**2.1 Unreconstructed anatase surfaces**

The atomic structures of the perfect anatase terminations with different crystal planes are presented in **Figure 1**. Starting from the top-left side, the (0 0 1) surface is

### **Figure 1.**

*Perfect, bulk-cut atomic geometries of different anatase surfaces in their isomeric (ball-and-stick models) and top (space-filling models) views. Ti atoms are large, gray spheres and O atoms are small red ones. In the top view, the undercoordinated atoms are marked with dots. The bulk crystal unit cell and the unit cell vectors are presented to help navigate between different structures. Visualizations were performed with the VESTA program.*

flat, exposing all of the Ti atoms as 5-fold coordinated sites (5f-Ti) and ½ of the O as 2-fold coordinated ones (2f-O). The high density of the undercoordinated species leads to a high surface energy of about 0.90–1.08 J<sup>m</sup><sup>2</sup> . Noticeable relaxation of the atomic structure, compared to the bulk (0 0 1) crystal plane, includes breaking of the bond symmetry between 5f-Ti and two neighboring 2f-O, resulting in one Ti-O bond being visibly longer than the other. For the (1 0 0) surface, exposed atoms consist of both undercoordinated 5f-Ti and 2f-O, as well as fully coordinated 6f-Ti and 3f-O. Here, all Ti atoms exposed directly at the first atomic layer are 5f-coordinated, while only ½ of oxygens are 2f-coordinated, as shown in **Figure 1b**. Moreover, visible steps inward of the crystal structure give access to the second-layer atoms, which are always fully coordinated. Including these sites as surface, atoms give a final fraction of 5f-Ti is ½ and 2f-O is ⅓. The relaxed structure of the (1 0 0) facet shows outward relaxation of fully coordinated O atoms and inward relaxation of 5f-Ti, creating an oxygen-rich interface, while 6f-Ti relaxes outward. Corresponding surface energy is usually reported in the range of 0.53 to 0.79 J<sup>m</sup><sup>2</sup> .

Furthermore, the (1 0 1) surface of anatase is energetically the most stable, with the reported surface energy in a vacuum being 0.44–0.65 J<sup>m</sup><sup>2</sup> , and it is commonly observed in nature. The corresponding atomic structure consists of a sawtooth profile with ½ of Ti atoms being 5f-coordinated and ⅓ of O atoms being 2f-coordinated, as shown in **Figure 1c**. Here, the most exposed atoms are undercoordinated oxygens, and specifically, further relaxation leads to the outward rise of the 3f-O above the undercoordinated Ti. Similarly to the (1 0 0) surface, the (1 0 1) can be considered oxygen-rich. Next, the (1 0 3) surface is often discussed in two possible terminations, either smooth one (1 0 3)s or faceted (1 0 3)f, both presented in **Figure 1d**-**e**, respectively. The smooth (1 0 3) termination is one of the few facets that exposes 4-fold coordinated Ti atoms (4f-Ti) at the top of the surface, being ⅓ of the total surface Ti. Other Ti sites located below the 4f-Ti "tooth" are fully coordinated. Here, the 2f-O represents ⅖ of all exposed O and two 2f-O are always bonded to the single 6f-Ti. The outermost O atoms are 3f-coordinated and, similar to other facets, undergo significant relaxation outward of the crystal structure. On the contrary, on the faceted (1 0 3) termination relatively large fraction of Ti atoms is 5f-coordinated, being ⅔ of all Ti. Two different 5f-Ti sites exist on this surface, one bonded to a single 2f-O and the other bonded to three 2f-O atoms. The total fraction of 2f-O is the same as for the smooth (1 0 3), that is, ⅖. Similar to the (0 0 1) surface, significant symmetry breaking is observed for the 2f-O bridging two equivalent 5f-Ti sites (the one bonded to three 2f-O), resulting in one bond being longer than the other. Analogically to other facets, 3f-coordinated O relaxes outward; however, the change is smaller than for a (1 0 3)s structure. Energetically, Lazzeri et al. reported that the (1 0 3)f is slightly more stable than (1 0 3)s, with surface energies being 0.83 and 0.93 J<sup>m</sup><sup>2</sup> , respectively [5]. However, different results were presented by Zhao et al. with analogical energies of 1.14 and 1.05 J<sup>m</sup><sup>2</sup> [6].

The (1 0 5) surface structure is rarely discussed; however, Jiang et al. have proposed possible geometry of such facet with a corresponding surface energy of 0.84 J<sup>m</sup><sup>2</sup> . In their model, the atomic structure of the (1 0 5) facet composes of both 4f-Ti (¼) and 5f-Ti (¼) exposed, together with 2f-O (3 ∕7), as shown schematically in **Figure 1f** [17]. Although performed, relaxation of the geometry was not described. Furthermore, the (1 1 0) surface has a characteristic layered structure with deep cavities running along the [0 0 1] direction. Such structure exposes up to four atomic Ti layers and three O layers at different depths. As shown in **Figure 1g**, the first layer composes only of 4f-Ti and 2f-O atoms, while further layers are fully coordinated. As

*Crystal Facet Engineering of TiO2 from Theory to Application DOI: http://dx.doi.org/10.5772/intechopen.111565*

described by Zhao et al., this surface also shows a "layered" relaxation pattern, where O atoms relax outward for the odd-numbered letters and inward for the evennumbered ones [6]. Simultaneously, Ti relaxes in the opposite pattern, ultimately leading to the breaking of the perfect 2D symmetry of the surface structure (i.e., the surface stops being perfectly flat, in contrast to the bulk crystal plane). Following this description and maximum exposition of the first four Ti and first three O layers, the fraction of undercoordinated species is ¼ for 4f-Ti and ⅓ for 2f-O. Corresponding surface energy is commonly reported between 01.02 and 1.33 J<sup>m</sup><sup>2</sup> .

Finally, the (1 1 2) surface is also rarely considered; however, Mino et al. analyzed its surface model with surface energy between 0.95 and 0.98 J<sup>m</sup><sup>2</sup> , depending on the possible relaxation of the cell parameters (exact value was approximated by the authors from the graph) [9]. Similar to the (1 1 0) surface, the (1 1 2) geometry exposes the first layer of undercoordinated species (5f-Ti and 2f-O, both being ½ of all Ti/O atoms) and the second layer of fully coordinated atoms, as shown in **Figure 1h**. A detailed relaxation pattern was not described.

### **2.2 Unreconstructed rutile surfaces**

Concerning the rutile crystal structure of TiO2, its possible terminations with different crystal planes are shown in **Figure 2**, analogically to the anatase. Starting from the (0 0 1) crystal plane, the corresponding termination shows structure similar to anatase (1 1 0), with the first atomic layer composed fully of undercoordinated 4f-Ti and 2f-O species and the second layer being fully coordinated. Assuming that the second layer is also partially exposed to the environment, the final fraction of undercoordinated sites is again ½ for both Ti and O. The relaxation of this surface is also similar to that of anatase (1 1 0), where the 4f-Ti atoms on the surface relax inward toward the bulk structure, while the 2f-O and 6f-Ti atoms relax outward. The high density of the broken bonds results in high surface energy, with reported values between 1.21 and 1.58 J<sup>m</sup><sup>2</sup> , making it one of the least stable rutile facets. Furthermore, **Figure 1b** shows (0 1 1) surface structure of the rutile phase with a little corrugated profile. Here, the uppermost part composes fully of 5f-Ti and 2f-O, while subsurface 3f-O atoms are also partially exposed, ultimately being ½ of all O atoms. Surface relaxation described by Barnard et al. showed that all 5f-Ti, 2f-O, and 3f-O atoms relax outward on this surface; however, a bit different pattern was also reported by Ramamoorthy et al. [14]. Along the (0 0 1) surface, the (0 1 1) is reported to be one of the least stable rutile surfaces, with surface energies reported in the range of 0.95 to 1.11 J<sup>m</sup><sup>2</sup> .

Furthermore, the (1 0 0) surface shows a layered structure with rows of 5f-Ti and 2f-O atoms at the top of the exposed "tooths," as well as fully coordinated species in the cavities. The corresponding fraction of the undercoordinated atoms is ½ for Ti and ⅓ for O. Relaxation pattern described by Ramamoorthy et al. includes the moving of the surface Ti and O atoms in opposite directions along the [0 1 0] axis [14]. Simultaneously, surface Ti relaxes outward the crystal structure. Corresponding surface energy was reported in the range between 0.60 and 0.83 J<sup>m</sup><sup>2</sup> . Next, the (1 1 0) structure is energetically the most stable surface of the rutile polymorph, with the reported surface energy between 0.34 and 0.59 J<sup>m</sup><sup>2</sup> . Its surface structure exposes both 5f-Ti atoms (½) and 2f-O (⅓) in the subsequent rows, as presented schematically in **Figure 2d**. Relaxation of the (1 1 0) structure includes an inward shift of all the undercoordinated species and outward of the 6f-Ti and 3f-O, therefore making the final structure more puckered.

*Perfect, bulk-cut atomic geometries of different rutile surfaces. Figure features are analogical to the anatase one.*

Finally, the rutile (1 1 1) surface is rarely discussed; however, a detailed analysis of its possible structure was presented by Wang et al. [18]. For the unreconstructed, bulk-cut, stoichiometric surface, the corresponding surface energy was found to be in the range of 1.34 J<sup>m</sup><sup>2</sup> , exposing ⅓ of Ti atoms as 4f-Ti in the first layer, ⅓ of Ti as 5f-Ti in the second one, and hypothetically ⅓ of 6f-Ti in the third one. Here, all O atoms in the first layers are 2f-coordinated and 3f-O can be found only below the 5f-Ti sites, as shown in **Figure 2e**. According to Jiang et al., the 4f-Ti atoms show significant inward relaxation for such a structure [13]. However, very high surface energy and density of undercoordinated atoms generally lead to the instability of such "perfect" (1 1 1) surface, and further stabilization by hydroxylation was discussed in the following parts.
