Coordinated Hard Sphere Mixture (CHaSM): A simplified model for oxide and silicate melts at mantle pressures and temperatures

Abstract

We develop a new model to understand and predict the behavior of oxide and silicate melts at extreme temperatures and pressures, including deep mantle conditions like those in the early Earth magma ocean. The Coordinated Hard Sphere Mixture (CHaSM) is based on an extension of the hard sphere mixture model, accounting for the range of coordination states available to each cation in the liquid. By utilizing approximate analytic expressions for the hard sphere model, this method is capable of predicting complex liquid structure and thermodynamics while remaining computationally efficient, requiring only minutes of calculation time on standard desktop computers. This modeling framework is applied to the MgO system, where model parameters are trained on a collection of crystal polymorphs, producing realistic predictions of coordination evolution and the equation of state of MgO melt over a wide range of pressures and temperatures. We find that the typical coordination number of the Mg cation evolves continuously upward from 5.25 at 0 GPa to 8.5 at 250 GPa. The results produced by CHaSM are evaluated by comparison with predictions from published first-principles molecular dynamics calculations, indicating that CHaSM is accurately capturing the dominant physics controlling the behavior of oxide melts at high pressure. Finally, we present a simple quantitative model to explain the universality of the increasing Grüneisen parameter trend for liquids, which directly reflects their progressive evolution toward more compact solid-like structures upon compression. This general behavior is opposite that of solid materials, and produces steep adiabatic thermal profiles for silicate melts, thus playing a crucial role in magma ocean evolution.