**2.3 Unreconstructed brookite surfaces**

Finally, **Figure 3** shows unreconstructed brookite surfaces, which are analogical to the anatase and rutile. Compared to the other polymorphs, brookite surfaces form rather complex structures, often exposing 4f-Ti. Due to such complexity, the calculated fraction of undercoordinated species for brookite surfaces is presented only for Ti atoms. Moreover, in the case of most surfaces, multiple terminations can be considered. Here, we have highlighted only those, which were found to be most stable, or whose reconstructed geometries showed significant stabilization.

**Figure 3.**

*Perfect, bulk-cut atomic geometries of different brookite surfaces. Figure features are analogical to the anatase one. The "X" mark indicates possible bond breaking after relaxation.*

The (0 0 1) brookite surface directly exposes 4f-Ti and 6f-Ti; however, some additional 6f-Ti, that are partially exposed can be found in the deeper parts of the surface, as presented in **Figure 3a** (after including deeper-layer Ti fraction of 4f-Ti is ¼). The top Ti atoms are bridged with a network of 2f-O and saturated O can be found only in the deeper parts of the surface. The calculated energy of such geometry after

straightforward optimization was found to be 1.18 J<sup>m</sup><sup>2</sup> ; however, possible reconstruction is known to stabilize alternate geometry, which will be discussed later.

Furthermore, the (0 1 0) brookite surface shows structure similar to the anatase (1 1 0) and rutile (0 0 1), with a top layer of (2f-O)-(4f-Ti)-(2f-O) bonding to the 6f-Ti in cavities. Assuming exposition up to the first three Ti layers, the fraction of 4f-Ti is ¼ for such geometry. Moreover, reported relaxation has shown that the uppermost 6f-Ti significantly rises to the top, breaking one bond with a deeper layer 3f-O, as highlighted with "X" in **Figure 3b**. Therefore, additional 5f-Ti is expected to be exposed on the relaxed surface. The final surface energy of such a structure was found to be 0.77 J<sup>m</sup><sup>2</sup> . Focusing on the next structure, the (0 1 1) brookite surface is shown in **Figure 3c**, exposing a combination of both 4f-Ti (⅛), 5f-Ti (⅜), and 6f-Ti (½), which are connected by a quite complex network of both undercoordinated and fully coordinated O atoms. Relaxation of the structure leads to outward displacement of 6f-Ti, while undercoordinated titanium relaxes inward the crystal structure, giving final surface energy of 0.74 J<sup>m</sup><sup>2</sup> . The (1 0 0) brookite surface is similar to the anatase (1 1 2), with a sawtooth-like profile, as shown in **Figure 3d**. The top of the surface directly exposes a row of 5f-Ti (½) atoms connected by the 2f-O, while deeper layers are fully coordinated. It can be noted that this structure can possess two very similar, but not strictly identical, configurations, where the top of the surface is composed of either the first or the second Ti layer, as shown in **Figure 3d**. Gong and Selloni [15] reported that these two configurations differ slightly in surface energy (either 0.88 or 0.93 J<sup>m</sup><sup>2</sup> ). Nevertheless, their overall geometry is very similar, and both configurations differ mostly due to slight changes in the exact bond lengths and angles at the very top. Next, **Figure 3e** shows the structure of the perfect (1 0 1) brookite surface, again exposing a combination of 4f-Ti (¼), 5f-Ti (⅛), and 6f-Ti (⅝), connected with both saturated and 2f-coordinated O atoms. Significant changes in the perfect structure during the relaxation include bond breaking between 3f-O that bridges two surface 4f-Ti atoms and the subsurface 6f-Ti, highlighted in **Figure 3e** with "X." In this case, the resulting 5f-Ti is located in the subsurface region; however, additional 2f-O appears exposed directly on the surface top. The resulting surface energy for such geometry is 0.87 J<sup>m</sup><sup>2</sup> . The surface structure of brookite (1 1 0) presented in **Figure 3f** is characterized by terraces that end with a 4f-Ti edge and further step-down. Again a variety of Ti species are exposed at this surface (<sup>1</sup> ∕<sup>7</sup> of 4f-Ti and <sup>2</sup> ∕<sup>7</sup> of 5f-Ti). Undercoordinated atoms undergo large relaxation at the edges, with O atoms relaxing outward the crystal structure and Ti atoms relaxing inward. The corresponding surface energy was found to be 0.85 J<sup>m</sup><sup>2</sup> . The (1 1 1) surface of brookite can be considered in a variety of different, complex terminations, which were studied in detail by Gong and Selloni. Following their results, **Figure 3g** shows the most probable (1 1 1) structure, exposing ⅛ of Ti sites as 4-fold coordinated and ⅜ as 5f-Ti. No significant relaxation changes were reported for such a structure and the corresponding surface energy was 0.72 J<sup>m</sup><sup>2</sup> . Next, the (1 2 0) brookite surface is shown in **Figure 3h**, exposing 4f-Ti (<sup>3</sup> ∕13) and 5f-Ti (<sup>2</sup> ∕13). This is another brookite surface that shows possible bond breaking between saturated Ti and O after the relaxation, as indicated in the surface model with "X," which results in the appearance of the additional 5f-Ti site at the surface's top. The corresponding surface energy was 0.82 J<sup>m</sup><sup>2</sup> . Furthermore, the (2 0 1) brookite surface was not investigated in detail through a computational approach; however, it has gained significant experimental attention due to reported relatively high photocatalytic activity. The atomic model of the (2 0 1) surface, proposed by Lin et al., and Zhou et al., is shown in **Figure 3i** [16, 19]. This surface composes of little up-and-down terraces, exposing either 4f-Ti

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

( 2 ∕7) or 5f-Ti (2 ∕7), respectively. On the "flat" parts, the two 5f-Ti are bridged with two 2f-O, while two 4f-Ti are bridged with one 2f-O and one 3f-O. Additional 2f-O are present at the edge of each step. Finally, **Figure 3j** shows the energetically most stable brookite surface (2 1 0), with reported surface energy of 0.70 J<sup>m</sup><sup>2</sup> . The atomic geometry of this surface shows similarities with anatase (1 0 1), as both expose characteristic steps of undercoordinated 5f-Ti bonded to the 2f-O at the edge of the step. Lower parts of the surface, below the (5f-Ti)-(2f-O) steps, are fully coordinated. The final fraction of 5f-Ti for this surface is ½. Similar to other TiO2 surfaces, the 6f-Ti and topmost 3f-O show visible relaxation outward of the crystal structure, while 5f-Ti relax inward.

## **2.4 Surface energies and reconstructions**

The above description shows possible terminations of the TiO2 crystals by different crystal planes, resulting in different surface energies calculated for relaxed models. Concerning analyses in a vacuum, these energies roughly correspond to the density of theoretical bonds that needs to be broken to form particular termination. However, as presented in **Figure 4**, considering different values reported in the literature, the relationship is not always strict and should be considered more as a guidance than an actual rule. It should also be noted that different computational details will lead to different computed energy values, which should be especially minded.

As presented in **Figure 4**, some of the reported energies can achieve quite large values, which is commonly the reason why such hypothetical structures are not necessarily observed experimentally. This may include the fact that analyzed crystals/ nanoparticles do not terminate in such orientation or that the final structure does not correspond to such particular atomic geometry. The second option is generally known as surface reconstruction, where interface atoms adopt geometry different from the corresponding crystal plane to minimize final surface energy.

### **Figure 4.**

*Relation between reported surface energies of different, unreconstructed TiO2 surfaces in vacuum and a density of broken bonds, needed to form the surface from bulk crystal. To give better comparison between values obtained in different studies (no single study reports all considered surfaces), final values are presented as a mean.*

Surface reconstruction was reported as an important process for several possible TiO2 terminations. Probably, the most notable is the (1 x 4) reconstruction of the anatase (0 0 1) surface, which was described in the early 2000s and should be especially considered under ultra-high vacuum conditions [20–22]. The probable structure of such termination was proposed by Lazzeri and Selloni with the "admolecule" model, which was found to be energetically more stable than the unreconstructed surface (0.51 J<sup>m</sup><sup>2</sup> for the reconstructed geometry, vs. 0.90 J<sup>m</sup><sup>2</sup> for the unreconstructed one) [8]. In their model, they propose that every fourth of the (5f-Ti)-(2f-O)-(5f-Ti) periodic units, shown in **Figure 1a**, is replaced by the row of TiO3 bridging species that rise above the perfect surface. The stability of such a configuration was explained due to the stress relief induced by the change in the bond length between the 5f-Ti and 2f-O atoms "left" in the unreconstructed part of the surface. Specifically, the (1 x 4) periodicity of such reconstruction resulted in the bond length being the closest to the "natural" length and, in consequence, the lowest surface energy. Nevertheless, despite the energetical stability of the proposed model, such a structure was not found to be completely in agreement with the experiment. This was mostly due to the relatively low activity of such structures, despite the expected exposition of the 4f-Ti atoms at the formed bridges, which should act as good adsorption and dissociation centers. This has led to further refinement of the proposed geometry by Wang et al. where they suggested that exposed 4f-Ti became oxidized to the fully-coordinated 6f-Ti [23]. The atomic geometry of their model is shown in **Figure 5**, where 5a and 5b correspond to the non-defected surface, while other images show different defect sites observed during the scanning tunneling microscopy (STM) analysis. In conclusion, they have shown that oxidized reconstruction is chemically inert and only reduced 4f-Ti sites show considerable activity.

However, despite a lot of attention being given to such (1 x 4) reconstruction, the actual geometry of the anatase (0 0 1) surface during growth and in aqueous suspensions is still probable to be unreconstructed. This fact is firstly justified by the fluorine stabilization of the (0 0 1) surface in its unreconstructed form, which is commonly used during the preparation procedure of such nanocrystals (details of this stabilization are described in the following section). After such preparation, fluorine has to be removed from the surface, as well an energy barrier needs to be overcome to induce the reconstruction. Both of these processes are known to occur in temperatures above 500–600°C, and below this temperature, reconstruction is not obvious [24–26]. Moreover, the possible stability of the unreconstructed geometry was experimentally confirmed by DeBenedetti et al. in the aqueous carboxylic acid solution [27]. Therefore, although (1 x 4) reconstruction of the anatase (0 0 1) surface should be minded, the actual geometry should be carefully considered, depending on the experimental details and available techniques.

Furthermore, different reconstructions were also proposed for other TiO2 surfaces, and their general summation is presented in **Table 1**. Noticeably, a variety of rutile surfaces are expected to reconstruct, including (0 0 1), (0 1 1), and (1 0 0) terminations. Interestingly, these surfaces are also expected to be present in the equilibrium shape of the rutile crystal, as shown later. The (0 0 1) rutile surface is generally known to reconstruct or facet, especially in higher temperatures [28–30]. Commonly, the {0 1 1} and {1 1 4} facets are reported to form at the (0 0 1) surface, from which the {0 1 1} facets are also expected to adopt the geometry of the (2 x 1) reconstruction of the (0 1 1) surface itself. Detailed studies of this (2 x 1) reconstruction were presented by several authors, generally proposing a "brookite (0 0 1)-like" atomic structure [31–33]. This structure shows a characteristic topmost zigzag, composed of

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

### **Figure 5.**

*Atomic models of the anatase (0 0 1) surface after the oxidized (1 x 4) reconstruction proposed by Wang et al. [23]. Non-defected (a) and defected (c, e) structures. Panels (b, d, and f) show corresponding simulated scanning tunneling microscope images. Please note that models (a, c, and e) are shown in parallel to the (1 x 4) periodicity of the reconstruction. Reprinted from [23] under a creative commons attribution 3.0 Unported license.*


### **Table 1.**

*Summation of the most important reported reconstructions of the TiO2 surfaces.*

the 5f-Ti and 2f-O, observed in the STM images. As reported by Gong et al., surface energy of such a configuration was found to be 0.42 J<sup>m</sup><sup>2</sup> , while the unreconstructed surface of about 0.89 J<sup>m</sup><sup>2</sup> is under the same computational parameters [33]. Furthermore, the (1 0 0) rutile surface can especially reconstruct after annealing in the

ultra-high vacuum conditions, showing the formation of the {1 1 0} microfacets with several reconstruction patterns, such as a (1 x 3), (1 x 5), and (1 x 7). Commonly, the (1 x 3) reconstruction is considered, which was recently studied by Balzaretti et al. concerning its surface energy and interactions with water [34]. Interestingly, they observed that reconstructed geometry is slightly less stable (0.04 J<sup>m</sup><sup>2</sup> difference) than unreconstructed one. It is also noteworthy that photoemission experiments have shown that such annealed, reconstructed surface is partially reduced, which might influence its stability [29]. Finally, reports about brookite surfaces are relatively rare. Therefore, possible reconstructions of its geometries are also not discussed. Nevertheless, Gong and Selloni reported an important reconstruction of the (0 0 1) surface, which results in a reduction of its surface energy from 1.18 to 0.62 J<sup>m</sup><sup>2</sup> , making it one of the most exposed surfaces in the equilibrium shape [15]. This structure is very similar to the proposed (2 x 1) reconstruction of the rutile (0 1 1) surface. In this reconstruction, the 3f-O atoms, that were originally bridging the 4f-Ti atoms (see **Figure 2a**), break their bonds with subsurface 6f-Ti and rise above the 4f-Ti. Simultaneously, two subsurface 3f-O break their bonds with surface 6f-Ti and move toward each other, ultimately locating below the 4f-Ti pair.
