Solution of the dynamical theory

Authier, A.

doi:10.1107/97809553602060000569

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

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International Tables for Crystallography (2006). Vol. B. ch. 5.1, p. 540 | 1 | 2 |

Section 5.1.3.6. Solution of the dynamical theory

A. Authier^a ^*

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

5.1.3.6. Solution of the dynamical theory

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The coordinates of the tie points excited by the incident wave are obtained by looking for the intersection of the dispersion surface, (5.1.2.22), with the normal Mz to the crystal surface (Figs. 5.1.3.4 and 5.1.3.5). The ratio ξ of the amplitudes of the waves of the corresponding wavefields is related to these coordinates by (5.1.2.24) and is found to be $[\eqalign{\xi_{j} &= D_{hj}/D_{oj}\cr &= -\hbox{S}(C)\hbox{S} (\gamma_{h}) [(F_{h} F_{\bar{h}})^{1/2} / F_{\bar{h}}]\cr &\quad \times \left\{\eta \pm \left[\eta^{2} + \hbox{S} (\gamma_{h})\right]^{1/2}\right\} / (|\gamma |)^{1/2},} \eqno(5.1.3.10)]$ where the plus sign corresponds to a tie point on branch 1 (j = 1) and the minus sign to a tie point on branch 2 (j = 2), and $[\hbox{S}(\gamma_{h})]$ is the sign of $[\gamma_{h}]$ (+1 in transmission geometry, −1 in reflection geometry).

References

International Tables for Crystallography (2006). Vol. B. ch. 5.1, p. 540