Metal-silicate partitioning of W and Mo and the role of carbon in controlling their abundances in the Bulk Silicate Earth

The liquid metal-liquid silicate partitioning of molybdenum and tungsten during core formation must be well-constrained in order to understand the evolution of Earth and other planetary bodies, in particular because the Hf-W isotopic system is used to date early planetary evolution. We combine 48 new high pressure and temperature experimental results with a comprehensive database of previous experiments to re-examine the systematics of Mo and W partitioning. W partitioning is particularly sensitive to silicate and metallic melt compositions and becomes more siderophile with increasing temperature. We show that W has a 6+ oxidation state in silicate melts over the full experimental fO2 range of $\Delta$IW -1.5 to -3.5. Mo has a 4+ oxidation state and its partitioning is less sensitive to silicate melt composition, but also depends on metallic melt composition. DMo stays approximately constant with increasing depth in Earth. Both W and Mo become more siderophile with increasing C content of the metal, so we fit epsilon interaction parameters. W and Mo along with C are incorporated into a combined N-body accretion and core-mantle differentiation model. We show that W and Mo require the early accreting Earth to be sulfur-depleted and carbon-enriched so that W and Mo are efficiently partitioned into Earth's core and do not accumulate in the mantle. If this is the case, the produced Earth-like planets possess mantle compositions matching the BSE for all simulated elements. However, there are two distinct groups of estimates of the bulk mantle's C abundance in the literature: low (100 ppm), and high (800 ppm), and all models are consistent with the higher estimated carbon abundance. The low BSE C abundance would be achievable when the effects of the segregation of dispersed metal droplets produced in deep magma oceans by the disproportionation of Fe2+ to Fe3+ plus metallic Fe is considered.


Introduction
The accretion of Earth and segregation of its core are now widely regarded as being parts of a simultaneous, heterogeneous process. The composition of accreting impactors is likely to have changed through time with increased mixing in the protoplanetary disk, which would have resulted in changing oxygen fugacity and volatile contents throughout the formation of the early Earth (Wänke, 1981). Calculations and simulations suggest that large impacts release enough kinetic energy to cause widespread melting of the silicate Earth, resulting in magma ocean stages during its accretion (Melosh, 1990;Piarazzo et al., 1997;de Vries et al., 2016). Magma ocean formation would allow metal and silicate from an impacting body to equilibrate with at least a localised portion of the bulk silicate Earth (BSE). The distribution of siderophile elements, as estimated from the composition of the BSE, must trace this process. Different elements have partition coefficients which are affected by pressure, temperature, oxygen fugacity and melt composition in different ways (e.g. Mann et al., 2009;Siebert et al., 2011). Earth's accretionary history can therefore be understood by identifying the set of conditions that is compatible with all such elements. Such an approach is followed in the combined N-body accretion and core -mantle differentiation model of Rubie et al. (2015;. W and Mo are members of the same group (VIb) of the periodic table and will therefore display similar behaviour in geochemical systems. Being refractory, they should be present in the bulk Earth in chondritic proportions, and they are moderately siderophile, so measurable concentrations should remain in the silicate portion of the Earth following fractionation by the segregation of the core. In addition, W and Mo are both highly charged in silicate melts (O'Neill et al., 2008;Cottrell et al., 2009;Wade et al., 2012;: because metal-silicate partitioning of siderophile elements usually involves a redox reaction, their high charges mean that their distribution will be particularly sensitive to the oxygen fugacity conditions during core segregation. However, their high charge also means that their activity in silicate melts is dependent on silicate melt composition Wade et al., 2012), and their activities in metallic melts are known to be highly dependent on the metallic melt's light element content (Jana and Walker, 1997a;Chabot et al., 2006;Cottrell et al., 2009;Righter et al., 2010). These dependencies on a variety of factors mean that W and Mo have the potential to be sensitive tracers of a range of aspects of core formation -especially oxygen fugacity and metal composition, but likewise mean that a large number of experiments are required to constrain the competing effects.
The Mo/W ratio in the BSE is 3.9 (Palme and O'Neill, 2014), which is low relative to the chondrite value of 10, and implies fractionation during core formation. Wade et al. (2012) found this low ratio difficult to reproduce with their partitioning data and a continuous accretion-differentiation model, which predicted that core formation should increase, not decrease, the mantle Mo/W ratio (for conditions that satisfy other siderophile elements): thus, they proposed that S in core-forming metal may resolve this. In a preliminary investigation, we added the parametrised partition coefficients of Wade et al. (2012) to the model of Rubie et al. (2015) (which also considers heterogeneous accretion but uses partial, rather than full, equilibration of the silicate Earth with the cores of impactors) and predicted a BSE that is overabundant in both Mo and W at conditions that satisfy the other elements considered, together with a Mo/W ratio that is low relative to that of the BSE.
Despite a large experimental effort by the community (section 1.1), there is some still uncertainty and disagreement regarding the partitioning behaviour of Mo and W between metal and silicate. The partitioning of these elements is not only important for core formation and accretion modelling: W partitioning needs to be well-constrained, given the importance of the short-lived 182 Hf-182 W system in dating core formation and early planetary evolution of Earth, Moon and other solar system objects (Kleine et al., 2009). For example, a higher initial W content than that assumed from the present-day terrestrial mantle would require core-formation to end earlier in order to explain the ingrowth of radiogenic W.
In this study, we thoroughly constrain the partitioning behaviour of W and Mo in terms of valence (oxygen fugacity dependence), pressure and temperature dependencies of equilibration, and the composition of the metallic melts, by combining results from 48 new experiments with a larger database of all existing ones (subject to certain filters and quality control). The BSE concentrations of W and Mo are interpreted by adding these elements, together with C, to the combined accretion/core formation model of Rubie et al. (2015. With such a large experimental database, we are confident that the partitioning of these elements, including dependence on P, T, fO2 and other compositional effects (using both new and recently-published interaction parameters), is now well-enough constrained to be used as a tool to investigate the processes of Earth's accretion.

Previous studies and a big dataset approach
Previous studies paint a somewhat contradictory picture of the P-T partitioning systematics of W and Mo. Cottrell et al. (2009) found that increasing temperature slightly decreases the metalsilicate partition coefficient of W, whereas other studies (Righter et al., 2010;Siebert et al., 2011, Wade et al., 2012 have found the opposite. Likewise, the metal-silicate partition coefficient of Mo may either decrease (Righter et al., 2010;Siebert et al., 2011) or increase (Wade et al., 2013) with temperature at a fixed pressure. Whereas Righter et al. (1997) found a significant positive pressure dependence of the partitioning of W, Cottrell et al. (2009) determined that increasing pressure increases DW at low pressures (< ~ 4 GPa) but decreases it at higher pressures. Later, Wade et al. (2012) argued that the data are consistent with just a negative pressure dependence over the full pressure range. All studies, including ours, suffer from covariance of P and T, i.e. higher temperatures are needed to melt the higher pressure experiments, so some disagreement is unsurprising. Whilst the impact of this uncertainty on accretion models is diminished by considering correlated P-T profiles along a geotherm, these terms are still worth refining from a larger combined dataset in order to decrease uncertainty.
The compositions of both silicate and metallic melt phases are known to strongly affect the partitioning of W and Mo Righter and Drake, 1999;Righter et al., 1997Righter et al., , 2010O'Neill and Eggins, 2002;Chabot et al., 2006;O'Neill et al., 2008;Siebert et al., 2011;Wade et al., 2012;Steenstra et al., 2016Steenstra et al., , 2017Steenstra et al., , 2020sections 4.4 and 4.7 below). A potential cause of apparent discrepancies between previous studies is therefore the range in starting compositions and capsule materials used, which also affects the way in which experimental results should be applied to understanding planetary accretion. Many experiments have been performed in graphite capsules and have several wt.% carbon in the metal as a result (e.g. Jana and Walker, 1997a;Cottrell et al., 2009;Righter et al., 2010;Siebert et al., 2011): they yield partition coefficients for W and Mo that are around an order of magnitude higher than for C-free experiments, requiring activity corrections with large associated uncertainties for direct comparison with C-free experiments. Some studies used basaltic silicate compositions for ease of melting and quenching to a glass, whereas others use peridotitic compositions to emulate magma ocean compositions: different partition coefficients would be expected. Compositional controls can also be convoluted with the effect of temperature, because higher temperatures and/or longer experimental durations in MgO capsules will result in greater reaction between capsule and silicate, resulting in increased MgO concentrations and decreased concentrations of other components.
For this study, we have created new parameterisations of W and Mo partitioning based on a large number of experiments from many new and published studies, whereas previously published parameterisations are based on experiments from single laboratories or research groups. Using a compiled dataset approach means that we can interrogate pressure, temperature and melt composition effects simultaneously and more thoroughly than is possible with smaller datasets. In particular, including published data means that a wide range of silicate and metal compositions are considered at different conditions. This should reduce problems of covariance (though not eliminate them), allow fitting over a large parameter space (i.e. reduce the amount of extrapolation needed when modelling) and gives us the opportunity to filter the data to cover a narrower range of compositions that are relevant to magma oceans. There will also be inter-laboratory differences in pressure calibrations, temperature measurements, and analytical calibrations and techniques, that contribute to the offsets between studies: a large database approach smooths out these differences.
From a statistical perspective, the more data that contributes to a parameterisation, the more robust that parameterisation will be.

Methods
We performed new experiments and re-analysed some previously published experimental data and combined these with a collated database of published experimental data to re-determine pressure, temperature and compositional dependencies of W and Mo partitioning. Within our new database, experiments were performed and analysed at different times by different protocols. Experiments which belong together as a set are indicated by the label under ''group'', and full experimental and analytical details as well as starting materials are documented in supplementary Table S1. All experiments were performed to examine the partitioning of W and/or Mo as well as other elements, except those labelled ESJ, which were performed to revise the dependencies of partitioning on the concentrations of C in Fe-rich liquid metal alloy.

Experimental methods
Experiments were performed over a range of pressures and temperatures using piston-cylinder and multi-anvil apparatus at the Bayerisches Geoinstitut. Starting silicates had compositions that were either high-Mg basalt, simple primitive mantle, or olivine, and were prepared either using glassed and powdered high-purity oxide mixtures, or powdered synthetic or natural olivine. Metals were ground mixtures or ground sintered mixtures of high-purity metals. Materials were loaded as finegrained mixtures or in the case of experiments labelled AV, as sandwiched layers (further details in supplementary Table S1). Starting materials were packed into MgO capsules in all experiments except A962b, for which a graphite capsule was used. Piston cylinder experiments were performed using a 1/2" talc-pyrex assembly with a graphite heater and type-D thermocouple using a hot-pistonin technique with a friction correction applied. Multi-anvil experiments used Cr-doped MgO octahedra positioned between truncated tungsten carbide anvils. Octahedra and truncation dimensions were appropriate to the pressure generated in each case. Assembly components and furnaces were heated at 1000 °C for several hours before use. Straight or stepped LaCrO3 heaters were used, depending on the size of the assembly. Temperatures were either directly measured by a type-D thermocouple, or extrapolated along power-temperature curves. Uncertainties on pressure and temperature in the multi-anvil are around ± 0.5-1 GPa and ± 100 K, respectively. Details of starting materials and experimental conditions for each set of experiments can be found in supplementary Table S1 and Table 1.

Analytical methods
Samples were mounted, sectioned, polished, and subsequently analysed by electron probe microanalyser (EPMA) and/or laser-ablation inductively-coupled plasma mass spectrometry (LA-ICP-MS), both at the Bayerisches Geoinstitut. Major and minor elements in silicate and metal were measured by a JXA-8200 EPMA using wavelength-dispersive X-ray spectroscopy with a 15 kV beam. It should be noted that EPMA analyses of some multi-anvil experiments (labelled YN*) were previously published by Fischer et al. (2015), where further analytical details can be found. However, the LA-ICP-MS analyses of these samples are new.
A range of appropriate primary standards of metals, oxides, and silicates were used in the calibrations. LA-ICP-MS measurements were performed using a laser system which consists of an Elan DRC-e quadrupole mass spectrometer attached to a Geolas M 193 nm ArF Excimer Laser. The ablation cell was flushed with He to enhance sensitivity (Eggins et al., 1998;Günther and Heinrich, 1999). The concentration of S in the silicate melt, where present, was quantified using either Afghanite (Seo et al., 2011) or a S-bearing basaltic glass (SB19; Botcharnikov et al., 2011) standards. Ablation yields were standardised and drift was monitored with a NIST SRM 610 glass standard, and yields were normalised to EPMA Si (experiments labelled YN, AV and ESJ) or Ca (LRW) content. Spot sizes by EPMA and LA-ICP-MS in both silicate and metal were adjusted to account for the coarseness of the quench textures in order to obtain representative average compositions. In addition, a larger number of EPMA points were measured in the case of more problematic quench textures. Details of the analytical methods used for each set of experiments can be found in supplementary Table S1, Fischer et al. (2015), and Vogel et al. (2018). The resulting data are given in Table 2(a, b) and supplementary Table S2. Where the precision and accuracy of minor or trace elements was found to be similar for EPMA and LA-ICP-MS, the EPMA value is usually listed unless concentrations of that element are near or below the EPMA detection limit.

Carbon analysis
Experiments labelled 'ESJ' in Tables 1 and 2 included graphite powder in the starting mixture. Carbon partitions strongly into metal and will only be present in trace amounts in the silicate melt (Dasgupta and Walker, 2008;Chi et al., 2014;Duncan et al., 2017). The carbon content of the metal phase was measured in these experiments by EPMA. The measurement procedure was a modified version of that of Dasgupta and Walker (2008) with care taken to minimise and quantify carbon contamination, as described below.
A Fe3C primary standard was synthesised by inserting a 1 mm diameter, 10 mm long, 99.99 % purity Fe wire into a thick graphite sleeve and heating it to 1423 K at 15 kbar for one week.
The reaction product was confirmed to have the Fe3C cementite structure by XRD and would be near-stoichiometric (Walker et al., 2013).
Organic C contamination prior to analysis was minimised by taking the following steps: 1) the epoxy sample mounts were left for one month and were then stored for 12 hours under a high vacuum to promote degassing; 2) samples and standards were subjected to N plasma cleaning immediately prior to analysis. For the metal analyses, neither the mounts nor the standards were carbon coated. Copper strips and Ag paint were used to create an electrical connection between the metal sample or standards and their respective metal holders. Analyses were performed at 15 kV and 25 nA using a 30 μm defocussed beam. The extent to which carbon drifts towards the beam was tested by measuring a continuous time series on a single spot on the pure Fe standard: it was found that over a period of ten minutes of continuous beam exposure, the increase in C counts was negligible, and the apparent decrease in C over the first ten seconds noted by Dasgupta and Walker (2008) was not observed (supplementary Fig. S1). Carbon was measured using a LDE2 crystal, and a pure Fe standard was measured between the analysis of each sample in order to monitor and quantify the carbon background. This background of 0.58 ± 0.09 wt. % C was constant throughout the analytical session, and was subtracted from the final measurements of the metals. Carbon was measured for 10 s with background measurements of 5 s, to further mitigate organic carbon contamination (Dasgupta and Walker, 2008). The C peak was very broad, and required a wide background interval. Final C contents were broadly similar to those expected from the weight ratio used in starting material preparation.

Definitions and data treatment
Partitioning of an element M with a valence n between liquid metal and silicate melt can be described by the exchange reaction: [eq. 1] MOn/2 + Fe = M + FeO This reaction includes oxygen, and thus by expressing partitioning as an exchange reaction rather than an abundance ratio, the effect of fO2 is implicitly accounted for. This is convenient, because fO2 has a major effect on partitioning, and its determination is not without uncertainty. The equilibrium constant K can be split into an observed concentration ratio (KD) and an activity correction: where X always denotes mole fraction. In this study, we generally present findings in terms of K (which can be considered as the activity-corrected observed KD). We apply activity corrections for the metal compositions by multiplying X by the activity coefficient γ, but neglect the silicate activity coefficients by assuming that their ratios remain constant. This approximation is useful for data presentation purposes in the absence of a well-constrained activity model for the components FeO, WO3 and MoO2 in silicate melts, and it is made in other studies (e.g. Wade and Wood, 2005).
However, melt compositional effects identified by O'Neill and Eggins (2002) and Wade et al. (2012) indicate that this approximation may be over-simplistic for WO3 and MoO2: this point is further examined in section 4.4 below. K can also be written in terms of the molar partition coefficient D (eq. 5) and fO2 (relative to the iron-wüstite buffer: ΔIW): We follow the approach used by Wade and Wood (2005) of using ε interaction parameters (Wagner, 1952) with the equations of Ma (2001) to quantify the activity terms for components in the metal (γFe, γM). This procedure accounts for first-order interactions between the various solutes and iron in a way that is consistent with the Gibbs-Duhem equation. We calculate γFe using eq. 23 of Ma (2001) and M with their eq. 24. For these calculations, the composition of the metal is simplified by have recently been revised in high pressure studies with a focus on metal-silicate partitioning in the context of core formation (e.g. Tuff et al., 2011;Wood et al., 2014;Fischer et al., 2015). Here we use only values that were determined independently, i.e. that were not potentially affected by covariance with other fitting parameters. The values and references used in our activity corrections are listed in Table 3. The parameters C W and C Mo have been re-evaluated in the present study (see section 4.7).

Results
Major and trace element analyses of metal and silicate portions of the experimental samples are presented in Table 2(a, b), and calculated values of fO2 (relative to the iron-wüstite buffer, IW), KD and other parameters are listed in Table 4. The complete data, including trace elements omitted in high-MgO experiments are clearly texturally distinct from quench crystals (Fig. 1c) and grew during the experiment rather than precipitating during quench, saturating at the run temperature as melt MgO concentrations increased. Such crystals were therefore avoided when selecting analytical points.
The metal phase always coalesced into one or more large spheres. These spheres sometimes displayed an intricate texture (heterogeneity on the order of 5-10 μm; Fig. 1), caused by exsolution into two immiscible metals during the quench. Tiny crystals of SiO2 were also occasionally observed.
The textures suggest complete miscibility at experimental temperatures, so that an integrated composition is required: a defocussed electron beam and/or a large number of analytical points were used to obtain the metal or silicate bulk compositions. The experimental textures are similar to those reported in previous studies (e.g. Corgne et al., 2008Wade et al., 2012).

Attainment of equilibrium
Previously-published time-series experiments on a variety of elements show that equilibration times in metal-silicate partitioning experiments are generally very short, for example, 15 minutes or less at 1823 K, through to seconds to tens of seconds at 2300 K (Righter et al., 2010;Tuff et al., 2011;Thibault and Walter, 1995;Corgne et al., 2008). Specifically, Righter et al. (2010) Hillgren et al. (1996); Jana and Walker (1997a); Kilburn and Wood (1997); Righter and Drake (1999)  show an apparent change if the oxide activity coefficients change. The effect of silicate melt composition can therefore be seen by plotting K as a function of various melt compositional parameters (Fig. 2). Because DW is sensitive to temperature but not to pressure (section 4.5), experiments are grouped by temperature in Fig. 2. It should be noted that the melt composition is to some extent correlated with temperature (higher temperatures are needed to reach the peridotite liquidus than the basalt liquidus, and reaction with the MgO capsule occurs more rapidly at high temperatures), so the temperature and compositional effects on partitioning are convoluted. There is a small resolvable dependence of K on composition within a given temperature range and a stronger trend is observed when considering all data, indicating that much of the apparent compositional dependence is really a temperature effect. However, there do appear to be real compositional dependencies within the narrower temperature brackets, highlighting some non-ideal interactions. Two causes are proposed in the literature, and the data are consistent with both: 1) K W positively correlates with Al2O3 and SiO2, suggesting a melt polymerisation control Jana and Walker, 1997b), and 2) K W correlates negatively with CaO, suggesting that the formation of Ca-W complexes in the silicate melt reduces the activity of W (O'Neill and Eggins, 2002;O'Neill et al., 2008;Steenstra et al., 2017).
The effect of silicate composition on K Mo in this data compilation is not resolvable (except for some anomalously high K Mo values at > 2 wt. % Na2O; Supplementary Fig. S2). This is in contrast to the findings of O'Neill and Eggins (2002) Previous studies have included an activity correction for the silicate melt composition by: (1) fitting an NBO/T term as a proxy for silicate melt effects Righter et al., 1997;Siebert et al., 2011); (2)  and it may not correctly describe melt structure at high pressure. The other approaches involve the simultaneous fitting of numerous highly-correlated terms which will be convoluted with both oneanother and with the effect of temperature. We instead chose to restrict the silicate melt compositions to those relevant to early Earth magma oceans, i.e. broadly pyrolite-like to picritic, and check that there are no resolvable correlations between residuals in the fitted models and major element oxides in the silicate.

P and T controls on partitioning
After filtering the data according to the silicate compositional limits given in Table 5, 57 experiments (29 from this study and 28 previously published) remained for fitting K W and 68 (13 this study; 55 published) for K Mo . Pressure and temperature dependencies for K i were parametrised in the form: [eq. 7] log K i = a + b/T + cP/T as proposed by Righter et al. (1997) and used in numerous previous studies. Because K relates to ΔG°, the terms a, b and c relate to ΔS°/R, ΔH°/R and ΔV°/R respectively, although the ratio of silicate melt activity terms also accounts for some portion of the fitted parameters in eq. 7. Compositional effects in the metal phase are accounted for by the activity terms in eq. 4. Fitted terms (except the intercept) with a p-value of < 0.05 are considered significant and the goodness of fit of the model to the data is expressed by the root mean square (RMS) error. Because the reporting of uncertainties is inconsistent between different studies, fitting is not weighted according to uncertainty (although reported uncertainties are shown as error bars on figures). It should be noted that pressure and temperature are correlated parameters: as such, pressure and temperature dependencies cannot be interpreted independently when fitted together. Variance-covariance matrices are provided in Supplementary Table S4.
log K W : The pressure term (c) is statistically insignificant, so has a value of 0. Higher temperatures make W more siderophile over the experimental range, as is shown by a significant negative temperature term (b) (Fig. 3a). The temperature term is somewhat smaller than that of There is no resolvable correlation between the residual errors and oxide concentrations in the silicate for K Mo or K W . The model fits to the data are shown in Fig. 3. For both W and Mo, the full range of observed D values are well-predicted by the model (Fig. 4). We note that the highest pressure experiments in the calibration dataset are at 25 GPa, so these expressions (and previously published ones) may lose accuracy when extrapolated to higher pressures.

Valence
A good constraint on the valence of the oxide species is crucial for predicting the partitioning behaviour of Mo and W during core formation, by defining the dependence of DM on fO2. By studying the solubility of W, Ertel et al. (1996) determined that W 4+ was the stable cation in silicate melts over their entire experimental fO2 range (ΔIW -3.9 to -0.5). Later, Cottrell et al. (2009) used metal-silicate partitioning data to suggest that W was present as W 6+ at low pressures, also under reducing conditions, but that W 4+ stabilises at pressures greater than 11 GPa. Oxidation states from partitioning data were revisited and reviewed by Wade et al. (2012Wade et al. ( , 2013, who conclude that W exists in the 6+ state and Mo at 4+ up to at least 24 GPa, even at very low fO2. Most recently, W 6+ was also suggested from partitioning data over a wide fO2 range by Steenstra et al. (2020). When the summed terms on the left side of eq. 8 are plotted against fO2, the slope will be (n/4) and the intercept should be zero. Plotting the data in this way removes compositional and P-T effects on partitioning (Fig. 5). To avoid circularity (the gradient of the trend is mostly independent of the data treatment, but the a, b and c terms will introduce a small bias towards the valence n that was assumed when calculating K; eq. 2 and 7), we show the results obtained by separately fitting a, b and c for the valence states of +2, +4 and +6, and consider which produces the best quality fit (similar to Vogel et al., 2018). For DW, using the a and b terms obtained with n = 6, a line fitted through the data has a slope of -1.49 and yields a formal valence of 5.95 (root mean square RMS mismatch = 0.31). This result is robust regardless of n assumed during fitting: if the data are plotted using the a and b terms obtained with n = 4 yields almost the same gradient, corresponding to a formal valence of 5.50 (RMS = 0.35). The expected gradients corresponding to different valence states are shown on Fig. 5, and it is clear that, regardless of the valence assumed during fitting, the data still yield a steep gradient consistent with a high valence state of +6. Likewise for DMo, a formal valence ranging from 3.6 to 4.6 is obtained over the range of n values (2 to 6) assumed during fitting: the best fit (lowest RMS) of n = 4.12 is obtained when taking n = 4 for fitting eq. 7. Again, the data support a 4+ valence state over the entire fO2 range represented by the data. A lack of a systematic offset between predicted and actual values at extremes of fO2 or extremes of D (figs. 4 and 5) are good evidence that the valence state does not change over the fO2 range considered.

C-W and C-Mo interactions
It is well-known that C in metal can have a strong influence on the activities of other species, and that Mo and W are more siderophile when the metal is C-saturated (J.S.P.S. 1988; Jana and Walker, 1997a;Chabot et al., 2006;Cottrell et al., 2009;Righter et al., 2010). An increase in DM by around an order of magnitude in graphite-saturated experiments relative to C-free experiments can be seen both log(KD Mo ) and log(KD W ) increase linearly with C content XC (Fig. 7), and the slope can be fitted with revised epsilon interaction parameters of C Mo = -7.03 ± 0.30 and C W = -7.38 ± 0.57 at a reference temperature of 1873 K. These values are similar to those listed in the Steelmaking Sourcebook (-6.03 and -6.45, respectively).
In fig. 7, the result of an experiment performed in a graphite capsule at the same conditions as those of the other ESJ experiments is also shown. KD M is higher than predicted by the linear trend.
This may be due to the effects of the lower MgO content of the silicate melt and higher content of other lithophile elements, as the starting composition has not been diluted by MgO derived from the capsule (Fig. 2). Alternatively, the interaction may no longer be linear at C-saturation and is not welldescribed with only first-order interaction parameters and the present activity model (indeed, the model of Ma, 2001, describes interactions between dilute components and is not intended for saturated systems). The latter explanation is consistent with solid-liquid iron partitioning data on many trace elements, where log(D) values (as a function of C content) often begin to deviate from a linear trend at around 3-4 wt.% C (Chabot et al., 2006). that of most other elements if significant C is sequestered into core-forming metal (Jana and Walker, 1997a).

Accretion/core formation model prediction of BSE W and Mo concentrations
The formation of Earth's core was a multi-stage heterogeneous process, during which accretion and differentiation occurred simultaneously. Modelling core formation as a heterogeneous process can rigorously consider the full range of accretionary processes, including, for example, the consequences of late accreted material mixed in from the outer Solar system. Unlike simple geochemical models of homogeneous core formation, which treat core-mantle equilibration as a single event, this requires a sophisticated modelling approach. The effects of impacts, changing impactor origins, and core formation throughout accretion must be considered in order to properly interpret BSE Mo and W concentrations.
We use the planetary accretion and differentiation model of Rubie et al. (2015) with the addition of S and the highly siderophile elements (HSEs)    (Hirschmann, 2016). DC has been shown experimentally to decrease with increasing pressure and temperature (Li et al. 2016;Malavergne et al., 2019;Fischer et al., 2020), as well as with increasing oxygen fugacity (Hirschmann, 2016;Malavergne et al., 2019).
However, we found no changes to our results when we varied DC between 500 and 3000, which corresponds to more oxidised and reduced metal-silicate equilibration conditions, respectively (Hirschmann, 2016).  Rubie et al., 2015, Fig. 3). We assume that the metallic core of the projectile is fully emulsified as it sinks through the magma ocean (Deguen et al., 2014;Kendall and Melosh, 2016), so that the fraction of accreted metal that equilibrates with the small fraction of the silicate mantle is 100% (for a discussion of this assumption see Rubie et al., 2015). Following Rubie et al. (2015, a combination of rigorous mass balance and partitioning expressions is used to calculate the compositions of the metal and silicate portions of the planetary bodies after each equilibration event (Rubie et al., 2011).
Six Earth-like planets were selected from a suite of Grand Tack scenario terrestrial planet formation simulations (Jacobson and Morbidelli, 2014). These are the same six simulations presented in Rubie et al., 2015: (1) 4:1-0.25-7, (2) 4:1-0.5-8, (3)  There is a heliocentric oxidation gradient in the disk, which mimics what is seen amongst the chondritic meteorites and is necessary to obtain the correct mantle composition of Earth . The oxidation gradient is such that the most reduced and volatile-depleted materials originate closest to the Sun, whereas the most oxidised and volatile-rich materials originate in the outer Solar system. The four parameters, which define the gradient and therefore the iron-rich metallic fraction of the starting bodies, are refined using a least squares regression, which fits the  Fig. 1). Furthermore, fully oxidized material originates from the giant planet forming region (exterior to 4.5 AU in the model) and contributes less than 1% of each Earth-like planet's final mass. These fully oxidized outer solar system bodies contain no metallic core, but they do contain 20 wt.% water, consistent with carbonaceous chondrites and their C-type asteroid progenitors (Young, 2001): this results in a mantle water content of about 0.2 wt.% in each Earth-like planet, see supplemental Fig. S4.
The pressure of metal-silicate equilibration is also a fitted free parameter and is found to be about 70% of the target's core-mantle boundary pressure at the time of each accretional impact , which is broadly consistent with calculations of impact-induced melting (de Vries et al., 2016).  Rubie et al. (2015). Note that we did not include the effect of interaction with C on any element other than W and Mo. The changes in the abundances of the elements in supplementary Figs. S4-S6 between low-and high-C simulations are not due directly to the change in C abundance, but indirectly through the change in the fitted disk parameters such as the heliocentric gradient of Fe-metal abundance, which are different if attempting to match the low or high C mantle abundances.
In a separate second least squares minimisation, following the approach of Rubie et al. composition. In addition, we add Mo, W, and C to the model (Palme and O'Neill, 2014;Marty, 2012;Halliday, 2013). Mo and W were added by incorporating the metal-silicate partitioning models for Mo and W developed here (including the interaction parameters of Table 3). As described by Rubie et al. (2011Rubie et al. ( , 2015, the most refractory non-volatile elements in starting bodies are enriched by a factor of 22% relative to CI chondrites. W and Mo are therefore also enriched by a factor of 22%. Since Mo and W are refractory, they are not explicitly associated with any free model fitting parameters. Thus, using eight estimated mantle abundances (Pt, Pd, Ru, Ir, S, Mo, W, and C) as constraints, we fit four free parameters (S and C heliocentric abundance gradients, pressure of silicate-sulphide equilibration, lifetime of post-giant impact mantle magma ocean), each of which are described in detail below. The final highly siderophile element abundances for each simulation are shown in supplementary Fig. S6 and Table S6.
Following , we assume that volatile elements condensed to an increasing extent as temperatures decreased in the protoplanetary disk -i.e. with increasing heliocentric distance. Thus, the concentration of S within the initial planetesimals and embryos is modelled as a simple linear gradient through the protoplanetary disk with an abundance of 5.35 wt.% (consistent with CI chondrites) in the outer solar system (at ≥ 4.5 AU). The distance in the inner solar system at which the S concentration linearly drops to zero from a value of 5.35 wt% at 4.5 AU is adjusted as a free parameter so that the final mantle S abundance of the Earth-like planet matches estimates of Earth's mantle abundance. The resulting fitted gradients (Fig. 8) predict that the highly-reduced material that originates at <1 AU contains low concentrations of S (according to one of our accretion simulations the S concentration at <1 AU is zero). In contrast, enstatite chondrites (ECs), which have been proposed to be Earth's main building blocks, are highly reduced with high S concentrations of up to 5-6 wt%. However, et al. (2020) have shown that the ECs formed with relatively high volatile concentrations from residual gas in the solar nebular and are quite distinct from Earth's main building blocks which were highly reduced and volatile-poor. It has also been proposed that Mercury's highly reduced bulk composition includes a high S concentration, but this is currently very uncertain.

In addition to S, C is a necessary addition to the Rubie et al. (2016) model because it
increases the siderophility of both W and Mo when C is dissolved in the metal liquid. Similar to S, the concentration of C within the initial planetesimals and embryos is modelled as a simple linear gradient through the protoplanetary disk with an abundance of 3.48 wt.% (consistent with CI chondrites) in the outer solar system (at ≥ 4.5 AU), and the distance at which the C concentration linearly drops to zero from a value of 3.48 wt% at 4.5 AU is adjusted as a free parameter to match the bulk silicate Earth abundance of C. However, there are two distinct groups of estimates of the bulk mantle or BSE C abundance: low (estimates range from 66 to 164 ppm; Hirschmann & Dasgupta, 2009;Halliday, 2013;Rosenthal et al., 2015;Hirschmann, 2016Hirschmann, , 2018 and high (786 ± 308 ppm; Marty, 2012). The best fit S and C concentration gradients for each simulation 1-6 are shown in Figs. 8 and 9 for a high (786 ± 308 ppm; Halliday, 2013) and a low (66 ± 21 ppm) C mantle abundance esimate, respectively.
The partitioning of S between metal and silicate during core formation is modelled using Eq. of a magma ocean which causes it to become saturated in FeS. This occurs because the sulfur concentration at sulfide saturation (SCSS) decreases strongly with decreasing temperature (e.g. Mavrogenes and O'Neill, 1999;Liu et al., 2007;Laurenz et al., 2016). Thus, exsolution of FeS droplets is a pervasive process that occurs over a large depth interval. To understand the chemical consequences of equilibration between these dispersed FeS droplets as they sink to the core and the convecting magma ocean is clearly a complex problem.  took a highlysimplified approach by assuming that equilibration could be modelled at a single effective pressure which is constrained by the final mantle concentrations of the HSEs and S. This pressure is considerably lower than the metal-silicate equilibration pressure and is found to be about 30% of the target's core-mantle boundary pressure.
We added Mo and W to the model of  as before. In all simulations, we obtained good matches to the BSE abundances of W, Mo, and C when fitting the high C abundance estimate for the BSE, but we obtained much poorer fits for W and C when attempting to fit the low C abundance BSE estimate (Fig. 10). S is better matched when fitting the low C BSE estimate than when fitting the higher value, but is generally within two-sigma of the S BSE abundance estimate of Palme and O'Neill (2014) and below the highest estimates (e.g. Sun 1982). From these results, it is clear that the importance of the effects of C and S on the partitioning of W and Mo cannot be overstated. If C is not present in the equilibrating liquids, then too much W will remain in the silicate liquid after equilibration and it will accumulate too much in the mantle over time (Figs. 11 and 12).
This is what occurs when the C abundance is suppressed by varying the zero-abundance distance of the C gradient in the disk so that C is brought nearly exclusively from outer disk planetesimals.
When the C abundance in the disk is increased, thereby increasing the abundance in Earth's mantle to be consistent with the high (786 ppm) estimate, the abundance of W in the mantle decreases to match the best estimates of Earth's silicate W abundance. It's important to note that the effect of C is regulated by the presence of S, which has the opposite effect of C on the partitioning of W. Thus, if S accumulates too quickly relative to C in an Earth-like planet's mantle during accretion, then the abundance of W becomes too great relative to Earth's BSE value. The accretion of S must remain sufficient enough though, so that S will be exsolved during magma ocean crystallization in order to explain the abundances of the HSEs ). Thus, in order to match the abundance of Mo, S, and HSEs in the BSE, the final C mantle abundance must always be greater than 300 ppm and to match the abundance of W, the final mantle C abundance must be greater than 700 ppm.

Implications for magma ocean crystallisation and fractionation processes in the case of a low C mantle abundance
If Earth's mantle abundance of C is low (Hirschmann & Dasgupta, 2009;Halliday, 2013;Rosenthal et al., 2015;Hirschmann, 2016Hirschmann, , 2018 However, even at very high equilibrating mantle fractions, the model W abundance is about a factor of two greater than observed. In addition, concentrations of non-volatile elements deviate significantly from BSE values as indicated by an increase in the reduced chi squared (see also Rubie et al., 2015). Thus, a small fraction of equilibration most realistically reproduces Earth, in agreement with laboratory experiments (Deguen et al. 2011, Landeau et al. 2017, and forces us to reject the hypothesis that the mismatch between model W concentrations and BSE W concentrations is an artefact of choosing a low extent of equilibration. This leaves a significant problem regarding W in the mantle. Here, we speculate on possible subsequent processing that is not included in the model. In This is in contrast to a high metallic S content, which would have the opposite effect on the metalsilicate partitioning of W (Wood et al., 2014), so a sulphide "Hadean Matte" cannot be responsible .
The precipitation of metallic iron is an expected consequence of deep magma ocean formation and crystallisation. Frost et al. (2004)  The accretion, differentiation and potential iron disproportionation scenario presented here has interesting implications for planetary accretion and early differentiation. Our results have implications for the interpretation of isotope data, and likewise must fit constraints imposed by that data. If the BSE was indeed initially higher in W and C than today, then these results demonstrate the need to consider the effects of late fractionation processes on the composition of the BSE (which is known to be important for the HSE elements; Laurenz et al., 2016;. The model presented here involves a number of simplifying assumptions. For example, it is assumed that volatile element concentrations in starting bodies are a linear function of heleocentric distance, which may not be realistic. It is also assumed that all metal-bearing starting bodies underwent core-mantle differentiation prior to being accreted to protoplanets. In reality some bodies must have been undifferentiated and would have released small dispersed metal grains into the magma ocean; the effect of this on the evolving compositions of the simulated planets remains to be determined. In future, incorporating isotopic constraints (including the Hf-W isotopic system) could be used to reduce the number of simplifying assumptions.

Implications for isotope systematics
Late core formation has important implications for the interpretation for the short-lived 182 Hf-  (Kleine et al., 2009), restricting the apparent timing of core-formation to a narrower time period after Earth's formation. In addition, the W content is increased by partial equilibration with impactors, which is compatible with evidence of preserved 182 W heterogeneities in the mantle (Touboul et al., 2012). Zube et al. (2019) found that the Grand Tack model creates Earthlike planets too quickly so that too much 182 W remains in their mantles today to match Earth.
However, they assumed a constant partition coefficient of W. Here, and in previous experimental studies, it has been shown that the partitioning of W depends predominantly on fO2 and additionally on temperature and on the presence of C and S in the equilibrating liquids. This complicates the analysis and demands further study. Wade and Wood (2016) incorporated 182 Hf-182 W isotopic constraints from the Earth-Moon system in an accretion and differentiation model, and suggested that such constraints were best met with a reduced moon-forming impactor, in contrast to our conclusions. The implications for the W-Hf system, core formation ages and the moon-forming impactor are clearly not yet resolved.
We predict that the majority of W and Mo present in Earth's mantle, along with S, was delivered relatively late during its accretion, by a higher fraction of more oxidised impactor material.
Heterogeneity exists across many isotopic systems in the meteorite record, with an apparent dichotomy between carbonaceous and non-carbonaceous chondrite compositions (Kruijer et al., 2020). Given that carbonaceous chondrites originate further from the sun, the isotopic identity of the BSE, like its elemental composition, can also record the timing of mixing and accretion between materials originating from different locations within the Solar System (Dauphas, 2017). Various isotopic systems, including Mo isotopes, may qualitatively agree with our model in that they imply the later addition of more carbonaceous chondrites relative to non-carbonaceous chondrites (Budde et al., 2019;Kruijer et al., 2020).
An important future line of enquiry would thus be to resolve these different records, to reconcile partitioning behaviour and accretionary events with the elemental and isotopic identity of Earth's building blocks. Our interpretation therefore requires testing in the future in order to 1) check its effect on the concentrations of other moderately siderophile elements in the mantle (the effect of C interaction and disproportionation on them has not been considered here), and 2) to understand in detail its implications for, and compatibility with, 182 Hf-182 W systematics (and potentially other isotope systems).

Conclusions
We have re-evaluated the metal-silicate partition coefficients DMo and DW and the fO2- KD Mo is sensitive to pressure and temperature, but these two intensive parameters mostly counteract one another at experimentally-attained conditions such that KD Mo decreases only gradually with increasing depth in Earth. Our parametrisation of KD Mo gives fairly similar results to all previous studies, so changes in KD Mo with pressure and temperature seem known with reasonable certainty. From our compilation of metal-silicate partitioning data, it is not possible to distinguish correlations between KD Mo and silicate melt composition within uncertainty, so we make an approximation that KD Mo is insensitive to silicate melt composition. KD Mo was, however, found to depend strongly on the light element content of the metallic phase.
KD W is sensitive to temperature but not pressure, becoming more siderophile with depth in Earth's mantle because of the temperature increase; this conclusion is broadly in agreement with some other studies Wade et al., 2012). However, different studies have more divergent models for KD W and its changes with P and T (see supplementary fig. S3), perhaps because of the higher sensitivity of KD W to both silicate and metal melt composition compared to KD Mo , making W behaviour somewhat more challenging to characterise than Mo. If W experimental data are restricted to those with silicate compositions similar to magma ocean compositions (broadly pyrolite-like), compositional effects on partitioning become weaker and can be neglected to some extent. Note that this excludes the use of data based on basaltic compositions. KD W was found to be particularly sensitive to the silicate melt CaO content, in agreement with previous suggestions of possible complexing behaviour or melt polymerisation control on the activity coefficient of WO3 (O'Neill et al., 2008;Steenstra et al., 2017).
KD W and KD Mo are both sensitive to the carbon content of the metal phase, such that W and Mo become increasingly siderophile when the metal is carbon-bearing. However, this effect is less dramatic than is predicted by interpolating linearly between carbon-free and carbon-saturated partitioning experiments (cf. Cottrell et al., 2009). Our newly-fitted epsilon interaction parameters can be used to predict the effect of C on Mo and W partitioning up to around 3 wt. % C in the metal.
We added the updated parametrisations of partitioning coefficients of W and Mo as well as the interaction parameters of W and Mo with C to the combined accretion and core-formation model of Rubie et al. (2015, in order to interpret the concentrations of Mo and W in the BSE in terms of planetary formation processes. In this model, oxidation and volatility gradients extend through the solar nebular. In this protoplanetary disk, Earth accretes heterogeneously and undergoes a multistage core formation process. We found that C plays an important role in the partitioning of W and Mo into the core, in agreement with previous suggestions (Jana and Walker, 1997a;Righter and Drake, 1999;Chabot et al., 2006;Cottrell et al., 2009). The model results show that W and Mo concentrations require the early accreting Earth to be sulfur-depleted and carbon-enriched so that W and Mo are efficiently partitioned into Earth's core and do not accumulate in the mantle. Indeed, without considering the presence of C, too much Mo and W accumulates in the mantle to match terrestrial abundances. In order for C to have a substantial enough effect on the partitioning of Mo and W to bring their final abundances down into agreement with measured values, the final C abundance is more consistent with the high C BSE abundance of about 800 ppm (Marty, 2012) than the low C abundance estimates ranging from 70 to 140 ppm (Hirschmann & Dasgupta, 2009;Halliday, 2013;Hirschmann, 2018). Alternatively, Earth's mantle C abundance was very high directly after planetary accretion, but then a subsequent core formation event triggered by disproportionation of Fe 2+ to Fe 3+ plus metallic Fe during deep magma ocean formation and crystallization may sequester more W and C from the mantle into the core and leave behind abundances that are consistent with measurements that favour the lower abundance of C. These concepts are required to reconcile model results with the BSE composition, and should be testable by applying constraints from Hf-W isotope systematics.

Acknowledgements
We would like to thank Andreas Audétat for performing the LA-ICP-MS measurements of the quenched silicate melts, Tiziana Boffa Ballaran for performing the XRD analysis of the carbide standard, Detlef Krauße for assistance with the electron microprobe, Hubert Schulze for sample preparation, Jon Wade for providing the data of Walter and Thibault (1995), and Alessandro Morbidelli for discussions. We also thank Nicolas Dauphas and Wim van Westrenen for editorial handling and additional perceptive comments, and four anonymous reviewers and Jon Wade for their thorough and constuctive reviews that enabled us to significantly increase the quality of our work. We acknowledge financial support from the European Research Council (ERC) Advanced                mantle C abundance estimates using the left-hand ordinate. The vertical bars on the right edge illustrate the two-sigma estimated W (blue) and Mo (green) abundance uncertainty for the BSE (Palme & O'Neill, 2014). For reference, the planetary growth curve (grey, dashed) for each Earth-like planet is shown on the right-hand ordinate. Vertical jumps in Earth's growth curve indicate giant impacts whereas low slope sections show periods of slow growth from the accretion of planetesimals. Fig. 12: For each Earth-like planet in accretion simulations 1-6, the time evolution of the mantle abundances of C (red) and S (black) is shown for fits to both the high (dashed) and low (solid) mantle C abundance estimates using the left-hand ordinate. The vertical bars on the right edge illustrate the estimated C (red) and S (black) abundance uncertainty for the BSE (Palme & O'Neill, 2014). For reference, the planetary growth curve (grey, dashed) for each Earth-like planet is shown on the right-hand ordinate.

Supplementary Information
Partitioning of sulfur between metal and silicate The partitioning of sulfur between liquid metal and silicate melt during each core formation event was calculated using the model of Boujibar et al. (2014, Eq. 11): In this equation, S / is the metal-silicate partition coefficient of sulfur, FeO is the weight % concentration of FeO in the silicate melt, and the other terms are as defined in Boujibar et al. (2014).  used this equation but with the incorrect assumption that FeO is the mole fraction of FeO in the silicate melt. This mistake arose because (a) FeO in Eq. 11 of Boujibar et al. (2014) is simply defined as "concentration" and (b) in Eq. 6 of Boujibar et al. (2014) (on the same page as Eq. 11) FeO is defined as mole fraction.
The incorrect definition of FeO used by  resulted in the maximum concentrations of S in Earth's mantle during accretion being too high. Using the correct definition in the current paper causes the maximum concentrations to be lower by a factor of 3 to 4. However, the error in  has no effect on their results in terms of the final concentrations of S and the HSEs in Earth's mantle and core.
Tungsten and molybdenum loss from the silicate mantle from pervasive metal saturation We calculate the potential impact of a pervasive metal saturation event in a magma ocean using a simplified heterogeneous accretion model on mantle W and Mo concentrations.
High-pressure experiments have shown that Fe 3+ becomes increasingly stable relative to Fe 2+ at increasing pressures, which drives the disproportionation of FeO: 3FeO = Fe2O3 + Fe This disproportionation may force the saturation of an immiscible Fe metal phase, and can be driven either by the crystallisation of Fe 3+ -bearing aluminous bridgmanite in the lower mantle at pressures greater than around 26 GPa (Frost et al., 2003), or could occur in the liquid silicate at pressures of greater than around 23 GPa (Armstrong et al., 2019). Unlike metal added to Earth from impactor cores, which only equilibrate with a small fraction of Earth's silicate mantle, this pervasive precipitation event allows the complete equilibration of silicate with the fractionating metal throughout the mantle at the relevant high pressures.
For the sake of demonstrating the effect of such an event on W and Mo concentrations, we assume that this precipitation occurred throughout accretion from the point at which Earth was large enough for the deep mantle to be at pressures above 23 GPa threshold where this process may start to take place.
We have modelled the effect of iron precipitation on the tungsten concentration of the mantle using the same parametrisations for D given in section 4.5 of the main text. For simplicity, we ignore activity effects and assume that W or Mo alloy with a pure Fe liquid. The model conceptually can be thought of as a growing planet, where a precipitation front at 23 GPa moves upwards with progressive accretion. We assume that a constant 0.5% metal precipitates from all parts of the silicate that are deeper than 23 GPa. log(fO2) increases linearly with fraction accreted to approximate the trend of impactors becoming more oxidised as accretion progresses, beginning at ΔIW-4 and ending at ΔIW-0.6, with an average ΔIW-2.3. We assume that precipitation occurs throughout the entire depth of the mantle to the CMB, rather than to the base of the magma ocean, because iron precipitation can occur within a crystal mush as well as a liquid, with a pyrolite liquidus pressure-temperature profile.
We find that 56% of mantle W is lost when Earth is fully accreted. This value is relatively insensitive to the choice of the pressure of the onset of precipitation (26 GPa gives 52% reduction), but decreases to 38% if the same overall amount of precipitation occurs at depths of 0.5*CMB to represent the magma ocean base. If 1% metal fractionates, mantle W loss increases to 62%, whereas if only 0.1% metal is lost, W loss decreases to 41%. The most sensitive parameter is fO2, because of the high charge of the W 6+ cation. The amount of W lost increases to 74% if fO2 evolution is not considered and a constant ΔIW-2.3 is assumed. Decreasing constant fO2 by 1 log unit to ΔIW-3.3 increases this value to 92% and decreasing it by 1 log unit to ΔIW-1.3 dramatically decreases W loss to just 11%.
Mo follows a similar pattern of behaviour, but is less strongly sequestered by the precipitating metal (44% Mo is lost when Earth is fully accreted), and the fO2-dependent response is dampened.
Whilst this model represents a significant simplification over reality because it does not couple iron precipitation with fO2, it indicates that pervasive metal saturation is an efficient mechanism for the removal of W from the mantle (and, to a lesser extent, Mo). If pervasive metal saturation occurred, it provides a straightforward mechanism to reduce W and Mo concentrations. Fig. S1 Time series showing apparent counts per second of Carbon measured on a pure Fe standard by EPMA on a single focussed spot. The observed drift, thought to result from C migrating towards the beam, is negligible over this time period.  Table 4, where the limits are shown here by dotted lines. Circles are literature data and triangles are new data from this study.

Fig. S4
The best fit mantle abundances of major oxides (SiO2, MgO, FeO, Al2O3, CaO, and H2O) for the simulated Earth-like planets from simulations 1-6 when considering both a high (blue) and a low (red) C concentration estimate for Earth's mantle. Error bars of the best fit mantle uncertainties, when large enough to be visible, are the one-sigma laboratory measurement partition coefficient uncertainties propagated through the numerical model into absolute mantle abundances. The horizontal black dashed lined is the estimated mantle abundance for each major oxide with a corresponding shaded horizontal band indicating the one-sigma uncertainties of that estimate (Palme & O'Neill, 2014).

Fig. S5
The best fit mantle abundances of refractory lithophile and moderately siderophile elements (Cr, Ni, Co, V, Nb, and Ta) for the simulated Earth-like planets from simulations 1-6 when considering both a high (blue) and a low (red) C concentration estimate for Earth's mantle. Error bars of the best fit mantle uncertainties, when large enough to be visible, are the one-sigma laboratory measurement partition coefficient uncertainties propagated through the numerical model into absolute mantle abundances. The horizontal black dashed lined is the estimated mantle abundance for each major oxide with a corresponding shaded horizontal band indicating the one-sigma uncertainties of that estimate (Palme & O'Neill, 2014).

Fig. S6
The best fit mantle abundances of highly siderophile elements (Pt, Pd, Ru, and Ir) for the simulated Earth-like planets from simulations 1-6 when considering both a high (blue) and a low (red) C concentration estimate for Earth's mantle. Error bars of the best fit mantle uncertainties, when large enough to be visible, are the one-sigma laboratory measurement partition coefficient uncertainties propagated through the numerical model into absolute mantle abundances. The horizontal black dashed lined is the estimated mantle abundance for each major oxide with a corresponding shaded horizontal band indicating the one-sigma uncertainties of that estimate (Palme & O'Neill, 2014).