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The faceted nanocrystals, whether metals or semiconductors, can be achieved through many synthesis methods, including solution‐phase, vapor‐phase, and solid‐phase methods. The solid‐phase methods include gas oxidation route, topotactic transformation method, and crystallization transformation method [8, 9]; the vapor‐phase methods include thermal decomposition method, metal–organic chemical vapor deposition [10, 11]; and the solution‐phase methods are more powerful and versatile than others. It includes basic wet chemical route, sol–gel method, hydrothermal [12, 13] and solvothermal [14] methods, microwave treatments [15, 16], electrochemical [17] and photochemical [18, 19] methods. It should be noted that the synthesis of metal crystals is quite different from semiconductor crystals, although they sometimes share the same methods. Metal crystal catalysts are composed of single or binary metal atoms. Their synthesis process, including the steps from ions to nuclei or cluster, to seed, and then to nanocrystals, might be far different from the synthesis of semiconductors, which are composed of metal and nonmetal elements. However, no matter metals or semiconductors, and regardless of the synthesis methods, the one common feature is the spontaneous reaction that dictates the crystal formation is under thermodynamic control.

The excess energy at the surface of a material compared with the bulk is defined as the surface energy. Without facets engineering, the most stable free surface will occupy the greatest portion of the crystal surface as it attempts to minimize the total surface energy in a given growth condition. According to the Gibbs–Wulff theorem, the facets with higher surface energies always grow faster and end up with a tiny fraction or even vanish [20]. The Wulff construction method predicts the shape of a crystal with the lowest surface energy, and the most stable form is called the equilibrium shape of a crystal. Owing to the anisotropic surface energy of crystal facets, the final shape of a single crystal is usually enclosed with the facets of lowest surface energy and smallest surface area in a given volume. For example, for a metal crystal that contains N_A atoms and each bulk (i.e., nonsurface) atom that is defined by a coordination number of CN, there will be (N_A × CN)/2 bonds in the crystal. As such, the energy of each bond can be calculated as

where ΔH_s is the molar enthalpy of the metal sublimation.

A face‐centered cubic (fcc) structured metal crystal typically has three low‐index facets, i.e. {111}, {100}, and {110} facets. While each bulk atom has a CN of 12 (6 around the side perimeter of the atom and 3 each on top and bottom), depending on the direction of the surface cut, which, in turn, dictates the exposed facets, the atom on terminated surface would lose a certain number of atoms and result in dangling bonds.

As shown in Figure 2.1a, the CN of the atoms at the {111} surface is 9, which means 3 bonds are broken. Therefore, the energy required per atom to form the {111} surface can be calculated as

Then, the surface energy of {111} facet γ_{111} can be calculated as follows:

where is the number of surface atoms per area.

Similarly, the CN of the atoms at the {100} surface is 8, which means 4 bonds are broken (Figure 2.1b). Therefore, the energy required per atom to form the {100} surface can be calculated as

Then, the surface energy of {100} facet γ_{100} can be calculated as follows:

The {110} surface contains two layers of atoms (Figure 2.1c). The CN of the first‐layer atoms is 7, that is, 5 bonds are broken. And the CN of the second atoms is 11, that is, 1 bond is broken. Therefore, the energy required per atom at the first layer and second layer can be calculated as

The surface energy of {110} facet γ_{110} can be calculated as follows:

If a₀ is the lattice constant, of each surface can be obtained as

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].