Structural, electronic properties and stability of tungsten mono- and semi-carbides: A first principles investigation

First principles calculations have been performed with the purpose to understand the comparative peculiarities of the structural, electronic properties and stability for all phases formed in the tungsten-carbon system: hexagonal and cubic mono-carbides WC and four polymorphs (α, β, γ and ε) of semi-carbide W₂C. All calculations were performed by means of the full-potential linearized augmented plane wave method (FLAPW). The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) formalism was used for the exchange and correlation energy functional. The geometries of all WC and W₂C phases were optimized and their structural parameters and theoretical density were established. Besides, we have evaluated the formation energies (E_form) of all the tungsten carbides. Based on our estimations we can arrange all investigated W-C phases depending on their stability in the following sequence: h-WC>ε-W₂C>β-W₂C>γ-W₂C>α-W₂C>c-WC. Here three carbides (h-WC, ε-W₂C and β-W₂C) are stable (E_form<0), γ-W₂C belongs to metastable systems (E_form∼0), whereas α-W₂C and c-WC appear to be unstable (E_form>0). Moreover, band structures, total and partial densities of states were obtained and analyzed systematically for all W-C phases in comparison with other available theoretical and experimental data.