Absorbing crystals

Authier, A.

doi:10.1107/97809553602060000569

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

pdf | chapter contents | chapter index | related articles

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

Section 5.1.6.5.2. Absorbing crystals

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

5.1.6.5.2. Absorbing crystals

| top | pdf |

The integration was performed for absorbing crystals by Kato (1955). The integrated intensity in this case is given by $[\eqalign{I_{hi} &= A |F_{h}/F_{\bar{h}}| \exp \left[-1/2 \mu_{o} t (\gamma_{o}^{-1} + \gamma_{h}^{-1})\right]\cr &\quad \times \left[\textstyle\int\limits_{0}^{2\pi t\Lambda_{L}^{-1}} J_{0}(z) \hbox{ d}z - 1 + I_{0} (\zeta)\right],}]$ where $[\zeta = \mu_{o} t \left\{\left[\left|C\right|^{2} |F_{ih}/F_{io}|^{2} \cos^{2} \varphi + (\gamma_{h} - \gamma_{o})/(4\gamma_{o} \gamma_{h})\right] / (\gamma_{o} \gamma_{h})\right\}^{1/2}]$ and $[I_{0} (\zeta)]$ is a modified Bessel function of zeroth order.

References

Kato, N. (1955). Integrated intensities of the diffracted and transmitted X-rays due to ideally perfect crystal. J. Phys. Soc. Jpn, 10, 46–55.Google Scholar

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