## 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

• Preface to the third edition  (p. xxxi) | html | pdf |
• Part 1. 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 = 2 a ) with twin index 4  (p. 12) | html | pdf |
• Tables
• Table 1.3.2.1. Lattice planes and rows that are perpendicular to each other independently of the metrical parameters  (p. 11) | html | pdf |
• Table 1.3.4.1. Possible twin operations for twins by merohedry  (p. 13) | html | pdf |
• Table 1.3.4.2. Simulated Laue classes, extinction symbols, simulated possible space groups', and possible true space groups for crystals twinned by merohedry (type 2)  (p. 13) | html | pdf |
• 1.4. Arithmetic crystal classes and symmorphic space groups  (pp. 15-22)
• 1.4.1. Arithmetic crystal classes  (pp. 15-19) | html | pdf |
• 1.4.1.1. Arithmetic crystal classes in three dimensions  (p. 15) | html | pdf |
• 1.4.1.2. Arithmetic crystal classes in one, two and higher dimensions  (p. 16) | html | pdf |
• 1.4.2. Classification of space groups  (pp. 20-21) | html | pdf |
• 1.4.2.1. Symmorphic space groups  (p. 21) | html | pdf |
• 1.4.3. Effect of dispersion on diffraction symmetry  (p. 21) | html | pdf |
• 1.4.3.1. Symmetry of the Patterson function  (p. 21) | html | pdf |
• 1.4.3.2. Laue' symmetry  (p. 21) | html | pdf |
• References | html | pdf |
• Tables
• Table 1.4.1.1. The two-dimensional arithmetic crystal classes  (p. 15) | html | pdf |
• Table 1.4.2.1. The three-dimensional space groups, arranged by arithmetic crystal class  (pp. 16-19) | html | pdf |
• Table 1.4.3.1. Arithmetic crystal classes classified by the number of space groups that they contain  (p. 20) | html | pdf |
• Part 2. Diffraction geometry and its practical realization
• 2.1. Classification of experimental techniques  (pp. 24-25)
• 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 = λ max min 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 K α doublet  (pp. 62-63) | html | pdf |
• 2.3.3.3. Use of peak or centroid for angle definition  (p. 63) | html | pdf |
• 2.3.3.4. Rate-meter/strip-chart recording  (p. 63) | html | pdf |
• 2.3.3.5. Computer-controlled automation  (pp. 63-64) | html | pdf |
• 2.3.3.6. Counting statistics  (pp. 64-65) | html | pdf |
• 2.3.3.7. Peak search  (pp. 65-66) | html | pdf |
• 2.3.3.8. Profile fitting  (pp. 66-69) | html | pdf |
• 2.3.3.9. Computer graphics for powder patterns  (p. 69) | html | pdf |
• 2.3.4. Powder cameras  (pp. 70-71) | html | pdf |
• 2.3.4.1. Cylindrical cameras (Debye–Scherrer)  (p. 70) | html | pdf |
• 2.3.4.2. Focusing cameras (Guinier)  (pp. 70-71) | html | pdf |
• 2.3.4.3. Miscellaneous camera types  (p. 71) | html | pdf |
• 2.3.5. Generation, modifications, and measurement of X-ray spectra  (pp. 71-79) | html | pdf |
• 2.3.5.1. X-ray tubes  (pp. 71-74) | html | pdf |
• 2.3.5.1.1. Stability  (p. 72) | html | pdf |
• 2.3.5.1.2. Spectral purity  (p. 72) | html | pdf |
• 2.3.5.1.3. Source intensity distribution and size  (p. 73) | html | pdf |
• 2.3.5.1.4. Air and window transmission  (pp. 73-74) | html | pdf |
• 2.3.5.1.5. Intensity variation with take-off angle  (p. 74) | html | pdf |
• 2.3.5.2. X-ray spectra  (pp. 74-75) | html | pdf |
• 2.3.5.2.1. Wavelength selection  (p. 75) | html | pdf |
• 2.3.5.3. Other X-ray sources  (p. 75) | html | pdf |
• 2.3.5.4. Methods for modifying the spectrum  (pp. 75-79) | html | pdf |
• 2.3.5.4.1. Crystal monochromators  (pp. 76-78) | html | pdf |
• 2.3.5.4.2. Single and balanced filters  (pp. 78-79) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 2.3.1.1. Basic arrangements of focusing diffractometer methods  (p. 43) | html | pdf |
• Fig. 2.3.1.2. Specimen orientation for three diffractometer geometries  (p. 44) | html | pdf |
• Fig. 2.3.1.3. X-ray optics in the focusing plane of a conventional' diffractometer with reflection specimen, diffracted-beam monochromator, and θ–2θ scanning  (p. 44) | html | pdf |
• Fig. 2.3.1.4. Length of specimen irradiated, S l , as a function of 2θ for various angular apertures  (p. 45) | html | pdf |
• Fig. 2.3.1.5. Slit designs made with ( a ) rods, ( b ) bars, and ( c ) machined from single piece  (p. 45) | html | pdf |
• Fig. 2.3.1.6. Zero-angle calibration  (p. 46) | html | pdf |
• Fig. 2.3.1.7. ( a ) θ–2θ setting at 0°  (p. 47) | html | pdf |
• Fig. 2.3.1.8. Diffractometer profiles  (p. 48) | html | pdf |
• Fig. 2.3.1.9. ( a ) Effect of source size on profile shape, Cu K α, α ES 1°, α RS 0.05°, Si(111)  (p. 49) | html | pdf |
• Fig. 2.3.1.10. ( a ) Origin of specimen-related aberrations in focusing plane of conventional reflection specimen diffractometer (Fig. 2.3.1.3)  (p. 50) | html | pdf |
• Fig. 2.3.1.11. Effect of axial divergence on profile shape  (p. 50) | html | pdf |
• Fig. 2.3.1.12. X-ray optics of the transmission specimen with asymmetric focusing monochromator and θ–2θ scanning  (p. 51) | html | pdf |
• Fig. 2.3.1.13. Seemann–Bohlin method  (p. 52) | html | pdf |
• Fig. 2.3.1.14. Optics of θ–θ scanning diffractometer  (p. 53) | html | pdf |
• Fig. 2.3.1.15. Rigaku microdiffractometer for microanalysis  (p. 54) | html | pdf |
• Fig. 2.3.2.1. Method to obtain parallel beam from X-ray tube for powder diffraction  (p. 54) | html | pdf |
• Fig. 2.3.2.2. Silicon powder pattern with 1 Å synchrotron radiation using method shown in Fig. 2.3.2.4( a )  (p. 54) | html | pdf |
• Fig. 2.3.2.3. Synchrotron-radiation patterns of a mixture of Ni and ZnO powders  (p. 55) | html | pdf |
• Fig. 2.3.2.4. ( a ) Optics of dispersive parallel-beam method for synchrotron X-rays  (p. 56) | html | pdf |
• Fig. 2.3.2.5. Comparison of patterns obtained with a conventional focusing diffractometer ( a ) and ( c ), and synchrotron parallel-beam method ( b ) and ( d )  (p. 57) | html | pdf |
• Fig. 2.3.2.6. ( a ) and ( c ) Fourier maps of orthorhombic Mg 2 GeO 4 calculated directly from profile-fitted synchrotron powder data  (p. 57) | html | pdf |
• Fig. 2.3.2.7. Penetration depth t ' as a function of grazing-incidence angle α for γ-Fe 2 O 3 thin film  (p. 58) | html | pdf |
• Fig. 2.3.2.8. Synchrotron diffraction patterns of annealed 5000 Å iron oxide film, λ = 1.75 Å  (p. 58) | html | pdf |
• Fig. 2.3.2.9. ( a )–( d ) High-resolution energy-dispersive diffraction patterns of quartz powder sample obtained with 2θ settings shown in upper left corners  (p. 59) | html | pdf |
• Fig. 2.3.2.10. Specimen orientation for symmetric reflection ( a ) from ( hkl ) planes and ( b ) specimen rotated θ r for symmetric reflection from ( pqr ) planes  (p. 59) | html | pdf |
• Fig. 2.3.3.1. Differences in relative intensities due to preferred orientation as seen in synchrotron X-ray patterns of m -chlorobenzoic acid obtained with a specimen in reflection and transmission compared with calculated pattern  (p. 61) | html | pdf |
• Fig. 2.3.3.2. Effect of specimen rotation and particle size on Si powder intensity using a conventional diffractometer (Fig. 2.3.1.3) and Cu K α  (p. 62) | html | pdf |
• Fig. 2.3.3.3. Various measures of profile  (p. 62) | html | pdf |
• Fig. 2.3.3.4. Rate-meter strip-chart recordings  (p. 63) | html | pdf |
• Fig. 2.3.3.5. Fig  (p. 64) | html | pdf |
• Fig. 2.3.3.6. Percentage error as a function of the total number of counts N for several confidence levels  (p. 64) | html | pdf |
• Fig. 2.3.3.7. Effect of 4 σ maximum peak height (horizontal line) on dropping weak peaks from inclusion in computer calculation  (p. 65) | html | pdf |
• Fig. 2.3.3.8. ( a ) Si(220) Cu K α reflection  (p. 66) | html | pdf |
• Fig. 2.3.3.9. ( a ) Computer-generated symmetrical Lorentzian profile L and Gaussian G with equal peak heights, 2θ and FWHM  (p. 66) | html | pdf |
• Fig. 2.3.3.10. Profile fitting with sum-of-Lorentzians method  (p. 68) | html | pdf |
• Fig. 2.3.3.11. Profile fitting of poor statistical data  (p. 69) | html | pdf |
• Fig. 2.3.3.12. Some examples of computer graphics of powder patterns  (p. 69) | html | pdf |
• Fig. 2.3.4.1. Powder-camera geometries  (p. 70) | html | pdf |
• Fig. 2.3.5.1. Sealed X-ray diffraction tube (Philips), dimensions are given in mm  (p. 71) | html | pdf |
• Fig. 2.3.5.2. ( a ) Transmission of Be, Al and air as a function of wavelength  (p. 73) | html | pdf |
• Fig. 2.3.5.3. X-ray spectrum of copper target tube with Be window, 50 kV constant potential, 12° take-off angle  (p. 75) | html | pdf |
• Fig. 2.3.5.4. ( a ) Continuous X-ray spectrum of tungsten target X-ray tube as a function of voltage and constant current  (p. 76) | html | pdf |
• Fig. 2.3.5.5. Portion of diffractometer pattern of topaz showing effect of increasing dispersion on separation of peaks  (p. 76) | html | pdf |
• Fig. 2.3.5.6. Crystal monochromators most frequently used in powder diffraction  (p. 77) | html | pdf |
• Tables
• Table 2.3.3.1. Preferred-orientation data for silicon  (p. 61) | html | pdf |
• Table 2.3.3.2. R (Bragg) values obtained with different preferred-orientation formulae  (p. 61) | html | pdf |
• Table 2.3.5.1. X-ray tube maximum ratings  (p. 72) | html | pdf |
• Table 2.3.5.2. β filters for common target elements  (p. 78) | html | pdf |
• Table 2.3.5.3. Calculated thickness of balanced filters for common target elements  (p. 79) | html | pdf |
• 2.4. Powder and related techniques: electron and neutron techniques  (pp. 80-83)
• 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: 2θ 0 = fixed scattering angle  (p. 84) | html | pdf |
• Fig. 2.5.1.2. XED powder spectrum of BaTiO 3 recorded with synchrotron radiation from the electron storage ring DORIS at DESY-HASYLAB in Hamburg, Germany  (p. 84) | html | pdf |
• Fig. 2.5.1.3. Relative resolution, , 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 + d r within the particle  (p. 91) | html | pdf |
• Fig. 2.6.1.2. Comparison of the scattering functions of a sphere (dashed line) and a cube (continuous line) with same radius of gyration  (p. 94) | html | pdf |
• Fig. 2.6.1.3. Distance distribution function of a sphere (dashed line) and a cube (continuous line) with the same radius of gyration and the same scattering intensity at zero angle  (p. 94) | html | pdf |
• Fig. 2.6.1.4. Comparison of the p ( r ) function of a sphere (continuous line), a prolate ellipsoid of revolution 1:1:3 (dash-dotted line), and an oblate ellipsoid of revolution 1:1:0.2 (dashed line) with the same radius of gyration  (p. 94) | html | pdf |
• Fig. 2.6.1.5. Comparison of the I ( h ) functions of a sphere, a prolate, and an oblate ellipsoid (see legend to Fig  (p. 94) | html | pdf |
• Fig. 2.6.1.6. Distance distributions from homogeneous parallelepipeds with edge lengths of: ( a ) 50 × 50 × 500 Å; ( b ) 50 × 50 × 250 Å; ( c ) 50 × 50 × 150 Å  (p. 95) | html | pdf |
• Fig. 2.6.1.7. Three parallelepipeds with constant length L (400 Å) and a constant cross section but varying length of the edges: continuous line 40 × 40 Å; dash-dotted line 80 × 20 Å; dashed line 160 × 10 Å  (p. 95) | html | pdf |
• Fig. 2.6.1.8. Circular cylinder with a constant length of 480 Å and an outer diameter of 48 Å  (p. 96) | html | pdf |
• Fig. 2.6.1.9. Inhomogeneous circular cylinder with periodical changes of the electron density along the cylinder axis compared with a homogeneous cylinder with the same mean electron density  (p. 97) | html | pdf |
• Fig. 2.6.1.10. p ( r ) function of a lamellar particle  (p. 97) | html | pdf |
• Fig. 2.6.1.11. Characteristic types of scattering functions: ( a ) gas type; ( b ) particle scattering; ( c ) liquid type  (p. 98) | html | pdf |
• Fig. 2.6.1.12. Distance distribution – hard-sphere interference model  (p. 98) | html | pdf |
• Fig. 2.6.1.13. Schematic drawing of the block collimation (Kratky camera): E edge; B 1 centre piece; B 2 bridge; P primary-beam profile; PS primary-beam stop; PR plane of registration  (p. 99) | html | pdf |
• Fig. 2.6.1.14. Function systems ϕ v ( r ); Ψ v ( h ); and χ v ( h ) used for the approximation of the scattering data in the indirect transformation method  (p. 102) | html | pdf |
• Tables
• Table 2.6.1.1. Formulae for the various parameters for h (left) and m (right) scales  (p. 92) | html | pdf |
• 2.7. Topography  (pp. 113-123)
• 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 |
• Part 3. 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 V M and V solv 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 |
• 3.6. Specimens for neutron diffraction  (pp. 177-184)
• Part 4. 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 μ l or (μ/ρ)  (p. 215) | html | pdf |
• 4.2.3.3. Normal attenuation coefficients  (p. 215) | html | pdf |
• 4.2.3.4. Attenuation coefficients in the neighbourhood of an absorption edge  (pp. 216-219) | html | pdf |
• 4.2.3.4.1. XAFS  (pp. 216-219) | html | pdf |
• 4.2.3.4.1.1. Theory  (pp. 216-217) | html | pdf |
• 4.2.3.4.1.2. Techniques of data analysis  (pp. 217-218) | html | pdf |
• 4.2.3.4.1.3. XAFS experiments  (pp. 218-219) | html | pdf |
• 4.2.3.4.2. X-ray absorption near edge structure (XANES)  (p. 219) | html | pdf |
• 4.2.3.5. Comments  (p. 220) | html | pdf |
• 4.2.4. X-ray absorption (or attenuation) coefficients  (pp. 220-229) | html | pdf |
• 4.2.4.1. Introduction  (pp. 220-221) | html | pdf |
• 4.2.4.2. Sources of information  (pp. 221-229) | html | pdf |
• 4.2.4.2.1. Theoretical photo-effect data: σ pe   (p. 221) | html | pdf |
• 4.2.4.2.2. Theoretical Rayleigh scattering data: σ R   (pp. 221-229) | html | pdf |
• 4.2.4.2.3. Theoretical Compton scattering data: σ C   (p. 229) | html | pdf |
• 4.2.4.3. Comparison between theoretical and experimental data sets  (p. 229) | html | pdf |
• 4.2.4.4. Uncertainty in the data tables  (p. 229) | html | pdf |
• 4.2.5. Filters and monochromators  (pp. 229-241) | html | pdf |
• 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-L 3 at a series of different accelerating voltages (in kV)  (p. 192) | html | pdf |
• Fig. 4.2.1.2. Experimental measurements of for Cu K-L 3 as functions of the accelerating voltage for different take-off angles  (p. 193) | html | pdf |
• Fig. 4.2.1.3. Intensity per unit frequency interval versus frequency in the continuous spectrum from a thick target at different accelerating voltages  (p. 193) | html | pdf |
• Fig. 4.2.1.4. The function μ in Müller's equation (equation 4.2.1.12) as a function of the ratio of width to length of the focal spot  (p. 195) | html | pdf |
• Fig. 4.2.1.5. Synchrotron radiation emitted by a relativistic electron travelling in a curved trajectory  (p. 197) | html | pdf |
• Fig. 4.2.1.6. Synchrotron-radiation spectrum: percentage per unit wavelength interval ( a ) of power of total power and ( b ) of number of photons of total number of photons at wavelengths greater than λ versus λ/λ c   (p. 197) | html | pdf |
• Fig. 4.2.1.7. Main components of a dedicated electron storage-ring synchrotron-radiation source  (p. 198) | html | pdf |
• Fig. 4.2.1.8. Electron trajectory within a multipole wiggler or undulator  (p. 198) | html | pdf |
• Fig. 4.2.1.9. Spectral distribution and critical wavelengths for ( a ) a dipole magnet, ( b ) a wavelength shifter, and ( c ) a multipole wiggler for the proposed ESRF  (p. 198) | html | pdf |
• Fig. 4.2.1.10. Comparison of the spectra from the storage ring SPEAR in photons s −1  mA −1  mrad −1  per 1% passband (1978 performance) and a rotating-anode X-ray generator  (p. 198) | html | pdf |
• Fig. 4.2.1.11. The evolution of storage-ring synchrotron-radiation sources over the decades, as illustrated by their increasing number and range of machine energies (based on Suller, 1992)  (p. 200) | html | pdf |
• Fig. 4.2.1.12. X-ray emission from various laser-produced plasmas  (p. 200) | html | pdf |
• Fig. 4.2.2.1. Relative deviations between theoretical and experimental results for K -series spectra  (p. 212) | html | pdf |
• Fig. 4.2.2.2. Comparison of L -series data with experiment for the indicated range of Z   (p. 212) | html | pdf |
• Fig. 4.2.3.1. Theoretical cross sections for photon interactions with carbon showing the contributions of photoelectric, elastic (Rayleigh), inelastic (Compton), and pair-production cross sections to the total cross sections  (p. 213) | html | pdf |
• Fig. 4.2.3.2. The dependence of the X-ray attenuation coefficient on energy for a range of germanium compounds, taken in the neighbourhood of the germanium absorption edge (from IT IV, 1974)  (p. 214) | html | pdf |
• Fig. 4.2.3.3. Schematic representations of experimental apparatus used in the IUCr X-ray Attenuation Project (Creagh & Hubbell, 1987; Creagh, 1985)  (p. 214) | html | pdf |
• Fig. 4.2.3.4. Steps in the reduction of data from an XAFS experiment using the Fourier transform technique: ( a ) after the removal of background χ( k ) versus k ; ( b ) after multiplication by a weighting function (in this case k 3 ); ( c ) after Fourier transformation to determine r ′  (p. 217) | html | pdf |
• Fig. 4.2.3.5. Schematic representations of the scattering processes undergone by the ejected photoelectron in the single-scattering (XAFS) case and the full multiple-scattering regime (XANES)  (p. 219) | html | pdf |
• Fig. 4.2.4.1. Agreement between theory and experiment for oxygen ( Z = 8) in the soft' X-ray region  (p. 220) | html | pdf |
• Fig. 4.2.4.2. The total cross section for silicon ( Z = 14) compared with the unrenormalized Scofield values  (p. 221) | html | pdf |
• Fig. 4.2.4.3. The total cross section for uranium ( Z = 92): The theoretical values (solid line) are partially obscured by the high density of available measurements  (p. 222) | html | pdf |
• Fig. 4.2.4.4. Comparison between this tabulation and experimental data contained in Saloman & Hubbell (1986)  (p. 222) | html | pdf |
• Fig. 4.2.5.1. The variation of specular reflectivity with incident photon energy is shown for materials of different atomic number and a constant angle of incidence of 0.2°  (p. 236) | html | pdf |
• Fig. 4.2.5.2. The use of mirrors in a typical synchrotron-radiation beamline  (p. 237) | html | pdf |
• Fig. 4.2.5.3. The reflectivity of a multiple-quantum-well device is shown  (p. 238) | html | pdf |
• Fig. 4.2.5.4. In ( a ), the schematic rocking curve for a silicon crystal in the neighbourhood of the 111 Bragg peak is shown  (p. 239) | html | pdf |
• Fig. 4.2.5.5. A schematic diagram of a beamline designed to produce circularly polarized light from initially linearly polarized light using Laue-case reflections  (p. 240) | html | pdf |
• Fig. 4.2.5.6. A schematic diagram of a Hart-type tuneable channel-cut monochromator is shown  (p. 241) | html | pdf |
• Fig. 4.2.5.7. A schematic diagram of the use of a Bragg–Fresnel lens to focus hard X-rays onto a high-pressure cell  (p. 241) | html | pdf |
• Fig. 4.2.6.1. The relativistic correction in electrons per atom for: ( a ) the modified form-factor approach; ( b ) the relativistic multipole approach; ( c ) the relativistic dipole approach  (p. 247) | html | pdf |
• Fig. 4.2.6.2. Measured values of f ′(ω, 0) at the K -edge of Nb in LiNbO 3 and the Kramers–Kronig transformation of f ′′(ω, 0)  (p. 247) | html | pdf |
• Tables
• Table 4.2.1.1. Correspondence between X-ray diagram levels and electron configurations  (p. 191) | html | pdf |
• Table 4.2.1.2. Correspondence between IUPAC and Siegbahn notations for X-ray diagram lines  (p. 191) | html | pdf |
• Table 4.2.1.3. Copper-target X-ray tubes and their loading  (p. 194) | html | pdf |
• Table 4.2.1.4. Relative permissible loading for different target materials  (p. 196) | html | pdf |
• Table 4.2.1.5. Radionuclides decaying wholly by electron capture, and yielding little or no γ-radiation  (p. 196) | html | pdf |
• Table 4.2.1.6. Comparison of storage-ring synchrotron-radiation sources  (p. 199) | html | pdf |
• Table 4.2.1.7. Intensity gain with storage rings over conventional sources  (p. 200) | html | pdf |
• Table 4.2.2.1. K -series reference wavelengths in Å  (p. 203) | html | pdf |
• Table 4.2.2.2. Directly measured L -series reference wavelengths in Å  (p. 204) | html | pdf |
• Table 4.2.2.3. Directly measured and emission + binding energies (see text) K -absorption edges in Å  (p. 205) | html | pdf |
• Table 4.2.2.4. Wavelengths of K -emission lines and K -absorption edges in Å  (pp. 206-208) | html | pdf |
• Table 4.2.2.5. Wavelengths of L -emission lines and L -absorption edges in Å  (pp. 209-211) | html | pdf |
• Table 4.2.2.6. Wavelength conversion factors  (p. 212) | html | pdf |
• Table 4.2.3.1. Some synchrotron-radiation facilities providing XAFS databases and analysis utilities  (p. 219) | html | pdf |
• Table 4.2.4.1. Table of wavelengths and energies for the characteristic radiations used in Tables 4.2.4.2 and 4.2.4.3  (p. 221) | html | pdf |
• Table 4.2.4.2. Total phonon interaction cross section  (pp. 223-229) | html | pdf |
• Table 4.2.4.3. Mass attenuation coefficients  (pp. 230-236) | html | pdf |
• Table 4.2.6.1. Values of E tot / mc 2 listed as a function of atomic number Z   (p. 246) | html | pdf |
• Table 4.2.6.2. Comparison between the S -matrix calculations of Kissel (K) (1977) and the form-factor calculations of Cromer & Liberman (C & L) (1970, 1981, 1983) and Creagh & McAuley (C & M) for the noble gases and several common metals  (p. 249) | html | pdf |
• Table 4.2.6.3. A comparison of the forward-scattering amplitudes computed using different theoretical approaches  (p. 250) | html | pdf |
• Table 4.2.6.4. Comparison of measurements of the real part of the dispersion correction for LiF, Si, Al and Ge for characteristic wavelengths Ag K α 1 , Mo K α 1 and Cu K α 1 with theoretical predictions  (p. 252) | html | pdf |
• Table 4.2.6.5. Comparison of measurements of f ′(ω, 0) for C, Si and Cu for characteristic wavelengths Ag K α 1 , Mo K α 1 and Cu K α 1 with theoretical predictions  (p. 253) | html | pdf |
• Table 4.2.6.6. Comparison of 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 |
• 4.3.6.1. The multislice method   (pp. 414-415) | html | pdf |
• 4.3.6.2. The Bloch-wave method  (pp. 415-416) | 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 E 0 and wavevector k is inelastically scattered into a state of energy E 0 ΔE and wavevector k ′  (p. 392) | html | pdf |
• Fig. 4.3.4.3. Excitation spectrum of aluminium from 1 to 250 eV, investigated by EELS on 300 keV primary electrons  (p. 393) | html | pdf |
• Fig. 4.3.4.4. Complete electron energy-loss spectrum of a thin rhodizite crystal (thickness ~60 nm)  (p. 393) | html | pdf |
• Fig. 4.3.4.5. Schematic energy-level representation of the origin of a core-loss excitation (from a core level C at energy E c to an unoccupied state U above the Fermi level E f ) and its general shape in EELS, as superimposed on a continuously decreasing background  (p. 393) | html | pdf |
• Fig. 4.3.4.6. Energy-loss spectrum, in the meV region, of an evaporated germanium film (thickness 25 nm)  (p. 394) | html | pdf |
• Fig. 4.3.4.7. Schematic drawing of a uniform magnetic sector spectrometer with induction B normal to the plane of the figure  (p. 395) | html | pdf |
• Fig. 4.3.4.8. Different factors contributing to the energy resolution in the dispersion plane  (p. 395) | html | pdf |
• Fig. 4.3.4.9. Optical coupling of a magnetic sector spectrometer on a STEM column  (p. 396) | html | pdf |
• Fig. 4.3.4.10. Principle of the Wien filter used as an EELS spectrometer: the trajectories are shown in the two principal (dispersive and focusing) sections  (p. 396) | html | pdf |
• Fig. 4.3.4.11. Principle of the Castaing & Henry filter made from a magnetic prism and an electrostatic mirror  (p. 396) | html | pdf |
• Fig. 4.3.4.12. A commercial EELS spectrometer designed for parallel detection on a photodiode array  (p. 397) | html | pdf |
• Fig. 4.3.4.13. The dispersion curve for the excitation of a plasmon (curve 1) merges into the continuum of individual electron–hole excitations (between curves 2 and 4) for a critical wavevector q c   (p. 398) | html | pdf |
• Fig. 4.3.4.14. Measured angular dependence of the differential cross section d σ /d Ω for the 15 eV plasmon loss in Al (dots) compared with a calculated curve by Ferrell (solid curve) and with a sharp cut-off approximation at θ c (dashed curved)  (p. 399) | html | pdf |
• Fig. 4.3.4.15. Variation of plasmon excitation mean free path Λ p as a function of accelerating voltage V in the case of carbon and aluminium  (p. 399) | html | pdf |
• Fig. 4.3.4.16. Dielectric and optical functions calculated in the Drude model of a free-electron gas with ħω p = 16 eV and τ = 1.64 × 10 −16  s  (p. 400) | html | pdf |
• Fig. 4.3.4.17. Same as previous figure, but for a Lorentz model with an oscillator of eigenfrequency ħω 0 = 10 eV and relaxation time τ 0 = 6.6 × 10 −16  s superposed on the free-electron term  (p. 401) | html | pdf |
• Fig. 4.3.4.18. Dielectric coefficients , 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 E c ( i.e. the electric field vector being in the layer plane) and for E || c   (p. 403) | html | pdf |
• Fig. 4.3.4.20. Geometric conditions for investigating the anisotropic energy-loss function  (p. 404) | html | pdf |
• Fig. 4.3.4.21. Definition of electron shells and transitions involved in core-loss spectroscopy  (p. 404) | html | pdf |
• Fig. 4.3.4.22. Chart of edges encountered in the 50 eV up to 3 keV energy-loss range with symbols identifying the types of shapes  (p. 405) | html | pdf |
• Fig. 4.3.4.23. A selection of typical profiles ( K, L 2,3 , M 4,5 , and N 2,3 ) illustrating the most important behaviours encountered on major edges through the Periodic Table  (p. 406) | html | pdf |
• Fig. 4.3.4.24. Bethe surface for K -shell ionization, calculated using a hydrogenic model  (p. 407) | html | pdf |
• Fig. 4.3.4.25. A novel technique for simulating an energy-loss spectrum with two distinct edges as a superposition of theoretical contributions (hydrogenic saw-tooth for O K , Lorentzian white lines and delayed continuum for Fe L 2,3 calculated with the Hartree–Slater description)  (p. 407) | html | pdf |
• Fig. 4.3.4.26. Definition of the different fine structures visible on a core-loss edge  (p. 408) | html | pdf |
• Fig. 4.3.4.27. High-energy resolution spectra on the L 2,3 titanium edge from two phases (rutile and anatase) of TiO 2   (p. 408) | html | pdf |
• Fig. 4.3.4.28. The dramatic change in near-edge fine structures on the L 3 and L 2 lines of Cu, from Cu metal to CuO  (p. 409) | html | pdf |
• Fig. 4.3.4.29. Illustration of the single and multiple scattering effects used to describe the final wavefunction on the excited site  (p. 409) | html | pdf |
• Fig. 4.3.4.30. Comparison of the experimental O K edge (solid line) with calculated profiles in the multiple scattering approach  (p. 409) | html | pdf |
• Fig. 4.3.4.31. The conventional method of background subtraction for the evaluation of the characteristic signals S O K and S Fe L 2,3 used for quantitative elemental analysis  (p. 410) | html | pdf |
• Fig. 4.3.4.32. Values of n eff for metallic aluminium based on composite optical data  (p. 411) | html | pdf |
• Fig. 4.3.5.1. The relative orientations of the direct and the reciprocal axes and their projections on the plane ab , with indication of the distances B hk and D hkl that define the positions of reflections in lamellar texture patterns  (p. 412) | html | pdf |
• Fig. 4.3.5.2. ( a ) Part of the OTED pattern of the clay mineral kaolinite and ( b ) the intensity profile of a characteristic quadruplet of reflections recorded with the electron diffractometry system  (p. 413) | html | pdf |
• Fig. 4.3.5.3. The projections of the reciprocal axes on the plane ab of the direct lattice, with indications of the distances B and D of the hk rows from the fibre-texture axes a or [ hk ]  (p. 413) | html | pdf |
• Fig. 4.3.7.1. ( a ) Dispersion-surface section for the symmetric four-beam case (0, g, g + h, m ), γ k is a function of k x , referred to ( b ), where k x = k y = 0 corresponds to the exact Bragg condition for all three reflections  (p. 418) | html | pdf |
• Fig. 4.3.8.1. Atomic resolution image of a tantalum-doped tungsten trioxide crystal (pseudo-cubic structure) showing extended crystallographic shear-plane defects (C), pentagonal-column hexagonal-tunnel (PCHT) defects (T), and metallization of the surface due to oxygen desorption (JEOL 4000EX, crystal thickness less than 200 Å, 400 kV, C s = 1 mm)  (p. 419) | html | pdf |
• Fig. 4.3.8.2. Imaging conditions for few-beam lattice images  (p. 420) | html | pdf |
• Fig. 4.3.8.3. A summary of three- (or five-) beam axial imaging conditions  (p. 422) | html | pdf |
• Fig. 4.3.8.4. The contrast of few-beam lattice images as a function of focus in the neighbourhood of the stationary-phase focus  (p. 422) | html | pdf |
• Fig. 4.3.8.5. ( a ) The transfer function for a 400 kV electron microscope with a point resolution of 1.7 Å at the Scherzer focus; the curve is based on equation (4.3.8.17)  (p. 424) | html | pdf |
• Fig. 4.3.8.6. Structure image of a thin lamella of the 6 H polytype of SiC projected along [110] and recorded at 1.2 MeV  (p. 426) | html | pdf |
• Tables
• Table 4.3.1.1. Atomic scattering amplitudes (Å) for electrons for neutral atoms  (pp. 263-271) | html | pdf |
• Table 4.3.1.2. Atomic scattering amplitudes (Å) for electrons for ionized atoms  (pp. 272-281) | html | pdf |
• Table 4.3.2.1. Parameters useful in electron diffraction as a function of accelerating voltage  (p. 281) | html | pdf |
• Table 4.3.2.2. Elastic atomic scattering factors of electrons for neutral atoms and s up to 2.0 Å −1   (pp. 282-283) | html | pdf |
• Table 4.3.2.3. Elastic atomic scattering factors of electrons for neutral atoms and s up to 6.0 Å −1   (pp. 284-285) | html | pdf |
• Table 4.3.3.1. Partial wave elastic scattering factors for neutral atoms interactive version   (pp. 286-377) | html | pdf |
• Table 4.3.3.2. Inelastic scattering factors  (pp. 378-388) | html | pdf |
• Table 4.3.4.1. Different possibilities for using EELS information as a function of the different accessible parameters ( r , , Δ E )  (p. 394) | html | pdf |
• Table 4.3.4.2. Plasmon energies measured (and calculated) for a few simple metals  (p. 397) | html | pdf |
• Table 4.3.4.3. Experimental and theoretical values for the coefficient α in the plasmon dispersion curve together with estimates of the cut-off wavevector  (p. 398) | html | pdf |
• Table 4.3.4.4. Comparison of measured and calculated values for the halfwidth Δ E 1/2 (0) of the plasmon line  (p. 398) | html | pdf |
• 4.4. Neutron techniques  (pp. 430-487)
• 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 v k   (p. 435) | html | pdf |
• Fig. 4.4.2.4. In a curved neutron guide, the transmission becomes λ dependent: ( a ) the possible types of reflection (garland and zig-zag), the direct line-of-sight length, the critical angle θ*, which is related to the characteristic wavelength ; ( b ) transmission across the exit of the guide for different wavelengths, normalized to unity at the outside edge; ( c ) total transmission of the guide as a function of λ  (p. 436) | html | pdf |
• Fig. 4.4.2.5. Illustration of how a variation in the bilayer period can be used to produce a monochromator, a broad-band device, or a supermirror  (p. 437) | html | pdf |
• Fig. 4.4.2.6. Typical applications of polycapillary devices: ( a ) lens used to refocus a divergent beam; ( b ) half-lens to produce a nearly parallel beam or to focus a nearly parallel beam; ( c ) a compact bender  (p. 437) | html | pdf |
• Fig. 4.4.2.7. Total cross section for beryllium in the energy range where it can be used as a filter for neutrons with energy below 5 meV (Freund, 1983)  (p. 438) | html | pdf |
• Fig. 4.4.2.8. Energy-dependent cross section for a neutron beam incident along the c axis of a pyrolytic graphite filter  (p. 439) | html | pdf |
• Fig. 4.4.2.9. Geometry of a polarizing monochromator showing the lattice planes ( hkl ) with | F N | = | F M |, the direction of P and , the expected spin direction and intensity  (p. 439) | html | pdf |
• Fig. 4.4.2.10. Measured reflectivity curve of an FeCoV/TiZr polarizing supermirror with an extended angular range of polarization of three times that of γ c (Ni) for neutrons without spin flip, ↑↑, and with spin flip, ↑↓  (p. 440) | html | pdf |
• Tables
• Table 4.4.2.1. Some important properties of materials used for neutron monochromator crystals  (p. 433) | html | pdf |
• Table 4.4.2.2. Neutron scattering-length densities, Nb coh , for some commonly used materials  (p. 435) | html | pdf |
• Table 4.4.2.3. Characteristics of some typical elements and isotopes used as neutron filters  (p. 439) | html | pdf |
• Table 4.4.2.4. Properties of polarizing crystal monochromators  (p. 440) | html | pdf |
• Table 4.4.2.5. Scattering-length densities for some typical materials used for polarizing multilayers  (p. 441) | html | pdf |
• Table 4.4.4.1. Bound scattering lengths, b , in fm and cross sections, σ, in barns (1 barn = 100 fm 2 ) of the elements and their isotopes interactive version   (pp. 445-452) | html | pdf |
• Table 4.4.5.1. < j 0 > form factors for 3 d transition elements and their ions  (p. 454) | html | pdf |
• Table 4.4.5.2. < j 0 > form factors for 4 d atoms and their ions  (p. 455) | html | pdf |
• Table 4.4.5.3. < j 0 > form factors for rare-earth ions  (p. 455) | html | pdf |
• Table 4.4.5.4. < j 0 > form factors for actinide ions  (p. 455) | html | pdf |
• Table 4.4.5.5. < j 2 > form factors for 3 d transition elements and their ions  (p. 456) | html | pdf |
• Table 4.4.5.6. < j 2 > form factors for 4 d atoms and their ions  (p. 457) | html | pdf |
• Table 4.4.5.7. < j 2 > form factors for rare-earth ions  (p. 457) | html | pdf |
• Table 4.4.5.8. < j 2 > form factors for actinide ions  (p. 457) | html | pdf |
• Table 4.4.5.9. < j 4 > form factors for 3 d atoms and their ions  (p. 458) | html | pdf |
• Table 4.4.5.10. < j 4 > form factors for 4 d atoms and their ions  (p. 459) | html | pdf |
• Table 4.4.5.11. < j 4 > form factors for rare-earth ions  (p. 459) | html | pdf |
• Table 4.4.5.12. < j 4 > form factors for actinide ions  (p. 459) | html | pdf |
• Table 4.4.5.13. < j 6 > form factors for rare-earth ions  (p. 460) | html | pdf |
• Table 4.4.5.14. < j 6 > form factors for actinide ions  (p. 460) | html | pdf |
• Table 4.4.6.1. Absorption of the elements for neutrons  (p. 461) | html | pdf |
• Part 5. Determination of lattice parameters
• 5.1. Introduction  (p. 490)
• 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 00 l standard reflection angles  (p. 503) | html | pdf |
• Table 5.2.10.7. Silver behenate 00 l standard reflection angles  (p. 503) | html | pdf |
• Table 5.2.11.1. NIST intensity standards, SRM 674  (p. 503) | html | pdf |
• 5.3. X-ray diffraction methods: single crystal  (pp. 505-536)
• 5.3.1. Introduction  (pp. 505-508) | html | pdf |
• 5.3.1.1. General remarks  (pp. 505-506) | html | pdf |
• 5.3.1.2. Introduction to single-crystal methods  (pp. 506-508) | html | pdf |
• 5.3.2. Photographic methods  (pp. 508-516) | html | pdf |
• 5.3.2.1. Introduction  (p. 508) | html | pdf |
• 5.3.2.2. The Laue method  (p. 508) | html | pdf |
• 5.3.2.3. Moving-crystal methods  (pp. 508-510) | html | pdf |
• 5.3.2.3.1. Rotating-crystal method  (pp. 508-509) | html | pdf |
• 5.3.2.3.2. Moving-film methods  (p. 509) | html | pdf |
• 5.3.2.3.3. Combined methods  (p. 509) | html | pdf |
• 5.3.2.3.4. Accurate and precise lattice-parameter determinations  (pp. 509-510) | html | pdf |
• 5.3.2.3.5. Photographic cameras for investigation of small lattice-parameter changes  (p. 510) | html | pdf |
• 5.3.2.4. The Kossel method and divergent-beam techniques  (pp. 510-516) | html | pdf |
• 5.3.2.4.1. The principle  (pp. 510-512) | html | pdf |
• 5.3.2.4.2. Review of methods of accurate lattice-parameter determination  (pp. 512-515) | html | pdf |
• 5.3.2.4.3. Accuracy and precision  (p. 515) | html | pdf |
• 5.3.2.4.4. Applications  (pp. 515-516) | html | pdf |
• 5.3.3. Methods with counter recording  (pp. 516-534) | html | pdf |
• 5.3.3.1. Introduction  (p. 516) | html | pdf |
• 5.3.3.2. Standard diffractometers  (pp. 516-517) | html | pdf |
• 5.3.3.2.1. Four-circle diffractometer  (pp. 516-517) | html | pdf |
• 5.3.3.2.2. Two-circle diffractometer  (p. 517) | html | pdf |
• 5.3.3.3. Data processing and optimization of the experiment  (pp. 517-520) | html | pdf |
• 5.3.3.3.1. Models of the diffraction profile  (pp. 517-519) | html | pdf |
• 5.3.3.3.2. Precision and accuracy of the Bragg-angle determination; optimization of the experiment  (pp. 519-520) | html | pdf |
• 5.3.3.4. One-crystal spectrometers  (pp. 521-526) | html | pdf |
• 5.3.3.4.1. General characteristics  (p. 521) | html | pdf |
• 5.3.3.4.2. Development of methods based on an asymmetric arrangement and their applications  (pp. 521-522) | html | pdf |
• 5.3.3.4.3. The Bond method  (pp. 522-526) | html | pdf |
• 5.3.3.4.3.1. Description of the method  (pp. 522-523) | html | pdf |
• 5.3.3.4.3.2. Systematic errors  (pp. 523-524) | html | pdf |
• 5.3.3.4.3.3. Development of the Bond method and its applications  (pp. 524-525) | html | pdf |
• 5.3.3.4.3.4. Advantages and disadvantages of the Bond method  (p. 526) | html | pdf |
• 5.3.3.5. Limitations of traditional methods  (p. 526) | html | pdf |
• 5.3.3.6. Multiple-diffraction methods  (pp. 526-528) | html | pdf |
• 5.3.3.7. Multiple-crystal – pseudo-non-dispersive techniques  (pp. 528-533) | html | pdf |
• 5.3.3.7.1. Double-crystal spectrometers  (pp. 528-530) | html | pdf |
• 5.3.3.7.2. Triple-crystal spectrometers  (pp. 530-531) | html | pdf |
• 5.3.3.7.3. Multiple-beam methods  (p. 531) | html | pdf |
• 5.3.3.7.4. Combined methods  (pp. 531-533) | html | pdf |
• 5.3.3.8. Optical and X-ray interferometry – a non-dispersive technique  (pp. 533-534) | html | pdf |
• 5.3.3.9. Lattice-parameter and wavelength standards  (p. 534) | html | pdf |
• 5.3.4. Final remarks  (pp. 534-536) | html | pdf |
• References | html | pdf |
• Figures
• Fig. 5.3.2.1. ( a ) Photographic recording of lattice-parameter changes  (p. 511) | html | pdf |
• Fig. 5.3.2.2. Schematic representation of the origin of the Kossel lines  (p. 512) | html | pdf |
• Fig. 5.3.2.3. ( a ) The Kossel pattern from iron and ( b ) the corresponding stereographic projection (Tixier & Waché, 1970)  (p. 513) | html | pdf |
• Fig. 5.3.2.4. Lens-shaped figures formed by pairs of intersecting conics  (p. 514) | html | pdf |
• Fig. 5.3.2.5. Schematic representation of the multiple-exposure technique (after Fischer & Harris, 1970)  (p. 514) | html | pdf |
• Fig. 5.3.3.1. Determination of reciprocal-lattice angles on the θ circle (after Luger, 1980)  (p. 517) | html | pdf |
• Fig. 5.3.3.2. The extrapolated-peak procedure (after Bearden, 1933)  (p. 518) | html | pdf |
• Fig. 5.3.3.3. Determination of the Bragg angle by means of the one-crystal spectrometer using ( a ) an asymmetric or ( b ) a symmetric arrangement  (p. 521) | html | pdf |
• Fig. 5.3.3.4. Schematic representation of the Bond (1960) method  (p. 522) | html | pdf |
• Fig. 5.3.3.5. Schematic representation of multiple diffraction in reciprocal space (after Post, 1975)  (p. 526) | html | pdf |
• Fig. 5.3.3.6. Schematic representation of the multiple-diffraction method  (p. 527) | html | pdf |
• Fig. 5.3.3.7. The multiple-diffraction pattern at the 222 position in germanium (Cole, Chambers & Dunn, 1962)  (p. 527) | html | pdf |
• Fig. 5.3.3.8. Schematic representation of the double-crystal spectrometer  (p. 528) | html | pdf |
• Fig. 5.3.3.9. Schematic representation of the double-crystal arrangement of Hart & Lloyd (1975) for the examination of epitaxic layers  (p. 529) | html | pdf |
• Fig. 5.3.3.10. Schematic representation of the double-crystal arrangement of Okazaki & Kawaminami (1973 a ); white incident X-rays are used  (p. 529) | html | pdf |
• Fig. 5.3.3.11. Schematic representation of the triple-crystal spectrometer developed by Buschert (1965) (after Hart, 1981)  (p. 530) | html | pdf |
• Fig. 5.3.3.12. Schematic representation of the double-beam comparator of Hart (1969)  (p. 531) | html | pdf |
• Fig. 5.3.3.13. The double-axis lattice-spacing comparator of Ando, Bailey & Hart (1978); a triple-diffracted beam is used  (p. 532) | html | pdf |
• Fig. 5.3.3.14. Schematic representation of the double-beam triple-crystal spectrometer of Buschert et al   (p. 532) | html | pdf |
• Fig. 5.3.3.15. The geometry of the diffractometer used by Fewster & Andrew (1995)  (p. 533) | html | pdf |
• Fig. 5.3.3.16. Optical and X-ray interferometry  (p. 533) | html | pdf |
• Fig. 5.3.3.17. Portion of a dual-channel recording of X-ray and optical fringes (Deslattes, 1969)  (p. 533) | html | pdf |
• Fig. 5.3.3.18. Synchrotron radiation, SR, from the bending magnet incident on the Si(111) double-crystal monochromator and, after four reflections from the monolithic monochromator (0.1410 nm), impinges on sample Si(444)  (p. 534) | html | pdf |
• Fig. 5.3.3.19. Synchrotron radiation, SR, from the bending magnet incident on the Si(111) double-crystal monochromator and, after four reflections from the monolithic monochromator (0.1612 nm), impinges on sample Si(153)  (p. 535) | html | pdf |
• Fig. 5.3.3.20. Experimental set-up for measuring lattice parameters  (p. 535) | html | pdf |
• 5.4. Electron-diffraction methods  (pp. 537-540)
• 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 |
• 5.5. Neutron methods  (pp. 541-551)
• Part 6. 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 < j 0 >, < j 2 >, and < j 4 > for the Fe 2+ ion plotted against   (p. 592) | html | pdf |
• Fig. 6.1.2.2. Comparison of 3 d , 4 d , 4 f , and 5 f form factors  (p. 592) | html | pdf |
• Fig. 6.1.3.1. Dependence on neutron wavelength of the coherent scattering length of 113 Cd  (p. 594) | html | pdf |
• Tables
• Table 6.1.1.1. Mean atomic scattering factors in electrons for free atoms  (pp. 555-564) | html | pdf |
• Table 6.1.1.2. Spherical bonded hydrogen-atom scattering factors  (p. 565) | html | pdf |
• Table 6.1.1.3. Mean atomic scattering factors in electrons for chemically significant ions  (pp. 566-577) | html | pdf |
• Table 6.1.1.4. Coefficients for analytical approximation to the scattering factors of Tables 6.1.1.1 and 6.1.1.3  (pp. 578-580) | html | pdf |
• Table 6.1.1.5. Coefficients for analytical approximation to the scattering factors of Table 6.1.1.1 for the range 2.0 < (sin )/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. f nl (α, S ) = ∫ 0 r n exp(−α r ) j l ( Sr ) d r   (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 n x , n y , n z allowed for the basis functions H n x ( Ax ) H n y ( By ) H n z ( Cz )  (p. 587) | html | pdf |
• 6.2. Trigonometric intensity factors  (pp. 596-598)
• 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 σ ph with wavelength λ  (p. 599) | html | pdf |
• Fig. 6.3.3.1. Geometry of the Eulerian cradle with the axis of a cylindrical specimen coincident with the ϕ axis  (p. 604) | html | pdf |
• Fig. 6.3.3.2. Cross section of the plane of diffraction for a cylindrical specimen coincident with the ϕ axis  (p. 604) | html | pdf |
• Fig. 6.3.3.3. The crystal ABC divided into polygons by the dashed lines AE and CF parallel to the incident ( i ) and diffracted ( d ) beams, respectively  (p. 605) | html | pdf |
• Fig. 6.3.3.4. Crystal oriented with the normal N ( S ) to the face ABCD in the plane of view  (p. 608) | html | pdf |
• Fig. 6.3.3.5. Geometry of the Eulerian cradle in the bisecting position  (p. 608) | html | pdf |
• Tables
• Table 6.3.3.1. Transmission coefficients  (p. 601) | html | pdf |
• Table 6.3.3.2. Values of A * for cylinders  (p. 602) | html | pdf |
• Table 6.3.3.3. Values of A * for spheres  (p. 602) | html | pdf |
• Table 6.3.3.4. Values of (1/ A *)(d A */dμ R ) 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 |
• Part 7. 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 K α and Mo K α 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 3 He 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 10 B-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 3 He gas detector and ( b ) a scintillation detector  (p. 648) | html | pdf |
• Fig. 7.3.4.2. ( a ) Characteristic 10 BF 3 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 LiNbO 3 (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, 1980 a )  (p. 656) | html | pdf |
• Fig. 7.4.3.1. Schematic diagram of the inelastic scattering interactions, Δ E = E 1 E 2 is the energy transferred from the photon and K the momentum transfer  (p. 657) | html | pdf |
• Fig. 7.4.3.2. The incoherent scattering function, S ( x, Z )/ Z , per electron for aluminium shown as a function of x = (sin θ)/λ  (p. 660) | html | pdf |
• Fig. 7.4.3.3. The cross section for resonant Raman scattering (RRS) and fluorescence (F) as a function of the ratio of the incident energy, E , and the K -binding energy, E B   (p. 661) | html | pdf |
• Fig. 7.4.4.1. Equatorial phase-space diagrams for a conventional X-ray source and parallel-beam geometry; x is the size and x ′ = d x /d z 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 K α 1 radiation (solid curve)  (p. 662) | html | pdf |
• Fig. 7.4.4.3. Equatorial phase-space diagrams for two wavelengths, λ 1 (solid lines) and λ 2 (broken lines), projected on the plane λ = λ 1   (p. 662) | html | pdf |
• Fig. 7.4.4.4. Two reflections of beryllium acetate measured with Mo K α  (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 K α X-radiation through 170° from 2 s 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 |
• Part 8. 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 χ 2 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 χ 2 /ν for which the c.d.f. ψ(χ 2 , 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 , ν 1 , ν 2 ) has the value 0.95, for various choices of ν 1 and ν 2   (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 δ x , δ y , and δ z   (p. 719) | html | pdf |
• Table 8.7.3.3. The matrix M −1 relating d -orbital occupancies P ij to multipole populations P lm   (p. 722) | html | pdf |
• Table 8.7.3.4. Orbital–multipole relations for square-planar complexes (point group D 4 h )  (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 |
• Part 9. 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 CdI 2   (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 Sb 2 VO 5   (pp. 769-771) | html | pdf |
• 9.2.2.3.3. γ-Hg 3 S 2 Cl 2   (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-6 H structure  (p. 753) | html | pdf |
• Fig. 9.2.1.5. The layer structure of CdI 2 : 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 2 H close packing  (p. 755) | html | pdf |
• Fig. 9.2.1.7. A rhombohedral lattice ( a 1 , a 2 , a 3 ) referred to hexagonal axes ( A 1 , A 2 , 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) m 1|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-1 M , 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-2 M   (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-2 O   (p. 772) | html | pdf |
• Fig. 9.2.2.20. The structural principle of γ -Hg 3 S 2 Cl 2   (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 6 H ( A 0 B 1 C 2 A 3 C 4 B 5 ;. . .) structure  (p. 758) | html | pdf |
• Table 9.2.1.4. Intrinsic fault configurations in the 9 R ( A 0 B 1 A 2 C 0 A 1 C 2 B 0 C 1 B 2 ;. . .) 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 d AB versus for the binary compounds crystallizing in hP 3 AlB 2   (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 ( N ent ) published in a given year  (p. 790) | html | pdf |
• Fig. 9.5.2.1. Effect of the removal of outliers (contributors that are > 4σ from the mean) for the C—C bond in C ar —C≡N fragments  (p. 791) | html | pdf |
• Fig. 9.5.2.2. Skewed distribution of B—F bond lengths in ions  (pp. 791-792) | html | pdf |
• Fig. 9.5.2.3. Resolution of the bimodal distribution of C—N bond lengths in C ar —N(C sp 3 ) 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 ( N ent ) added annually  (p. 812) | html | pdf |
• Fig. 9.6.2.1. Effects of outlier removal and subdivision based on coordination number and oxidation state  (p. 814) | html | pdf |
• Fig. 9.6.3.1. Diagrams of ligands in Table 9.6.3.3, showing table entry number and ligand atom labelling  (p. 816) | html | pdf |
• Tables
• Table 9.6.3.1. Ligand index  (pp. 814-815) | html | pdf |
• Table 9.6.3.2. Numbers of entries in Table 9.6.3.3  (p. 817) | html | pdf |
• Table 9.6.3.3. Interatomic distances (Å)  (pp. 818-883) | html | pdf |
• 9.7. The space-group distribution of molecular organic structures  (pp. 897-906)
• 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 (1993 a )  (p. 898) | html | pdf |
• Table 9.7.1.2. Space groups arranged by arithmetic crystal class and degree of symmorphism (Wilson, 1993 d ), 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 groups superspace 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 |
• Part 10. Precautions against radiation injury
• 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) |