Percolation threshold for electronic conduction in β-alumina-type compounds

Abstract It is found that the addition of more than a certain amount of mixed valent ions would be necessary to render mixed conducting characteristics to β-alumina-type compounds. Based on the assumption that the electronic conduction is due to the hopping of small polarons to the nearest neighboring ions on the octahedral sites in the spinel block of β-alumina similar to that in magnetite, the pair approximation of the cluster variation method indicates that the threshold composition of such a mixed valent additive must exceed at least 0.24 of the number of octahedral ions. A new method of calculating the percolation limit is shown.