A Critical Examination of the Mott–Schottky Model of Grain-Boundary Space-Charge Layers in Oxide-Ion Conductors

Abstract

The electrical properties of grain boundaries in ionic conductors are studied most frequently and most easily by Electrochemical Impedance Spectroscopy (EIS). The resistance data obtained in this manner are typically analyzed with the Mott–Schottky space-charge model to extract a space-charge potential. In this study, taking CeO2 containing acceptor-dopant cations and oxygen vacancies as our model system, we calculate impedance spectra by solving the drift–diffusion equation for oxygen vacancies for a bicrystal geometry with space-charge layers at the grain boundary. Three different cases are considered for the behavior of the acceptor-dopant cations: a uniform distribution (Mott–Schottky), an equilibrium distribution (Gouy–Chapman), and a distribution frozen-in from a much higher temperature (restricted equilibrium). Analyzing our impedance data for the restricted-equilibrium case with the Mott–Schottky model, we find that the obtained space-charge potentials are substantially underestimated. In view of such a discrepancy not normally being apparent (the true values being unknown), we propose a specific set of EIS experiments that allow the Mott–Schottky model to be discounted.