A Theoretical Study of the Diffuse Scattering of X-Rays by Crystals

Abstract

A new derivation is made of the intensity expression for the coherent scattering of x-rays by a small crystal. The accepted intensity formula for the diffuse scattering—the well-known Debye formula—is shown to be incorrect and is replaced by a more complicated expression. According to the revised theory the intensity of the diffuse scattering varies much more rapidly with the scattering direction and exhibits a series of diffraction maxima. These maxima are found in the directions ${\mathrm{k}}_m$ satisfying equations of the type $(1+\lambda {\tau }_{min}){\mathrm{k}}_m={\mathrm{k}}_0+{\mathrm{B}}_H$, where ${\mathrm{k}}_{\mathrm{o}}$ is the direction of incidence (with $k_m=k_0=\frac{1}{\lambda }$, the reciprocal wave-length) and ${\mathrm{B}}_H$ a reciprocal lattice vector. The consequences of the theory are discussed in detail.