Volatile delivery to Earth during single-stage core formation

To test whether C, N, and S abundances and ratios in the present-day BSE can be satisfied by volatile delivery during a single-stage core formation, with or without an early atmospheric loss, we assumed the P-T conditions of alloy-silicate equilibration in a deep MO based on Ni and Co abundances in the BSE (31). To incorporate the effect of S on the alloy, the equilibrating alloy was assumed to contain 2 wt % S based on the estimates of the composition of Earth’s core (28). As Earth’s core was predicted to have undergone incomplete equilibration with the mantle (60), the percentage of alloy-silicate equilibration was varied between 0 and 100%, where 0% alloy-silicate equilibration would simulate volatile delivery of CI-chondritic material after core formation as a late veneer, while 100% alloy-silicate equilibration would simulate complete equilibration of Earth’s core with the mantle (fig. S6). For a deep MO, the DCalloy/silicate was not experimentally constrained, whereas the DNalloy/silicate [for S-free alloys (29)] and DSalloy/silicate (30) are known for deep MO conditions. Using the parameterized relationship defined in Eq. 4, a DCalloy/silicate ~5500 was assumed, while a DSalloy/silicate ~10 was predicted using the parametric equation from (30). Relatively low P-T experiments in this study predict that the DNalloy/silicate remains unchanged between S-free and S-poor alloys. Therefore, using relatively higher P-T data for S-free alloys (29), a DNalloy/silicate ~20 was used in our models.

To account for the effect of early atmospheric loss in addition to the effect of core formation (fig. S6B), an atmosphere overlying an MO that equilibrates with a core-forming alloy was assumed. The composition of the MO was calculated on the basis of the vapor pressure–induced solubilities of C, N, and S in the overlying atmosphere that equilibrates with the MO (1, 12). On the basis of their solubilities under relevant fO₂ conditions during single-stage core formation, the solubility constants (parts per million/megapascal) for C, N, and S were assumed to be 0.55, 5, and 5000, respectively, based on the results of several previous studies (1, 53, 56, 61). The C, N, and S concentrations of the BSE after early atmospheric loss were calculated by subtracting their abundances in the atmosphere from the pre-atmospheric loss BSE reservoir (mantle + atmosphere).