Non-coherent diffusion of a vacancy in a one-dimensional lattice in the quasiclassical approximation

Abstract

A vacancy in a one-dimensional lattice is considered as a vacant site in a one-dimensional chain of atoms. The energy model of this system is a double potential well with two levels. Based on the relations of nonequilibrium statistical mechanics, including the Kubo formula for the transport coefficient, the frequency of vacancy jumps is calculated. In this case, two factors of the system perturbation are taken into account: lattice deformation associated with the formation of an empty site, and phonon scattering by mass fluctuations in the chain. An analysis of two high-temperature jumps is given. First, the classical limit of vacancy motion under weak coupling conditions is considered for small values of the gradient of the interaction potential of the defect with the chain. In the classical case, the transition of an atom adjacent to a vacancy occurs through a quasy-stationary excited state. Secondly, a jump under tight binding conditions, when the motion of a neighboring atom occurs through a quasistationary state of finite width, and therefore having a finite lifetime.