In Part I (Vinograd, 2002) the relationship between temperature, composition and free energy of the diopside–jadeite solid solution was described using a CVM model. Here the same relationship is described using a combination of Redlich-Kister (RK) polynomials and Gaussian functions. The use of the Gaussians permits an accurate description of the free energy dip centred at Jd50, which is caused by the long-range ordering, while the effect of the short-range ordering can be easily modelled using the RK polynomial The simplified RK-Gaussian description is extended to the three-component diopside–jadeite–hedenbergite solid solution. The polynomial description permits an easy incorporation of the derived activity-composition relations into phase-equilibrium computation software.

Solution calorimetry and phase equilibrium data for the diopside–jadeite system are assessed using a combination of the cluster variation method (CVM) and Redlich-Kister (RK) polynomial expansion. The CVM is used to model part of the free energy of mixing which depends on short-range order (SRO) and long-range order (LRO) effects. The SRO/LRO independent part of the free energy is modelled using an RK polynomial. The parameters of the RK and CVM models are obtained through the fit to the experimental data. The best-fit parameters are used to calculate activity-composition relations and a temperature-composition phase diagram of the diopside–jadeite system.

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.