Analysis of kinetics regimes in grain boundary self-diffusion†

The evolution of self-diffusion concentration depth profiles into a bulk polycrystalline material from a thin-film tracer source was studied using the lattice Monte Carlo method. The onset of the Type-B kinetics regime from the Type-A kinetics regime was investigated for a cubic grain model, which can be expected to capture the three-dimensional nature of the problem better than the usual grain boundary slab model. The solutions of Whipple–Le Claire (derived for the constant source condition), Suzuoka (derived for the instantaneous source condition), Bokstein and colleagues (derived for the constant source condition) and Levine and MacCallum (derived for the constant source condition) are tested. All these solutions describe the tail region of the profiles well for this model (provided that a simple empirical factor in the case of the first three solutions is introduced). The intermediate Type-AB kinetics regime proposed by Divinski and Larikov between the Type-A and Type-B kinetics regimes was also investigated but could not be located from analyses of best-fit exponents. Forcing the fitting nonetheless to the tail regions shows that their analysis needs some further refinement before application to this model.