First-principles investigation of equilibrium iron isotope fractionation in Fe_1−xS_x alloys at Earth's core formation conditions

Highlights

• Equilibrium isotope fraction factors from solid alloys can be used as proxies for molten systems.

• The effect of sulphur on isotope fractionation factors are within a 0.02‰ for all the studied alloys.

• Bond type and local environment are the controlling parameters of Fe isotope fractionation in Fe_1−xS_x alloys.

• No measurable Fe fractionation should be seen between liquid and solid Fe_1−xS_x alloys at Earth's core formation conditions.

Abstract

Iron is one of the most abundant non-volatile elements in the solar system. As a major component of planetary metallic alloys, its immiscibility with silicates plays a major role in planetary formation and differentiation. Information about these processes can be gained by studying the equilibrium Fe isotope fractionation between metal alloys and molten silicates at conditions of core formation. In particular, recent attention has been paid to ⁵⁶Fe/⁵⁴Fe equilibrium isotope fractionation at conditions relevant to Earth's core formation and the influence that light elements (O, H, C, Ni, Si and S) have had in this process. Most of these experimental studies relied on the measurement of Fe isotope fractionation from quenched phases of silicate melts and molten iron alloys. The experimental works are extremely challenging, and may suffer different drawbacks. To overcome this, we use ab-initio computational methods to perform a systematic study of the ⁵⁶Fe/⁵⁴Fe equilibrium isotope fractionation in molten and solid Fe_1−xS_x alloys at conditions of the core formation (60 GPa, 3000 K). We show for the first time, that equilibrium isotope fractionation factors from solid systems can be used as proxies for molten systems with differences between these two methods less than 0.01‰ at the relevant P-T conditions. Additionally, we discuss the effect of sulphur concentration on the equilibrium Fe isotope fractionation and show that although there are some structural changes due to atom substitutions, the wide range of studied concentrations produces β-factors that are constant within ∼0.02‰. Finally, we discuss the implications of our results for the interpretation of recent experiments and the understanding of core crystallisation processes.

Introduction

Iron is the major element of solar system planetary cores, in relation with the nucleosynthesis sequence. Iron plays a major role in every stance of planetary formation and differentiation. Geophysical approaches have confirmed the presence of iron for Earth's core but with almost 10% of light elements required to make up its mass (Hirose et al., 2013). Traditionally the effects due to the presence of light elements in the core are being inferred by geophysical studies where the density and sound velocity propagation are studied as function of light element concentration to match those values reported from geophysical models such as PREM. However, recently it has been suggested that the Fe isotopic composition in the mantle could be used to infer the composition of Earth's core (Bourdon et al., 2018; Craddock and Dauphas, 2010; Craddock et al., 2013; Lesher et al., 2020; Shahar et al., 2016; Sossi et al., 2016). This is based on the assumption that the presence of elements such as C, O, Si, S should affect the partitioning of iron isotopes between the mantle and the core. Originally, it has been suggested that core-mantle differentiation will leave imprints on the iron isotope signature of Earth's mantle because of the difference of Fe valence state and coordination in the mantle (Fe²⁺) and in the core (Fe⁰ metal) (Polyakov, 2009). That study suggested that the mantle should be enriched in heavy isotopes, product of equilibrium isotope fractionation during differentiation. However, subsequent explanations argue that the bulk silicate Earth is chondritic in its iron isotopic composition and that any difference in isotope composition seen in basalts is due to fractionation during partial melting of the rock from which they have been formed (Craddock et al., 2013). Indeed, isotope compositions in natural rocks are scattered in values, with ${\delta }^{56}$Fe ∼−0.01‰ for carbonaceous chondrites, ${\delta }^{56}$Fe ∼−0.1 to +0.1‰ for enstatite chondrites and ${\delta }^{56}$Fe $\sim +0.1\mathrm{‰}$ for basalts (Craddock and Dauphas, 2011; Liu et al., 2017; Poitrasson et al., 2013). These scattered values are therefore interpreted to suggest that the accessible mantle has a Fe isotope composition that is indistinguishable from chondritic composition (i.e. ${\delta }^{56}$Fe ∼0‰). Apart from expected evidence of the presence of light elements in the core due to difference in chemical bonds, one must also consider the effects of pressure and temperature. It is well known that equilibrium fractionation effects should vanish at high temperatures. However, in the case of lower mantle and core conditions where pressures are also high, these fractionation effects might still be important. Recently, Shahar et al. (2016) have carried out experiments and computational modelling on the effects of pressure and light elements (such as H, C, O) on the equilibrium isotope fractionation of ⁵⁷Fe/⁵⁴Fe at the core-mantle boundary. Their work has found a significant imprint on isotope fractionation due to light elements such as C and H (${\delta }^{56}$Fe∼0.03-0.05‰) whilst elements such as O leave almost no imprint (${\delta }^{56}$Fe∼0.007-0.01‰). Their results support the suggestions by Craddock et al. (2013) that in order to have a mantle with a ${\delta }^{56}$Fe near 0‰, light elements such as C and H that provide a large imprint in fractionation should not be present in the core at a significant level. Additionally, it favours the presence of O as a light element in the core. However, the effects of other light elements such as S on equilibrium Fe isotope fractionation at core conditions are yet unclear as well as any pressure induced magnetic effects that can be of relevance. There has been recent experimental work by Ni et al. (2020), Shahar et al. (2015) on the effects of S on Fe isotope fractionation between solid metal and liquid metal, or between metal and silicate. In both cases, sulfur enters into the metallic phases and preferentially into the liquid metal phase. Shahar et al. (2015) found that metal-silicate fractionation increases significantly with the sulfur content in the metal, whereas Ni et al. (2020) observed that the solid-liquid fractionation in this system does not depend on the sulfur content of the liquid metal. Obviously, much work needs to be done to understand these effects at temperature and pressure conditions of the terrestrial core, far away from experimental studies performed below 2 GPa. In this context, the difficulty to carry out experiments at high pressure and high temperature leads to the use of crystalline phases such as hcp Iron or I4 Fe₃S as proxies of the molten systems leading to large extrapolations and possible errors in the interpretation of final results. This approach is used for instance in Liu et al. (2017) where high-pressure data (up to 206 GPa) suggest a minuscule Fe isotope fractionation between metal and silicate that is one order of magnitude lower than the one found by Shahar et al. (2015) at 1-2 GPa.

In recent years, computational techniques have become useful tools to estimate isotope fractionation factors in mineral systems. This is particularly true for methods based on quantum mechanics that allow to describe the vibrational properties of light and heavy isotopes at any pressure and temperature conditions (Blanchard et al., 2017). However, the weakness of these methods typically lies in the use of the quasi-harmonic approximation that falls when temperature increases or when the systems become fully molten. In addition, in dynamical systems such as liquids and melts, it has been shown that configurational disorder needs to be taken into account in order to obtain meaningful equilibrium fractionation factors (Blanchard et al., 2017; Pinilla et al., 2015).

In this work, we use ab-initio computational methods to perform a systematic study of the ⁵⁶Fe/⁵⁴Fe equilibrium isotope fractionation in molten and solid Fe_1−xS_x alloys at conditions of the core formation. By comparing the fractionation factors obtained from solid and molten systems, we estimate the validity of the experimental approximation consisting in using solid metals as a proxy for molten alloys. Additionally, we comment on the effects of S concentration on Fe isotope fractionation in liquid systems. We discuss our findings on view of latest results on equilibrium Fe isotope fractionation and their relevance for the formation of the Earth's core.