The results of a comprehensive and systematic ab-initio based ground-state search for the structural arrangement of oxygen vacancies in rutile phase TiO 2 provide new insights into their memristive properties. We find that O vacancies tend to form planar arrangements which relax into structures exhibiting metallic behavior. These meta-stable arrangements are structurally akin to, yet distinguishable from the Magnéli phase. They exhibit a more pronounced metallic nature, but are energetically less favorable. Our results confirm a clear structure-property relationship between segregated oxygen vacancy arrangement and metallic behavior in reduced oxides. 1 arXiv:1509.08412v2 [cond-mat.mtrl-sci]

We simulate the thermodynamics and kinetics of the drift/diffusion of oxygen vacancy defects in rutile TiO 2 , using the density-functional based tight-binding (DFTB) method. Both static and dynamic simulations have been performed. Results indicate that DFTB is well suited to examine the dynamic behavior of oxygen vacancies in TiO 2 . Detailed analysis shows, that strong model size dependence in relative diffusion barrier heights between different diffusion processes requires great care in defect diffusion simulations in TiO 2 . Thermodynamic results on the influence of an external electric field show that, due to the large dielectric constant, the coulomb driving force on oxygen vacancy diffusion is very small. Dynamic simulation of the influence of electric fields on the diffusion requires the use of advanced molecular dynamics acceleration schemes.

Vacancy dynamics in oxides are vital for understanding redox reactions and resulting memristive effects or catalytic activity. We present a method to track and drive vacancies which we apply to metadynamics simulation of oxygen vacancies (V 2+ O ) in rutile, demonstrating its effectiveness. Using the density functional based tight binding method, it is possible to explore the free energy hyperplane of oxygen vacancies in TiO2. We show that the migration of V 2+O in TiO2 is governed by the jump with the highest degree of topological interconnection. Free energy profiles are consistent with minimum energy paths. PACS numbers: 61.72.jd, 66.30.Lw, 02.70.Ns Transition metal oxides exhibit a highly complex behavior, with strong coupling between electronic and ionic transport processes, making them highly interesting as electronic materials beyond their traditional use as dielectrics. The most prominent example of such effects is the memristive behavior 1 of TiO 2−x and many other substoichiometric oxides 2 . In titania, the memristive behavior is linked to the formation and dissolution of conducing filaments 1 or layers 3 of room-temperature metallic Ti n O 2n−1 Magnéli phases 4 in the insulating TiO 2 . These phases of titania are modifications of the rutile crystal structure in which oxygen vacancies (V O ) are ordered in slip-planes. In order to understand their formation and dissolution it is essential to understand the dynamics of oxygen vacancies aggregating and dispersing.Yet, the memristive effect is far from being the only interesting physics of metal oxides in which vacancy dynamics play a crucial role. Catalytic effects at oxide surfaces can rely on the presence and ability to replenish surface vacancies 5,6 or O ion transport through the catalyst 5,7 . To be efficient, the latter relies on vacancies and can in fact be mapped to a vacancy transport process in the reverse direction. Oxide based (photo)catalysis is regarded as one of the most promising fields of renewable energy conversion.These examples show that complex physical processes at the surface and in the bulk of reducible metal oxides require intimate understanding of the dynamical behavior of V O defects and the relevant driving forces. Many of these processes are rare events, i.e. their activation energy is larger than the average thermal energy at relevant conditions, which makes them inaccessible to unbiased molecular dynamics simulation. Techniques for rare event simulation8-11 rely on reaction coordinates describing the transition of interest. In most cases, the reaction coordinate is required to be continuous and at least piecewise differentiable with respect to the atomic positions r lat i . Achieving this for a vacancy coordinate r v is difficult, as vacancies are not directly simulated objects but an emergent property. In the strictest sense, the position of a vacancy cannot be continuous, as it is defined as an unoccupied lattice position. Yet, since a vacancy can change its position, albeit indirectly, a generalization of the vacanc...

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