Surface structure and water adsorption on ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(111\right)$: Spin-density functional theory and on-site Coulomb interactions

The surface structure of magnetite ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(111\right)$ in contact with oxygen and water is investigated using spin-density functional theory plus on-site Coulomb interactions. The present results unravel apparent contradictions in the experimental data regarding the equilibrium stoichiometry of the bare surface termination. Both for 298 and $1200\mathrm{K}$, the equilibrium structure is terminated by $\frac{1}{4}$ monolayer (ML) of iron (Fe) on top of a full oxygen layer, consistent with an earlier low-energy electron diffraction analysis. Nonetheless, the calculated negative slope of the surface energies vs oxygen partial pressure shows that a $\frac{1}{2}$ ML Fe termination would become stable under oxygen-poor conditions at high temperatures, in agreement to interpretation of scanning tunneling microscopy experiments. Initial water adsorption is dissociative and saturates when all Fe sites are occupied by OH groups, while the H atoms bind to surface oxygen. Further, water bridges the OH and H groups resulting in a unique type of H-bonded molecular water with its oxygen forming a hydronium-ion-like structure $\mathrm{O}{\mathrm{H}}_3^{+}\text{−}\mathrm{O}\mathrm{H}$. This water structure is different from the water dimeric structures found as yet on oxide and metal surfaces for partially dissociated $\left({\mathrm{H}}_2\mathrm{O}\text{−}\mathrm{O}\mathrm{H}\text{−}\mathrm{H}\right)$ overlayers.

Figure 1

(a) Side and (b) top views of the ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(111\right)\text{−}(1\times 1)$ unit cell. The symmetrically inequivalent oxygen atoms ${\mathrm{O}}_a$ and ${\mathrm{O}}_b$ are indicated in the top view. The side view shows the stacking sequence of planes along the [111] direction for the ${\mathrm{Fe}}_{\mathrm{tet}1}$ termination. The sequence of planes ${\mathrm{Fe}}_{\mathrm{tet}1}\text{−}{\mathrm{O}}_1\text{−}{\mathrm{Fe}}_{\mathrm{oct}1}\text{−}{\mathrm{O}}_2\text{−}{\mathrm{Fe}}_{\mathrm{tet}2}\text{−}{\mathrm{Fe}}_{\mathrm{oct}2}$-comprises the surface region.

Figure 2

Surface energies $\sigma$ vs ${\log }_{10}(p_{{\mathrm{O}}_2}∕p^{\circ })$ at $298.15\mathrm{K}$ (top $x$ axis) and $1200\mathrm{K}$ (bottom $x$ axis) for the $\frac{1}{4}$ ML $\left({\mathrm{Fe}}_{\mathrm{tet}1}\text{−}{\mathrm{O}}_1\text{−}\right)$ and $\frac{1}{2}$ ML $\left({\mathrm{Fe}}_{\mathrm{oct}2}\text{−}{\mathrm{Fe}}_{\mathrm{tet}1}\text{−}\right)$ Fe-terminated and the $\left({\mathrm{O}}_1\text{−}{\mathrm{Fe}}_{{\mathrm{oct}}_1}\text{−}\right)$ oxygen-terminated surfaces.

Figure 3

Top view of the $\frac{1}{4}$ ML dissociated ${\mathrm{H}}_2\mathrm{O}$ overlayer on the ${\mathrm{Fe}}_{\mathrm{tet}1}$ termination. The dark gray and small white spheres represent the oxygen and hydrogen atoms of the dissociation products $(\mathrm{H}+\mathrm{O}\mathrm{H})$, respectively. Light gray and black spheres represent the surface oxygen (O) and iron (Fe) atoms, respectively.

Figure 4

Side and top views of the $\frac{1}{2}$ ML half-dissociated $\left({\mathrm{H}}_2\mathrm{O}\text{−}\mathrm{O}\mathrm{H}\text{−}\mathrm{H}\right)$ overlayer on the ${\mathrm{Fe}}_{\mathrm{tet}1}$ termination. The dark gray and small white spheres represent the oxygen atoms of the partially dissociated overlayer and corresponding hydrogens. Light gray and black spheres represent the surface oxygens (O) and iron (Fe) atoms, respectively. Hydrogen bonds formed by ${\mathrm{H}}_2\mathrm{O}$ molecules bridging between the surface hydroxyls (OH) and surface hydrogens (H) are shown. Dashed lines indicate the ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(111\right)\text{−}(1\times 1)$ surface unit cells.

Figure 5

Surface energy change $\Delta {\sigma }_W$ with ${\mathrm{H}}_2\mathrm{O}$ adsorption and corresponding adsorption energy change $\Delta E$ (dashed line) vs $T$ for $\frac{1}{4}$ ML dissociated (OH-H) and for $\frac{1}{2}$ ML half-dissociated $\left({\mathrm{H}}_2\mathrm{O}\text{−}\mathrm{O}\mathrm{H}\text{−}\mathrm{H}\right)$ overlayers on the ${\mathrm{Fe}}_{\mathrm{tet}1}$ termination at $p_{{\mathrm{H}}_2\mathrm{O}}={10}^{-8}\mathrm{mbar}$.