Kinetics of Anatase Electrodes: The Role of Ordering, Anisotropy, and Shape Memory Effects

We perform a comprehensive first-principles statistical mechanical study of the thermodynamic and kinetic properties of lithiated anatase Li_<i>x</i>TiO₂. We establish that the experimentally observed step in the voltage vs lithium composition curve between <i>x</i> = 0.5 and 0.6 is due to Li ordering. Furthermore, we predict that full lithiation of anatase TiO₂ is thermodynamically possible at positive voltages but that there is an enormous difference in Li diffusion coefficients in the dilute and fully lithiated forms of TiO₂, providing an explanation for the limited capacity in large electrode particles. We also predict that Li diffusion in the ordered phase (Li_0.5TiO₂) is strictly one-dimensional. The TiO₂ to Li_0.5TiO₂ phase transition has much in common with shape memory alloys. Crystallographically, it can support strain invariant interfaces separating TiO₂ and Li_0.5TiO₂ within the same particle. The strain invariant interfaces are parallel to the one-dimensional diffusion direction in Li_0.5TiO₂, which, we argue, has important consequences for the role of particle shape on achievable capacity, charge and discharge rates, and hysteresis