Boron is considered a principal tracer for crustal recycling into the depleted mantle, and high boron anomalies and isotopically light boron (10B) in mantle-derived samples have been interpreted as the result of subduction. Using density functional theory, we predict that boron behavior changes from lithophile to siderophile, with the calculated boron partition coefficients (Dm/s) between liquid metal and silicate ranging from log10Dm/s ≤ −0.8 at low pressure–temperature conditions (10 GPa, 3000 K) to log10Dm/s ≥ 3.7 at high pressure and temperature (130 GPa, 5000 K). We further predict that the silicate becomes enriched in the heavier boron isotope (11B) by >1‰ relative to metal at high pressure–temperature. Our results suggest that Earth's core may hold >50% of Earth's boron budget and that a high boron content in deep diamonds and isotopically light boron in ocean islands basalts may reflect contributions from metallic reservoirs, rather than being attributed to crustal subduction and recycling.
Using density functional theory calculations we show that boron behavior changes from lithophile to siderophile at deep mantle conditions
Liquid silicate is enriched in the heavier boron isotope by ∼1‰ relative to liquid metal at high pressure and temperature
High boron contents in deep diamonds and isotopically light boron in oceanic hotspots may reflect contributions from metallic reservoirs
Plain Language Summary
Plate tectonics promotes the transport of surface rocks into the mantle, producing much of its chemical heterogeneity. Boron, a quintessential crustal element, is often used as a proxy for crustal contributions when found in mantle rocks and is, therefore, one of the central tools in geochemistry to trace recycling/mixing in the mantle. Using quantum mechanical calculations, we find that the chemical behavior of boron changes from lithophile (rock-loving) to siderophile (iron-loving) under pressure–temperature conditions relevant to core formation. Thus, much boron may have been transported to the core, and the core may be Earth's largest boron reservoir, rather than the crust. Chemical heterogeneity in the mantle inferred from boron signatures could therefore also result from chemical exchange between the core and mantle or equilibration with metallic iron dispersed throughout the mantle.
Boron (B) is an incompatible, lithophile element (Ottolini et al., 2009), depleted in the upper mantle (<0.2 μg/g) (Marschall et al., 2017) and enriched in the oceanic crust by orders of magnitude (up to 200 μg/g) (Leeman & Sisson, 1996). At the same time, its two isotopes, 11B and 10B, are highly fractionated in geological reservoirs (δ11B = (11B/10B)sample/(11B/10B)standard−1, values given in ‰) with, for example, average compositions of δ11B = +39.6‰ in seawater, and δ11B = −7.1‰ in mantle-derived rocks (Palmer, 2017). Boron is thus often used as a tracer of recycled crust in the mantle (De Hoog & Savov, 2018) because minor additions strongly alter its B signature.
Due to its scarcity in the deep Earth, the origin of boron in mantle-derived samples, most prominently in blue Type IIb diamonds with up to 8 μg/g B (Gaillou et al., 2012; Smith et al., 2018), has been linked to subduction (Smith et al., 2018). However, a recent petrographic study showing that naturally occurring titanium diboride (TiB2) crystallizes predominantly from metallic melts at low oxygen fugacity (Griffin et al., 2020) suggests that metals can exert control on Earth's boron distribution given that low likely governed core formation (Rubie et al., 2011). As metallic iron is present predominantly in the core and likely at percent level throughout the mantle (Frost et al., 2004), its impact on Earth's boron budget merits consideration.
Some ocean island basalts (OIB) with deep origin show isotopically lighter δ11B (as low as −20.7‰) than depleted mantle, which has been interpreted as a signature of recycled slab material that is successively stripped of boron and becomes isotopically lighter during dehydration (Walowski et al., 2019, 2021). However, other aspects of OIB geochemistry appear to require a core contribution (Brandon et al., 1998; Herzberg et al., 2013; Humayun, 2004; Rizo et al., 2019), with low 182W/184W reported for Icelandic lavas (Mundl-Petermeier et al., 2020) the most significant example; ocean island basalts (OIB) δ11B may be influenced in a similar fashion.
To establish boron composition of Earth's core, its metal–silicate partitioning at high pressure–temperature (P–T) conditions during core formation must be known. Measuring boron in samples recovered from high P–T experiments, however, presents significant challenges (Bourdon et al., 2018), which have prevented such studies. Here, we perform density functional theory (DFT) molecular dynamics (MD) simulations with boron in metallic and silicate melts to determine partitioning and isotope fractionation at 10–130 GPa and 3000–5000 K, covering P–T conditions of core differentiation (Siebert et al., 2012). We consider partitioning of elemental B and B2O3, reflecting reduced and oxidized magma ocean conditions, and integrate the results in core formation models (Rudge et al., 2010).
2 Computational Methods
2.1 Density Functional Theory Molecular Dynamics Simulations
We perform electronic structure calculations based on Kohn-Sham (KS) density functional theory (DFT) to obtain internal energy, Hellmann-Feynman stresses and forces with a plane wave approach (with an energy cutoff of 450 eV), and periodic boundary conditions using the Vienna ab initio simulation package (VASP) (Kresse & Furthmüller, 1996). We use the projector augmented wave implementation and atomic files (Kresse & Joubert, 1999) in the generalized gradient approximation to exchange and correlation (Perdew et al., 1996). Electronic KS-density functional theory (DFT) states are calculated at the Brillouin zone center. Molecular dynamics (MD) simulations are performed in the N–V–T ensemble, where the number of atoms (N) and the volume (V) of the cell are kept fixed, and T is controlled by a Nosé-Hoover thermostat. After convergence of the electronic cycle, atoms are advanced with a time step of Δt = 1.0 fs along the Hellmann-Feynman forces.
2.2 Partition Coefficient
We use two-phase simulations to model partitioning directly, mimicking an experiment by putting metallic and silicate phases in direct contact in a simulation cell and tracking the distribution of boron atoms as the system reaches equilibrium, providing a semi-quantitative understanding.
With G calculated at several solute concentrations and P–T, we can regress values of and λsolu (Equation 5); μsolu and μsolv can then be obtained for the silicate and metal separately (Equations 3 and 4). Finally, the equilibrium partition coefficient is calculated as .
2.3 Equilibrium Isotope Fractionation
3.1 Boron Metal–Silicate Partitioning
Two-phase simulations are designed with liquid metal (Fe150) and silicate (Mg35Si35O105) cells put together (Figure S1 in Supporting Information S1), both initially containing equal numbers of boron atoms (Bm and Bs denote boron atoms in metal and silicate, respectively). From the time-evolution of the boron distribution at ∼40 GPa and ∼3500 K, we observe strong boron partitioning into the metal, with Bm/Bs = 2.43 ± 0.02 (Figure 1a; Movie S1). Additional two-phase simulations reveal lithophile behavior of B at low P (∼10 GPa) (Bm/Bs = 0.79 ± 0.01) (Figure S2a in Supporting Information S1), while the siderophile nature of B observed at ∼40 GPa persists to ∼130 GPa, with enhanced Bm/Bs = 5.19 ± 0.05 (Figure S2b in Supporting Information S1). When more oxygen is available in the form of B2O3, Bm is slightly smaller than Bs (Bm/Bs = 0.95 ± 0.01) at ∼40 GPa (Figure 1b and Movie S1 in Supporting Information S1), suggesting lower boron compatibility in the metal under more oxidizing conditions. Nevertheless, appreciable amounts of boron partition into the metal, more so than conventionally expected (see, e.g., review by Grew 2017; Shearer & Simon 2017).
As an equilibrium property, boron distribution between metal and silicate can be understood in terms of the Gibbs energy difference () of B incorporation. With this involves three contributions (Wilson & Militzer, 2012): (a) a potential energy term , (b) from the difference of partial molar volume () of boron, and (c) an entropic term . Among these, (b) is directly accessible from DFT-MD simulations, which provides insight into a critical aspect of the underlying processes. We compute of B dissolved in the metal () considering different Fe1-cBc compositions, and in the silicate () for (MgSiO3)1-cBc compositions (for correspondingly). We find for both B and B2O3 at all P–T conditions considered (Figure 2), that is, . At low P (0–20 GPa), is highly compressible and remains essentially constant, leading to a rapid decrease in . Similarly, at 0 GPa, but they become comparable at 20 GPa. for boron varies little in the higher-P range, with significantly larger than , and similar to . The term increasingly favors boron dissolution in metal with P, much more strongly for B than for B2O3.
To quantitatively address the energetics of boron exchange, we compute Gibbs energies G(P, T, c) for B-bearing MgSiO3 silicate and Fe liquids by thermodynamic integration at three P–T conditions relevant for core formation: 10 GPa and 3000 K, 40 GPa and 3500 K, and 130 GPa and 5000 K (Tables S4 and S5 in Supporting Information S1). We fit G(P, T, c) results for four boron concentrations (cB or ) and the boron-free silicate and iron with a concentration-dependent expression (Equation 5; Figure S9 in Supporting Information S1) from which the chemical potentials of boron in silicate () and metallic () solutions are calculated (Equation 3; Figures 3a–3f): at 10 GPa, reflecting lithophile behavior; becomes larger than at higher P–T, indicating siderophile behavior, consistent with the results from the two-phase simulations. A similar transition from lithophile to siderophile is predicted for B2O3—with substantially smaller than at 10 GPa, slightly smaller at 40 GPa, but significantly larger at 130 GPa. From the chemical potentials, the boron metal–silicate partition coefficient can be readily calculated utilizing Equation 1 (Figure 3g): increases from −0.8 ± 0.3 at 10 GPa and 3000 K to 3.7 ± 0.1 at 130 GPa and 5000 K; for B2O3, increases from −3.6 ± 0.4 to 4.6 ± 1.1 over the same conditions.
Both thermodynamic integration and two-phase simulations indicate that boron is lithophile at low P, but turns siderophile at high P. As no experiment has directly measured boron metal–silicate partitioning, a discussion must rely on indirect evidence. (a) Experimental charges, both silicate (Shahar et al., 2015) and iron liquids (Sokol et al., 2019) in boron nitride sample capsules, recovered from P < 10 GPa reveal boron incorporation, with concentrations in silicate (2–5 wt%) orders of magnitude larger than in Fe metal (500–800 μg/g). This qualitatively agrees with the lithophile character of boron from our low-P simulations. (b) At higher P, numerous iron borides (e.g., FeB4, Fe2B7). have been predicted (Kolmogorov et al., 2010) or synthesized (Gou et al., 2013); the enhanced reactivity between iron and boron may reflect the transition from lithophile to siderophile behavior. Given our results and previous experimental observations that conventional highly lithophile elements partition strongly into Fe–S liquids over coexisting silicate melts at low (e.g., Nb and Ta in Wood & Kiseeva, 2015, Ti in Kiseeva & Wood, 2015; Steenstra et al., 2020, and U in Wohlers & Wood, 2015), the chemical behavior of elements may strongly deviate from Goldschmidt's original classification at conditions of planetary formation and differentiation.
While our DFT-MD simulations are performed with the goal of first-order constraints on the lithophile and siderophile characteristics of boron on three P–T points (Figure 3 and S10 in Supporting Information S1), extrapolating for elemental B at 10 GPa to higher P tentatively puts the transition between lithophile and siderophile behavior at ∼20 GPa. With metal saturation in the transition zone and below, our results suggest that the amount of boron in metallic reservoirs in the mantle can be significantly larger than that recycled into the lower mantle via subduction, particularly because dehydration at subarc depths (Chemia et al., 2015; Syracuse et al., 2010) leads to a removal of >99% boron from the slab crust during subduction (Marshall et al., 2022; McCaig et al., 2018).
3.2 Equilibrium Boron Isotope Fractionation
Previous experiments have demonstrated that metallic phases are depleted in heavy isotopes of light elements such as carbon (Satish-Kumar et al., 2011), silicon (Hin et al., 2014; Shahar et al., 2009), and nitrogen (Dalou et al., 2019) even at mantle T. As isotope fractionation arises from the influence of mass differences on vibrational energies in coexisting phases, and scales with (mh − ml)/(mh · ml) approximately (Equation 10) (Schauble, 2004), metal–silicate equilibration is expected to fractionate boron isotopes more strongly than the heavier elements mentioned above. We estimate boron isotope fractionation based on configuration snapshots extracted from DFT-MD trajectories in Fe50B1 and (MgSiO3)15B1 cells. Force constants acting on the boron atom in the silicate are 2–4 times larger than in the metal at all P–T conditions considered (Figures S11a–S11c in Supporting Information S1), leading to larger δ11B values in silicate than coexisting metal. Assuming core–mantle segregation at 40 GPa and 3500 K (Siebert et al., 2012), the core would have smaller δ11B by ∼1‰. Fractionation is predicted to depend on T, but not on P (Figure S11d in Supporting Information S1). This difference should be resolvable in modern isotope measurements (δ11B ± 0.3‰) (Foster et al., 2018).
4.1 Earth's Boron Budget
Establishing volatile depletion requires information on the representative compositions of both bulk silicate Earth (BSE) and CI chondrites. Fresh mid-ocean ridge basalt (MORB) glasses have been used to derive the bulk silicate Earth (BSE) boron budget, with B compatibility during MORB extraction following that of praseodymium (Pr) (Marschall et al., 2017). Using the well-constrained Pr content of the depleted mantle and B/Pr ratios from MORB, Marschall et al. (2017) tightly constrain the B budget in the BSE to 0.19 μg/g. By contrast, the B content for CI chondrites is reported as 0.27–1.2 μg/g (Shaw et al., 1988; Zhai & Shaw, 1994; see also Marschall et al., 2017 and references therein), partly due to sample history and analytical challenges. This suggests a range of depletion factors, fB = (B/Mg)BSE/(B/Mg)CI = 0.07–0.30, rather than a single value of fB ∼ 0.10 used, for example, by Wood et al. (2019).
The concept of condensation T for boron is problematic due to its nucleosynthesis. Unlike other elements, boron, together with lithium and beryllium, has a low nuclear binding energy (Prantzos, 2007). Production of boron is attributed primarily to spallation reactions between galactic cosmic rays (GCR, mainly composed of protons and α particles) and interstellar gas/dust nuclei (carbon, nitrogen, and oxygen) (Prantzos, 2012; Reeves et al., 1970). The inefficient nature of spallogenic nucleosynthesis leads to an abundance of B several orders of magnitude lower than that of the stable neighboring elements (helium and carbon) (Palme et al., 2013), and the resulting isotopic composition varies significantly depending on the energy of GCR (Cassé et al., 1995; Ramaty et al., 1996). The isotope heterogeneity is documented by δ11B in chondrules spanning −50‰ to +50‰ (Chaussidon & Robert, 1995), which is too large to be controlled by mass-dependent fractionation through evaporation or condensation, but can be explained by presolar grains contributing anomalous δ11B. Boron condensation from the solar nebular gas at a unique T is therefore not a meaningful concept (Chaussidon & Robert, 1997; M. C. Liu & Chaussidon, 2018).
Alternatively, the boron budget in the BSE may have been replenished by boron-rich, late-accreted material after core–mantle differentiation. This late veneer scenario is supported by an excess of highly siderophile elements (HSEs: Os, Ir, Ru, Rh, Pt, Pd, Re, and Au) in the BSE and their ratios (e.g., Os/Ir) resembling those in carbonaceous chondrites (Chou, 1978), the abundance ratios (Wang & Becker, 2013) and isotopic compositions (Varas-Reus et al., 2019) of moderately volatile and chalcogen elements (S, Se, and Te), and would account for large portions of Earth's volatile budget, including boron. However, several studies (Hellmann et al., 2021; König et al., 2014; Yierpan et al., 2019) have argued that S–Se–Te compositions are subject to mantle fractionation processes (e.g., partial melting, metasomatic overprinting), such that peridotite samples (Varas-Reus et al., 2019; Wang & Becker, 2013) do not provide reliable proxies for the composition of the BSE. Recent studies based on nucleosynthetic isotope anomalies for the siderophile elements ruthenium and molybdenum (Bermingham & Walker, 2017; Fischer-Gödde & Kleine, 2017; Worsham & Kleine, 2021) are not prone to post-accretionary modifications and characterized late-accreted material as isotopically distinct from carbonaceous chondrites, but identical to enstatite chondrites originating from the inner solar system. These studies support a scenario of homogeneous accretion (Wood et al., 2010) and volatiles delivery to the Earth during the main phase of accretion and differentiation (Jin & Bose, 2019; Piani et al., 2020).
With a substantial amount of boron likely present during planetary differentiation, we explore two core formation scenarios to determine boron partitioning based on our predicted and . We consider a range of initial concentrations such that the resulting BSE content after core segregation is close to 0.19 μg/g (Marschall et al., 2017). Single-stage core formation at 40 GPa and 3500 K (Siebert et al., 2012), as a first-order approximation, yields a boron content in the core of 0.1–2.3 μg/g (i.e., 2.7–46 × 1017 kg), 1–18 times the crustal reservoir of ∼2.6 × 1017 kg (Marschall et al., 2017), with the large variation arising from the difference in partition coefficients and . Continuous core formation considers planetary accretion and differentiation as synchronous processes and accounts for accreting material heterogeneity and metal–silicate equilibrium over a wide P–T range during planetary growth. We follow the framework of Rudge et al. (2010) for the accretion of differentiated embryos: their cores partially re-equilibrate with the proto-Earth mantle, while the remainder is directly added to Earth's core (details in Supporting Information S1). In multiple sets of calculations, we find 0.7–6.2 μg/g in the core (i.e., 13–120 × 1017 kg), both larger values and a larger concentration range than from single-stage core formation.
4.2 Core Contributions to Anomalous δ11B in Oceanic Hotspots
Isotopically light boron signatures in hotspot lavas have been broadly interpreted as sampling crustal boron in their sources (Walowski et al., 2019, 2021). This scenario is consistent with the standard view that (a) OIBs contain materials recycled from the surface of the Earth (Hofmann & White, 1982); (b) boron is exclusively hosted in the crust/seawater (De Hoog & Savov, 2018); and (c) the magnitude of equilibrium isotope fractionation – scaling with T−2 (Schauble, 2004) – is expected to be negligible at high T of the deep Earth. Our results provide evidence for previously unrecognized primordial boron reservoirs possibly enriched in 10B in the deep mantle and core.
To explore potential core components in the mantle sources responsible for the isotopically light boron in OIB, we assemble a global set of OIB δ11B data (Chaussidon & Marty, 1995; Hartley et al., 2021; Kobayashi et al., 2004; Marschall & Jackson, 2020; Walowski et al., 2021), together with μ182W (deviation of 182W/184W from the terrestrial Alfa Aesar W standard in ppm) data (Jackson et al., 2020; Mundl-Petermeier et al., 2020) from nine volcanic hotspots (Table S8 in Supporting Information S1). Negative μ182W anomalies have been traditionally used as fingerprints of the core (e.g., Rizo et al., 2019) and a correlation between δ11B and μ182W may support the core as a B reservoir. However, strong isotopic heterogeneity at regional/outcrop scales, with μ182W in individual hotspots spanning >50% of the total variability of the mean (Figure S13 in Supporting Information S1), obscures any potential correlation between δ11B and μ182W. Concurrent measurements of δ11B and other geochemical indices (e.g., μ182W) in terrestrial rocks at smaller scales will be needed to assess whether, and to what extent, core formation elevated δ11B of the BSE relative to chondrites, and whether OIBs entrain isotopically light B from the core.
4.3 Reappraisal of the Origin of Blue Diamonds
In addition to a high boron content, Type IIb diamonds are characterized by the presence of Fe and Fe-carbide inclusions (Smith et al., 2018) which potentially suggests that they grew from iron–carbon melts rather than the recycled crust. This diamond formation mechanism is supported by (a) the inference that up to 90% of Earth's carbon resides in metallic iron (Fischer et al., 2020); (b) several experiments strongly suggest that iron–carbon melts play a role both as a source and crystallization medium for diamond growth (Palyanov et al., 2013, 2020; Sokol et al., 2019). Notably, diamonds synthesized this way incorporate boron up to hundreds of μg/g (Sokol et al., 2019); (c) natural diamonds containing metallic inclusions suggest direct diamond precipitation from metallic liquids by carbon saturation (Smith et al., 2016) due to physical or chemical perturbations.
Rather than boron in Type IIb diamonds representing crustal recycling, its predicted siderophile nature suggests the fingerprint of a metallic reservoir. The Earth's core provides an unlimited source of metal, which may deliver boron through infiltration into the lowermost mantle (e.g., Bull et al., 2009). Such mechanism has been explored as the potential cause of the chemical diversity in OIBs, for example, low 182W/184W (Mundl-Petermeier et al., 2020), high 3He/4He (Bouhifd et al., 2013), 186Os/188Os (Brandon et al., 1998) and Fe/Mn ratios (Humayun, 2004). The hypothesis of a core contribution to the boron signature of Type IIb is highly conjectural as it requires more than 2,000 km of vertical migration of dense core components with minimal dilution of boron signatures.
Alternatively, metallic Fe prevalent throughout the deep mantle (Frost & McCammon, 2008) offers a simple explanation for boron anomalies in Type IIb diamonds. The high stability of Fe3+ in high-P minerals (e.g., Frost et al., 2004; Kiseeva et al., 2018; Rohrbach et al., 2007) would drive Fe2+ to disproportionate (3Fe2+ → 2Fe3+ + Fe0), with Fe0 being exsolved as metal at >250 km depths (Frost et al., 2004; Rohrbach et al., 2007). Recent petrologic observations of natural samples, including metallic inclusions in diamonds (Anzolini et al., 2020; Smith et al., 2016) and the intergrowth of bridgmanite and metal in shock veins of meteorites (Bindi et al., 2020; Ghosh et al., 2021) strongly suggest the presence of metallic iron in the mantle created via the charge disproportionation reaction.
The carbon isotope composition of blue Type IIb diamonds, with low δ13C(−13‰) compared to mantle carbon (−5‰), is typically taken as further evidence of a subduction-related origin with a significant organic contribution (δ13C = −25‰) (Smith et al., 2018). However, other mechanisms may account for this isotopic signature, including high-T fractionation. An analysis of mantle-derived samples (Mikhail et al., 2014), high P–T experiments (Satish-Kumar et al., 2011), and calculations (J. Liu et al., 2019) reveals that iron–carbon melts become significantly depleted in 13C when coexisting with other carbon-bearing phases, including diamond. Rayleigh distillation fractionation would progressively remove 13C and concentrate incompatible B in iron–carbon melt. Metallic reservoirs in the mantle could therefore serve both as a 13C-depleted and B-enriched source for Type IIb diamonds.
We use density functional theory molecular dynamics to predict the metal–silicate partitioning behavior of boron at pressures and temperatures of core formation. We find that boron becomes increasingly compatible with metal with increasing pressure–temperature, such that its behavior changes from lithophile to siderophile at conditions expected in magma oceans during core–mantle segregation. We illustrate this change in fundamental behavior qualitatively in two-phase simulations, and quantify metal–silicate partition coefficients (Dm/s) of boron by combining density functional theory molecular dynamics with thermodynamic integration calculations; log10Dm/s increases from −0.8 ± 0.3 at low pressure–temperature (10 GPa and 3000 K) to 3.7 ± 0.1 at high pressure–temperature (130 GPa and 5000 K). We further predict that liquid silicates become enriched in the heavier boron isotope by >1‰ relative to liquid metal at conditions relevant to core formation. Our results provide evidence that metallic iron, present in the mantle and core, can serve as a major boron reservoir that may account for more than one half of Earth's overall boron inventory. This scenario offers an explanation for the anomalous elemental and isotopic boron signature in the deep Earth, alternative to mixing of recycled crust into the depleted mantle.
This work is supported by Deutsche Forschungsgemeinschaft (German Science Foundation, DFG) with grants STE1105/12-1 and STE1105/13-2 to G.S.N. Computations were performed at the Leibniz Supercomputing Center of the Bavarian Academy of Sciences and the Humanities, and the research center for scientific computing at the University of Bayreuth. Liang Yuan thanks the Alexander von Humboldt Foundation for financial support. Comments by Kate Kiseeva and an anonymous reviewer have significantly improved the manuscript. Open access funding enabled and organized by Projekt DEAL.
Data Availability Statement
The data reported in this paper can be freely downloaded in Figshare (https://doi.org/10.6084/m9.figshare.17086412.v3). All computations in this study were carried out using the Vienna ab initio simulation package (VASP) which is available for licensing at https://www.vasp.at/.
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