A self-consistent optimization of multicomponent solution properties: Ab initio molecular dynamic simulations and the MgO–SiO2 miscibility gap under pressure

Abstract

We propose a new approach to parameterizing the Gibbs energy of a multicomponent solution as a function of temperature, pressure and composition. It uses the quasichemical model in the second nearest neighbor approximation and considers both a polynomial representation (for low pressure) and an exponential decay representation (for moderate-to-high pressure) of the excess molar volume νxs to extend thermodynamic behavior to elevated pressure. This approach differs from previous configuration-independent regular or associated solution-type models of multicomponent silicate liquids at elevated pressure and can account for any structural or short-range order data that may be available. A simultaneous least squares fit of the molar volume and the molar enthalpy of mixing data obtained from First Principles Molecular Dynamics (FPMD) simulations at various pressures enables complete parameterization of the excess thermodynamic properties of the solution. Together with consistently optimized properties of coexisting solids, this enables prediction of pressure–temperature–composition phase diagrams associated with melting. Although the method is extensible to natural multicomponent systems, we apply the procedure as a first test case to the important planetary model system MgO–SiO2 using FPMD data found in the literature. One key result of this optimization, which depends only on the derived excess properties of the liquid phase, is that the consolute temperature of the SiO2-rich miscibility gap is predicted to decrease with increasing pressure. This appears to be in disagreement with available experimental constraints and suggests possible thermodynamic inconsistency between FPMD data and experimental phase equilibrium data in the 0–5GPa pressure range. We propose a new thermodynamic consistency criterion relating the signs of νxs and other excess properties and discuss the need for precise calculations of derivatives of excess properties. Finally, the potential reappearance of the miscibility gap in the MgO–SiO2 system above 5GPa is discussed in light of this work.