The reflexion of X-rays from the ‘anti-phase nuclei’ of AuCu 3

Abstract

Jones & Sykes have observed that the superlattice lines in X-ray photographs of AuCu$_{3}$ are not always as sharp as the main lines, and that the broadening depends markedly on the indices of the line. They explain these phenomena by assuming that the crystals of AuCu$_{3}$ contain many 'anti-phase nuclei' in which the superlattice is organized in different ways. In the present paper it is shown that the integral breadth of a reflexion from a crystal in which all the unit cells are not the same is $\lambda $J$_{0}$/cos $\theta \int $J$_{t}$ dt, where J$_{t}$ is the mean value of the product FF$^{\ast}$ of the structure factors of two unit cells separated a distance t in the hkl direction. Detailed calculations are made of the broadening to be expected from five different ways in which the nuclei can 'change step'. Closest agreement with the observed broadening is given by a manner of 'changing step' in which the gold atoms avoid one another.