Self-Consistent Treatment of the Vacancy Mechanism for Metallic Diffusion

Previous calculations have indicated the predominance of the vacancy mechanism in metallic self-diffusion. Here a more detailed calculation of the energy needed to form a vacancy has been carried out. A self-consistent solution to the Hartree-Fock equation was used with a free-electron model corresponding to the copper lattice. The result agreed essentially with the value predicted by Huntington and Seitz. In addition a rough upper limit was established for the energy required to move a vacancy. This value compares satisfactorily with the observed energy of activation for copper self-diffusion. The anisotropy recently observed in zinc self-diffusion can also be qualitatively explained to some extent on the basis of a vacancy process. In the case of the alkali metals present considerations are insufficient to decide between the interstitial and vacancy mechanisms.