A predictive thermodynamic model of garnet-melt trace element partitioning

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) bet ween garnet and anhydrous silicate melt as a function of pressure, temperat ure and bulk composition. The model for the magnesium partition coefficient , D-Mg, is based on a thermodynamic description of the pyrope (Mg3Al2Si3O12 ) melting reaction between garnet and melt. Simple activity-composition rel ations, which take explicit account of garnet non-ideality, link D-Mg to th e free energy of fusion (DeltaG(f)) of pure pyrope without the need to invo ke non-ideality in the liquid phase. The resulting predictive equation, bas ed on the compositions of a large set (n = 160) of published garnet-melt pa irs, produces values of Dm, that are within 20% of measured values at tempe ratures between 1,450 and 1,930 degreesC, and pressures between 2.5 and 7.5 GPa. The model for trivalent (3+) trace elements is based on the lattice s train approach to partitioning, which describes mineral-melt partition coef ficients in terms of three parameters: the effective radius, r(0)(3+), of t he 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 D -0(3+) for a fictive trivalent element J(3+), with radius r(0)(3+) that doe s not strain the crystal lattice when entering the garnet X-site. Analogous to the model for D-Mg, simple activity-composition relations link D-0(3+) to AGI of a hypothetical garnet component incorporating a hypothetical rare earth element J(3+) through a YAG-type charge-balancing mechanism (J(3+)Mg (2)Al(3)Si(2)O(12)). Through analysis of existing garnet-melt rare earth el ement partitioning data (n = 18 garnet-melt pairs), an expression is derive d relating D-0(3+) to pressure, temperature and D-Mg. Predicted DREE/Y/Sc v alues agree to within 5-50 % of experimental measurements for all elements except La and Ce, which are liable to large experimental errors, spanning p ressures between 2.5 and 5.0 GPa and temperatures between 1,430 and 1,640 d egreesC. In conjunction with our new parameterisation for D-Mg and previous ly published equations linking r(0)(3+) and E-X(3+) to garnet major element composition, this model gives a description of trivalent REE, Y, In and Se partitioning between garnets and anhydrous melts over a range of pressures , temperatures and compositions relevant to melting of garnet-bearing sourc es in the Earth's upper mantle.