Vacancy concentration in Al from combined first-principles and model potential calculations

We present a comprehensive study of vacancy formation enthalpies and entropies in aluminum. The calculations are done in the framework of the local-density and generalized-gradient approximations in the density-functional formalism. To assess anharmonic contributions to the formation free energies, we use an interatomic potential with parameters determined from density-functional-theory calculations. We find that the binding energy for the nearest-neighbor divacancy is negative, i.e., it is energetically unstable. The entropy contributions slightly stabilize the divacancy but also the binding free energy at the melting temperature is found to be negative. We show that the anharmonic atomic vibrations explain the non-Arrhenius temperature dependence of the vacancy concentration in contrast to the commonly accepted interpretation of the experimental data in terms of the monovacancy-divacancy model.