A linear diffusion model for ion current across blocking grain boundaries in oxygen-ion and proton conductors

We demonstrate the applicability of the linear diffusion model recently proposed for the current-voltage, I_gb-U_gb, characteristics of blocking grain boundaries in solid electrolytes to various oxygen-ion and proton conductors: the model precisely reproduces the I_gb-U _gb characteristics of La-, Sm-, Gd-, and Y-doped ceria as well as Y-doped barium zirconate to provide accurate explanations to the "power law" behavior of the I_gb-U_gb relationship, i.e. I_gb ∝ U_gbⁿ, experimentally observed. The model also predicts that the grain-boundary potential, Ψ_gb, in doped ceria weakly depends on temperature, if the trapped charge remains constant, and that the value of Ψ_gb can be determined from the value of the power n. Furthermore, the model provides a plausible explanation for the increase in the Ψ_gb with temperature observed for the proton conductor in which the concentration of the charge carrier decreases with temperature. Hence, it is evident that the linear diffusion model is robust and applicable to grain boundaries in a large variety of practically important solid electrolytes.