Formation and diffusion of vacancy-polaron complex in olivine-type LiMnPO4and LiFePO4

Abstract

Formation and diffusion of a vacancy-polaron complex in olivine-type cathode-active materials, namely, LiMPO${}_{4}$ (M $=$ Fe, Mn), were theoretically investigated by using the first-principles density functional theory within a framework of GGA $+$ $U$ method. It is shown that a lithium vacancy and a corresponding hole-polaron form the complex at the fully lithiated limit owing to lattice distortion and Coulomb interaction between them. It is also shown that the formation energy of the complex in LiMnPO${}_{4}$ is 0.19 eV higher than that in LiFePO${}_{4}$, since a hole polaron in LiMnPO${}_{4}$ is not sufficiently relaxed. As a result, the nucleation rate of MnPO${}_{4}$ phase in LiMnPO${}_{4}$ is 10${}^{\ensuremath{-}3}$ times slower than that in LiFePO${}_{4}$ and represents the main difference between the kinetics in the initial stage of charging of the two olivine materials. It was also found that the activation energy of the complex diffusion is limited by vacancy hopping in LiMnPO${}_{4}$, while it is determined by both vacancy hopping and polaron hopping in LiFePO${}_{4}$. The activation energy in LiMnPO${}_{4}$, 0.38 eV, is comparable with that in LiFePO${}_{4}$, 0.42 eV. The calculated potential energy profile, showed that the minimum energy path of the diffusing lithium in LiMnPO${}_{4}$ has the same winding shape as that in LiFePO${}_{4}$.