It was recalled that the analogy between electrical conductivity and matter transport held only in simple cases: where the point defect which was responsible for the diffusion did not alter the shape of the percolating cluster. In 5 variants of a model for matter transport via a dumb-bell interstitial defect mechanism in face-centered cubic alloys, the point defect migrated on a sub-lattice of coordination 8 and had only 2 jump frequencies at its disposal. When the difference between these frequencies tended to infinity, a percolative diffusion regime was observed, but a critical threshold which arose in the diffusion problem could be identified with a standard percolation threshold only under restrictive conditions. Here, the site percolation threshold which corresponded to one of the 5 variants was evaluated by using the usual series method. Extensive computer analysis yielded perimeter polynomials for clusters which contained up to 14 sites. A classical analysis, which involved the application of Dlog-Padé approximants to the first 2 moments of the cluster density function, yielded critical exponents which were associated with the percolation probability and with the mean cluster size; as functions of the (unknown) percolation threshold. It was shown that, by using higher-order moments of the cluster density function, a very narrow range (0.2775 to 0.2782) could be obtained for the percolation threshold. The corresponding values of the percolation probability and cluster density were in close agreement with recent and commonly used values of these exponents.

J.L.Bocquet: Physical Review B, 1994, 50[22], 16386-402