Evidence for Fe-Si-O liquid immiscibility at deep Earth pressures

Stratification in planetary cores by liquid immiscibility in Fe-S-H

Liquid-liquid immiscibility has been widely observed in iron alloy systems at ambient pressure and is important for the structure and dynamics in iron cores of rocky planets. While such previously known liquid immiscibility has been demonstrated to disappear at relatively low pressures, here we report immiscible S(±Si,O)-rich liquid and H(±C)-rich liquid above ~20 GPa, corresponding to conditions of the Martian core. Mars’ cosmochemically estimated core composition is likely in the miscibility gap, and the separation of two immiscible liquids could have driven core convection and stable stratification, which explains the formation and termination of the Martian planetary magnetic field. In addition, we observed liquid immiscibility in Fe-S-H(±Si,O,C) at least to 118 GPa, suggesting that it can occur in the Earth’s topmost outer core and form a low-velocity layer below the core-mantle boundary.

Yokoo et al. find the liquid immiscibility between H-rich and S-rich liquids Fe above 20 GPa. The separation of immiscible liquids could explain the disappearance of Mars’ magnetic field and the formation of low-velocity layer atop the Earth’s core.

Minimization of Gibbs Energy in High-Pressure Multiphase, Multicomponent Mixtures through Particle Swarm Optimization

We present a global optimization method to construct phase boundaries in multicomponent mixtures by minimizing the Gibbs energy. The minimization method is, in essence, an extension of the Maxwell construction procedure that is used in single-component systems. For a given temperature, pressure, and overall mixture composition, it reveals the mole fractions of the thermodynamically stable phases and the composition of these phases. Our approach is based on particle swarm optimization (PSO), which is a gradient-free, stochastic method. It is not reliant on good initial guesses for the phase fractions and compositions, which is an important requirement for the high-pressure applications considered in this study because data on phase boundaries at high pressures tend to be extremely limited. One practical use of this method is to create equation-of-state tables needed by continuum-scale, multiphysics codes that are ubiquitous in high-pressure science. Currently, there does not exist a method to generate such tables that rigorously account for changes in phase boundaries due to mixing. We have done extensive testing to demonstrate that PSO can reliably determine the Gibbs energy minimum and can capture nontrivial features like eutectic and peritectic temperatures to produce coherent phase diagrams. As part of our testing, we have developed a PSO-based Helmholtz-energy minimization procedure that we have used to cross-check the results of the Gibbs energy minimization. We conclude with a critique of our approach and provide suggestions for future work, including a PSO-based entropy-maximization method that would enable the aforementioned continuum codes to perform on-the-fly, phase-equilibria calculations of multicomponent mixtures.