Enhanced mobility of cations and anions in the redox state: The polaronium mechanism

Hugely enhanced slow-ion diffusivity has been widely observed under extreme redox conditions and for unclear reasons. Aided by first-principles calculations on model systems of ZrO ₂, CeO ₂, BaTiO ₃ and Li _4/3Mn _2/3O ₂ , here we successfully explained the intriguing phenomenon by a polaronium mechanism. We found a polaronium, defined as a transitory complex of a polaronic electron or hole and a migrating counterion, becomes highly mobile when the counterion comes from a d ⁰ or f ⁰ cation (e.g., Zr ⁴⁺, Ti ⁴⁺ and Ce ⁴) or a p ⁶ anion (e.g., O ²⁻ ) in the host compound. Upon a redox reaction, the complex attains a d ¹/ f ¹ or p ⁵ configuration, which spontaneously forms because it is favored by an electron-phonon interaction (manifest as the Jahn-Teller effect in high symmetry systems) that enables local relaxation and lowers the system energy. Our calculations found such interaction reaching its peak at the saddle point where the local environment is softest, so soft that it allows a reorientation of the anisotropic d/f/p orbital to minimize the electron repulsion locally. Since the complex may dissolve after a successful ion-migration event, the redox electron/hole can be recycled to form another free-radical-like polaronium elsewhere, thereby enhancing ion migration repeatedly. The proposed polaronium mechanism, which also operates in ceramics doped with mixed-valence cations, is most relevant under dynamic and extreme thermal/field/irradiation conditions where extra electrons/holes are abundantly generated by non-equilibrium redox reactions. For such operations, some with emerging applications, our diffusion-enhancing mechanism may provide new theoretical insight to help understand their material/microstructure stability and performance.