functions (pp. 588-589) | html | pdf |
      - 6.1.1.6.5. Model-based curvilinear density functions (pp. 589-590) | html | pdf |
      - 6.1.1.6.6. The quasi-Gaussian approximation for curvilinear motion (p. 590) | html | pdf |
    - 6.1.1.7. Structure factor (p. 590) | html | pdf |
    - 6.1.1.8. Reflecting power of a crystal (p. 590) | html | pdf |
  - 6.1.2. Magnetic scattering of neutrons (pp. 590-593) | html | pdf |
    P. J. Brown
    - 6.1.2.1. Glossary of symbols (pp. 590-591) | html | pdf |
    - 6.1.2.2. General formulae for the magnetic cross section (p. 591) | html | pdf |
    - 6.1.2.3. Calculation of magnetic structure factors and cross sections (p. 591) | html | pdf |
    - 6.1.2.4. The magnetic form factor (p. 592) | html | pdf |
    - 6.1.2.5. The scattering cross section for polarized neutrons (pp. 592-593) | html | pdf |
    - 6.1.2.6. Rotation of the polarization of the scattered neutrons (p. 593) | html | pdf |
  - 6.1.3. Nuclear scattering of neutrons (pp. 593-595) | html | pdf |
    B. T. M. Willis
    - 6.1.3.1. Glossary of symbols (p. 593) | html | pdf |
    - 6.1.3.2. Scattering by a single nucleus (pp. 593-594) | html | pdf |
    - 6.1.3.3. Scattering by a single atom (p. 594) | html | pdf |
    - 6.1.3.4. Scattering by a single crystal (pp. 594-595) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 6.1.1.1. Scattering by an electron (p. 554) | html | pdf |
    - Fig. 6.1.2.1. The integrals 〈j₀〉, 〈j₂〉, and 〈j₄〉 for the Fe²⁺ ion plotted against $[(\sin\theta)/\lambda]$ (p. 592) | html | pdf |
    - Fig. 6.1.2.2. Comparison of 3d, 4d, 4f, and 5f form factors (p. 592) | html | pdf |
    - Fig. 6.1.3.1. Dependence on neutron wavelength of the coherent scattering length of ¹¹³Cd (p. 594) | html | pdf |
  - Tables
    - Table 6.1.1.1. Mean atomic scattering factors in electrons for free atoms (pp. 555-564) | html | pdf |
    - Table 6.1.1.2. Spherical bonded hydrogen-atom scattering factors (p. 565) | html | pdf |
    - Table 6.1.1.3. Mean atomic scattering factors in electrons for chemically significant ions (pp. 566-577) | html | pdf |
    - Table 6.1.1.4. Coefficients for analytical approximation to the scattering factors of Tables 6.1.1.1 and 6.1.1.3 (pp. 578-580) | html | pdf |
    - Table 6.1.1.5. Coefficients for analytical approximation to the scattering factors of Table 6.1.1.1 for the range 2.0 < (sin $[\theta]$ )/λ < 6.0 Å⁻¹ [equation (6.1.1.16)] (p. 581) | html | pdf |
    - Table 6.1.1.6. Angle dependence of multipole functions, normalized as in equation (6.1.1.23); ω = cos $[\theta]$ and S, D, Q, O, H denote scalar, dipole, quadrupole, octupole, and hexadecapole terms, respectively (p. 583) | html | pdf |
    - Table 6.1.1.7. Indices allowed by the site symmetry for the real form of the spherical harmonics $[Y_{lmp(\theta,\varphi)}]$ (p. 584) | html | pdf |
    - Table 6.1.1.8. Cubic harmonics $[K_{lj}(\theta,\,\varphi)]$ for cubic site symmetries (p. 585) | html | pdf |
    - Table 6.1.1.9. f_nl(α, S) = ∫^∞₀rⁿ exp(−αr)j_l(Sr) dr (p. 586) | html | pdf |
    - Table 6.1.1.10. Indices nmp allowed by the site symmetry for the functions $[H_n(z)\Phi_{mp}(\varphi)]$ (p. 586) | html | pdf |
    - Table 6.1.1.11. Indices n_x, n_y, n_z allowed for the basis functions H_{n_x}(Ax)H_{n_y}(By)H_{n_z}(Cz) (p. 587) | html | pdf |
- 6.2. Trigonometric intensity factors (pp. 596-598) | html | pdf | chapter contents |
  H. Lipson, J. I. Langford and H.-C. Hu
  - 6.2.1. Expressions for intensity of diffraction (p. 596) | html | pdf |
  - 6.2.2. The polarization factor (p. 596) | html | pdf |
  - 6.2.3. The angular-velocity factor (p. 596) | html | pdf |
  - 6.2.4. The Lorentz factor (p. 596) | html | pdf |
  - 6.2.5. Special factors in the powder method (pp. 596-598) | html | pdf |
  - 6.2.6. Some remarks about the integrated reflection power ratio formulae for single-crystal slabs (p. 598) | html | pdf |
  - 6.2.7. Other factors (p. 598) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 6.2.1.1. Summary of formulae for integrated powers of reflection (pp. 597-598) | html | pdf |
- 6.3. X-ray absorption (pp. 599-608) | html | pdf | chapter contents |
  E. N. Maslen
  - 6.3.1. Linear absorption coefficient (pp. 599-600) | html | pdf |
    - 6.3.1.1. True or photoelectric absorption (p. 599) | html | pdf |
    - 6.3.1.2. Scattering (p. 599) | html | pdf |
    - 6.3.1.3. Extinction (pp. 599-600) | html | pdf |
    - 6.3.1.4. Attenuation (mass absorption) coefficients (p. 600) | html | pdf |
  - 6.3.2. Dispersion (p. 600) | html | pdf |
  - 6.3.3. Absorption corrections (pp. 600-608) | html | pdf |
    - 6.3.3.1. Special cases (p. 600) | html | pdf |
    - 6.3.3.2. Cylinders and spheres (pp. 600-604) | html | pdf |
    - 6.3.3.3. Analytical method for crystals with regular faces (pp. 604-606) | html | pdf |
    - 6.3.3.4. Gaussian integration (pp. 606-607) | html | pdf |
    - 6.3.3.5. Empirical methods (pp. 607-608) | html | pdf |
    - 6.3.3.6. Measuring crystals for absorption (p. 608) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 6.3.1.1. Idealized diagram showing the variation of the photoelectric absorption coefficient σ_ph with wavelength λ (p. 599) | html | pdf |
    - Fig. 6.3.3.1. Geometry of the Eulerian cradle with the axis of a cylindrical specimen coincident with the φ axis (p. 604) | html | pdf |
    - Fig. 6.3.3.2. Cross section of the plane of diffraction for a cylindrical specimen coincident with the φ axis (p. 604) | html | pdf |
    - Fig. 6.3.3.3. The crystal ABC divided into polygons by the dashed lines AE and CF parallel to the incident (i) and diffracted (d) beams, respectively (p. 605) | html | pdf |
    - Fig. 6.3.3.4. Crystal oriented with the normal N(S) to the face ABCD in the plane of view (p. 608) | html | pdf |
    - Fig. 6.3.3.5. Geometry of the Eulerian cradle in the bisecting position (p. 608) | html | pdf |
  - Tables
    - Table 6.3.3.1. Transmission coefficients (p. 601) | html | pdf |
    - Table 6.3.3.2. Values of A* for cylinders (p. 602) | html | pdf |
    - Table 6.3.3.3. Values of A* for spheres (p. 602) | html | pdf |
    - Table 6.3.3.4. Values of (1/A*)(dA*/dμR) for spheres (p. 603) | html | pdf |
    - Table 6.3.3.5. Coefficients for interpolation of A* and $[\bar T]$ (p. 603) | html | pdf |
- 6.4. The flow of radiation in a real crystal (pp. 609-616) | html | pdf | chapter contents |
  T. M. Sabine
  - 6.4.1. Introduction (p. 609) | html | pdf |
  - 6.4.2. The model of a real crystal (p. 609) | html | pdf |
  - 6.4.3. Primary and secondary extinction (pp. 609-610) | html | pdf |
  - 6.4.4. Radiation flow (p. 610) | html | pdf |
  - 6.4.5. Primary extinction (p. 610) | html | pdf |
  - 6.4.6. The finite crystal (p. 610) | html | pdf |
  - 6.4.7. Angular variation of E (p. 610) | html | pdf |
  - 6.4.8. The value of x (pp. 610-611) | html | pdf |
  - 6.4.9. Secondary extinction (p. 611) | html | pdf |
  - 6.4.10. The extinction factor (p. 611) | html | pdf |
    - 6.4.10.1. The correlated block model (p. 611) | html | pdf |
    - 6.4.10.2. The uncorrelated block model (p. 611) | html | pdf |
  - 6.4.11. Polarization (pp. 611-612) | html | pdf |
  - 6.4.12. Anisotropy (p. 612) | html | pdf |
  - 6.4.13. Asymptotic behaviour of the integrated intensity (p. 612) | html | pdf |
    - 6.4.13.1. Non-absorbing crystal, strong primary extinction (p. 612) | html | pdf |
    - 6.4.13.2. Non-absorbing crystal, strong secondary extinction (p. 612) | html | pdf |
    - 6.4.13.3. The absorbing crystal (p. 612) | html | pdf |
  - 6.4.14. Relationship with the dynamical theory (p. 612) | html | pdf |
  - 6.4.15. Definitions (p. 612) | html | pdf |
  - References | html | pdf |

Measurement of intensities
- 7.1. Detectors for X-rays (pp. 618-638) | html | pdf | chapter contents |
  Y. Amemiya, U. W. Arndt, B. Buras, J. Chikawa, L. Gerward, J. I. Langford, W. Parrish and P. M. de Wolff
  - 7.1.1. Photographic film (p. 618) | html | pdf |
    P. M. de Wolff
    - 7.1.1.1. Visual estimation (p. 618) | html | pdf |
    - 7.1.1.2. Densitometry (p. 618) | html | pdf |
  - 7.1.2. Geiger counters (pp. 618-619) | html | pdf |
    W. Parrish and J. I. Langford
  - 7.1.3. Proportional counters (p. 619) | html | pdf |
    W. Parrish and J. I. Langford
    - 7.1.3.1. The detector system (p. 619) | html | pdf |
    - 7.1.3.2. Proportional counters (p. 619) | html | pdf |
    - 7.1.3.3. Position-sensitive detectors (p. 619) | html | pdf |
    - 7.1.3.4. Resolution, discrimination, efficiency (p. 619) | html | pdf |
  - 7.1.4. Scintillation and solid-state detectors (pp. 619-622) | html | pdf |
    W. Parrish and J. I. Langford
    - 7.1.4.1. Scintillation counters (pp. 619-620) | html | pdf |
    - 7.1.4.2. Solid-state detectors (p. 620) | html | pdf |
    - 7.1.4.3. Energy resolution and pulse-amplitude discrimination (pp. 620-621) | html | pdf |
    - 7.1.4.4. Quantum-counting efficiency and linearity (pp. 621-622) | html | pdf |
    - 7.1.4.5. Escape peaks (p. 622) | html | pdf |
  - 7.1.5. Energy-dispersive detectors (pp. 622-623) | html | pdf |
    B. Buras and L. Gerward
  - 7.1.6. Position-sensitive detectors (pp. 623-633) | html | pdf |
    U. W. Arndt
    - 7.1.6.1. Choice of detector (pp. 623-626) | html | pdf |
      - 7.1.6.1.1. Detection efficiency (p. 624) | html | pdf |
      - 7.1.6.1.2. Linearity of response (pp. 624-625) | html | pdf |
      - 7.1.6.1.3. Dynamic range (p. 625) | html | pdf |
      - 7.1.6.1.4. Spatial resolution (p. 625) | html | pdf |
      - 7.1.6.1.5. Uniformity of response (p. 625) | html | pdf |
      - 7.1.6.1.6. Spatial distortion (p. 625) | html | pdf |
      - 7.1.6.1.7. Energy discrimination (pp. 625-626) | html | pdf |
      - 7.1.6.1.8. Suitability for dynamic measurements (p. 626) | html | pdf |
      - 7.1.6.1.9. Stability (p. 626) | html | pdf |
      - 7.1.6.1.10. Size and weight (p. 626) | html | pdf |
    - 7.1.6.2. Gas-filled counters (pp. 626-629) | html | pdf |
      - 7.1.6.2.1. Localization of the detected photon (p. 627) | html | pdf |
      - 7.1.6.2.2. Parallel-plate counters (pp. 627-628) | html | pdf |
      - 7.1.6.2.3. Current ionization PSD's (pp. 628-629) | html | pdf |
    - 7.1.6.3. Semiconductor detectors (pp. 629-630) | html | pdf |
      - 7.1.6.3.1. X-ray-sensitive semiconductor PSD's (pp. 629-630) | html | pdf |
      - 7.1.6.3.2. Light-sensitive semiconductor PSD's (p. 630) | html | pdf |
      - 7.1.6.3.3. Electron-sensitive PSD's (p. 630) | html | pdf |
    - 7.1.6.4. Devices with an X-ray-sensitive photocathode (p. 630) | html | pdf |
    - 7.1.6.5. Television area detectors with external phosphor (pp. 630-632) | html | pdf |
      - 7.1.6.5.1. X-ray phosphors (p. 631) | html | pdf |
      - 7.1.6.5.2. Light coupling (p. 632) | html | pdf |
      - 7.1.6.5.3. Image intensifiers (p. 632) | html | pdf |
      - 7.1.6.5.4. TV camera tubes (p. 632) | html | pdf |
    - 7.1.6.6. Some applications (pp. 632-633) | html | pdf |
  - 7.1.7. X-ray-sensitive TV cameras (pp. 633-635) | html | pdf |
    J. Chikawa
    - 7.1.7.1. Signal-to-noise ratio (pp. 633-634) | html | pdf |
    - 7.1.7.2. Imaging system (pp. 634-635) | html | pdf |
    - 7.1.7.3. Image processing (p. 635) | html | pdf |
  - 7.1.8. Storage phosphors (pp. 635-638) | html | pdf |
    Y. Amemiya and J. Chikawa
  - References | html | pdf |
  - Figures
    - Fig. 7.1.2.1. Detectors used for diffractometry: (a) Geiger counter, (b) side-window proportional counter, (c) end-window scintillation counter (p. 618) | html | pdf |
    - Fig. 7.1.4.1. Calculated pulse-amplitude distributions of Cu Kα and Mo Kα in the form of (a) integral curves and (b) differential curves (p. 621) | html | pdf |
    - Fig. 7.1.5.1. Intrinsic efficiency of semiconductor detectors (p. 622) | html | pdf |
    - Fig. 7.1.6.1. Possible combinations of detection processes, localization methods and read-out procedures in PSD's (p. 624) | html | pdf |
    - Fig. 7.1.6.2. Absorption of 8 keV and 17 keV photons in argon and xenon as a function of pressure in atm × column length in mm (p. 625) | html | pdf |
    - Fig. 7.1.6.3. Spherical drift chamber multiwire proportional chamber (MWPC) (p. 627) | html | pdf |
    - Fig. 7.1.6.4. Read-out methods for gas-filled LPSD's (p. 628) | html | pdf |
    - Fig. 7.1.6.5. Three-plane MWPC (p. 629) | html | pdf |
    - Fig. 7.1.6.6. Integrating LPSD (p. 629) | html | pdf |
    - Fig. 7.1.6.7. Fast-scanning television X-ray detector (after Arndt, 1985) (p. 631) | html | pdf |
    - Fig. 7.1.7.1. Schematic illustration of an X-ray sensing Saticon camera tube (p. 633) | html | pdf |
    - Fig. 7.1.7.2. Square-wave modulation transfer function (MTF) measured for the DIS-type, conventional-type Se–As and PbO camera tubes (p. 634) | html | pdf |
    - Fig. 7.1.7.3. Typical example showing dependence of the avalanche amplification on the electric field applied on the amorphous photoconductor (HARP) (p. 634) | html | pdf |
    - Fig. 7.1.7.4. Principles of a noise reducer (p. 635) | html | pdf |
    - Fig. 7.1.8.1. Mechanism of photo-stimulated luminescence (p. 636) | html | pdf |
    - Fig. 7.1.8.2. Measured detective quantum efficiency (DQE) of the imaging plate and high-sensitivity X-ray film as a function of the exposure level (p. 636) | html | pdf |
    - Fig. 7.1.8.3. Fluctuation noise in the signal as a function of the exposure level (p. 636) | html | pdf |
    - Fig. 7.1.8.4. Diagram showing a cascade of stochastic elementary processes during X-ray exposure and image read out of the imaging plate (p. 637) | html | pdf |
    - Fig. 7.1.8.5. Dynamic range of the photo-stimulated luminescence of the imaging plate (p. 637) | html | pdf |
    - Fig. 7.1.8.6. Dependence of the IP response as a function of the energy of an X-ray photon (p. 637) | html | pdf |
    - Fig. 7.1.8.7. Fading of the IP signals as a function of time with two different X-ray energies (5.9 and 59.5 keV) (p. 638) | html | pdf |
  - Tables
    - Table 7.1.6.1. The importance of some detector properties for different X-ray patterns (p. 624) | html | pdf |
    - Table 7.1.6.2. X-ray phosphors (from Arndt, 1982) (p. 631) | html | pdf |
- 7.2. Detectors for electrons (pp. 639-643) | html | pdf | chapter contents |
  J. N. Chapman
  - 7.2.1. Introduction (p. 639) | html | pdf |
  - 7.2.2. Characterization of detectors (pp. 639-640) | html | pdf |
  - 7.2.3. Parallel detectors (pp. 640-642) | html | pdf |
    - 7.2.3.1. Fluorescent screens (p. 640) | html | pdf |
    - 7.2.3.2. Photographic emulsions (pp. 640-641) | html | pdf |
    - 7.2.3.3. Detector systems based on an electron-tube device (p. 641) | html | pdf |
    - 7.2.3.4. Electronic detection systems based on solid-state devices (p. 641) | html | pdf |
    - 7.2.3.5. Imaging plates (pp. 641-642) | html | pdf |
  - 7.2.4. Serial detectors (pp. 642-643) | html | pdf |
    - 7.2.4.1. Faraday cage (p. 642) | html | pdf |
    - 7.2.4.2. Scintillation detectors (p. 642) | html | pdf |
    - 7.2.4.3. Semiconductor detectors (pp. 642-643) | html | pdf |
  - 7.2.5. Conclusions (p. 643) | html | pdf |
  - References | html | pdf |
- 7.3. Thermal neutron detection (pp. 644-652) | html | pdf | chapter contents |
  P. Convert and P. Chieux
  - 7.3.1. Introduction (p. 644) | html | pdf |
  - 7.3.2. Neutron capture (p. 644) | html | pdf |
  - 7.3.3. Neutron detection processes (pp. 644-648) | html | pdf |
    - 7.3.3.1. Detection via gas converter and gas ionization: the gas detector (pp. 644-645) | html | pdf |
    - 7.3.3.2. Detection via solid converter and gas ionization: the foil detector (p. 645) | html | pdf |
    - 7.3.3.3. Detection via scintillation (pp. 645-646) | html | pdf |
    - 7.3.3.4. Films (pp. 646-648) | html | pdf |
  - 7.3.4. Electronic aspects of neutron detection (pp. 648-649) | html | pdf |
    - 7.3.4.1. The electronic chain (p. 648) | html | pdf |
    - 7.3.4.2. Controls and adjustments of the electronics (pp. 648-649) | html | pdf |
  - 7.3.5. Typical detection systems (pp. 649-650) | html | pdf |
    - 7.3.5.1. Single detectors (p. 649) | html | pdf |
    - 7.3.5.2. Position-sensitive detectors (pp. 649-650) | html | pdf |
    - 7.3.5.3. Banks of detectors (p. 650) | html | pdf |
  - 7.3.6. Characteristics of detection systems (p. 651) | html | pdf |
  - 7.3.7. Corrections to the intensity measurements depending on the detection system (p. 652) | html | pdf |
    - 7.3.7.1. Single detector (p. 652) | html | pdf |
    - 7.3.7.2. Banks of detectors (p. 652) | html | pdf |
    - 7.3.7.3. Position-sensitive detectors (p. 652) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 7.3.2.1. The capture cross sections for a number of nuclei used in neutron detection (p. 644) | html | pdf |
    - Fig. 7.3.3.1. (a) Neutron capture by an ³He atom and random-direction trajectory (Ox) of the secondary charged particles in the gas mixture (p. 647) | html | pdf |
    - Fig. 7.3.3.2. Typical design of a ¹⁰B-foil detector (p. 647) | html | pdf |
    - Fig. 7.3.3.3. (a) Schematic representation of the neutron capture, secondary α, and triton ionization volumes, and scintillator light emission in a cerium-doped lithium silicate glass (p. 647) | html | pdf |
    - Fig. 7.3.4.1. Electronic chain following (a) an ³He gas detector and (b) a scintillation detector (p. 648) | html | pdf |
    - Fig. 7.3.4.2. (a) Characteristic ¹⁰BF₃ gas-detector analogue pulses seen on an oscilloscope (p. 649) | html | pdf |
  - Tables
    - Table 7.3.2.1. Neutron capture reactions used in neutron detection (p. 645) | html | pdf |
    - Table 7.3.3.1. Commonly used detection processes (p. 646) | html | pdf |
    - Table 7.3.3.2. A few examples of gas-detector characteristics (p. 646) | html | pdf |
    - Table 7.3.5.1. Characteristics of some PSDs (p. 651) | html | pdf |
- 7.4. Correction of systematic errors (pp. 653-665) | html | pdf | chapter contents |
  N. G. Alexandropoulos, M. J. Cooper, P. Suortti and B. T. M. Willis
  - 7.4.1. Absorption (p. 653) | html | pdf |
  - 7.4.2. Thermal diffuse scattering (pp. 653-657) | html | pdf |
    B. T. M. Willis
    - 7.4.2.1. Glossary of symbols (pp. 653-654) | html | pdf |
    - 7.4.2.2. TDS correction factor for X-rays (single crystals) (pp. 654-656) | html | pdf |
      - 7.4.2.2.1. Evaluation of J(q) (pp. 654-655) | html | pdf |
      - 7.4.2.2.2. Calculation of α (pp. 655-656) | html | pdf |
    - 7.4.2.3. TDS correction factor for thermal neutrons (single crystals) (pp. 656-657) | html | pdf |
    - 7.4.2.4. Correction factor for powders (p. 657) | html | pdf |
  - 7.4.3. Compton scattering (pp. 657-661) | html | pdf |
    N. G. Alexandropoulos and M. J. Cooper
    - 7.4.3.1. Introduction (p. 657) | html | pdf |
    - 7.4.3.2. Non-relativistic calculations of the incoherent scattering cross section (pp. 657-659) | html | pdf |
      - 7.4.3.2.1. Semi-classical radiation theory (pp. 657-659) | html | pdf |
      - 7.4.3.2.2. Thomas–Fermi model (p. 659) | html | pdf |
      - 7.4.3.2.3. Exact calculations (p. 659) | html | pdf |
    - 7.4.3.3. Relativistic treatment of incoherent scattering (pp. 659-660) | html | pdf |
    - 7.4.3.4. Plasmon, Raman, and resonant Raman scattering (pp. 660-661) | html | pdf |
    - 7.4.3.5. Magnetic scattering (p. 661) | html | pdf |
  - 7.4.4. White radiation and other sources of background (pp. 661-665) | html | pdf |
    P. Suortti
    - 7.4.4.1. Introduction (p. 661) | html | pdf |
    - 7.4.4.2. Incident beam and sample (pp. 661-663) | html | pdf |
    - 7.4.4.3. Detecting system (pp. 663-664) | html | pdf |
    - 7.4.4.4. Powder diffraction (pp. 664-665) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 7.4.2.1. 060 reflection of LiNbO₃ (Mössbauer diffraction) (p. 653) | html | pdf |
    - Fig. 7.4.2.2. Diagrams in reciprocal space illustrating the volume abcd swept out for (a) an ω scan, and (b) a θ/2θ, or ω/2θ, scan (p. 655) | html | pdf |
    - Fig. 7.4.2.3. Scattering surfaces for one-phonon scattering of neutrons: (a) for neutrons faster than sound (β < 1); (b) for neutrons slower than sound (β > 1) (p. 656) | html | pdf |
    - Fig. 7.4.2.4. One-phonon scattering calculated for polycrystalline nickel of lattice constant a (after Suortti, 1980a) (p. 656) | html | pdf |
    - Fig. 7.4.3.1. Schematic diagram of the inelastic scattering interactions, ΔE = E₁ − E₂ is the energy transferred from the photon and K the momentum transfer (p. 657) | html | pdf |
    - Fig. 7.4.3.2. The incoherent scattering function, S(x, Z)/Z, per electron for aluminium shown as a function of x = (sin θ)/λ (p. 660) | html | pdf |
    - Fig. 7.4.3.3. The cross section for resonant Raman scattering (RRS) and fluorescence (F) as a function of the ratio of the incident energy, E, and the K-binding energy, E_B (p. 661) | html | pdf |
    - Fig. 7.4.4.1. Equatorial phase-space diagrams for a conventional X-ray source and parallel-beam geometry; x is the size and x′ = dx/dz the divergence of the X-rays (p. 662) | html | pdf |
    - Fig. 7.4.4.2. Reflection 400 of LiH measured with a parallel beam of Mo Kα₁ radiation (solid curve) (p. 662) | html | pdf |
    - Fig. 7.4.4.3. Equatorial phase-space diagrams for two wavelengths, λ₁ (solid lines) and λ₂ (broken lines), projected on the plane λ = λ₁ (p. 662) | html | pdf |
    - Fig. 7.4.4.4. Two reflections of beryllium acetate measured with Mo Kα (p. 663) | html | pdf |
    - Fig. 7.4.4.5. Components of scattering at small scattering angles when the incident energy is just below the K absorption edge of the sample [upper part, (a)], and at large scattering angles when the incident energy is about twice the K-edge energy [upper part, (b)] (p. 663) | html | pdf |
    - Fig. 7.4.4.6. Equatorial phase-space diagrams for powder diffraction in the Bragg–Brentano geometry (p. 664) | html | pdf |
    - Fig. 7.4.4.7. Three measurements of the 220 reflection of Ni at λ = 1.541 Å scaled to the same peak value; (a) in linear scale, (b) in logarithmic scale (p. 664) | html | pdf |
  - Tables
    - Table 7.4.3.1. The energy transfer, in eV, in the Compton scattering process for selected X-ray energies (p. 657) | html | pdf |
    - Table 7.4.3.2. The incoherent scattering function for elements up to Z = 55 (p. 658) | html | pdf |
    - Table 7.4.3.3. Compton scattering of Mo Kα X-radiation through 170° from 2s electrons (p. 659) | html | pdf |
- 7.5. Statistical fluctuations (pp. 666-676) | html | pdf | chapter contents |
  A. J. C. Wilson
  - 7.5.1. Distributions of intensities of diffraction (p. 666) | html | pdf |
  - 7.5.2. Counting modes (p. 666) | html | pdf |
  - 7.5.3. Fixed-time counting (pp. 666-667) | html | pdf |
  - 7.5.4. Fixed-count timing (p. 667) | html | pdf |
  - 7.5.5. Complicating phenomena (p. 667) | html | pdf |
    - 7.5.5.1. Dead time (p. 667) | html | pdf |
    - 7.5.5.2. Voltage fluctuations (p. 667) | html | pdf |
  - 7.5.6. Treatment of measured-as-negative (and other weak) intensities (p. 667) | html | pdf |
  - 7.5.7. Optimization of counting times (pp. 667-668) | html | pdf |
  - References | html | pdf |

Refinement of structural parameters
- 8.1. Least squares (pp. 678-688) | html | pdf | chapter contents |
  E. Prince and P. T. Boggs
  - 8.1.1. Definitions (pp. 678-680) | html | pdf |
    - 8.1.1.1. Linear algebra (pp. 678-679) | html | pdf |
    - 8.1.1.2. Statistics (pp. 679-680) | html | pdf |
  - 8.1.2. Principles of least squares (pp. 680-681) | html | pdf |
  - 8.1.3. Implementation of linear least squares (pp. 681-682) | html | pdf |
    - 8.1.3.1. Use of the QR factorization (pp. 681-682) | html | pdf |
    - 8.1.3.2. The normal equations (p. 682) | html | pdf |
    - 8.1.3.3. Conditioning (p. 682) | html | pdf |
  - 8.1.4. Methods for nonlinear least squares (pp. 682-685) | html | pdf |
    - 8.1.4.1. The Gauss–Newton algorithm (p. 683) | html | pdf |
    - 8.1.4.2. Trust-region methods – the Levenberg–Marquardt algorithm (p. 683) | html | pdf |
    - 8.1.4.3. Quasi-Newton, or secant, methods (pp. 683-684) | html | pdf |
    - 8.1.4.4. Stopping rules (pp. 684-685) | html | pdf |
    - 8.1.4.5. Recommendations (p. 685) | html | pdf |
  - 8.1.5. Numerical methods for large-scale problems (pp. 685-687) | html | pdf |
    - 8.1.5.1. Methods for sparse matrices (pp. 685-686) | html | pdf |
    - 8.1.5.2. Conjugate-gradient methods (pp. 686-687) | html | pdf |
  - 8.1.6. Orthogonal distance regression (pp. 687-688) | html | pdf |
  - 8.1.7. Software for least-squares calculations (p. 688) | html | pdf |
  - References | html | pdf |
- 8.2. Other refinement methods (pp. 689-692) | html | pdf | chapter contents |
  E. Prince and D. M. Collins
  - 8.2.1. Maximum-likelihood methods (p. 689) | html | pdf |
  - 8.2.2. Robust/resistant methods (pp. 689-691) | html | pdf |
  - 8.2.3. Entropy maximization (pp. 691-692) | html | pdf |
    - 8.2.3.1. Introduction (p. 691) | html | pdf |
    - 8.2.3.2. Some examples (pp. 691-692) | html | pdf |
  - References | html | pdf |
- 8.3. Constraints and restraints in refinement (pp. 694-701) | html | pdf | chapter contents |
  E. Prince, L. W. Finger and J. H. Konnert
  - 8.3.1. Constrained models (pp. 693-698) | html | pdf |
    - 8.3.1.1. Lagrange undetermined multipliers (p. 693) | html | pdf |
    - 8.3.1.2. Direct application of constraints (pp. 693-698) | html | pdf |
  - 8.3.2. Stereochemically restrained least-squares refinement (pp. 698-701) | html | pdf |
    - 8.3.2.1. Stereochemical constraints as observational equations (pp. 698-701) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 8.3.1.1. Symmetry conditions for second-cumulant tensors (pp. 695-696) | html | pdf |
    - Table 8.3.2.1. Coordinates of atoms (in Å) in standard groups appearing in polypeptides and proteins (pp. 699-700) | html | pdf |
    - Table 8.3.2.2. Ideal values for distances (Å), torsion angles (°), etc. for a glycine–alanine dipeptide with a trans peptide bond (p. 700) | html | pdf |
    - Table 8.3.2.3. Typical values of standard deviations for use in determining weights in restrained refinement of protein structures (p. 701) | html | pdf |
- 8.4. Statistical significance tests (pp. 702-706) | html | pdf | chapter contents |
  E. Prince and C. H. Spiegelman
  - 8.4.1. The χ² distribution (pp. 702-703) | html | pdf |
  - 8.4.2. The F distribution (pp. 703-704) | html | pdf |
  - 8.4.3. Comparison of different models (pp. 704-705) | html | pdf |
  - 8.4.4. Influence of individual data points (pp. 705-706) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 8.4.1.1. Values of χ²/ν for which the c.d.f. ψ(χ², ν) has the values given in the column headings, for various values of ν (p. 703) | html | pdf |
    - Table 8.4.2.1. Values of the F ratio for which the c.d.f. ψ(F, ν₁, ν₂) has the value 0.95, for various choices of ν₁ and ν₂ (p. 704) | html | pdf |
    - Table 8.4.3.1. Values of t for which the c.d.f. Ψ(t, ν) has the values given in the column headings, for various values of ν (p. 704) | html | pdf |
- 8.5. Detection and treatment of systematic error (pp. 707-709) | html | pdf | chapter contents |
  E. Prince and C. H. Spiegelman
  - 8.5.1. Accuracy (p. 707) | html | pdf |
  - 8.5.2. Lack of fit (pp. 707-708) | html | pdf |
  - 8.5.3. Influential data points (p. 708) | html | pdf |
  - 8.5.4. Plausibility of results (p. 709) | html | pdf |
  - References | html | pdf |
- 8.6. The Rietveld method (pp. 710-712) | html | pdf | chapter contents |
  A. Albinati and B. T. M. Willis
  - 8.6.1. Basic theory (pp. 710-711) | html | pdf |
  - 8.6.2. Problems with the Rietveld method (pp. 711-712) | html | pdf |
    - 8.6.2.1. Indexing (p. 711) | html | pdf |
    - 8.6.2.2. Peak-shape function (PSF) (p. 711) | html | pdf |
    - 8.6.2.3. Background (p. 711) | html | pdf |
    - 8.6.2.4. Preferred orientation and texture (p. 712) | html | pdf |
    - 8.6.2.5. Statistical validity (p. 712) | html | pdf |
  - References | html | pdf |
- 8.7. Analysis of charge and spin densities (pp. 713-734) | html | pdf | chapter contents |
  P. Coppens, Z. Su and P. J. Becker
  - 8.7.1. Outline of this chapter (p. 713) | html | pdf |
  - 8.7.2. Electron densities and the n-particle wavefunction (p. 713) | html | pdf |
  - 8.7.3. Charge densities (pp. 714-725) | html | pdf |
    - 8.7.3.1. Introduction (p. 714) | html | pdf |
    - 8.7.3.2. Modelling of the charge density (pp. 714-715) | html | pdf |
    - 8.7.3.3. Physical constraints (p. 715) | html | pdf |
      - 8.7.3.3.1. Electroneutrality constraint (p. 715) | html | pdf |
      - 8.7.3.3.2. Cusp constraint (p. 715) | html | pdf |
      - 8.7.3.3.3. Radial constraint (p. 715) | html | pdf |
      - 8.7.3.3.4. Hellmann–Feynman constraint (p. 715) | html | pdf |
    - 8.7.3.4. Electrostatic moments and the potential due to a charge distribution (pp. 716-721) | html | pdf |
      - 8.7.3.4.1. Moments of a charge distribution  (pp. 716-718) | html | pdf |
        8.7.3.4.1.1. Moments as a function of the atomic multipole expansion  (pp. 716-717) | html | pdf |
        8.7.3.4.1.2. Molecular moments based on the deformation density  (p. 717) | html | pdf |
        8.7.3.4.1.3. The effect of an origin shift on the outer moments  (pp. 717-718) | html | pdf |
        8.7.3.4.1.4. Total moments as a sum over the pseudoatom moments  (p. 718) | html | pdf |
        8.7.3.4.1.5. Electrostatic moments of a subvolume of space by Fourier summation  (p. 718) | html | pdf |
      - 8.7.3.4.2. The electrostatic potential  (pp. 718-720) | html | pdf |
        8.7.3.4.2.1. The electrostatic potential and its derivatives  (pp. 718-719) | html | pdf |
        8.7.3.4.2.2. Electrostatic potential outside a charge distribution  (p. 720) | html | pdf |
        8.7.3.4.2.3. Evaluation of the electrostatic functions in direct space  (p. 720) | html | pdf |
      - 8.7.3.4.3. Electrostatic functions of crystals by modified Fourier summation (pp. 720-721) | html | pdf |
      - 8.7.3.4.4. The total energy of a crystal as a function of the electron density (p. 721) | html | pdf |
    - 8.7.3.5. Quantitative comparison with theory (pp. 721-722) | html | pdf |
    - 8.7.3.6. Occupancies of transition-metal valence orbitals from multipole coefficients (pp. 722-723) | html | pdf |
    - 8.7.3.7. Thermal smearing of theoretical densities (pp. 723-724) | html | pdf |
      - 8.7.3.7.1. General considerations (p. 723) | html | pdf |
      - 8.7.3.7.2. Reciprocal-space averaging over external vibrations (pp. 723-724) | html | pdf |
    - 8.7.3.8. Uncertainties in experimental electron densities (pp. 724-725) | html | pdf |
    - 8.7.3.9. Uncertainties in derived functions (p. 725) | html | pdf |
  - 8.7.4. Spin densities (pp. 725-734) | html | pdf |
    - 8.7.4.1. Introduction (p. 725) | html | pdf |
    - 8.7.4.2. Magnetization densities from neutron magnetic elastic scattering (pp. 725-726) | html | pdf |
    - 8.7.4.3. Magnetization densities and spin densities (pp. 726-727) | html | pdf |
      - 8.7.4.3.1. Spin-only density at zero temperature (p. 726) | html | pdf |
      - 8.7.4.3.2. Thermally averaged spin-only magnetization density (pp. 726-727) | html | pdf |
      - 8.7.4.3.3. Spin density for an assembly of localized systems (p. 727) | html | pdf |
      - 8.7.4.3.4. Orbital magnetization density (p. 727) | html | pdf |
    - 8.7.4.4. Probing spin densities by neutron elastic scattering (pp. 727-729) | html | pdf |
      - 8.7.4.4.1. Introduction (pp. 727-728) | html | pdf |
      - 8.7.4.4.2. Unpolarized neutron scattering (p. 728) | html | pdf |
      - 8.7.4.4.3. Polarized neutron scattering (p. 728) | html | pdf |
      - 8.7.4.4.4. Polarized neutron scattering of centrosymmetric crystals (p. 728) | html | pdf |
      - 8.7.4.4.5. Polarized neutron scattering in the noncentrosymmetric case (p. 728) | html | pdf |
      - 8.7.4.4.6. Effect of extinction (pp. 728-729) | html | pdf |
      - 8.7.4.4.7. Error analysis (p. 729) | html | pdf |
    - 8.7.4.5. Modelling the spin density (pp. 729-730) | html | pdf |
      - 8.7.4.5.1. Atom-centred expansion  (pp. 729-730) | html | pdf |
        8.7.4.5.1.1. Spherical-atom model  (p. 729) | html | pdf |
        8.7.4.5.1.2. Crystal-field approximation  (pp. 729-730) | html | pdf |
        8.7.4.5.1.3. Scaling of the spin density  (p. 730) | html | pdf |
      - 8.7.4.5.2. General multipolar expansion (p. 730) | html | pdf |
      - 8.7.4.5.3. Other types of model (p. 730) | html | pdf |
    - 8.7.4.6. Orbital contribution to the magnetic scattering (pp. 730-731) | html | pdf |
      - 8.7.4.6.1. The dipolar approximation (p. 731) | html | pdf |
      - 8.7.4.6.2. Beyond the dipolar approximation (p. 731) | html | pdf |
      - 8.7.4.6.3. Electronic structure of rare-earth elements (p. 731) | html | pdf |
    - 8.7.4.7. Properties derivable from spin densities (pp. 731-732) | html | pdf |
      - 8.7.4.7.1. Vector fields (p. 732) | html | pdf |
      - 8.7.4.7.2. Moments of the magnetization density (p. 732) | html | pdf |
    - 8.7.4.8. Comparison between theory and experiment (p. 732) | html | pdf |
    - 8.7.4.9. Combined charge- and spin-density analysis (p. 732) | html | pdf |
    - 8.7.4.10. Magnetic X-ray scattering separation between spin and orbital magnetism (pp. 733-734) | html | pdf |
      - 8.7.4.10.1. Introduction (p. 733) | html | pdf |
      - 8.7.4.10.2. Magnetic X-ray structure factor as a function of photon polarization (pp. 733-734) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 8.7.4.1. Some geometrical definitions (p. 733) | html | pdf |
  - Tables
    - Table 8.7.3.1. Definition of difference density functions (p. 714) | html | pdf |
    - Table 8.7.3.2. Expressions for the shape factors S for a parallelepiped with edges δ_x, δ_y, and δ_z (p. 719) | html | pdf |
    - Table 8.7.3.3. The matrix M⁻¹ relating d-orbital occupancies P_ij to multipole populations P_lm (p. 722) | html | pdf |
    - Table 8.7.3.4. Orbital–multipole relations for square-planar complexes (point group D_4h) (p. 723) | html | pdf |
    - Table 8.7.3.5. Orbital–multipole relations for trigonal complexes (p. 723) | html | pdf |
- 8.8. Accurate structure-factor determination with electron diffraction (pp. 735-743) | html | pdf | chapter contents |
  J. Gjønnes
  - References | html | pdf |
  - Figures
    - Fig. 8.8.1. Schematic representations of four convergent-beam configurations used for structure-factor determination: (a) intensity profile of a low-order reflection, g; (b) non-systematic three- or four-beam configuration with a strong coupling reflection, h; (c) symmetric many-beam configuration in a dense zone; (d) integrated intensity measurement of high-order reflections using a wide aperture (Taftø & Metzger, 1985) (p. 736) | html | pdf |

Basic structural features
- 9.1. Sphere packings and packings of ellipsoids (pp. 746-751) | html | pdf | chapter contents |
  E. Koch and W. Fischer
  - 9.1.1. Sphere packings and packings of circles (pp. 746-751) | html | pdf |
    - 9.1.1.1. Definitions (p. 746) | html | pdf |
    - 9.1.1.2. Homogeneous packings of circles (p. 746) | html | pdf |
    - 9.1.1.3. Homogeneous sphere packings (pp. 746-750) | html | pdf |
    - 9.1.1.4. Applications (pp. 750-751) | html | pdf |
    - 9.1.1.5. Interpenetrating sphere packings (p. 751) | html | pdf |
  - 9.1.2. Packings of ellipses and ellipsoids (p. 751) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 9.1.1.1. Two triangular nets representing two densest packed layers of spheres. The layers are stacked in such a way that each sphere is in contact with three spheres of the other layer (p. 747) | html | pdf |
    - Fig. 9.1.1.2. Two triangular nets representing two densest packed layers of spheres. The layers are stacked in such a way that each sphere is in contact with two spheres of the other layer (p. 749) | html | pdf |
    - Fig. 9.1.1.3. Two square nets representing two layers of spheres stacked in such a way that each sphere is in contact with four spheres of the other layer (p. 749) | html | pdf |
    - Fig. 9.1.1.4. Two square nets representing two layers of spheres stacked in such a way that each sphere is in contact with two spheres of the other layer (p. 749) | html | pdf |
    - Fig. 9.1.1.5. Sphere packing of type 8 (p. 749) | html | pdf |
    - Fig. 9.1.1.6. Sphere packing of type 19 (p. 750) | html | pdf |
    - Fig. 9.1.1.7. Least dense sphere packing known so far (p. 750) | html | pdf |
  - Tables
    - Table 9.1.1.1. Types of circle packings in the plane (p. 747) | html | pdf |
    - Table 9.1.1.2. Examples for sphere packings with high contact numbers and high densities and with low contact numbers and low densities (p. 748) | html | pdf |
- 9.2. Layer stacking (pp. 752-773) | html | pdf | chapter contents |
  S. Ďurovič, P. Krishna and D. Pandey
  - 9.2.1. Layer stacking in close-packed structures (pp. 752-760) | html | pdf |
    D. Pandey and P. Krishna
    - 9.2.1.1. Close packing of equal spheres (pp. 752-753) | html | pdf |
      - 9.2.1.1.1. Close-packed layer (p. 752) | html | pdf |
      - 9.2.1.1.2. Close-packed structures (p. 752) | html | pdf |
      - 9.2.1.1.3. Notations for close-packed structures (pp. 752-753) | html | pdf |
    - 9.2.1.2. Structure of compounds based on close-packed layer stackings (pp. 753-755) | html | pdf |
      - 9.2.1.2.1. Voids in close packing (p. 753) | html | pdf |
      - 9.2.1.2.2. Structures of SiC and ZnS (pp. 753-754) | html | pdf |
      - 9.2.1.2.3. Structure of CdI₂ (p. 754) | html | pdf |
      - 9.2.1.2.4. Structure of GaSe (pp. 754-755) | html | pdf |
    - 9.2.1.3. Symmetry of close-packed layer stackings of equal spheres (p. 755) | html | pdf |
    - 9.2.1.4. Possible lattice types (p. 755) | html | pdf |
    - 9.2.1.5. Possible space groups (pp. 755-756) | html | pdf |
    - 9.2.1.6. Crystallographic uses of Zhdanov symbols (p. 756) | html | pdf |
    - 9.2.1.7. Structure determination of close-packed layer stackings (pp. 756-758) | html | pdf |
      - 9.2.1.7.1. General considerations (p. 756) | html | pdf |
      - 9.2.1.7.2. Determination of the lattice type (p. 757) | html | pdf |
      - 9.2.1.7.3. Determination of the identity period (p. 757) | html | pdf |
      - 9.2.1.7.4. Determination of the stacking sequence of layers (pp. 757-758) | html | pdf |
    - 9.2.1.8. Stacking faults in close-packed structures (pp. 758-760) | html | pdf |
      - 9.2.1.8.1. Structure determination of one-dimensionally disordered crystals (pp. 759-760) | html | pdf |
  - 9.2.2. Layer stacking in general polytypic structures (pp. 760-773) | html | pdf |
    S. Ďurovič
    - 9.2.2.1. The notion of polytypism (pp. 760-761) | html | pdf |
    - 9.2.2.2. Symmetry aspects of polytypism (pp. 761-766) | html | pdf |
      - 9.2.2.2.1. Close packing of spheres (p. 761) | html | pdf |
      - 9.2.2.2.2. Polytype families and OD groupoid families (pp. 761-762) | html | pdf |
      - 9.2.2.2.3. MDO polytypes (p. 762) | html | pdf |
      - 9.2.2.2.4. Some geometrical properties of OD structures (pp. 762-763) | html | pdf |
      - 9.2.2.2.5. Diffraction pattern – structure analysis (p. 763) | html | pdf |
      - 9.2.2.2.6. The vicinity condition (pp. 763-764) | html | pdf |
      - 9.2.2.2.7. Categories of OD structures  (pp. 764-765) | html | pdf |
        9.2.2.2.7.1. OD structures of equivalent layers  (pp. 764-765) | html | pdf |
        9.2.2.2.7.2. OD structures with more than one kind of layer  (p. 765) | html | pdf |
      - 9.2.2.2.8. Desymmetrization of OD structures (pp. 765-766) | html | pdf |
      - 9.2.2.2.9. Concluding remarks (p. 766) | html | pdf |
    - 9.2.2.3. Examples of some polytypic structures (pp. 766-772) | html | pdf |
      - 9.2.2.3.1. Hydrous phyllosilicates  (pp. 766-769) | html | pdf |
        9.2.2.3.1.1. General geometry  (pp. 767-769) | html | pdf |
        9.2.2.3.1.2. Diffraction pattern and identification of individual polytypes  (p. 769) | html | pdf |
      - 9.2.2.3.2. Stibivanite Sb₂VO₅ (pp. 769-771) | html | pdf |
      - 9.2.2.3.3. γ-Hg₃S₂Cl₂ (pp. 771-772) | html | pdf |
      - 9.2.2.3.4. Remarks for authors (p. 772) | html | pdf |
    - 9.2.2.4. List of some polytypic structures (pp. 772-773) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 9.2.1.1. The close packing of equal spheres in a plane (p. 752) | html | pdf |
    - Fig. 9.2.1.2. (a) Symmetry axes of a single close-packed layer of spheres and (b) the minimum symmetry of a three-dimensional close packing of spheres (p. 752) | html | pdf |
    - Fig. 9.2.1.3. Voids in a close packing: (a) tetrahedral void; (b) tetrahedron formed by the centres of spheres; (c) octahedral void; (d) octahedron formed by the centres of spheres (p. 753) | html | pdf |
    - Fig. 9.2.1.4. Tetrahedral arrangement of Si and C atoms in the SiC-6H structure (p. 753) | html | pdf |
    - Fig. 9.2.1.5. The layer structure of CdI₂: small circles represent Cd ions and larger ones I ions (p. 754) | html | pdf |
    - Fig. 9.2.1.6. The primitive unit cell of the 2H close packing (p. 755) | html | pdf |
    - Fig. 9.2.1.7. A rhombohedral lattice (a₁, a₂, a₃) referred to hexagonal axes (A₁, A₂, C) (p. 755) | html | pdf |
    - Fig. 9.2.1.8. The relationship between the f.c.c. and the primitive rhombohedral unit cell of the c.c.p. structure (p. 756) | html | pdf |
    - Fig. 9.2.1.9. The a*−b* reciprocal-lattice net for close-packed layer stackings (p. 756) | html | pdf |
    - Fig. 9.2.2.1. Symmetry interpretation of close packings of equal spheres (p. 761) | html | pdf |
    - Fig. 9.2.2.2. Schematic representation of three structures belonging to the OD groupoid family P(1)m1|1 (p. 762) | html | pdf |
    - Fig. 9.2.2.3. Schematic examples of the three categories of OD structures consisting of equivalent layers (perpendicular to the plane of the drawing) (p. 764) | html | pdf |
    - Fig. 9.2.2.4. Schematic examples of the four categories of OD structures consisting of more than one kind of layer (perpendicular to the plane of the drawing) (p. 764) | html | pdf |
    - Fig. 9.2.2.5. Hierarchy of VC structures indicating the position of OD structures within it (p. 765) | html | pdf |
    - Fig. 9.2.2.6. (a) Tetrahedral sheet in a normal projection (p. 767) | html | pdf |
    - Fig. 9.2.2.7. Two possible combinations of one tetrahedral and one octahedral sheet (a) by shared apical O atoms, (b) by hydrogen bonds (side projection) (p. 767) | html | pdf |
    - Fig. 9.2.2.8. Combination of two adjacent tetrahedral sheets (a) in the mica group, (b) in the talc–pyrophyllite group (side projection) (p. 767) | html | pdf |
    - Fig. 9.2.2.9. The nine possible displacements in the structures of polytypes of phyllosilicates (p. 768) | html | pdf |
    - Fig. 9.2.2.10. The NFZ relations (a) for the pair tetrahedral sheet–homo-octahedral sheet (with shared apical O atoms), (b), (c) for the pair homo-octahedral sheet–tetrahedral sheet (by hydrogen bonds) (p. 768) | html | pdf |
    - Fig. 9.2.2.11. Stereopair showing the sequence of sheets in the structures of the serpentine–kaolin group (p. 769) | html | pdf |
    - Fig. 9.2.2.12. Stereopair showing the sequence of sheets in the structures of the mica group (p. 770) | html | pdf |
    - Fig. 9.2.2.13. Stereopair showing the sequence of sheets in the structures of the talc–pyrophyllite group (p. 770) | html | pdf |
    - Fig. 9.2.2.14. Stereopair showing the sequence of sheets in the structures of the chlorite–vermiculite group (chlorite-1M, courtesy of Zoltai & Stout, 1985) (p. 770) | html | pdf |
    - Fig. 9.2.2.15. Clinographic projection of the general scheme of a single-crystal diffraction pattern of hydrous phyllosilicates (p. 771) | html | pdf |
    - Fig. 9.2.2.16. Normal projection of the general scheme of a single-crystal diffraction pattern of hydrous phyllosilicates (p. 771) | html | pdf |
    - Fig. 9.2.2.17. The structure of stibivanite-2M (p. 771) | html | pdf |
    - Fig. 9.2.2.18. The two kinds of OD layers in the stibivanite family (p. 772) | html | pdf |
    - Fig. 9.2.2.19. The structure of stibivanite-2O (p. 772) | html | pdf |
    - Fig. 9.2.2.20. The structural principle of γ-Hg₃S₂Cl₂ (p. 772) | html | pdf |
  - Tables
    - Table 9.2.1.1. Common close-packed metallic structures (p. 753) | html | pdf |
    - Table 9.2.1.2. List of SiC polytypes with known structures in order of increasing periodicity (p. 754) | html | pdf |
    - Table 9.2.1.3. Intrinsic fault configurations in the 6H (A₀B₁C₂A₃C₄B₅;. . .) structure (p. 758) | html | pdf |
    - Table 9.2.1.4. Intrinsic fault configurations in the 9R (A₀B₁A₂C₀A₁C₂B₀C₁B₂;. . .) structure (p. 759) | html | pdf |
- 9.3. Typical interatomic distances: metals and alloys (pp. 774-777) | html | pdf | chapter contents |
  J. L. C. Daams, J. R. Rodgers and P. Villars
  - 9.3.1. Glossary (p. 777) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 9.3.1. (a) The radii for CN = 12 (p. 774) | html | pdf |
    - Fig. 9.3.2. (a) Plot of d_AB versus $[\bar R]$ for the binary compounds crystallizing in hP3 AlB₂ (p. 775) | html | pdf |
    - Fig. 9.3.3. (a) A typical example of a next-neighbour histogram (NNH) and (b) the atomic environment (AE) coordination polyhedron belonging to this NNH (p. 775) | html | pdf |
    - Fig. 9.3.4. (a) The 23 most frequently occurring atomic environment types (AET) with their polyhedron code (pp. 776-777) | html | pdf |
- 9.4. Typical interatomic distances: inorganic compounds (pp. 778-789) | html | pdf | chapter contents |
  G. Bergerhoff and K. Brandenburg
  - 9.4.1. Introduction (p. 778) | html | pdf |
  - 9.4.2. The retrieval system (p. 778) | html | pdf |
  - 9.4.3. Interpretation of frequency distributions (p. 778) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 9.4.1.1. Atomic distances between halogens and main-group elements in their preferred oxidation states (pp. 779-780) | html | pdf |
    - Table 9.4.1.2. Atomic distances between halogens and main-group elements in their special oxidation states (pp. 780-781) | html | pdf |
    - Table 9.4.1.3. Atomic distances between halogens and transition metals (pp. 781-784) | html | pdf |
    - Table 9.4.1.4. Atomic distances between halogens and lanthanoids (p. 784) | html | pdf |
    - Table 9.4.1.5. Atomic distances between halogens and actinoids (p. 785) | html | pdf |
    - Table 9.4.1.6. Atomic distances between oxygen and main-group elements in their preferred oxidation states (p. 785) | html | pdf |
    - Table 9.4.1.7. Atomic distances between oxygen and main-group elements in their special oxidation states (p. 786) | html | pdf |
    - Table 9.4.1.8. Atomic distances between oxygen and transition elements in their preferred and special oxidation states (pp. 786-787) | html | pdf |
    - Table 9.4.1.9. Atomic distances between oxygen and lanthanoids (p. 787) | html | pdf |
    - Table 9.4.1.10. Atomic distances between oxygen and actinoids (p. 788) | html | pdf |
    - Table 9.4.1.11. Atomic distances in sulfides and thiometallates (pp. 788-789) | html | pdf |
    - Table 9.4.1.12. Contact distances between some negatively charged elements (p. 789) | html | pdf |
- 9.5. Typical interatomic distances: organic compounds (pp. 790-811) | html | pdf | chapter contents |
  F. H. Allen, D. G. Watson, L. Brammer, A. G. Orpen and R. Taylor
  - 9.5.1. Introduction (p. 790) | html | pdf |
  - 9.5.2. Methodology (pp. 790-791) | html | pdf |
    - 9.5.2.1. Selection of crystallographic data (p. 790) | html | pdf |
    - 9.5.2.2. Program system (pp. 790-791) | html | pdf |
    - 9.5.2.3. Classification of bonds (p. 791) | html | pdf |
    - 9.5.2.4. Statistics (p. 791) | html | pdf |
  - 9.5.3. Content and arrangement of the table (pp. 791-794) | html | pdf |
    - 9.5.3.1. Ordering of entries: the `Bond' column (p. 792) | html | pdf |
    - 9.5.3.2. Definition of `Substructure' (pp. 792-793) | html | pdf |
    - 9.5.3.3. Use of the `Note' column (pp. 793-794) | html | pdf |
  - 9.5.4. Discussion (p. 794) | html | pdf |
  - Appendix 9.5.1. Notes to Table 9.5.1.1 (p. 794) | html | pdf |
  - Appendix 9.5.2. Short-form references to individual CSD entries cited by reference code in Table 9.5.1.1 (pp. 794-795) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 9.5.1.1. Growth of the Cambridge Structural Database 1965–1985 as number of entries (N_ent) published in a given year (p. 790) | html | pdf |
    - Fig. 9.5.2.1. Effect of the removal of outliers (contributors that are > 4σ from the mean) for the C—C bond in C_ar—C≡N fragments (p. 791) | html | pdf |
    - Fig. 9.5.2.2. Skewed distribution of B—F bond lengths in $[{\rm BF}_{4}^{-}]$ ions (pp. 791-792) | html | pdf |
    - Fig. 9.5.2.3. Resolution of the bimodal distribution of C—N bond lengths in C_ar —N(Csp³)₂ fragments (p. 792) | html | pdf |
    - Fig. 9.5.3.1. (a) Distribution of mean bond-length values reported in the table by element pair (p. 792) | html | pdf |
    - Fig. 9.5.3.2. Alphabetized index of ring systems referred to in the table; the numbering scheme used in assembling the bond-length data is given where necessary (p. 793) | html | pdf |
  - Tables
    - Table 9.5.1.1. Average lengths (Å) for bonds involving the elements H, B, C, N, O, F, Si, P, S, Cl, As, Se, Br, Te, and I (pp. 796-811) | html | pdf |
- 9.6. Typical interatomic distances: organometallic compounds and coordination complexes of the d- and f-block metals (pp. 812-896) | html | pdf | chapter contents |
  A. G. Orpen, L. Brammer, F. H. Allen, D. G. Watson and R. Taylor
  - 9.6.1. Introduction (p. 812) | html | pdf |
  - 9.6.2. Methodology (pp. 812-814) | html | pdf |
    - 9.6.2.1. Selection of crystallographic data (p. 812) | html | pdf |
    - 9.6.2.2. Program system (p. 813) | html | pdf |
    - 9.6.2.3. Classification of bonds (p. 813) | html | pdf |
    - 9.6.2.4. Statistics (pp. 813-814) | html | pdf |
  - 9.6.3. Content and arrangement of table of interatomic distances (pp. 814-818) | html | pdf |
    - 9.6.3.1. The `Bond' column (p. 815) | html | pdf |
    - 9.6.3.2. Definition of `Substructure' (pp. 815-817) | html | pdf |
    - 9.6.3.3. Use of the `Note' column (pp. 817-818) | html | pdf |
    - 9.6.3.4. Locating an entry in Table 9.6.3.3 (p. 818) | html | pdf |
  - 9.6.4. Discussion (pp. 818-884) | html | pdf |
  - Appendix 9.6.1. Notes and references to Tables 9.6.3.2 and 9.6.3.3 (pp. 884-886) | html | pdf |
  - Appendix 9.6.2. Short-form references to individual CSD entries cited in Table 9.6.3.3 (pp. 886-896) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 9.6.1.1. Growth of the Cambridge Structural Database as number of entries (N_ent) added annually (p. 812) | html | pdf |
    - Fig. 9.6.2.1. Effects of outlier removal and subdivision based on coordination number and oxidation state (p. 814) | html | pdf |
    - Fig. 9.6.3.1. Diagrams of ligands in Table 9.6.3.3, showing table entry number and ligand atom labelling (p. 816) | html | pdf |
  - Tables
    - Table 9.6.3.1. Ligand index (pp. 814-815) | html | pdf |
    - Table 9.6.3.2. Numbers of entries in Table 9.6.3.3 (p. 817) | html | pdf |
    - Table 9.6.3.3. Interatomic distances (Å) (pp. 818-883) | html | pdf |
- 9.7. The space-group distribution of molecular organic structures (pp. 897-906) | html | pdf | chapter contents |
  A. J. C. Wilson, V. L. Karen and A. Mighell
  - 9.7.1. A priori classifications of space groups (pp. 897-900) | html | pdf |
    - 9.7.1.1. Kitajgorodskij's categories (p. 897) | html | pdf |
    - 9.7.1.2. Symmorphism and antimorphism (pp. 897-899) | html | pdf |
    - 9.7.1.3. Comparison of Kitajgorodskij's and Wilson's classifications (pp. 899-900) | html | pdf |
    - 9.7.1.4. Relation to structural classes (p. 900) | html | pdf |
  - 9.7.2. Special positions of given symmetry (pp. 900-902) | html | pdf |
  - 9.7.3. Empirical space-group frequencies (p. 902) | html | pdf |
  - 9.7.4. Use of molecular symmetry (pp. 902-904) | html | pdf |
    - 9.7.4.1. Positions with symmetry 1 (p. 902) | html | pdf |
    - 9.7.4.2. Positions with symmetry $[{\overline 1}]$ (pp. 902-903) | html | pdf |
    - 9.7.4.3. Other symmetries (p. 903) | html | pdf |
    - 9.7.4.4. Positions with the full symmetry of the geometric class (pp. 903-904) | html | pdf |
  - 9.7.5. Structural classes (p. 904) | html | pdf |
  - 9.7.6. A statistical model (p. 904) | html | pdf |
  - 9.7.7. Molecular packing (pp. 904-906) | html | pdf |
    - 9.7.7.1. Relation to sphere packing (pp. 904-906) | html | pdf |
    - 9.7.7.2. The hydrogen bond and the definition of the packing units (p. 906) | html | pdf |
  - 9.7.8. A priori predictions of molecular crystal structures (p. 906) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 9.7.1.1. Kitajgorodskij's categorization of the triclinic, monoclinic and orthorhombic space groups, as modified by Wilson (1993a) (p. 898) | html | pdf |
    - Table 9.7.1.2. Space groups arranged by arithmetic crystal class and degree of symmorphism (Wilson, 1993d), as frequented by homomolecular structures with one molecule in the general position (in superscript numerals; according to Belsky, Zorkaya & Zorky, 1995) (pp. 899-901) | html | pdf |
    - Table 9.7.2.1. Statistics of the use of Wyckoff positions of specified symmetry $[{\cal G}]$ in the homomolecular organic crystals, based on the data by Belsky, Zorkaya & Zorky (1995) (p. 903) | html | pdf |
    - Table 9.7.4.1. Occurrence of molecules with specified point group in centred symmorphic and other space groups, based on the statistics by Belsky, Zorkaya & Zorky (1995) (p. 905) | html | pdf |
- 9.8. Incommensurate and commensurate modulated structures (pp. 907-955) | html | pdf | chapter contents |
  T. Janssen, A. Janner, A. Looijenga-Vos and P. M. de Wolff
  - 9.8.1. Introduction (pp. 907-913) | html | pdf |
    - 9.8.1.1. Modulated crystal structures (pp. 907-908) | html | pdf |
    - 9.8.1.2. The basic ideas of higher-dimensional crystallography (pp. 908-909) | html | pdf |
    - 9.8.1.3. The simple case of a displacively modulated crystal (pp. 909-910) | html | pdf |
      - 9.8.1.3.1. The diffraction pattern (p. 909) | html | pdf |
      - 9.8.1.3.2. The symmetry (pp. 909-910) | html | pdf |
    - 9.8.1.4. Basic symmetry considerations (pp. 910-913) | html | pdf |
      - 9.8.1.4.1. Bravais classes of vector modules (pp. 910-911) | html | pdf |
      - 9.8.1.4.2. Description in four dimensions (p. 911) | html | pdf |
      - 9.8.1.4.3. Four-dimensional crystallography (pp. 911-912) | html | pdf |
      - 9.8.1.4.4. Generalized nomenclature (p. 912) | html | pdf |
      - 9.8.1.4.5. Four-dimensional space groups (pp. 912-913) | html | pdf |
    - 9.8.1.5. Occupation modulation (p. 913) | html | pdf |
  - 9.8.2. Outline for a superspace-group determination (pp. 913-915) | html | pdf |
  - 9.8.3. Introduction to the tables (pp. 915-937) | html | pdf |
    - 9.8.3.1. Tables of Bravais lattices (pp. 915-916) | html | pdf |
    - 9.8.3.2. Table for geometric and arithmetic crystal classes (p. 916) | html | pdf |
    - 9.8.3.3. Tables of superspace groups (pp. 916-935) | html | pdf |
      - 9.8.3.3.1. Symmetry elements (pp. 916-921) | html | pdf |
      - 9.8.3.3.2. Reflection conditions (pp. 921-935) | html | pdf |
    - 9.8.3.4. Guide to the use of the tables (pp. 935-936) | html | pdf |
    - 9.8.3.5. Examples (p. 936) | html | pdf |
    - 9.8.3.6. Ambiguities in the notation (pp. 936-937) | html | pdf |
  - 9.8.4. Theoretical foundation (pp. 937-945) | html | pdf |
    - 9.8.4.1. Lattices and metric (pp. 937-938) | html | pdf |
    - 9.8.4.2. Point groups (pp. 938-939) | html | pdf |
      - 9.8.4.2.1. Laue class (pp. 938-939) | html | pdf |
      - 9.8.4.2.2. Geometric and arithmetic crystal classes (p. 939) | html | pdf |
    - 9.8.4.3. Systems and Bravais classes (pp. 939-940) | html | pdf |
      - 9.8.4.3.1. Holohedry (pp. 939-940) | html | pdf |
      - 9.8.4.3.2. Crystallographic systems (p. 940) | html | pdf |
      - 9.8.4.3.3. Bravais classes (p. 940) | html | pdf |
    - 9.8.4.4. Superspace groups (pp. 940-941) | html | pdf |
      - 9.8.4.4.1. Symmetry elements (p. 940) | html | pdf |
      - 9.8.4.4.2. Equivalent positions and modulation relations (pp. 940-941) | html | pdf |
      - 9.8.4.4.3. Structure factor (p. 941) | html | pdf |
  - 9.8.5. Generalizations (pp. 941-943) | html | pdf |
    - 9.8.5.1. Incommensurate composite crystal structures (pp. 941-942) | html | pdf |
    - 9.8.5.2. The incommensurate versus the commensurate case (pp. 942-943) | html | pdf |
  - Appendix 9.8.1. Glossary of symbols (pp. 943-944) | html | pdf |
  - Appendix 9.8.2. Basic definitions (pp. 944-945) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 9.8.3.1. (2 + 1)- and (2 + 2)-Dimensional Bravais classes for incommensurate structures (pp. 915-916) | html | pdf |
    - Table 9.8.3.2. (3 + 1)-Dimensional Bravais classes for incommensurate and commensurate structures (pp. 917-918) | html | pdf |
    - Table 9.8.3.3. (3 + 1)-Dimensional point groups and arithmetic crystal classes (pp. 919-920) | html | pdf |
    - Table 9.8.3.4. (2 + 1)- and (2 + 2)-Dimensional superspace groups (pp. 920-921) | html | pdf |
    - Table 9.8.3.5. (3 + 1)-Dimensional superspace groupssuperspace group finder (pp. 922-934) | html | pdf |
    - Table 9.8.3.6. Centring reflection conditions for (3 + 1)-dimensional Bravais classes (p. 935) | html | pdf |

Precautions against radiation injury
- 10.1. Introduction (pp. 958-961) | html | pdf | chapter contents |
  D. C. Creagh and S. Martinez-Carrera
  - 10.1.1. Definitions (pp. 958-960) | html | pdf |
    - 10.1.1.1. Ionizing radiation (p. 958) | html | pdf |
    - 10.1.1.2. Absorbed dose (p. 958) | html | pdf |
    - 10.1.1.3. Activity (p. 958) | html | pdf |
    - 10.1.1.4. Adequate protection (p. 958) | html | pdf |
    - 10.1.1.5. Background (radiation) (p. 958) | html | pdf |
    - 10.1.1.6. Becquerel (Bq) (p. 958) | html | pdf |
    - 10.1.1.7. Designated radiation area (p. 958) | html | pdf |
    - 10.1.1.8. Dose equivalent (p. 958) | html | pdf |
    - 10.1.1.9. Exposure of X-ray or γ-radiation (p. 958) | html | pdf |
    - 10.1.1.10. External radiation (p. 958) | html | pdf |
    - 10.1.1.11. Glove box (p. 959) | html | pdf |
    - 10.1.1.12. Gray (Gy) (p. 959) | html | pdf |
    - 10.1.1.13. Half life (p. 959) | html | pdf |
    - 10.1.1.14. Internal radiation (p. 959) | html | pdf |
    - 10.1.1.15. Irradiating apparatus (p. 959) | html | pdf |
    - 10.1.1.16. Leakage radiation (p. 959) | html | pdf |
    - 10.1.1.17. Licensable quantity (p. 959) | html | pdf |
    - 10.1.1.18. Maximum permissible concentration (p. 959) | html | pdf |
    - 10.1.1.19. Natural background (p. 959) | html | pdf |
    - 10.1.1.20. Non-stochastic effects (p. 959) | html | pdf |
    - 10.1.1.21. Nuclide (p. 959) | html | pdf |
    - 10.1.1.22. Occupied area (p. 959) | html | pdf |
    - 10.1.1.23. Protective housing (p. 959) | html | pdf |
    - 10.1.1.24. Quality factor (QF) (p. 959) | html | pdf |
    - 10.1.1.25. Radiation laboratory (p. 959) | html | pdf |
    - 10.1.1.26. Radioactive contamination (p. 959) | html | pdf |
    - 10.1.1.27. Radioactive material (p. 959) | html | pdf |
    - 10.1.1.28. Radioisotope laboratory (p. 959) | html | pdf |
    - 10.1.1.29. Radiological hazard (p. 959) | html | pdf |
    - 10.1.1.30. Radiological laboratory (p. 959) | html | pdf |
    - 10.1.1.31. Radionuclide (p. 959) | html | pdf |
    - 10.1.1.32. Radiotoxicity (p. 959) | html | pdf |
    - 10.1.1.33. Sealed source (p. 959) | html | pdf |
    - 10.1.1.34. Sievert (Sv) (p. 959) | html | pdf |
    - 10.1.1.35. Stochastic effects (p. 959) | html | pdf |
    - 10.1.1.36. Unsealed source (p. 959) | html | pdf |
    - 10.1.1.37. Useful beam (p. 960) | html | pdf |
  - 10.1.2. Objectives of radiation protection (p. 960) | html | pdf |
  - 10.1.3. Responsibilities (pp. 960-961) | html | pdf |
    - 10.1.3.1. General (p. 960) | html | pdf |
    - 10.1.3.2. The radiation safety officer (p. 960) | html | pdf |
    - 10.1.3.3. The worker (pp. 960-961) | html | pdf |
    - 10.1.3.4. Primary-dose limits (p. 961) | html | pdf |
  - References | html | pdf |
  - Tables
    - Table 10.1.1. The relationship between SI and the earlier system of units (p. 958) | html | pdf |
    - Table 10.1.2. Maximum primary-dose limit per quarter [based on National Health and Medical Research Council (1977), as amended] (p. 960) | html | pdf |
    - Table 10.1.3. Quality factors (QF) (p. 960) | html | pdf |
- 10.2. Protection from ionizing radiation (pp. 962-963) | html | pdf | chapter contents |
  D. C. Creagh and S. Martinez-Carrera
  - 10.2.1. General (p. 962) | html | pdf |
  - 10.2.2. Sealed sources and radiation-producing apparatus (pp. 962-963) | html | pdf |
    - 10.2.2.1. Enclosed installations (p. 962) | html | pdf |
    - 10.2.2.2. Open installations (p. 962) | html | pdf |
    - 10.2.2.3. Sealed sources (p. 962) | html | pdf |
    - 10.2.2.4. X-ray diffraction and X-ray analysis apparatus (p. 962) | html | pdf |
    - 10.2.2.5. Particle accelerators (pp. 962-963) | html | pdf |
  - 10.2.3. Ionizing-radiation protection – unsealed radioactive materials (p. 963) | html | pdf |
  - References | html | pdf |
- 10.3. Responsible bodies (pp. 964-967) | html | pdf | chapter contents |
  D. C. Creagh and S. Martinez-Carrera
  - References | html | pdf |
  - Tables
    - Table 10.3.1. Regulatory authorities (pp. 964-966) | html | pdf |

Resources | html |

International Tables for CrystallographyVolume C: Mathematical, physical and chemical tables

Edited by E. Prince

Contents

International Tables for Crystallography
Volume C: Mathematical, physical and chemical tables