Garnet-spinel-olivine-orthopyroxene equilibria in the FeO-MgO-Al2O3-SiO2-Cr2O3 system: II. Thermodynamic analysis

Abstract

Experimental results for the four-phase assemblage in the MASCr (Doroshev et al., 1997) and FMASCr (Brey et al., 1999) systems are evaluated with respect to exchange (Fe-Mg and Cr-Al) and displaced equilibrium reactions (Al solubility in orthopyroxene and spinel-orthopyroxene to garnet-olivine transition). These equilibria are considered on the basis of the thermodynamic data of Berman (1988). The effects of non-ideal mixing in solid solutions is approximated by a subregular Margules formulation, independent for each site of spinel, garnet, and orthopyroxene solid solutions. Mixing parameters were calculated by linear programming considering each experimental point as an independent half-bracket for the concentration term in the respective equilibrium. Cr-Al mixing in all phases is not ideal, but the magnitudes of excess mixing energies are not large. Spinel solid solution shows asymmetric Cr-Al and Mg-Fe excess mixing energy. Cr-Al mixing in garnet is close to an ideal model with a symmetric Margules parameter 0 to 6 kJ/mol. Standard state properties of knorringite, Mg 3 Cr 2 Si 3 O 12 and orthopyroxene end-member MgCrAlSiO 6 are estimated. The major factor determining concentration dependencies of equilibrium constants is the Gibbs free energy changes of reciprocal reactions FeCr+MgAl = FeAl+MgCr in spinel and garnet. The derived thermodynamic parameters are used to calculate phase relationships in the four-mineral region of the FMASCr system, which models depleted mantle harzburgite. The Cr/(Cr+Al) ratio of garnet increases with both pressure and temperature, while that of spinel depends mainly on pressure. The distribution of Cr and Al between spinel and garnet in equilibrium with orthopyroxene and olivine may be used as a thermobarometer for deep mantle xenoliths and inclusions in diamonds.