Anomalous dispersion

From Online Dictionary of Crystallography

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Dispersion anormale (Fr). Anomale Dispersion (Ge). Dispersion anómala (Sp). Dispersione anomala (It)


The 'anomalous' dispersion corrections, which have nothing anomalous, come in to into account the effect of absorption in the scattering of phonons by electrons. In the classic picture the electron is then approximated by a damped harmonic oscillator. The scattering factor of the electron is then complex and the atomic scattering factor, or atomic form factor is given by:

f + f' + i f"

where f' and f" are the real and imaginary parts of the anomalous dispersion correction. Their importance increases as one gets closer to an absorption edge (resonant scattering). Numerical calculations usually follow the Hartree-Fock approximations. For details on the non-relativistic and relativostic approaches, see Section 4.2.6 of International Tables of Crystallography, Volume C.


The dispersion of X-rays was theoretically predicted by Waller (Waller, I., 1928, Über eine verallgemeinerte Streuungsformel. Z. Phys. 51, 213-231.) and first calculated by Hönl (Hönl, H., 1933, Zur Dispersionstheorie der Röntgenstrahlen. Z. Phys. 84, 1-16; Hönl, H., 1933, Atomfactor für Röntgenstrahlen als Problem der Dispersionstheorie (K-Schale). Ann. Phys. (Leipzig), 18, 625-657.

See also

anomalous scattering
multiwavelength anomalous diffraction (MAD)
Section 4.2.6 of International Tables of Crystallography, Volume C