Russian Journal of Electrochemistry

, Volume 41, Issue 11, pp 1165–1175 | Cite as

On a Stochastic Theory of Ion Transfer at Intermediate Damping

  • A. L. Samgin


The stochastic method, which was formulated earlier by Gurevich and Kharkats on the basis of a classic solution of the Fokker-Planck equation in a phase space of coordinates and momenta, is developed to extend it to the case of intermediate damping. In contradistinction to the Gurevich-Kharkats model, the new theory is based on the Fokker-Planck equation in the energy-action coordinates. Analytical expressions for the exchange current and conductance are derived. The expressions are valid in a broad damping regime. As compared with the Gurevich-Kharkats model, the expression for the exchange current contains an additional factor, which depends on the energy losses sustained by the ion upon its collision with the cage of a crystal lattice. An explanation for the isotope effect in the high-temperature protonic conductors is suggested. It is demonstrated that the friction coefficient for these solid electrolytes may correspond to the underdamped-to-intermediate-damping regime. This fact makes it possible to put forth an explanation for the existing contradictions between their properties and simple hopping models, which ignore the interaction of ions with the crystal lattice.

Key words

Fokker-Planck equation solid electrolyte isotope effect protonic conductor 


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Copyright information

© MAIK "Nauka/Interperiodica" 2005

Authors and Affiliations

  • A. L. Samgin
    • 1
  1. 1.Institute of High-Temperature Electrochemistry, Ural DivisionRussian Academy of SciencesYekaterinburgRussia

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