Theory for impedance response of grain and grain boundary in solid state electrolyte

We develop a generic phenomenological theory for the electrochemical impedance response of solid state electrolytes (SSEs). The theory describes dynamics of various physical processes in grain (g) and grain boundary (gb). Leaking capacitor model for the dynamics of ions in grain accounts compositional heterogeneity, ion reorganization and transfer across the surface of the grain. Model for ion relaxation in the grain boundary is determined through generalized electric double layer (EDL) theory over heterogeneous surface (Singh and Kant, 2013). The theory accounts for ion transfer and reorganization in grain boundary has the following components: (i) ions distribution at energetically heterogeneous surface of grain; (ii) space charge layer (SCL) in the grain boundary. Predicted impedance response of SSE evinces three frequency regimes, viz. (i) high frequency regime, attributed to relaxation of ions in grain and grain boundary (SCL), (ii) intermediate frequency regime, related to ion reorganization and transfer across heterogeneous grain and grain boundary (iii) low frequency regime, ascribed to the SSE/metal interface. The model emphasizes that ions encounter energetic heterogeneity in the grain causing distribution of relaxation time with a characteristic exponent gamma(g). Doped grain with aliovalent cations further enhances the structural/energetic heterogeneity and concentration of mobile ions therefore decreases the ion transfer resistance from grain to grain boundary. Doping also enhances the surface concentration of mobile ions at the grain boundary region resulting in enhanced capacitance and prolonged relaxation time of compact layer.