Li and Na Diffusion in TiO₂ from Quantum Chemical Theory versus Electrochemical Experiment

Abstract

Diffusion of Li and Na ions in TiO 2 , anatase, has been studied using theoretical (quantum chemical ab initio periodic Hartree-Fock and a modified semiempirical INDO) as well as electrochemical (chronocoloumetry) methods. On the basis of the theoretical calculations, the geometry of equilibrium and transition states for the impurities as well as the crystalline framework are analyzed and discussed. The calculated activation energies for Li + and Na + diffusion were found to be only slightly higher than 0.5 eV by both theoretical methods. The agreement of either theoretical method with the electrochemical experiments, 0.60 and 0.52 eV for Li + and Na + , respectively, is also remarkably good. Theoretical MethodAb Initio Periodic Hartree-Fock Calculations. The structures of the alkali-doped crystal and the ion diffusion path were investigated by means of the ab initio quantum-chemical program Crystal95. 6 Using this program it is possible to treat not only molecules or clusters but, in particular, crystalline solids at an ab initio level of theory, since the Hartree-Fock one-electron eq are solved subject to periodic boundary conditions. 7 Whereas semiempirical and density-functional methods early on were applied to the solid state, especially in the discipline of solid state physics, ab initio calculations were not applied in a larger scale until the late 1980s and increasingly in the 1990s. Some examples include Al 2O3, 8 Li2O, Na2O and K2O, 9 LiOH‚H2O, 10 the TiO2 rutile 11,12 and anatase 13 phases, C-doped Si, 14 Li-doped NiO, 15 and bulk WO3. 16

GGA+Udescription of lithium intercalation into anataseTiO2

“…The calculated GGA+ U diffusion barriers of ϳ0.6 eV agree with experimental values due to Lunell et al 49 who reported a diffusion barrier of 0.6Ϯ 0.1 eV. The GGA value of 0.511 eV is still compatible with this range, although lies at the limits of the experimental data.…”

“…49,79 The strength of the interaction between the Li + and Ti 3+ is, however, predicted to be much weaker than suggested by previous atomistic simulations, 27,79 which would indicate the dual Li-electron motion is less strongly correlated than predicted previously. Depending on the strength of the Li + -Ti 3+ interaction, and the effect this has on the relative diffusion barriers for a bound Li + -Ti 3+ and a well separated Li + , it may be possible to probe this difference with suitable experiments.…”

“…[37][38][39][40][41][42][43][44][45][46][47] Previous theoretical studies of Li-intercalated TiO 2 have supported the transfer of charge to Ti sites. [48][49][50][51][52][53][54][55][56][57] The distribution of charge and corresponding electronic structure, however, depends strongly on the choice of theoretical method. Stashans et al employed Hartree-Fock to model Li intercalated rutile and anatase TiO 2 , and reported that the electron is transferred to the closest Ti atom to produce Ti 3+ , which gives rise to a defect peak in the band gap.…”

“…Stashans et al employed Hartree-Fock to model Li intercalated rutile and anatase TiO 2 , and reported that the electron is transferred to the closest Ti atom to produce Ti 3+ , which gives rise to a defect peak in the band gap. 48 Lunell et al 49 also used Hartree-Fock to model anatase Li 0.5 TiO 2 , and again reported charge transfer to individual titanium sites, although it should be noted that experimental samples with this stoichiometry adopt the tetragonal lithium titanate structure.…”

Tuning the carbon content on TiO 2 nanosheets for optimized sodium storage

“…Amongst them, anatase TiO2 which was previously investigated as a lithium-ion host material in LIBs due to its low price, high safety, non-toxicity, abundance in the earth's crust, and negligible volume change(<4%) during Li + insertion/extraction [20][21][22][23][24][25][26], has attracted great attention. Yet the reports on TiO2 as Na anode material are quite limited up to date [23,[27][28][29]. Nevertheless the theoretical study by Hagfeldt et al demonstrated the activation barrier for sodium insertion into the TiO2 anatase crystal lattice was supposed to be close to that for lithium which indicates promising candidate role of TiO2 in NIBs considering the large sodium ionic radius [27]. )…”