A predictive thermodynamic model of garnet–melt trace element partitioning

Abstract

We have developed a predictive model for the partitioning of magnesium and a range of trivalent trace elements (rare earth elements, Y, In and Sc) between garnet and anhydrous silicate melt as a function of pressure, temperature and bulk composition. The model for the magnesium partition coefficient, DMg, is based on a thermodynamic description of the pyrope (Mg3Al2Si3O12) melting reaction between garnet and melt. Simple activity–composition relations, which take explicit account of garnet non-ideality, link DMg to the free energy of fusion (ΔGf) of pure pyrope without the need to invoke non-ideality in the liquid phase. The resulting predictive equation, based on the compositions of a large set (n=160) of published garnet–melt pairs, produces values of DMg that are within 20% of measured values at temperatures between 1,450 and 1,930 °C, and pressures between 2.5 and 7.5 GPa. The model for trivalent (3+) trace elements is based on the lattice strain approach to partitioning, which describes mineral–melt partition coefficients in terms of three parameters: the effective radius, r0(3+), of the site on which partitioning takes place (in this case, the garnet X-site); the apparent site Young's modulus EX(3+); and the partition coefficient D0(3+) for a fictive trivalent element J3+, with radius r0(3+), that does not strain the crystal lattice when entering the garnet X-site. Analogous to the model for DMg, simple activity–composition relations link D0(3+) to ΔGf of a hypothetical garnet component incorporating a hypothetical rare earth element J3+ through a YAG-type charge-balancing mechanism (J3+Mg2Al3Si2O12). Through analysis of existing garnet–melt rare earth element partitioning data (n=18 garnet–melt pairs), an expression is derived relating D0(3+) to pressure, temperature and DMg. Predicted DREE/Y/Sc values agree to within 5–50% of experimental measurements for all elements except La and Ce, which are liable to large experimental errors, spanning pressures between 2.5 and 5.0 GPa and temperatures between 1,430 and 1,640 °C. In conjunction with our new parameterisation for DMg, and previously published equations linking r0(3+) and EX(3+) to garnet major element composition, this model gives a description of trivalent REE, Y, In and Sc partitioning between garnets and anhydrous melts over a range of pressures, temperatures and compositions relevant to melting of garnet-bearing sources in the Earth's upper mantle.