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

International Tables for Crystallography (2006). Vol. C, ch. 6.4, p. 612

Section 6.4.13.3. The absorbing crystal

T. M. Sabinea

aANSTO, Private Mail Bag 1, Menai, NSW 2234, Australia

6.4.13.3. The absorbing crystal

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Only the Bragg case for thick crystals will be considered here. The asymptotic values of A, B, and C are [1/(2\mu L^{*})], [1/(\mu L^{*})], and [2/(\mu L^{*})], respectively, so that [ BCx=2N_{{c}}^2\lambda ^2F^2/\mu ^2. \eqno (6.4.13.4)]For BCx small, the integrated intensity, [I_{{B}}], is given by [ I_{{B}}=(Q_\theta /2\mu)[1-(N_{{c}}F/)2]V^{2/3}. \eqno (6.4.13.5)]For BCx large, [ I_{{B}}=(1/2\sqrt {2})[1-(\mu /2\lambda N_{{c}}F)^2]\lambda ^2N_{{\rm c}}FV^{2/3}/\sin 2\theta. \eqno (6.4.13.6)]It can be shown that the parameter g (which has no relation to the parameter g used to describe the mosaic-block distribution) used by Zachariasen (1945[link]) in discussing this case is equal to −μ/2NCF. Hence, on his y scale, [ I_{{B}}=(\pi /2\sqrt {2})[1-g^2]. \eqno (6.4.13.7)]The value he obtained is IB = 8/3[1 − 2|g|], while Sabine & Blair (1992[link]) found IB = 8/3[1 − 2.36|g|].

References

Sabine, T. M. & Blair, D. G. (1992). The Ewald and Darwin limits obtained from the Hamilton–Darwin energy transfer equations. Acta Cryst. A48, 98–103.
Zachariasen, W. H. (1945). Theory of X-ray diffraction in crystals. New York: John Wiley, Dover.








































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