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

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

## Contents

• Crystal geometry and symmetry
• 1.1. Summary of general formulae  (pp. 2-5)
• 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)
• 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 to pairs h, k with   (p. 7) | html | pdf |
• Table 1.2.5.1. Assignment of integers to pairs h, k with   (p. 8) | html | pdf |
• Table 1.2.5.2. Assignment of integers to triplets h, k, l with and to integers   (p. 8) | html | pdf |
• Table 1.2.6.1. Assignment of integers to triplets h, k, l with   (p. 9) | html | pdf |
• 1.3. Twinning  (pp. 10-14)
• 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 = a) with twin index 2  (p. 12) | html | pdf |
• Fig. 1.3.2.3. Projection of the lattices of the twin components of an orthorhombic twinned crystal (oC, b = 2a) with twin index 4  (p. 12) | html | pdf |
• Tables
• Table 1.3.2.1. Lattice planes and rows that are perpendicular to each other independently of the metrical parameters  (p. 11) | html | pdf |
• Table 1.3.4.1. Possible twin operations for twins by merohedry  (p. 13) | html | pdf |
• Table 1.3.4.2. Simulated Laue classes, extinction symbols, simulated possible space groups', and possible true space groups for crystals twinned by merohedry (type 2)  (p. 13) | html | pdf |
• 1.4. Arithmetic crystal classes and symmorphic space groups  (pp. 15-22)
• 1.4.1. Arithmetic crystal classes  (pp. 15-19) | html | pdf |
• 1.4.1.1. Arithmetic crystal classes in three dimensions  (p. 15) | html | pdf |
• 1.4.1.2. Arithmetic crystal classes in one, two and higher dimensions  (p. 16) | html | pdf |
• 1.4.2. Classification of space groups  (pp. 20-21) | html | pdf |
• 1.4.2.1. Symmorphic space groups  (p. 21) | html | pdf |
• 1.4.3. Effect of dispersion on diffraction symmetry  (p. 21) | html | pdf |
• 1.4.3.1. Symmetry of the Patterson function  (p. 21) | html | pdf |
• 1.4.3.2. Laue' symmetry  (p. 21) | html | pdf |
• References | html | pdf |
• Tables
• Table 1.4.1.1. The two-dimensional arithmetic crystal classes  (p. 15) | html | pdf |
• Table 1.4.2.1. The three-dimensional space groups, arranged by arithmetic crystal class  (pp. 16-19) | html | pdf |
• Table 1.4.3.1. Arithmetic crystal classes classified by the number of space groups that they contain  (p. 20) | html | pdf |
• Diffraction geometry and its practical realization
• 2.1. Classification of experimental techniques  (pp. 24-25)
• 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)
• 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 = λmaxmin of the proportions of relp's lying on single, double, and triple rays for the case   (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 () setting photograph  (p. 35) | html | pdf |
• 2.3. Powder and related techniques: X-ray techniques  (pp. 42-79)
• 2.3.1. Focusing diffractometer geometries  (pp. 43-54) | html | pdf |
• 2.3.1.1. Conventional reflection specimen, θ–2θ scan  (pp. 44-50) | html | pdf |
• 2.3.1.1.1. Geometrical instrument parameters  (pp. 44-46) | html | pdf |
• 2.3.1.1.2. Use of monochromators  (p. 46) | html | pdf |
• 2.3.1.1.3. Alignment and angular calibration  (pp. 46-47) | html | pdf |
• 2.3.1.1.4. Instrument broadening and aberrations  (pp. 47-48) | html | pdf |
• 2.3.1.1.5. Focal line and receiving-slit widths  (p. 48) | html | pdf |
• 2.3.1.1.6. Aberrations related to the specimen  (pp. 48-49) | html | pdf |
• 2.3.1.1.7. Axial divergence  (p. 50) | html | pdf |
• 2.3.1.1.8. Combined aberrations  (p. 50) | html | pdf |
• 2.3.1.2. Transmission specimen, θ–2θ scan  (pp. 50-52) | html | pdf |
• 2.3.1.3. Seemann–Bohlin method  (pp. 52-53) | html | pdf |
• 2.3.1.4. Reflection specimen, θ–θ scan  (p. 53) | html | pdf |
• 2.3.1.5. Microdiffractometry  (pp. 53-54) | html | pdf |
• 2.3.2. Parallel-beam geometries, synchrotron radiation  (pp. 54-60) | html | pdf |
• 2.3.2.1. Monochromatic radiation, θ–2θ scan  (pp. 55-57) | html | pdf |
• 2.3.2.2. Cylindrical specimen, 2θ scan  (pp. 57-58) | html | pdf |
• 2.3.2.3. Grazing-incidence diffraction  (p. 58) | html | pdf |
• 2.3.2.4. High-resolution energy-dispersive diffraction  (pp. 58-60) | html | pdf |
• 2.3.3. Specimen factors, angle, intensity, and profile-shape measurement  (pp. 60-69) | html | pdf |
• 2.3.3.1. Specimen factors  (pp. 60-62) | html | pdf |
• 2.3.3.1.1. Preferred orientation  (pp. 60-61) | html | pdf |
• 2.3.3.1.2. Crystallite-size effects  (p. 62) | html | pdf |
• 2.3.3.2. Problems arising from the Kα doublet  (pp. 62-63) | html | pdf |
• 2.3.3.3. Use of peak or centroid for angle definition  (p. 63) | html | pdf |
• 2.3.3.4. Rate-meter/strip-chart recording  (p. 63) | html | pdf |
• 2.3.3.5. Computer-controlled automation  (pp. 63-64) | html | pdf |
• 2.3.3.6. Counting statistics  (pp. 64-65) | html | pdf |
• 2.3.3.7. Peak search  (pp. 65-66) | html | pdf |
• 2.3.3.8. Profile fitting  (pp. 66-69) | html | pdf |
• 2.3.3.9. Computer graphics for powder patterns  (p. 69) | html | pdf |
• 2.3.4. Powder cameras  (pp. 70-71) | html | pdf |
• 2.3.4.1. Cylindrical cameras (Debye–Scherrer)  (p. 70) | html | pdf |
• 2.3.4.2. Focusing cameras (Guinier)  (pp. 70-71) | html | pdf |
• 2.3.4.3. Miscellaneous camera types  (p. 71) | html | pdf |
• 2.3.5. Generation, modifications, and measurement of X-ray spectra  (pp. 71-79) | html | pdf |
• 2.3.5.1. X-ray tubes  (pp. 71-74) | html | pdf |
• 2.3.5.1.1. Stability  (p. 72) | html | pdf |
• 2.3.5.1.2. Spectral purity  (p. 72) | html | pdf |
• 2.3.5.1.3. Source intensity distribution and size  (p. 73) | html | pdf |
• 2.3.5.1.4. Air and window transmission  (pp. 73-74) | html | pdf |
• 2.3.5.1.5. Intensity variation with take-off angle  (p. 74) | html | pdf |
• 2.3.5.2. X-ray spectra  (pp. 74-75) | html | pdf |
• 2.3.5.2.1. Wavelength selection  (p. 75) | html | pdf |
• 2.3.5.3. Other X-ray sources  (p. 75) | html | pdf |
• 2.3.5.4. Methods for modifying the spectrum  (pp. 75-79) | html | pdf |
• 2.3.5.4.1. Crystal monochromators  (pp. 76-78) | html | pdf |
• 2.3.5.4.2. Single and balanced filters  (pp. 78-79) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 2.3.1.1. Basic arrangements of focusing diffractometer methods  (p. 43) | html | pdf |
• Fig. 2.3.1.2. Specimen orientation for three diffractometer geometries  (p. 44) | html | pdf |
• Fig. 2.3.1.3. X-ray optics in the focusing plane of a conventional' diffractometer with reflection specimen, diffracted-beam monochromator, and θ–2θ scanning  (p. 44) | html | pdf |
• Fig. 2.3.1.4. Length of specimen irradiated, Sl, as a function of 2θ for various angular apertures  (p. 45) | html | pdf |
• Fig. 2.3.1.5. Slit designs made with (a) rods, (b) bars, and (c) machined from single piece  (p. 45) | html | pdf |
• Fig. 2.3.1.6. Zero-angle calibration  (p. 46) | html | pdf |
• Fig. 2.3.1.7. (a) θ–2θ setting at 0°  (p. 47) | html | pdf |
• Fig. 2.3.1.8. Diffractometer profiles  (p. 48) | html | pdf |
• Fig. 2.3.1.9. (a) Effect of source size on profile shape, Cu Kα, αES 1°, αRS 0.05°, Si(111)  (p. 49) | html | pdf |
• Fig. 2.3.1.10. (a) Origin of specimen-related aberrations in focusing plane of conventional reflection specimen diffractometer (Fig. 2.3.1.3)  (p. 50) | html | pdf |
• Fig. 2.3.1.11. Effect of axial divergence on profile shape  (p. 50) | html | pdf |
• Fig. 2.3.1.12. X-ray optics of the transmission specimen with asymmetric focusing monochromator and θ–2θ scanning  (p. 51) | html | pdf |
• Fig. 2.3.1.13. Seemann–Bohlin method  (p. 52) | html | pdf |
• Fig. 2.3.1.14. Optics of θ–θ scanning diffractometer  (p. 53) | html | pdf |
• Fig. 2.3.1.15. Rigaku microdiffractometer for microanalysis  (p. 54) | html | pdf |
• Fig. 2.3.2.1. Method to obtain parallel beam from X-ray tube for powder diffraction  (p. 54) | html | pdf |
• Fig. 2.3.2.2. Silicon powder pattern with 1 Å synchrotron radiation using method shown in Fig. 2.3.2.4(a)  (p. 54) | html | pdf |
• Fig. 2.3.2.3. Synchrotron-radiation patterns of a mixture of Ni and ZnO powders  (p. 55) | html | pdf |
• Fig. 2.3.2.4. (a) Optics of dispersive parallel-beam method for synchrotron X-rays  (p. 56) | html | pdf |
• Fig. 2.3.2.5. Comparison of patterns obtained with a conventional focusing diffractometer (a) and (c), and synchrotron parallel-beam method (b) and (d)  (p. 57) | html | pdf |
• Fig. 2.3.2.6. (a) and (c) Fourier maps of orthorhombic Mg2GeO4 calculated directly from profile-fitted synchrotron powder data  (p. 57) | html | pdf |
• Fig. 2.3.2.7. Penetration depth t' as a function of grazing-incidence angle α for γ-Fe2O3 thin film  (p. 58) | html | pdf |
• Fig. 2.3.2.8. Synchrotron diffraction patterns of annealed 5000 Å iron oxide film, λ = 1.75 Å  (p. 58) | html | pdf |
• Fig. 2.3.2.9. (a)–(d) High-resolution energy-dispersive diffraction patterns of quartz powder sample obtained with 2θ settings shown in upper left corners  (p. 59) | html | pdf |
• Fig. 2.3.2.10. Specimen orientation for symmetric reflection (a) from (hkl) planes and (b) specimen rotated θr for symmetric reflection from (pqr) planes  (p. 59) | html | pdf |
• Fig. 2.3.3.1. Differences in relative intensities due to preferred orientation as seen in synchrotron X-ray patterns of m-chlorobenzoic acid obtained with a specimen in reflection and transmission compared with calculated pattern  (p. 61) | html | pdf |
• Fig. 2.3.3.2. Effect of specimen rotation and particle size on Si powder intensity using a conventional diffractometer (Fig. 2.3.1.3) and Cu Kα  (p. 62) | html | pdf |
• Fig. 2.3.3.3. Various measures of profile  (p. 62) | html | pdf |
• Fig. 2.3.3.4. Rate-meter strip-chart recordings  (p. 63) | html | pdf |
• Fig. 2.3.3.5. Fig  (p. 64) | html | pdf |
• Fig. 2.3.3.6. Percentage error as a function of the total number of counts N for several confidence levels  (p. 64) | html | pdf |
• Fig. 2.3.3.7. Effect of 4σ maximum peak height (horizontal line) on dropping weak peaks from inclusion in computer calculation  (p. 65) | html | pdf |
• Fig. 2.3.3.8. (a) Si(220) Cu Kα reflection  (p. 66) | html | pdf |
• Fig. 2.3.3.9. (a) Computer-generated symmetrical Lorentzian profile L and Gaussian G with equal peak heights, 2θ and FWHM  (p. 66) | html | pdf |
• Fig. 2.3.3.10. Profile fitting with sum-of-Lorentzians method  (p. 68) | html | pdf |
• Fig. 2.3.3.11. Profile fitting of poor statistical data  (p. 69) | html | pdf |
• Fig. 2.3.3.12. Some examples of computer graphics of powder patterns  (p. 69) | html | pdf |
• Fig. 2.3.4.1. Powder-camera geometries  (p. 70) | html | pdf |
• Fig. 2.3.5.1. Sealed X-ray diffraction tube (Philips), dimensions are given in mm  (p. 71) | html | pdf |
• Fig. 2.3.5.2. (a) Transmission of Be, Al and air as a function of wavelength  (p. 73) | html | pdf |
• Fig. 2.3.5.3. X-ray spectrum of copper target tube with Be window, 50 kV constant potential, 12° take-off angle  (p. 75) | html | pdf |
• Fig. 2.3.5.4. (a) Continuous X-ray spectrum of tungsten target X-ray tube as a function of voltage and constant current  (p. 76) | html | pdf |
• Fig. 2.3.5.5. Portion of diffractometer pattern of topaz showing effect of increasing dispersion on separation of peaks  (p. 76) | html | pdf |
• Fig. 2.3.5.6. Crystal monochromators most frequently used in powder diffraction  (p. 77) | html | pdf |
• Tables
• Table 2.3.3.1. Preferred-orientation data for silicon  (p. 61) | html | pdf |
• Table 2.3.3.2. R(Bragg) values obtained with different preferred-orientation formulae  (p. 61) | html | pdf |
• Table 2.3.5.1. X-ray tube maximum ratings  (p. 72) | html | pdf |
• Table 2.3.5.2. β filters for common target elements  (p. 78) | html | pdf |
• Table 2.3.5.3. Calculated thickness of balanced filters for common target elements  (p. 79) | html | pdf |
• 2.4. Powder and related techniques: electron and neutron techniques  (pp. 80-83)
• 2.4.1. Electron techniques  (pp. 80-82) | html | pdf |
• 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 |
• 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)
• 2.5.1. Techniques for X-rays  (pp. 84-87) | html | pdf |
• 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 |
• 2.5.2.1. Neutron single-crystal Laue diffraction  (p. 87) | html | pdf |
• 2.5.2.2. Neutron time-of-flight powder diffraction  (pp. 87-88) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 2.5.1.1. Standard and conical diffraction geometries: 2θ0 = fixed scattering angle  (p. 84) | html | pdf |
• Fig. 2.5.1.2. XED powder spectrum of BaTiO3 recorded with synchrotron radiation from the electron storage ring DORIS at DESY-HASYLAB in Hamburg, Germany  (p. 84) | html | pdf |
• Fig. 2.5.1.3. Relative resolution, , as function of Bragg angle, , 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)
• 2.6.1. X-ray techniques  (pp. 89-104) | html | pdf |
• 2.6.1.1. Introduction  (pp. 89-90) | html | pdf |
• 2.6.1.2. General principles  (pp. 90-91) | html | pdf |
• 2.6.1.3. Monodisperse systems  (pp. 91-99) | html | pdf |
• 2.6.1.3.1. Parameters of a particle  (pp. 91-93) | html | pdf |
• 2.6.1.3.2. Shape and structure of particles  (pp. 93-97) | html | pdf |
• 2.6.1.3.2.1. Homogeneous particles  (pp. 93-96) | html | pdf |
• 2.6.1.3.2.2. Hollow and inhomogeneous particles  (pp. 96-97) | html | pdf |
• 2.6.1.3.3. Interparticle interference, concentration effects  (pp. 97-99) | html | pdf |
• 2.6.1.4. Polydisperse systems  (p. 99) | html | pdf |
• 2.6.1.5. Instrumentation  (pp. 99-100) | html | pdf |
• 2.6.1.5.1. Small-angle cameras  (pp. 99-100) | html | pdf |
• 2.6.1.5.2. Detectors  (p. 100) | html | pdf |
• 2.6.1.6. Data evaluation and interpretation  (pp. 100-103) | html | pdf |
• 2.6.1.6.1. Primary data handling  (pp. 100-101) | html | pdf |
• 2.6.1.6.2. Instrumental broadening – smearing  (p. 101) | html | pdf |
• 2.6.1.6.3. Smoothing, desmearing, and Fourier transformation  (pp. 101-103) | html | pdf |
• 2.6.1.6.4. Direct structure analysis  (p. 103) | html | pdf |
• 2.6.1.6.5. Interpretation of results  (p. 103) | html | pdf |
• 2.6.1.7. Simulations and model calculations  (pp. 103-104) | html | pdf |
• 2.6.1.7.1. Simulations  (p. 103) | html | pdf |
• 2.6.1.7.2. Model calculation  (p. 104) | html | pdf |
• 2.6.1.7.3. Calculation of scattering intensities  (p. 104) | html | pdf |
• 2.6.1.7.4. Method of finite elements  (p. 104) | html | pdf |
• 2.6.1.7.5. Calculation of distance-distribution functions  (p. 104) | html | pdf |
• 2.6.1.8. Suggestions for further reading  (p. 104) | html | pdf |
• 2.6.2. Neutron techniques  (pp. 105-112) | html | pdf |
• 2.6.2.1. Relation of X-ray and neutron small-angle scattering  (pp. 105-106) | html | pdf |
• 2.6.2.1.1. Wavelength  (pp. 105-106) | html | pdf |
• 2.6.2.1.2. Geometry  (p. 106) | html | pdf |
• 2.6.2.1.3. Correction of wavelength, slit, and detector-element effects  (p. 106) | html | pdf |
• 2.6.2.2. Isotopic composition of the sample  (pp. 106-107) | html | pdf |
• 2.6.2.2.1. Contrast variation  (p. 107) | html | pdf |
• 2.6.2.2.2. Specific isotopic labelling  (p. 107) | html | pdf |
• 2.6.2.3. Magnetic properties of the neutron  (pp. 107-108) | html | pdf |
• 2.6.2.3.1. Spin-contrast variation  (p. 108) | html | pdf |
• 2.6.2.4. Long wavelengths  (p. 108) | html | pdf |
• 2.6.2.5. Sample environment  (p. 108) | html | pdf |
• 2.6.2.6. Incoherent scattering  (pp. 108-110) | html | pdf |
• 2.6.2.6.1. Absolute scaling  (pp. 108-109) | html | pdf |
• 2.6.2.6.2. Detector-response correction  (p. 109) | html | pdf |
• 2.6.2.6.3. Estimation of the incoherent scattering level  (p. 109) | html | pdf |
• 2.6.2.6.4. Inner surface area  (pp. 109-110) | html | pdf |
• 2.6.2.7. Single-particle scattering  (pp. 110-112) | html | pdf |
• 2.6.2.7.1. Particle shape  (p. 110) | html | pdf |
• 2.6.2.7.2. Particle mass  (p. 110) | html | pdf |
• 2.6.2.7.3. Real-space considerations  (pp. 110-111) | html | pdf |
• 2.6.2.7.4. Particle-size distribution  (p. 111) | html | pdf |
• 2.6.2.7.5. Model fitting  (p. 111) | html | pdf |
• 2.6.2.7.6. Label triangulation  (p. 111) | html | pdf |
• 2.6.2.7.7. Triple isotropic replacement  (pp. 111-112) | html | pdf |
• 2.6.2.8. Dense systems  (p. 112) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 2.6.1.1. The height of the p(r) function for a certain value of r is proportional to the number of lines with a length between r and r + dr within the particle  (p. 91) | html | pdf |
• Fig. 2.6.1.2. Comparison of the scattering functions of a sphere (dashed line) and a cube (continuous line) with same radius of gyration  (p. 94) | html | pdf |
• Fig. 2.6.1.3. Distance distribution function of a sphere (dashed line) and a cube (continuous line) with the same radius of gyration and the same scattering intensity at zero angle  (p. 94) | html | pdf |
• Fig. 2.6.1.4. Comparison of the p(r) function of a sphere (continuous line), a prolate ellipsoid of revolution 1:1:3 (dash-dotted line), and an oblate ellipsoid of revolution 1:1:0.2 (dashed line) with the same radius of gyration  (p. 94) | html | pdf |
• Fig. 2.6.1.5. Comparison of the I(h) functions of a sphere, a prolate, and an oblate ellipsoid (see legend to Fig  (p. 94) | html | pdf |
• Fig. 2.6.1.6. Distance distributions from homogeneous parallelepipeds with edge lengths of: (a) 50 × 50 × 500 Å; (b) 50 × 50 × 250 Å; (c) 50 × 50 × 150 Å  (p. 95) | html | pdf |
• Fig. 2.6.1.7. Three parallelepipeds with constant length L (400 Å) and a constant cross section but varying length of the edges: continuous line 40 × 40 Å; dash-dotted line 80 × 20 Å; dashed line 160 × 10 Å  (p. 95) | html | pdf |
• Fig. 2.6.1.8. Circular cylinder with a constant length of 480 Å and an outer diameter of 48 Å  (p. 96) | html | pdf |
• Fig. 2.6.1.9. Inhomogeneous circular cylinder with periodical changes of the electron density along the cylinder axis compared with a homogeneous cylinder with the same mean electron density  (p. 97) | html | pdf |
• Fig. 2.6.1.10. p(r) function of a lamellar particle  (p. 97) | html | pdf |
• Fig. 2.6.1.11. Characteristic types of scattering functions: (a) gas type; (b) particle scattering; (c) liquid type  (p. 98) | html | pdf |
• Fig. 2.6.1.12. Distance distribution – hard-sphere interference model  (p. 98) | html | pdf |
• Fig. 2.6.1.13. Schematic drawing of the block collimation (Kratky camera): E edge; B1 centre piece; B2 bridge; P primary-beam profile; PS primary-beam stop; PR plane of registration  (p. 99) | html | pdf |
• Fig. 2.6.1.14. Function systems φv(r); Ψv(h); and χv(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)
• 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)
• 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)
• 2.9.1. Introduction  (p. 126) | html | pdf |
• 2.9.2. Theory of elastic specular neutron reflection  (pp. 126-127) | html | pdf |
• 2.9.3. Polarized neutron reflectivity  (p. 127) | html | pdf |
• 2.9.4. Surface roughness  (p. 128) | html | pdf |
• 2.9.5. Experimental methodology  (pp. 128-129) | html | pdf |
• 2.9.6. Resolution in real space  (p. 129) | html | pdf |
• 2.9.7. Applications of neutron reflectometry  (pp. 129-130) | html | pdf |
• 2.9.7.1. Self-diffusion  (pp. 129-130) | html | pdf |
• 2.9.7.2. Magnetic multilayers  (p. 130) | html | pdf |
• 2.9.7.3. Hydrogenous materials  (p. 130) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 2.9.2.1. Schematic diagram of reflection geometry  (p. 126) | html | pdf |
• Fig. 2.9.2.2. Arbitrary scattering density profile represented by slabs of uniform potential  (p. 127) | html | pdf |
• Fig. 2.9.2.3. Neutron reflectivities calculated for an infinite Si substrate (dashed line) and 1000 Å Ni film on an Si substrate (solid line)  (p. 127) | html | pdf |
• Fig. 2.9.6.1. Calculated neutron reflectivity curves corresponding to the three density profiles in the inset  (p. 128) | html | pdf |
• Fig. 2.9.7.1. Measured neutron reflectivities from boron bilayers  (p. 128) | html | pdf |
• Fig. 2.9.7.2. The fitted real part of the scattering density profiles for the measured reflectivities of Fig. 2.9.7.1  (p. 128) | html | pdf |
• Fig. 2.9.7.3. Co/Cu(111) spin-dependent reflectivities (top)  (p. 129) | html | pdf |
• Fig. 2.9.7.4. (a) Measured neutron reflectivity for the Langmuir–Blodgett multilayer described in the text along with the fit  (p. 129) | html | pdf |
• Preparation and examination of specimens
• 3.1. Preparation, selection, and investigation of specimens  (pp. 148-155)
• 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)
• 3.2.1. Introduction  (p. 156) | html | pdf |
• 3.2.1.1. General precautions  (p. 156) | html | pdf |
• 3.2.2. Description and discussion of techniques  (pp. 156-159) | html | pdf |
• 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 |
• 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 VM and Vsolv for proteins  (p. 159) | html | pdf |
• 3.3. Measurement of refractive index  (pp. 160-161)
• 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)
• 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)
• 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 |
• Production and properties of radiations
• 4.1. Radiations used in crystallography  (pp. 186-190)
• 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)
• 4.2.1. Generation of X-rays  (pp. 191-200) | html | pdf |
• 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 |
• 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 |
• 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 μl 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 |
• 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: σpe  (p. 221) | html | pdf |
• 4.2.4.2.2. Theoretical Rayleigh scattering data: σR  (pp. 221-229) | html | pdf |
• 4.2.4.2.3. Theoretical Compton scattering data: σC  (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 |
• 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 |
• 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:   (pp. 248-250) | html | pdf |
• 4.2.6.3.2. Determination of the real part of the dispersion correction:   (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   (pp. 251-252) | html | pdf |
• 4.2.6.3.3.2. Measurements in the vicinity of an absorption edge  (pp. 252-253) | html | pdf |
• 4.2.6.3.3.3. Accuracy in the tables of dispersion corrections  (p. 253) | html | pdf |
• 4.2.6.3.3.4. Towards a tensor formalism  (pp. 253-258) | html | pdf |
• 4.2.6.3.3.5. Summary  (p. 258) | html | pdf |
• 4.2.6.4. Table of wavelengths, energies, and linewidths used in compiling the tables of the dispersion corrections  (p. 258) | html | pdf |
• 4.2.6.5. Tables of the dispersion corrections for forward scattering, averaged polarization using the relativistic multipole approach  (p. 258) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 4.2.1.1. f(χ) curves for Cu K-L3 at a series of different accelerating voltages (in kV)  (p. 192) | html | pdf |
• Fig. 4.2.1.2. Experimental measurements of for Cu K-L3 as functions of the accelerating voltage for different take-off angles  (p. 193) | html | pdf |
• Fig. 4.2.1.3. Intensity per unit frequency interval versus frequency in the continuous spectrum from a thick target at different accelerating voltages  (p. 193) | html | pdf |
• Fig. 4.2.1.4. The function μ in Müller's equation (equation 4.2.1.12) as a function of the ratio of width to length of the focal spot  (p. 195) | html | pdf |
• Fig. 4.2.1.5. Synchrotron radiation emitted by a relativistic electron travelling in a curved trajectory  (p. 197) | html | pdf |
• Fig. 4.2.1.6. Synchrotron-radiation spectrum: percentage per unit wavelength interval (a) of power of total power and (b) of number of photons of total number of photons at wavelengths greater than λ versus λ/λc  (p. 197) | html | pdf |
• Fig. 4.2.1.7. Main components of a dedicated electron storage-ring synchrotron-radiation source  (p. 198) | html | pdf |
• Fig. 4.2.1.8. Electron trajectory within a multipole wiggler or undulator  (p. 198) | html | pdf |
• Fig. 4.2.1.9. Spectral distribution and critical wavelengths for (a) a dipole magnet, (b) a wavelength shifter, and (c) a multipole wiggler for the proposed ESRF  (p. 198) | html | pdf |
• Fig. 4.2.1.10. Comparison of the spectra from the storage ring SPEAR in photons s−1 mA−1 mrad−1 per 1% passband (1978 performance) and a rotating-anode X-ray generator  (p. 198) | html | pdf |
• Fig. 4.2.1.11. The evolution of storage-ring synchrotron-radiation sources over the decades, as illustrated by their increasing number and range of machine energies (based on Suller, 1992)  (p. 200) | html | pdf |
• Fig. 4.2.1.12. X-ray emission from various laser-produced plasmas  (p. 200) | html | pdf |
• Fig. 4.2.2.1. Relative deviations between theoretical and experimental results for K-series spectra  (p. 212) | html | pdf |
• Fig. 4.2.2.2. Comparison of L-series data with experiment for the indicated range of Z  (p. 212) | html | pdf |
• Fig. 4.2.3.1. Theoretical cross sections for photon interactions with carbon showing the contributions of photoelectric, elastic (Rayleigh), inelastic (Compton), and pair-production cross sections to the total cross sections  (p. 213) | html | pdf |
• Fig. 4.2.3.2. The dependence of the X-ray attenuation coefficient on energy for a range of germanium compounds, taken in the neighbourhood of the germanium absorption edge (from IT IV, 1974)  (p. 214) | html | pdf |
• Fig. 4.2.3.3. Schematic representations of experimental apparatus used in the IUCr X-ray Attenuation Project (Creagh & Hubbell, 1987; Creagh, 1985)  (p. 214) | html | pdf |
• Fig. 4.2.3.4. Steps in the reduction of data from an XAFS experiment using the Fourier transform technique: (a) after the removal of background χ(k) versus k; (b) after multiplication by a weighting function (in this case k3); (c) after Fourier transformation to determine r′  (p. 217) | html | pdf |
• Fig. 4.2.3.5. Schematic representations of the scattering processes undergone by the ejected photoelectron in the single-scattering (XAFS) case and the full multiple-scattering regime (XANES)  (p. 219) | html | pdf |
• Fig. 4.2.4.1. Agreement between theory and experiment for oxygen (Z = 8) in the soft' X-ray region  (p. 220) | html | pdf |
• Fig. 4.2.4.2. The total cross section for silicon (Z = 14) compared with the unrenormalized Scofield values  (p. 221) | html | pdf |
• Fig. 4.2.4.3. The total cross section for uranium (Z = 92): The theoretical values (solid line) are partially obscured by the high density of available measurements  (p. 222) | html | pdf |
• Fig. 4.2.4.4. Comparison between this tabulation and experimental data contained in Saloman & Hubbell (1986)  (p. 222) | html | pdf |
• Fig. 4.2.5.1. The variation of specular reflectivity with incident photon energy is shown for materials of different atomic number and a constant angle of incidence of 0.2°  (p. 236) | html | pdf |
• Fig. 4.2.5.2. The use of mirrors in a typical synchrotron-radiation beamline  (p. 237) | html | pdf |
• Fig. 4.2.5.3. The reflectivity of a multiple-quantum-well device is shown  (p. 238) | html | pdf |
• Fig. 4.2.5.4. In (a), the schematic rocking curve for a silicon crystal in the neighbourhood of the 111 Bragg peak is shown  (p. 239) | html | pdf |
• Fig. 4.2.5.5. A schematic diagram of a beamline designed to produce circularly polarized light from initially linearly polarized light using Laue-case reflections  (p. 240) | html | pdf |
• Fig. 4.2.5.6. A schematic diagram of a Hart-type tuneable channel-cut monochromator is shown  (p. 241) | html | pdf |
• Fig. 4.2.5.7. A schematic diagram of the use of a Bragg–Fresnel lens to focus hard X-rays onto a high-pressure cell  (p. 241) | html | pdf |
• Fig. 4.2.6.1. The relativistic correction in electrons per atom for: (a) the modified form-factor approach; (b) the relativistic multipole approach; (c) the relativistic dipole approach  (p. 247) | html | pdf |
• Fig. 4.2.6.2. Measured values of f′(ω, 0) at the K-edge of Nb in LiNbO3 and the Kramers–Kronig transformation of f′′(ω, 0)  (p. 247) | html | pdf |
• Tables
• Table 4.2.1.1. Correspondence between X-ray diagram levels and electron configurations  (p. 191) | html | pdf |
• Table 4.2.1.2. Correspondence between IUPAC and Siegbahn notations for X-ray diagram lines  (p. 191) | html | pdf |
• Table 4.2.1.3. Copper-target X-ray tubes and their loading  (p. 194) | html | pdf |
• Table 4.2.1.4. Relative permissible loading for different target materials  (p. 196) | html | pdf |
• Table 4.2.1.5. Radionuclides decaying wholly by electron capture, and yielding little or no γ-radiation  (p. 196) | html | pdf |
• Table 4.2.1.6. Comparison of storage-ring synchrotron-radiation sources  (p. 199) | html | pdf |
• Table 4.2.1.7. Intensity gain with storage rings over conventional sources  (p. 200) | html | pdf |
• Table 4.2.2.1. K-series reference wavelengths in Å  (p. 203) | html | pdf |
• Table 4.2.2.2. Directly measured L-series reference wavelengths in Å  (p. 204) | html | pdf |
• Table 4.2.2.3. Directly measured and emission + binding energies (see text) K-absorption edges in Å  (p. 205) | html | pdf |
• Table 4.2.2.4. Wavelengths of K-emission lines and K-absorption edges in Å  (pp. 206-208) | html | pdf |
• Table 4.2.2.5. Wavelengths of L-emission lines and L-absorption edges in Å  (pp. 209-211) | html | pdf |
• Table 4.2.2.6. Wavelength conversion factors  (p. 212) | html | pdf |
• Table 4.2.3.1. Some synchrotron-radiation facilities providing XAFS databases and analysis utilities  (p. 219) | html | pdf |
• Table 4.2.4.1. Table of wavelengths and energies for the characteristic radiations used in Tables 4.2.4.2 and 4.2.4.3  (p. 221) | html | pdf |
• Table 4.2.4.2. Total phonon interaction cross section  (pp. 223-229) | html | pdf |
• Table 4.2.4.3. Mass attenuation coefficients  (pp. 230-236) | html | pdf |
• Table 4.2.6.1. Values of Etot/mc2 listed as a function of atomic number Z  (p. 246) | html | pdf |
• Table 4.2.6.2. Comparison between the S-matrix calculations of Kissel (K) (1977) and the form-factor calculations of Cromer & Liberman (C & L) (1970, 1981, 1983) and Creagh & McAuley (C & M) for the noble gases and several common metals  (p. 249) | html | pdf |
• Table 4.2.6.3. A comparison of the forward-scattering amplitudes computed using different theoretical approaches  (p. 250) | html | pdf |
• Table 4.2.6.4. Comparison of measurements of the real part of the dispersion correction for LiF, Si, Al and Ge for characteristic wavelengths Ag Kα1, Mo Kα1 and Cu Kα1 with theoretical predictions  (p. 252) | html | pdf |
• Table 4.2.6.5. Comparison of measurements of f′(ω, 0) for C, Si and Cu for characteristic wavelengths Ag Kα1, Mo Kα1 and Cu Kα1 with theoretical predictions  (p. 253) | html | pdf |
• Table 4.2.6.6. Comparison of 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)
• 4.3.1. Scattering factors for the diffraction of electrons by crystalline solids  (pp. 259-262) | html | pdf |
• 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 |
• 4.3.3. Complex scattering factors for the diffraction of electrons by gases  (pp. 262-391) | html | pdf |
• 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 |
• 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 |
• 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 |
• 4.3.7. Measurement of structure factors and determination of crystal thickness by electron diffraction  (pp. 416-419) | html | pdf |
• 4.3.8. Crystal structure determination by high-resolution electron microscopy  (pp. 419-429) | html | pdf |
• 4.3.8.1. Introduction  (pp. 419-421) | html | pdf |
• 4.3.8.2. Lattice-fringe images  (pp. 421-422) | html | pdf |
• 4.3.8.3. Crystal structure images  (pp. 422-424) | html | pdf |
• 4.3.8.4. Parameters affecting HREM images  (pp. 424-425) | html | pdf |
• 4.3.8.5. Computing methods  (pp. 425-427) | html | pdf |
• 4.3.8.6. Resolution and hyper-resolution  (p. 427) | html | pdf |
• 4.3.8.7. Alternative methods  (pp. 427-428) | html | pdf |
• 4.3.8.8. Combined use of HREM and electron diffraction  (pp. 428-429) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 4.3.4.1. Definition of the regions in (E, q) space that can be investigated with the different primary sources of particles available at present  (p. 392) | html | pdf |
• Fig. 4.3.4.2. A primary electron of energy E0 and wavevector k is inelastically scattered into a state of energy E0ΔE 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 Ec to an unoccupied state U above the Fermi level Ef) 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 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 qc  (p. 398) | html | pdf |
• Fig. 4.3.4.14. Measured angular dependence of the differential cross section dσ/dΩ for the 15 eV plasmon loss in Al (dots) compared with a calculated curve by Ferrell (solid curve) and with a sharp cut-off approximation at θc (dashed curved)  (p. 399) | html | pdf |
• Fig. 4.3.4.15. Variation of plasmon excitation mean free path Λp 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 ħωp = 16 eV and τ = 1.64 × 10−16 s  (p. 400) | html | pdf |
• Fig. 4.3.4.17. Same as previous figure, but for a Lorentz model with an oscillator of eigenfrequency ħω0 = 10 eV and relaxation time τ0 = 6.6 × 10−16 s superposed on the free-electron term  (p. 401) | html | pdf |
• Fig. 4.3.4.18. Dielectric coefficients , and 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 Ec (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, L2,3, M4,5, and N2,3) 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 L2,3 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 L2,3 titanium edge from two phases (rutile and anatase) of TiO2  (p. 408) | html | pdf |
• Fig. 4.3.4.28. The dramatic change in near-edge fine structures on the L3 and L2 lines of Cu, from Cu metal to CuO  (p. 409) | html | pdf |
• Fig. 4.3.4.29. Illustration of the single and multiple scattering effects used to describe the final wavefunction on the excited site  (p. 409) | html | pdf |
• Fig. 4.3.4.30. Comparison of the experimental O K edge (solid line) with calculated profiles in the multiple scattering approach  (p. 409) | html | pdf |
• Fig. 4.3.4.31. The conventional method of background subtraction for the evaluation of the characteristic signals SO K and SFe L2,3 used for quantitative elemental analysis  (p. 410) | html | pdf |
• Fig. 4.3.4.32. Values of neff 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 Bhk and Dhkl that define the positions of reflections in lamellar texture patterns  (p. 412) | html | pdf |
• Fig. 4.3.5.2. (a) Part of the OTED pattern of the clay mineral kaolinite and (b) the intensity profile of a characteristic quadruplet of reflections recorded with the electron diffractometry system  (p. 413) | html | pdf |
• Fig. 4.3.5.3. The projections of the reciprocal axes on the plane ab of the direct lattice, with indications of the distances B and D of the hk rows from the fibre-texture axes a or [hk]  (p. 413) | html | pdf |
• Fig. 4.3.7.1. (a) Dispersion-surface section for the symmetric four-beam case (0, g, g + h, m), γk is a function of kx, referred to (b), where kx = ky = 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, Cs = 1 mm)  (p. 419) | html | pdf |
• Fig. 4.3.8.2. Imaging conditions for few-beam lattice images  (p. 420) | html | pdf |
• Fig. 4.3.8.3. A summary of three- (or five-) beam axial imaging conditions  (p. 422) | html | pdf |
• Fig. 4.3.8.4. The contrast of few-beam lattice images as a function of focus in the neighbourhood of the stationary-phase focus  (p. 422) | html | pdf |
• Fig. 4.3.8.5. (a) The transfer function for a 400 kV electron microscope with a point resolution of 1.7 Å at the Scherzer focus; the curve is based on equation (4.3.8.17)  (p. 424) | html | pdf |
• Fig. 4.3.8.6. Structure image of a thin lamella of the 6H polytype of SiC projected along [110] and recorded at 1.2 MeV  (p. 426) | html | pdf |
• Tables
• Table 4.3.1.1. Atomic scattering amplitudes (Å) for electrons for neutral atoms  (pp. 263-271) | html | pdf |
• Table 4.3.1.2. Atomic scattering amplitudes (Å) for electrons for ionized atoms  (pp. 272-281) | html | pdf |
• Table 4.3.2.1. Parameters useful in electron diffraction as a function of accelerating voltage  (p. 281) | html | pdf |
• Table 4.3.2.2. Elastic atomic scattering factors of electrons for neutral atoms and s up to 2.0 Å−1  (pp. 282-283) | html | pdf |
• Table 4.3.2.3. Elastic atomic scattering factors of electrons for neutral atoms and s up to 6.0 Å−1  (pp. 284-285) | html | pdf |
• Table 4.3.3.1. Partial wave elastic scattering factors for neutral atomsinteractive version  (pp. 286-377) | html | pdf |
• Table 4.3.3.2. Inelastic scattering factors  (pp. 378-388) | html | pdf |
• Table 4.3.4.1. Different possibilities for using EELS information as a function of the different accessible parameters (r, , ΔE)  (p. 394) | html | pdf |
• Table 4.3.4.2. Plasmon energies measured (and calculated) for a few simple metals  (p. 397) | html | pdf |
• Table 4.3.4.3. Experimental and theoretical values for the coefficient α in the plasmon dispersion curve together with estimates of the cut-off wavevector  (p. 398) | html | pdf |
• Table 4.3.4.4. Comparison of measured and calculated values for the halfwidth ΔE1/2(0) of the plasmon line  (p. 398) | html | pdf |
• 4.4. Neutron techniques  (pp. 430-487)
• 4.4.1. Production of neutrons  (pp. 430-431) | html | pdf |
• 4.4.2. Beam-definition devices  (pp. 431-443) | html | pdf |
• 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 |
• 4.4.4. Scattering lengths for neutrons  (pp. 444-454) | html | pdf |
• 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 |
• 4.4.6. Absorption coefficients for neutrons  (p. 461) | html | pdf |
• 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 vk  (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 ; (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 |FN| = |FM|, the direction of P and , 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 γc(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, Nbcoh, for some commonly used materials  (p. 435) | html | pdf |
• Table 4.4.2.3. Characteristics of some typical elements and isotopes used as neutron filters  (p. 439) | html | pdf |
• Table 4.4.2.4. Properties of polarizing crystal monochromators  (p. 440) | html | pdf |
• Table 4.4.2.5. Scattering-length densities for some typical materials used for polarizing multilayers  (p. 441) | html | pdf |
• Table 4.4.4.1. Bound scattering lengths, b, in fm and cross sections, σ, in barns (1 barn = 100 fm2) of the elements and their isotopesinteractive version  (pp. 445-452) | html | pdf |
• Table 4.4.5.1. j0〉 form factors for 3d transition elements and their ions  (p. 454) | html | pdf |
• Table 4.4.5.2. j0〉 form factors for 4d atoms and their ions  (p. 455) | html | pdf |
• Table 4.4.5.3. j0〉 form factors for rare-earth ions  (p. 455) | html | pdf |
• Table 4.4.5.4. j0〉 form factors for actinide ions  (p. 455) | html | pdf |
• Table 4.4.5.5. j2〉 form factors for 3d transition elements and their ions  (p. 456) | html | pdf |
• Table 4.4.5.6. j2〉 form factors for 4d atoms and their ions  (p. 457) | html | pdf |
• Table 4.4.5.7. j2〉 form factors for rare-earth ions  (p. 457) | html | pdf |
• Table 4.4.5.8. j2〉 form factors for actinide ions  (p. 457) | html | pdf |
• Table 4.4.5.9. j4〉 form factors for 3d atoms and their ions  (p. 458) | html | pdf |
• Table 4.4.5.10. j4〉 form factors for 4d atoms and their ions  (p. 459) | html | pdf |
• Table 4.4.5.11. j4〉 form factors for rare-earth ions  (p. 459) | html | pdf |
• Table 4.4.5.12. j4〉 form factors for actinide ions  (p. 459) | html | pdf |
• Table 4.4.5.13. j6〉 form factors for rare-earth ions  (p. 460) | html | pdf |
• Table 4.4.5.14. j6〉 form factors for actinide ions  (p. 460) | html | pdf |
• Table 4.4.6.1. Absorption of the elements for neutrons  (p. 461) | html | pdf |
• Determination of lattice parameters
• 5.2. X-ray diffraction methods: polycrystalline  (pp. 491-504)
• 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 and variance W of certain aberrations of an energy-dispersive diffractometer  (p. 497) | html | pdf |
• Table 5.2.8.1. Some geometrical aberrations in the Debye–Scherrer method   (p. 498) | html | pdf |
• Table 5.2.10.1. NIST values for silicon standards  (p. 499) | html | pdf |
• Table 5.2.10.2. Reflection angles (°) for tungsten, silver, and silicon  (p. 499) | html | pdf |
• Table 5.2.10.3. Silicon standard reflection angles (°)  (p. 500) | html | pdf |
• Table 5.2.10.4. Silicon standard high reflection angles (°)  (p. 501) | html | pdf |
• Table 5.2.10.5. Tungsten reflection angles (°)   (p. 502) | html | pdf |
• Table 5.2.10.6. Fluorophlogopite 00l standard reflection angles  (p. 503) | html | pdf |
• Table 5.2.10.7. Silver behenate 00l standard reflection angles  (p. 503) | html | pdf |
• Table 5.2.11.1. NIST intensity standards, SRM 674  (p. 503) | html | pdf |
• 5.3. X-ray diffraction methods: single crystal  (pp. 505-536)
• 5.3.1. Introduction  (pp. 505-508) | html | pdf |
• 5.3.1.1. General remarks  (pp. 505-506) | html | pdf |
• 5.3.1.2. Introduction to single-crystal methods  (pp. 506-508) | html | pdf |
• 5.3.2. Photographic methods  (pp. 508-516) | html | pdf |
• 5.3.2.1. Introduction  (p. 508) | html | pdf |
• 5.3.2.2. The Laue method  (p. 508) | html | pdf |
• 5.3.2.3. Moving-crystal methods  (pp. 508-510) | html | pdf |
• 5.3.2.3.1. Rotating-crystal method  (pp. 508-509) | html | pdf |
• 5.3.2.3.2. Moving-film methods  (p. 509) | html | pdf |
• 5.3.2.3.3. Combined methods  (p. 509) | html | pdf |
• 5.3.2.3.4. Accurate and precise lattice-parameter determinations  (pp. 509-510) | html | pdf |
• 5.3.2.3.5. Photographic cameras for investigation of small lattice-parameter changes  (p. 510) | html | pdf |
• 5.3.2.4. The Kossel method and divergent-beam techniques  (pp. 510-516) | html | pdf |
• 5.3.2.4.1. The principle  (pp. 510-512) | html | pdf |
• 5.3.2.4.2. Review of methods of accurate lattice-parameter determination  (pp. 512-515) | html | pdf |
• 5.3.2.4.3. Accuracy and precision  (p. 515) | html | pdf |
• 5.3.2.4.4. Applications  (pp. 515-516) | html | pdf |
• 5.3.3. Methods with counter recording  (pp. 516-534) | html | pdf |
• 5.3.3.1. Introduction  (p. 516) | html | pdf |
• 5.3.3.2. Standard diffractometers  (pp. 516-517) | html | pdf |
• 5.3.3.2.1. Four-circle diffractometer  (pp. 516-517) | html | pdf |
• 5.3.3.2.2. Two-circle diffractometer  (p. 517) | html | pdf |
• 5.3.3.3. Data processing and optimization of the experiment  (pp. 517-520) | html | pdf |
• 5.3.3.3.1. Models of the diffraction profile  (pp. 517-519) | html | pdf |
• 5.3.3.3.2. Precision and accuracy of the Bragg-angle determination; optimization of the experiment  (pp. 519-520) | html | pdf |
• 5.3.3.4. One-crystal spectrometers  (pp. 521-526) | html | pdf |
• 5.3.3.4.1. General characteristics  (p. 521) | html | pdf |
• 5.3.3.4.2. Development of methods based on an asymmetric arrangement and their applications  (pp. 521-522) | html | pdf |
• 5.3.3.4.3. The Bond method  (pp. 522-526) | html | pdf |
• 5.3.3.4.3.1. Description of the method  (pp. 522-523) | html | pdf |
• 5.3.3.4.3.2. Systematic errors  (pp. 523-524) | html | pdf |
• 5.3.3.4.3.3. Development of the Bond method and its applications  (pp. 524-525) | html | pdf |
• 5.3.3.4.3.4. Advantages and disadvantages of the Bond method  (p. 526) | html | pdf |
• 5.3.3.5. Limitations of traditional methods  (p. 526) | html | pdf |
• 5.3.3.6. Multiple-diffraction methods  (pp. 526-528) | html | pdf |
• 5.3.3.7. Multiple-crystal – pseudo-non-dispersive techniques  (pp. 528-533) | html | pdf |
• 5.3.3.7.1. Double-crystal spectrometers  (pp. 528-530) | html | pdf |
• 5.3.3.7.2. Triple-crystal spectrometers  (pp. 530-531) | html | pdf |
• 5.3.3.7.3. Multiple-beam methods  (p. 531) | html | pdf |
• 5.3.3.7.4. Combined methods  (pp. 531-533) | html | pdf |
• 5.3.3.8. Optical and X-ray interferometry – a non-dispersive technique  (pp. 533-534) | html | pdf |
• 5.3.3.9. Lattice-parameter and wavelength standards  (p. 534) | html | pdf |
• 5.3.4. Final remarks  (pp. 534-536) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 5.3.2.1. (a) Photographic recording of lattice-parameter changes  (p. 511) | html | pdf |
• Fig. 5.3.2.2. Schematic representation of the origin of the Kossel lines  (p. 512) | html | pdf |
• Fig. 5.3.2.3. (a) The Kossel pattern from iron and (b) the corresponding stereographic projection (Tixier & Waché, 1970)  (p. 513) | html | pdf |
• Fig. 5.3.2.4. Lens-shaped figures formed by pairs of intersecting conics  (p. 514) | html | pdf |
• Fig. 5.3.2.5. Schematic representation of the multiple-exposure technique (after Fischer & Harris, 1970)  (p. 514) | html | pdf |
• Fig. 5.3.3.1. Determination of reciprocal-lattice angles on the θ circle (after Luger, 1980)  (p. 517) | html | pdf |
• Fig. 5.3.3.2. The extrapolated-peak procedure (after Bearden, 1933)  (p. 518) | html | pdf |
• Fig. 5.3.3.3. Determination of the Bragg angle by means of the one-crystal spectrometer using (a) an asymmetric or (b) a symmetric arrangement  (p. 521) | html | pdf |
• Fig. 5.3.3.4. Schematic representation of the Bond (1960) method  (p. 522) | html | pdf |
• Fig. 5.3.3.5. Schematic representation of multiple diffraction in reciprocal space (after Post, 1975)  (p. 526) | html | pdf |
• Fig. 5.3.3.6. Schematic representation of the multiple-diffraction method  (p. 527) | html | pdf |
• Fig. 5.3.3.7. The multiple-diffraction pattern at the 222 position in germanium (Cole, Chambers & Dunn, 1962)  (p. 527) | html | pdf |
• Fig. 5.3.3.8. Schematic representation of the double-crystal spectrometer  (p. 528) | html | pdf |
• Fig. 5.3.3.9. Schematic representation of the double-crystal arrangement of Hart & Lloyd (1975) for the examination of epitaxic layers  (p. 529) | html | pdf |
• Fig. 5.3.3.10. Schematic representation of the double-crystal arrangement of Okazaki & Kawaminami (1973a); white incident X-rays are used  (p. 529) | html | pdf |
• Fig. 5.3.3.11. Schematic representation of the triple-crystal spectrometer developed by Buschert (1965) (after Hart, 1981)  (p. 530) | html | pdf |
• Fig. 5.3.3.12. Schematic representation of the double-beam comparator of Hart (1969)  (p. 531) | html | pdf |
• Fig. 5.3.3.13. The double-axis lattice-spacing comparator of Ando, Bailey & Hart (1978); a triple-diffracted beam is used  (p. 532) | html | pdf |
• Fig. 5.3.3.14. Schematic representation of the double-beam triple-crystal spectrometer of Buschert et al  (p. 532) | html | pdf |
• Fig. 5.3.3.15. The geometry of the diffractometer used by Fewster & Andrew (1995)  (p. 533) | html | pdf |
• Fig. 5.3.3.16. Optical and X-ray interferometry  (p. 533) | html | pdf |
• Fig. 5.3.3.17. Portion of a dual-channel recording of X-ray and optical fringes (Deslattes, 1969)  (p. 533) | html | pdf |
• Fig. 5.3.3.18. Synchrotron radiation, SR, from the bending magnet incident on the Si(111) double-crystal monochromator and, after four reflections from the monolithic monochromator (0.1410 nm), impinges on sample Si(444)  (p. 534) | html | pdf |
• Fig. 5.3.3.19. Synchrotron radiation, SR, from the bending magnet incident on the Si(111) double-crystal monochromator and, after four reflections from the monolithic monochromator (0.1612 nm), impinges on sample Si(153)  (p. 535) | html | pdf |
• Fig. 5.3.3.20. Experimental set-up for measuring lattice parameters  (p. 535) | html | pdf |
• 5.4. Electron-diffraction methods  (pp. 537-540)
• 5.4.1. Determination of cell parameters from single-crystal patterns  (pp. 537-538) | html | pdf |
• 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 |
• 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 |
• Interpretation of diffracted intensities
• 6.1. Intensity of diffracted intensities  (pp. 554-595)
• 6.1.1. X-ray scattering  (pp. 554-590) | html | pdf |
• 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 |
• 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 |
• 6.1.3.1. Glossary of symbols  (p. 593) | html | pdf |
• 6.1.3.2. Scattering by a single nucleus  (pp. 593-594) | html | pdf |
• 6.1.3.3. Scattering by a single atom  (p. 594) | html | pdf |
• 6.1.3.4. Scattering by a single crystal  (pp. 594-595) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 6.1.1.1. Scattering by an electron  (p. 554) | html | pdf |
• Fig. 6.1.2.1. The integrals 〈j0〉, 〈j2〉, and 〈j4〉 for the Fe2+ ion plotted against   (p. 592) | html | pdf |
• Fig. 6.1.2.2. Comparison of 3d, 4d, 4f, and 5f form factors  (p. 592) | html | pdf |
• Fig. 6.1.3.1. Dependence on neutron wavelength of the coherent scattering length of 113Cd  (p. 594) | html | pdf |
• Tables
• Table 6.1.1.1. Mean atomic scattering factors in electrons for free atoms  (pp. 555-564) | html | pdf |
• Table 6.1.1.2. Spherical bonded hydrogen-atom scattering factors  (p. 565) | html | pdf |
• Table 6.1.1.3. Mean atomic scattering factors in electrons for chemically significant ions  (pp. 566-577) | html | pdf |
• Table 6.1.1.4. Coefficients for analytical approximation to the scattering factors of Tables 6.1.1.1 and 6.1.1.3  (pp. 578-580) | html | pdf |
• Table 6.1.1.5. Coefficients for analytical approximation to the scattering factors of Table 6.1.1.1 for the range 2.0 < (sin )/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 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   (p. 584) | html | pdf |
• Table 6.1.1.8. Cubic harmonics for cubic site symmetries  (p. 585) | html | pdf |
• Table 6.1.1.9. fnl(α, S) = ∫0rn exp(−αr)jl(Sr) dr  (p. 586) | html | pdf |
• Table 6.1.1.10. Indices nmp allowed by the site symmetry for the functions   (p. 586) | html | pdf |
• Table 6.1.1.11. Indices nx, ny, nz allowed for the basis functions Hnx(Ax)Hny(By)Hnz(Cz)  (p. 587) | html | pdf |
• 6.2. Trigonometric intensity factors  (pp. 596-598)
• 6.2.1. Expressions for intensity of diffraction  (p. 596) | html | pdf |
• 6.2.2. The polarization factor  (p. 596) | html | pdf |
• 6.2.3. The angular-velocity factor  (p. 596) | html | pdf |
• 6.2.4. The Lorentz factor  (p. 596) | html | pdf |
• 6.2.5. Special factors in the powder method  (pp. 596-598) | html | pdf |
• 6.2.6. Some remarks about the integrated reflection power ratio formulae for single-crystal slabs  (p. 598) | html | pdf |
• 6.2.7. Other factors  (p. 598) | html | pdf |
• References | html | pdf |
• Tables
• Table 6.2.1.1. Summary of formulae for integrated powers of reflection  (pp. 597-598) | html | pdf |
• 6.3. X-ray absorption  (pp. 599-608)
• 6.3.1. Linear absorption coefficient  (pp. 599-600) | html | pdf |
• 6.3.1.1. True or photoelectric absorption  (p. 599) | html | pdf |
• 6.3.1.2. Scattering  (p. 599) | html | pdf |
• 6.3.1.3. Extinction  (pp. 599-600) | html | pdf |
• 6.3.1.4. Attenuation (mass absorption) coefficients  (p. 600) | html | pdf |
• 6.3.2. Dispersion  (p. 600) | html | pdf |
• 6.3.3. Absorption corrections  (pp. 600-608) | html | pdf |
• 6.3.3.1. Special cases  (p. 600) | html | pdf |
• 6.3.3.2. Cylinders and spheres  (pp. 600-604) | html | pdf |
• 6.3.3.3. Analytical method for crystals with regular faces  (pp. 604-606) | html | pdf |
• 6.3.3.4. Gaussian integration  (pp. 606-607) | html | pdf |
• 6.3.3.5. Empirical methods  (pp. 607-608) | html | pdf |
• 6.3.3.6. Measuring crystals for absorption  (p. 608) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 6.3.1.1. Idealized diagram showing the variation of the photoelectric absorption coefficient σph with wavelength λ  (p. 599) | html | pdf |
• Fig. 6.3.3.1. Geometry of the Eulerian cradle with the axis of a cylindrical specimen coincident with the φ axis  (p. 604) | html | pdf |
• Fig. 6.3.3.2. Cross section of the plane of diffraction for a cylindrical specimen coincident with the φ axis  (p. 604) | html | pdf |
• Fig. 6.3.3.3. The crystal ABC divided into polygons by the dashed lines AE and CF parallel to the incident (i) and diffracted (d) beams, respectively  (p. 605) | html | pdf |
• Fig. 6.3.3.4. Crystal oriented with the normal N(S) to the face ABCD in the plane of view  (p. 608) | html | pdf |
• Fig. 6.3.3.5. Geometry of the Eulerian cradle in the bisecting position  (p. 608) | html | pdf |
• Tables
• Table 6.3.3.1. Transmission coefficients  (p. 601) | html | pdf |
• Table 6.3.3.2. Values of A* for cylinders  (p. 602) | html | pdf |
• Table 6.3.3.3. Values of A* for spheres  (p. 602) | html | pdf |
• Table 6.3.3.4. Values of (1/A*)(dA*/dμR) for spheres  (p. 603) | html | pdf |
• Table 6.3.3.5. Coefficients for interpolation of A* and   (p. 603) | html | pdf |
• 6.4. The flow of radiation in a real crystal  (pp. 609-616)
• 6.4.1. Introduction  (p. 609) | html | pdf |
• 6.4.2. The model of a real crystal  (p. 609) | html | pdf |
• 6.4.3. Primary and secondary extinction  (pp. 609-610) | html | pdf |
• 6.4.4. Radiation flow  (p. 610) | html | pdf |
• 6.4.5. Primary extinction  (p. 610) | html | pdf |
• 6.4.6. The finite crystal  (p. 610) | html | pdf |
• 6.4.7. Angular variation of E  (p. 610) | html | pdf |
• 6.4.8. The value of x  (pp. 610-611) | html | pdf |
• 6.4.9. Secondary extinction  (p. 611) | html | pdf |
• 6.4.10. The extinction factor  (p. 611) | html | pdf |
• 6.4.10.1. The correlated block model  (p. 611) | html | pdf |
• 6.4.10.2. The uncorrelated block model  (p. 611) | html | pdf |
• 6.4.11. Polarization  (pp. 611-612) | html | pdf |
• 6.4.12. Anisotropy  (p. 612) | html | pdf |
• 6.4.13. Asymptotic behaviour of the integrated intensity  (p. 612) | html | pdf |
• 6.4.13.1. Non-absorbing crystal, strong primary extinction  (p. 612) | html | pdf |
• 6.4.13.2. Non-absorbing crystal, strong secondary extinction  (p. 612) | html | pdf |
• 6.4.13.3. The absorbing crystal  (p. 612) | html | pdf |
• 6.4.14. Relationship with the dynamical theory  (p. 612) | html | pdf |
• 6.4.15. Definitions  (p. 612) | html | pdf |
• References | html | pdf |
• Measurement of intensities
• 7.1. Detectors for X-rays  (pp. 618-638)
• 7.1.1. Photographic film  (p. 618) | html | pdf |
• 7.1.1.1. Visual estimation  (p. 618) | html | pdf |
• 7.1.1.2. Densitometry  (p. 618) | html | pdf |
• 7.1.2. Geiger counters  (pp. 618-619) | html | pdf |
• 7.1.3. Proportional counters  (p. 619) | html | pdf |
• 7.1.3.1. The detector system  (p. 619) | html | pdf |
• 7.1.3.2. Proportional counters  (p. 619) | html | pdf |
• 7.1.3.3. Position-sensitive detectors  (p. 619) | html | pdf |
• 7.1.3.4. Resolution, discrimination, efficiency  (p. 619) | html | pdf |
• 7.1.4. Scintillation and solid-state detectors  (pp. 619-622) | html | pdf |
• 7.1.4.1. Scintillation counters  (pp. 619-620) | html | pdf |
• 7.1.4.2. Solid-state detectors  (p. 620) | html | pdf |
• 7.1.4.3. Energy resolution and pulse-amplitude discrimination  (pp. 620-621) | html | pdf |
• 7.1.4.4. Quantum-counting efficiency and linearity  (pp. 621-622) | html | pdf |
• 7.1.4.5. Escape peaks  (p. 622) | html | pdf |
• 7.1.5. Energy-dispersive detectors  (pp. 622-623) | html | pdf |
• 7.1.6. Position-sensitive detectors  (pp. 623-633) | html | pdf |
• 7.1.6.1. Choice of detector  (pp. 623-626) | html | pdf |
• 7.1.6.1.1. Detection efficiency  (p. 624) | html | pdf |
• 7.1.6.1.2. Linearity of response  (pp. 624-625) | html | pdf |
• 7.1.6.1.3. Dynamic range  (p. 625) | html | pdf |
• 7.1.6.1.4. Spatial resolution  (p. 625) | html | pdf |
• 7.1.6.1.5. Uniformity of response  (p. 625) | html | pdf |
• 7.1.6.1.6. Spatial distortion  (p. 625) | html | pdf |
• 7.1.6.1.7. Energy discrimination  (pp. 625-626) | html | pdf |
• 7.1.6.1.8. Suitability for dynamic measurements  (p. 626) | html | pdf |
• 7.1.6.1.9. Stability  (p. 626) | html | pdf |
• 7.1.6.1.10. Size and weight  (p. 626) | html | pdf |
• 7.1.6.2. Gas-filled counters  (pp. 626-629) | html | pdf |
• 7.1.6.2.1. Localization of the detected photon  (p. 627) | html | pdf |
• 7.1.6.2.2. Parallel-plate counters  (pp. 627-628) | html | pdf |
• 7.1.6.2.3. Current ionization PSD's  (pp. 628-629) | html | pdf |
• 7.1.6.3. Semiconductor detectors  (pp. 629-630) | html | pdf |
• 7.1.6.3.1. X-ray-sensitive semiconductor PSD's  (pp. 629-630) | html | pdf |
• 7.1.6.3.2. Light-sensitive semiconductor PSD's  (p. 630) | html | pdf |
• 7.1.6.3.3. Electron-sensitive PSD's  (p. 630) | html | pdf |
• 7.1.6.4. Devices with an X-ray-sensitive photocathode  (p. 630) | html | pdf |
• 7.1.6.5. Television area detectors with external phosphor  (pp. 630-632) | html | pdf |
• 7.1.6.5.1. X-ray phosphors  (p. 631) | html | pdf |
• 7.1.6.5.2. Light coupling  (p. 632) | html | pdf |
• 7.1.6.5.3. Image intensifiers  (p. 632) | html | pdf |
• 7.1.6.5.4. TV camera tubes  (p. 632) | html | pdf |
• 7.1.6.6. Some applications  (pp. 632-633) | html | pdf |
• 7.1.7. X-ray-sensitive TV cameras  (pp. 633-635) | html | pdf |
• 7.1.7.1. Signal-to-noise ratio  (pp. 633-634) | html | pdf |
• 7.1.7.2. Imaging system  (pp. 634-635) | html | pdf |
• 7.1.7.3. Image processing  (p. 635) | html | pdf |
• 7.1.8. Storage phosphors  (pp. 635-638) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 7.1.2.1. Detectors used for diffractometry: (a) Geiger counter, (b) side-window proportional counter, (c) end-window scintillation counter  (p. 618) | html | pdf |
• Fig. 7.1.4.1. Calculated pulse-amplitude distributions of Cu Kα and Mo Kα in the form of (a) integral curves and (b) differential curves  (p. 621) | html | pdf |
• Fig. 7.1.5.1. Intrinsic efficiency of semiconductor detectors  (p. 622) | html | pdf |
• Fig. 7.1.6.1. Possible combinations of detection processes, localization methods and read-out procedures in PSD's  (p. 624) | html | pdf |
• Fig. 7.1.6.2. Absorption of 8 keV and 17 keV photons in argon and xenon as a function of pressure in atm × column length in mm  (p. 625) | html | pdf |
• Fig. 7.1.6.3. Spherical drift chamber multiwire proportional chamber (MWPC)  (p. 627) | html | pdf |
• Fig. 7.1.6.4. Read-out methods for gas-filled LPSD's  (p. 628) | html | pdf |
• Fig. 7.1.6.5. Three-plane MWPC  (p. 629) | html | pdf |
• Fig. 7.1.6.6. Integrating LPSD  (p. 629) | html | pdf |
• Fig. 7.1.6.7. Fast-scanning television X-ray detector (after Arndt, 1985)  (p. 631) | html | pdf |
• Fig. 7.1.7.1. Schematic illustration of an X-ray sensing Saticon camera tube  (p. 633) | html | pdf |
• Fig. 7.1.7.2. Square-wave modulation transfer function (MTF) measured for the DIS-type, conventional-type Se–As and PbO camera tubes  (p. 634) | html | pdf |
• Fig. 7.1.7.3. Typical example showing dependence of the avalanche amplification on the electric field applied on the amorphous photoconductor (HARP)  (p. 634) | html | pdf |
• Fig. 7.1.7.4. Principles of a noise reducer  (p. 635) | html | pdf |
• Fig. 7.1.8.1. Mechanism of photo-stimulated luminescence  (p. 636) | html | pdf |
• Fig. 7.1.8.2. Measured detective quantum efficiency (DQE) of the imaging plate and high-sensitivity X-ray film as a function of the exposure level  (p. 636) | html | pdf |
• Fig. 7.1.8.3. Fluctuation noise in the signal as a function of the exposure level  (p. 636) | html | pdf |
• Fig. 7.1.8.4. Diagram showing a cascade of stochastic elementary processes during X-ray exposure and image read out of the imaging plate  (p. 637) | html | pdf |
• Fig. 7.1.8.5. Dynamic range of the photo-stimulated luminescence of the imaging plate  (p. 637) | html | pdf |
• Fig. 7.1.8.6. Dependence of the IP response as a function of the energy of an X-ray photon  (p. 637) | html | pdf |
• Fig. 7.1.8.7. Fading of the IP signals as a function of time with two different X-ray energies (5.9 and 59.5 keV)  (p. 638) | html | pdf |
• Tables
• Table 7.1.6.1. The importance of some detector properties for different X-ray patterns  (p. 624) | html | pdf |
• Table 7.1.6.2. X-ray phosphors (from Arndt, 1982)  (p. 631) | html | pdf |
• 7.2. Detectors for electrons  (pp. 639-643)
• 7.2.1. Introduction  (p. 639) | html | pdf |
• 7.2.2. Characterization of detectors  (pp. 639-640) | html | pdf |
• 7.2.3. Parallel detectors  (pp. 640-642) | html | pdf |
• 7.2.3.1. Fluorescent screens  (p. 640) | html | pdf |
• 7.2.3.2. Photographic emulsions  (pp. 640-641) | html | pdf |
• 7.2.3.3. Detector systems based on an electron-tube device  (p. 641) | html | pdf |
• 7.2.3.4. Electronic detection systems based on solid-state devices  (p. 641) | html | pdf |
• 7.2.3.5. Imaging plates   (pp. 641-642) | html | pdf |
• 7.2.4. Serial detectors  (pp. 642-643) | html | pdf |
• 7.2.4.1. Faraday cage  (p. 642) | html | pdf |
• 7.2.4.2. Scintillation detectors  (p. 642) | html | pdf |
• 7.2.4.3. Semiconductor detectors  (pp. 642-643) | html | pdf |
• 7.2.5. Conclusions  (p. 643) | html | pdf |
• References | html | pdf |
• 7.3. Thermal neutron detection  (pp. 644-652)
• 7.3.1. Introduction  (p. 644) | html | pdf |
• 7.3.2. Neutron capture  (p. 644) | html | pdf |
• 7.3.3. Neutron detection processes  (pp. 644-648) | html | pdf |
• 7.3.3.1. Detection via gas converter and gas ionization: the gas detector  (pp. 644-645) | html | pdf |
• 7.3.3.2. Detection via solid converter and gas ionization: the foil detector  (p. 645) | html | pdf |
• 7.3.3.3. Detection via scintillation  (pp. 645-646) | html | pdf |
• 7.3.3.4. Films  (pp. 646-648) | html | pdf |
• 7.3.4. Electronic aspects of neutron detection  (pp. 648-649) | html | pdf |
• 7.3.4.1. The electronic chain  (p. 648) | html | pdf |
• 7.3.4.2. Controls and adjustments of the electronics  (pp. 648-649) | html | pdf |
• 7.3.5. Typical detection systems  (pp. 649-650) | html | pdf |
• 7.3.5.1. Single detectors  (p. 649) | html | pdf |
• 7.3.5.2. Position-sensitive detectors  (pp. 649-650) | html | pdf |
• 7.3.5.3. Banks of detectors  (p. 650) | html | pdf |
• 7.3.6. Characteristics of detection systems  (p. 651) | html | pdf |
• 7.3.7. Corrections to the intensity measurements depending on the detection system  (p. 652) | html | pdf |
• 7.3.7.1. Single detector  (p. 652) | html | pdf |
• 7.3.7.2. Banks of detectors  (p. 652) | html | pdf |
• 7.3.7.3. Position-sensitive detectors  (p. 652) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 7.3.2.1. The capture cross sections for a number of nuclei used in neutron detection  (p. 644) | html | pdf |
• Fig. 7.3.3.1. (a) Neutron capture by an 3He atom and random-direction trajectory (Ox) of the secondary charged particles in the gas mixture  (p. 647) | html | pdf |
• Fig. 7.3.3.2. Typical design of a 10B-foil detector  (p. 647) | html | pdf |
• Fig. 7.3.3.3. (a) Schematic representation of the neutron capture, secondary α, and triton ionization volumes, and scintillator light emission in a cerium-doped lithium silicate glass  (p. 647) | html | pdf |
• Fig. 7.3.4.1. Electronic chain following (a) an 3He gas detector and (b) a scintillation detector  (p. 648) | html | pdf |
• Fig. 7.3.4.2. (a) Characteristic 10BF3 gas-detector analogue pulses seen on an oscilloscope  (p. 649) | html | pdf |
• Tables
• Table 7.3.2.1. Neutron capture reactions used in neutron detection  (p. 645) | html | pdf |
• Table 7.3.3.1. Commonly used detection processes  (p. 646) | html | pdf |
• Table 7.3.3.2. A few examples of gas-detector characteristics  (p. 646) | html | pdf |
• Table 7.3.5.1. Characteristics of some PSDs  (p. 651) | html | pdf |
• 7.4. Correction of systematic errors  (pp. 653-665)
• 7.4.1. Absorption  (p. 653) | html | pdf |
• 7.4.2. Thermal diffuse scattering  (pp. 653-657) | html | pdf |
• 7.4.2.1. Glossary of symbols  (pp. 653-654) | html | pdf |
• 7.4.2.2. TDS correction factor for X-rays (single crystals)  (pp. 654-656) | html | pdf |
• 7.4.2.2.1. Evaluation of J(q)  (pp. 654-655) | html | pdf |
• 7.4.2.2.2. Calculation of α  (pp. 655-656) | html | pdf |
• 7.4.2.3. TDS correction factor for thermal neutrons (single crystals)  (pp. 656-657) | html | pdf |
• 7.4.2.4. Correction factor for powders   (p. 657) | html | pdf |
• 7.4.3. Compton scattering  (pp. 657-661) | html | pdf |
• 7.4.3.1. Introduction  (p. 657) | html | pdf |
• 7.4.3.2. Non-relativistic calculations of the incoherent scattering cross section  (pp. 657-659) | html | pdf |
• 7.4.3.2.1. Semi-classical radiation theory  (pp. 657-659) | html | pdf |
• 7.4.3.2.2. Thomas–Fermi model  (p. 659) | html | pdf |
• 7.4.3.2.3. Exact calculations  (p. 659) | html | pdf |
• 7.4.3.3. Relativistic treatment of incoherent scattering  (pp. 659-660) | html | pdf |
• 7.4.3.4. Plasmon, Raman, and resonant Raman scattering  (pp. 660-661) | html | pdf |
• 7.4.3.5. Magnetic scattering  (p. 661) | html | pdf |
• 7.4.4. White radiation and other sources of background  (pp. 661-665) | html | pdf |
• 7.4.4.1. Introduction  (p. 661) | html | pdf |
• 7.4.4.2. Incident beam and sample  (pp. 661-663) | html | pdf |
• 7.4.4.3. Detecting system  (pp. 663-664) | html | pdf |
• 7.4.4.4. Powder diffraction  (pp. 664-665) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 7.4.2.1. 060 reflection of LiNbO3 (Mössbauer diffraction)  (p. 653) | html | pdf |
• Fig. 7.4.2.2. Diagrams in reciprocal space illustrating the volume abcd swept out for (a) an ω scan, and (b) a θ/2θ, or ω/2θ, scan  (p. 655) | html | pdf |
• Fig. 7.4.2.3. Scattering surfaces for one-phonon scattering of neutrons: (a) for neutrons faster than sound (β < 1); (b) for neutrons slower than sound (β > 1)  (p. 656) | html | pdf |
• Fig. 7.4.2.4. One-phonon scattering calculated for polycrystalline nickel of lattice constant a (after Suortti, 1980a)  (p. 656) | html | pdf |
• Fig. 7.4.3.1. Schematic diagram of the inelastic scattering interactions, ΔE = E1E2 is the energy transferred from the photon and K the momentum transfer  (p. 657) | html | pdf |
• Fig. 7.4.3.2. The incoherent scattering function, S(x, Z)/Z, per electron for aluminium shown as a function of x = (sin θ)/λ  (p. 660) | html | pdf |
• Fig. 7.4.3.3. The cross section for resonant Raman scattering (RRS) and fluorescence (F) as a function of the ratio of the incident energy, E, and the K-binding energy, EB  (p. 661) | html | pdf |
• Fig. 7.4.4.1. Equatorial phase-space diagrams for a conventional X-ray source and parallel-beam geometry; x is the size and x′ = dx/dz the divergence of the X-rays  (p. 662) | html | pdf |
• Fig. 7.4.4.2. Reflection 400 of LiH measured with a parallel beam of Mo Kα1 radiation (solid curve)  (p. 662) | html | pdf |
• Fig. 7.4.4.3. Equatorial phase-space diagrams for two wavelengths, λ1 (solid lines) and λ2 (broken lines), projected on the plane λ = λ1  (p. 662) | html | pdf |
• Fig. 7.4.4.4. Two reflections of beryllium acetate measured with Mo Kα  (p. 663) | html | pdf |
• Fig. 7.4.4.5. Components of scattering at small scattering angles when the incident energy is just below the K absorption edge of the sample [upper part, (a)], and at large scattering angles when the incident energy is about twice the K-edge energy [upper part, (b)]  (p. 663) | html | pdf |
• Fig. 7.4.4.6. Equatorial phase-space diagrams for powder diffraction in the Bragg–Brentano geometry  (p. 664) | html | pdf |
• Fig. 7.4.4.7. Three measurements of the 220 reflection of Ni at λ = 1.541 Å scaled to the same peak value; (a) in linear scale, (b) in logarithmic scale  (p. 664) | html | pdf |
• Tables
• Table 7.4.3.1. The energy transfer, in eV, in the Compton scattering process for selected X-ray energies  (p. 657) | html | pdf |
• Table 7.4.3.2. The incoherent scattering function for elements up to Z = 55  (p. 658) | html | pdf |
• Table 7.4.3.3. Compton scattering of Mo Kα X-radiation through 170° from 2s electrons  (p. 659) | html | pdf |
• 7.5. Statistical fluctuations  (pp. 666-676)
• 7.5.1. Distributions of intensities of diffraction  (p. 666) | html | pdf |
• 7.5.2. Counting modes  (p. 666) | html | pdf |
• 7.5.3. Fixed-time counting  (pp. 666-667) | html | pdf |
• 7.5.4. Fixed-count timing  (p. 667) | html | pdf |
• 7.5.5. Complicating phenomena  (p. 667) | html | pdf |
• 7.5.5.1. Dead time  (p. 667) | html | pdf |
• 7.5.5.2. Voltage fluctuations  (p. 667) | html | pdf |
• 7.5.6. Treatment of measured-as-negative (and other weak) intensities  (p. 667) | html | pdf |
• 7.5.7. Optimization of counting times  (pp. 667-668) | html | pdf |
• References | html | pdf |
• Refinement of structural parameters
• 8.1. Least squares  (pp. 678-688)
• 8.1.1. Definitions  (pp. 678-680) | html | pdf |
• 8.1.1.1. Linear algebra  (pp. 678-679) | html | pdf |
• 8.1.1.2. Statistics  (pp. 679-680) | html | pdf |
• 8.1.2. Principles of least squares  (pp. 680-681) | html | pdf |
• 8.1.3. Implementation of linear least squares  (pp. 681-682) | html | pdf |
• 8.1.3.1. Use of the QR factorization  (pp. 681-682) | html | pdf |
• 8.1.3.2. The normal equations  (p. 682) | html | pdf |
• 8.1.3.3. Conditioning  (p. 682) | html | pdf |
• 8.1.4. Methods for nonlinear least squares  (pp. 682-685) | html | pdf |
• 8.1.4.1. The Gauss–Newton algorithm  (p. 683) | html | pdf |
• 8.1.4.2. Trust-region methods – the Levenberg–Marquardt algorithm  (p. 683) | html | pdf |
• 8.1.4.3. Quasi-Newton, or secant, methods  (pp. 683-684) | html | pdf |
• 8.1.4.4. Stopping rules  (pp. 684-685) | html | pdf |
• 8.1.4.5. Recommendations  (p. 685) | html | pdf |
• 8.1.5. Numerical methods for large-scale problems  (pp. 685-687) | html | pdf |
• 8.1.5.1. Methods for sparse matrices  (pp. 685-686) | html | pdf |
• 8.1.5.2. Conjugate-gradient methods  (pp. 686-687) | html | pdf |
• 8.1.6. Orthogonal distance regression  (pp. 687-688) | html | pdf |
• 8.1.7. Software for least-squares calculations  (p. 688) | html | pdf |
• References | html | pdf |
• 8.2. Other refinement methods  (pp. 689-692)
• 8.2.1. Maximum-likelihood methods  (p. 689) | html | pdf |
• 8.2.2. Robust/resistant methods  (pp. 689-691) | html | pdf |
• 8.2.3. Entropy maximization  (pp. 691-692) | html | pdf |
• 8.2.3.1. Introduction  (p. 691) | html | pdf |
• 8.2.3.2. Some examples  (pp. 691-692) | html | pdf |
• References | html | pdf |
• 8.3. Constraints and restraints in refinement  (pp. 694-701)
• 8.3.1. Constrained models  (pp. 693-698) | html | pdf |
• 8.3.1.1. Lagrange undetermined multipliers  (p. 693) | html | pdf |
• 8.3.1.2. Direct application of constraints  (pp. 693-698) | html | pdf |
• 8.3.2. Stereochemically restrained least-squares refinement  (pp. 698-701) | html | pdf |
• 8.3.2.1. Stereochemical constraints as observational equations  (pp. 698-701) | html | pdf |
• References | html | pdf |
• Tables
• Table 8.3.1.1. Symmetry conditions for second-cumulant tensors  (pp. 695-696) | html | pdf |
• Table 8.3.2.1. Coordinates of atoms (in Å) in standard groups appearing in polypeptides and proteins  (pp. 699-700) | html | pdf |
• Table 8.3.2.2. Ideal values for distances (Å), torsion angles (°), etc. for a glycine–alanine dipeptide with a trans peptide bond  (p. 700) | html | pdf |
• Table 8.3.2.3. Typical values of standard deviations for use in determining weights in restrained refinement of protein structures  (p. 701) | html | pdf |
• 8.4. Statistical significance tests  (pp. 702-706)
• 8.4.1. The χ2 distribution  (pp. 702-703) | html | pdf |
• 8.4.2. The F distribution  (pp. 703-704) | html | pdf |
• 8.4.3. Comparison of different models  (pp. 704-705) | html | pdf |
• 8.4.4. Influence of individual data points  (pp. 705-706) | html | pdf |
• References | html | pdf |
• Tables
• Table 8.4.1.1. Values of χ2/ν for which the c.d.f. ψ(χ2, ν) has the values given in the column headings, for various values of ν  (p. 703) | html | pdf |
• Table 8.4.2.1. Values of the F ratio for which the c.d.f. ψ(F, ν1, ν2) has the value 0.95, for various choices of ν1 and ν2  (p. 704) | html | pdf |
• Table 8.4.3.1. Values of t for which the c.d.f. Ψ(t, ν) has the values given in the column headings, for various values of ν  (p. 704) | html | pdf |
• 8.5. Detection and treatment of systematic error  (pp. 707-709)
• 8.5.1. Accuracy  (p. 707) | html | pdf |
• 8.5.2. Lack of fit  (pp. 707-708) | html | pdf |
• 8.5.3. Influential data points  (p. 708) | html | pdf |
• 8.5.4. Plausibility of results  (p. 709) | html | pdf |
• References | html | pdf |
• 8.6. The Rietveld method  (pp. 710-712)
• 8.6.1. Basic theory  (pp. 710-711) | html | pdf |
• 8.6.2. Problems with the Rietveld method  (pp. 711-712) | html | pdf |
• 8.6.2.1. Indexing  (p. 711) | html | pdf |
• 8.6.2.2. Peak-shape function (PSF)  (p. 711) | html | pdf |
• 8.6.2.3. Background  (p. 711) | html | pdf |
• 8.6.2.4. Preferred orientation and texture  (p. 712) | html | pdf |
• 8.6.2.5. Statistical validity  (p. 712) | html | pdf |
• References | html | pdf |
• 8.7. Analysis of charge and spin densities  (pp. 713-734)
• 8.7.1. Outline of this chapter  (p. 713) | html | pdf |
• 8.7.2. Electron densities and the n-particle wavefunction  (p. 713) | html | pdf |
• 8.7.3. Charge densities  (pp. 714-725) | html | pdf |
• 8.7.3.1. Introduction  (p. 714) | html | pdf |
• 8.7.3.2. Modelling of the charge density  (pp. 714-715) | html | pdf |
• 8.7.3.3. Physical constraints  (p. 715) | html | pdf |
• 8.7.3.3.1. Electroneutrality constraint  (p. 715) | html | pdf |
• 8.7.3.3.2. Cusp constraint  (p. 715) | html | pdf |
• 8.7.3.3.3. Radial constraint  (p. 715) | html | pdf |
• 8.7.3.3.4. Hellmann–Feynman constraint  (p. 715) | html | pdf |
• 8.7.3.4. Electrostatic moments and the potential due to a charge distribution  (pp. 716-721) | html | pdf |
• 8.7.3.4.1. Moments of a charge distribution  (pp. 716-718) | html | pdf |
• 8.7.3.4.1.1. Moments as a function of the atomic multipole expansion  (pp. 716-717) | html | pdf |
• 8.7.3.4.1.2. Molecular moments based on the deformation density  (p. 717) | html | pdf |
• 8.7.3.4.1.3. The effect of an origin shift on the outer moments  (pp. 717-718) | html | pdf |
• 8.7.3.4.1.4. Total moments as a sum over the pseudoatom moments  (p. 718) | html | pdf |
• 8.7.3.4.1.5. Electrostatic moments of a subvolume of space by Fourier summation  (p. 718) | html | pdf |
• 8.7.3.4.2. The electrostatic potential  (pp. 718-720) | html | pdf |
• 8.7.3.4.2.1. The electrostatic potential and its derivatives  (pp. 718-719) | html | pdf |
• 8.7.3.4.2.2. Electrostatic potential outside a charge distribution  (p. 720) | html | pdf |
• 8.7.3.4.2.3. Evaluation of the electrostatic functions in direct space  (p. 720) | html | pdf |
• 8.7.3.4.3. Electrostatic functions of crystals by modified Fourier summation  (pp. 720-721) | html | pdf |
• 8.7.3.4.4. The total energy of a crystal as a function of the electron density  (p. 721) | html | pdf |
• 8.7.3.5. Quantitative comparison with theory  (pp. 721-722) | html | pdf |
• 8.7.3.6. Occupancies of transition-metal valence orbitals from multipole coefficients  (pp. 722-723) | html | pdf |
• 8.7.3.7. Thermal smearing of theoretical densities  (pp. 723-724) | html | pdf |
• 8.7.3.7.1. General considerations  (p. 723) | html | pdf |
• 8.7.3.7.2. Reciprocal-space averaging over external vibrations  (pp. 723-724) | html | pdf |
• 8.7.3.8. Uncertainties in experimental electron densities  (pp. 724-725) | html | pdf |
• 8.7.3.9. Uncertainties in derived functions  (p. 725) | html | pdf |
• 8.7.4. Spin densities  (pp. 725-734) | html | pdf |
• 8.7.4.1. Introduction  (p. 725) | html | pdf |
• 8.7.4.2. Magnetization densities from neutron magnetic elastic scattering  (pp. 725-726) | html | pdf |
• 8.7.4.3. Magnetization densities and spin densities  (pp. 726-727) | html | pdf |
• 8.7.4.3.1. Spin-only density at zero temperature  (p. 726) | html | pdf |
• 8.7.4.3.2. Thermally averaged spin-only magnetization density  (pp. 726-727) | html | pdf |
• 8.7.4.3.3. Spin density for an assembly of localized systems  (p. 727) | html | pdf |
• 8.7.4.3.4. Orbital magnetization density  (p. 727) | html | pdf |
• 8.7.4.4. Probing spin densities by neutron elastic scattering  (pp. 727-729) | html | pdf |
• 8.7.4.4.1. Introduction  (pp. 727-728) | html | pdf |
• 8.7.4.4.2. Unpolarized neutron scattering  (p. 728) | html | pdf |
• 8.7.4.4.3. Polarized neutron scattering  (p. 728) | html | pdf |
• 8.7.4.4.4. Polarized neutron scattering of centrosymmetric crystals  (p. 728) | html | pdf |
• 8.7.4.4.5. Polarized neutron scattering in the noncentro­symmetric case  (p. 728) | html | pdf |
• 8.7.4.4.6. Effect of extinction  (pp. 728-729) | html | pdf |
• 8.7.4.4.7. Error analysis  (p. 729) | html | pdf |
• 8.7.4.5. Modelling the spin density  (pp. 729-730) | html | pdf |
• 8.7.4.5.1. Atom-centred expansion  (pp. 729-730) | html | pdf |
• 8.7.4.5.1.1. Spherical-atom model  (p. 729) | html | pdf |
• 8.7.4.5.1.2. Crystal-field approximation  (pp. 729-730) | html | pdf |
• 8.7.4.5.1.3. Scaling of the spin density  (p. 730) | html | pdf |
• 8.7.4.5.2. General multipolar expansion  (p. 730) | html | pdf |
• 8.7.4.5.3. Other types of model  (p. 730) | html | pdf |
• 8.7.4.6. Orbital contribution to the magnetic scattering  (pp. 730-731) | html | pdf |
• 8.7.4.6.1. The dipolar approximation  (p. 731) | html | pdf |
• 8.7.4.6.2. Beyond the dipolar approximation  (p. 731) | html | pdf |
• 8.7.4.6.3. Electronic structure of rare-earth elements  (p. 731) | html | pdf |
• 8.7.4.7. Properties derivable from spin densities  (pp. 731-732) | html | pdf |
• 8.7.4.7.1. Vector fields  (p. 732) | html | pdf |
• 8.7.4.7.2. Moments of the magnetization density  (p. 732) | html | pdf |
• 8.7.4.8. Comparison between theory and experiment  (p. 732) | html | pdf |
• 8.7.4.9. Combined charge- and spin-density analysis  (p. 732) | html | pdf |
• 8.7.4.10. Magnetic X-ray scattering separation between spin and orbital magnetism  (pp. 733-734) | html | pdf |
• 8.7.4.10.1. Introduction  (p. 733) | html | pdf |
• 8.7.4.10.2. Magnetic X-ray structure factor as a function of photon polarization  (pp. 733-734) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 8.7.4.1. Some geometrical definitions  (p. 733) | html | pdf |
• Tables
• Table 8.7.3.1. Definition of difference density functions  (p. 714) | html | pdf |
• Table 8.7.3.2. Expressions for the shape factors S for a parallelepiped with edges δx, δy, and δz  (p. 719) | html | pdf |
• Table 8.7.3.3. The matrix M−1 relating d-orbital occupancies Pij to multipole populations Plm  (p. 722) | html | pdf |
• Table 8.7.3.4. Orbital–multipole relations for square-planar complexes (point group D4h)  (p. 723) | html | pdf |
• Table 8.7.3.5. Orbital–multipole relations for trigonal complexes  (p. 723) | html | pdf |
• 8.8. Accurate structure-factor determination with electron diffraction  (pp. 735-743)
• References | html | pdf |
• Figures
• Fig. 8.8.1. Schematic representations of four convergent-beam configurations used for structure-factor determination: (a) intensity profile of a low-order reflection, g; (b) non-systematic three- or four-beam configuration with a strong coupling reflection, h; (c) symmetric many-beam configuration in a dense zone; (d) integrated intensity measurement of high-order reflections using a wide aperture (Taftø & Metzger, 1985)  (p. 736) | html | pdf |
• Basic structural features
• 9.1. Sphere packings and packings of ellipsoids  (pp. 746-751)
• 9.1.1. Sphere packings and packings of circles  (pp. 746-751) | html | pdf |
• 9.1.1.1. Definitions  (p. 746) | html | pdf |
• 9.1.1.2. Homogeneous packings of circles  (p. 746) | html | pdf |
• 9.1.1.3. Homogeneous sphere packings  (pp. 746-750) | html | pdf |
• 9.1.1.4. Applications  (pp. 750-751) | html | pdf |
• 9.1.1.5. Interpenetrating sphere packings  (p. 751) | html | pdf |
• 9.1.2. Packings of ellipses and ellipsoids  (p. 751) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 9.1.1.1. Two triangular nets representing two densest packed layers of spheres. The layers are stacked in such a way that each sphere is in contact with three spheres of the other layer  (p. 747) | html | pdf |
• Fig. 9.1.1.2. Two triangular nets representing two densest packed layers of spheres. The layers are stacked in such a way that each sphere is in contact with two spheres of the other layer  (p. 749) | html | pdf |
• Fig. 9.1.1.3. Two square nets representing two layers of spheres stacked in such a way that each sphere is in contact with four spheres of the other layer  (p. 749) | html | pdf |
• Fig. 9.1.1.4. Two square nets representing two layers of spheres stacked in such a way that each sphere is in contact with two spheres of the other layer  (p. 749) | html | pdf |
• Fig. 9.1.1.5. Sphere packing of type 8  (p. 749) | html | pdf |
• Fig. 9.1.1.6. Sphere packing of type 19  (p. 750) | html | pdf |
• Fig. 9.1.1.7. Least dense sphere packing known so far  (p. 750) | html | pdf |
• Tables
• Table 9.1.1.1. Types of circle packings in the plane  (p. 747) | html | pdf |
• Table 9.1.1.2. Examples for sphere packings with high contact numbers and high densities and with low contact numbers and low densities  (p. 748) | html | pdf |
• 9.2. Layer stacking  (pp. 752-773)
• 9.2.1. Layer stacking in close-packed structures  (pp. 752-760) | html | pdf |
• 9.2.1.1. Close packing of equal spheres  (pp. 752-753) | html | pdf |
• 9.2.1.1.1. Close-packed layer  (p. 752) | html | pdf |
• 9.2.1.1.2. Close-packed structures  (p. 752) | html | pdf |
• 9.2.1.1.3. Notations for close-packed structures  (pp. 752-753) | html | pdf |
• 9.2.1.2. Structure of compounds based on close-packed layer stackings  (pp. 753-755) | html | pdf |
• 9.2.1.2.1. Voids in close packing  (p. 753) | html | pdf |
• 9.2.1.2.2. Structures of SiC and ZnS  (pp. 753-754) | html | pdf |
• 9.2.1.2.3. Structure of CdI2  (p. 754) | html | pdf |
• 9.2.1.2.4. Structure of GaSe  (pp. 754-755) | html | pdf |
• 9.2.1.3. Symmetry of close-packed layer stackings of equal spheres  (p. 755) | html | pdf |
• 9.2.1.4. Possible lattice types  (p. 755) | html | pdf |
• 9.2.1.5. Possible space groups  (pp. 755-756) | html | pdf |
• 9.2.1.6. Crystallographic uses of Zhdanov symbols  (p. 756) | html | pdf |
• 9.2.1.7. Structure determination of close-packed layer stackings  (pp. 756-758) | html | pdf |
• 9.2.1.7.1. General considerations  (p. 756) | html | pdf |
• 9.2.1.7.2. Determination of the lattice type  (p. 757) | html | pdf |
• 9.2.1.7.3. Determination of the identity period  (p. 757) | html | pdf |
• 9.2.1.7.4. Determination of the stacking sequence of layers  (pp. 757-758) | html | pdf |
• 9.2.1.8. Stacking faults in close-packed structures  (pp. 758-760) | html | pdf |
• 9.2.1.8.1. Structure determination of one-dimensionally disordered crystals  (pp. 759-760) | html | pdf |
• 9.2.2. Layer stacking in general polytypic structures  (pp. 760-773) | html | pdf |
• 9.2.2.1. The notion of polytypism  (pp. 760-761) | html | pdf |
• 9.2.2.2. Symmetry aspects of polytypism  (pp. 761-766) | html | pdf |
• 9.2.2.2.1. Close packing of spheres  (p. 761) | html | pdf |
• 9.2.2.2.2. Polytype families and OD groupoid families  (pp. 761-762) | html | pdf |
• 9.2.2.2.3. MDO polytypes  (p. 762) | html | pdf |
• 9.2.2.2.4. Some geometrical properties of OD structures  (pp. 762-763) | html | pdf |
• 9.2.2.2.5. Diffraction pattern – structure analysis  (p. 763) | html | pdf |
• 9.2.2.2.6. The vicinity condition  (pp. 763-764) | html | pdf |
• 9.2.2.2.7. Categories of OD structures  (pp. 764-765) | html | pdf |
• 9.2.2.2.7.1. OD structures of equivalent layers  (pp. 764-765) | html | pdf |
• 9.2.2.2.7.2. OD structures with more than one kind of layer  (p. 765) | html | pdf |
• 9.2.2.2.8. Desymmetrization of OD structures  (pp. 765-766) | html | pdf |
• 9.2.2.2.9. Concluding remarks  (p. 766) | html | pdf |
• 9.2.2.3. Examples of some polytypic structures  (pp. 766-772) | html | pdf |
• 9.2.2.3.1. Hydrous phyllosilicates  (pp. 766-769) | html | pdf |
• 9.2.2.3.1.1. General geometry  (pp. 767-769) | html | pdf |
• 9.2.2.3.1.2. Diffraction pattern and identification of individual polytypes  (p. 769) | html | pdf |
• 9.2.2.3.2. Stibivanite Sb2VO5  (pp. 769-771) | html | pdf |
• 9.2.2.3.3. γ-Hg3S2Cl2  (pp. 771-772) | html | pdf |
• 9.2.2.3.4. Remarks for authors  (p. 772) | html | pdf |
• 9.2.2.4. List of some polytypic structures  (pp. 772-773) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 9.2.1.1. The close packing of equal spheres in a plane  (p. 752) | html | pdf |
• Fig. 9.2.1.2. (a) Symmetry axes of a single close-packed layer of spheres and (b) the minimum symmetry of a three-dimensional close packing of spheres  (p. 752) | html | pdf |
• Fig. 9.2.1.3. Voids in a close packing: (a) tetrahedral void; (b) tetrahedron formed by the centres of spheres; (c) octahedral void; (d) octahedron formed by the centres of spheres  (p. 753) | html | pdf |
• Fig. 9.2.1.4. Tetrahedral arrangement of Si and C atoms in the SiC-6H structure  (p. 753) | html | pdf |
• Fig. 9.2.1.5. The layer structure of CdI2: small circles represent Cd ions and larger ones I ions  (p. 754) | html | pdf |
• Fig. 9.2.1.6. The primitive unit cell of the 2H close packing  (p. 755) | html | pdf |
• Fig. 9.2.1.7. A rhombohedral lattice (a1, a2, a3) referred to hexagonal axes (A1, A2, C)  (p. 755) | html | pdf |
• Fig. 9.2.1.8. The relationship between the f.c.c. and the primitive rhombohedral unit cell of the c.c.p. structure  (p. 756) | html | pdf |
• Fig. 9.2.1.9. The a*−b* reciprocal-lattice net for close-packed layer stackings  (p. 756) | html | pdf |
• Fig. 9.2.2.1. Symmetry interpretation of close packings of equal spheres  (p. 761) | html | pdf |
• Fig. 9.2.2.2. Schematic representation of three structures belonging to the OD groupoid family P(1)m1|1  (p. 762) | html | pdf |
• Fig. 9.2.2.3. Schematic examples of the three categories of OD structures consisting of equivalent layers (perpendicular to the plane of the drawing)  (p. 764) | html | pdf |
• Fig. 9.2.2.4. Schematic examples of the four categories of OD structures consisting of more than one kind of layer (perpendicular to the plane of the drawing)  (p. 764) | html | pdf |
• Fig. 9.2.2.5. Hierarchy of VC structures indicating the position of OD structures within it  (p. 765) | html | pdf |
• Fig. 9.2.2.6. (a) Tetrahedral sheet in a normal projection  (p. 767) | html | pdf |
• Fig. 9.2.2.7. Two possible combinations of one tetrahedral and one octahedral sheet (a) by shared apical O atoms, (b) by hydrogen bonds (side projection)  (p. 767) | html | pdf |
• Fig. 9.2.2.8. Combination of two adjacent tetrahedral sheets (a) in the mica group, (b) in the talc–pyrophyllite group (side projection)  (p. 767) | html | pdf |
• Fig. 9.2.2.9. The nine possible displacements in the structures of polytypes of phyllosilicates  (p. 768) | html | pdf |
• Fig. 9.2.2.10. The NFZ relations (a) for the pair tetrahedral sheet–homo-octahedral sheet (with shared apical O atoms), (b), (c) for the pair homo-octahedral sheet–tetrahedral sheet (by hydrogen bonds)  (p. 768) | html | pdf |
• Fig. 9.2.2.11. Stereopair showing the sequence of sheets in the structures of the serpentine–kaolin group  (p. 769) | html | pdf |
• Fig. 9.2.2.12. Stereopair showing the sequence of sheets in the structures of the mica group  (p. 770) | html | pdf |
• Fig. 9.2.2.13. Stereopair showing the sequence of sheets in the structures of the talc–pyrophyllite group  (p. 770) | html | pdf |
• Fig. 9.2.2.14. Stereopair showing the sequence of sheets in the structures of the chlorite–vermiculite group (chlorite-1M, courtesy of Zoltai & Stout, 1985)  (p. 770) | html | pdf |
• Fig. 9.2.2.15. Clinographic projection of the general scheme of a single-crystal diffraction pattern of hydrous phyllosilicates  (p. 771) | html | pdf |
• Fig. 9.2.2.16. Normal projection of the general scheme of a single-crystal diffraction pattern of hydrous phyllosilicates  (p. 771) | html | pdf |
• Fig. 9.2.2.17. The structure of stibivanite-2M  (p. 771) | html | pdf |
• Fig. 9.2.2.18. The two kinds of OD layers in the stibivanite family  (p. 772) | html | pdf |
• Fig. 9.2.2.19. The structure of stibivanite-2O  (p. 772) | html | pdf |
• Fig. 9.2.2.20. The structural principle of γ-Hg3S2Cl2  (p. 772) | html | pdf |
• Tables
• Table 9.2.1.1. Common close-packed metallic structures  (p. 753) | html | pdf |
• Table 9.2.1.2. List of SiC polytypes with known structures in order of increasing periodicity  (p. 754) | html | pdf |
• Table 9.2.1.3. Intrinsic fault configurations in the 6H (A0B1C2A3C4B5;. . .) structure  (p. 758) | html | pdf |
• Table 9.2.1.4. Intrinsic fault configurations in the 9R (A0B1A2C0A1C2B0C1B2;. . .) structure  (p. 759) | html | pdf |
• 9.3. Typical interatomic distances: metals and alloys  (pp. 774-777)
• 9.3.1. Glossary  (p. 777) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 9.3.1. (a) The radii for CN = 12  (p. 774) | html | pdf |
• Fig. 9.3.2. (a) Plot of dAB versus for the binary compounds crystallizing in hP3 AlB2  (p. 775) | html | pdf |
• Fig. 9.3.3. (a) A typical example of a next-neighbour histogram (NNH) and (b) the atomic environment (AE) coordination polyhedron belonging to this NNH  (p. 775) | html | pdf |
• Fig. 9.3.4. (a) The 23 most frequently occurring atomic environment types (AET) with their polyhedron code  (pp. 776-777) | html | pdf |
• 9.4. Typical interatomic distances: inorganic compounds  (pp. 778-789)
• 9.4.1. Introduction  (p. 778) | html | pdf |
• 9.4.2. The retrieval system  (p. 778) | html | pdf |
• 9.4.3. Interpretation of frequency distributions   (p. 778) | html | pdf |
• References | html | pdf |
• Tables
• Table 9.4.1.1. Atomic distances between halogens and main-group elements in their preferred oxidation states  (pp. 779-780) | html | pdf |
• Table 9.4.1.2. Atomic distances between halogens and main-group elements in their special oxidation states  (pp. 780-781) | html | pdf |
• Table 9.4.1.3. Atomic distances between halogens and transition metals  (pp. 781-784) | html | pdf |
• Table 9.4.1.4. Atomic distances between halogens and lanthanoids  (p. 784) | html | pdf |
• Table 9.4.1.5. Atomic distances between halogens and actinoids  (p. 785) | html | pdf |
• Table 9.4.1.6. Atomic distances between oxygen and main-group elements in their preferred oxidation states  (p. 785) | html | pdf |
• Table 9.4.1.7. Atomic distances between oxygen and main-group elements in their special oxidation states  (p. 786) | html | pdf |
• Table 9.4.1.8. Atomic distances between oxygen and transition elements in their preferred and special oxidation states  (pp. 786-787) | html | pdf |
• Table 9.4.1.9. Atomic distances between oxygen and lanthanoids  (p. 787) | html | pdf |
• Table 9.4.1.10. Atomic distances between oxygen and actinoids  (p. 788) | html | pdf |
• Table 9.4.1.11. Atomic distances in sulfides and thiometallates  (pp. 788-789) | html | pdf |
• Table 9.4.1.12. Contact distances between some negatively charged elements  (p. 789) | html | pdf |
• 9.5. Typical interatomic distances: organic compounds  (pp. 790-811)
• 9.5.1. Introduction  (p. 790) | html | pdf |
• 9.5.2. Methodology  (pp. 790-791) | html | pdf |
• 9.5.2.1. Selection of crystallographic data  (p. 790) | html | pdf |
• 9.5.2.2. Program system  (pp. 790-791) | html | pdf |
• 9.5.2.3. Classification of bonds  (p. 791) | html | pdf |
• 9.5.2.4. Statistics  (p. 791) | html | pdf |
• 9.5.3. Content and arrangement of the table  (pp. 791-794) | html | pdf |
• 9.5.3.1. Ordering of entries: the Bond' column  (p. 792) | html | pdf |
• 9.5.3.2. Definition of Substructure'  (pp. 792-793) | html | pdf |
• 9.5.3.3. Use of the Note' column  (pp. 793-794) | html | pdf |
• 9.5.4. Discussion  (p. 794) | html | pdf |
• Appendix 9.5.1. Notes to Table 9.5.1.1  (p. 794) | html | pdf |
• Appendix 9.5.2. Short-form references to individual CSD entries cited by reference code in Table 9.5.1.1  (pp. 794-795) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 9.5.1.1. Growth of the Cambridge Structural Database 1965–1985 as number of entries (Nent) published in a given year  (p. 790) | html | pdf |
• Fig. 9.5.2.1. Effect of the removal of outliers (contributors that are > 4σ from the mean) for the C—C bond in Car—C≡N fragments  (p. 791) | html | pdf |
• Fig. 9.5.2.2. Skewed distribution of B—F bond lengths in ions  (pp. 791-792) | html | pdf |
• Fig. 9.5.2.3. Resolution of the bimodal distribution of C—N bond lengths in Car —N(Csp3)2 fragments  (p. 792) | html | pdf |
• Fig. 9.5.3.1. (a) Distribution of mean bond-length values reported in the table by element pair  (p. 792) | html | pdf |
• Fig. 9.5.3.2. Alphabetized index of ring systems referred to in the table; the numbering scheme used in assembling the bond-length data is given where necessary  (p. 793) | html | pdf |
• Tables
• Table 9.5.1.1. Average lengths (Å) for bonds involving the elements H, B, C, N, O, F, Si, P, S, Cl, As, Se, Br, Te, and I  (pp. 796-811) | html | pdf |
• 9.6. Typical interatomic distances: organometallic compounds and coordination complexes of the d- and f-block metals  (pp. 812-896)
• 9.6.1. Introduction  (p. 812) | html | pdf |
• 9.6.2. Methodology  (pp. 812-814) | html | pdf |
• 9.6.2.1. Selection of crystallographic data  (p. 812) | html | pdf |
• 9.6.2.2. Program system  (p. 813) | html | pdf |
• 9.6.2.3. Classification of bonds  (p. 813) | html | pdf |
• 9.6.2.4. Statistics  (pp. 813-814) | html | pdf |
• 9.6.3. Content and arrangement of table of interatomic distances  (pp. 814-818) | html | pdf |
• 9.6.3.1. The Bond' column  (p. 815) | html | pdf |
• 9.6.3.2. Definition of Substructure'  (pp. 815-817) | html | pdf |
• 9.6.3.3. Use of the `Note' column  (pp. 817-818) | html | pdf |
• 9.6.3.4. Locating an entry in Table 9.6.3.3  (p. 818) | html | pdf |
• 9.6.4. Discussion  (pp. 818-884) | html | pdf |
• Appendix 9.6.1. Notes and references to Tables 9.6.3.2 and 9.6.3.3  (pp. 884-886) | html | pdf |
• Appendix 9.6.2. Short-form references to individual CSD entries cited in Table 9.6.3.3  (pp. 886-896) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 9.6.1.1. Growth of the Cambridge Structural Database as number of entries (Nent) added annually  (p. 812) | html | pdf |
• Fig. 9.6.2.1. Effects of outlier removal and subdivision based on coordination number and oxidation state  (p. 814) | html | pdf |
• Fig. 9.6.3.1. Diagrams of ligands in Table 9.6.3.3, showing table entry number and ligand atom labelling  (p. 816) | html | pdf |
• Tables
• Table 9.6.3.1. Ligand index  (pp. 814-815) | html | pdf |
• Table 9.6.3.2. Numbers of entries in Table 9.6.3.3  (p. 817) | html | pdf |
• Table 9.6.3.3. Interatomic distances (Å)  (pp. 818-883) | html | pdf |
• 9.7. The space-group distribution of molecular organic structures  (pp. 897-906)
• 9.7.1. A priori classifications of space groups  (pp. 897-900) | html | pdf |
• 9.7.1.1. Kitajgorodskij's categories  (p. 897) | html | pdf |
• 9.7.1.2. Symmorphism and antimorphism  (pp. 897-899) | html | pdf |
• 9.7.1.3. Comparison of Kitajgorodskij's and Wilson's classifications  (pp. 899-900) | html | pdf |
• 9.7.1.4. Relation to structural classes  (p. 900) | html | pdf |
• 9.7.2. Special positions of given symmetry  (pp. 900-902) | html | pdf |
• 9.7.3. Empirical space-group frequencies  (p. 902) | html | pdf |
• 9.7.4. Use of molecular symmetry  (pp. 902-904) | html | pdf |
• 9.7.4.1. Positions with symmetry 1  (p. 902) | html | pdf |
• 9.7.4.2. Positions with symmetry   (pp. 902-903) | html | pdf |
• 9.7.4.3. Other symmetries  (p. 903) | html | pdf |
• 9.7.4.4. Positions with the full symmetry of the geometric class  (pp. 903-904) | html | pdf |
• 9.7.5. Structural classes  (p. 904) | html | pdf |
• 9.7.6. A statistical model  (p. 904) | html | pdf |
• 9.7.7. Molecular packing  (pp. 904-906) | html | pdf |
• 9.7.7.1. Relation to sphere packing  (pp. 904-906) | html | pdf |
• 9.7.7.2. The hydrogen bond and the definition of the packing units  (p. 906) | html | pdf |
• 9.7.8. A priori predictions of molecular crystal structures  (p. 906) | html | pdf |
• References | html | pdf |
• Tables
• Table 9.7.1.1. Kitajgorodskij's categorization of the triclinic, monoclinic and orthorhombic space groups, as modified by Wilson (1993a)  (p. 898) | html | pdf |
• Table 9.7.1.2. Space groups arranged by arithmetic crystal class and degree of symmorphism (Wilson, 1993d), as frequented by homomolecular structures with one molecule in the general position (in superscript numerals; according to Belsky, Zorkaya & Zorky, 1995)  (pp. 899-901) | html | pdf |
• Table 9.7.2.1. Statistics of the use of Wyckoff positions of specified symmetry in the homomolecular organic crystals, based on the data by Belsky, Zorkaya & Zorky (1995)  (p. 903) | html | pdf |
• Table 9.7.4.1. Occurrence of molecules with specified point group in centred symmorphic and other space groups, based on the statistics by Belsky, Zorkaya & Zorky (1995)  (p. 905) | html | pdf |
• 9.8. Incommensurate and commensurate modulated structures  (pp. 907-955)
• 9.8.1. Introduction  (pp. 907-913) | html | pdf |
• 9.8.1.1. Modulated crystal structures  (pp. 907-908) | html | pdf |
• 9.8.1.2. The basic ideas of higher-dimensional crystallography  (pp. 908-909) | html | pdf |
• 9.8.1.3. The simple case of a displacively modulated crystal  (pp. 909-910) | html | pdf |
• 9.8.1.3.1. The diffraction pattern  (p. 909) | html | pdf |
• 9.8.1.3.2. The symmetry  (pp. 909-910) | html | pdf |
• 9.8.1.4. Basic symmetry considerations  (pp. 910-913) | html | pdf |
• 9.8.1.4.1. Bravais classes of vector modules  (pp. 910-911) | html | pdf |
• 9.8.1.4.2. Description in four dimensions  (p. 911) | html | pdf |
• 9.8.1.4.3. Four-dimensional crystallography  (pp. 911-912) | html | pdf |
• 9.8.1.4.4. Generalized nomenclature  (p. 912) | html | pdf |
• 9.8.1.4.5. Four-dimensional space groups  (pp. 912-913) | html | pdf |
• 9.8.1.5. Occupation modulation  (p. 913) | html | pdf |
• 9.8.2. Outline for a superspace-group determination  (pp. 913-915) | html | pdf |
• 9.8.3. Introduction to the tables  (pp. 915-937) | html | pdf |
• 9.8.3.1. Tables of Bravais lattices  (pp. 915-916) | html | pdf |
• 9.8.3.2. Table for geometric and arithmetic crystal classes  (p. 916) | html | pdf |
• 9.8.3.3. Tables of superspace groups  (pp. 916-935) | html | pdf |
• 9.8.3.3.1. Symmetry elements  (pp. 916-921) | html | pdf |
• 9.8.3.3.2. Reflection conditions  (pp. 921-935) | html | pdf |
• 9.8.3.4. Guide to the use of the tables  (pp. 935-936) | html | pdf |
• 9.8.3.5. Examples  (p. 936) | html | pdf |
• 9.8.3.6. Ambiguities in the notation  (pp. 936-937) | html | pdf |
• 9.8.4. Theoretical foundation  (pp. 937-945) | html | pdf |
• 9.8.4.1. Lattices and metric  (pp. 937-938) | html | pdf |
• 9.8.4.2. Point groups  (pp. 938-939) | html | pdf |
• 9.8.4.2.1. Laue class  (pp. 938-939) | html | pdf |
• 9.8.4.2.2. Geometric and arithmetic crystal classes  (p. 939) | html | pdf |
• 9.8.4.3. Systems and Bravais classes  (pp. 939-940) | html | pdf |
• 9.8.4.3.1. Holohedry  (pp. 939-940) | html | pdf |
• 9.8.4.3.2. Crystallographic systems  (p. 940) | html | pdf |
• 9.8.4.3.3. Bravais classes  (p. 940) | html | pdf |
• 9.8.4.4. Superspace groups  (pp. 940-941) | html | pdf |
• 9.8.4.4.1. Symmetry elements  (p. 940) | html | pdf |
• 9.8.4.4.2. Equivalent positions and modulation relations  (pp. 940-941) | html | pdf |
• 9.8.4.4.3. Structure factor  (p. 941) | html | pdf |
• 9.8.5. Generalizations  (pp. 941-943) | html | pdf |
• 9.8.5.1. Incommensurate composite crystal structures  (pp. 941-942) | html | pdf |
• 9.8.5.2. The incommensurate versus the commensurate case  (pp. 942-943) | html | pdf |
• Appendix 9.8.1. Glossary of symbols  (pp. 943-944) | html | pdf |
• Appendix 9.8.2. Basic definitions  (pp. 944-945) | html | pdf |
• References | html | pdf |
• Tables
• Table 9.8.3.1. (2 + 1)- and (2 + 2)-Dimensional Bravais classes for incommensurate structures  (pp. 915-916) | html | pdf |
• Table 9.8.3.2. (3 + 1)-Dimensional Bravais classes for incommensurate and commensurate structures  (pp. 917-918) | html | pdf |
• Table 9.8.3.3. (3 + 1)-Dimensional point groups and arithmetic crystal classes  (pp. 919-920) | html | pdf |
• Table 9.8.3.4. (2 + 1)- and (2 + 2)-Dimensional superspace groups  (pp. 920-921) | html | pdf |
• Table 9.8.3.5. (3 + 1)-Dimensional superspace groupssuperspace group finder  (pp. 922-934) | html | pdf |
• Table 9.8.3.6. Centring reflection conditions for (3 + 1)-dimensional Bravais classes  (p. 935) | html | pdf |
• 10.1. Introduction  (pp. 958-961)
• 10.1.1. Definitions  (pp. 958-960) | html | pdf |
• 10.1.1.1. Ionizing radiation  (p. 958) | html | pdf |
• 10.1.1.2. Absorbed dose  (p. 958) | html | pdf |
• 10.1.1.3. Activity  (p. 958) | html | pdf |
• 10.1.1.4. Adequate protection  (p. 958) | html | pdf |
• 10.1.1.5. Background (radiation)  (p. 958) | html | pdf |
• 10.1.1.6. Becquerel (Bq)  (p. 958) | html | pdf |
• 10.1.1.7. Designated radiation area  (p. 958) | html | pdf |
• 10.1.1.8. Dose equivalent  (p. 958) | html | pdf |
• 10.1.1.9. Exposure of X-ray or γ-radiation  (p. 958) | html | pdf |
• 10.1.1.10. External radiation  (p. 958) | html | pdf |
• 10.1.1.11. Glove box  (p. 959) | html | pdf |
• 10.1.1.12. Gray (Gy)  (p. 959) | html | pdf |
• 10.1.1.13. Half life  (p. 959) | html | pdf |
• 10.1.1.14. Internal radiation  (p. 959) | html | pdf |
• 10.1.1.15. Irradiating apparatus  (p. 959) | html | pdf |
• 10.1.1.16. Leakage radiation  (p. 959) | html | pdf |
• 10.1.1.17. Licensable quantity  (p. 959) | html | pdf |
• 10.1.1.18. Maximum permissible concentration  (p. 959) | html | pdf |
• 10.1.1.19. Natural background  (p. 959) | html | pdf |
• 10.1.1.20. Non-stochastic effects  (p. 959) | html | pdf |
• 10.1.1.21. Nuclide  (p. 959) | html | pdf |
• 10.1.1.22. Occupied area  (p. 959) | html | pdf |
• 10.1.1.23. Protective housing  (p. 959) | html | pdf |
• 10.1.1.24. Quality factor (QF)  (p. 959) | html | pdf |
• 10.1.1.25. Radiation laboratory  (p. 959) | html | pdf |
• 10.1.1.26. Radioactive contamination  (p. 959) | html | pdf |
• 10.1.1.27. Radioactive material  (p. 959) | html | pdf |
• 10.1.1.28. Radioisotope laboratory  (p. 959) | html | pdf |
• 10.1.1.29. Radiological hazard  (p. 959) | html | pdf |
• 10.1.1.30. Radiological laboratory  (p. 959) | html | pdf |
• 10.1.1.31. Radionuclide  (p. 959) | html | pdf |
• 10.1.1.32. Radiotoxicity  (p. 959) | html | pdf |
• 10.1.1.33. Sealed source  (p. 959) | html | pdf |
• 10.1.1.34. Sievert (Sv)  (p. 959) | html | pdf |
• 10.1.1.35. Stochastic effects  (p. 959) | html | pdf |
• 10.1.1.36. Unsealed source  (p. 959) | html | pdf |
• 10.1.1.37. Useful beam  (p. 960) | html | pdf |
• 10.1.2. Objectives of radiation protection  (p. 960) | html | pdf |
• 10.1.3. Responsibilities  (pp. 960-961) | html | pdf |
• 10.1.3.1. General  (p. 960) | html | pdf |
• 10.1.3.2. The radiation safety officer  (p. 960) | html | pdf |
• 10.1.3.3. The worker  (pp. 960-961) | html | pdf |
• 10.1.3.4. Primary-dose limits  (p. 961) | html | pdf |
• References | html | pdf |
• Tables
• Table 10.1.1. The relationship between SI and the earlier system of units  (p. 958) | html | pdf |
• Table 10.1.2. Maximum primary-dose limit per quarter [based on National Health and Medical Research Council (1977), as amended]  (p. 960) | html | pdf |
• Table 10.1.3. Quality factors (QF)  (p. 960) | html | pdf |
• 10.2. Protection from ionizing radiation  (pp. 962-963)
• 10.2.1. General  (p. 962) | html | pdf |
• 10.2.2. Sealed sources and radiation-producing apparatus  (pp. 962-963) | html | pdf |
• 10.2.2.1. Enclosed installations  (p. 962) | html | pdf |
• 10.2.2.2. Open installations  (p. 962) | html | pdf |
• 10.2.2.3. Sealed sources  (p. 962) | html | pdf |
• 10.2.2.4. X-ray diffraction and X-ray analysis apparatus  (p. 962) | html | pdf |
• 10.2.2.5. Particle accelerators  (pp. 962-963) | html | pdf |
• 10.2.3. Ionizing-radiation protection – unsealed radioactive materials  (p. 963) | html | pdf |
• References | html | pdf |
• 10.3. Responsible bodies  (pp. 964-967)
• References | html | pdf |
• Tables
• Table 10.3.1. Regulatory authorities  (pp. 964-966) | html | pdf |
• Resources  | html |