Oxygen self-diffusion through fine-grained polycrystalline films into single crystalline substrates—a mathematical description

Interface exchange limited transport of oxygen through a polycrystalline film into a substrate with a higher oxygen diffusivity is characteristic for mixed ionic and electronic conductor (MIEC) electrode films on ionic conductors in solid oxide fuel cells. Such films can generally be approximately represented as a homogeneous medium with some effective diffusivity (type A regime), so that the mathematical description of the oxygen diffusion in such films is significantly simplified. In this paper, we present the solution of the diffusion equations in a film/substrate system with the practically important boundary conditions that the oxygen exchange is limited at the gas/film and at the film/substrate interface. Furthermore, we will derive an approximate solution that simplifies the evaluation of the interface exchange coefficients from oxygen isotope exchange depth profile experiments.