First principles study of small hole polaron formation in doped olivine LiFe_1−xCo_xPO₄: Effects of Li deficiency

Small hole polarons, charge carriers for electronic conductivity, play crucial roles in the performance of olivine LiMPO₄ (M = Fe, Co, Mn, Ni) batteries, yet their formation mechanism and effects have not been completely explored. This work is aimed to apply density functional theory with additional on-site Hubbard corrections (DFT+U) to investigate the formation mechanism and the effects of small hole polarons in olivine LiFe_1−xCo_xPO₄. It is found that small hole polarons always localize first at the Fe sites and then at the Co sites only when the Fe sites are fully occupied. The results show that much less bond-length distortion of CoO₆ than that of FeO₆ is required to form a small hole polaron; hence, Co doping helps to create small hole polarons and to stabilize the structures, as indicated by lower formation energy. Moreover, Co doping enhances the electronic conductivity of LiFePO₄ because of Co donor states and also increases the intercalation voltage due to the difference of 3d electron configurations between the Fe²⁺/Fe³⁺ states and the Co²⁺/Co³⁺ states.