On the theory of grain-boundary diffusion in nanostructured materials under conditions of saturation of the subboundary region by the diffusant

In this work, which is the continuation of our previous work (Phys. Met. Metallogr. 109 (6), 329–336 (2010)), we give an extension of the theory of the coefficient of grain-boundary diffusion for the case of relatively large annealing times, when the width of the saturated subboundary zone exceeds the characteristic scale of decreasing coefficient of diffusion but no overlap of diffusion zones occurs in the bulk of nanograins. An analysis of the diffusion problem in this case leads to solutions that in form are analogous to the solution of the problem of one-dimensional diffusion along grain boundaries, corresponding to the C regime of annealing in conventional polycrystals but with time-dependent effective parameters (the grain-boundary diffusion width and the grain-boundary diffusion coefficient). It has been shown that the allowance for the existence of a subboundary region of enhanced diffusion leads to a decrease in the depth of the diffusant penetration along the boundary and to a simultaneous increase in the average sheet concentration. Estimates of these diffusion characteristics for nanocrystalline copper are given. Results of numerical calculations of the diffusion problem are presented, which make it possible to establish the field of the applicability of the approach suggested.