Electronic structure and elasticity of Z-phases in the Cr-Nb-V-N system

Structural properties and energetics of Cr-based Z-phases (CrNbN, Cr(Nb,V)N and CrVN) were investigated using the Vienna ab initio simulation package (VASP) code employing the projector augmented wave (PAW) pseudopotentials by means of both local density approximation (LDA) and generalized gradient approximation (GGA) for the exchange and correlation term. The geometry of all studied phases including NbN, VN and elemental constituents (nonmagnetic bcc Nb and V and antiferromagnetic bcc Cr) was fully relaxed, providing the equilibrium structure parameters and total energies. The calculated lattice parameters of Z-phases correspond very well to the experimental data and decrease with increasing molar fraction of vanadium. Enthalpies of formation show that all three Z-phases are stable at T = 0 K. The electronic structures of Z-phases including densities of states and charge densities were analysed. The calculated bulk moduli and elastic constants were used to evaluate stability conditions and elastic anisotropy ratios. It was confirmed that Z-phases are mechanically stable. Additional information on ductility was obtained from Cauchy pressures, Pugh ratios, Young moduli, and Poisson ratios. The ductility evaluated using the Pugh ratio decreases with number of vanadium atoms.