X-rays

Arndt, U. W.; Creagh, D. C.; Deslattes, R. D.; Hubbell, J. H.; Indelicato, P.; Kessler, E. G. Jr; Lindroth, E.

doi:10.1107/97809553602060000592

International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 191-258
https://doi.org/10.1107/97809553602060000592

Chapter 4.2. X-rays

4.2. X-rays (pp. 191-258) | html | pdf | chapter contents |
U. W. Arndt, D. C. Creagh, R. D. Deslattes, J. H. Hubbell, P. Indelicato, E. G. Kessler Jr and E. Lindroth
- 4.2.1. Generation of X-rays (pp. 191-200) | html | pdf |
  U. W. Arndt
  - 4.2.1.1. The characteristic line spectrum (pp. 191-192) | html | pdf |
    - 4.2.1.1.1. The intensity of characteristic lines (pp. 191-192) | html | pdf |
  - 4.2.1.2. The continuous spectrum (pp. 192-193) | html | pdf |
  - 4.2.1.3. X-ray tubes (pp. 193-195) | html | pdf |
    - 4.2.1.3.1. Power dissipation in the anode (p. 195) | html | pdf |
  - 4.2.1.4. Radioactive X-ray sources (pp. 195-196) | html | pdf |
  - 4.2.1.5. Synchrotron-radiation sources (pp. 196-198) | html | pdf |
  - 4.2.1.6. Plasma X-ray sources (pp. 198-199) | html | pdf |
  - 4.2.1.7. Other sources of X-rays (pp. 199-200) | html | pdf |
- 4.2.2. X-ray wavelengths (pp. 200-212) | html | pdf |
  R. D. Deslattes, E. G. Kessler Jr, P. Indelicato and E. Lindroth
  - 4.2.2.1. Historical introduction (pp. 200-201) | html | pdf |
  - 4.2.2.2. Known problems (p. 201) | html | pdf |
  - 4.2.2.3. Alternative strategies (p. 201) | html | pdf |
  - 4.2.2.4. The X-ray wavelength scales, old and new (pp. 201-202) | html | pdf |
  - 4.2.2.5. K-series reference wavelengths (p. 202) | html | pdf |
  - 4.2.2.6. L-series reference wavelengths (p. 202) | html | pdf |
  - 4.2.2.7. Absorption-edge locations (pp. 202-204) | html | pdf |
  - 4.2.2.8. Outline of the theoretical procedures (pp. 204-205) | html | pdf |
  - 4.2.2.9. Evaluation of the uncorrelated energy with the Dirac–Fock method (p. 205) | html | pdf |
  - 4.2.2.10. Correlation and Auger shifts (p. 205) | html | pdf |
  - 4.2.2.11. QED corrections (pp. 205-208) | html | pdf |
  - 4.2.2.12. Structure and format of the summary tables (pp. 211-212) | html | pdf |
  - 4.2.2.13. Availability of a more complete X-ray wavelength table (p. 212) | html | pdf |
  - 4.2.2.14. Connection with scales used in previous literature (p. 212) | html | pdf |
- 4.2.3. X-ray absorption spectra (pp. 213-220) | html | pdf |
  D. C. Creagh
  - 4.2.3.1. Introduction (pp. 213-214) | html | pdf |
    - 4.2.3.1.1. Definitions (p. 213) | html | pdf |
    - 4.2.3.1.2. Variation of X-ray attenuation coefficients with photon energy (p. 213) | html | pdf |
    - 4.2.3.1.3. Normal attenuation, XAFS, and XANES (pp. 213-214) | html | pdf |
  - 4.2.3.2. Techniques for the measurement of X-ray attenuation coefficients (pp. 214-215) | html | pdf |
    - 4.2.3.2.1. Experimental configurations (pp. 214-215) | html | pdf |
    - 4.2.3.2.2. Specimen selection (p. 215) | html | pdf |
    - 4.2.3.2.3. Requirements for the absolute measurement of μ_l or (μ/ρ) (p. 215) | html | pdf |
  - 4.2.3.3. Normal attenuation coefficients (p. 215) | html | pdf |
  - 4.2.3.4. Attenuation coefficients in the neighbourhood of an absorption edge (pp. 216-219) | html | pdf |
    - 4.2.3.4.1. XAFS (pp. 216-219) | html | pdf |
      - 4.2.3.4.1.1. Theory (pp. 216-217) | html | pdf |
      - 4.2.3.4.1.2. Techniques of data analysis (pp. 217-218) | html | pdf |
      - 4.2.3.4.1.3. XAFS experiments (pp. 218-219) | html | pdf |
    - 4.2.3.4.2. X-ray absorption near edge structure (XANES) (p. 219) | html | pdf |
  - 4.2.3.5. Comments (p. 220) | html | pdf |
- 4.2.4. X-ray absorption (or attenuation) coefficients (pp. 220-229) | html | pdf |
  D. C. Creagh and J. H. Hubbell
  - 4.2.4.1. Introduction (pp. 220-221) | html | pdf |
  - 4.2.4.2. Sources of information (pp. 221-229) | html | pdf |
    - 4.2.4.2.1. Theoretical photo-effect data: σ_pe (p. 221) | html | pdf |
    - 4.2.4.2.2. Theoretical Rayleigh scattering data: σ_R (pp. 221-229) | html | pdf |
    - 4.2.4.2.3. Theoretical Compton scattering data: σ_C (p. 229) | html | pdf |
  - 4.2.4.3. Comparison between theoretical and experimental data sets (p. 229) | html | pdf |
  - 4.2.4.4. Uncertainty in the data tables (p. 229) | html | pdf |
- 4.2.5. Filters and monochromators (pp. 229-241) | html | pdf |
  D. C. Creagh
  - 4.2.5.1. Introduction (pp. 229-236) | html | pdf |
  - 4.2.5.2. Mirrors and capillaries (pp. 236-238) | html | pdf |
    - 4.2.5.2.1. Mirrors (pp. 236-237) | html | pdf |
    - 4.2.5.2.2. Capillaries (p. 237) | html | pdf |
    - 4.2.5.2.3. Quasi-Bragg reflectors (pp. 237-238) | html | pdf |
  - 4.2.5.3. Filters (p. 238) | html | pdf |
  - 4.2.5.4. Monochromators (pp. 238-241) | html | pdf |
    - 4.2.5.4.1. Crystal monochromators (pp. 238-239) | html | pdf |
    - 4.2.5.4.2. Laboratory monochromator systems (p. 239) | html | pdf |
    - 4.2.5.4.3. Multiple-reflection monochromators for use with laboratory and synchrotron-radiation sources (pp. 239-240) | html | pdf |
    - 4.2.5.4.4. Polarization (pp. 240-241) | html | pdf |
- 4.2.6. X-ray dispersion corrections (pp. 241-258) | html | pdf |
  D. C. Creagh
  - 4.2.6.1. Definitions (pp. 242-243) | html | pdf |
    - 4.2.6.1.1. Rayleigh scattering (p. 242) | html | pdf |
    - 4.2.6.1.2. Thomson scattering by a free electron (p. 242) | html | pdf |
    - 4.2.6.1.3. Elastic scattering from electrons bound to atoms: the atomic scattering factor, the atomic form factor, and the dispersion corrections (pp. 242-243) | html | pdf |
  - 4.2.6.2. Theoretical approaches for the calculation of the dispersion corrections (pp. 243-248) | html | pdf |
    - 4.2.6.2.1. The classical approach (pp. 243-244) | html | pdf |
    - 4.2.6.2.2. Non-relativistic theories (pp. 244-245) | html | pdf |
    - 4.2.6.2.3. Relativistic theories (pp. 245-248) | html | pdf |
      - 4.2.6.2.3.1. Cromer and Liberman: relativistic dipole approach (pp. 245-246) | html | pdf |
      - 4.2.6.2.3.2. The scattering matrix formalism (pp. 246-248) | html | pdf |
    - 4.2.6.2.4. Intercomparison of theories (p. 248) | html | pdf |
  - 4.2.6.3. Modern experimental techniques (pp. 248-258) | html | pdf |
    - 4.2.6.3.1. Determination of the real part of the dispersion correction: $[f'(\omega,0)]$ (pp. 248-250) | html | pdf |
    - 4.2.6.3.2. Determination of the real part of the dispersion correction: (pp. 250-251) | html | pdf |
      - 4.2.6.3.2.1. Measurements using the dynamical theory of X-ray diffraction (pp. 250-251) | html | pdf |
      - 4.2.6.3.2.2. Friedel- and Bijvoet-pair techniques (p. 251) | html | pdf |
    - 4.2.6.3.3. Comparison of theory with experiment (pp. 251-258) | html | pdf |
      - 4.2.6.3.3.1. Measurements in the high-energy limit $[(\omega/\omega_\kappa\rightarrow0)]$ (pp. 251-252) | html | pdf |
      - 4.2.6.3.3.2. Measurements in the vicinity of an absorption edge (pp. 252-253) | html | pdf |
      - 4.2.6.3.3.3. Accuracy in the tables of dispersion corrections (p. 253) | html | pdf |
      - 4.2.6.3.3.4. Towards a tensor formalism (pp. 253-258) | html | pdf |
      - 4.2.6.3.3.5. Summary (p. 258) | html | pdf |
  - 4.2.6.4. Table of wavelengths, energies, and linewidths used in compiling the tables of the dispersion corrections (p. 258) | html | pdf |
  - 4.2.6.5. Tables of the dispersion corrections for forward scattering, averaged polarization using the relativistic multipole approach (p. 258) | html | pdf |
- References | html | pdf |
- Figures
  - Fig. 4.2.1.1. f(χ) curves for Cu K-L₃ at a series of different accelerating voltages (in kV) (p. 192) | html | pdf |
  - Fig. 4.2.1.2. Experimental measurements of $[N_\varphi]$ for Cu K-L₃ as functions of the accelerating voltage for different take-off angles (p. 193) | html | pdf |
  - Fig. 4.2.1.3. Intensity per unit frequency interval versus frequency in the continuous spectrum from a thick target at different accelerating voltages (p. 193) | html | pdf |
  - Fig. 4.2.1.4. The function μ in Müller's equation (equation 4.2.1.12) as a function of the ratio of width to length of the focal spot (p. 195) | html | pdf |
  - Fig. 4.2.1.5. Synchrotron radiation emitted by a relativistic electron travelling in a curved trajectory (p. 197) | html | pdf |
  - Fig. 4.2.1.6. Synchrotron-radiation spectrum: percentage per unit wavelength interval (a) of power of total power and (b) of number of photons of total number of photons at wavelengths greater than λ versus λ/λ_c (p. 197) | html | pdf |
  - Fig. 4.2.1.7. Main components of a dedicated electron storage-ring synchrotron-radiation source (p. 198) | html | pdf |
  - Fig. 4.2.1.8. Electron trajectory within a multipole wiggler or undulator (p. 198) | html | pdf |
  - Fig. 4.2.1.9. Spectral distribution and critical wavelengths for (a) a dipole magnet, (b) a wavelength shifter, and (c) a multipole wiggler for the proposed ESRF (p. 198) | html | pdf |
  - Fig. 4.2.1.10. Comparison of the spectra from the storage ring SPEAR in photons s⁻¹ mA⁻¹ mrad⁻¹ per 1% passband (1978 performance) and a rotating-anode X-ray generator (p. 198) | html | pdf |
  - Fig. 4.2.1.11. The evolution of storage-ring synchrotron-radiation sources over the decades, as illustrated by their increasing number and range of machine energies (based on Suller, 1992) (p. 200) | html | pdf |
  - Fig. 4.2.1.12. X-ray emission from various laser-produced plasmas (p. 200) | html | pdf |
  - Fig. 4.2.2.1. Relative deviations between theoretical and experimental results for K-series spectra (p. 212) | html | pdf |
  - Fig. 4.2.2.2. Comparison of L-series data with experiment for the indicated range of Z (p. 212) | html | pdf |
  - Fig. 4.2.3.1. Theoretical cross sections for photon interactions with carbon showing the contributions of photoelectric, elastic (Rayleigh), inelastic (Compton), and pair-production cross sections to the total cross sections (p. 213) | html | pdf |
  - Fig. 4.2.3.2. The dependence of the X-ray attenuation coefficient on energy for a range of germanium compounds, taken in the neighbourhood of the germanium absorption edge (from IT IV, 1974) (p. 214) | html | pdf |
  - Fig. 4.2.3.3. Schematic representations of experimental apparatus used in the IUCr X-ray Attenuation Project (Creagh & Hubbell, 1987; Creagh, 1985) (p. 214) | html | pdf |
  - Fig. 4.2.3.4. Steps in the reduction of data from an XAFS experiment using the Fourier transform technique: (a) after the removal of background χ(k) versus k; (b) after multiplication by a weighting function (in this case k³); (c) after Fourier transformation to determine r′ (p. 217) | html | pdf |
  - Fig. 4.2.3.5. Schematic representations of the scattering processes undergone by the ejected photoelectron in the single-scattering (XAFS) case and the full multiple-scattering regime (XANES) (p. 219) | html | pdf |
  - Fig. 4.2.4.1. Agreement between theory and experiment for oxygen (Z = 8) in the `soft' X-ray region (p. 220) | html | pdf |
  - Fig. 4.2.4.2. The total cross section for silicon (Z = 14) compared with the unrenormalized Scofield values (p. 221) | html | pdf |
  - Fig. 4.2.4.3. The total cross section for uranium (Z = 92): The theoretical values (solid line) are partially obscured by the high density of available measurements (p. 222) | html | pdf |
  - Fig. 4.2.4.4. Comparison between this tabulation and experimental data contained in Saloman & Hubbell (1986) (p. 222) | html | pdf |
  - Fig. 4.2.5.1. The variation of specular reflectivity with incident photon energy is shown for materials of different atomic number and a constant angle of incidence of 0.2° (p. 236) | html | pdf |
  - Fig. 4.2.5.2. The use of mirrors in a typical synchrotron-radiation beamline (p. 237) | html | pdf |
  - Fig. 4.2.5.3. The reflectivity of a multiple-quantum-well device is shown (p. 238) | html | pdf |
  - Fig. 4.2.5.4. In (a), the schematic rocking curve for a silicon crystal in the neighbourhood of the 111 Bragg peak is shown (p. 239) | html | pdf |
  - Fig. 4.2.5.5. A schematic diagram of a beamline designed to produce circularly polarized light from initially linearly polarized light using Laue-case reflections (p. 240) | html | pdf |
  - Fig. 4.2.5.6. A schematic diagram of a Hart-type tuneable channel-cut monochromator is shown (p. 241) | html | pdf |
  - Fig. 4.2.5.7. A schematic diagram of the use of a Bragg–Fresnel lens to focus hard X-rays onto a high-pressure cell (p. 241) | html | pdf |
  - Fig. 4.2.6.1. The relativistic correction in electrons per atom for: (a) the modified form-factor approach; (b) the relativistic multipole approach; (c) the relativistic dipole approach (p. 247) | html | pdf |
  - Fig. 4.2.6.2. Measured values of f′(ω, 0) at the K-edge of Nb in LiNbO₃ and the Kramers–Kronig transformation of f′′(ω, 0) (p. 247) | html | pdf |
- Tables
  - Table 4.2.1.1. Correspondence between X-ray diagram levels and electron configurations (p. 191) | html | pdf |
  - Table 4.2.1.2. Correspondence between IUPAC and Siegbahn notations for X-ray diagram lines (p. 191) | html | pdf |
  - Table 4.2.1.3. Copper-target X-ray tubes and their loading (p. 194) | html | pdf |
  - Table 4.2.1.4. Relative permissible loading for different target materials (p. 196) | html | pdf |
  - Table 4.2.1.5. Radionuclides decaying wholly by electron capture, and yielding little or no γ-radiation (p. 196) | html | pdf |
  - Table 4.2.1.6. Comparison of storage-ring synchrotron-radiation sources (p. 199) | html | pdf |
  - Table 4.2.1.7. Intensity gain with storage rings over conventional sources (p. 200) | html | pdf |
  - Table 4.2.2.1. K-series reference wavelengths in Å (p. 203) | html | pdf |
  - Table 4.2.2.2. Directly measured L-series reference wavelengths in Å (p. 204) | html | pdf |
  - Table 4.2.2.3. Directly measured and emission + binding energies (see text) K-absorption edges in Å (p. 205) | html | pdf |
  - Table 4.2.2.4. Wavelengths of K-emission lines and K-absorption edges in Å (pp. 206-208) | html | pdf |
  - Table 4.2.2.5. Wavelengths of L-emission lines and L-absorption edges in Å (pp. 209-211) | html | pdf |
  - Table 4.2.2.6. Wavelength conversion factors (p. 212) | html | pdf |
  - Table 4.2.3.1. Some synchrotron-radiation facilities providing XAFS databases and analysis utilities (p. 219) | html | pdf |
  - Table 4.2.4.1. Table of wavelengths and energies for the characteristic radiations used in Tables 4.2.4.2 and 4.2.4.3 (p. 221) | html | pdf |
  - Table 4.2.4.2. Total phonon interaction cross section (pp. 223-229) | html | pdf |
  - Table 4.2.4.3. Mass attenuation coefficients (pp. 230-236) | html | pdf |
  - Table 4.2.6.1. Values of E_tot/mc² listed as a function of atomic number Z (p. 246) | html | pdf |
  - Table 4.2.6.2. Comparison between the S-matrix calculations of Kissel (K) (1977) and the form-factor calculations of Cromer & Liberman (C & L) (1970, 1981, 1983) and Creagh & McAuley (C & M) for the noble gases and several common metals (p. 249) | html | pdf |
  - Table 4.2.6.3. A comparison of the forward-scattering amplitudes computed using different theoretical approaches (p. 250) | html | pdf |
  - Table 4.2.6.4. Comparison of measurements of the real part of the dispersion correction for LiF, Si, Al and Ge for characteristic wavelengths Ag Kα₁, Mo Kα₁ and Cu Kα₁ with theoretical predictions (p. 252) | html | pdf |
  - Table 4.2.6.5. Comparison of measurements of f′(ω, 0) for C, Si and Cu for characteristic wavelengths Ag Kα₁, Mo Kα₁ and Cu Kα₁ with theoretical predictions (p. 253) | html | pdf |
  - Table 4.2.6.6. Comparison of $[f'(\omega_A,0)]$ for copper, nickel, zirconium, and niobium for theoretical and experimental data sets (p. 254) | html | pdf |
  - Table 4.2.6.7. Lists of wavelengths, energies, and linewidths used in compiling the table of dispersion corrections (p. 254) | html | pdf |
  - Table 4.2.6.8. Dispersion corrections for forward scattering (pp. 255-257) | html | pdf |

Chapter 4.2. X-rays

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