A comprehensive study was made of vacancy formation enthalpies and entropies in Al. The calculations were performed within the framework of the local-density and generalized-gradient approximations in the density-functional formalism. In order to assess anharmonic contributions to the formation free energies, an interatomic potential was used; with parameters determined from density-functional-theory calculations. It was found that the binding energy for the nearest-neighbor divacancy was negative, i.e., it was energetically unstable. The entropy contributions slightly stabilize the divacancy but also the binding free energy at the melting temperature was found to be negative. It was shown 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.

Vacancy Concentration in Al from Combined First-Principles and Model Potential Calculations. K.M.Carling, G.Wahnström, T.R.Mattsson, N.Sandberg, G.Grimvall: Physical Review B, 2003, 67[5], 054101 (9pp)