A new derivation of the Darwin-Prins formula of X-ray reflection

Abstract

In this paper is described a new derivation of the formulæ for the reflection of X-rays by perfect crystals, which forms an alternative approach to the problem to that adopted by Darwin and Prins. It consists in obtaining a solution of the difference equations which occur in the problem for a crystal containing a finite number (n) of laminations. The case of a crystal of infinite depth is obtained from this by proceeding to the limit when n→∞. The formulae thus obtained are identical with those of Prins for an absorbing crystal, while for a non-absorbing crystal, the width of the region of perfect reflection is in agreement with Darwin's value. However, there is a difference in the formulae for the variation of intensity with angle outside this region. This has been shown to be due to an assumption made by Darwin which is not altogether justifiable.