On the use of the constant phase element to understand variation in grain boundary properties

The impedance of polycrystalline electrolytes with heterogeneous grain boundary properties was studied using a two-dimensional numerical simulation. Simulated impedance spectra were generated for samples with random distributions of grain boundary conductivity, permittivity, or both. Equivalent circuit fitting using constant phase elements was then employed to analyze the simulation results with the goal of understanding to what extent such fitting can quantify the average grain boundary parameter values and estimate the spread of these parameters. It was determined that even for quite broad parameter distributions, the mean grain boundary conductivity could be estimated within 30%. The mean grain boundary permittivity could be estimated within 45% using a newly developed empirical expression for effective capacitance. While the degree of heterogeneity of the conductivity and/or permittivity values could be estimated in the case of a single heterogeneous parameter, this was not possible in the case of multiple heterogeneous parameters.