International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 253

Section 4.2.6.3.3.3. Accuracy in the tables of dispersion corrections

D. C. Creaghb

4.2.6.3.3.3. Accuracy in the tables of dispersion corrections

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Experimentalists must be aware of two potential sources of error in the values of [f'(\omega,0)] listed in Table 4.2.6.5[link]. One is computational, arising from the error in calculating the relativistic correction. Stibius-Jensen (1980[link]) has suggested that this error may be as large as [\pm0.25(E_{\rm tot}/mc^2)]. This means, for example, that the real part of the dispersion correction [f'(\omega,0)] for lead at the wavelength of 0.55936 Å is −(1.168 ± 0.146). The effect of this error is to shift the dispersion curve vertically without distorting its shape. Note, however, that the direction of the shift is either up or down for all atoms: the effect of multipole cancellation and retardation will be in the same direction for all atoms.

The second possible source of error occurs because the position of the absorption edge varies somewhat depending on the oxidation state of the scattering atom. This has the effect of displacing the dispersion curve laterally. Large discrepancies may occur for those regions in which the dispersion corrections are varying rapidly with photon energy, i.e. near absorption edges.

It must also be borne in mind that in the neighbourhood of an absorption edge polarization effects may occur. The tables are valid only for average polarization.

References

First citation Stibius-Jensen, M. (1980). Atomic X-ray scattering factors for forward scattering beyond the dipole approximation. Personal communication.Google Scholar








































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