A mathematical analysis of diffusion in dislocations. III. Diffusion in a dislocation array with diffusion zone overlap

A. D. Le Claire, A. Rabinovitch

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Abstract

For pt.II see ibid., vol.15, p.3445 (1982). The authors consider diffusion from a surface y=0 into a solid containing a regular array of d dislocations per unit area, all normal to the surface and each represented as a pipe of radius a within which the diffusion coefficient D' is very much greater than that, D, for diffusion in a regular crystal. They calculate the mean concentrations (c(y)) at depths y, as determined in conventional sectioning experiments, for both constant concentration and thin-finite-source conditions at y=0. (c) is evaluated as a function of eta =y/(Dt)12/, alpha =a/(Dt) 12/, Delta =D'/D, epsilon 2= pi a2d and of epsilon / alpha , the ratio of the mean diffusion length, (Dt)12/, to the effective half-spacing between dislocations, ( pi d)-12/. Full account is taken, through an appropriate Wigner-Seitz-like boundary condition, of the effects of the mutual overlap of the diffusion zones around dislocations. For epsilon / alpha <or approximately=1, values of (c) do not differ by more than a few per cent from those previously calculated by the authors for well spaced non-interacting dislocations; for epsilon / alpha <or approximately=0.4 the two solutions are numerically identical. As epsilon / alpha increases above one the effects of overlap rapidly become increasingly important. They examine the nature of the penetration plots, log(c) versus y2, and the effective diffusion coefficients, Deff, deduced from them. The case epsilon / alpha <or=1 was discussed previously by the authors. The plots show maximum curvature around epsilon / alpha approximately=5 but would be difficult experimentally to distinguish from linear when epsilon / alpha >or approximately=10. For this range Deff is found to be closely represented by the Hart relation, Deff=D(1+ pi a2d( Delta -1)), the condition of validity of which can now be specified more precisely than heretofore.

Original languageEnglish
Article number012
Pages (from-to)2087-2104
Number of pages18
JournalJournal of Physics C: Solid State Physics
Volume16
Issue number11
DOIs
StatePublished - 1 Dec 1983
Externally publishedYes

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