Effect of C atomic concentration on the structural, mechanical, thermodynamic, and electronic properties of Cr–C binary carbides

Cr–C carbides have important applications in high-temperature fields due to their high melting point and hardness. The current research mainly focuses on the common Cr₂₃C₆ and Cr₇C₃ phases, and there is insufficient research on the other Cr–C binary carbides, especially for the effect of C atomic concentration on the basic physicochemical properties. Here, the structural stability, mechanical, thermodynamic, electronic, and chemical bond characteristics of eight Cr–C binary carbides, including Cr₂₃C₆, Cr₃C, Cr₇C₃, Cr₃C₂, and CrC along with three newly developed Cr₂C, Cr₄C₃, and Cr₈C₇ structures were systematically investigated by first-principles calculations. The stability of these carbides was confirmed through formation enthalpy, Born stability criterion, and phonon dispersion analysis, with Cr₃C₂ exhibiting the best stability. The elastic constants and moduli show that Cr–C carbides have high bulk modulus (B > 220 GPa) and shear modulus (G > 110 GPa). Their B/G ratio and Poisson’s ratio reveal the characteristics of both high hardness and good ductility, with the maximum hardness of 17.2 GPa (Cr₃C₂). In addition, the theoretical fracture toughness and critical energy release rate of such carbides indicating well consist. Electronic structure analysis indicates that the strong Cr-d and C-p orbital hybridization near the Fermi level dominates the metallic conductivity of the material, while population analysis further confirms the covalent metal bond-type mixing characteristics of Cr–C carbides. For the high Debye temperature (\(\theta_{{\text{D}}}\) > 630 K) and thermal stability, indicating that these carbides have significant potential for application in wear-resistant coatings, high-precision cutting tools, and high-temperature structural components.