First-principles study of Li ion diffusion inLiFePO4

The diffusion mechanism of Li ions in the olivine ${\mathrm{LiFePO}}_{4}$ is investigated from first-principles calculations. The energy barriers for possible spatial hopping pathways are calculated with the adiabatic trajectory method. The calculations show that the energy barriers running along the $c$ axis are about 0.6, 1.2, and 1.5 eV for ${\mathrm{LiFePO}}_{4},$ ${\mathrm{FePO}}_{4},$ and ${\mathrm{Li}}_{0.5}{\mathrm{FePO}}_{4},$ respectively. However, the other migration pathways have much higher energy barriers resulting in very low probability of Li-ion migration. This means that the diffusion in ${\mathrm{LiFePO}}_{4}$ is one dimensional. The one-dimensional diffusion behavior has also been shown with full ab initio molecular dynamics simulation, through which the diffusion behavior is directly observed.