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

${\mathrm{TiO}}_2$ 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.

Figure 1

Side view of the anatase (101) surface supercell of 72 atoms (a) and 216 atoms (b). Oxygen vacancy positions are labeled for easy references. The larger 216-atom slab is used to compute bulk vacancy formation energy as well, which is denoted as $V_{\mathrm{O}6}^0$ for neutral vacancy and $V_{\mathrm{O}6}^{+2}$ for +2 charged vacancy. Vacancies are presented as yellow dots, oxygen red, and titanium blue.

Figure 2

Potential-energy profile along $V_{\mathrm{O}5}^{+2}/V_{\mathrm{O}5}^0\to V_{\mathrm{O}1}^{+2}/V_{\mathrm{O}1}^0$ computed at GGA-PBE level of theory with coupled ARTn/QE on 216-atom slab. Upper panel shows diffusion pathway with selected atomic configurations. Both +2 charged and neutral vacancy pathways are similar and only one is illustrated here. Diffusion begins with a single bond dissociation of ${\mathrm{O}}_{3\mathrm{c}}$ atom, creating an undercoordinated surface Ti ion (${\mathrm{Ti}}_{4\mathrm{c}}$). Displacement of ${\mathrm{Ti}}_{4\mathrm{c}}$ ion vertically opens up the passage to downward migration of the surface-bridging oxygen. This oxygen eventually forms sub-bridging oxygen immediately below the topmost surface vacancy. The vacancy migrates through an intermediate unstable state $V_{\mathrm{O}4}$; hence, a characteristic two-step diffusion mechanism is observed. Potential-energy profile of the +2 charged vacancy is on the left, and that for neutral vacancy on the right. Two oxygen atoms that undergo large displacement are black, Ti light blue, the oxygen red, and oxygen vacancy yellow.

Figure 3

Potential-energy profile along $V_{\mathrm{O}6}^{+2}/V_{\mathrm{O}6}^0\to V_{\mathrm{O}5}^{+2}/V_{\mathrm{O}5}^0$ computed at GGA-PBE level of theory with coupled ARTn/QE on 216-atom slab. Upper panel shows diffusion pathway with selected atomic configurations. Both +2 charged and neutral vacancy pathways are similar and only one is illustrated here. Surrounding atoms are removed for better visualization of the diffusion pathway. Diffusion begins with a single bond dissociation of ${\mathrm{O}}_{3\mathrm{c}}$ atoms indicated in black color. These oxygen atoms significantly displaced during the vacancy migration. The vacancy migrates through an intermediate unstable state; hence, characteristic two-step diffusion mechanism is observed. Potential-energy profile of the +2 charged vacancy is on the left, and that for neutral vacancy on the right. The two oxygen atoms that undergo large displacement are black, Ti light blue, the oxygen red, and oxygen vacancy yellow.