Thermodynamics in the Fe-Si-O system at Earth's core pressures

Authors: Ch.-Ed. Boukaré, J. Badro

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 [1][2] and then precipitates upon core cooling. Similarly, ex-solution of SiO2 can occur if the liquid core start over saturated in Si and O and reach the saturation limit during secular cooling [3]. The issue of light elements ex-solution/precipitation is crucial as it is a powerful source to drive the 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 Fe-Si-O system. The model is based on global Gibbs free energy minimization  inspired from [4][5]. The Gibbs free energy of end-members are taken from [6] for Fe-liquid, Fe-HcP, Fe-Fcc, FeO-liquid, FeO-solid; [7] and [5]  for stishovite and SiO2-liquid; and [8] for FeSi-B2. The EoS of FeSi-liquid is extrated from [9] and a Gibbs free energy model for FeSi-liquid is fitted to match the FeSi melting curve of [10]. Liquids activities in the Fe-Si-O system are taken from [11] . 

By gathering a large set of ab-initio and experimental measurements, our model provide 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 isotherms corresponding to the saturation condition, i.e., liquidus temperature. We then show how our model can be used to compute solidification sequences of iron alloys up to 350 GPa. 

Caption: Liquidus surfaces in the Fe-Si-O system at 55 GPa (top) and 135 GPa (bottom). The colors correspond to different liquidus phase : FeHcP (blue), stishovite (red), wustite (green) and FeSiB2 (orange). At a given pressure and for a given bulk core composition, once the temperature drops below that depicted by the isotherms, the liquid metal alloy exsolves/precipitates/saturates in the corresponding liquidus phase, indicated by the color code.

References:

[1] O’Rourke, J. G., & Stevenson, D. J. (2016). Powering Earth’s dynamo with magnesium precipitation from the core. Nature, 529(7586), 387.

[2] Badro, J., Aubert, J., Hirose, K., Nomura, R., Blanchard, I., Borensztajn, S., & Siebert, J. (2018). Magnesium Partitioning Between Earth's Mantle and Core and its Potential to Drive an Early Exsolution Geodynamo. Geophysical Research Letters, 45(24), 13-240.

[3] Hirose, K., Morard, G., Sinmyo, R., Umemoto, K., Hernlund, J., Helffrich, G., & Labrosse, S. (2017). Crystallization of silicon dioxide and compositional evolution of the Earth’s core. Nature, 543(7643), 99.[4] Mattern, E., Matas, J., Ricard, Y., & Bass, J. (2005). Lower mantle composition and temperature from mineral physics and thermodynamic modelling. Geophysical Journal International, 160(3), 973-990.

 [5] Boukaré, C. E., Ricard, Y., & Fiquet, G. (2015). Thermodynamics of the MgO‐FeO‐SiO2 system up to 140 GPa: Application to the crystallization of Earth's magma ocean. Journal of Geophysical Research: Solid Earth, 120(9), 6085-6101.  

Related paper:

C.-É. Boukaré, J. Badro, 2020, Thermodynamics in the Fe-Si-O system at Earth's core pressures, in prep.