Quantifying Small Polaron Formation and Hopping Kinetics in FePO ₄ : First-Principles Rate Theory Calculations

The formation and migration of small polarons are fundamental microscopic processes governing the charge transport properties of FePO 4 -based materials. However, as the initial step in this kinetic chain, the rate constant k form for the delocalized electron → small polaron transition lacks quantitative characterization, hindering the establishment of a complete structure-dynamics-property correlation. In this work, we systematically investigate the kinetics of delocalized electrons relaxing to form small polarons in FePO 4 using first-principles calculations combined with rate theories and perform a comparative analysis with the polaron hopping rate constant k hop . The results reveal that at room temperature, k form reaches as high as 10 13 s –1, approximately 2 orders of magnitude faster than the small polaron hopping process. Furthermore, k form is nearly temperature-independent. This significant disparity originates from the combined effects of asymmetric energy barriers, modulation by divergent band structures, and differential dynamic lattice effects. These findings may supply possible optimization strategies to modulate the k form / k hop ratio and establish a rate engineering paradigm for designing high-power FePO 4 -based cathode materials.