Approximate solution of the Takagi-Taupin equations for a semi-infinite crystal in the three-beam Laue-Laue case.

Abstract

An analytical approximate solution of the Takagi-Taupin equations for a symmetrical three-beam Laue-Laue case in a perfect non-absorbing semi-infinite crystal slab has been obtained. The expression, a second-order expansion, is valid for situations where the effective crystal thickness does not exceed half the actual extinction length and it is shown to be in perfect agreement with the full numerical solution of the fundamental equations.