Geometric Structure of ${\mathrm{TiO}}_2(011)(2\times 1)$

Surface x-ray diffraction has been employed to elucidate the surface structure of the $(011)-(2\times 1)$ termination of rutile ${\mathrm{TiO}}_2$. The data are inconsistent with previously proposed structures. Instead, an entirely unanticipated geometry emerges from the structure determination, which is terminated by zigzag rows of twofold coordinated oxygen atoms asymmetrically bonded to fivefold titanium atoms. The energetic stability of this structure is demonstrated by ab initio total energy calculations.

Figure 1

Ball and stick models of ${\mathrm{TiO}}_2(011)$. Larger (smaller) spheres are oxygen (titanium) atoms. (a) and (b) illustrate the structures proposed by Beck et al. [8], and Kubo et al. [12], respectively, for the ($2\times 1$) reconstruction. (c) depicts the ($2\times 1$) geometry deduced in this study. (d) shows bulk-terminated ${\mathrm{TiO}}_2(011)(1\times 1)$. The left (right) shaded area indicates the atoms lost from ($1\times 1$) surface during formation of Beck et al.’s (Kubo et al.’s) ($2\times 1$) structure.

Figure 2

Comparison of experimental (dots with error bars) and theoretically simulated [broken (blue) markers and solid (red) line] SSR and CTR data. The broken (blue) markers indicate the best fit (${\chi }^2=2.9$) following refinement of Beck et al.’s structure [8]. The solid (red) line is for the optimum structure proposed in this work (${\chi }^2=0.9$). The $R$-factor known as the unweighted residual [26] has an average value of 17% for the fractional and crystal truncation rods compared with 31% for Beck et al.’s structure [8]. SSR data are displayed in the first two vertical panels and CTR data in the third.

Figure 3

Ball and stick models of ideal bulk terminated ${\mathrm{TiO}}_2(011)(1\times 1)$ (top), and the optimum ${\mathrm{TiO}}_2(011)\mathrm{\text{−}}(2\times 1)$ geometry (bottom). Larger (smaller) spheres are oxygen (titanium) atoms. The numerical labelling of the atoms is employed in Table  for identification purposes. Symmetry paired atoms are denoted by *.