How space-charge behaviour at grain boundaries in electroceramic oxides is modified by two restricted equilibria

Determining the space-charge potential at grain boundaries in oxides by various experimental methods bears the promise of providing a comprehensive, quantitative description of interfacial defect chemistry. In this study, we draw attention to the problem of unifying data measured in different temperature ranges. We focus on unifying data from elevated-temperature electrical methods, such as impedance spectroscopy and current-voltage measurements, with data from room-temperature imaging techniques, such as Scanning Probe Microscopy (SPM), Transmission Electron Microscopy (TEM), and Atom Probe Tomography (APT). By means of continuum simulations, we calculate the space-charge potential Φ₀ at grain boundaries in the model electroceramic oxide acceptor-doped SrTiO₃, taking into account, first, a restricted equilibrium that leads to frozen-in acceptor-dopant profiles, and subsequently, a restricted equilibrium that leads to frozen-in bulk oxygen-vacancy concentrations. Our results indicate non-trivial differences between experimental values of Φ₀ obtained from electrical and from imaging methods, differences that arise from the different measurement temperatures and that are aggravated by the restricted equilibria. We also show that grain-boundary widths determined from elemental acceptor-cation profiles will not, on principle, agree with the electrical width extracted from impedance spectroscopy data.