Computer Simulation of Modulated Structures and Diffuse Scattering inB8-type (Co, Ni, Cu)_1+x(Ge, Sn) Phases

The compounds (Co, Ni)(Ge, Sn) and Cu_1+xhave hexagonal average structures intermediate between those of NiAs and Ni₂In. Ordering of atoms and vacancies in the partially occupiedA′ sites produces a variety of superstructures of lower symmetry. In the structures of this study, the modulation vector is always in the (hhl) plane. Diffuse scattering observed in some cases implies the occurrence of short-range order only. The effect of two-site interactions on determining the preferred long-range and short-range ordering patterns was investigated by using a Monte Carlo simulation technique to generate two-dimensional arrays of "atoms" and "vacancies" and calculating the corresponding scattering patterns. It is shown that many of the 18 symmetrically distinct first- and second-nearest-neighbor interaction energies are nonzero in these systems but that the preferred ordering pattern is in most cases determined by variation in only three second-nearest-neighbor terms. These three parameters vary with both composition and temperature. The undulating diffuse streaks observed in electron diffraction in the Sn-bearing and Co-Ge systems are shown to arise from a combination of negligible interactions along z, strong interactions in the xy plane, and weak diagonal interactions.