The linear-mixing approximation in silica-water mixtures at planetary conditions

TL;DR

This study evaluates the accuracy of the Linear Mixing Approximation for silica-water mixtures under planetary interior conditions, revealing its validity within a few percent and highlighting the influence of composition and electronic theory choices.

Contribution

The paper provides ab-initio molecular dynamics simulations to test the LMA's accuracy at high pressures and temperatures relevant to Uranus and Neptune, and explores effects of composition and electronic functional choices.

Findings

LMA is accurate within ~5% between 150-600 GPa.

Rock presence delays superionic water transition by ~70 GPa.

Electronic functional choice causes ~10% density uncertainty.

Abstract

The Linear Mixing Approximation (LMA) is often used in planetary models for calculating the equations of state (EoSs) of mixtures. A commonly assumed planetary composition is a mixture of rock and water. Here we assess the accuracy of the LMA for pressure-temperature conditions relevant to the interiors of Uranus and Neptune. We perform MD simulations using ab-initio simulations and consider pure-water, pure-silica, and 1:1 and 1:4 silica-water molecular fractions at temperature of 3000 K and pressures between 30 and 600 GPa. We find that the LMA is valid within a few percent (<~5%) between ~150-600 Gpa, where the sign of the difference in inferred density depends on the specific composition of the mixture. We also show that the presence of rocks delays the transition to superionic water by ~70 GPa for the 1:4 silica-water mixture. Finally, we note that the choice of electronic theory (functionals) affect the EoS and introduces an uncertainty in of the order of 10% in density. Our study demonstrates the complexity of phase diagrams in planetary conditions and the need for a better understanding of rock-water mixtures and their effect on the inferred planetary composition.