AbstractIon diffusion across material interfaces is considered in a sequence of approximations with increasing complexity. First, the one-dimensional lattice gas model of particle diffusion is generalized to include a finite width interface region, and the possible existence of an energy barrier at the interface. Overvoltage measurements on InSe, and dielectric loss measurements on B2O3 - 0.5Li20 - 0.15Li2SO4 are used to determine the field-free hopping rates in the two materials. It is shown that the energy barrier is a dominant parameter. This model is then modified by considering the disorder of the glass structure and the blocking effect resulting from the ion interaction. Next, a more rigorous treatment is presented by solving the Poisson equation with appropriate boundatry conditions, and a self-consistent theory of the ionic diffusion is proposed. To clarify this problem, an intermediate step and two additional models with increasing sophistication are considered: first, the potential φ(x) of the moving charge density n(x) is calculated and it is shown that φ(x) is not negligible. Then, a feed-back is provided by including this potential in the diffusion equation. This treatment is already self-consistent and more realistic but leads to long computations even for the simple one dimensional lattice-gas model. A remedy of this difficulty is proposed whereby the theory is reformulated in order to guarantee from the beginning the self-consistency of the solution of the non-linear diffusion problem. Straightforward extensions to the two-dimensional case are then possible. The results of the computations are illustrated with numerical examples for different values of the physical parameters.
Analytical solution of a one-dimensional lattice gas model with an infinite number of multiatom interactions