Applying point defect thermodynamics to Prussian Blue: Experiments and modelling

Prussian Blue, Na 1 + ξ Fe[Fe(CN) 6 ] is a promising low-cost cathode material for sodium-ion batteries (SIB). Despite its importance, the range of stoichiometry ξ of this mixed ionic and electronic conducting phase and the point defect structure are not known in adequate detail. An electrochemical cell using a sodium electrode, the solid Na + electrolyte NASICON and Prussian Blue is assembled. The course of the cell potential U cell vs. ξ is measured by galvanostatic intermittent coulometric titration (GITT), the chemical diffusion coefficient D ̃ Na of sodium is determined by evaluation of the cell potential transients. Point defect thermodynamics is used to model relations between stoichiometry ξ , defect concentrations, cell potential U cell , chemical potential and chemical diffusion coefficient D ̃ Na of sodium. The thermal equilibrium between high-spin Fe 3＋ , low-spin Fe 2＋ , low-spin Fe 3＋ and high-spin Fe 2＋ , i.e. “electrons” and “holes”, is decisive for the electrochemical properties. U cell vs. ξ and D ̃ Na vs. ξ exhibit characteristic sigmoidal courses with an inflection point at ξ = 0 . The equilibrium constant K el for electron–hole formation is obtained by fitting the experimental data. The corresponding Gibbs free enthalpy Δ G el 0 has a value of 0.3 eV, in accordance to Marcus-Hush theory, the energy of optically and thermally excited intervalence charge transfer. D ̃ Na is in the order of 10 −12 to 10 −11 cm 2 s −1 , the electronic charge carrier mobilities u e ′ and u h ⋅ in the order of 10 −10 and 10 −9 cm 2 (Vs) −1 , indicating the presence of strongly localised small polarons. A full sodiation results in a Prussian White phase with a nominal composition Na 2 Fe[Fe(CN) 6 ]. A full desodiation seems to be impossible, ending up at a limiting composition of approximately Na 0.2 Fe[Fe(CN) 6 ]. The results of this study offer valuable insights for a better understanding the electrochemical (cycling) behaviour.