Cluster model of the energy of vacancy formation in metals

The energy of vacancy formation Ev is discussed in the framework of a cluster model. It is shown that this value depends on the vacancies concentration in a metal, cv, and has a form Ev=Ev,crystal(0) -1/3Acv1/3 where the second term takes into consideration the surface of the clusters and the first term is concentration independent [Ev,crystal(0) and A are constants]. The additional term makes it possible to explain the curvature of self-diffusion plots in metals. Numerical results are obtained for Cu and β-Ti in the tight-binding model.