The lattice and grain boundary diffusivities that could be extracted from tracer concentration depth profiles resulting from tracer diffusion from a thin film source in the presence of equally spaced parallel boundary slabs. The situation was treated by putting a grid over the phenomenologically conceived system and exploring this grid with independent particles using Monte Carlo methods. It was shown that the transition from Harrison type-A kinetics (where the Hart equation provided the effective diffusivity) to Harrison type-B kinetics (where the lattice and grain boundary sections of the depth profile were delineated) occurred at a much shorter diffusion length than previously thought. In addition to the usual model where the mobility of tracers at the (surface) tracer source was matched to the immediate substrate, a model was also investigated in which this mobility was made equal to the grain-boundary mobility. A similar behavior was found.

The Transition from Harrison Type-B to Type-A Kinetics in Grain-Boundary Tracer Diffusion. I.V.Belova, G.E.Murch: Philosophical Magazine A, 2001, 81[10], 2447-55