Correlated complete-path equations for diffusion in an electric field

Publisher Website
Google Scholar
Abstract
Diffusion of a substitutional solute in a face-centered-cubic metal is discussed in terms of the complete path of the defect giving rise to mass transport. For diffusion in the absence of an applied field, these results are equivalent to the matrix method of Howard for the calculation of the correlation factor. In an applied field, however, the possibility that during the lifetime of a defect it may cause a tracer atom to make a series of successive jumps in the positive field direction or alternatively a series of successive jumps antiparallel to the field can appreciably influence the form of the equations. The tracer can, with decreasing probability, find itself several or many jump distances from its original position. Previous descriptions of this process restricted the tracer to two adjacent planes perpendicular to the applied field. In the present paper, generalized equations are derived for diffusion in an applied field with successive jumps by the tracer in one direction being explicitly allowed. To illustrate the use of these equations, the diffusion of an isolated tracer by a single vacancy is evaluated for a case where successive jumps in one direction are allowed, and also for comparison it is evaluated with the assumption that arrival of the vacancy at the symmetry plane passing through the tracer normal to the diffusion direction returns the vacancy to equilibrium. The latter approach restricts the tracer to two adjacent planes in a sequence of correlated jumps but is shown to give the same mobility. Thus use of the symmetry plane does not affect the results. In contrast to previous equations, the present treatment is applicable to situations where symmetry planes are not present. Thus, it will allow calculation of drift mobilities when the defect or crystal symmetry is more complex, as for diffusion via divacancies which can dissociate.