We perform a comprehensive first-principles statistical mechanical study of the thermodynamic and kinetic properties of lithiated anatase LixTiO2. We establish that the experimentally observed step in the voltage vs lithium composition curve between x = 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 (Li0.5TiO2) is strictly one-dimensional. The TiO2 to Li0.5TiO2 phase transition has much in common with shape memory alloys. Crystallographically, it can support strain invariant interfaces separating TiO2 and Li0.5TiO2 within the same particle. The strain invariant interfaces are parallel to the one-dimensional diffusion direction in Li0.5TiO2, which, we argue, has important consequences for the role of particle shape on achievable capacity, charge and discharge rates, and hysteresis.
