Effects of Ta on the Structural, mechanical and electronic properties of the ternary alloys TaxHf1−xN: A computational study

The structural, elastic and electronic properties of the ternary transition metal nitrides alloys Ta${}_x$Hf${}_{1-x}$N at ($0<x<1$) in the rock-salt structure are investigated by ab initio calculations. The calculations were performed using the first-principles Exact Muffin-Tin Orbitals method using full charge density technique within the framework of density functional theory. The compositional disorder is treated within the coherent potential approximation. The estimated formation enthalpy indicates that Ta_0.5Hf_0.5N is thermodynamically the most stable alloy. The obtained lattice parameters of the Ta${}_x$Hf${}_{1-x}$N alloys are in good agreement with other available theoretical and experimental values. The predicted elastic stiffness constants $C_{11}$, $C_{12}$ and $C_{44}$ indicate that the Ta${}_x$Hf${}_{1-x}$N alloys are mechanically stable and the addition of Ta increases their ductility. The Ta_0.7Hf_0.3N found to be hardest alloy. The correlation between Pettifor’s criterion ($C_{12}-C_{44}$) normalized by bulk modulus $B$ and Pugh’s ratio $G/B$ with increasing the degree of alloying x allowed us to predict that the critical value $(G/B)=0.53$, which correspond to x around $0.6\pm 0.05$, marks the brittle to ductile transition.