Investigations of Ion-Hopping Conduction by Effective Medium Approximation

Abstract

In one- through three-dimensional (1D–3D) simple lattices equipped with a uniform distribution of symmetric activation energies, effective medium approximation (EMA) is examined to see how it accurately reproduces the exact dynamic behavior of ion-hopping conduction obtained by the relaxation mode theory (RMT). Without introducing any other approximations, dc conductivity is derived and compared with RMT results. It is found that the activation energies are quite consistent with RMT and percolation results in the 1D and 2D systems, but deviate from those in the 3D system. On the other hand, the ac conductivity formulas are carefully obtained at low frequencies, and the accompanying scaling properties are investigated and compared in terms of RMT behavior; again, 2D- and 3D-EMAs do not well reproduce RMT results. The ac part of EMA conductivity is also clarified in the lowest-frequency regime, giving rise to another power law as has already been discussed in RMT.