An integrated thermodynamic mixing model for sphalerite geobarometry from 300 to 850°C and up to 1 GPa

An asymmetric, Margules-type, solid solution model was used to model the mixing behavior of Fe-Zn sphalerites. The model is based on an analysis of experimental results from fifteen independent data sources. After a careful, stepwise, analysis of the available runs, the solid solution model was constrained using a refined experimental database of 279 experiments which were simultaneously regressed to obtain the excess parameters and a general geobarometric equation. The model indicates that, when pressures are low, the value of γ_FeS^Sph, which is always greater than one, is higher at low FeS contents and an increase in temperature causes it to decline. However, for certain compositions γ_FeS^Sph values might be slightly less at low T than at high T. This behavior is corrected when pressure increases, regardless of the composition. The excess Gibbs free energy has positive values at any P&T while it is asymmetric. Pressure increases the value of the excess free energy. On the other hand, the Gibbs free energy of mixing is always negative, with a single minimum that tends to move towards Fe-poorer compositions as the pressure goes up. An increase in temperature leads to a more negative Gibbs free energy mixing function suggesting that increasingly Fe-poorer sphalerite would be expected at high temperatures and pressures. The application of the solid solution model to a selection of case-studies provided results which are consistent with independent pressure estimates. However, the pressure determinations for sphalerite + pyrite + pyrrhotite and sphalerite + pyrrhotite assemblages are very sensitive to uncertainties in the composition of the phases involved and, to a lesser extent, to temperature. The results of the application of the model to a field case (scheelite-mineralized Hercynian veins from the Central Pyrenees) were also consistent when compared with independent pressure-constraining silicate assemblages. Thus, the solid solution model described in this paper provides a workable framework with which to compute the pressures of the formation of rocks over a wide range of geological conditions.