| Summary: | 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 (Mg3Al2-Si3O12) 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, ro(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 Do(3+) for a fictive trivalent element J3+, with radius ro(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 Do(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 Do(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 ro(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.
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