Dissimilar Diffusion Mechanisms of Li+, Na+, and K+ Ions in Anhydrous Fe-Based Prussian Blue Cathode

Prussian Blue (PB, AFe[Fe(CN)6], where A = Li, Na, K, etc.), a three-dimensional (3D) metal-organic framework (MOF), emerges as a promising cathode material, particularly for next-generation Na- and K-ion batteries. However, the microscopic occupation positions and diffusion behaviors of A+ ions in the unit cell have been inadequately elucidated. This study systematically compares the diffusion mechanisms of multiple Li+, Na+, and K+ ions using density functional theory calculations. We clarified the new stable occupation sites for Li+ and Na+ ions: the face-centered (FC) 24d and off-FC 48g sites, respectively. The smaller ionic radii of Li+ and Na+ ions contribute to their enhanced Coulombic attractions from CN- anions. Li+ ions are more self-diffusive than Na+ at high temperatures; however, at room temperature, Na+ ions have comparable self-diffusivities and lower activation energies than Li+ ions. This is attributed to the smaller tilting of [Fe(CN)6]-octahedra induced by Na+ ions' transfers, resulting in a shallower potential energy landscape than for Li+ ions. These results demonstrated that the anhydrous Fe-based pristine PB crystal is an excellent Na+-ion conductor. Meanwhile, K+ ions prefer the conventional body center (8c site) and exhibit negligible self-diffusivities without anionic defects. Surprisingly, they show anisotropic diffusion along anion vacancy channels in the defective crystal, in contrast with the isotropic pathways for Li+ and Na+ ions. These findings update the fundamental chemistry of the diffusivity correlation with the electronic orbital interactions and framework distortion within general MOF materials.