Formation entropy and the diffusion constant for vacancies in Cu and α -Fe

The formation entropy of single vacancies and divacancies and the frequency factors entering in the diffusion constants are calculated for Cu and α-Fe based on a pair-potential approach. For Cu a Morse and a Born-Mayer potential have been employed, for α-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 cm²/sec, respectively. For α-Fe, the Chang-Graham potential leads to a formation entropy of $2.1k$ and to a diffusion constant of 0.16 cm²/sec for single vacancies.