**3. Facets stabilization, crystal shapes, and synthesis strategies**

According to general thermodynamics, the total surface energy of the crystal should be minimized for the whole system to achieve minimum energy. Therefore, the exposition of some crystal planes is not expected. However, to consider such a lowest-energy shape, it is first necessary to consider the formation of surfaces equivalent to the specific model. For example, for the anatase polymorph, the (1 0 0), (1̅0 0), (0 1 0), and (0 1̅0) have the same atomic arrangement and are equivalent. Therefore, if the (1 0 0) surface became stable at the considered conditions, it is expected that four analogical facets will form in the crystal, with their orientation being the same as the orientation between the crystal planes. The family of such equivalent crystal planes is denoted using brackets and their Miller indices, which are also used to index observed crystal facets. The most important TiO2 facets and their corresponding equivalent crystal planes are listed in **Table 2**.

Finally, after considering possible surface terminations, their energies, and equivalent planes, the 3-dimensional minimum-energy crystal shape can be obtained, according to the Gibbs-Curie-Wulff theorem [35]. This shape is also called the Wulff construction. Concerning the anatase, rutile, and brookite, their corresponding Wulff constructions are shown in **Figure 6**, according to the existing studies [5, 14, 15].

Constructions shown in **Figure 6** can be seen as a perfect case, and therefore, it is not unusual that experimentally obtained micro- or nanostructures can exhibit a variety of very different shapes. This results from two important aspects of the preparation procedure. Firstly, the adsorption of a different species can drastically change the energy of a final surface. Moreover, and more importantly, the relative energy of different surfaces might also change, leading to a situation where minimumenergy construction will expose a completely new set of different facets. Such energetic stabilization is often achieved by the addition of specific capping agents, pH control, or growing on a substrate. The second aspect is the kinetics of such growth. Particularly, very fast nucleation of the substrate can lead to the situation where final nanoparticles will not form a well-defined geometry, despite a thermodynamic preference to grow in some specific direction. In the case of TiO2, this can typically be

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


### **Table 2.**

*Summation of the most important TiO2 facets and their corresponding crystal planes.*

**Figure 6.**

*Wulff constructions of the (a) anatase, (b) rutile, and (c) brookite TiO2 crystals, based on the existing studies [5, 14, 15]. Adapted colors generally follow the reported surface energy.*

addressed using "dissolution-recrystallization" processes, where nucleated seeds are dynamically dissolved and then recrystallized in the rebuilt, stable crystal shape [36]. Alternatively, Ti-precursors, which will nucleate slower, can be used to achieve more stable growth. For example, when using Ti-alkoxides as precursors, it is known that a longer carbon chain should result in slower nucleation [37]. Ultimately, both kinetic and thermodynamic aspects should be considered when designing a synthesis route

**Figure 7.**

*Summation of the most important aspects and some strategies used for the preparation of faceted TiO2 nanostructures.*

for a specific facet exposition. It is also noteworthy that multiple effects can be ascribed to the same additive. For example, during the HF-assisted growth of anatase nanostructures, hydrofluoric acid enables both dissolution of the TiO2 nuclei and thermodynamically stabilized {0 0 1} facets [26]. A summation of general synthesis strategies is presented in **Figure 7**.

The hydrothermal process is usually used under specific synthesis conditions to obtain desired crystal shapes, considering the appropriate precursor, capping agent, and solvent. Various reaction substrates or ions can play a role as a capping agent in the synthesis. Therefore, in the next subsections, the most important synthesis strategies are described, together with highlighting the key factors.

## **3.1 Anatase crystal facets and shapes**

The evolution of the anatase crystal shapes due to the exposition of different crystal facets is shown in **Figure 8**. Although the formation of a range of different facets was reported, the most investigated anatase crystal facets in the literature are {1 0 1}, {1 0 0}, and {0 0 1}, from which the first two facets are low energetic. Due to the symmetry of anatase crystal structure, nanocrystals with exposed {1 0 1} facets are octahedral, whereas the {0 0 1} facets form anatase nanosheets. Moreover, the combination of {1 0 1} and {0 0 1} facets (decahedral anatase nanostructures) and {0 0 1} and {1 0 0} (anatase cuboids) are also extensively studied. Decahedral nanocrystals may also undergo further flattening to nanosheets, resulting in dominant {0 0 1} facets. As reported by Barnard and Curtiss, the relative stability of these three facets depends heavily on the hydrogenation/oxygenation of the surface and, therefore, is strongly affected by the pH of the solution [11]. One of the consequences is that {1 0 1} and {1 0 0} exposing structures can be prepared in similar conditions, but {1 0 0} requires a higher pH. Alternatively, due to our best knowledge, the formation of the {0 0 1} exposing structures in the basic pH was not yet reported.

Anatase with exposed {1 0 1} facets is characterized by the lowest surface energy. Alone they form octahedral nanostructures, which synthesis methods are presented in **Table 3**. The most described procedure is a two-step synthesis, in which the first step is the fabrication of potassium titanate nanowires from a hydrothermal reaction of TiO2 P25 (or other commercial TiO2) in KOH solution. The second step is not always the same. For example, Amano et al. proposed direct hydrothermal treatment of titanate

**Figure 8.**

*The possible anatase crystal shapes resulting from the exposition of different crystal facets.*


### **Table 3.**

*Selected synthesis of octahedral anatase nanocrystals with exposed {1 0 1} facets.*

nanowires. This synthesis resulted in the formation of mesoparticles with exposed {1 0 1} facets. The proportion of regular octahedral bipyramids in the nanostructures was about 70% [38]. A different route is the production of ammonium-exchanged titanate nanowires from K2Ti6O13 precipitates obtained during the first step [39]. The above description considers mainly octahedral anatase nanostructures with the exposed {1 0 1} facets. However, according to Wang et al., these bipyramidal facets were obtained under hydrothermal conditions using potassium titanate nanowires as a precursor, hydrogen peroxide, and hydrofluoric acid as capping agents [43]. Alternatively, hydrazine-assisted formation of the {1 0 1} octahedrons was reported when starting from the precursors like TiOF2 and Ti(SO4)2 [41, 42].

Another low-energetic anatase crystal facet is {1 0 0}, which synthesis methods are presented in **Table 4**. This crystal facet usually co-exists with other crystal facets and forms cuboids or rectangular prisms with truncated prisms [40, 41]. However, some


**Table 4.**

*Selected synthesis of anatase nanocrystals with exposed {1 0 0} facets.*

syntheses with a high percentage of {1 0 0} crystal were also successfully performed. For example, Xu et al. reported the preparation of anatase nanosheets with exposed {1 0 0} facets [44]. Previously, nanosheets and nanocrystals were combined with {0 0 1} facets exposition. The second possible shape of nanostructures is nanorod, which synthesis was described by Li and Xu. The precursor was sodium titanate obtained from a facile hydrothermal route during the reaction of P25 in sodium hydroxide solution. Anatase nanorods with {1 0 0} facets were transformed from Na-titanate *via* exchanging alkali-ions with protons under alkaline conditions to form the H-titanates [45].

The starting point for the investigation on the high-energetic anatase crystal facets was the research of Yang et al. [26], who proved that {0 0 1} facets could be energetically preferable to {1 0 1}, although the surface energy of {0 0 1} facets is, in general, higher than {1 0 1}. The main requirement was the addition of fluorine to the reaction environment. In these theoretical studies, among the surface termination using 12 elements (H, B, C, N, O, F, Si, P, S, Cl, Br, or I), only fluorine-terminated surface allowed to stabilize {0 0 1} facets rather than {1 0 1}. These calculations were completed by experiments in which anatase nanostructures with exposed {0 0 1} facets were successfully synthesized using the hydrothermal approach with hydrofluoric acid as a capping agent. However, in the above experiments, {0 0 1} facets accounted for only 47% of all exposed crystal facets. In the meantime, Wen et al. [46] showed the synthesis of anatase nanocrystals with exposed {0 0 1} facets using 1-butanol as a solvent. This procedure allowed obtaining of large-sized well-defined anatase nanosheets wholly dominated with {0 0 1} and {1 0 0} facets, which had a percentage of 98.7% and 1.3%, respectively. The results can be explained by the alcohol stabilization effect associated with fluorine adsorption over the (0 0 1) surface. The role of particular alcohols, especially aliphatic with different chain lengths, was systematically studied recently [37, 47, 48].

The comparison of the anatase nanosheets with exposed {0 0 1} facets is presented in **Table 5**. In most studies concerning TiO2 with exposed {0 0 1} facets, hydrofluoric acid was used in the experimental procedure. However, other fluoride-based reagents were also investigated. For example, ionic liquids (IL) were applied for stabilization of these high-energetic facets, e.g., 1-butyl-3-methylimidazolium hydrogen sulfate [Bmim]HSO4 and 3-methyl-1-(3-sulfonyl propyl) imidazolium trifluoro methane sulfonate [HO3S(CH2)3MIM][CF3SO3] [18]. Moreover, the fluorine atoms can be delivered by using an appropriate Ti source. An example of the compound in the Ti-O-F


### **Table 5.**

*Selected synthesis of anatase nanocrystals with exposed {0 0 1} facets.*

system is titanium oxyfluoride (TiOF2), which can transform to TiO2 *via* a solvothermal process [36] or simple calcination at a temperature above 600°C [58].

Moreover, next to {0 0 1} and {1 0 1} facets, a small rhombus originating from {1 1 0} facet exposition with a surface energy of about 1.09 J <sup>m</sup><sup>2</sup> can be formed. Liu et al*.* reported that the hydrothermal treatment of metallic Ti powder together with the combination of hydrofluoric acid and hydrogen peroxide allowed the formation of these highly energetic facets. It was described that HF was responsible for Ti dissolution, whereas H2O2 reacted with Ti4+ to obtain peroxotitanium acid. This complex slows down the hydrolysis rate, which is necessary to pack the Ti–O–Ti chains and finally form {1 1 0} facets [59]. Similar results were obtained by Li et al., who used TiCl3 instead of Ti powder for the fabrication of {1 1 0} facets of anatase [49].

Excluding {1 1 0} facets, other synthesis procedures of anatase crystals with exposed high-index facets have been reported in the literature. For example, Xu et al. reported the synthesis of anatase single crystals with the exposed {1 1 1} facets. According to the density functional theory calculations, their surface energy was 1.61 J<sup>m</sup><sup>2</sup> , which was explained by a high percentage of undercoordinated Ti and O atoms on the (1 1 1) surface [50]. Finally, Jiang et al. performed a gas-phase oxidation process using TiCl4 as a precursor, which led to obtaining anatase single crystals with exposed high-index {1 0 5} facets. The regulation of the Ti/O ratio in the reaction system enabled inhibition of the growth of other crystal facets like {1 0 1} or {1 0 3}

[17]. Therefore, the research direction to obtain high-index crystal facets with relatively high surface energy is still under further investigation. However, there is a probability that non-equilibrium conditions and sophisticated synthesis will be necessary to preserve this surface.

### **3.2 Rutile and brookite crystal facets and shapes**

Compared to anatase, preparation procedures of both rutile and brookite polymorphs are far less investigated. Moreover, observed nanocrystals are commonly not consistent with a theoretical Wulff construction. In the case of rutile, above all, this is due to the commonly observed appearance of the {1 1 1} facets after the hydrothermal processes. As discussed previously, the (1 1 1) surface in its bulk-terminated form is very energetic, and its stabilization can be achieved only through hydroxylation, as reported by Wang et al. [18]. Interestingly, their calculations suggested that after the hydroxylation, the surface energy of the {1 1 1} facets can be similar or even lower than the most stable {1 1 0}. Ultimately, commonly prepared nanocrystals expose a combination of these two facets [51, 52]. However, some authors report even 100% of the {1 1 1} exposition. For example, Wu et al. reported that wholly exposition of the {1 1 1} can be achieved with a suitably high addition of NaF to the reaction solution [53]. Truong et al. synthesized the rutile nanocrystals with unusual {3 3 1} facets [54]. Their preparation route was based on the solvothermal treatment of titaniumglycolate complex in the presence of picolinic acid as an additive. The resulting product possessed a specific aggregated flower-like structure with facets exposed along the (3 3 1) plane. Based on the detailed experimental investigation, it was further proposed that {3 3 1} facets are composed with the periodically repeating {1 1 0} and {1 1 1} microfacets. Other rutile crystals with a less common shape were synthesized by Chen and Lou, who have reported stabilization of the {0 0 1} rutile facets during the hydrothermal growth in the presence of amorphous MoO3 [55]. The detailed procedure involved the hydrothermal treatment of mixed TiF4 + HCl and (NH4)6Mo7O244H2O + HNO3 solutions for 5 hours at 180°C. The final product comprised nanosized rutile platelets with {0 0 1} facets exposed aggregated to approximately 500-nm diameter spheres. The summation of the observed rutile crystal shapes is presented in **Figure 9**.

The research on brookite with exposed facets is the most overlooked issue in facet engineering of TiO2. Three main challenges can be distinguished: firstly, difficulties in obtaining pure brookite phase. Secondly, the pristine brookite is supposed to be

photocatalytic inactive. Finally, this TiO2 polymorph is metastable and undergoes a thermal transition to rutile at high temperatures [56].

However, the rising investigations about brookite in recent years have led to the recognition of this metastable phase as an active photocatalyst. One of the first studies by Lin et al. reported single-crystalline nanosheets surrounded with four {2 1 0}, two {1 0 1}, and two {2 0 1} facets. These nanostructures exhibited higher photocatalytic performance toward methylene orange removal and hydroxyl radical production than commercial TiO2 P25 [16]. Furthermore, {2 1 0} facets were also predominant in nanocrystals described by Xu et al., who demonstrated a tunable synthesis of brookite nanomaterials with the following shapes: quasi-octahedral, ellipsoid-tipped, and wedge-tipped nanorods [57]. The above results can be explained by the lowest surface energy of (2 1 0) surface among brookite crystals. However, Zhao et al. synthesized and investigated brookite nanostructures with exposed {1 2 1} and {2 1 1} facets. Particularly, TiO2 with a majority of {1 2 1} facets exposition, which had many undercoordinated atoms on the surface and a lower VB potential, exhibited enhanced photocatalytic activity toward Rhodamine B degradation under simulated solar light. Therefore, the presented examples from the literature proved that crystal facets engineering is a promising approach to obtaining photocatalytic active material from the inactive phase [60].
