Grain size-dependent electrical conductivity of polycrystalline cerium oxide II: Space charge model

The effect of space charges along grain boundaries on the electrical conductivity of polycrystalline mixed ionic/electronic conductors (MIECs) was investigated. The bulk concentrations of point defects were calculated using the defect chemistry of corresponding single crystalline materials, taking into account the charge neutrality condition. The accumulation or depletion of charged point defects in space charge layers along grain boundaries was described in terms of the Gouy–Chapman theory of liquid electrolytes. Analytical expressions were obtained for the contribution of space charge layers to the electrical conductivity. These expressions were used to calculate the partial conductivities of a polycrystalline material with a simple brick-layer topology. The space charge model was applied to cerium oxide including acceptor ions at typical impurity concentrations. The major objective of the study was the calculation of the grain size dependence of electrical conductivity. In particular, the effect of a positive space charge potential on acceptor segregation, the ionic and electronic partial conductivities and also on the temperature and oxygen partial pressure dependence of electrical conductivity was studied. It was shown that the space charge model yielded a consistent explanation for experimental results on the grain size dependent electrical conductivity of polycrystalline cerium oxide.