Diffusion of oxygen vacancies formed at the anatase (101) surface: An activation-relaxation technique study

Abstract

${\mathrm{TiO}}_{2}$ is a technologically important material. In particular, its anatase polymorph plays a major role in photocatalysis, which can also accommodate charged and neutral vacancies. There is, however, scant theoretical work on the vacancy charge and associated diffusion from surface to subsurface and bulk in the literature. Here, we aim to understand +2 charge and neutral vacancy diffusion on anatase (101) surface using 72- and 216-atom surface slabs employing a semilocal density functional and the Hubbard model. The activation-relaxation technique nouveau coupled with quantum espresso is used to investigate the activated mechanisms responsible for the diffusion of oxygen vacancies. The small-slab model overstabilizes the +2 charged topmost surface vacancy, which is attributed to the strong Coulomb repulsion between vacancy and neighboring ${\mathrm{Ti}}^{+4}$ ions. The larger slab allows atoms to relax parallel to the surface, decreasing the +2 charged topmost surface vacancy stability. The calculated surface-to-subsurface barriers for the +2 charged vacancy and diffusion of the neutral vacancy on a slab of 216 atoms are 0.82 and 0.52 eV, respectively. Furthermore, the bulk vacancy prefers to migrate toward the subsurface with relatively low activation barriers 0.19 and 0.27 eV and the reverse process has to overcome 0.38- and 0.40-eV barriers for the +2 charged and the neutral vacancies. This explains the experimentally observed high concentration of vacancies at the subsurface sites rather than in the bulk, and the dynamic diffusion of vacancies from the bulk to the subsurface and from the subsurface to the bulk is highly likely on the surface of anatase (101). Finally, we provide a plausible explanation for the origin of recently observed subsurface-to-surface diffusion of oxygen vacancy from the calculated results.