Effect of the defectiveness of the carbon sublattice on the elastic properties of cubic titanium carbide TiC$_{y}$

Changes in the elastic constants c$_{ij}$ of disordered cubic titanium carbide TiC$_{y}$ with an increasing the defectiveness of the carbon sublattice are estimated for the first time. It was found that the deviation of titanium carbide from the stoichiometric composition TiC$_{1.0}$ leads to a decrease in the elastic stiffness constants c$_{ij}$ of disordered TiC$_{y}$ carbide with a simultaneous increase in elastic anisotropy. The distributions of Young's modulus $E$ and Poisson's ratio $\mu$ in the (100) plane and the distributions of the shear modulus $G$ in the (100), (110), and (111) planes have been calculated as functions on the crystallographic direction $[hkl]$ and on the relative carbon content $y$ in TiC$_{y}$ carbide. The lowest values of the shear modulus G$_{hkl}$ for TiC$_{y}$ are observed in the (111) plane.