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

Abstract

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.