Interpretation of the critical length scale determining the conductivity in ionically conducting silicate glasses

Abstract Implications of basic percolation theories based on a random-barrier model for hopping conductivity have been explored for the interpretation of length scales determining dc conduction in ionically conducting alumina-silicate glasses. Independent measurements of activation energy Ec, conductivity spectra and Mott–Schottky capacitance–voltage characteristics indicate a common typical size for the average extent of displacement at the frequency of onset of ac conduction, Lc∼10 nm, which is interpreted as the effective correlation length of the infinite cluster determined by the percolation threshold ξc=Ec/kBT. The localization of carriers in clusters of sites between critical barriers causes a reduction of the effective mobile ion concentration (≈4 × 1016 cm−3) by many orders of magnitude below the nominal alkali concentration.