Elastic and Thermodynamic Properties of Anti-Perovskite Type Superconductor $MCNi_3$ (M = Zn, Cd)

The elastic and thermodynamic properties of the anti-perovskite superconductor $ZnCNi_3$ and $CdCNi_3$ are investigated by first-principles calculations. With the local density approximation as well as the generalized gradient approximation for exchange and correlation, the ground state properties and equation of state are obtained, which agree well with other theoretical calculations and experiments. Furthermore, by the elastic stability criteria, we predict that $ZnCNi_3$ and $CdCNi_3$ are not stable above 98.1 GPa and 196.5 GPa, respectively. The dependences of the heat capacity, thermal expansion coefficient, the Grüneisen parameter and bulk modulus ($B_{T}$ and $B_{S}$) on pressure and temperature for $ZnCNi_3$ and $CdCNi_3$ are also obtained successfully.