Partitioning of sulfur between solid and liquid iron under Earth's core conditions: Constraints from atomistic simulations with machine learning potentials

Partition coefficients of light elements between the solid and liquid iron phases are crucial for uncovering the state and dynamics of the Earth's core. As one of the major light element candidates, sulfur has attracted extensive interests for measuring its partitioning and phase behaviors over the last several decades, but the relevant experimental data under Earth's core conditions are still scarce. In this study, using a toolkit consisting of electronic structure theory, high-accuracy machine learning potentials and rigorous free energy calculations, we establish an efficient and extendible framework for predicting complex phase behaviors of iron alloys under extreme conditions. As a first application of this framework, we predict the partition coefficients of sulfur over wide range of temperatures and pressures (from 4000 K, 150 GPa to 6000 K, 330 GPa), which are demonstrated to be in good agreement with previous experiments and ab initio simulations. After a continuous increase below ∼250 GPa, the partition coefficient is found to be around 0.75 ± 0.07 at higher pressures and are essentially temperature-independent. Given these predictions, the partitioning of sulfur is confirmed to be insufficient to account for the observed density jump across the Earth's inner core boundary and its roles on the geodynamics of the Earth's core should be minor.