Formation entropy and the diffusion constant for vacancies in Cu and $\alpha$-Fe

The formation entropy of single vacancies and divacancies and the frequency factors entering in the diffusion constants are calculated for Cu and $\alpha$-Fe based on a pair-potential approach. For Cu a Morse and a Born-Mayer potential have been employed, for $\alpha$-Fe the potential of Chang and Graham. The calculations have been performed by a determinant method and partly also by the Green's-function method. The effects of the long-range displacements have been carefully estimated and are very important. For the Morse potential the formation entropy is $2.3k$ for a single and $4.0k$ for the divacancy in Cu, whereas the temperature-independent part of the diffusion constant is 0.12 and 3.7 ${\mathrm{cm}}^2$/sec, respectively. For $\alpha$-Fe, the Chang-Graham potential leads to a formation entropy of $2.1k$ and to a diffusion constant of 0.16 ${\mathrm{cm}}^2$/sec for single vacancies.