Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T17:38:43.008Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Microionics: Solid State Integrable Batteries, edited by Balkanski, M., (North Holland, Amsterdam (1991)).Google Scholar
2. Heyne, L., in Mass Transport in Ionic Solids, eds Beniere, F. and Catlow, C.A., NATO ASI Series B 97 (Plenum, NY (1983)) p. 425.Google Scholar
3. Jennings, P.J. and Jones, R.O., Adv. Phys. 37, 341, (1988).Google Scholar
4. Balkanski, M., Wallis, R.F., Deppe, J. and Massot, M., Mat. Sci. Engin. B 12, 281, (1992).Google Scholar
5. Balkanski, M., Phys. Scripta T39, 9, (1991).Google Scholar
6. Dietrich, W., Fulde, P. and Peschel, I., Adv. Phys. 29, 527, (1980).Google Scholar
7. Bernasconi, J., Schneider, W.R. and Wyss, W., Z. Phys. B 37, 175, (1980).Google Scholar
8. Alexander, S., Bemasconi, J., Schneider, W.R. and Orbach, R., Rev. Mod. Phys. 53, 175, (1981).Google Scholar
9. Blender, R., Dietrich, W. and Frisch, H.L., Phys. Rev. B 33, 3538, (1986).Google Scholar
10. Deppe, J., Wallis, R.F. and Balkanski, M., Bull. Amer. Phys. Soc. 37, 554, (1992).Google Scholar
11. Nachev, I., Deppe, J., Wallis, R.F. and Balkanski, M., Mat. Sci. Engin. to be published in vol B15, (1992).Google Scholar
12. Deppe, J., Nachev, I., Wallis, R.F. and Balkanski, M., to be published.Google Scholar
13. Deppe, J., I. Nachev and Wallis, R.F., Univ. Pierre et Marie Curie (Paris VI), Laboratoire de Physique des Solides, Int. Rep. 003 (1992).Google Scholar
14. Pernas, P.L., Flores, F. and Anda, E.V., J. Phys.: Cond. Matt. 4, 5309, (1992).Google Scholar
15. Glauber, R.J., J. Math. Phys. 4, 294, (1963).Google Scholar
16. Brak, R. and Elliott, R.J., Mat. Sci. Engin. B 3, 159, (1989).Google Scholar
17. Oven, R., private communication.Google Scholar
18. Julien, C., Thesis, Paris (1991).Google Scholar
19. Kunc, K. and Zeyher, R., Europhys. Lett. 7, 611, (1988).Google Scholar
20. Mao, Z. and White, R.E., Sixth Int. Meeting Lithium Batt., Mdnster, p. 84 (1992).Google Scholar
21. Maass, P., Bunde, A. and Ingram, M.D., Phys. Rev. Lett. 68, 3064, (1992).Google Scholar
22. Bunde, A. and Maass, P., to appear in Physica A (1992).Google Scholar