Modeling of Structural Properties of Zr(Nb)-Doped c-LTO–Zr(Nb) Materials With Spinel Structure for Li-Ion Batteries

Using the density functional theory (DFT), we investigated the electronic, magnetic and energy properties of Li4Ti5-xMxO12 (M = Zr, Nb; x = 0–0.01) (or c-LTO–Zr (Nb)) supercells, which are isostructural to the high-temperature spinel (cubic; sp.gr. 𝐹𝑑3̅𝑚) modification of the Li4Ti5O12-based anode material (c-LTO) for lithium-ion batteries (LIB). In DFT calculations with a generalized gradient approximation (functional GGA), spin-orbit coupling (SOC) and the Hubbard correction were considered (DFT SGGA+ 𝑈). For the Ti 3d and Zr(Nb) 4d states, pd and dd-model values of the U effective interaction energies were used. To account for the effective Coulomb intra-atomic interaction (U) between particles, the DFT SGGA+U calculations were performed using 𝑈eff = 4 eV, O 2p, Ti 3d, Zr (Nb) 4d. The band structure and density of states (DOS) of c-LTO supercells calculated by DFT SGGA+𝑈 are consistent with both theoretical and experimental data for c-LTO. The theoretical band gap (𝐸g ) is smaller than the experimental value of c-LTO. Taking into account the chemical potentials of the doping impurities, the formation energy of c-LTO–Zr(Nb) was calculated. The decrease in the total energy due to the change in the partial densities of states (PDOS) of the filled spin-up and spin-down subbands indicates that c-LTO–Zr(Nb) is thermodynamically stable. The density of spin-up d-states exceeds the density of spin-down d-states in c-LTO–Zr(Nb), so the 𝐸g values in these structures differ from each other. Doping with Zr(Nb) narrows 𝐸g and improves the electrical conductivity of c-LTO–Zr(Nb) due to the contribution of Zr4+ 4d and Nb3+ 4d orbitals to the particle transport. The Fermi level of the band structure of c-LTO–Zr(Nb) supercells shifts to the conduction band as a result of Zr(Nb) doping. The local magnetic moments of Zr(Nb) impurity atoms in c-LTO–Zr(Nb) are calculated.