Elastic and thermal properties of Zr$_z$Nb$_{1-z}$C$_x$N$_y$ solid solutions

The temperature and concentration dependences of the elastic moduli and the thermal linear expansion coefficient of Zr$_z$Nb$_{1-z}$C$_x$N$_y$ solid solutions containing from 3 to 8 at% of structural vacancies in a nonmetallic sublattice have been found. The temperature dependences of the Debye temperature $\Theta_{\mathrm{D}}(T)$ have been calculated using the elastic data and the data on the heat capacity. It has been shown, using carbide NbC$_{0.97}$ as an example, that the $\Theta_{\mathrm{D}}(T)$ dependences found from the elastic properties and the heat capacity coincide in the temperature range $\sim$220–300 K. By analogy with the niobium carbide, the heat capacity $C_p$ (300) of Zr$_z$Nb$_{1-z}$C$_x$N$_y$ solid solutions of various compositions is calculated based on the values of $\Theta_{\mathrm{D}}$(300) determined from the elastic properties.