Approximate solutions of grain boundary diffusion in thin films in the B2 regime

Exact mathematical solutions of the grain boundary diffusion equation in thin films have generally a complicated form, which is too cumbersome for the evaluation of experimental average concentration depth profiles obtained by sectioning techniques. On the other hand the accuracy of the exact solutions is not necessary for practical purposes so that it is useful to derive sufficiently accurate approximate solutions. We propose a method to derive such solutions for a thin film if the grain boundary diffusion is in the B(2) regime. These solutions are derived for different diffusion sources.