The surface energy of {110} facet γ{110} can be calculated as follows:
If a0 is the lattice constant,
The surface energy of each facet is
where γ{110} > γ{100} > γ{111}.
Considering the surface energy order is {110} > {100} > {111}, the final crystal has a tendency to form an octahedron‐shaped crystal that is dominated with {111} facet, rather than a cube enclosed by {100} facet (as shown in Figure 2.1). However, the octahedral shape has a larger surface area than the cube of the same volume. As a consequence, the shape turns to be a truncated octahedron with a mix of {100} and {111} facets [1]. Another example is anatase TiO2. According to the Wulff construction and surface energy calculation, the equilibrium shape of anatase TiO2 crystal (as shown in Figure 2.1) is a slightly truncated bipyramid enclosed with 94% {101} facet and 6% {001} facet [21], although the order of the surface energy of low‐index facets is {001} (0.90 J/m2) > {010} (0.53 J/m2) > {101} (0.44 J/m2) [22].
Figure 2.1 (a) Octahedron, truncated octahedron, and cube with the same volume. (b) The equilibrium shape of anatase TiO2 (middle) and two variants.
In practice, the product often shows a different shape from that predicted by equilibrium. The possible reasons may be that (i) the equilibrium condition was not fully satisfied during the synthesis, and/or (ii) the anisotropic surface energies of different facets were interfered by impurities or other factors. In other words, this allows the manipulation of the nucleation and crystal growth by intentional addition of impurities and tuning of synthesis conditions to achieve product particles with desired shape and exposed facets. This is the core concept of facets engineering.
Selectively controlling the nucleation and anisotropic growth rate is known as the bottom‐up route. The most common method is to use a selective capping agent to reduce the surface energies of the adsorbed facets, or to change the order of surface energies of different facets, or to terminate the crystal growth of a selective facet. Figure 2.2 indicates how the solvents and capping agents can be used to tune the morphologies during the crystal growth [23]. The capping agents can be atomic or molecular species originating from a gas or liquid environment. As early as in 1986, it was found that H2S could cause drastic morphological changes of Pt nanocrystals [24]. Pt{100} facet had a stronger interaction with sulfur than Pt{111} facet, resulting in the formation of Pt nanocubes rather than Pt nanospheres. More capping agents are generally used in the solution‐phase synthesis. For example, inorganic species such as bromides and organic species such as poly(vinylpyrrolidone) (PVP) are very popular for tailoring both metal [25–27] and semiconductor crystals [28–30].
Figure 2.2 Schematic of the effect of solvent and capping agents on the morphology control of crystal facets.
Source: Adapted from Liu et al. 2011 [23].
Selectivity and adsorption capability of the capping agents, regardless of organic or inorganic capping agents, are basically controlled by the density and arrangement of undercoordinated atoms on different surfaces. The capping agents stabilize these high‐energy surfaces by covering the undercoordinated atoms. This also means that the reactive sites on the surfaces are also likely to be covered. For instance, fluorine is the most frequently used capping agent for faceted TiO2 crystals. Fluorine always exists in the surface of as‐prepared faceted TiO2 crystals. Pan et al. demonstrated that the fluorine‐terminated anatase TiO2 crystals with different percentages of {001}/{101}/{010} facets have similar low photocatalytic performance. After the removal of fluorine by calcination, all TiO2 crystals exhibited much higher and diverse performance depending on the ratio of different facets. Although most studies suggest that the removal of the surface fluorine improves the performance in photocatalytic hydrogen evolution from water splitting with sacrificial agents, in some cases, the capping agents may also tune the activity and selectivity of the catalysts by involving in the catalytic process.
Another strategy to tailor the crystal morphology is via the top‐down route, where a starting particle sample is selectively etched to remove the undesirable facets. This method is more often used in the synthesis of semiconductors. The protective capping agents can be used to shield the desirable facets, leaving the uncapped and unwanted facets to be dissolved in the etching process. For instance, truncated octahedral Cu2O crystals can be synthesized via the hydrothermal method by using PVP as a capping agent. PVP is preferentially adsorbed on the Cu2O{111} facet. And then, in the following oxidative etching process, PVP can protect the Cu2O{111} facet. As a result, the truncated octahedral Cu2O crystals turned into a hollow structure with six {100} facets absent [31]. In some cases, even without any protective agents, selective etching can be used to prepare hollow structures, due to anisotropic corrosion of different facets. For example, a rectangular rutile TiO2 nanorod can be selectively etched along the [001] direction in hydrochloric acid, turning into a hollow rutile TiO2 tube. This is because the rutile TiO2{001} facets have a higher dissolution rate than the {110} facets [32].
2.3 Anisotropic Properties of Crystal Facets
The properties of crystal surface differ from the ones inside crystal bulk, due to the termination of the periodic arrangement of the atoms. The anisotropy of the crystal lattice determines the anisotropy of the atomic arrangement of the facets exposed, leading to anisotropic properties of the crystal surface.
2.3.1 Anisotropic Adsorption
Heterogeneous