## 3 Results and Discussion
### Ligand-Assisted Growth of Nanowires  
The picture is completely changed if we choose slightly different anisotropy in LCN sizes \(L_{yz}=\alpha L_{xy}\), \(L_{xz}=\beta L_{xy}\) with, for example, \(\alpha=1.2\) and \(\beta=1\). Then, looking at the conditions  
\[\mathbf{y}(z)>y\geq\mathbf{y}(x),\ z>\mathbf{z}(x) \tag{11}\]  
one can also expect the formation of nanowires. The corresponding construction is illustrated in Figure 2. Panel (a) in this figure is identical to that in Figure 1a. Figure 2b illustrates the range of \(z\)-edge values, for which either a nanoplatelet (blue arrow in the range \(z\leq 1\)) or a nanowire (red arrow in the range \(1<z\leq\alpha\)) can grow. The reason why nanowires require the condition \(1<z\leq\alpha\) becomes clear in Figure 2c, which shows that for these \(z\)-edge values, the growing \(x\)-edge will ultimately cross the red boundary curve. Crossing this curve means that the \(xz\)-facet becomes covered with a compact layer of ligands, thus fixing the length of the crystal's \(y\)-edge. The \(x\)-edge would still grow and lead to the formation of a nanowire-like crystal shape. It is worth noting that this kind of shape can be produced only if the anisotropy in LCN sizes is such that only one of the crystal facets, e.g., \(yz\)-facet, has a larger LCN size than the other two (\(xy\)- and \(xz\)-facets). Figure 1: Illustration of ligand-assisted growth of a nanoplatelet from an ideal cuboid crystal and anisotropy of the LCN sizes \(L_{yz}=\alpha L_{xy}\) and \(L_{xz}=\beta L_{xy}\). The curves represent the boundary functions given by Equation (10): (**a**) \(\mathbf{y}(x)\), (**b**) \(\mathbf{y}(z)\), and (**c**) \(\mathbf{z}(x)\) with parameters \(C=0.2,\ \alpha=\beta=1.2\). The points \((x_{0},y_{0})\), \((z_{1},y_{0})\) and \((x_{0},z_{2})\) on the corresponding curves indicate the formation of compact layers of ligands on the \(xy\), \(zy\) and \(xz\) facets, respectively. The compact layer of ligands is supposed to be formed first at the point \((x_{0},y_{0})\). Therefore, the \(z\)-edge of the crystal at this point has to be significantly lower than \(z_{\text{max}}=\min\{z_{1},z_{2}\}\). (**b**) The vertical arrow indicates the growth of the crystal’s \(y\)-edge for \(z\leq\alpha\). (**c**) The horizontal arrow indicates the growth of the crystal’s \(x\)-edge for \(z\leq\beta\). (**d**) Nanolatelet-like shape of the crystal growing with \(z\leq\alpha=\beta\) after its \(xy\)-facet is covered with a compact layer of ligands. These two simple cases of LCN sizes anisotropy when two of the crystal facets have the same size can be easily generalized. As can be seen in Figure 2c, the nanowire-like crystals are formed in the range \(\alpha>z>\beta\) (the coordinate system is chosen such that \(\alpha>\beta\)), which means that for efficient fabrication of nanowires using the LAG method, one has to find a way of achieving a large enough difference between \(\alpha=L_{yz}/L_{xy}\) and \(\beta=L_{xz}/L_{xy}\) for the seed crystals. It is worth pointing out that the cuboid morphology characterized by three different ligand-facet interaction energies is quite generic. If all the energies are different, it describes the crystals with orthorhombic symmetry. In the case of equal ligand-facet interaction energies, we have the case of cubic crystal symmetry; using the LAG regime, it is possible to generate a platelet if the seed shape is a platelet of appropriate thickness (see discussion of Figure 1). If only two ligand-facet interaction energies are equal, then we reproduce tetragonal crystal symmetry. The approach can easily be extended onto hexagonal crystal symmetry and even the cylindrical shape of the seed crystals. To qualitatively illustrate this, recall that the key parameters in our approach are the ligand-facet and ligand-ligand interaction energies, which along with the ligand concentration in the solution, determine the ligand critical nucleus size. The latter is specific for each crystal facet.