International Tables for Crystallography (2006). Vol. C, ch. 2.3, pp. 42-79
doi: 10.1107/97809553602060000578

Chapter 2.3. Powder and related techniques: X-ray techniques

Contents

  • 2.3. Powder and related techniques: X-ray techniques  (pp. 42-79) | html | pdf | chapter contents |
    • 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 |