Rhenium carbides phase diagram under pressure and explaining why WC-type ReC does not exist

The stability of W–C compounds (WC)-type ReC has been controversial for many years. Here, based on ab initio algorithm, we systematically searched for stable structures in the rhenium–carbon (Re–C) system at 0–300 gigapascal (GPa) pressure and analyzed the phase diagram within the pressure range. Only P63/mmc-Re2C, C2/m-Re3C, P21/m-Re4C, and C2/m-Re5C2 phases are found to be stable under 0–300 GPa, while WC-type ReC has high enthalpy and does not appear in the phase diagram. We also discussed the stability of WC-type ReC. Among these structures, C2/m-Re3C, P21/m-Re4C, and C2/m-Re5C2 are hitherto unknown structures, which could maintain dynamic and mechanical stability under ambient pressure. In addition, through the analysis of the structural and mechanical properties, P63/mmc-Re2C is the hardest metal among them with 31.5 GPa Vickers hardness at 0 GPa, and the metastable P 6 ¯ m 2-Re5C3 has the second-highest hardness (29.3 GPa), both of which exceed the hardness of TiN (18.7 GPa), the commercial material used for cutting tools. The study of Re–C compounds with high hardness provides theoretical guidance for further experimental research.