A kinetic Monte Carlo study for Haven ratio of proton transport in perovskite ceramics

Abstract

In the present study, tracer and conductivity diffusion coefficients (D* and D_σ), and the Haven ratio H_R defined as D*/D_σ have been theoretically estimated in proton-conducting perovskite ceramics using the kinetic Monte Carlo (KMC) simulations. D* was estimated from the mean square displacement of protons in the equilibrium state by the ordinary KMC simulations, while D_σ was estimated from the drift velocity of protons in the non-equilibrium KMC simulations with an applied electric field. Taking proton-conducting yttrium-doped barium zirconate (BaZr_1−xY_xO₃, 0 < x ≤ 0.3) with the cubic perovskite structure as a model system, the D*, D_σ, and H_R of protons were estimated at intermediate temperatures. The estimated H_R are almost unity in the range of 0.99 and 1.04, indicating that the conventional mobility and conductivity estimation using the tracer diffusion coefficient D* through the Nernst-Einstein equation is reasonable approximation for this model system. Exactly, the estimated H_R are slightly higher than unity in the case of high doping levels particularly at low temperatures, which is an opposite trend to the general H_R (≤ 1) in solid state ionic conductors.