International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.4, pp. 265-266   | 1 | 2 |

## Section 2.4.3.1. Dispersion correction

M. Vijayana* and S. Ramaseshanb

aMolecular Biophysics Unit, Indian Institute of Science, Bangalore 560 012, India, and bRaman Research Institute, Bangalore 560 080, India
Correspondence e-mail:  mv@mbu.iisc.ernet.in

#### 2.4.3.1. Dispersion correction

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Atomic scattering factors are normally calculated on the assumption that the binding energy of the electrons in an atom is negligible compared to the energy of the incident X-rays and the distribution of electrons is spherically symmetric. The transition frequencies within the atom are then negligibly small compared to the frequency of the radiation used and the scattering power of each electron in the atom is close to that of a free electron. When this assumption is valid, the atomic scattering factor is a real positive number and its value decreases as the scattering angle increases because of the finite size of the atom. When the binding energy of the electrons is appreciable, the atomic scattering factor at any given angle is given by where is a real positive number and corresponds to the atomic scattering factor for a spherically symmetric collection of free electrons in the atom. The second and third terms are, respectively, referred to as the real and the imaginary components of the `dispersion correction' (IT IV, 1974). f′ is usually negative whereas f″ is positive. For any given atom, f″ is obviously ahead of the real part of the scattering factor given by

The variation of f′ and f″ as a function of atomic number for two typical radiations is given in Fig. 2.4.3.1 (Srinivasan, 1972; Cromer, 1965). The dispersion effects are pronounced when an absorption edge of the atom concerned is in the neighbourhood of the wavelength of the incident radiation. Atoms with high atomic numbers have several absorption edges and the dispersion-correction terms in their scattering factors always have appreciable values. The values of f′ and f″ do not vary appreciably with the angle of scattering as they are caused by core electrons confined to a very small volume around the nucleus. An atom is usually referred to as an anomalous scatterer if the dispersion-correction terms in its scattering factor have appreciable values. The effects on the structure factors or intensities of Bragg reflections resulting from dispersion corrections are referred to as anomalous-dispersion effects or anomalous-scattering effects.

 Figure 2.4.3.1 | top | pdf |Variation of (a) and (b) as a function of atomic number for Cu and Mo radiations. Adapted from Fig. 3 of Srinivasan (1972).

### References

International Tables for X-ray Crystallography (1974). Vol. IV, pp. 148–151. Birmingham: Kynoch Press. (Present distributor Kluwer Academic Publishers, Dordrecht.)Google Scholar
Cromer, D. T. (1965). Anomalous dispersion corrections computed from self-consistent field relativistic Dirac–Slater wave functions. Acta Cryst. 18, 17–23.Google Scholar
Templeton, D. H., Templeton, L. K., Phillips, J. C. & Hodgson, K. O. (1980). Anomalous scattering of X-rays by cesium and cobalt measured with synchrotron radiation. Acta Cryst. A36, 436–442.Google Scholar