Calculation of transport coefficients for matter transport from linear response formulae by a random walk technique with application to the dumb-bell mechanism

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Abstract
The well-known matrix method for calculating tracer diffusion coefficients from the Einstein relation proceeds by a classification of tracer jumps into non-equivalent ‘types’, followed by matrix inversions to evaluate generating functions of random walks of the point defect occurring between successive tracer atom jumps. It is shown that the linear response expressions for the phenomenological coefficients LAA' LAB and LBB characterizing transport in an alloy of dilute component B in the solvent component A can be treated by a generalization of this procedure. The method is illustrated by exact calculations for a model of the dumb-bell mechanism in a random f.c.c. lattice. Results confirm the expression for LBB obtained for this model by Bocquet by other means and add corresponding results for LAB and LAA . This is the first dumb-bell model for which these three coefficients are accurately known when rotation about a lattice site is allowed for all dumb-bells in addition to the usual translation-plus-rotation jumps.