Thermodynamics in the system Fe-Si-O up to 350 GPa

The composition of the Earth's core in light elements such as Si, Mg, O or S, remains largely controversial. Conditions under which liquid metal saturates in these elements offer strong constrains on core composition. For instance, MgO can dissolve in the metallic phase at high temperature (Badro et al., 2016) and then precipitates upon core cooling (O'Rourke and Stevenson, 2016, 2017; Badro et al., 2016, 2018). Similarly, ex-solution of SiO₂ can occur if the liquid core starts over saturated in Si and O and reaches the saturation limit during secular cooling (Hirose et al., 2017). The issue of light elements ex-solution/precipitation is crucial as it is an essential buoyancy source required to drive Earth's dynamo prior to inner-core growth.

We present a self-consistent thermodynamics approach that aims to determine the saturation conditions of liquid iron alloys in the system Fe-Si-O. The model is based on global Gibbs free energy minimization inspired from (Mattern et al., 2004). The Gibbs free energy of end-members are taken from (Komabayahi, 2014) for Fe-liquid, Fe-HcP, Fe-Fcc, FeO-liquid, FeO-solid; (de Koker et al., 2013) and (Boukaré et al, 2015) for stishovite and SiO₂-liquid; and (Fisher et al., 2014) for FeSi-B2. The EoS of FeSi-liquid is extracted from (Huang et al., 2019) and a Gibbs free energy model for FeSi-liquid is fitted to match the FeSi melting curve of (Lord et al., 2010). Liquids activities in the Fe-Si-O system are taken from (Badro et al., 2015).

By gathering a large set of ab-initio and experimental measurements, our model provides a self-consistent framework for modeling thermo-chemical evolution of planetary iron cores. We first present phase diagrams in the Fe-Si-O system and the isotherms that correspond to the saturation conditions, i.e., liquidus temperature. We then show how our model can be used to compute solidification sequences of iron alloys up to 350 GPa.