Tuning the Area Percentage of Reactive Surface of ${\mathrm{TiO}}_2$ by Strain Engineering

Surfaces with high reactivity usually have a low area percentage, which greatly limits the efficiency of surface reactivity. In this Letter we demonstrate a generic way of increasing the percentage of the highly reactive surface by using external strain. Bulk and surface elastic properties of ${\mathrm{TiO}}_2$ are studied via density functional theory calculations. The equilibrium shape of anatase ${\mathrm{TiO}}_2$ under applied strain is discussed based on the elastic properties. We find that when 5% compressive strain is applied biaxially along [100] and [010]; directions, the area percentage of the anatase (001) surface can be increased by $\sim 5$ times in comparison with the case when no strain is applied. Since the moderate strain does not introduce extrinsic defects into the material, we propose that it is an ideal way to increase the reactivity of titanium dioxide crystallites by applying biaxial compressive external strain along the $a$ axis.

Figure 1

Top views of the unrelaxed structures of the rutile and anatase surfaces. Gray and red (dark gray) spheres indicate the titanium and oxygen atoms. The size of the spheres stands for the distance of the atoms from the surfaces schematically. The length scale between different surfaces is not kept.

Figure 2

Variation of the surface energy of the anatase (101) (a)–(c), (100) (d)–(f), (001) (g)–(i), and (110) (j)–(l) surface with the applied uniaxial (first two columns) and biaxial strain (last column). Dots are calculated results and dashed curves are the three order polynomial fits. Subscripts 11 and 22 denote $x$ and $y$ directions of each surface as displayed in Fig. 1.

Figure 3

(a) The area percentage of anatase (001) facets with variation of the applied strain. External strain is applied uniaxially along the surface bonds in (001) (up triangles), across the bonds (down triangles), biaxially along [100] and [010] (circles), or along the $c$ axis (squares). The dashed curve shows the average of the area percentage when strain is applied along and across the surface bonds of (001) surface separately. The inset displays the equilibrium shape of the anatase crystallite, where the lines along [100] direction of (001) surfaces shows the surface bonds schematically. (b)–(d) The surface energy ratio ${\gamma }_{(001)}/{\gamma }_{(101)}$ and the ratio of $1/\cos \theta$ with the variation of the applied strain. The anatase (001) surface appears only when the surface energy ratio is smaller than $1/\cos \theta$.

Figure 4

Comparison of the surface energy normalized to ${\gamma }_{(101)}$ (solid curves) and the critical condition (dotted curves) of presentation of the two low-index surfaces (100) (a) and (110) (b). The surface appears only when the corresponding solid curve goes below the dotted curve.