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Theory of Ionic Diffusion Across Material Interfaces

Published online by Cambridge University Press:  25 February 2011

M. Balkanski ,
I. Nachev ,
J. Deppe  and
R. F. Wallis
M. Balkanski
Affiliation:
Laboratoire de Physique des Solides, Université Pierre et Marie Curie, CNRS 154, 4, Place Jussieu, Tour 13 - E2, 75252 Paris Cédex 05, France
I. Nachev
Affiliation:
Laboratoire de Physique des Solides, Université Pierre et Marie Curie, CNRS 154, 4, Place Jussieu, Tour 13 - E2, 75252 Paris Cédex 05, France
J. Deppe
Affiliation:
Laboratoire de Physique des Solides, Université Pierre et Marie Curie, CNRS 154, 4, Place Jussieu, Tour 13 - E2, 75252 Paris Cédex 05, France
R. F. Wallis
Affiliation:
Laboratoire de Physique des Solides, Université Pierre et Marie Curie, CNRS 154, 4, Place Jussieu, Tour 13 - E2, 75252 Paris Cédex 05, France
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Abstract

Ion 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.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 293: Symposium U – Solid State Ionics III , 1992 , 193
Copyright
Copyright © Materials Research Society 1993

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