The storage of carbon in Earth’s mantle is an important consideration within the framework of the deep carbon cycle. In the deep (>250 km depth) reduced mantle, carbon storage mechanisms differ greatly from those in the oxidized shallow mantle. To investigate the stability of carbon-bearing phases in Earth’s deep mantle, we experimentally constrained compositional effects on phase stability in the Fe-Ni-S-C system at conditions relevant to the deep upper mantle and mantle transition zone. Our experiments suggest that carbide is absent at 10 GPa and 1450 °C in the Ni-poor (molar Ni/(Ni+Fe) = 0.2) portion of the metal-sulfide-carbon ternary, with carbon occurring as diamond or dissolved in the Fe-Ni-S-C melt. At 19 GPa and 1450 and 1600 °C, (Fe,Ni)₇C₃ saturates in the melt with C-rich (4.78–9.47 wt.%), S-poor (2.29–6.98 wt.%) bulk compositions. In comparison, Fe-Ni alloy only saturates with the C- and S-poor bulk composition 77.88 wt.% Fe, 19.47 wt.% Ni, 1.93 wt.% S, and 0.72 wt.% C. Based on these results, we trained machine learning models to predict carbon solubility in Fe-Ni-S-C melts. Compared to classical regression models, machine learning models significantly improve the accuracy of carbon solubility predictions. Combined, our experimental and machine learning results suggest that diamond and Fe-Ni-S-C melt are the primary hosts of carbon in the convecting deep upper mantle and throughout most of the mantle transition zone. In the deepest parts of the transition zone, however, carbide is likely to precipitate at adiabatic temperatures in C-rich mantle sources.

地幔中的碳储存是深碳循环框架内的一个重要考虑因素。在深部（>250 km 深度）还原地幔中，碳储存机制与氧化浅地幔中的碳储存机制有很大不同。为了研究地球深部地幔中含碳相的稳定性，我们在与深部上地幔和地幔过渡带相关的条件下，通过实验限制了成分对 Fe-Ni-SC 系统中相稳定性的影响。我们的实验表明，在 10 GPa 和 1450 °C 时，金属-硫化物-碳三元的贫镍（摩尔 Ni/(Ni+Fe) = 0.2）部分中不存在碳化物，碳以金刚石形式存在或溶解在Fe-Ni-SC熔体。在 19 GPa 和 1450 和 1600 °C 时，(Fe,Ni) ₇ C ₃在熔体中饱和富含 C (4.78–9.47 wt.%)、S-贫 (2.29–6.98 wt.%) 的本体成分。相比之下，Fe-Ni 合金仅在 77.88 wt.% Fe、19.47 wt.% Ni、1.93 wt.% S 和 0.72 wt.% C 的 C 和 S 贫乏的块体成分中饱和。基于这些结果，我们训练机器学习模型来预测 Fe-Ni-SC 熔体中的碳溶解度。与经典回归模型相比，机器学习模型显着提高了碳溶解度预测的准确性。综合起来，我们的实验和机器学习结果表明，金刚石和 Fe-Ni-SC 熔体是对流深部上地幔和大部分地幔过渡带中碳的主要宿主。然而，在过渡带的最深处，碳化物很可能在绝热温度下在富碳地幔源中沉淀。