Structural and elastic properties of single-crystal and polycrystalline Ti1−xZrxN alloys: A computational study

Abstract

First-principles pseudopotential calculations of the lattice constants and of the single-crystal elastic constants of Ti1−xZrxN (0≤x≤1) alloys were carried out. These calculations were performed using density functional perturbation theory (DFPT) within the virtual crystal approximation (VCA) for the disordered alloys and the supercell method (SC) for the ordered alloys. For the exchange-correlation potential we used both the local density (LDA) and the generalized gradient methods (GGA). The calculated equilibrium lattice parameters exhibit a positive deviation from Vegard's rule corresponding to a positive bowing parameter, while the calculated single-crystal stiffnesses, namely C11, C12 and C44, gradually decrease from TiN to ZrN. In a second stage, in the frame of anisotropic elasticity, we have estimated by homogenization methods the averaged stiffnesses 〈Cij〉, direction dependent Young's moduli and Poisson's ratios of polycrystalline Ti1−xZrxN (0≤x≤1) alloys considering a {111}-fiber texture.