A first-principles study of the stability and mechanical properties of ternary transition metal carbide alloys

First-principles calculations were carried out to investigate electronic structure, phase stability, elastic properties, Debye temperature, and hardness of the TiC-HfC and TiC-TaC random solid solutions as functions of composition. For TiC-HfC, significant miscibility gaps with consolute temperatures about 1975K are revealed in the binodal and spinodal curves. The negative deviation of the elastic moduli and hardness from linearity are obtained for TiC-HfC, whereas, for TiC-TaC, these characteristics are above their linear interpolation between the end members. Concentration dependences of the Debye temperature for both systems have a negative curvature. To clarify a possible mechanism of stabilization or destabilization of these solid solutions and other similar carbide systems, mixing energies of the M1 xM2xC alloys, where M1 and M2 are the transition metals of the IV, V, and partially VI groups, were calculated. It is found that the behavior of mixing energies for the M1C-M2C alloys with M1 and M2 of different groups depending on composition is determined by the difference between cell volumes of the end members, C, the degree of occupancy of the metal band, and the shape of the density of states in the metal band region. Values of C mainly are responsible for positive mixing energies of the alloys with valence electron concentrations (VECs) equal to 8 and 9 for which occupancy of the metal band weakly changes with composition. The maximum hardness of the solid solutions for which VECs of the end members are different is predicted to be reached for the compositions with VECs=8.5-8.75.