A mathematical analysis of diffusion in dislocations. IV. Diffusion-controlled absorption or desorption for a solid containing dislocations

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, , Citation A D Le Claire and A Rabinovitch 1984 J. Phys. C: Solid State Phys. 17 991 DOI 10.1088/0022-3719/17/6/008

0022-3719/17/6/991

Abstract

For pt.III see ibid., vol.16, no.11, p.2087 (1983). The well-known relations for the total amount W of material that diffuses in time t into or out of a semi-infinite solid when the surface y=0 is held at some constant concentration, are to be multiplied by a factor (1+ epsilon 2U) when the solid contains dislocations. epsilon 2 is the volume fraction of material in dislocations. U is calculated for the model previously employed by the authors of a solid containing a regular array of straight dislocations all normal to and ending in y=0 and each represented as a pipe of radius a within which the diffusion coefficient D'>>D, the coefficient in regular crystal. U, an integral, is a function of alpha =a/(Dt)1/2, of Delta =D'/D, and of the ratio, identical to epsilon / alpha , of the diffusion length (Dt)1/2 to the half-spacing between dislocations. U is represented graphically as a function of alpha for various values of Delta and epsilon 2. An application is made to experimental data on dislocation-enhanced isotope exchange rate measurements of anion diffusion in KBr by Dawson and Barr (1967).

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10.1088/0022-3719/17/6/008