International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 5.1, p. 545   | 1 | 2 |

Section 5.1.6.6. Thin crystals – comparison with geometrical theory

A. Authiera*

aLaboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France
Correspondence e-mail: authier@lmcp.jussieu.fr

5.1.6.6. Thin crystals – comparison with geometrical theory

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Using (5.1.6.6)[link] and (5.1.6.7)[link], the reflecting power of the reflected beam may also be written [I_{h} = \pi^{2} t^{2} \Lambda_{o}^{-2} f(\eta),] where [f(\eta) = \left[{\sin U(1 + \eta^{2})^{1/2} \over U(1 + \eta^{2})^{1/2}}\right]^{2}] and [U = \pi t \Lambda_{o}^{-1}.] When [t \Lambda_{o}^{-1}] is very small, [f(\eta)] tends asymptotically towards the function [f_{1}(\eta) = \left[{\sin U\eta \over U\eta}\right]^{2}] and [I_{h}] towards the value given by geometrical theory. The condition for geometrical theory to apply is, therefore, that the crystal thickness be much smaller than the Pendellösung distance. In practice, the two theories agree to within a few per cent for a crystal thickness smaller than or equal to a third of the Pendellösung distance [see Authier & Malgrange (1998[link])].

References

Authier, A. & Malgrange, C. (1998). Diffraction physics. Acta Cryst. A54, 806–819.Google Scholar








































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