Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

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

Section Solution of the dynamical theory

A. Authiera*

aLaboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France
Correspondence e-mail: 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, ([link], with the normal Mz to the crystal surface (Figs.[link] and[link]). The ratio ξ of the amplitudes of the waves of the corresponding wavefields is related to these coordinates by ([link] 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(] 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).

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