Equilibrium fractionation of S, Fe, and Ni isotopes in Fe-Ni sulfides: A first-principles investigation

Abstract

Fe, Ni, and S isotopes are important chemical tracers, and they complement each other to improve our understanding of the Earth's evolution. As common accessory minerals in the Earth's interior and the most important group of ore minerals, sulfide minerals display a wide range of Fe and Ni contents. Using first-principles methods, we investigated the equilibrium fractionation factors of Fe, Ni, and S isotopes of the β-(Ni, Fe)S, FeS₂-NiS₂, and Fe₃S₄-Ni₃S₄ solid solutions, to constrain the effect of cation contents on Fe, Ni, and S isotopic signatures. For the β-(Ni, Fe)S solid solution, the iron β-factors, nickel β-factors, and sulfur β-factors all decrease approximately linearly with the increasing Fe content. For the FeS₂-NiS₂ solid solution, the iron β-factors, nickel β-factors, and sulfur β-factors show a positive linear relationship with the Fe content. For the Fe₃S₄-Ni₃S₄ solid solution, the iron β-factors and nickel β-factors have a strong negative correlation with the Fe content, while the sulfur β-factors have a weak negative correlation with the Fe content. In general, the trend of variation of the β-factors with Fe content is the opposite to that of the average bond lengths with the Fe content. Our results provide an improved understanding of Fe, Ni, and S isotopic fractionation in natural systems that may be used to better constrain physical, chemical, and geo-biological evolution on Earth.

Introduction

Since the pioneering work of Urey (1947) and Bigeleisen and Mayer (1947), the traditional light stable isotopes (e.g., C, H, S, O, N) have been widely used to study physical, chemical, and biological evolution on Earth and beyond (e.g., Thiemens and Heidenreich, 1983; Thiemens, 2006; Thiemens et al., 2012; Hayes et al., 1999; Farquhar et al., 2000a, Farquhar et al., 2000b). To accurately interpret the isotopic compositions of the light stable isotopes in nature and understand their fractionation mechanisms, it is essential to study the temperature dependence of the isotope fractionation factors between minerals and fluids (O'Neil, 1986). As one of the major advances in stable isotope geochemistry, the development of multi-collector inductively-coupled plasma mass-spectrometry (MC-ICPMS) has enabled high-precision measurements of isotopic compositions for so called non-traditional isotopes (e.g., Fe, Ni, Cu, Zn, Ge, Se) (e.g., Halliday et al., 1998; Johnson et al., 2004; Anbar and Rouxel, 2007; Teng et al., 2017). Compared to the traditional stable isotopes, the non-traditional stable isotopes have unique geochemical characteristics, such as the bonding environment, widely varying concentrations in different geological reservoirs, redox-sensitivity, and biologically active. These attributes make different non-traditional elements susceptible to different fractionation mechanisms, and thus they can provide new constraints on the Earth's evolution (e.g., Teng et al., 2019; Teng et al., 2017 and references therein).

As one of the most important traditional stable isotopes, S isotopes have been widely used to investigate the evolution of the Earth and solar system (Thiemens, 1999, Thiemens, 2006; Farquhar et al., 2000b, Farquhar et al., 2002; Rai et al., 2005), mantle and high temperature geological processes (e.g., Ohmoto and Goldhaber, 1997; Marini et al., 2011; Cabral et al., 2013), and biogeochemical cycles (e.g., Shen et al., 2001, Shen et al., 2009; Halevy, 2013). One of the prerequisites for these applications is the determination of the S isotope fractionation factors between S-bearing phases. Indeed, sulfur β-factors of numerous sulfides, especially ore minerals, have been studied (e.g., Li and Liu, 2006; Liu et al., 2014, Liu et al., 2015, Liu et al., 2016, Liu et al., 2018b). However, most sulfide minerals investigated previously are simple binary and ternary compounds while sulfides containing impurities have not been examined. In nature, Fe and Ni atoms can substitute for each other in certain sulfides, and more extensive substitutions associated with solid solutions can also occur, such as the millerite solid solution β-(Ni, Fe)S (Misra and Fleet, 1974), pyrite (FeS₂)-vaesite (NiS₂) solid solution (Bayliss, 1989), and greigite (Fe₃S₄)-polydymite (Ni₃S₄) solid solution (Vaughan and Craig, 1985). Therefore, calculating sulfur β-factors for these solid solutions of Fe-Ni sulfides may shed light on the effects of Fe-Ni substitution on equilibrium isotope fractionation and their applications.

Among the non-traditional stable isotopes, Fe isotopes have received much attention due in part to the importance and large abundance of Fe in the Earth and other terrestrial planets, and because Fe isotopes provided important constraints on the low and high temperature geological and geochemical processes (e.g., Dauphas et al., 2017; Johnson et al., 2020 and references therein). Using Mössbauer spectroscopy and nuclear resonant inelastic X-ray scattering, the iron β-factors of several Fe-bearing minerals have been constrained (e.g., Polyakov, 1997, Polyakov, 2009; Polyakov and Mineev, 2000; Polyakov et al., 2007, Polyakov et al., 2013, Polyakov et al., 2019; Polyakov and Soultanov, 2011; Dauphas et al., 2012, Dauphas et al., 2014; Blanchard et al., 2015; Roskosz et al., 2015). In addition, ab initio calculations have been used to calculate iron β-factors for a variety of aqueous species and minerals (e.g., Schauble et al., 2001; Anbar et al., 2005; Domagal-Goldman and Kubicki, 2008; Hill and Schauble, 2008; Blanchard et al., 2009, Blanchard et al., 2015; Ottonello and Zuccolini, 2009; Rustad and Dixon, 2009; Fujii et al., 2014; Nie et al., 2021; Rabin et al., 2021). However, apart from pyrite (FeS₂), marcasite (FeS₂), troilite (FeS), mackinawite (FeS), chalcopyrite (CuFeS₂), and Fe₃S, the iron β-factors of most sulfides, such as greigite, violarite and other Fe-Ni sulfides, have not yet been studied. Numerous studies have focused on Fe isotopic compositions of sulfides in nature and found that sulfide minerals display the largest range of variation of Fe isotopic compositions on Earth (e.g., Polyakov and Soultanov, 2011; Wu et al., 2012). Therefore, to accurately interpret the Fe isotope variations in sulfide minerals, it is essential to determine their iron β-factors.

Compared to Fe, Ni is less abundant in the Earth and has received less attention. However, Ni has the distinct advantage that it is almost exclusively present as Ni²⁺ in natural terrestrial environments (Nicholls, 1974), allowing us to investigate geological and geochemical processes without the influence of changing oxidation state. Because Fe and Ni may behave differently, the integration of Fe and Ni stable isotopes has been used to address important questions in planetology, including planetary differentiation processes, the thermal histories of the parent bodies of metal-rich meteorites, and the origin of metal in CB chondrites (e.g., Chernonozhkin et al., 2016, Chernonozhkin et al., 2017; Weyrauch et al., 2019). On the other hand, the Fe and Ni contents may influence Fe and Ni isotopic compositions. For example, Fe isotope fractionation factors between Fe alloy and silicate were positively correlated with the Ni content in Fe alloy (Elardo and Shahar, 2017). Saunders et al. (2020) reported that Ni isotopic compositions were negatively correlated with the Fe content in the Kilbourne Hole xenoliths, while for mineral separates, Ni isotopic compositions were poorly correlated with the Ni content. Our previous study indicated that the nickel β-factors of polydymites, millerite, and vaesite decrease with increasing Fe content (Liu et al., 2018a). Calculating the Fe and Ni isotope fractionation factors of sulfides with different Fe and Ni contents can help understand the effects of Fe and Ni contents on equilibrium Fe and Ni isotope fractionation, and provide a new perspective on the combined use of Fe and Ni isotopes to study mantle and planetary processes.

Naturally occurring sulfide minerals also display a range of Fe and Ni isotopic compositions (e.g., Gueguen et al., 2013; Dauphas et al., 2017). Compared to the measurements of both Fe and S isotopes of sulfides (e.g., Fabre et al., 2011; Busigny et al., 2017; He et al., 2020), the measurements of both Fe and Ni isotopes of sulfides is less common. It is important to note that Hofmann et al. (2014) used multiple S, Fe, and Ni isotope data to constrain the generation of komatiite-hosted Ni sulfide mineralization, which may help the interpretation of Ni isotopic record measured from sedimentary rocks (Li et al., 2021). It has also been shown that Fe-Ni sulfides are ubiquitous in ore deposits, upper-mantle peridotites, and extraterrestrial samples (e.g., Kiseeva et al., 2017; Vaughan and Corkhill, 2017; Schrader and Zega, 2019); hence they offer an opportunity to use combined Fe, Ni, and S isotopes to constrain the genesis and evolution of ore deposits, mantle processes, and planetary differentiation. However, the temperature dependence of Fe, Ni, and S isotope fractionation factors for most Fe-Ni sulfides remains poorly constrained, limiting their applications.

In this study, first-principles methods based on density functional theory were used to calculate the equilibrium S, Fe and Ni isotope fractionation parameters of Fe-Ni sulfide minerals, including the β-(Ni, Fe)S, FeS₂-NiS₂, and Fe₃S₄-Ni₃S₄ solid solutions. The results may enhance our understanding of the effect of cation contents on equilibrium isotope fractionation in sulfides, and they provide a theoretical basis for the application of Fe, Ni, and S isotopes in the study of physical, chemical, and geo-biological evolution of the Earth and possibly beyond.