Ab initiostudy of the migration of small polarons in olivineLixFePO4and their association with lithium ions and vacancies

Abstract

Using first-principles pseudopotential calculations, we investigate the formation and transport of small polarons in olivine ${\mathrm{Li}}_x{\mathrm{FePO}}_4$. It is demonstrated that excess charge carriers form small polarons in ${\mathrm{LiFePO}}_4$ and ${\mathrm{FePO}}_4$. Lower limits to the activation barrier for small polaron migration are calculated within the $\mathrm{GGA}+\mathrm{U}$ framework. Additionally, the interaction between lithium ions and polarons is investigated and estimates of binding energies between lithium ions and polarons are provided. Our results show that the binding energy between electron polarons and ${\mathrm{Li}}^{+}$ ions in ${\mathrm{FePO}}_4$ is lower than that between hole polarons and lithium vacancies in ${\mathrm{LiFePO}}_4$. The electron transfer rate is predicted to be higher in ${\mathrm{FePO}}_4$ than in ${\mathrm{LiFePO}}_4$.