By means of density-functional theory with the generalized gradient approximation and using the virtual-crystal approximation, we report first-principles calculation results on the structural and elastic properties of Ti_{1-x}Zr_{x}N alloy. In order to gain some further information on the mechanical properties of Ti_{0.5}Zr_{0.5}N compound, we also calculated the Young modulus, Poisson ratio, and anisotropy factor. The variation of calculated unit cell parameter for Ti_{1-x}Zr_{x}N structure increases with Zr content x. A linear dependence of the elastic constants and the bulk modulus over a range of composition x is found. All the C_{ij} of Ti_{0.5}Zr_{0.5}N increase linearly with increasing pressure. The same behaviour is observed for the other compounds with Zr compositions x.
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