Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 5.1, p. 539   | 1 | 2 |

Section Deviation parameter

A. Authiera*

aLaboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France
Correspondence e-mail: Deviation parameter

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The solutions of dynamical theory are best described by introducing a reduced parameter called the deviation parameter, [\eta = (\Delta \theta - \Delta \theta_{o})/\delta, \eqno(] where [\delta = R\lambda^{2}|C|(|\gamma |F_{h}F_{\bar{h}})^{1/2}/(\pi V \sin 2\theta), \eqno(] whose real part is equal to the half width of the rocking curve (Sections 5.1.6[link] and 5.1.7[link]). The width 2δ of the rocking curve is sometimes called the Darwin width.

The definition ([link] of the deviation parameter is independent of the geometrical situation (reflection or transmission case); this is not followed by some authors. The present convention has the advantage of being quite general.

In an absorbing crystal, [\eta, \Delta \theta_{o}] and δ are complex, and it is the real part, [\Delta \theta_{or}], of [\Delta \theta_{o}] which has the geometrical interpretation given in Section[link]. One obtains [\eqalign{\eta &= \eta_{r} + i\eta_{i}\cr \eta_{r} &= (\Delta \theta - \Delta \theta_{or})/\delta_{r}\hbox{;} \ \eta_{i} = A\eta_{r} + B\cr A &= - \tan \beta\cr B &= \left\{\chi_{io}/\left[|C|(|\chi_{h} \chi_{\bar{h}}|)^{1/2} \cos \beta\right]\right\} (1 - \gamma)/2(|\gamma |)^{1/2},} \eqno(] where β is the phase angle of [(\chi_{h} \chi_{\bar{h}})^{1/2}] [or that of [(F_{h} F_{\bar{h}})^{1/2}]].

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