Medium-energy ion-scattering study of the structure of clean ${\mathrm{TiO}}_2\left(110\right)\text{−}(1\times 1)$

$100\mathrm{keV}$ ${\mathrm{H}}^{+}$ medium-energy ion scattering has been applied to investigate the surface relaxations of the clean rutile ${\mathrm{TiO}}_2\left(110\right)\text{−}(1\times 1)$ surface structure. A set of blocking curves in four different incident directions show clear differences between the surface and bulk attributable to surface relaxation. Optimized values of the surface relaxation parameters to give the best fit to the surface structure are generally in quite good agreement with a recent experimental determination of this structure using quantitative low-energy electron diffraction. In particular, both solutions favor an outward relaxation of the bridging O atoms on the surface rather than the strong inward displacement favored by the only previous experimental structure determination based on surface x-ray diffraction.

Figure 1

(Color online) Perspective view of the rutile ${\mathrm{TiO}}_2$ bulk structure with a (110) surface exposed on the top and the atoms in the outermost three layers numbered following the convention of Diebold (Ref. 3). The surface displacements of these atoms relative to the ideally terminated bulk structure are given in the tables. Note that, following the usual chemical convention for oxides, the O atoms are shown as the larger spheres in this model.

Figure 2

(Color online) Scattered ion energy spectrum in the energy range of the Ti scattering peak for $100\mathrm{keV}$ incident ${\mathrm{H}}^{+}$ and ${\mathrm{He}}^{+}$ ions as a function of total incident ion does on a single point on the ${\mathrm{TiO}}_2\left(110\right)$ surface. Measurements are made with $\left[0\overline{1}0\right]$ incidence and [100] detection directions.

Figure 3

(Color online) Scattered ion blocking curves from surface Ti atoms recorded for successively higher doses of $100\mathrm{keV}$ ${\mathrm{H}}^{+}$ incident ions along $\left[0\overline{1}0\right]$ onto the same region of the ${\mathrm{TiO}}_2\left(110\right)$ surface. The deep Ti blocking dip at $90°$ scattering angle corresponds to emission along [100], the weaker dip around $77°$ is due to blocking by surface O atoms (see Fig. 4).

Figure 4

(Color online) Sectional views through the ${\mathrm{TiO}}_2\left(110\right)$ surface in the two principal azimuthal planes for an ideally terminated bulk structure, showing the incident ion directions used in the MEIS experiments and a few of the blocking directions. In these diagrams, the Ti atoms are shown as the larger spheres as a reminder that in MEIS the Ti scattering factors are (much) larger than those of the O atoms. However, the coloring and/or shading of the Ti and O atoms is the same as in Fig. 1.

Figure 5

(Color online) Comparison of bulk and surface blocking curves (as described in the text) recorded in the $\left[0\overline{1}0\right]$ and $\left[1\overline{3}0\right]$ incidence directions from the clean ${\mathrm{TiO}}_2\left(110\right)\text{−}(1\times 1)$ surface. The bulk blocking curves are recorded at $80\mathrm{keV}$ scattered ion energy.

Figure 6

(Color online) Comparison of the complete set of surface blocking curves, recorded in the $\left[\overline{11}1\right]$, $\left[\overline{11}2\right]$, $\left[0\overline{1}0\right]$, and $\left[1\overline{3}0\right]$ incidence directions from the clean ${\mathrm{TiO}}_2\left(110\right)\text{−}(1\times 1)$ surface using incident $100\mathrm{keV}$ ${\mathrm{H}}^{+}$ ions, with the results of simulations based on three different sets of surface relaxation parameter values obtained from the SXRD experiment (Ref. 4) and the LCAO and FP-LAPW theoretical calculations (Ref. 5) (see Table ).

Figure 7

(Color online) Comparison of the complete set of surface blocking curves, recorded in the $\left[\overline{11}1\right]$, $\left[\overline{11}2\right]$, $\left[0\overline{1}0\right]$, and $\left[1\overline{3}0\right]$ incidence directions from the clean ${\mathrm{TiO}}_2\left(110\right)\text{−}(1\times 1)$ surface using incident $100\mathrm{keV}$ ${\mathrm{H}}^{+}$ ions, with the results of simulations based on the experimental LEED investigation (Ref. 6) (see Table ).

Figure 8

(Color online) Comparison of the complete set of surface blocking curves, recorded in the $\left[\overline{11}1\right]$, $\left[\overline{11}2\right]$, $\left[0\overline{1}0\right]$, and $\left[1\overline{3}0\right]$ incidence directions from the clean ${\mathrm{TiO}}_2\left(110\right)\text{−}(1\times 1)$ surface using incident $100\mathrm{keV}$ ${\mathrm{H}}^{+}$ ions, with the results of simulations based on the structure giving the best fit to the current MEIS experiments (see Table ).