First-principles study on surface stability of tantalum carbides

Using first-principles method, surface energies of crystal planes of different tantalum carbide phases have been calculated. Quantum size effects are shown to possibly play a considerable role in determining accurate surface energies of these metallic films, which have been neglected in previous works. The γ-TaC phase has a more stable (0 0 1) surface than the close-packed (1 1 1) surface. In the α-Ta2C phase, (0 0 1) surface with only Ta termination is more stable than that of mixed Ta-C termination because the metallic bonds between Ta atoms are weaker than the Ta-C covalent bonds. The same is true for the ζ-Ta4C3 phase. The introduction of structural vacancies in the ζ-Ta4C3 −x phase creates more direct Ta metallic bonds, making the Ta-terminated surfaces even more stable. This is consistent with the experimental observations of cleavage of the basal planes, lamellae bridging of cracks, and the high fracture toughness of ζ-Ta4C3 −x.