A two-dimensional square grain model was used to model oxygen exchange between a gas phase and a ceramic composite consisting of two randomly distributed phases of equal grain size (side length of squares). Both average diffusion profiles for thin films and the time dependence of the total amount of exchanged oxygen (relaxation curves) were calculated by using finite element methods. The boundary conditions imposed an instantaneous change in the oxygen partial pressure in the surrounding gas phase, giving rise to surface exchange reactions as well as to diffusion in the composite. Both local equilibrium at the interface between different phases (host phase and inclusions) and blocking heterophase boundaries were taken into account. The numerical results were compared with the analytical solution for diffusion in an homogeneous medium introducing effective diffusion and surface exchange coefficients. When the relaxation time for effective medium diffusion was considerably shorter than that for transport from the host phase into the inclusions, relaxation curves with two separate time-constants were predicted.

Surface Exchange Reactions and Diffusion in Composite Materials - a Finite Element Approach. W.Preis: Journal of Physics and Chemistry of Solids, 2009, 70[3-4], 616-21