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

Abstract

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.

History and Future of the Martian Dynamo and Implications of a Hypothetical Solid Inner Core

“…If the mass fraction of light elements in the core is χ S , the core's bulk density (neglecting compression, which is discussed in Section 2.2) is given by where we use the subscript S because we assume sulfur to be the principal light element species in the Martian core (Franz et al., 2019; Gaillard & Scaillet, 2009), and where ρ Fe and ρ S are the densities of the major and minor species (assumed to be iron and sulfur), respectively. Neglecting the small density differences between the solid and liquid forms of both the major and minor species (i.e., assuming ρ Fe, sol = ρ Fe, liq = 6,980 kg/m 3 and ρ S,sol = ρ S,liq = 1,819 kg/m 3 ), we can approximate the light element‐enriched liquid density using where, assuming small control volumes partition into equal parts solid and liquid by mass, it can be shown that is the mass fraction of light elements in the residual liquid, where D S is the solid‐liquid phase partitioning coefficient for the light elements (i.e., the mole fraction of light elements that partition into the solid phase vs. the liquid phase) (Zhang et al., 2020). Note that if sulfur partitions into the solid and liquid phases in equal proportions (i.e., if D S = 1), then ρ χ remains the same as the bulk core density and Δ ρ χ = 0; if sulfur partitions preferentially into the liquid, then D S < 1 and ρ χ < ρ c so the residual liquid is positively buoyant.…”

Gaussian Process Regression for Materials and Molecules

“…As an example of an application at the other extreme of the temperature and pressure scale (where magnetism is suppressed), a GAP was developed to study liquid iron and sulfur under conditions corresponding to those at the Earth’s core: temperatures ranging from 4000 to 7000 K and pressures between 110 and 430 GPa. 248 One of the objectives of that work was to study the partition coefficient of sulfur between solid and liquid iron. The GAP model reproduced the radial distribution functions of Fe, S, and Fe–S with high fidelity with respect to a DFT reference, as well as the melting curve of Fe.…”

Preface to Multiscale Simulation in Geochemistry

“…The emerging use of machine-learning methods was also illustrated in two contributions that parameterize atomic scale simulations, and upscale geomaterials microscopic properties to continuum-scale modeling. Finally, the topics explored in these contributions span a wide range of geochemical topics applicable to environments from the Earth's core to its surface, including: solid-liquid partitioning under Earth's core conditions (Zhang et al, 2020b), chemical geodynamics of the mantle (Zhang and Liu, 2020), recycling of noble gas in the subduction zones (Wang et al, 2020), thermodynamics of hydrothermal fluids (Mei et al, 2020), interfacial and structural properties of clay and (Fe, Mn) oxide materials (Bylaska et al, 2020;Newton and Kwon, 2020;Zhang et al, 2020a), and a machine learning-based framework for coupling and upscaling of reactive transport processes and parameters across spatial scales (Prasianakis et al, 2020). These papers are briefly introduced in the following.…”

“…Sulfur is one of the major candidates for the light elements in the Earth's core and its partitioning across the inner core boundary may be important to drive the magnetic field related convection in the outer core. To obtain the accurate partition coefficients of sulfur under Earth's core conditions, which is still unclear from experiments, Zhang et al (Zhang et al, 2020b) present a new framework based on a machine learning approach trained on high quality quantum mechanics data. By extending the data to higher T-P conditions unavailable with current experimental approaches, they show that the partition coefficient of sulfur is essentially insensitive to temperatures and pressures.…”

“…By extending the data to higher T-P conditions unavailable with current experimental approaches, they show that the partition coefficient of sulfur is essentially insensitive to temperatures and pressures. Technically, Zhang et al (2020b) provide a new approach to efficiently and accurately predict the chemical potential of mixtures that is central for the thermodynamic equilibrium problems in geochemistry, and can thus be applicable to a variety of complex problems involving equilibrium between multiple phases.…”