Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 5.1, p. 538   | 1 | 2 |

Section Departure from Bragg's law of the incident wave

A. Authiera*

aLaboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France
Correspondence e-mail: Departure from Bragg's law of the incident wave

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The wavefields excited in the crystal by the incident wave are determined by applying the boundary condition mentioned above for the continuity of the tangential component of the wavevectors (Section[link]). Waves propagating in a vacuum have wavenumber [k = 1/\lambda]. Depending on whether they propagate in the incident or in the reflected direction, the common extremity, M, of their wavevectors [{\bf OM} = {\bf K}_{{\bf o}}^{(a)} \hbox{ and } {\bf HM} = {\bf K}_{{\bf h}}^{(a)}] lies on spheres of radius k and centred at O and H, respectively. The intersections of these spheres with the plane of incidence are two circles which can be approximated by their tangents [T'_{o}] and [T'_{h}] at their intersection point, [L_{a}], or Laue point (Fig.[link].


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Departure from Bragg's law of an incident wave.

Bragg's condition is exactly satisfied according to the geometrical theory of diffraction when M lies at [L_{a}]. The departure Δθ from Bragg's incidence of an incident wave is defined as the angle between the corresponding wavevectors OM and [{\bf OL}_{a}]. As Δθ is very small compared to the Bragg angle in the general case of X-rays or neutrons, one may write [\eqalign{{\bf K}_{{\bf o}}^{(a)} &= {\bf OM} = {\bf OL}_{a} + {\bf L}_{a}{\bf M},\cr \Delta \theta &= \overline{L_{a}M} / k.} \eqno(]

The tangent [T'_{o}] is oriented in such a way that Δθ is negative when the angle of incidence is smaller than the Bragg angle.

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