Density functional calculations of the formation and migration enthalpies of monovacancies in Ni: Comparison of local and nonlocal approaches

Abstract

We examine in this work the potential and the functional to be used in a density functional theory approach in order to describe correctly the formation and migration energies of monovacancies in nickel. As the formation enthalpy is not well-known experimentally at $0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, we choose in a first step to determine some structural, magnetic, and elastic properties of the bulk, which are well-established experimentally. The comparison between both approaches, i.e., the local spin density approximation (LSDA) and the generalized gradient approximation (GGA) exchange-correlation functionals is analyzed. We conclude that the contribution of nonlocal GGA terms in order to describe correctly the electronic density is necessary to determine the formation and migration enthalpies and activation energy of monovacancy. The calculated formation ${H}_{v}^{f}$ and migration ${H}_{v}^{m}$ enthalpies differ significantly between both approaches. The overestimation of the LSDA approximation is of $0.25\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${H}_{v}^{f}$ and of $0.23\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${H}_{v}^{m}$ with respect to the GGA one, leading to a gap of $0.48\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ between both methods for the activation energy ${Q}_{1}$. We show that the GGA results are comparable with experimental data if the thermal expansion contribution is taken into account through the lattice parameter variation. Finally, it is shown that the activation energy is nearly independent of the thermal expansion effects; thus we can expect that the curvature of the Arrhenius plot of the diffusion factor near the melting point is essentially due to the contribution of divacancies.