Monovacancy and divacancy formation and migration in copper: A first-principles theory

The formation and migration of monovacancies and divacancies in copper have been studied from first-principles in order to resolve the discrepancies between previously published experimental and theoretical data. The monovacancy and divacancy formation, migration and binding enthalpies as well as the formation volumes have been calculated in the framework of a plane-wave pseudopotential implementation of the density functional theory, with full structural relaxations included. The monovacancy and divacancy formation entropies have been estimated from experimental data by performing a least-squares analysis. We show that the complete set of first-principles data, taking into account the presence of both vacancies and divacancies as well as the temperature dependence of the formation enthalpies and entropies allow one to reproduce the Arrhenius plot of the total vacancy concentration and the diffusion coefficient, both in good agreement with the most accurate experiments.

Figure 1

Arrhenius plot of the diffusion coefficient $D$. $T_M$ is the melting temperature of copper and is equal to $1357.77\mathrm{K}$.

Figure 2

(Color online) Arrhenius plot of the total vacancy concentration $C_v$.

Figure 3

Arrhenius plot of the total vacancy concentration $C_v$. The present work includes temperature dependent formation enthalpies and entropies. The inset shows the ratio of $S_{2v}^F$ and $S_{1v}^F$.