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An equation of state for silicate melts. I. Formulation of a general model

Department of Geophysical Sciences, The University of Chicago, 5734 S Ellis Avenue, Chicago, Illinois 60637

ghiorso{at}geosci.uchicago.edu

A simple, empirical, volume-explicit equation of state (EOS) is developed for use in describing the volumetric properties of materials that exhibit large thermal expansivities and strongly non-linear, pressure-dependent compressibilities. Existing and commonly used EOS expressions, like the Universal and Birch-Murnaghan equations, develop singularities at critical values of temperature and pressure that prevent the calculation of derived thermodynamic properties for this class of substances. The proposed EOS reduces to a simple polynomial form at low-pressure; this form is utilized in the literature to describe the properties of silicate melts at 10⁵ Pa. At high-pressures, the proposed EOS can be parameterized to yield a finite, non-zero volume limit, unlike other formulations. Thermodynamic properties can be calculated using the proposed EOS without the need for iterative solutions and all derivative and integral representations of the equation are analytic.

A detailed example is developed demonstrating how the proposed EOS can be utilized in modeling the Gibbs free energy of amorphous silica at elevated temperature and pressure. The thermodynamic model described in the example accounts for vibrational contributions to the energy of the system as well as configurational effects arising from increases in the coordination number of Si with temperature and pressure. Vibrational contributions are modeled at elevated pressure by the proposed EOS. Configurational contributions are described by a simple associated solution model for the entropy of mixing. Parameters are calibrated from molecular dynamical simulations of the configurational and volumetric properties of amorphous silica. The calibration is used to calculate the phase diagram of silica to 3000 K and 15 GPa, which compares quite favorably with experimental data on melting.