Quasi-Debye response of ion-hopping conduction at lowest frequencies

On the basis of the relaxation mode theory, quasi-Debye response in the dynamic conductivity by hopping ions is theoretically investigated in three-dimensional random lattices with a uniform distribution of activation energies. It is shown at lowest frequencies that the dynamic conductivity is approximately given by σ(ω) ∼ σ(0) + A″ω s″, s″ = 2 - n, where n is a non-integer exponent originated from the mode diffusion length and density of states. The numerical analyses give rise to some values of s″ < 2, for example s″ ∼ 1.5, which behaves as s″ → 2 with increasing temperature. © 2003 Elsevier Ltd. All rights reserved.