On the asymmetric limits for the scattering of X-rays from imperfect crystals in the Bragg case

It is pointed out that there is some uncertainty as to the correct behaviour of the integrated reflectivity as a function of the degree of asymmetry for the scattering of X-rays from imperfect crystals in the extremely asymmetric Bragg case. Numerical calculations based on the Takagi-Taupin equations are exemplified and indicate that the integrated reflectivity for such crystals tends asymptotically to the perfect-crystal result in the asymmetric limits, the perfect-crystal result, in turn, tends to the kinematical value at these limits, as has been shown previously. In addition, comments are offered on the relevance of the present work to the study of highly imperfect crystals by section topography, and in particular to the study of the near-surface grain-boundary structure of crystals.