Thermodynamics and Kinetics of Na-Ion Insertion into Hollandite-TiO₂ and O3-Layered NaTiO₂: An Unexpected Link between Two Promising Anode Materials for Na-Ion Batteries

First principle DFT calculations are used to study the thermodynamic and kinetic properties of Na-ion insertion in TiO 2 hollandite, a potential anode for Na-ion batteries. The experimentally observed phase transformation from tetragonal TiO 2 ( I 4/ m ) to monoclinic Na 0.25 TiO 2 ( I 2/ m ) is confirmed. At high Na-ion concentrations the calculated formation energies predict a first-order phase transition toward the layered O′3-Na 0.68 TiO 2 structure. Further sodiation initiates a solid solution reaction toward the layered O3-NaTiO 2 phase, which was recently brought forward as a promising anode for Na-ion batteries. This transformation irreversibly transforms the one-dimensional hollandite tunnel structure into the layered structure and potentially brings forward an alternative route toward the preparation of the hard to prepare O3-NaTiO 2 material. Energy barrier calculations reveal fast Na-ion diffusion at low concentrations and sluggish diffusion upon reaching the N 0.25 TiO 2 phase, rationalizing why experimentally the Na 0.5 TiO 2 phase is not achieved. Detailed analysis of the kinetic behavior in the hollandite structure via molecular dynamics simulations reveals the importance of correlated atomic motions and dynamic lattice deformations for the Na-ion diffusion. In addition, exceptional Na-ion kinetics were predicted for the layered O′3-Na 0.75 TiO 2 phase through a dominating divacancy hopping mechanism.