The kinetics of oxygen exchange between oxide ceramics and the surrounding gas phase was modelled by taking account of surface exchange reactions and fast grain boundary diffusion. Numerical Laplace inversion was used with respect to a spherical grain model, while numerical solutions for a square grain model were obtained by means of the finite element method. The time dependence of the total amount of exchanged oxygen (relaxation curves) was predicted within Harrison's type-A kinetics.

Appropriate relations for the effective diffusion coefficient and the effective surface exchange coefficient were given.  If the grain boundary diffusion coefficient exceeds the bulk diffusion coefficient by many orders of magnitude, the new oxygen activity was attained instantaneously at the surface of each grain (grain boundary) after a step-wise alteration of the oxygen partial pressure. The rate-determining step for the oxygen stoichiometry change was slow bulk diffusion from the grain boundaries into the grains. This mechanism allowed the interpretation of the re-oxidation kinetics of donor doped barium titanate ceramics.

Modelling of Fast Diffusion along Grain Boundaries in Oxide Ceramics. W.Preis, W.Sitte: Solid State Ionics, 2008, 179[21-26], 765-70