Publication date: 10th April 2024
The excess resistivity of grain boundaries in ion-conducting oxides is generally attributed to the presence of space-charge layers in which oxygen vacancies are depleted. Acceptor cations are commonly assumed to take a uniform concentration profile throughout the sample (Mott–Schottky case). This simplification enables a simple analysis of impedance data with closed-form expressions, but it disregards that acceptor cations will typically be able to accumulate within the space-charge layers at sintering temperatures, at which the acceptor cations are mobile. Upon cooling, the immobilised acceptors will then retain an accumulated profile. This aspect is taken account of by the restricted-equilibrium model.
In this work, we explore the effects of restricted equilibria on grain-boundary properties by means of continuum simulations. Our implementation of a drift–diffusion framework allows for the calculation of impedance spectra for space-charge scenarios with a realistic thermal history, using acceptor-doped CeO2 as a model system. These results reveal the errors that arise from analysing complex space-charge situations with the simplified Mott–Schottky expressions. We also discuss how fundamental differences between elevated-temperature and room-temperature experimental techniques may arise, in the model electroceramic SrTiO3, from the influence of restricted equilibria.