Abstract
The ionic conductivity of a binary system consisting of two kinds of monovalent ions in the two-dimensional honeycomb lattice is calculated by the path probability method of irreversible statistical mechanics. The main purpose is to gain insight into the probable cause of the mixed-alkali effect observed in $\ensuremath{\beta}$-alumina-type systems and glass systems in general. It is shown that if the interaction between the two components is attractive, the existence of a sharp minimum which is caused by ordering can be expected at a certain composition. The minimum is shown to be mainly due to a percolation difficulty created by mutual arrangements of two kinds of ions. Based on these findings, it is suggested that the major cause of the mixed-alkali effect is the drop in the percolation efficiency due to the blocking of the diffusion (percolation) path created by mutual interaction of different kinds of ions.
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