InternationalReciprocal spaceTables for Crystallography Volume B Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B. ch. 2.3, p. 246
## Section 2.3.4.1. Introduction |

The physical basis for anomalous dispersion has been well reviewed by Ramaseshan & Abrahams (1975), James (1965), Cromer (1974) and Bijvoet (1954). As the wavelength of radiation approaches the absorption edge of a particular element, then an atom will disperse X-rays in a manner that can be defined by the complex scattering factor where is the scattering factor of the atom without the anomalous absorption and re-scattering effect, is the real correction term (usually negative), and is the imaginary component. The real term is often written as *f*′, so that the total scattering factor will be . Values of and are tabulated in *IT* IV (Cromer, 1974), although their precise values are dependent on the environment of the anomalous scatterer. Unlike , and are almost independent of scattering angle as they are caused by absorption of energy in the innermost electron shells. Thus, the anomalous effect resembles scattering from a point atom.

The structure factor of index **h** can now be written as (Note that the only significant contributions to the second term are from those atoms that have a measurable anomalous effect at the chosen wavelength.)

Let us now write the first term as and the second as . Then, from (2.3.4.1), Therefore, and similarly demonstrating that Friedel's law breaks down in the presence of anomalous dispersion. However, it is only for noncentrosymmetric reflections that .

Now, Hence, by using (2.3.4.2) and simplifying, The first term in (2.3.4.3) is the usual real Fourier expression for electron density, while the second term is an imaginary component due to the anomalous scattering of a few atoms in the cell.

### References

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*The optical principles of the diffraction of X-rays.*Ithaca: Cornell University Press.Google Scholar

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