Diffuse scattering of X-rays by crystals - The Faxén-Waller theory and the surfaces of isodiffusion for cubic crystals

An elementary derivation is given of the Faxen-Waller formula for the diffuse scattering of X-rays by thermally excited lattice vibrations and the shapes of the surfaces of isodiffusion in reciprocal space for cubic crystals investigated. It is shown that for substances with high elastic anisotropy large deviations from spherical character are to be expected for the surfaces of isodiffusion belonging to each of the individual lattice planes and, moreover, marked differences in shape between surfaces belonging to different lattice planes. The theory is illustrated by calculations made for a single crystal of sodium.