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 (∆Gf) 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 ∆Gf 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.