Abstract
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.