Molecular dynamics studies of CaAl 2Si 2O 8 liquid. Part II: Equation of state and a thermodynamic model

Abstract

A thermodynamic model and equation of state (EOS) is developed from the molecular dynamics simulation experiments of Spera et al. (2009) for CaAl 2Si 2O 8 liquid over the temperature range 3500–6000 K and pressure interval 0–125 GPa. The model is constructed utilizing the isothermal Universal EOS of Vinet et al. (1986) combined with an expression for the temperature-dependence of the internal energy derived from density functional theory ( Rosenfeld and Tarazona, 1998). It is demonstrated that this model is more successful at reproducing the data than the temperature-dependent Universal EOS ( Vinet et al., 1987) or the volume-explicit EOS of Ghiorso (2004a). Distinct parameterizations are required to model low (<20 GPa) and high (>20 GPa) pressure regimes. This result is ascribed to the affect of liquid structure on macroscopic thermodynamic properties, specifically the interdependence of average cation-oxygen coordination number on the bulk modulus. The thermodynamic transition between the high- and low-pressure parameterizations is modeled as second order, although the nature of the transition is open to question and may well be first order or lambda-like in character. Analysis of the thermodynamic model reveals a predicted region of liquid–liquid un-mixing at low-temperatures (<1624 K) and pressures (<1.257 GPa). These pressure–temperature conditions are above the glass transition temperature but within the metastable liquid region. They represent the highest temperatures yet suggested for liquid–liquid un-mixing in a silicate bulk composition. A shock wave Hugoniot curve is calculated for comparison with the experimental data of Rigden et al. (1989) and of Asimow and Ahrens (2008). The comparison suggests that the model developed in this paper underestimates the density of the liquid by roughly 10% at pressures greater than ∼20 GPa.