International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B, ch. 5.1, p. 538
Section 5.1.3.1. Departure from Bragg's law of the incident wave^{a}Laboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France |
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 5.1.2.3). Waves propagating in a vacuum have wavenumber . Depending on whether they propagate in the incident or in the reflected direction, the common extremity, M, of their wavevectors 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 and at their intersection point, , or Laue point (Fig. 5.1.3.1).
Bragg's condition is exactly satisfied according to the geometrical theory of diffraction when M lies at . The departure Δθ from Bragg's incidence of an incident wave is defined as the angle between the corresponding wavevectors OM and . As Δθ is very small compared to the Bragg angle in the general case of X-rays or neutrons, one may write
The tangent is oriented in such a way that Δθ is negative when the angle of incidence is smaller than the Bragg angle.