Diffuse X-ray scattering from cubic ZnS crystals having substitutional elastic distortion centres

Diffuse X-ray scattering is studied theoretically from a crystal of cubic ZnS having distortion centres at the sulphur sites (having T_d symmetry). The atomic displacement due to a distortion centre is expressed as a sum of components consisting of radial functions combined with the appropriate Kubic Harmonics (KH) of Von der Lage & Bethe [Phys. Rev. (1947), 71, 612- 622]. The final expression for the intensity from the distorted crystal is used to study the shape of the diffuse spot around the (0,0,l) reciprocal lattice point. For isotropic distortion, the diffuse spot has cylindrical symmetry about the reciprocal z axis and there is no diffuse intensity in the reciprocal plane passing through (0,0,l) and normal to the z axis. For anisotropic distortion, however, the diffuse spot has fourfold symmetry about the reciprocal z axis. In particular, the reciprocal plane normal to the z axis and passing through (0,0,l) has four diffuse regions midway between the reciprocal x and y axes.