Abstract
The problem of diffusion-limited reactions is treated in lattice theory. We calculate the probability that a mobile interstitial by jump diffusion reaches a site of the recombination region around a vacancy (assumed to be given) if it starts at a distanceR p from the vacancy. We show that the continuum treatment with the recombination region represented by a spherical volume with an effective recombination radiusR a is a good approximation even for small regions and short diffusion paths. We give an explicit expression forR a in terms of the Green's function for stationary diffusion. The results for cubic lattices are discussed for recombination regions containing 1 to about 100 sites. As a rule of thumb we find that the effective recombination radiusR a is equal to the average distance\(\bar R\) of the surface sites from the recombination center.
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This paper is a condensed version of the first part of the report [1], Berichte der Kernforschungsanlage Jülich — Nr. 1083 FF (205 pages), available from: Zentralbibliothek der Kernforschungsanlage Jülich GmbH, D-517 Jülich 1 (Fed. Rep. Germany), Postfach 365.
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Schroeder, K., Eberlein, E. Lattice theory of diffusion reactions. Z Physik B 22, 181–187 (1975). https://doi.org/10.1007/BF01322363
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DOI: https://doi.org/10.1007/BF01322363