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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 DYb and DCe, and the ratio DYb/DCe increase with the Ca-Tschermaks content of the clinopyroxene. The compositional dependence of DYb/DCe 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 DYb and DCe can be eliminated by accounting for configurational entropy in pyroxene and melt using ionic activity models for the component REEMgAlSiO6. 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 REEMgAlSiO6 pyroxene from its molten component oxides using available thermochemical data for MgO, Al2O3 and SiO2 and Henry's law for REEO1.5. In complex systems the simple ionic approach provides a useful means of predicting the compositional dependence of partition coefficients.

We have used modified Born theory to extend the Shock-Helgeson-Sverjensky equation of state of aqueous silica to 20 kbar and 900°C. An important requirement of this equation of state is the dielectric constant of the solvent (ε{lunate}), which has been experimentally measured only to 5 kbar and 550°C. Our extension of the Shock-Helgeson-Svetjensky equation relies, therefore, on molecular dynamics simulations which we have previously shown to reproduce the experimental data at densities between 0.25 and 1.0 g cm-3 and temperatures up to 1000°C (pressure ranging from 0.5 to 20 kbar). A combination of recent solubility measurements and of simulated values of e provide the basis for a quantitative description of the thermodynamic properties of aqueous silica over most of the range of geologic interest from 1 bar to 20 kbar and 25-900°C. © 1995.