Formation and stability of di-transition-metal carbides TixZr1−xC, TixHf1−xC and HfxZr1−xC

We have carried out the first-principles total energy calculations, using the pseudopotential plane-waves approach based on density functional theory, within the generalized gradient approximation (GGA) for the exchange and correlation potential, to investigate the formation and stability of di-transition-metal carbides. We report total energy calculations for TixZr1−xC, TixHf1−xC, and HfxZr1−xC crystal structure over a range of composition x and we present a description of formation energies, stability and elastic properties. Our results for elastic stiffness coefficients and equilibrium volume as well as their dependence on composition were compared with experimental data and previous calculations.