Light element partitioning between silicate and metallic melts: Insights into the formation and composition of Earth's core

The mass deficit of the Earth's core, and the increasing solubility of light elements into metallic iron with increasing pressure demonstrate that the Earth's core must contain several weight percent of light elements such as Si, O, C and S. These light elements place important constraints on the depth of the primordial magma ocean(s), the chemical potentials of many of these elements in coexisting phases during differentiation, the temperature of the inner core boundary, and the composition of the bulk Earth. The P-wave velocity, Earth's mass deficit, and depth of the inner core boundary place two important constraints on the chemical composition of the core, but there are multiple trade-offs which cannot be resolved using seismology alone. In this study, we use a large experimental partitioning dataset to build activity-composition models for light elements in metallic melts in equilibrium with oxide and silicate phases (both solid and liquid). We avoid the use of epsilon models, which commonly fail at solute concentrations above a few weight percent. Instead we employ a modified subregular solution model, using intermediate species to calculate excess free energies of mixing. Flexible models like these are required to fit the experimental data which spans 0 - 100 GPa and 1500 - 5500 K. Several heuristics are used to reduce the number of free parameters where they are not independently constrained. We use our models to investigate the conditions of core formation and the chemical composition of the Earth's core using the approach of Rubie et al. (2015; Icarus v.248; pp 89-108).