Surface-Like Diffusion of Fast Ions in Framework Energy Materials for Li- and Na-Ion Batteries.

The rate performance, power density, and energy efficiency of electrochemical devices are often limited by ionic conductivities in electrolyte and electrode materials. Framework Prussian blue analogs and dense niobium oxides have been identified as high-rate electrodes for sodium- and lithium-ion batteries, respectively, yet the origin of the extremely high solid-state Na + /Li + transport is not fully understood. Of critical importance is the fact that their ultra-low activation energy and anomalous pre-exponent factor cannot be satisfactorily rationalized from conventional theory of solid-state diffusion in the crystal lattice. Here, assisted by density-functional-theory calculations, we argued that the true origin is a unique surface-like diffusion mechanism of the intercalation ions. In a surface-like migration event, a mobile ion moves along the channel wall via a low coordination number and low migration barrier experiencing minimal steric hindrance. It is similar to surface diffusion in the conventional picture and contrasts with lattice diffusion from one interstitial/vacancy site to another one with high coordination number, crowded saddle-point geometry and high migration barrier. We found that the shifting from solid-state lattice diffusion to surface-like diffusion is determined by the size difference between the mobile ion and the diffusion channel, and a lowest migration energy barrier can be reached by mediating the channel size. The analogy to gas diffusion in molecular sieves shall be discussed. Additionally, the effects of defects and crystal water in Prussian blue analogs were also discussed for better understanding their rate performances in experimental scenarios.