Whether Earth’s core is a significant repository of noble gases is an open question because their partitioning between liquid metal and silicate melt during core formation is poorly known. Here we calculated the He and Ar partition coefficients (D) between liquid Fe and MgSiO₃ melt from 20 to 135 GPa at 5,000 K using ab initio molecular dynamics combined with thermodynamic integration. Our simulations show that D_He does not change significantly with pressure, while D_Ar increases strongly with increasing pressure. Furthermore, we found that the metal/silicate partitioning behaviors of He and Ar are controlled by their atomic size and the charge density properties of the host compositions. These results indicate that Earth’s core is a plausible reservoir for ³He and could possibly account for the high ³He/⁴He ratios in the OIBs that associated with deep-rooted plumes, but the core is unlikely to be a significant source for ³⁶Ar.

Key Points

D_He is insensitive to pressure from 20 to 135 GPa, while D_Ar is positively dependent on pressure
The pressure dependences of D_He and D_Ar are controlled by the atomic size of the noble gas and the charge density of the host phase
Earth’s core is a plausible source of ³He in the OIBs associated with plumes, but is unlikely to be a significant source of ³⁶Ar

Plain Language Summary

The deep Earth source of primordial noble gases that are emitted at volcanoes is currently in active debate. Previous studies have mainly focused on the silicate mantle, but the metallic core is also a potential noble gas reservoir. In this work, by calculating the metal/silicate partition coefficients of He and Ar under conditions corresponding to core formation, we found that the concentration of He dissolved into Earth’s core is much higher than that of Ar. Therefore, Earth’s core could serve as a source for ³He degassing throughout geological time, but not as a source for ³⁶Ar.

1 Introduction

Elevated ³He/⁴He, ²⁰Ne/²²Ne, and ³⁶Ar/⁴⁰Ar ratios in some ocean island basalts (OIBs) demonstrate the presence of primordial noble gases in the Earth’s interior (e.g., Dixon et al., 2000; Harrison et al., 1999; Honda et al., 1991; Valbracht et al., 1997; Trieloff et al., 2000). It has usually been assumed that the reservoirs for primordial noble gases are located in the lower mantle, and represent parts of the mantle that have never undergone partial melting or degassing (Allègre et al., 1987; Gonnermann & Mukhopadhyay, 2007; Kurz et al., 1982). However, none of the OIBs with high ratios of primordial to radiogenic noble gases have lithophile isotope signatures (e.g., ⁸⁶Sr/⁸⁷Sr, ¹⁴³Nd/¹⁴⁴Nd, ¹⁸⁷Os/¹⁸⁸Os, ²⁰⁴Pb/²⁰⁶Pb) that are consistent with those of the bulk silicate Earth (Class & Goldstein, 2005; Farley et al., 1993; Jackson et al., 2009; Kurz et al., 2004; Porcelli & Elliott, 2008). Furthermore, it is difficult to reconcile the preservation of primordial noble gases in the deep mantle over geological time (4.5 Ga) with increasing evidence for large-scale mantle mixing instead of separate layer convection (Van der Hilst et al., 1997; Wang et al., 2015).

Alternatively, Earth’s core could possibly serve as a source feeding primordial noble gases into the mantle. Seismological images show that plumes with primordial noble gas signatures such as those that underlie the Hawaiian and Iceland hotspots are rooted at the core-mantle boundary (French & Romanowicz, 2015; Montelli et al., 2006; Zhao, 2001). The Os and W isotope compositions of some plume-related OIBs have been suggested to reflect the contribution of materials from the core (Mundl et al., 2017; Rizo et al., 2019; Walker et al., 1995). However, a prerequisite for the core-source model is that considerable concentrations of noble gases were incorporated into the core, which depends on their equilibrium metal/silicate partitioning during core-mantle segregation.

In the experiments conducted by Matsuda et al. (1993), it was found that the metal/silicate partition coefficients (D) of noble gases (He, Ne, Ar, Kr, and Xe) consistently decrease from ∼4 × 10² to ∼3 × 10⁻⁴ as pressure increases from 0.5 to 10 GPa. Comparable results were obtained by Sudo et al. (1994), and these authors therefore suggested that only a negligible amount of noble gases could have been incorporated in the core. Two decades later, Bouhifd et al. (2013) measured the He partitioning between molten silicate and Fe-rich alloys up to ∼16 GPa. They reported that D_He decreases as pressure increases to ∼6 GPa, but then increases with further pressure increase and eventually becomes relatively constant (∼10⁻²) between 10 and 16 GPa. Based on the assumption that proto-Earth was initially gas-rich, they suggested that a significant amount of He was dissolved into Earth’s core. The Bouhifd et al. (2013) results are supported by an ab initio molecular dynamics (AIMD) study performed by Zhang and Yin (2012) that reported D_He of 9(3) × 10⁻³ at 40 GPa and 3,200 K. These studies demonstrate that the core could be a plausible source of primordial He, but further work is needed to evaluate the dependence of He partitioning on pressure, and to address the partitioning of heavier noble gases.

In this work, we calculate the partition coefficients of He and Ar between liquid Fe and MgSiO₃ melt by evaluating the Gibbs free energy changes (∆G) of their distribution reactions using ab initio molecular dynamics combined with thermodynamic integration. Our purpose is to evaluate the possibility that Earth’s core serves as a reservoir for primordial ³He and ³⁶Ar, and to elucidate the mechanism that control the values and pressure dependences of their metal/silicate partition coefficients.

2 Computational Method

Our simulations consider a silicate melt with 16 formula units of MgSiO₃ and liquid metal composed of 50 Fe atoms, with two noble gas atoms (He or Ar). Correspondingly, the Gibbs free energy change of the noble gas distribution reaction is defined as:

$urn:x-wiley:00948276:media:grl61754:grl61754-math-0001$

where NG stands for He or Ar. To estimate the Gibbs free energy of each composition, we calculated the Helmholtz free energy (F) individually using the ab initio molecular dynamics method combined with thermodynamic integration technique (Text S1, Figure S1, Taniuchi & Tsuchiya, 2018; Xiong et al., 2018). The calculations were performed in the canonical ensemble where the number of atoms (N), the temperature (T), and the volume (V) are constant. To evaluate the pressure dependence of noble gas partitioning, we conducted simulations at 20, 60, and 135 GPa, with a constant temperature of 5,000 K where the compositions are in the liquid state (Anzellini et al., 2013; Stixrude & Karki, 2005). The input lengths of the cubic supercells of MgSiO₃ melt and liquid Fe were from the literatures (Table S1, De Koker & Stixrude, 2009; Ichikawa et al., 2014). Two noble gas atoms were added into the cells with the volumes unchanged, which slightly increases the pressure. To evaluate ∆G in the designed pressure conditions, we made corrections using the thermodynamics equation $urn:x-wiley:00948276:media:grl61754:grl61754-math-0002$ .

The simulations were conducted using the Quantum ESPRESSO code (Giannozzi et al., 2009) with an original implementation of the constant-temperature TI-MD module (Taniuchi & Tsuchiya, 2018). The ab initio calculations are based on density functional theory (Hohenberg & Kohn, 1964; Kohn & Sham, 1965) with the generalized gradient approximation (Perdew et al., 1996) for the exchange and correlation potential. The ionic core potentials are approximated by means of ultrasoft pseudopotentials (Vanderbilt, 1990), where the valence shells are represented by 2s²2p⁴ for oxygen, 3s²3p⁰ for magnesium, 3s²3p²3 d⁰ for silicon, 3s²3p⁶3 d^6.54s¹4p⁰ for iron, 1s² for helium, and 3s²3p⁶ for argon (Ichikawa et al., 2014; Ichikawa & Tsuchiya, 2015, 2020). The electronic wave function and charge density are expanded by the plane wave basis up to a cutoff energy of 70 Ry. Newton’s equation of motion is solved with a time step ∆t = 2 fs. The Brillouin zone is sampled at the Γ point only, which is sufficient in the MD simulations of liquid systems (Ichikawa et al., 2014; Xiong et al., 2018).

3 Results and Discussions

3.1 Partition Coefficient and Electronic Structure

With the Gibbs free energy changes obtained from the simulations (Table S1), we calculated the partition coefficients using the same method as our previous study (Xiong et al., 2018). The metal/silicate partition coefficient of He (D_He) is estimated to be 5.8(17) × 10⁻³ at 20 GPa, indicating its preference to dissolve into MgSiO₃ melt. Moreover, D_He is found to be insensitive to pressure between 20 and 135 GPa (Figure 1 and Table S1). Our partition coefficients are comparable to the value calculated by Zhang and Yin (2012) at 40 GPa, and to the values measured experimentally by Bouhifd et al. (2013) at 10–16 GPa. These results indicate that He partitioning between metal and silicate systems is independent of pressure at P > 10 GPa. In contrast, D_Ar increases strongly with pressure, from 8.1(15) × 10⁻⁵ at 20 GPa to 1.6(6) × 10⁻² at 135 GPa (Figure 1 and Table S1).

Details are in the caption following the image — **Figure 1**
Open in figure viewer PowerPoint

The metal/silicate partition coefficients of He and Ar. The method of determining the D uncertainties is given in the supporting information.

To gain insights into the mechanisms controlling He and Ar partitioning between liquid Fe and MgSiO₃ melt, we explored the interactions between the noble gas and its neighboring atoms. Atomic structure analyses of our simulation results show that the neighboring atoms of noble gases in the silicate system are mainly O, (Text S2 and Figure S2). Therefore, our discussions focus on the interactions of NG-O pairs in the silicate melt, and NG-Fe pairs in the metallic liquid. As the essential factor determining the atomic interactions, we first investigated the electronic structure by calculating the projected density of states (pDoS). As shown in Figure 2, the He-1s state is lying at ∼−15 eV and has negligible overlap with O-2p and Fe-3d states, which indicates the weak interactions between He and its neighboring O/Fe atoms. In contrast, the Ar-3p state ranges from ∼−15 eV to the Fermi level. This indicates strong hybridizations of Ar-3p with O-2p and Fe-3d states and suggests that, unlike He, Ar has strong interactions with O atoms in silicate melt and with Fe atoms in metal system. More importantly, the distribution patterns of He-1s and Ar-3p states reveal that they are fully occupied, which means that the electronic structures of He and Ar are “closed-shell.” This implies that interactions of He and Ar with neighboring atoms are repulsive, according to the Pauling principles, and suggests that they will prefer to reside in spaces with low charge densities to reduce the repulsive interactions.

To further illustrate the interaction between NG-O and NG-Fe pairs, we also calculated the charge densities (ρ) of silicate melt and liquid Fe at different pressures. Our analyses show that the charge density of MgSiO₃ melt is lower than that of liquid Fe at ∼20 GPa (Text S3 and Figure s3). This implies that the repulsive interactions between noble gas atoms and their neighboring Fe atoms in the metal are stronger than the interactions between noble gas and oxygen in the silicate melt. Hence, noble gas incorporation into the metal is energetically unfavorable, relative to incorporation in the silicate melt. This is confirmed by the ∆G results (Table S1). As pressure increases, the volumes of MgSiO₃ melt and liquid Fe become smaller and their charge densities increase correspondingly (Table S1, Text S3, and Figure s3). The pressure induced changes in charge density have weak effects on the interactions of the He-O and He-Fe pairs, as revealed by the similar distribution patterns of the He-1s, O-2p, and Fe-3d states at different pressures (Figure 2). In contrast, the interactions between Ar and its neighboring O/Fe atoms are intensified with increasing pressure, which can be ascribed to the larger atomic size of Ar. Pressure has a stronger impact on the interaction of Ar-O pairs in the silicate than the Ar-Fe pairs in the metal, as indicated by the intensified overlap between Ar-3p and O-2p states (Figure 2). This can be ascribed to the fact that MgSiO₃ melt has a larger compressibility (Table S1), and therefore its charge density increases more rapidly compared to that of liquid Fe (Text S3 and Figure S3).

The interactions of He and Ar with their neighboring atoms can be further characterized by the charge density difference (∆ρ), which describes the charge redistribution associated with incorporation of the noble gas atoms. Our ∆ρ analyses show that the magnitude of the interaction is positively dependent on the size of the noble gas atom and the charge density of the host material (Text S4 and Figure s4). These two parameters ultimately govern the metal/silicate partitioning behaviors of He and Ar.

3.2 Effects of Temperature and Light Elements

Temperature is generally considered to be an essential factor affecting the partitioning behavior of elements (e.g., Chabot et al., 2005; Righter, 2011; Xiong et al., 2018), while the simulations in this work were conducted at a constant temperature of 5,000 K. Here, we extrapolated the metal/silicate partition coefficients of He and Ar to lower temperatures based on the Boltzmann relation (Text S5). The results show that D_He and D_Ar decrease by approximately one order of magnitude (Figure S5) as temperature decreases from 5,000 to 3,500 K. On the other hand, the density of the outer core is ∼10% lighter than pure liquid Fe, due to the presence of light elements(x) such as H, C, O, S, Si, etc. (Badro et al., 2015; Li et al., 2015; Ichikawa & Tsuchiya, 2020; Rubie et al., 2010). The presence of light elements in the core may affect the incorporation of He and Ar into the metal system, as the charge density of “Fe + x” is lower than that of pure liquid Fe. Consequently, it can be expected that the metal/silicate partition coefficients of He and Ar are higher in the core-forming alloy than in pure liquid iron. It is beyond the scope of this paper to quantitatively predict the magnitude of this change, due to the lack of the accurate knowledge of the interactions between the noble gas and neighboring atoms in the “Fe + x” composition. However, it should be noted that our D_He is comparable to the result of Zhang and Yin (2012) with light elements in the metal system, at ∼3200 K. These results suggest that temperature and the presence of light elements have opposite effects on noble gas partitioning, which largely counteract each other when considering the differences between our simulations and likely core-formation conditions. Therefore, it is reasonable to use our partition coefficients to estimate the quantities of He and Ar incorporated into Earth’s core.

4 Implications

The partition coefficients reveal that He and Ar preferentially dissolve into the silicate melt during core-mantle segregation. However, their concentrations in the core are determined not only by the partition coefficients but also their quantities available during core formation. The presence of Ne with solar isotopic ratios in mantle-derived samples indicates that the proto-Earth had reached a sufficient mass within a few million years to capture nebular volatiles and dissolve them into a magma ocean (Harper et al., 1996; Williams & Mukhopadhyay, 2019). In this scenario, ∼7 × 10¹² atoms/g ³He was dissolved in the molten mantle (Porcelli & Halliday, 2001), which yields ∼2.4(12) × 10¹¹ atoms/g ³He in the core based on the D_He calculated in this work. In the case of Ar, its initial concentration can be determined based on mass balance, because unlike He, Ar does not escape from Earth’s atmosphere. It was found that 50% of the ⁴⁰Ar generated by the decay of ⁴⁰K has been degassed to the atmosphere (Allègre et al., 1987). This represents a lower limit on ³⁶Ar degassing, due to the fact of that ³⁶Ar is not continuously produced in the mantle by radioactive decay. The ratio of Pu- to U-derived Xe suggests that the upper mantle has lost ∼99% of its original primordial volatiles (Tucker et al., 2012), and this is likely an upper limit for the extent of ³⁶Ar degassing of the whole mantle. Hence, it can be assumed that ³⁶Ar is 50–99% degassed from the solid earth to the atmosphere, which yields a primordial mantle ³⁶Ar concentration between 8.5 × 10¹¹ and 1.7 × 10¹² atoms/g. In combination with the Ar partition coefficient calculated in this work, the upper limit for the ³⁶Ar dissolved in the core is estimated to be 3.6(9) × 10⁹ atoms/g.

The incorporation of He and Ar into the Earth’s core during its formation implies that high ³He/⁴He and ³⁶Ar/⁴⁰Ar ratio components can be preserved therein, because the abundances of U, Th and K in the core are small (Faure et al., 2020; Wheeler et al., 2006; Xiong et al., 2018). An important question is whether the ³He/⁴He and ³⁶Ar/⁴⁰Ar compositions of mantle-derived samples can be explained by a contribution of noble gases from the core. The ³He flux in OIBs is reported ranging from 2.3 × 10²⁵ to 4 × 10²⁶ atoms/yr (Pepin & Porcelli, 2002). If the core is the source of ³He, this implies that 9.5 × 10¹³ to 1.7 × 10¹⁵ g/yr core materials are involved in supplying He to the overlaying mantle. It is unknown whether diffusive or advective processes are capable of transferring the required amount of ³He from core to mantle. However, over the age of the Earth, only 0.02–0.4% of the ³He in the core must be transferred to the mantle to explain the ³He flux. Therefore, the core is at least a plausible source of ³He and elevated ³He/⁴He ratios in OIBs.

On the other hand, it is unlikely that the core contributes significantly to the high ³⁶Ar/⁴⁰Ar ratios in OIBs. The concentrations of ³He and ³⁶Ar in the plumes are comparable to each other (Anderson, 1998; Farley & Poreda, 1993), so a similar flux of each from the core would be required. However, the ³⁶Ar concentration in the core is approximately two orders of magnitude smaller than that of ³He, which would make it difficult for the core to support a ³⁶Ar flux comparable to that of ³He. The alternative storage site for ³⁶Ar could be the lowermost mantle, such as the D″ layer, which is compositionally distinct (Coltice & Ricard, 1999; Helffrich & Wood, 2001). If this is the case, it can be expected that the plumes originating from the base region of the mantle are characterized by elevated ³⁶Ar/⁴⁰Ar ratios.

The results obtained in this work also have potential implications in interpreting the solar ²⁰Ne/²²Ne ratio reported in the mantle-derived samples (Caffee et al., 1999; Yokochi & Marty, 2004). We found that He and Ar partitioning between liquid Fe and MgSiO₃ melt are controlled by their atomic size and the charge density properties of the host compositions. Since the atomic radius of Ne is closer to that of He (Zhang and Xu, 1995; Zhang et al., 2009), it can be expected that the metal/silicate partitioning behavior of Ne is similar to that of He, which is confirmed by recent experimental measurements conducted by Bouhifd et al. (2020). This indicates that some primordial Ne trapped by the proto-Earth might be incorporated into the Earth’s core, and the core might be a source for the solar Ne isotope compositions found in mantle-derived samples.

In conclusion, our results reveal that high ³He/⁴He and ³⁶Ar/⁴⁰Ar ratios can both be preserved in the Earth’s core, but with the He concentration much higher than that of Ar. It is plausible that contributions from Earth’s core can explain the elevated ³He/⁴He ratios, but not the elevated ³⁶Ar/⁴⁰Ar, in plume-derived basalts. Our results also suggest that the Earth’s core is a plausible host for primordial Ne.

Acknowledgments

The authors thank two anonymous reviewers for providing thoughtful comments on this manuscript, and Dr. Steve Jacobsen for editorial handling. The work was financially supported by MEXT KAKENHI Grants JP15H05826 and JP15H05834.

Open Research

Data Availability Statement

Dataset used in this study has been deposited at the Open Science Framework (https://osf.io/ej6kn/) with DOI: 10.17605/OSF.IO/EJ6KN.

Supporting Information

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Citing Literature

Volume48, Issue3

16 February 2021

e2020GL090769

Helium and Argon Partitioning Between Liquid Iron and Silicate Melt at High Pressure

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Computational Method

3 Results and Discussions

3.1 Partition Coefficient and Electronic Structure

3.2 Effects of Temperature and Light Elements

4 Implications

Acknowledgments

Open Research

Data Availability Statement

Supporting Information

References

Citing Literature

Figures

References

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Helium and Argon Partitioning Between Liquid Iron and Silicate Melt at High Pressure

Abstract

Key Points

Plain Language Summary

1 Introduction

2 Computational Method

3 Results and Discussions

3.1 Partition Coefficient and Electronic Structure

3.2 Effects of Temperature and Light Elements

4 Implications

Acknowledgments

Open Research

Data Availability Statement

Supporting Information

References

Citing Literature

Figures

References

Related

Information

RESOURCES

PUBLICATION INFO