We have developed a cluster variation method (CVM) model based on cuboctahedral and octahedral basis clusters containing 13 and 6 atoms, respectively, and applied it to the analysis of the thermodynamic mixing properties of (Zn,Fe)S solid solutions. The model, in which the internal energy of the lattice is approximated by next to nearest neighbour (nnn) pair interactions and many-body interactions associated with nearest neighbour (nn) equilateral triangles, describes the FeS contents of sphalerites equilibrated with pyrrhotite and pyrite, and with pyrrhotite and iron metal within experimental uncertainties. The model predicts moderate deviations from ideality; the mean values of the Lewis and Randall activity coefficient of FeS and ZnS are, 1.48 and 1.03, respectively. Predictions of the model are in qualitative agreement with cell-edge data. The model also predicts that sphalerites undergo long-range ordering to lower-symmetry structures at temperatures only slightly below those investigated experimentally, a result in agreement with inferences from an existing Mössbauer investigation of synthetic sphalerites.
More realistic models in which interactions are ascribed to larger species (nn triangular and centred square species) predict that such long-range ordering occurs at even higher temperatures and underscore the need for better characterization of the structures of (Zn,Fe)S minerals.