Partitioning of carbon (C) into the cores of rocky protoplanets and planets is one of the primary causes of its depletion in their bulk silicate reservoirs. Most of the experimental studies that determined the alloy to silicate melt partition coefficient of carbon ($D_{\mathrm{C}}^{\mathrm{alloy}/\mathrm{silicate}}$) have been conducted in graphite-saturated conditions. Because carbon is a minor element in all known protoplanetary and planetary cores, it is not known whether graphite-saturated $D_{\mathrm{C}}^{\mathrm{alloy}/\mathrm{silicate}}$ values are applicable to core-mantle differentiation in rocky bodies which likely occurred in C-poor conditions. In this study we experimentally determined $D_{\mathrm{C}}^{\mathrm{alloy}/\mathrm{silicate}}$ in MgO capsules with variable bulk C contents between oxygen fugacity (fO₂) of IW–6.35 and IW–2.59 at a fixed P (3 GPa)-T (1700 °C). A mafic-ultramafic (NBO/T = 1.23-1.72) and mildly hydrous (bulk H = 44-161 ppm) nature of the silicate melts caused anhydrous C species (${\mathrm{CO}}_3^{2-}$ + CO) to dominate over a wider fO₂ range (>IW–4.2) in comparison to previous studies. This resulted in an increase in $D_{\mathrm{C}}^{\mathrm{alloy}/\mathrm{silicate}}$ with decreasing fO₂ from IW–2.6 to IW–4.2 followed by a drop at more reduced conditions due to the formation of C-H species. Importantly, $D_{\mathrm{C}}^{\mathrm{alloy}/\mathrm{silicate}}$ increases with increasing bulk C content of the system at a given fO₂. Partitioning of C between alloy and silicate melts follows non-Henrian behavior (i.e., it depends on bulk C content) because the activity coefficient of C in the alloy melt (${\gamma }_{\mathrm{C}}^{\mathrm{alloy}\mathrm{melt}}$) varies with C content in the alloy. Therefore, in addition to other intensive (P, T, fO₂) and extensive variables (alloy and silicate melt compositions), $D_{\mathrm{C}}^{\mathrm{alloy}/\mathrm{silicate}}$ also depends on the bulk C content available during core-mantle differentiation. Consequently, previously determined $D_{\mathrm{C}}^{\mathrm{alloy}/\mathrm{silicate}}$ for C-rich alloys are not directly applicable for core-mantle differentiation in relatively C-poor magma oceans (MOs). Because the experiments from the present study more realistically simulate C-poor cores and mildly hydrous, mafic-ultramafic silicate MOs, our data can be used to more accurately predict C fractionation between MOs and cores in inner Solar System rocky bodies. Our study suggests that closed system MO-core equilibration should have led to less severe depletion of C in the silicate reservoirs of inner Solar System rocky bodies than previously predicted.

将碳 (C) 分配到岩石原行星和行星的核心是其在大量硅酸盐储层中枯竭的主要原因之一。大多数确定合金与硅酸盐熔体碳分配系数的实验研究（$D_{\mathrm{C}}^{\mathrm{合金}/\mathrm{硅酸盐}}$) 已在石墨饱和条件下进行。由于碳是所有已知原行星和行星核心中的次要元素，因此不知道石墨是否饱和$D_{\mathrm{C}}^{\mathrm{合金}/\mathrm{硅酸盐}}$值适用于可能发生在贫碳条件下的岩体中的核-地幔分化。在这项研究中，我们通过实验确定$D_{\mathrm{C}}^{\mathrm{合金}/\mathrm{硅酸盐}}$在固定P (3 GPa) -T (1700 °C) 的氧逸度 ( f O ₂ ) 为 IW–6.35 和 IW–2.59之间具有可变体积 C 含量的 MgO 胶囊中。硅酸盐熔体的镁铁质-超镁铁质（NBO/T = 1.23-1.72）和轻度含水（体积 H = 44-161 ppm）性质导致无水 C 物质（ ${\mathrm{二氧化碳}}_3^{2-}$+ CO)与之前的研究相比，在更宽的f O ₂范围 (> IW–4.2 ) 上占主导地位。这导致了$D_{\mathrm{C}}^{\mathrm{合金}/\mathrm{硅酸盐}}$随˚F ö ₂从IW-2.6至IW-4.2，随后在更还原条件的下降由于CH物质的形成。重要的，$D_{\mathrm{C}}^{\mathrm{合金}/\mathrm{硅酸盐}}$在给定的f O _{2 下}，随着系统体积 C 含量的增加而增加。C 在合金熔体和硅酸盐熔体之间的分配遵循非亨利行为（即，它取决于整体 C 含量），因为合金熔体中 C 的活度系数（${\gamma }_{\mathrm{C}}^{\mathrm{合金}\mathrm{熔化}}$) 随合金中的 C 含量而变化。因此，除了其他密集型（P、T、f O ₂）和广泛的变量（合金和硅酸盐熔体成分）之外，$D_{\mathrm{C}}^{\mathrm{合金}/\mathrm{硅酸盐}}$还取决于核-地幔分化期间可用的大量 C 含量。因此，先前确定的$D_{\mathrm{C}}^{\mathrm{合金}/\mathrm{硅酸盐}}$对于富含 C 的合金，不能直接适用于相对缺乏 C 的岩浆海洋 (MO) 中的核-地幔分化。由于本研究中的实验更真实地模拟了贫碳核和轻度含水、镁铁质-超镁铁质硅酸盐 MO，我们的数据可用于更准确地预测 MO 与太阳系内部岩石体中核之间的 C 分馏。我们的研究表明，封闭系统的 MO 核心平衡应该导致太阳系内部岩石体硅酸盐储层中 C 的严重耗尽，而不是先前预测的。