Simulation of prefactor anomalies in superionic conductors in the case of arbitrary energy losses. III. Finite-barrier corrections

Abstract

In previous publications (Samgin and Ezin, Ionics 14:345–348, 2008; Samgin and Ezin, Ionics 15:717–723, 2009), we presented a numerical technique to study the prefactor in the ion diffusion coefficient as a function of the average energy losses of ions to the bath. In the present paper, we model the prefactor in a perturbation theoretical fashion when energy losses are not constant with the ion energy. Using cubic and quartic potentials as examples, we show that including the energy dependence to the energy losses to be converted in finite-barrier corrections may be expected to reduce further the value of the prefactor. We give an extension of the Huberman–Boyce formula for conductivity prefactors from constant to varying energy losses. The finite-barrier corrections in a protonic conductor are estimated to be of the order of 10 % to a leading-order term in the prefactor expansion. These corrections must be built into an accurate analysis of ion diffusion mechanism.