Summary

Creagh, D. C.

doi:10.1107/97809553602060000592

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

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 258

Section 4.2.6.3.3.5. Summary

D. C. Creagh^b

4.2.6.3.3.5. Summary

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For the imaginary part of the dispersion correction $[f''(\omega,{\boldDelta})]$ , the following observations can be made.

(i) Measurements of the linear absorption coefficient $[\mu_l]$ from which $[f'(\omega,0)]$ is deduced should follow the recommendations set out in Subsection 4.2.3.2.
(ii) There is no rational basis for preferring one set of relativistic calculations of atomic scattering cross sections over another, as Creagh & Hubbell (1987, 1990) and Kissel et al. (1980) have shown.
(iii) The total scattering cross section for an ensemble of atoms is not simply the sum of the individual scattering cross sections in the neighbourhood of an absorption edge and therefore $[f'(\omega,0)]$ will fluctuate as $[\omega\rightarrow\omega_\kappa]$ .
(iv) There is no dependence of $[f''(\omega,{\boldDelta})]$ and $[{\boldDelta}]$ .

For the real part of the dispersion correction $[f'(\omega,{\boldDelta})]$ , the following observations can be made.

(i) The relativistic multipole values listed here tend to accord better with experiment than the non-relativistic and relativistic dipole values.
(ii) There is no dependence of $[f'(\omega,{\boldDelta})]$ on $[{\boldDelta}]$ .
(iii) The theoretical tables are calculated for averaged polarizations.
(iv) Experimentalists wishing to compare their data with theoretical predictions should take account of the energy bandpass of their system when determining the appropriate theoretical value. They should also be aware of the fact that the position of the absorption edge depends on the oxidation state of the scattering atom, and that there is an inaccuracy in the tables of $[f'(\omega,0)]$ of either $[+0.20(E_{\rm tot}/mc^2)]$ or $[-0.10(E_{\rm tot}/mc^2)]$ .

References

Creagh, D. C. & Hubbell, J. H. (1987). Problems associated with the measurement of X-ray attenuation coefficients. I. Silicon. Acta Cryst. A43, 102–112.Google Scholar

Creagh, D. C. & Hubbell, J. H. (1990). Problems associated with the measurement of X-ray attenuation coefficients. II. Carbon. Acta Cryst. A46, 402–408.Google Scholar

Kissel, L., Pratt, R. H. & Roy, S. C. (1980). Rayleigh scattering by neutral atoms, 100 eV to 10 MeV. Phys. Rev. A, 22, 1970–2004.Google Scholar

International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 258