A Schottky barrier based model for the grain size effect on oxygen ion conductivity of acceptor-doped ZrO2 and CeO2

Oxygen ion conductivities of acceptor-doped ZrO2 and CeO2 are important for their solid oxide full cell applications. A quantitative model accounting for the widely observed grain size dependence of the conductivity is of significant interest. A concise model for the grain size dependence of Schottky barrier is proposed here. The model is deduced from a continuum model for curvature effect on defect formation energy and its modification by considering the discrete nature of lattice distortion. The model is in good agreement with experiments for grain size effect on the Schottky barrier height and the grain boundary conductivity of doped ZrO2 and CeO2. The model is combined with the brick layer model to systematically examine the size and temperature dependences of total ionic conductivities of doped ZrO2 and CeO2. The total conductivity decreases monotonically with grain size at high temperature, but shows a maximum at about 200 nm at low temperature.