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. 546547
Section 5.1.7.2.1. Nonabsorbing crystals^{a}Laboratoire de MinéralogieCristallographie, Université P. et M. Curie, 4 Place Jussieu, F75252 Paris CEDEX 05, France 
Boundary conditions. If the crystal is thin, the wavefield created at the reflecting surface at A and penetrating inside can reach the back surface at B (Fig. 5.1.7.4a). The incident direction there points towards the outside of the crystal, while the reflected direction points towards the inside. The wavefield propagating along AB will therefore generate at B:

Bragg case: thin crystals. Two wavefields propagate in the crystal. (a) Direct space; (b) reciprocal space. 
The corresponding tiepoints are obtained by applying the usual condition of the continuity of the tangential components of wavevectors (Fig. 5.1.7.4b). If the crystal is a planeparallel slab, these points are M and , respectively, and .
The boundary conditions are then written:
Rocking curve. Using (5.1.3.10), it can be shown that the expressions for the intensities reflected at the entrance surface and transmitted at the back surface, and , respectively, are given by different expressions within total reflection and outside it:
Integrated intensity. The integrated intensity is where t is the crystal thickness. When this thickness becomes very large, the integrated intensity tends towards
This expression differs from (5.1.7.3) by the factor π, which appears here in place of . von Laue (1960) pointed out that because of the differences between the two expressions for the reflecting power, (5.1.7.2) and (5.1.7.7b), perfect agreement could not be expected. Since some absorption is always present, expression (5.1.7.3), which includes the factor , should be used for very thick crystals. In the presence of absorption, however, expression (5.1.7.8) for the reflected intensity for thin crystals does tend towards that for thick crystals as the crystal thickness increases.
Comparison with geometrical theory. When is very small (thin crystals or weak reflections), (5.1.7.8) tends towards which is the expression given by geometrical theory. If we call this intensity (geom.), comparison of expressions (5.1.7.8) and (5.1.7.10) shows that the integrated intensity for crystals of intermediate thickness can be written which is the expression given by Darwin (1922) for primary extinction.
References
Batterman, B. W. & Hildebrandt, G. (1967). Observation of Xray Pendellösung fringes in Darwin reflection. Phys. Status Solidi, 23, K147–K149.Batterman, B. W. & Hildebrandt, G. (1968). Xray Pendellösung fringes in Darwin reflection. Acta Cryst. A24, 150–157.
Darwin, C. G. (1922). The reflection of Xrays from imperfect crystals. Philos. Mag. 43, 800–829.
Laue, M. von (1960). RöntgenstrahlInterferenzen. Frankfurt am Main: Akademische Verlagsgesellschaft.