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 γFeSSph, 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 γFeSSph 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.