Cation Diffusion and Conductivity in Solid Electrolytes. I

Abstract

The characteristics of cation diffusion and ionic conductivity in solid electrolytes are discussed using β‐ and β″‐alumina as examples. The problem is characterized by a cation migration by the vacancy mechanism in a “cation‐disordered phase,” a system in which the number of available vacant sites is of the same order of magnitude as the number of diffusing cations. The path probability method is used to derive both the tracer diffusion and the ionic conductivity; this method avoids the difficulties connected with the application of the ordinary random walk approach to such systems. β″‐Alumina is regarded as an example of the “cation‐disordered phases” in which all available cation sites are equivalent, while β‐alumina represents those in which available cation sites are divided into several nonequivalent sublattice sites. When the derived diffusion coefficient is interpreted using the language of the conventional random walk approach, the jump frequency of cations is found to include two factors, the vacancy availability factor $V$ and the effective jump frequency factor $W$ , both of which take into account the effect of surroundings of the migrating ion and characterize the cooperative mode of the cation motion. Both of these factors, as well as the correlation factor $f$ , depend strongly on composition of cations and on temperature. The Nernst–Einstein relation which relates the tracer diffusion and the charge diffusion is found to include characteristic correlation factors. Even in ionic conductivity, a correlation factor $f_I$ is found to appear in the β‐alumina‐type electrolytes. Although both $f$ and $f_I$ vary drastically depending on the cation concentration, the ratio of the two remains within limits determined by the geometry of the crystal lattice. The value of the ratio indicates the predominant mechanism of diffusion.