Ab initio study of the ZnSnSb$_2$ semiconductor

For the chalcopyrite-like ZnSnSb$_2$ crystal, the equilibrium crystal-lattice parameters $a$ = 6.2893 $\mathring{\mathrm{A}}$, $c$ = 12.5975 $\mathring{\mathrm{A}}$, and $u$ = 0.2314 and the band structure involving the band gap $E_g$ = 0.43 eV are determined by ab initio calculations based on density functional theory. The phonon vibrational frequencies, the elastic constants ($C_{11}$ = 89.3, $C_{12}$ = 41.9, $C_{13}$ = 41.8, $C_{33}$ = 90.4, $C_{44}$ = 43.9, and $C_{66}$ = 44.1), the phase velocities of elastic waves, the elasticity moduli, the microhardness (2.29 GPa), and the Grüneisen elastic parameter (1.5) are calculated. The temperature dependences of the heat capacity and thermodynamic potential are considered (in the range from 20 to 633 K).