Simulation of non-equilibrium energy distributions of current carriers in proton-conducting oxides with perovskite structure

Abstract

A simulation method based on the integral equation for the sticking probability of ion in well was discussed for its application to study energy distributions of protons carried in simple and complex perovskite-like structures. In the terms of the Wiener—Hopf computational technique, a numerical algorithm was developed to detect deviations of the energy distribution function from the Boltzmann distribution near the potential barrier peak due to random interaction of ion with the nearest environment. Being considered as non-equilibrium in this sense, the derived distributions essentially deviated from the equilibrium distribution for a wide energy loss range of protons carried from one lattice position to another. The developed simulation algorithm may be of methodological interest in general practice for numerical solution of the Wiener—Hopf equations, because the known solution techniques for integral equations of this type are inapplicable to the studied problems of electrochemical kinetics due to their essentially different boundary conditions.