(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 eISBN: 978-1-4020-5408-2 doi: 10.1107/97809553602060000103

Edited by E. Prince

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

Part 1. 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 = 2 a ) 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 |

Part 2. 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 K α 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 K α, 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 Mg ₂ GeO ₄ 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-Fe ₂ O ₃ 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 K α (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 4 σ 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 K α 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: 2θ ₀ = fixed scattering angle (p. 84) | html | pdf |
    - Fig. 2.5.1.2. XED powder spectrum of BaTiO ₃ 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 + d r within the particle (p. 91) | html | pdf |
    - Fig. 2.6.1.2. Comparison of the scattering functions of a sphere (dashed line) and a cube (continuous line) with same radius of gyration (p. 94) | html | pdf |
    - Fig. 2.6.1.3. Distance distribution function of a sphere (dashed line) and a cube (continuous line) with the same radius of gyration and the same scattering intensity at zero angle (p. 94) | html | pdf |
    - Fig. 2.6.1.4. Comparison of the p ( r ) function of a sphere (continuous line), a prolate ellipsoid of revolution 1:1:3 (dash-dotted line), and an oblate ellipsoid of revolution 1:1:0.2 (dashed line) with the same radius of gyration (p. 94) | html | pdf |
    - Fig. 2.6.1.5. Comparison of the I ( h ) functions of a sphere, a prolate, and an oblate ellipsoid (see legend to Fig (p. 94) | html | pdf |
    - Fig. 2.6.1.6. Distance distributions from homogeneous parallelepipeds with edge lengths of: ( a ) 50 × 50 × 500 Å; ( b ) 50 × 50 × 250 Å; ( c ) 50 × 50 × 150 Å (p. 95) | html | pdf |
    - Fig. 2.6.1.7. Three parallelepipeds with constant length L (400 Å) and a constant cross section but varying length of the edges: continuous line 40 × 40 Å; dash-dotted line 80 × 20 Å; dashed line 160 × 10 Å (p. 95) | html | pdf |
    - Fig. 2.6.1.8. Circular cylinder with a constant length of 480 Å and an outer diameter of 48 Å (p. 96) | html | pdf |
    - Fig. 2.6.1.9. Inhomogeneous circular cylinder with periodical changes of the electron density along the cylinder axis compared with a homogeneous cylinder with the same mean electron density (p. 97) | html | pdf |
    - Fig. 2.6.1.10. p ( r ) function of a lamellar particle (p. 97) | html | pdf |
    - Fig. 2.6.1.11. Characteristic types of scattering functions: ( a ) gas type; ( b ) particle scattering; ( c ) liquid type (p. 98) | html | pdf |
    - Fig. 2.6.1.12. Distance distribution – hard-sphere interference model (p. 98) | html | pdf |
    - Fig. 2.6.1.13. Schematic drawing of the block collimation (Kratky camera): E edge; B ₁ centre piece; B ₂ bridge; P primary-beam profile; PS primary-beam stop; PR plane of registration (p. 99) | html | pdf |
    - Fig. 2.6.1.14. Function systems ϕ _v ( r ); Ψ _v ( h ); and χ _v ( h ) used for the approximation of the scattering data in the indirect transformation method (p. 102) | html | pdf |
  - Tables
    - Table 2.6.1.1. Formulae for the various parameters for h (left) and m (right) scales (p. 92) | html | pdf |
- 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 |

Part 3. 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

Part 4. 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-L ₃ 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-L ₃ 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 k ³ ); ( 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 LiNbO ₃ 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 / mc ² 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 K α ₁ , Mo K α ₁ and Cu K α ₁ 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 K α ₁ , Mo K α ₁ and Cu K α ₁ 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 E ₀ and wavevector k is inelastically scattered into a state of energy E ₀ − 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 d σ /d Ω 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 ħω ₀ = 10 eV and relaxation time τ ₀ = 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 TiO ₂ (p. 408) | html | pdf |
    - Fig. 4.3.4.28. The dramatic change in near-edge fine structures on the L ₃ and L ₂ 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 ), γ k 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 6 H 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 atoms interactive 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 , $[\boldtheta]$ , Δ E ) (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 Δ E _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 fm ² ) of the elements and their isotopes interactive version (pp. 445-452) | html | pdf |
    - Table 4.4.5.1. < j ₀ > form factors for 3 d transition elements and their ions (p. 454) | html | pdf |
    - Table 4.4.5.2. < j ₀ > form factors for 4 d atoms and their ions (p. 455) | html | pdf |
    - Table 4.4.5.3. < j ₀ > form factors for rare-earth ions (p. 455) | html | pdf |
    - Table 4.4.5.4. < j ₀ > form factors for actinide ions (p. 455) | html | pdf |
    - Table 4.4.5.5. < j ₂ > form factors for 3 d transition elements and their ions (p. 456) | html | pdf |
    - Table 4.4.5.6. < j ₂ > form factors for 4 d atoms and their ions (p. 457) | html | pdf |
    - Table 4.4.5.7. < j ₂ > form factors for rare-earth ions (p. 457) | html | pdf |
    - Table 4.4.5.8. < j ₂ > form factors for actinide ions (p. 457) | html | pdf |
    - Table 4.4.5.9. < j ₄ > form factors for 3 d atoms and their ions (p. 458) | html | pdf |
    - Table 4.4.5.10. < j ₄ > form factors for 4 d atoms and their ions (p. 459) | html | pdf |
    - Table 4.4.5.11. < j ₄ > form factors for rare-earth ions (p. 459) | html | pdf |
    - Table 4.4.5.12. < j ₄ > form factors for actinide ions (p. 459) | html | pdf |
    - Table 4.4.5.13. < j ₆ > form factors for rare-earth ions (p. 460) | html | pdf |
    - Table 4.4.5.14. < j ₆ > form factors for actinide ions (p. 460) | html | pdf |
    - Table 4.4.6.1. Absorption of the elements for neutrons (p. 461) | html | pdf |

Part 5. 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 00 l standard reflection angles (p. 503) | html | pdf |
    - Table 5.2.10.7. Silver behenate 00 l 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 (1973 a ); 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

Part 6. 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 < j ₀ >, < j ₂ >, and < j ₄ > for the Fe ²⁺ ion plotted against $[(\sin\theta)/\lambda]$ (p. 592) | html | pdf |
    - Fig. 6.1.2.2. Comparison of 3 d , 4 d , 4 f , and 5 f form factors (p. 592) | html | pdf |
    - Fig. 6.1.3.1. Dependence on neutron wavelength of the coherent scattering length of ¹¹³ Cd (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 |

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