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

International Tables for Crystallography (2006). Vol. C, ch. 6.3, p. 600

Section 6.3.2. Dispersion

E. N. Maslena

aCrystallography Centre, The University of Western Australia, Nedlands, Western Australia 6009, Australia

6.3.2. Dispersion

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In the wavelength regime associated with anomalous scattering, where [f=\;f^0+f'+f'', \eqno (]the refractive index becomes complex, its imaginary component contributing an additional term to the absorption.

[f^0] is the scattering factor for ideal elastic scattering. The dispersion corrections f′ and f′′ are related to the absorption since (James, 1962[link]; Wagenfeld, 1975[link]) [f''(\omega) =mc\omega\sigma(\omega)/4\pi e^2, \quad \omega=2\pi c/\lambda \eqno (][f'(\omega)={2\over \pi}\, \int\limits^\infty_0\,[\omega'f''(\omega')/(\omega^2-\omega'^2)]\, {\rm d}\omega'. \eqno (]That is, the dispersion corrections are determined by the absorption cross sections. The relationships ([link] and ([link] can be used in measuring absorption coefficients, as described in Section 4.2.4[link] . The dispersion terms change rapidly near the absorption edge, especially on the short-wavelength side. The changes are anisotropic, sensitive to structure and to the direction of polarization. Details are given by Templeton & Templeton (1980[link], 1982[link], 1985[link]).

In near-perfect crystals, the changes near the absorption edge are also sensitive to temperature (Karamura & Fukamachi, 1979[link]; Fukamachi, Karamura, Hayakawa, Nakano & Koh, 1982[link]). The effective absorption coefficient can also be altered by the Borrmann effect (Azaroff, Kaplow, Kato, Weiss, Wilson & Young, 1974[link]).


Azaroff, L. V., Kaplow, R., Kato, N., Weiss, R. J., Wilson, A. J. C. & Young, R. A. (1974). X-ray diffraction, pp. 282–284. New York: McGraw-Hill.
Fukamachi, T., Karamura, T., Hayakawa, K., Nakano, Y. & Koh, F. (1982). Observation of effect of temperature on X-ray diffraction intensities across the In K absorption edge of InSb. Acta Cryst. A38, 810–813.
James, R. W. (1962). The optical principles of the diffraction of X-rays, pp. 135–192. Ithaca: Cornell University Press.
Karamura, T. & Fukamachi, T. (1979). Temperature dependence of X-ray reflection intensity from an absorbing perfect crystal near an absorption edge. Acta Cryst. A35, 831–835.
Templeton, D. H. & Templeton, L. K. (1980). Polarized X-ray absorption and double refraction in vanadyl bisacetylacetonate. Acta Cryst. A36, 237–241.
Templeton, D. H. & Templeton, L. K. (1982). X-ray dichroism and polarized anomalous scattering of the uranyl ion. Acta Cryst. A38, 62–67.
Templeton, D. H. & Templeton, L. K. (1985). Tensor optical properties of the bromate ion. Acta Cryst. A41, 133–142.
Wagenfeld, H. (1975). Theoretical computations of X-ray dispersion corrections. Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 13–24. Copenhagen: Munksgaard.

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