Structural evolution of Prussian blue analogues AxMFe(CN)6 upon intercalation of Na and K†

Prussian blue analogues (PBAs) are promising cathode candidates for sodium-ion and potassium-ion batteries; however, the complicate phase transitions occurring during charge/discharge affect intercalation dynamics and long-term stability. We discuss the structural evolution using hybrid-exchange DFT calculations to provide a theoretical foundation for the structural distortions in PBAs. The fully optimized geometries of PBAs A_xMFe(CN)₆ with different alkali metals (A = Na, K), transition metals (M = Mn, Fe) and intercalation levels (x) are compared and analysed through ligand field theory. The results evidence a 2-D like distortion of the hexacyanoferrate framework at low intercalation levels, and a 3-D like distortion at high concentrations, with stable superstructural arrangements of the intercalated ions. The correlations between framework distortion and the position of alkali metal ions are elucidated and rationalised by considering the combined effect of ionic sizes and the transition metal redox sequence.