As the C solubility in the alloy (C content in the alloy at graphite/diamond saturation) and the Embedded Image are strongly dependent on the S content in the alloy (Figs. 1B and 2B), using the current set of alloy-silicate partitioning experiments with a C-N-S system and data from similar previous studies with C (24, 62), C-S (3, 4), and C-N (12, 63) systems, we formulated empirical thermodynamic parameterizations for the Embedded Image and C solubility in an Fe alloy on the basis of the P, T, S content in the alloy, and N content in the alloyEmbedded Image(3)Embedded Image(4)where Embedded Image represents the C solubility in the alloy (wt %), Embedded Image represents the S content in the alloy (wt %), Embedded Image represents the N content in the alloy (wt %), T represents the temperature (K), and P represents the pressure (GPa).

For Earth, late-stage accretion of oxidized impactors has been postulated as a possible reason for the associated increase in fO2 (64, 65). Therefore, we chose to focus on a relatively oxidizing range of metal-silicate equilibration because a differentiated impactor made up of some contribution from volatile-rich, oxidized CI chondrites would have been accreted under oxidized conditions. As the experimental data from this study and selected data from previous studies lie in a narrow fO2 range (~IW −1.7 to −0.3), the fO2 term was not included in the parametric relationships. Although our parametric relationships for the C solubility in the alloy and the Embedded Image do not include an fO2 term, we can still well reproduce the experimental values within a factor of 2 through linear least-squares analyses (fig. S5, A and B). This new parameterization also reveals that the silicate melt composition has a less significant effect in modifying the Embedded Image because extrapolation based on NBO/T formulation [where NBO/T is a measure of degree of silicate melt polymerization and is expressed as total nonbridging oxygens per tetrahedral cations; NBO/T = (2 × total O)/T − 4, where T = Si + Ti + Al + Cr + P] tends to overestimate the effects of a changing melt composition, from mafic to ultramafic, on enhancing the C solubility in a silicate melt, and hence, lowering the Embedded Image (66).

The concentrations of C, N, and S in the silicate portion and the core of the present-day Earth were calculated, assuming a disequilibrium merger of an impactor containing C, N, and S with a volatile-free proto-EarthEmbedded Image(5)Embedded Image(6)where Embedded Image denotes the concentration of C, N, or S in the BSE (parts per million), Embedded Image denotes the concentration of C, N, or S in the core of Earth (wt %), alloy/silicateimp represents the alloy/silicate ratio of the impactor, and Mimpactor/MEarth represents the ratio of the mass of the impactor with respect to the present-day Earth’s mass.

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