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

In the present study, tracer and conductivity diffusion coefficients (D* and Dσ), and the Haven ratio HR defined as D*/Dσ 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 Dσ 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 (BaZr1−xYxO3, 0 < x ≤ 0.3) with the cubic perovskite structure as a model system, the D*, Dσ, and HR of protons were estimated at intermediate temperatures. The estimated HR 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 HR are slightly higher than unity in the case of high doping levels particularly at low temperatures, which is an opposite trend to the general HR (≤ 1) in solid state ionic conductors.