International Tables for Crystallography

U. W. Arndt, D. C. Creagh, R. D. Deslattes, J. H. Hubbell, P. Indelicato, E. G. Kessler Jr and E. Lindroth. International Tables for Crystallography (2006). Vol. C, ch. 4.2, pp. 191-258  [ doi:10.1107/97809553602060000592 ]


The generation of X-rays is discussed in the first section of this chapter. X-rays are generated by (1) the bombardment of a target by electrons, (2) the decay of certain radio isotopes, (3) as part of the synchrotron-radiation spectrum and (4) in plasmas produced by bombarding targets with high-energy laser beams. The spectra produced by the first method consist of a line spectrum characteristic of the target material accompanied by a continuum of white radiation (Bremsstrahlung). The intensities and wavelengths of these components are discussed and the nomenclatures of the lines in the characteristic spectrum are compared. Synchrotron radiation and plasma generation of X-rays are discussed very briefly. X-ray wavelengths are discussed in the second section of the chapter. Tables of K- and L-series reference wavelengths and K- and L-emission lines and absorption edges are provided. X-ray absorption spectra are discussed in the third section of the chapter. A detailed discussion of the problems associated with the measurement of X-ray absorption and the requirements for the absolute measurement of the X-ray attenuation coefficients is followed by a description of the problems which are encountered in making measurements at X-ray absorption edges of atomic species in materials. The popular, and extremely valuable, experimental technique of X-ray absorption fine structure (XAFS) is discussed. This is a relative, rather than an absolute measurement of X-ray absorption, and the theoretical analysis of XAFS spectra depends on the deviation of the data points from a cubic spline fit to the data rather that the deviation from the extrapolation of the free-atom absorption. A brief description of the origin and use of X-ray absorption near edge structure (XANES) is given. In the fourth section of the chapter, X-ray absorption (or attenuation) coefficients are considered. A detailed description of the theoretical and experimental techniques for the determination of X-ray absorption (and attenuation coefficients) is given. The tables supercede the existing experimental and theoretical tables that were available up to 2001. The theoretical values given here are restricted to the characteristic radiations commonly available from laboratory X-ray sources (Ti Kβ to Ag Kα). Computational problems become significant for elements in the lanthanide and actinide series of the periodic table. These tables include a significant recalculation of the absorption and attenuation coefficients for the lanthanide series. Note that although many theory-based tables exist, few accurate experimental measurements have been made on atomic species with atomic numbers greater than 50, especially in the region of absorption edges. A comparison is given of the extent to which theoretical and experimental data agree. A recent tabulation discusses soft X-ray absorption in the XANES region. Filters and monochromators are discussed in the fifth section of the chapter. This section serves as an introduction to the use of filters and monochromators in experimental apparatus. It discusses, using synchrotron-radiation experimental configurations as examples, the use of X-ray reflectivity, X-ray refraction and X-ray Bragg (and Laue) or Fresnel scattering for the production of monochromatic or quasi- monochromatic (pink) beams from polychromatic sources. Amongst the techniques discussed are: bent and curved mirrors, capillaries, quasi-Bragg (multilayer) mirrors, multiple filters, crystal monochromators, polarization and polarization-producing systems, and focusing using a Bragg–Fresnel optical system. The development of monochromators for synchrotron-radiation research is a rapidly evolving field, but in practice all depend on either the processes of reflection, refraction or scattering, or combinations of these processes. In the final section of the chapter, X-ray dispersion corrections are considered. The various theoretical methods for the computation of the X-ray dispersion corrections and the experimental techniques used for their determination are described in some detail. The theoretical values given here are restricted to the characteristic radiations commonly available from laboratory X-ray sources (Ti Kβ to Ag Kα). An artificial distinction is made between the relativistic Dirac–Hartree–Fock–Slater (RDHFS) formalism used to calculate the data in these tables and the S-matrix method used by a number of theoreticians. Formally, the two techniques are equivalent: in terms of the computations the two approaches are different, and the outcomes are different. Comparison with experimental data shows that the RDHFS formalism gives a better fit to experimental results.

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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The series consists of eight volumes and comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.