Percolative diffusion of a dumbbell interstitial defect on a fcc lattice: Calculation of a percolation threshold with use of a series method

摘要: The analogy between electrical conductivity and matter transport holds only in simple cases, where the point defect which is responsible for diffusion does not alter shape of percolating cluster. In five variants a model by dumbbell interstitial mechanism fcc alloys, migrates on sublattice coordinance 8 has two jump frequencies at its disposal. When disparity these tends to infinity, percolative regime observed, but critical threshold arising problem can be identified with standard percolation one under restrictive conditions. present paper evaluates site ${\mathit{p}}_{\mathit{c}}$ corresponding usual series method. Extensive computer enumeration yields perimeter polynomials clusters containing up 14 sites. A classical analysis Dlog-Pad\'e approximants first moments cluster density function n(s) exponents \ensuremath{\beta}(${\mathit{p}}_{\mathit{c}}$) \ensuremath{\gamma}(${\mathit{p}}_{\mathit{c}}$) associated probability mean size, respectively, as functions (unknown) ${\mathit{p}}_{\mathit{c}}$. It shown further that, using higher-order n(s), very tight range proposed (0.2775${\mathit{p}}_{\mathit{c}}$0.2782), that values are close agreement recent most commonly adopted both exponents.