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.