Phase diagrams and mechanical properties of TiC-SiC solid solutions from first-principles

First-principles calculations were carried out in order to investigate the stability and properties of the random Ti1-xSixC solid solutions (alloys) with both the B1 and B3 structures. Lattice parameter, total energy, formation energy, phonon spectra, and elastic properties were studied as functions of composition. The phase diagram, in particular, binodal and spinodal curves were calculated. It was established that at 0 K the B1 alloys are energetically favorable at 0 <= x < 0.5, while the B3 alloys are favorable at 0.5 <= x <= 1.0. It was found that the contribution to the Gibbs free energy coming from the lattice vibrations strongly reduces the critical temperature of stabilization of the solid solutions. Calculated elastic moduli, Debye temperature, and Vickers hardness do not point to any strength enhancement of the alloys compared to TiC and SiC. Analysis of the spatial distribution of the Young and shear moduli shows that the B3 alloys exhibit much more spatial anisotropy of the elastic moduli than the B1 alloys.