Composition, structure, and stability of the rutile ${\text{TiO}}_2\left(110\right)$ surface: Oxygen depletion, hydroxylation, hydrogen migration, and water adsorption

A comprehensive phase diagram of lowest-energy structures and compositions of the rutile ${\text{TiO}}_2\left(110\right)$ surface in equilibrium with a surrounding gas phase at finite temperatures and pressures has been determined using density-functional theory in combination with a thermodynamic formalism. The exchange of oxygen, hydrogen, and water molecules with the gas phase is considered. Particular attention is given to the convergence of all calculations with respect to lateral system size and slab thickness. In addition, the reliability of semilocal density functionals in describing the energetics of the reduced surfaces is critically evaluated. For ambient conditions the surface is found to be fully covered by molecularly adsorbed water. At low coverages, in the limit of single isolated water molecules, molecular and dissociative adsorption modes become energetically degenerate. Oxygen vacancies form in strongly reducing, oxygen-poor environments. However, already at slightly more moderate conditions it is shown that removing full ${\text{TiO}}_2$ units from the surface is thermodynamically preferred. In agreement with recent experimental observations it is furthermore confirmed that even under extremely hydrogen-rich environments the surface cannot be fully hydroxylated, but only a maximum coverage with hydrogen of about 0.6–0.7 monolayer can be reached. Finally, calculations of migration paths strongly suggest that hydrogen prefers diffusing into the bulk over desorbing from the surface into the gas phase.

Figure 1

(Color online) Atomic structure of the stoichiometric rutile ${\text{TiO}}_2\left(110\right)$ surface. Oxygen atoms are shown in red; Ti atoms are shown in gray. The two- and threefold-coordinated O sites and the fivefold-coordinated Ti sites are labeled as O(2), O(3), and Ti(5), respectively.

Figure 2

(Color online) Convergence of the unrelaxed (upper panel) and relaxed (lower panel) ${\text{TiO}}_2\left(110\right)$ surface energies with slab thickness; note the different energy scales. The solid black line in the lower panel represents the result from fully relaxed slabs. The calculation with the atoms in the bottom two trilayers fixed at the bulk positions is shown by the red dashed line.

Figure 3

(Color online) Convergence of the hydrogen adsorption energy $E_{\text{ad}}^{\text{H}}$ with slab thickness at full monolayer coverage. The atoms in the bottom two trilayers were fixed at the bulk positions. The solid black and the dashed red lines distinguish calculations without and with saturation of the broken surface bonds at the bottom of the slabs with pseudohydrogen atoms with nucleus charges of $+4/3$ and $+2/3$, respectively.

Figure 4

(Color online) Local densities of states (LDOS) of Ti and O atoms in bulk ${\text{TiO}}_2$ (black solid lines), of the fivefold- and twofold-coordinated Ti(5) and O(2) surface atoms at the bottom of a four-trilayer ${\text{TiO}}_2\left(110\right)$ slab (top two layers relaxed, bottom two layers fixed at bulk positions; red dashed lines), and after saturation of the bottom Ti(5) and O(2) surface atoms with pseudohydrogen atoms (see text; blue dashed-dotted lines). The top of the valence band is at 0 eV.

Figure 5

(Color online) Defect formation energy $E_v$ for O vacancies at the ${\text{TiO}}_2\left(110\right)$ surface as function of the oxygen chemical potential $\Delta {\mu }_{\text{O}}$. In the top $x$ axis, the chemical potential has been translated into a partial pressure scale $p_{{\text{O}}_2}$ of molecular oxygen at 800 and 1200 K.

Figure 6

(Color online) Schematic illustration of some configurations of the ${\text{TiO}}_2\left(110\right)$ surface with adsorbed H atoms. (a) Configurations with two adsorbed H atoms. Ti, O, and H atoms are depicted as small gray, large red, and small white spheres, respectively. (b) Configurations with higher H coverage. The arrows indicate the tilt of the OH groups after H adsorption. The corresponding adsorption energies $E_{\text{ad}}^{\text{H}}$ are given in Table .

Figure 7

Hydrogen adsorption energy $E_{\text{ad}}^{\text{H}}$ as function of the hydrogen coverage of the surface.

Figure 8

(Color online) Surface Gibbs free energy $\Delta \gamma$ of ${\text{TiO}}_2\left(110\right)$ surfaces with different hydrogen coverages as function of the hydrogen chemical potential $\Delta {\mu }_{\text{H}}$. In the top $x$ axis, the chemical potential has been translated into a partial pressure scale $p_{{\text{H}}_2}$ of molecular hydrogen at 400 K. Thermodynamically unstable surface structures are represented by dashed lines.

Figure 9

(Color online) Schematic illustration of water pairs adsorbed on the ${\text{TiO}}_2\left(110\right)$ surface. Ti, O, and H atoms are depicted as small gray, large red, and small white spheres, respectively. The labels are defined in Table .

Figure 10

(Color online) Convergence of the molecular and dissociative water adsorption energies, $E_{\text{ad}}^{\text{w}}$, and the difference $\Delta E_{\text{ad}}=E_{\text{ad}}^{\text{mol}}-E_{\text{ad}}^{\text{diss}}$ with slab thickness at full monolayer coverage (left) and for single water molecules in a $\left(4\times 2\right)$ surface unit cell (right). The solid black lines represent results from full relaxations with water adsorbed symmetrically on both sides of the slab. The calculations in which water was adsorbed only on one side of the slab with the bottom two trilayers fixed at the bulk positions and the broken surface bonds at the bottom of the slab saturated with pseudohydrogen atoms are shown by the red dashed lines.

Figure 11

Phase diagram for the ${\text{TiO}}_2\left(110\right)$ surface in thermodynamic equilibrium with ${\text{H}}_2$ and ${\text{O}}_2$ particle reservoirs controlling the chemical potentials $\Delta {\mu }_{\text{H}}$ and $\Delta {\mu }_{\text{O}}$.