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, pp. 540-541
Section 5.1.3.7. Geometrical interpretation of the solution in the zero-absorption case^{a}Laboratoire de Minéralogie-Cristallographie, Université P. et M. Curie, 4 Place Jussieu, F-75252 Paris CEDEX 05, France |
In this case (Fig. 5.1.3.4) is +1 and (5.1.3.10) may be written
Let and be the intersections of the normal to the crystal surface drawn from the Lorentz point with the two branches of the dispersion surface (Fig. 5.1.3.4). From Sections 5.1.3.3 and 5.1.3.4, they are the tie points excited for and correspond to the middle of the reflection domain. Let us further consider the tangents to the dispersion surface at and and let , and , be their intersections with and , respectively. It can be shown that and intersect the dispersion surface at the tie points excited for and , respectively, and that the Pendellösung distance , the width of the rocking curve and the deviation parameter , where and are the intersections of the normal to the crystal surface drawn from the extremity of any incident wavevector OM with and , respectively.
In this case (Fig. 5.1.3.5) is now −1 and (5.1.3.10) may be written
Now, let and be the points of the dispersion surface where the tangent is parallel to the normal to the crystal surface, and further let and be the intersections of these two tangents with and , respectively. For an incident wave of wavevector OM where M lies between I′ and I″, the normal to the crystal surface drawn from M has no real intersection with the dispersion surface and defines the total-reflection domain. The tie points and correspond to and , respectively, the extinction distance , the width of the total-reflection domain and the deviation parameter , where and are the intersections with and of the normal to the crystal surface drawn from the extremity of any incident wavevector OM.