Thermodynamics of aluminosilicate garnet solid solution: New experimental data, an optimized model, and thermometric applications

We have experimentally determined the displacement of the equilibrium Grossular + 2 Kyanite + Quartz ⇄ 3 Anorthite (GASP) as a function of garnet composition in the systems Mg-Ca-Mn, Fe-Mg-Ca and Fe-Mg-Ca-Mn at 1000°C. The results were treated along with selected experimental and observational data available in the literature as well as binary parameters from other workers to obtain a set of mutually compatible binary mixing parameters of the quaternary (Fe,Mg,Ca,Mn)- aluminosilicate garnet solid solution. Attempts to determine equilibrium garnet composition in the GASP equilibrium in the Ca-Mg binary were unsuccessful due to the formation of pyroxene. Calculations of binary and ternary miscibility gaps show that the P,T,X combination required for unmixing of garnet solid solution is not realized by natural samples. The solution model was applied to account for compositional effects on Fe-Mg exchange between garnet and ortho- or clinopyroxene. Applications of the revised thermometric formulations to selected natural assemblages yield P-T conditions which are much less sensitive to compositional effects compared to the other available formulations, and are consistent with independent constraints. ΔV̄ and ΔV°: Partial molar volume change and end-member molar volume change of a reaction, respectively. W_ij^G, W_ij^H, and W_ij^S: Subregular free energy, enthalpic and entropie binary interaction parameter, respectively, between the components i and j. W^G(i-j), W^H(i-j), and W^s(i-j): Regular solution or simple mixture free energy, enthalpic and entropie interaction parameter, respectively, between the components i and j. ΔW₁: W(Mg-i) - W(Fe-i). X₁^α: Atomic fraction of the component i in the phase α in the site of mixing.