2.2.1 Constraints from Isotopes of Refractory Elements

Geochemical models based on elemental abundances and isotopic constraints predict the accretion of bulk Earth primarily from chondritic meteorites.Reference Ringwood^25, Reference Anders and Ebihara²⁶ Because elemental and isotopic fractionation trends for bulk silicate samples and chondritic meteorites have well-defined relationships, it is widely assumed that the building blocks of Earth belong to a class of primitive objects that are sampled by chondritic meteorites.Reference Allègre, Manhès and Lewin²⁷ Close similarity of the abundances of refractory lithophile elements between the BSE and CI led to an early development of a CI model for Earth.Reference Ringwood²⁵ Allègre et al.Reference Allègre, Manhès and Lewin²⁷ further consolidated this model by arguing that volatile depletion trends in the BSE are matched most closely by CI chondrites. However, a distinct disparity of oxygen (second most abundant element in the BSE by mass) isotopes (i.e. ¹⁶O, ¹⁷O, and ¹⁸O) between CI chondrites and the BSE, which could not be explained by any fractionation or differentiation models,Reference Clayton, Onuma and Mayeda^28, Reference Clayton²⁹ was one of the first observed isotopic variations that challenged the CI model for Earth. Over the past decades, isotopic dissimilarity between CI chondrites and the BSE has been extended from Δ¹⁷O (deviation from a reference mass-dependent fractionation line in a triple isotope of oxygen plotReference Young³⁰) to several radiogenic as well as non-radiogenic isotopic anomalies for a wide suite of refractory elements with contrasting geochemical behaviors: lithophile elements (ε⁴⁸Ca (Ref. Reference Dauphas31), ε⁵⁰Ti, μ¹⁴²Nd), moderately siderophile elements (ε⁵⁴Cr, ε⁶⁴Ni, ε⁹²Mo), and highly siderophile elements (HSEs; ε¹⁰⁰Ru) (Refs. Reference Dauphas32, Reference Fischer-Gödde and Kleine33 and references therein). Interestingly, the BSE isotopic compositions for all of these elements are almost indistinguishable from enstatite chondrites (E-chondrites). This has led to the development of an E-chondrite model for Earth.Reference Dauphas^32, Reference Javoy^34, Reference Javoy³⁵ Tracking the isotopic evolution of the growing BSE by taking into account the alloy–silicate partitioning behavior of several lithophile, moderately siderophile, and HSEs during core–mantle equilibration, DauphasReference Dauphas³² proposed that half of the first 60% of accreted mass was composed of E-type chondrites, while the remaining 40% was all E-type chondritic materials. However, there are a few outstanding issues with an E-chondritic model for Earth, namely: (1) the Ca/Mg ratio of the BSE (0.118Reference McDonough and Sun³⁶) is distinctly higher than that of E-chondrites (0.080Reference Wasson and Kallemeyn³⁷), suggesting that the BSE has an enriched refractory elemental abundance relative to E-chondrites;Reference Fitoussi, Bourdon and Wang³⁸ (2) E-chondrites have an Mg/Si ratio that is lower than that of the BSE sampled by upper-mantle rocks,Reference Palme, O’Neill and Carlson³⁹ which can only be explained by either incorporation of Si into the core or via an unsampled lower mantle with a low Mg/Si ratio;Reference Murakami, Ohishi, Hirao and Hirose⁴⁰ and (3) δ³⁰Si_BSE is 0.3–0.4‰ higher than δ³⁰Si of E-chondrites and aubrites.Reference Fitoussi and Bourdon⁴¹ Experimentally determined Si isotopic fractionation parametersReference Shahar^42, Reference Shahar⁴³ rule out the possibility of explaining the Si isotopic composition as well as the Mg/Si ratio of the BSE via incorporation of Si in the core if Earth was primarily accreted from E-chondrites.Reference Fitoussi and Bourdon⁴¹ Although there are studies that argue for a lower mantle or at least a portion of the lower mantle being richer in silica compared to Earth’s upper mantle,Reference Murakami, Ohishi, Hirao and Hirose^40, Reference Ballmer, Houser, Hernlund, Wentzcovitch and Hirose⁴⁴ such findings are debated. To circumvent these issues, Dauphas et al.Reference Dauphas, Poitrasson, Burkhardt, Kobayashi and Kurosawa⁴⁵ proposed that the bulk Earth and the E-chondrites sample an isotopically similar reservoir with their subsequent chemical evolution offset by ensuing nebular fractionation and planetary differentiation processes. In summary, a large number of geochemical systematics point to the bulk Earth being made from E-chondrite-type materials, although questions on the major element and volatile element abundance mismatch remain.

2.2.2 Constraints from Isotopes of Highly Volatile Elements

In contrast to constraints from refractory elements, constraints from highly volatile elements (i.e. C, N and H (water)) paint a different picture on the potential sources of LEVEs. Although ordinary chondrites (OCs), which sample S-type asteroids in the inner belt (2.1–2.8 AU), have similar amounts of bulk water as the BSE, the D/H ratio of the BSE is not similar to that of OCs,Reference McNaughton, Borthwick, Fallick and Pillinger⁴⁶ but rather is strikingly similar to that of carbonaceous chondrites, especially CI chondrites,Reference Robert, Merlivat and Javoy⁴⁷ which are representative of C-type asteroids (beyond 2.8 AU) (Figure 2.2a). Similarity of ¹⁵N/¹⁴N between the BSE and CI chondrites also points toward a carbonaceous chondritic origin of volatiles on Earth (Figure 2.3b).Reference Marty^13, Reference Alexander^48, Reference Pearson, Sephton, Franchi, Gibson and Gilmour^{49 13}C/¹²C of the BSE cannot distinguish between a chondritic or cometary origin of C (Figure 2.2b).Reference Marty, Alexander and Raymond^50, Reference Sarafian, Nielsen, Marschall, McCubbin and Monteleone⁵¹ However, a clear distinction of the ¹⁵N/¹⁴N ratio of the BSE from the corresponding cometary values would necessitate C delivery by CI chondrites as well, assuming all the major volatiles (i.e. C, N, and water) were sourced from a similar parent body.

Figure 2.2 Comparison of isotopic compositions of (a) hydrogen and nitrogen and (b) carbon and nitrogen for several Solar System objects and reservoirs. The solar reservoir is depleted while the cometary reservoir is enriched in the heavier isotopes of nitrogen and hydrogen relative to all classes of meteorites as well as the BSE. Although δ¹³C alone cannot distinguish between the meteoritic and cometary sources, the isotopic compositions of all major LEVEs suggest that the BSE had a similar parent reservoir as carbonaceous chondrites.

Data sources: Carbonaceous chondrites, Refs. Reference Alexander48, Reference Pearson, Sephton, Franchi, Gibson and Gilmour49; E-chondrites, Refs. Reference Grady, Wright, Carr and Pillinger52, Reference Alexander, Swan and Prombo53; comets, Ref. Reference Alexander, McKeegan and Altwegg54; angrites and Vesta, Refs. Reference Sarafian, Nielsen, Marschall, McCubbin and Monteleone51, Reference Sarafian55; and solar, Refs. Reference Geiss and Gloeckler56–Reference Marty, Chaussidon, Wiens, Jurewicz and Burnett58.

Although thus far direct matching of the isotopes of C, H, and N of the BSE with undifferentiated meteorites has been the approachReference Marty and Yokochi⁵⁹ to determining the source of the LEVEs on Earth, there is a growing realization that there may be fractionation of stable isotopes during early terrestrial differentiation, such as devolatilization, MO degassing, and core–mantle fractionation. Indeed, such fractionation processes may be able to reconcile some of the observed differences between the LEVE isotopic compositions of the BSE and the chondrites.Reference Wood, Li and Shahar⁶⁰ For example, carbon isotopic compositions of many CI chondritic materials are distinctly lighter (δ¹³C, approximately –15 to –7‰Reference Marty, Alexander and Raymond⁵⁰) than the average carbon isotope composition of Earth’s mantle (δ¹³C, approximately –5‰Reference Kerridge^61, Reference Deines⁶²). Similarly, the sulfur isotope composition of Earth’s mantle has also been argued to be non-chondritic.Reference Labidi, Cartigny and Moreira⁶³ Graphite–Fe–carbide melt carbon isotope fractionation experimentsReference Satish-Kumar, So, Yoshino, Kato and Hiroi⁶⁴ showed that ¹²C preferentially incorporates into the metallic phase, leaving a ¹³C-enriched signature in the graphite or diamond. If similar fractionation behavior applies between silicate MO and core-forming alloy liquid, then core formation could explain how Earth’s mantle evolved to have a heavier carbon isotope value compared to the chondritic building blocks.

2.2.3 Constraints from Theoretical Modeling

Because isotopic compositions of refractory elements suggest bulk Earth to be composed of materials similar to E-chondrites while volatile elements favor their delivery via CI chondritic material, the timing of admixing of C-rich material into the accreting zone of Earth becomes key. Such admixing could have taken place either during the primary stage of Earth’s growth or after the main phase of accretion. Similarly, delivery of C-bearing materials may have occurred via accretion of undifferentiated bodies similar to chondrites or via amalgamation of differentiated bodies with C abundances in relevant reservoirs of those bodies set by core–mantle differentiation and atmospheric losses.Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16–Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ Theoretical models have been used to simulate the early evolution of the Solar System by accounting for dynamics of planetary accretion along with geochemical, cosmochemical, and chronological relationships between accreting and resulting bodies.Reference Walsh, Morbidelli, Raymond, O’Brien and Mandell^65, Reference Raymond, O’Brien, Morbidelli and Kaib⁶⁶ Constrains from Hf/W chronometry predict that Mars-sized planetary embryos were formed from mostly E-type chondritic material sourced from the inner part of the Solar System in the initial ~5 Ma.Reference Dauphas and Pourmand⁶⁷ Recent advancements like pebble accretion models predict that gas giants like Jupiter also grew synchronously to their present-day mass via trapping of proto-solar nebular gas within the lifetime of the protoplanetary disk.Reference Lambrechts and Johansen^68, Reference Johansen, Low, Lacerda and Bizzarro⁶⁹ However, the growth of gas giants is thought to rapidly deplete the asteroid belt, which would mean minimal interaction of C-rich carbonaceous chondritic material that condensed in the outer parts of the Solar System with the growth zone of terrestrial planet accretion within 2 AU.Reference Morbidelli, Lunine, O’Brien, Raymond and Walsh¹⁹ With the consideration that the presence of giant planets in the system affects the mixing and delivery of LEVEs from the outer regions to the terrestrial planet-forming region in the disk, the migration of giant planets has been argued to be necessary to perturb the orbits of cometary and asteroid-like bodies, bringing a fraction of these to the inner regions, where they can collide with terrestrial planets, delivering additional volatile elements to the rocky planets.Reference Morbidelli, Lunine, O’Brien, Raymond and Walsh¹⁹ A specific planetary migration model, the Grand Tack scenario,Reference Morbidelli, Lunine, O’Brien, Raymond and Walsh^19, Reference O’Brien, Walsh, Morbidelli, Raymond and Mandell^20, Reference Walsh, Morbidelli, Raymond, O’Brien and Mandell⁶⁵ postulated that the inward and outward movement of Jupiter likely repopulated the asteroid belt in the inner parts of the Solar System with C-type chondritic material. However, these models cannot constrain the net mass of volatile-rich material being delivered, as they allow for a total influx of volatile-rich material ≥0.5–2.0% of present-day Earth’s mass, assuming volatile-rich CI chondrites have water in the range of 5–10 wt.%.Reference Morbidelli, Lunine, O’Brien, Raymond and Walsh^19, Reference O’Brien, Walsh, Morbidelli, Raymond and Mandell²⁰ Delivery of a C budget that is larger than the present day in the BSE would require offsetting via later differentiation processes, while C delivery being restricted to the present-day budget of the BSE would have to be unaffected by later differentiation processes. A model such as Grand Tack does not directly constrain the relative timing of acquiring the C- and water-rich chondritic materials in the terrestrial planet-forming regions with respect to specific giant impact events. However, with the Moon formation being a specific event, similarity or a lack thereof between C and other LEVE budgets and volatile isotope signatures of Earth and Moon may shed light on when LEVE-rich materials were brought in with respect to the Moon-forming event. Little is known about the C budget of the Moon or the lunar mantle;Reference Wetzel, Hauri, Saal and Rutherford^70, Reference Chi, Dasgupta, Duncan and Shimizu⁷¹ however, if water and carbon were co-delivered, the appreciable water content of lunar glasses and melt inclusionsReference Saal^72, Reference Hauri, Weinreich, Saal, Rutherford and Van Orman⁷³ and the E-chondritic nature of late veneerReference Dauphas³² can only be reconciled if volatiles were delivered to the Earth–Moon system beforeReference Saal, Hauri, Van Orman and Rutherford^74, Reference Greenwood⁷⁵ or during the Moon-forming impact.Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ However, if C and other LEVEs were delivered during the main stage of Earth’s accretion, then differentiation processes like core–mantle separation, as well as the delivery mechanism of volatiles – either by smaller, undifferentiated planetesimals composed of primarily CI-chondritic material or via relatively large, differentiated planetary embryos heterogeneously composed of material sourced from both inner and outer parts of the Solar System – can provide additional information on the origin of LEVEs in the BSE.

2.4.1 The Role of Late Accretion

The theory of the addition of undifferentiated meteorites after the completion of metal–silicate differentiation chiefly stems from the approximately chondritic relative abundance of HSE (e.g. Re, Os, Ir, Ru, Pt, Rh, Pd, and Au) concentrations in Earth’s mantle and the BSE, plus the fact that the BSE is not as depleted of HSEs as it would have been if the entire HSE inventory of the bulk Earth was available before equilibrium core formation took place.Reference Walker^93, Reference Mann, Frost, Rubie, Becker and Audétat⁹⁴ Assuming that core formation originally left the silicate Earth virtually HSE free and later additions of chondritic materials elevated the HSE abundances to the present level, the chondritic mass added is estimated to be 0.5% of Earth’s mass (0.005 M_E). WalkerReference Walker⁹³ noted that this estimate may be ~1.5 times higher or a factor of four lowerReference Morgan, Walker, Brandon and Horan⁹⁵ depending on the exact concentrations of HSEs in the chondritic materials being added. Willbold et al.Reference Willbold, Elliott and Moorbath⁹⁶ also calculated that in order to offset the pre-late accretion ¹⁸²W-excess composition of the BSE, 0.08 M_E chondritic mass needs to be added. Given that many carbonaceous chondrites are rich in LEVEs, many studies have surmised that late accretion of these materials brought all of the LEVEs to the BSE.Reference Chi, Dasgupta, Duncan and Shimizu^71, Reference Albarede^97–Reference Dasgupta, Chi, Shimizu, Buono and Walker⁹⁹ If this was the mechanism, then the core formation would have no influence on the relative abundance of various LEVEs. Indeed, the addition of 0.0030–0.0075 M_E chondritic materials with 3.48–3.65 wt.% C to the BSE would set the BSE C budget to ~100–250 ppm C (or ~360–900 ppm CO₂ in the mantleReference Dasgupta⁸). Although this C budget may be sufficient to match even the enriched basalt source regions, as briefly discussed by Dasgupta,Reference Dasgupta⁸ there are several challenges in invoking CI-type carbonaceous chondrite as the chief or sole source of the BSE C and other LEVEs. Section 2.2 already discussed which elemental and isotopic compositions of the BSE are not satisfied if the BSE is chiefly made up of carbonaceous chondrites. Section 2.2 also outlined how the elemental abundance of C and the C/S ratio of the BSE can be satisfied if CI-type carbonaceous chondrite accreted to Earth after core formation was complete, but the C/N and C/H ratios and possibly δ¹³C and δ³⁴S of the BSE are difficult to explain. Here, we specifically discuss what challenges exist in invoking other known meteorites as the late-accreting materials to explain the entire inventory of carbon and other LEVEs in the BSE.

Given E-chondrites (e.g. (low enstatite) enstatite chondrite (EL) and (high enstatite) enstatite chondrite (EH)) are depleted in water and also poor in C and N,Reference Grady, Wright, Carr and Pillinger⁵² bringing LEVEs in general and water in particular to Earth exclusively by E-chondrite is not thought to be a realistic mechanism. EH and EL chondrites also have distinctly lower C/N and C/S ratios compared to the BSE (Figure 2.4a and c). Hence, unprocessed E-chondrite, known from the studied samples, could not have brought LEVEs to Earth after core formation in the right proportions. This is at odds with recent propositions that, based on Ru isotopic composition, argued for the late veneers having E-chondritic character.Reference Dauphas^32, Reference Fischer-Gödde and Kleine³³ One issue in evaluating E-chondrites as plausible terrestrial building blocks based on volatile element geochemistry is that all known E-chondrites studied thus far are heavily metamorphosed; hence, before thermal metamorphism, these chondrites might have been more LEVE rich and C could have been originally organic.Reference Alexander, Fogel, Yabuta and Cody¹⁰⁰

OCs are depleted in volatiles with respect to carbonaceous chondrites chiefly because the volatile-rich matrix volume percentage is less than that of carbonaceous chondrites.Reference Alexander, McKeegan and Altwegg⁵⁴ In fact, bulk C content of most primitive OCs can be perfectly explained by its matrix material being entirely CI-type material.Reference Alexander⁴⁸ OC matrices are drier, however, with bulk H of OCs falling below the concentration of what would be expected if the entire OC matrix was made up of CI-type materials.Reference Alexander, McKeegan and Altwegg⁵⁴ Therefore, the C/H ratio of OCs is higher than that of the BSE (Figure 2.4b). Similarly, the C/S ratios of OCs are lower and the C/N ratios of OCs are distinctly higher compared to the estimates for the BSE (Figure 2.4a and c). Hence after core formation, OC delivery cannot be considered as the chief process of origin of Earth’s LEVEs.

Among all stony meteorites, ureilites are the only group of primitive achondrites that are rich in C and depleted in N, leading to higher C/N ratios.Reference Vdovykin^101–Reference Downes¹⁰³ Carbon in ureilites is also present in relatively non-labile phases (i.e. as graphites, nanodiamonds, and lonsdaleite) and hence is likely to survive high-temperature accretional processes. Primarily motivated by their high C/N ratios, recent studiesReference Hirschmann^11, Reference Barrat, Sansjofre, Yamaguchi, Greenwood and Gillet⁸⁸ have suggested that C-rich achondrites such as ureilites may be responsible for establishing the abundances of LEVEs in the BSE through post-core formation addition. While the C/N ratio of the BSE could be heavily shaped by the addition of a ureilite-like achondrite, the C/S ratio of ureilite is significantly higher than that estimated for the BSE. Hence, any attempt to match the C/S ratios of the BSE through addition of a ureilite-like achondrite-rich late veneer requires a very unique consideration of the composition and extent of core–mantle equilibration of proto-Earth.Reference Hirschmann¹¹ No model of ureilite-like late-veneer addition can explain the C/N and C/S ratios simultaneously. For example, scenarios of C-rich late-silicate addition in which the superchondritic C/N ratio can be established also result in a superchondritic C/S ratio.Reference Hirschmann¹¹

Overall, late accretion alone does not seem to account for the C budget and C to other LEVE ratios of the present-day BSE (Figure 2.5). Hence, other early Earth processes need to be considered.

Figure 2.5 Application of alloy–silicate partition coefficients and solubilities of LEVEs in the silicate melts to examine the effect of core formation, with varying degrees of alloy–silicate equilibration, with or without loss of an early atmosphere formed via MO degassing on the remnant abundances of LEVEs in the bulk silicate reservoir. (a) LEVEs, when delivered as 0.015 M_E late-accreting materials (i.e. 0% alloy–silicate equilibration), cause the volatile abundance to be higher than the present-day BSE. Core formation with increasing degrees of alloy–silicate equilibration increasingly depletes the remnant MO in all LEVEs, with C being much more depleted than other LEVEs, leading to subchondritic C/N, C/H, and C/S ratios. (b) Combining early atmospheric loss with core formation cannot offset C loss to the core due to the lower solubility of C relative to the other LEVEs in the silicate MOs. Bulk Earth volatile abundance data are from McDonough,Reference McDonough and Carlson⁸³ while the alloy–silicate partition coefficients in a deep MO (P = 50 GPa, T = 3500 K; e.g. Siebert et al.Reference Siebert, Badro, Antonangeli and Ryerson¹⁰⁴) for C, N, S, and H are from the parametrized relationships of Chi et al.,Reference Chi, Dasgupta, Duncan and Shimizu⁷¹ Grewal et al.,Reference Grewal, Dasgupta, Holmes, Costin and Li¹⁰⁵ Boujibar et al.,Reference Boujibar¹⁰⁶ and Clesi et al.,Reference Clesi¹⁰⁷ respectively. Solubility constant data for C, N, S, and H in the silicate melt are from Armstrong et al.,Reference Armstrong, Hirschmann, Stanley, Falksen and Jacobsen¹⁰⁸ Roskosz et al.,Reference Roskosz, Bouhifd, Jephcoat, Marty and Mysen¹⁰⁹ O’Neill and Mavrogenes,Reference O’Neill and Mavrogenes¹¹⁰ and Hirschmann et al.Reference Hirschmann, Withers, Ardia and Foley¹¹¹

2.4.2 The Role of Post-core Formation Sulfide Segregation

The segregation of sulfide melt has been shown to be a necessary process for explaining the HSE geochemistry of the BSE.Reference Rubie¹¹² This would also deplete the BSE in terms of its S inventory, but owing to the low solubility of C in sulfide-rich melts (Figure 2.6a)Reference Tsuno, Grewal and Dasgupta^17, Reference Grewal, Dasgupta, Sun, Tsuno and Costin^18, Reference Corgne, Wood and Fei^113–Reference Zhang, Hastings, Von der Handt and Hirschmann¹¹⁶ caused by strong non-ideality of mixing between C- and S-rich components in Fe-rich alloy melts, such sulfide segregation should also elevate the C/S ratio of the BSE. Hence, if late accretion establishes a chondritic C/S ratio, sulfide segregation should alter such a ratio. N also is not compatible in S-rich Fe-alloy melts,Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ hence the S/N ratio of the BSE would also drop after sulfide melt segregation. Similarly, it is also unclear what the effects of late-stage sulfide melt segregation might be on the H budget of the BSE. If H is stored in nominally anhydrous silicate minerals in solid, post-core formation BSE, partitioning of H between segregating sulfide melts and solid silicate minerals could influence the H inventory and hence the C/H ratio of the BSE. If H partitions preferentially into sulfide liquid over relevant nominally anhydrous silicate minerals, then the C/H ratio may also increase above the chondritic value.

Figure 2.6 Experimental data showing the effects of S and Si contents in the Fe-rich alloy melt on C solubility. (a) Carbon solubility decreases monotonically with increases in sulfur content in the alloy melt. Si- and N-bearing alloys have lower C solubility for a given S content in the alloy melt. (b) Carbon solubility decreases linearly with increases in Si content in the alloy or decreases in oxygen fugacity (fO₂) of silicate–alloy systems. The presence of S in the alloy does not have a major effect on carbon solubility in silicon-bearing alloys.

Data for N-free alloys are from Dasgupta et al.,Reference Dasgupta, Chi, Shimizu, Buono and Walker^99, Reference Dasgupta, Buono, Whelan and Walker¹¹⁴ Chi et al.,Reference Chi, Dasgupta, Duncan and Shimizu⁷¹ Armstrong et al.,Reference Armstrong, Hirschmann, Stanley, Falksen and Jacobsen¹⁰⁸ and Li et al.,Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16, Reference Li, Dasgupta and Tsuno¹¹⁷ while data for N-bearing alloys are from Dalou et al.Reference Dalou, Hirschmann, von der Handt, Mosenfelder and Armstrong⁸⁵ and Grewal et al.Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸

2.4.3 The Role of MO–Atmosphere Interactions and Atmospheric Loss

Because C and other LEVEs are atmophile elements, they were likely heavily concentrated in the proto-atmospheres at various stages of MO evolution and terrestrial accretion. Hence, it is worth considering under what circumstances silicate magma–atmosphere interactions and possible atmospheric loss through impact-driven blow-offReference Schlichting, Sari and Yalinewich²³ could influence the inventory of LEVEs in the BSE. The timing of LEVE delivery is of critical importance in determining the role of silicate–atmosphere interactions (and atmospheric blow-off). For example, if a large fraction of core formation takes place before the LEVEs were available to the growing Earth,Reference O’Brien, Walsh, Morbidelli, Raymond and Mandell^20, Reference Raymond, Quinn and Lunine¹¹⁸ then such core formation would have had negligible influence on the BSE LEVE budget, with MO–atmosphere processes being more important. On the other hand, if LEVEs were delivered throughout the terrestrial accretion history,Reference Marty^13, Reference Sarafian, Nielsen, Marschall, McCubbin and Monteleone^51, Reference Hallis¹¹⁹ then both atmosphere–MO interactions and metal–silicate equilibration could have played roles in establishing the LEVE budget of the BSE.

If the BSE C–N–S–H budgets were established chiefly by loss of proto-atmosphere overlying MO, then N needed to be lost preferentially to C and C needed to be lost preferentially to H. In other words, the proto-atmosphere overlying MO has to be N rich relative to C, C rich relative to H, and with similar abundances of C and S. Indeed, the N-depleted nature of Earth has been explained previously by loss of an N-rich atmosphere.Reference Tucker and Mukhopadhyay¹²⁰ But evaluation of whether an atmosphere with a concentration of LEVEs in the order N > C~S > H can be generated overlying a silicate magma reservoir depends on the mixed-volatile solubility in shallow MO as a function of oxygen fugacity (fO₂; effective partial pressure of oxygen). HirschmannReference Hirschmann¹¹ considered a simple model evaluating the fractionation of C, N, H, and S between silicate MO, overlying atmosphere, and equilibrating core-forming liquid alloy with three distinct fO₂ conditions at the MO surface (i.e. IW – 3.5 (reduced), IW – 2 (intermediate fO₂), and IW + 1 (oxidized), where IW refers to the log fO₂ set by equilibrium of metallic iron and iron oxide (FeO)). Among these, the most oxidizing condition is not very realistic during or soon after core formation because, for a well-mixed MO with a near-constant Fe³⁺/Fe_T ratio, the fO₂ gradient is such that the shallow MO is always more reduced.Reference Kress and Carmichael^121–Reference Zhang, Hirschmann, Cottrell and Withers¹²³ Thus, if a well-mixed MO is close to equilibrium with an Fe-rich core at its base, its surface should be more reduced and therefore, for MO–atmosphere interactions, the relevant fO₂ would be less than IW. The only way this may be different is if at higher pressures the fO₂ gradient reverses (reduction with increasing depth) and iron disproportionation and subsequent Fe–metal segregation leads to oxidation of metal-free MO.Reference Schaefer and Elkins-Tanton¹²⁴ Solubility data for most LEVEs are lacking or sparse for peridotitic or ultramafic silicate melts due to difficulty in obtaining a glass and reliable chemical analyses for such compositions.Reference Duncan, Dasgupta and Tsuno¹²⁵ Based on the data available for silicic to mafic silicate liquids, for log fO₂ < IW – 0.5 and with decreasing fO₂, N becomes much more soluble (reaching the weight percentage level chiefly as N–H speciesReference Dalou, Hirschmann, von der Handt, Mosenfelder and Armstrong^85, Reference Libourel, Marty and Humbert^126, Reference Kadik¹²⁷) than C (tens of ppm by weight mostly as CO₃^2– and to some extent as C–H and C–N speciesReference Grewal, Dasgupta, Sun, Tsuno and Costin^18, Reference Chi, Dasgupta, Duncan and Shimizu^71, Reference Dasgupta, Chi, Shimizu, Buono and Walker^99, Reference Armstrong, Hirschmann, Stanley, Falksen and Jacobsen^108, Reference Li, Dasgupta and Tsuno^117, Reference Duncan, Dasgupta and Tsuno^125, Reference Holloway, Pan and Gudmundsson^128, Reference Li, Dasgupta and Tsuno¹²⁹), with the latter mostly decreasing with decreasing fO₂ and then leveling off with stabilization of C–H species. Similar to N, H also remains quite soluble in silicate melt in the form of OH^– and H₂O even in fairly reducing conditions such as log fO₂ of IW – 1 to IW – 2, with molecular hydrogen, H₂, contributing to some degree.Reference Hirschmann, Withers, Ardia and Foley¹¹¹ Therefore, at log fO₂ < IW – 1.5, atmospheric blow-off could lower the C/H ratio from a chondritic value, but this would result in an MO C/N ratio that is subchondritic. Similarly, S is much more soluble in mafic–ultramafic silicate melts (several thousands of ppmReference O’Neill and Mavrogenes^110, Reference Ding, Hough and Dasgupta^130, Reference Baker and Moretti¹³¹) compared to C and hence loss of an atmosphere would result in a residual silicate MO with a C/S ratio distinctly lower than that of chondritic value. Therefore, no condition exists where a proto-atmosphere overlying an MO can attain all of the compositional characteristics necessary to leave an MO with C/N, C/S, and C/H ratios of the modern-day BSE (Figure 2.5). Hence, late accretion of chondritic materials to an alloy-free MO followed by an atmospheric loss cannot be the chief origin of BSE LEVEs.

An alternative suggestionReference Tucker and Mukhopadhyay¹²⁰ is for atmospheric loss to help define the BSE C/N and C/H ratios, but at conditions where C would be retained in the form of carbonate or bicarbonate ions either as dissolved aqueous species or in the crust, mediated by the presence of a liquid water ocean. According to this model, a superchondritic C/N ratio and a subchondritic C/H ratio could have been attained via loss of an N-rich atmosphere overlying an ocean. This mode of atmospheric loss is supported by the dynamical model of a giant impact that shows that such an impact would preferentially remove the atmosphere relative to the ocean.Reference Genda and Abe¹³² However, it is unclear what the water chemistry would be in these oceans, which, if they existed, is expected to be highly anoxic and thus may not sequester significant dissolved carbonates.

2.5.1 Carbon Speciation in MO

$D_C^{\text{alloy}/\text{silicate}}$ and C solubility in silicate melts are affected by the incorporation mechanism of C in the silicate melt structure. Irrespective of the saturating phase such as CO₂-bearing vapor or graphite/diamond, carbon can dissolve in silicate melt as molecular CO₂ (CO₂^mol.${{\mathrm{CO}}_2}^{\mathrm{mol}.}$Reference Stolper, Fine, Johnson and Newman^144–Reference Duncan and Dasgupta¹⁴⁸), as carbonate anions (CO₃²⁻${{\mathrm{CO}}_3}^{2-}$Reference Duncan, Dasgupta and Tsuno^125, Reference Stolper and Holloway^149, Reference Pan, Holloway and Hervig¹⁵⁰) bonded to cation modifiers, possibly as molecular CO or carbonyl,Reference Yoshioka, McCammon, Shcheka and Keppler^151, Reference Wetzel, Rutherford, Jacobsen, Hauri and Saal¹⁵² and as possible C–H, C–N complexes.Reference Grewal, Dasgupta, Sun, Tsuno and Costin^18, Reference Li, Dasgupta and Tsuno¹¹⁷ For mafic–ultramafic melts, the chief species of interest is CO₃²⁻${{\mathrm{CO}}_3}^{2-}$, which complexes most strongly with Ca²⁺ cations and also with Na⁺, Mg²⁺, and maybe K⁺.Reference Duncan, Dasgupta and Tsuno^125, Reference Eguchi and Dasgupta^146, Reference Dasgupta, Hirschmann and Smith^153–Reference Ghiorso and Gualda¹⁵⁶ Most experiments on carbon dissolution at reducing conditions employed mafic compositions of variable degrees of polymerization (i.e. tholeiitic to alkali basalts or even more silicic melts). The most common approach to extrapolating C solubility and $D_C^{\text{alloy}/\text{silicate}}$ to systems containing peridotitic compositions is to use a compositional parameter NBO/T, where “NBO” is the total concentration of non-bridging oxygen in the silicate melt and “T” is the total number of tetrahedral cations. Although this method is thought to give reasonable predictions of ultramafic melt C solubility as CO₃²⁻${{\mathrm{CO}}_3}^{2-}$, Duncan et al.Reference Duncan, Dasgupta and Tsuno¹²⁵ showed that the NBO/T approach may overpredict the extent of CO₃²⁻${{\mathrm{CO}}_3}^{2-}$ dissolution in silicate melts if an increase of NBO/T is correlated with an increase in CaO rather than MgO in melts. This is because Ca²⁺ cations complex with CO₃²⁻${{\mathrm{CO}}_3}^{2-}$ much more than Mg²⁺,Reference Eguchi and Dasgupta¹⁴⁶ although peridotitic melts are still predicted to have higher CO₃²⁻${{\mathrm{CO}}_3}^{2-}$ dissolution capacities than basalts. Figure 2.7 shows CO₃²⁻${{\mathrm{CO}}_3}^{2-}$ dissolution as a function of fO₂ and shallow MO conditions. Also shown in Figure 2.7 are other possible species such as C–H that may become important at low fO₂.

2.5.2 $D_C^{\text{alloy}/\text{silicate}}$ and Its Impact on Carbon Distribution between BSE versus Core in Various Scenarios of Equilibrium Core Formation

Figure 2.8 provides the available data of $D_C^{\text{alloy}/\text{silicate}}$, showing their dependence on alloy composition and fO₂ at shallow MO conditions. Shallow MO $D_C^{\text{alloy}/\text{silicate}}$ at log fO₂ of IW – 2 to IW – 0.5 are in the order of ~10³, with the values increasing with increasing pressure and decreasing fO₂ and decreasing with increasing temperature and melt depolymerization.Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16, Reference Chi, Dasgupta, Duncan and Shimizu^71, Reference Li, Dasgupta and Tsuno¹¹⁷ In more reducing conditions where the Si content becomes significant in the equilibrium Fe-rich alloy melts and where decreasing C dissolution as CO₃²⁻${{\mathrm{CO}}_3}^{2-}$ is offset to some extent by the increasing fraction of C–H complexes (Figure 2.7), $D_C^{\text{alloy}/\text{silicate}}$ may be somewhat lower and may not monotonically increase with decreasing fO₂ (Figure 2.8b).Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16, Reference Li, Dasgupta and Tsuno¹¹⁷ Application of empirical parameterizations of $D_C^{\text{alloy}/\text{silicate}}$ as a function of temperature, pressure, fO₂, silicate melt composition, and alloy composition (e.g. Ni content) to conditions that many studies considered relevant for the deep terrestrial MO (e.g. pressure = 45–65 GPa, temperature = 3500–4000 K, log fO₂ = IW – 2) yields values in the order of 10³–10⁴. The existing constraints on $D_C^{\text{alloy}/\text{silicate}}$ in graphite-saturated conditions therefore suggest that carbon is highly siderophile. If core formation was an equilibrium process (i.e. if the entire terrestrial core mass equilibrated with a global silicate MO), post-core formation silicate Earth would be severely depleted in carbon (≪10 ppm), with the extent of depletion being dependent upon the available bulk carbon that participates in such core–mantle fractionation.Reference Dasgupta^8, Reference Tsuno, Grewal and Dasgupta^17, Reference Chi, Dasgupta, Duncan and Shimizu^71, Reference Dasgupta, Chi, Shimizu, Buono and Walker⁹⁹ This analysis does not imply that the core formation process was a single-stage alloy–silicate equilibration event, but rather what the C distribution between Earth’s metallic and nonmetallic portions would be for an average condition of core–mantle separation.

Figure 2.8 Experimental data showing the effects of S and Si in Fe-rich alloy melts on $D_C^{\text{alloy}/\text{silicate}}$. (a) $D_C^{\text{alloy}/\text{silicate}}$ decreases with increases in S content in the alloy melt. (b) $D_C^{\text{alloy}/\text{silicate}}$ decreases with increases in Si content in the alloy or indirect decreases in fO₂ of the alloy–silicate systems. The presence of S in Si-bearing alloy melts generally decreases $D_C^{\text{alloy}/\text{silicate}}$ in comparison to S-free systems.

Data for N-free alloys are from Dasgupta et al.,Reference Dasgupta, Chi, Shimizu, Buono and Walker^99, Reference Dasgupta, Buono, Whelan and Walker¹¹⁴ Chi et al.,Reference Chi, Dasgupta, Duncan and Shimizu⁷¹ Armstrong et al.,Reference Armstrong, Hirschmann, Stanley, Falksen and Jacobsen¹⁰⁸ Li et al.,Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16, Reference Li, Dasgupta and Tsuno¹¹⁷ and Tsuno et al.,Reference Tsuno, Grewal and Dasgupta¹⁷ while data for N-bearing alloys are from Dalou et al.Reference Dalou, Hirschmann, von der Handt, Mosenfelder and Armstrong⁸⁵ and Grewal et al.Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸

Figure 2.9 shows more realistic scenarios of alloy–silicate equilibration and subsequent core segregation in terrestrial MO where the depth, temperature, and fO₂ evolve with the extent of accretion.Reference Wade and Wood¹⁵⁸ This style of core–mantle fractionation is described as multistage, equilibrium core formation. Competing arguments exist in the literature as to whether, with continuing accretion, proto-Earth’s MO evolved from a relatively reduced to an oxidized conditionReference Wade and Wood^158, Reference Rubie¹⁵⁹ or a relatively oxidized to a reducing condition.Reference Badro, Brodholt, Piet, Siebert and Ryerson¹⁶⁰ Figure 2.9a therefore shows various plausible fO₂ paths of MO evolution of a growing Earth and computes the change of $D_C^{\text{alloy}/\text{silicate}}$ along those paths, following Li et al.Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu¹⁶ It must be noted that the current data sets of $D_C^{\text{alloy}/\text{silicate}}$ do not show any effects of pressure–temperature in relatively reducing conditions (e.g. log fO₂ < IW – 1.5). In such reducing conditions, the controlling variables appear to be fO₂, the Si content of the metal, and the water content of the silicate melt. At ~IW – 2 < log fO₂ < IW, however, the key variables controlling $D_C^{\text{alloy}/\text{silicate}}$ are pressure, temperature, fO₂, and silicate melt composition. Figure 2.9b, however, shows that irrespective of MO condition, $D_C^{\text{alloy}/\text{silicate}}$ remains ≫1, and in fact deeper MO, toward the later stage of accretion, leads to even higher $D_C^{\text{alloy}/\text{silicate}}$ predictions than those experimentally measured at shallow MO conditions. Therefore, the multistage core formation model also leads to C being stripped off highly efficiently from the silicate MO, leaving behind the BSE that is <1–10 ppm for a bulk Earth with 1000 ppm C (Figure 2.9c).

Figure 2.9 The effects of different accretion scenarios on the core–mantle partitioning behavior of carbon. (a) Four possible evolution paths for the FeO content of the mantle with its growth. The “very reduced” and “reduced” paths simulate the accretion of progressively oxidized material with time, and the “oxidized” path simulates accretion of progressively reduced material with time. All of the models converge at log fO₂ of IW – 1.8, or present-day FeO content (8 wt.%) of the primitive upper mantle. (b) $D_C^{\text{alloy}/\text{silicate}}$at each step of accretion (i.e. accretion of 1% M_E), calculated using parametrized relationships from Li et al.Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu¹⁶ For the “very reduced” and “reduced” paths, where methyl (or alkyl) groups would be the predominant dissolved carbon species in the silicate melt, eq. (4) is chosen from Li et al.,Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu¹⁶ whereas for the “intermediate” and “oxidized” paths, where carbonate groups would be the predominant dissolved carbon species in the silicate melt, eq. (3) is chosen from Li et al.Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu¹⁶ (c) Post-core formation MO resulting from a bulk system with 1000 ppm C and assuming 100% alloy–silicate equilibration at each accretional step. All of the models lead to MO with distinctly less C that those estimated for the BSE. (d) Carbon content in Earth’s core converges at ~3300 ppm at the end of all accretional models.

2.5.3 Comparison of $D_C^{\text{alloy}/\text{silicate}}$ with Alloy–Silicate Melt Partitioning of Other LEVEs

The preceding section argues that equilibrium core formation either via homogeneous or heterogeneous accretion results in a nonmetallic Earth that is too depleted in C compared to the present-day BSE. Explaining the origin of LEVEs in the BSE through equilibrium core formation is exacerbated when $D_C^{\text{alloy}/\text{silicate}}$ is compared with the alloy–silicate partition coefficients of other LEVEs such as S, N, and H.

The partition coefficient of sulfur between alloy and silicate melts, $D_S^{\text{alloy}/\text{silicate}}$, has been experimentally constrained in a number of studies,Reference Boujibar^106, Reference Rose-Weston, Brenan, Fei, Secco and Frost^140, Reference Suer, Siebert, Remusat, Menguy and Fiquet¹⁴² but only a few recent studies measured $D_S^{\text{alloy}/\text{silicate}}$ and $D_C^{\text{alloy}/\text{silicate}}$ simultaneously.Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16–Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ These studies show that over the entire range of shallow MO conditions explored experimentally thus far, $D_C^{\text{alloy}/\text{silicate}}$ ≫ $D_S^{\text{alloy}/\text{silicate}}$, with $D_C^{\text{alloy}/\text{silicate}}$/$D_S^{\text{alloy}/\text{silicate}}$ varying between ~1000 and 20 as log fO₂ varies from IW – 4.5 to IW – 0.5. Therefore, under any conditions of alloy–silicate equilibration, C is more siderophilic than S and equilibrium core formation leaves a subchondritic C/S ratio for the silicate MO.

Experiments also exist that constrained $D_N^{\text{alloy}/\text{silicate}}$.Reference Grewal, Dasgupta, Sun, Tsuno and Costin^18, Reference Roskosz, Bouhifd, Jephcoat, Marty and Mysen^109, Reference Kadik¹²⁷ Among these, the recent studies that constrain both $D_C^{\text{alloy}/\text{silicate}}$ and $D_N^{\text{alloy}/\text{silicate}}$ from the same experimentsReference Grewal, Dasgupta, Sun, Tsuno and Costin^18, Reference Dalou, Hirschmann, von der Handt, Mosenfelder and Armstrong⁸⁵ show that nitrogen is only mildly siderophile in relatively oxidizing conditions and possibly even lithophile in relatively reducing conditions (e.g. log fO₂ < IW – 3). Therefore, $D_C^{\text{alloy}/\text{silicate}}$/$D_N^{\text{alloy}/\text{silicate}}$ is ~6–120 at 1–7 GPa, 1400–1800°C, and fO₂ of IW – 3.5 to IW – 0.5, and hence any models of equilibrium core formation would also produce a subchondritic C/N ratio for the post-core formation BSE.

Alloy–silicate partitioning studies for H are limited, and two available studiesReference Clesi^107, Reference Okuchi¹⁶¹ provide contrasting data. OkuchiReference Okuchi¹⁶¹ estimates the $D_H^{\text{alloy}/\text{silicate}}$ value at a fixed pressure of 7.5 GPa and as a function of temperature, but does not provide any pressure effect. Based on the experiments of Okuchi,Reference Okuchi¹⁶¹ H is mildly siderophile. On the other hand, Clesi et al.Reference Clesi¹⁰⁷ conducted experiments at 5, 10, and 20 GPa with C-rich alloy melts and measured $D_H^{\text{alloy}/\text{silicate}}$ of 0.04–0.77. Therefore, it remains unclear whether H is retained mostly in the core of differentiated planets or in the silicate fraction. Despite the discrepancy in the available experimental data on $D_H^{\text{alloy}/\text{silicate}}$, the BSE could attain a subchondritic C/H ratio via an equilibrium core formation process where much more C would be sequestered to the metallic core than H (Figure 2.4). However, if the $D_H^{\text{alloy}/\text{silicate}}$ data of Clesi et al.Reference Clesi¹⁰⁷ are appropriate, then equilibrium core formation would lead to a BSE C/H ratio that is much lower than what is estimated for the present-day BSE.

2.6.1 Disequilibrium Core Formation

Models of protoplanetary disk dynamics, dust and planetesimal accretion, and planetary migration show that although the first 50% of proto-Earth mass growth was continuous, rapid, and completed within the first few million years of Solar System formation, the protracted growth of Earth spanning ~100 MyrReference Kleine¹⁶³ involved few abrupt increases in the accreted mass via several giant impacts of Mars-sized or perhaps even larger bodies.Reference Rubie¹⁶⁴ The final such impact is thought to be the Moon-forming giant impact.Reference Canup and Asphaug^165, Reference Ćuk and Stewart¹⁶⁶ A key aspect of accretion via these impacts is that proto-Earth collided with differentiated planetary embryos. Merger of proto-Earth with large differentiated bodies is thought to have taken place via near-disequilibrium merger of the core of the impactor with proto-Earth’s core owing to limited emulsification of the impactor’s core and the lack of complete mixing of the core with the entrained silicate melt.Reference Deguen, Olson and Cardin^167, Reference Deguen, Landeau and Olson¹⁶⁸ Therefore, core formation involving giant impacts may leave a silicate fraction with a very different LEVE budget than that predicted by equilibrium core formation models. One critical question is whether any differentiated, large impactor could bring LEVE attributes that would help proto-Earth to evolve to the present-day BSE. A full-parameter space involving not only the LEVEs but also other nonvolatile, highly siderophile, and moderately siderophile elements, major elements, and stable isotope anomalies, as well as various accretion and core formation model assumptions, is not yet explored. However, recent studiesReference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16–Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ showed how having an S-rich or Si-rich Fe-alloy in the cores of planetary embryos allow attaining high C/N and C/S ratios in the mantles of such embryos. This would occur as the cores of these embryos reach the C solubility limit and expel graphite or diamond to the overlying silicate fraction (Figure 2.10).Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16–Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ Therefore, a merger of the silicate reservoirs of such embryos with the proto-silicate Earth reservoir could give rise to the BSE LEVE inventory. Using inverse Monte Carlo simulations, Grewal et al.Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ showed that if the merger of the impactor is in perfect disequilibrium, depending on the core size of the impactor and bulk S content, the impactor could be similar in size as Mars (~0.1 M_E; Figure 2.10). It is also showed that the bulk C content of such an impactor would not need to be enriched in carbon and could have a bulk C concentration (~1000–5000 ppm C)Reference Tsuno, Grewal and Dasgupta^17, Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ similar to those of E-chondrites. These model results are intriguing because these potentially circumvent the long-standing challenge of reconciling the volatile element isotope constraintsReference Sarafian, Nielsen, Marschall, McCubbin and Monteleone^51, Reference Marty and Yokochi⁵⁹ and constraints from the isotopic anomalies of lithophile and siderophile elementsReference Dauphas^31, Reference Dauphas³² in the major building blocks of Earth. Some of these latest studies on the origins of terrestrial volatiles through late-stage accretion of a differentiated planetary embryo are also conceptually similar to models that call for the addition of a highly reduced rocky body to the growing Earth to potentially explain the superchondritic Sm/Nd and ¹⁴²Nd/¹⁴⁴Nd anomalies observed in Earth’s present mantle.Reference Wohlers and Wood^169, Reference Wohlers and Wood¹⁷⁰ The concept of bringing carbon and other LEVEs via accretion of the mantle of a differentiated embryo with little post-impact equilibration is also similar to the suggestion that Earth’s Nb/Ta may be explained by accretion of a differentiated asteroid with a reduced S-rich core that efficiently sequestered Nb.¹⁷¹ Grewal et al.Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ also posited that Earth’s volatile-delivering impactor may have been the Moon-forming giant impactor, given the geochemical similarity, including volatiles, between the BSE and the Moon. This is again broadly consistent with Wade and Wood,Reference Wade and Wood¹⁷² who demonstrated that near-disequilibrium accretion of a reduced planetary embryo of 0.1–0.2 M_E could explain the isotopic constraints, FeO contents, and Nb/Ta and Hf/W ratios of the silicate Earth and Moon.

Figure 2.10 A schematic depiction of the late-stage accretion for a large rocky planet such as Earth where a large fraction of mass increase takes place via giant impacts of small planets and planetary embryos (0.1–0.2 M_E).Reference Li, Dasgupta, Tsuno, Monteleone and Shimizu^16–Reference Grewal, Dasgupta, Sun, Tsuno and Costin¹⁸ This mode of accretion creates a unique possibility of establishing the LEVE inventory in the degassable portion of the rocky planets.