Mechanical and dynamic stability of complete and nonstoichiometric 3$C$-Si$_{x}$C$_{y}$ from ab initio calculations

The energies of formation of vacancies in the carbon and silicon sublattices, the independent elastic constants, the all-round compression, shear and Young's moduli, and the anisotropy coefficients are determined for the complete and nonstoichiometric cubic phases of 3$C$-Si$_{x}$C$_{y}$ ($x$, $y$ = 1.0 – 0.75) by ab initio methods of the band theory. In the formalism of the density functional perturbation theory (DFPT), the phonon dispersion dependences are obtained for these phases (the comparison with the experiment is given for the complete phase). It is shown that the mechanical characteristics of the phases become strongly anisotropic upon the transition from 3$C$-SiC$_{0.875}$ to 3$C$-SiC$_{0.75}$. It is established from the analysis of the phonon dispersion curves that the 3$C$-SiC$_{0.875}$ and 3$C$-SiC$_{0.75}$ phases, in contrast to the complete 3$C$-SiC phase, are dynamically unstable at $T$ = 0 K.