A systematic study on carrier transport processes in charging olivine phosphates LiMPO₄ (M = Fe and Mn) by hybrid DFT...

Charging lithiated olivine phosphates can be driven by the transport of a hole polaron (h⁺), a lithium ion vacancy (V-Li), and a h⁺-V-Li pair. While the individual process has been investigated by density functional calculations, systematic study on these processes, including an assessment of the effects of using a particular functional, has been scarce. This study compares the activation energies for these processes in LFP and LMP calculated at the same level of hybrid density functional theory. Not only the h⁺ and V-Li hopping energies but also the h⁺-V-Li binding energies were evaluated. The effect of modifying the fraction of Hartree-Fock exchange (HFX) on these energies was also investigated. The calculated h⁺ hopping energy in LMP increases significantly as the HFX fraction is increased. The sum of the increased h⁺ hopping energy and the h⁺-V-Li binding energy reproduces an experimental activation energy derived from the electronic conductivity of LMP. The activation energy for h⁺-V-Li transport is lower than those for the h⁺ and V-Li transport processes in LFP. In contrast, the activation energy for the h⁺-V-Li transport is comparable to that for the V-Li transport in LMP when using the modified hybrid functional.