On the statistical dynamical theory of diffraction: application to silicon

Abstract

A detailed solution of Kato's equations describing the propagation of X-rays or neutrons in a crystal containing a statistical distribution of imperfections is presented: this solution makes use of propagation operators to describe multiple scattering events. Corrections to Kato's original solution are given which have a significant effect, even in the case of crystals with a high degree of long-range perfection. The present modified solution is applied to experimental measurement on parallel plates of silicon with different dislocation densities by Olekhnovich, Karpei, Olekhnovich & Puzenkova [Acta Cryst. (1983), A39, 116-122]. The theory reproduces observations quite well, in contrast to conclusions reached by Olekhnovich et al. on the basis of the original solution. It can be inferred that the basic ideas of Kato allow for a correct interpretation of diffraction reflectivities in highly perfect crystals, where a significant contribution from incoherent components of scattered intensities must be incorporated. However, the theory has to be modified for the case of lower long-range perfection: this involves the modification of the expressions for the effective correlation lengths that enter the theory.