Statistical theory of diffusion. Application to a vacancy in a linear chain of atoms

The model for a vacancy in a lattice consists of a linear chain of the atoms, which contains one vacant site, together with a substrate potential. For this model the diffusion coefficient of vacancy is studied on the basis of the Kubo's expression for the transport coefficient. In deriving one a lattice distortion around the vacancy and massdifference scattering are taken into account. Two mechanisms of the transition the atom in the neighbouring vacant site is considered: the Orbach-type process at high temperatures which lead to the Arrhenius-type expression (the classical picture) and the tunnel transition at low temperatures. The phonon scattering is described by means of the $t$-matrix and Green function method.