Thermodynamic stability and superconductivity of tantalum carbides from first-principles cluster expansion and isotropic Eliashberg theory

Abstract

The phase stability of tantalum carbides, particularly cubic rocksalt TaCx and hexagonal Ta2Cx, where 0 ⩽x⩽ 1 due to the presence of vacancies on the C sites, is explored using a first-principles cluster-expansion method. Our results demonstrate that at 0 K, in addition to stoichiometric cubic TaC and hexagonal Ta2C both widely known in the literature, carbon-deficient face-centered orthorhombic TaC0.833 is identified as a thermodynamically stable phase in the binary Ta−C system. By investigating their vibrational and electronic properties, the three carbides are dynamically stable and are metallic. We further demonstrate, by adopting phonon mediated superconductivity based on the Bardeen–Cooper–Schrieffer theory, that cubic TaC, face-centered orthorhombic TaC0.833, and hexagonal Ta2C superconduct, whose transition temperatures are estimated by the Allen–Dynes equation to be 10.0 K, 6.8 K, and 1.4 K, respectively. The physical origin of superconductivity in these stable carbides are discussed and described, based on the detailed analysis of the materials’ electronic and phonon properties.