Geometric structure of anatase $\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$

Surface x-ray diffraction has been used to determine the quantitative structure of the (101) termination of anatase $\mathrm{Ti}{\mathrm{O}}_2$. The atomic displacements from the bulk-terminated structure are significantly different from those previously calculated with density functional theory (DFT) methods with discrepancies for the Ti displacements in the $\left[10\overline{1}\right]$ direction of up to $0.3\AA$. DFT calculations carried out as part of the current paper provide a much better agreement through improved accuracy and thicker slab models.

Figure 1

Ball and stick representation of the UHV-prepared a-$\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$ surface. Substrate oxygen and titanium atoms are colored blue and red, respectively. The numerical labeling of the atoms/layers is employed in Tables 1, 2, 3 and 5 for identification purposes. Vertical and horizontal arrows represent the direction of atomic displacements of the best-fit solution derived from SXRD in the [101] and $\left[10\overline{1}\right]$ directions, respectively. The length of the arrows is proportional to the relative magnitude. Also shown are the changes in interlayer distances $d_{1–6}$ from their bulk positions.

Figure 2

Normal emission Al $K\alpha$ XPS spectrum of the UHV-prepared anatase-$\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$ surface prior to the SXRD measurement.

Figure 3

STM image ($23.6\times 23.6{\mathrm{nm}}^2$, constant current mode, $V_{\mathrm{sample}}=+1.2\mathrm{V}, I_{\mathrm{tunnel}}=200$ pA) of the UHV-prepared anatase-${\mathrm{TiO}}_2$(101) surface. The white line highlights the apparent phase difference of the rows in the $\left[0\overline{1}0\right]$ direction across a step edge. The line scan evidences 3.5 $\AA$ steps between terraces.

Figure 4

STM image ($30\times 9.4\mathrm{n}{\mathrm{m}}^2, V_{\mathrm{sample}}=+1.2\mathrm{V}, I_{\mathrm{tunnel}}=100\mathrm{pA}$) of the UHV-prepared anatase-$\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$ surface after exposure to a residual vacuum of $\sim 4\times {10}^{-8}\mathrm{mbar}$ for 2 h. The white arrows indicate the presence of hydroxyls on the surface.

Figure 5

(Left) Reference rocking curve intensities (crosses) and fit (dashed lines) recorded throughout the SXRD measurement. (Right) The corresponding rocking curve fit peak height variation with the time of the CTRs from the a-$\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$ surface.

Figure 6

Experimental (error bars) and best-fit calculated CTRs of the UHV-prepared anatase-$\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$ surface using the bulk-terminated (green squares), $\beta$-roughness (blue circles), and terraced-roughness models (red line).

Figure 7

A comparison of anti-Bragg regions for three selected experimental (error bars) and best-fit calculated CTRs from the clean UHV-prepared anatase-$\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$ surface using the bulk terminated (green squares), $\beta$-roughness (blue circles), and terraced-roughness models (red line).

Figure 8

Illustration of the terraced-roughness approximation used for structure determination of the UHV-prepared a-$\mathrm{Ti}{\mathrm{O}}_2\left(101\right)$ surface.