Thermodynamics of rare earth element partitioning between clinopyroxene and melt in the system CaO - MgO - Al2O3 - SiO2

We use the experimental data of Gaetani and Grove (1995) on rare earth element (REE) partitioning between clinopyroxene and melt in the system CaO-MgO-Al2O3-SiO2 to constrain the energetics of the coupled substitution REEAl[CaSi](-1).The data show that the partition coefficients D-Yb and D-Ce and the ratio D-Yb/D-Ce increase with the Ca-Tschermaks content of the clinopyroxene. The compositional dependence of D-Yb/D-Ce can be reconciled with a simple model of lattice strain around the misfit Ce3+ and Yb3+ cations in the crystal, while the compositional dependence of D-Yb and D-Ce can be eliminated by accounting for configurational entropy in pyroxene and melt using ionic activity models for the component REEMgAlSiO(6). For pyroxene we assume ideal mixing on M1 and M2 sites with local charge balance on the T sites. For melt we adopt an ideal two-lattice mixture of cations and pyroxene-like six-oxygen anions. The ionic approach is validated by a more rigorous determination of the equilibrium constant for the formation of REEMgAlSiO(6) pyroxene from its molten component oxides using available thermochemical data for MgO, Al2O3 and SiO2 and Henry's law for REEO(1.5). In complex systems the simple ionic approach provides a useful means of predicting the compositional dependence of partition coefficients.