IntroductionLithium-ion batteries (LIBs) are widely used in electric vehicles and electronic devices due to their high energy density and long cycle life. The migration rate of lithium ions in cathode materials significantly affects the rate performance of LIBs. Previous studies showed that there were certain differences in the migration energy of lithium ions in LiCoO₂ materials at different concentrations of lithium vacancies, which could be due to the different interlayer distances caused by different concentrations of lithium vacancies. The construction of individual lithium vacancies in different supercells can lead to different concentrations of lithium vacancies, which in turn affects the parameters of the unit cell. In addition, the synergistic migration effect between lithium ions also lead to a decrease in the energy barrier for lithium-ion migration. This paper was to use first-principles calculations to investigate the effects of lithium vacancy concentration and synergistic migration on the lithium-ion migration energy in layered materials (i.e., LiCoO₂, LiNiO₂) and spinel material (i.e., LiMn₂O₄).MethodFirst principles calculations in this work were conducted using the DS-PAW package, which is based on the density functional theory (DFT) framework and the projector augmented wave (PAW) approach. The basis set is in the form of plane waves, and the cutoff energy is set to be 500 eV. The Monkhorst-Pack scheme was used to integrate the Brillouin zone. The calculations for the models of the Li_1−xCoO₂ and Li_1−xNiO₂ in supercells of 2×2×1, 3×3×1, and 4×4×1 were performed using the k-point meshes of 5×5×2, 3×3×2, and 2×2×2, respectively. The calculations for the models of the Li_xMn₂O₄ and Li_xTi₂O₄ in supercells of 1×1×1, 2×2×1, and 3×3×1 were performed using the k-point meshes of 3×3×3, 2×2×3, and 1×1×3, respectively. The exchange-correlation interactions were treated with Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) formalism. The strong correlation effects of the 3d electrons were considered by using the GGA+U method, with effective U value (U_eff) of 4.91, 5.00, and 3.50 eV for Co, Ni, and Mn, respectively. All atomic positions and cell parameters were relaxed using the conjugate gradient method until the maximum force on each atom was less than 0.03 eV/Å. The energy convergence criterion for the self-consistent field (SCF) loop was set to 10^–5 eV. The activation barriers for Li-ion migration were determined through the climbing image nudged elastic band (CI-NEB) method, and the convergence criterion for the forces on the transition state images was set to 0.1 eV/Å.Results and discussionThe results show that in LiCoO₂ material, the lithium-ion migration energy for the 2×2×1 supercell is significantly smaller than that of other supercells by using the CI-NEB method to calculate the lithium-ion migration energy barrier. This is because the 2×2×1 supercell of LiCoO₂ has a higher concentration of lithium vacancies, which can increase the interlayer distance and decrease in the lithium-ion migration energy. In addition, there are still some differences in the energy for lithium ion migration when different supercells of LiCoO₂ have the same interlayer distance. The synergistic migration effect of lithium ions can lead to a decrease in the energy for lithium ion migration when there are more lithium ion migration pathways in the LiCoO₂ supercell when LiCoO₂ is expanded to the same size. Also, the same pattern in LiNiO₂ material occurs.The results show that the higher the concentration of lithium vacancies in spinel materials is, the smaller the energy for lithium ion migration will be, after applying the same treatment to spinel materials LiMn₂O₄ and LiTi₂O₄. Unlike layered materials, however, the synergistic migration effect of lithium ions in spinel materials does not have a significant impact on the energy for lithium ion migration. This is because the interaction between transition metals and lithium ions has a certain hindering effect on lithium ion migration when lithium ions migrate in spinel materials.ConclusionsThe calculation results indicated that in layered materials like LiCoO₂ and LiNiO₂, the lower the concentration of lithium vacancies was, the smaller the interlayer distance would be, thus increasing the activation barrier for lithium-ion migration. The migration energy barriers for lithium ions within the 3×3×1 and 4×4×1 supercells of LiCoO₂ were similar, indicating that the energy barriers derived from these supercells could be considered as a representative of the migration energy barriers in the stoichiometric ratio of LiCoO₂. The synergistic migration effect of lithium ions in layered materials reduced migration energy, while the synergistic migration effect of lithium ions in spinel materials was not significant.