Defect chemistry of grain boundaries in proton-conducting solid oxides

The defect chemistry of charged grain boundaries in an acceptor-doped oxide in equilibrium with water vapour is examined theoretically. The basis of the theoretical approach is that the formation of charged grain boundaries and attendant space-charge zones is governed by differences in the standard chemical potentials of oxygen vacancies and hydroxide ions between bulk and grain-boundary core, that is, by the thermodynamic driving energies for defect redistribution. A one-dimensional continuum treatment is used to predict the space-charge potential and defect concentrations in the grain-boundary core as a function of water partial pressure, temperature and acceptor dopant concentration for various values of the two thermodynamic driving energies. The results are discussed with respect to experimental data in the literature for acceptor-doped perovskite oxides (e.g. BaZrO3) and fluorite oxides (e.g. CeO2).