Effect of Fe on garnet–melt trace element partitioning: experiments in FCMAS and quantification of crystal-chemical controls in natural systems

Garnet–melt trace element partitioning experiments were performed in the system FeO–CaO–MgO–Al₂O₃–SiO₂ (FCMAS) at 3 GPa and 1540°C, aimed specifically at studying the effect of garnet Fe²⁺ content on partition coefficients (D^Grt/Melt). D^Grt/Melt, measured by SIMS, for trivalent elements entering the garnet X-site show a small but significant dependence on garnet almandine content. This dependence is rationalised using the lattice strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal–melt partition coefficients from elastic moduli. Nature 372, 452–454], which describes partitioning of an element i with radius r_i and valency Z in terms of three parameters: the effective radius of the site r₀(Z), the strain-free partition coefficient D₀(Z) for a cation with radius r₀(Z), and the apparent compressibility of the garnet X-site given by its Young's modulus E_X(Z). Combination of these results with data in Fe-free systems [Van Westrenen, W., Blundy, J.D., Wood, B.J., 1999. Crystal-chemical controls on trace element partitioning between garnet and anhydrous silicate melt. Am. Mineral. 84, 838–847] and crystal structure data for spessartine, andradite, and uvarovite, leads to the following equations for r₀(3+) and E_X(3+) as a function of garnet composition (X) and pressure (P):

r₀(3+) [Å]=0.930X_Py+0.993X_Gr+0.916X_Alm+0.946X_Spes+1.05(X_And+X_Uv)−0.005(P [GPa]−3.0)(±0.005 Å)

E_X(3+) [GPa]=3.5×10¹²(1.38+r₀(3+) [Å])^−26.7(±30 GPa)

Accuracy of these equations is shown by application to the existing garnet–melt partitioning database, covering a wide range of P and T conditions (1.8 GPa<P<5.0 GPa; 975°C<T<1640°C). D^Grt/Melt for all 3+ elements entering the X-site (REE, Sc and Y) are predicted to within 10–40% at given P, T, and X, when D^Grt/Melt for just one of these elements is known. In the absence of such knowledge, relative element fractionation (e.g. D_Sm^Grt/Melt/D_Nd^Grt/Melt) can be predicted. As an example, we predict that during partial melting of garnet peridotite, group A eclogite, and garnet pyroxenite, r₀(3+) for garnets ranges from 0.939±0.005 to 0.953±0.009 Å. These values are consistently smaller than the ionic radius of the heaviest REE, Lu. The above equations quantify the crystal-chemical controls on garnet–melt partitioning for the REE, Y and Sc. As such, they represent a major advance en route to predicting D^Grt/Melt for these elements as a function of P, T and X.