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. 539
Section 5.1.3.3. Middle of the reflection domain
a
Laboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France |
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, , with (Figs. 5.1.3.4 and 5.1.3.5), while, according to Bragg's law, it should be . The angle Δθ between the incident wavevectors and OI, corresponding to the middle of the reflecting domain according to the geometrical and dynamical theories, respectively, is
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 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, is equal to zero for symmetric reflections .