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

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

Section 5.1.3.3. Middle of the reflection domain

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

5.1.3.3. Middle of the reflection domain

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It will be apparent from the equations given later that the incident wavevector corresponding to the middle of the reflection domain is, in both cases, OI, where I is the intersection of the normal to the crystal surface drawn from the Lorentz point, [L_{o}], with [T'_{o}] (Figs. 5.1.3.4[link] and 5.1.3.5[link]), while, according to Bragg's law, it should be [{\bf OL}_{a}]. The angle Δθ between the incident wavevectors [{\bf OL}_{a}] and OI, corresponding to the middle of the reflecting domain according to the geometrical and dynamical theories, respectively, is [\Delta \theta_{o} = \overline{L_{a}I}/k = R\lambda^{2} F_{o}(1 - \gamma)/(2\pi V \sin 2\theta). \eqno(5.1.3.4)]

[Figure 5.1.3.4]

Figure 5.1.3.4 | top | pdf |

Boundary conditions at the entrance surface for transmission geometry.

[Figure 5.1.3.5]

Figure 5.1.3.5 | top | pdf |

Boundary conditions at the entrance surface for reflection geometry. (a) Reciprocal space; (b) direct space.

In the Bragg case, the asymmetry ratio γ is negative and [\Delta \theta_{o}] is never equal to zero. This difference in Bragg angle between the two theories is due to the refraction effect, which is neglected in geometrical theory. In the Laue case, [\Delta \theta_{o}] is equal to zero for symmetric reflections [(\gamma = 1)].








































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