Quantitative determination of charge trapped at grain boundaries in ionic conductors by impedance spectroscopy

We propose a method for determining the density of space charge trapped at grain boundaries in polycrystalline solid state ionic conductors. The method is an extension of the earlier proposed Linear Diffusion Model (LDM) that relies on the impedance spectra-derived current-voltage characteristics of grain boundaries. The utility of the extended LDM version is demonstrated to successfully and nondestructively obtain values for the space charge density trapped at the grain boundaries in a variety of oxygen ion conductors including Sr-doped LaGaO₃, Y-doped CeO₂, and Gd-doped CeO₂, and proton conductors including Sr-doped LaNbO₃ and Y-doped BaZrO₃. For all cases, the density of the space charge trapped at the grain boundaries was <0.2C/m², corresponding to a fraction of electron charge per unit cell. The proposed technique, while it lacks the ability to determine the thickness of the grain boundary core when much smaller than the Debye length, it can be used to distinguish between space charge vs insulating layer contributions to the grain boundary resistance.