## 3 Results and Discussions
### First-Principles Modeling: Adsorption of C, N, and Si Atoms on Different Planes of W Crystal  
As mentioned above, W was demonstrated to be an effective catalyst to prepare CSed SiC NWs. However, for better comprehensive understanding, we further explained the formation of SiC NWs in a Si-C-N system, and also the role of N atoms. Moreover, the transformation mode of Si\({}_{3}\)N\({}_{4}\) and SiC whiskers into pure SiC whiskers with the increase of the amount of C was also explored. It is believed that the absorption sequence and site of the dissociated radical C, N, and Si atoms on the surfaces of the catalyst W particles determines the structure and growth orientation of the NWs. In order to understand the initial growing progress, we investigated the absorption behavior of C, N, and Si atoms on the crystal planes of W (100), W (110), and W (111) surfaces by using the first-principles calculations. The W surfaces were modeled by a seven-layer thick W slab with the middle layer being fixed. The vacuum region between adjacent slabs was 15 A, which was thick enough to cut off the influence of the neighboring surface. The absorption of C, N, and Si atoms was then investigated by placing a single type of atom on both sides of the W slabs. Figure 5 shows the top views of the studied W surfaces and the possible absorption positions for the dissociated inorganic atoms on the three different W surfaces. First-principles calculations within the density-functional theory (DFT) framework were carried out by using the Vienna ab initio simulation package (VASP) code [26; 27; 28; 29]. The projector augmented  
Figure 4: (**a**) Transmission electron microscopy (TEM) image of an individual CSed SiC NW and (**b**) Atomic TEM images taken from 4a. Figure 5: Top view of (**a**) 2 \(\times\) 2 W (100), (**b**) 2 \(\times\) 2 W (110), and (**c**) 2 \(\times\) 2 W (111) surfaces (all seven layers). Large green, blue, and gray spheres are for the surface, subsurface, and third layer W atoms, respectively. Small red spheres correspond to the X (X = C, N) atom absorbed at three different sites. wave (PAW) method [30] was used to describe the electron-ion interaction and the exchange correlation potential between electrons was simulated in the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) form [31]. An energy cutoff of 450 eV was set up for the plane wave basis set and a (\(4\times 4\times 1\)) \(k\)-mesh was adopted within the Monkhorst-Pack scheme [32] for sampling the Brillouin zone. All the calculations were carried out with fixed supercell volume and the relaxations were continued until the forces on all atoms converged to less than 10\({}^{-3}\) eV A\({}^{-1}\). In this study, the reproduced lattice constant for bcc W by GGA-PBE calculation was 3.17 A, which is in good agreement with the experimental value [33] and other theoretical results [34]. The calculated surface energy (\(E_{\text{surf}}\)) of the studied W surfaces and the absorption energy of C, N, and Si atoms on different sites are listed in Table 2. The \(E_{\text{surf}}\) is calculated as follows:  
\[Esurf=\frac{1|Eslab-N\text{-}Ebulk|}{2 Ahkl} \tag{1}\]  
where \(E_{\text{slab}}\) is the total energy of the seven-layer thick slab, \(E_{\text{bulk}}\) is the energy per W atom in bulk bcc W crystal, \(A_{\text{hkl}}\) is the area of sectional plane, and \(N\) is the number of atoms in the slab model. The adsorption energy (\(E_{\text{ad}}\)) is evaluated by using the following formula:  
\[E_{\text{ad}}=E_{\text{X/slab}}-E_{\text{X}}-E_{\text{slab}}\ (X=\text{C, N, and Si}) \tag{2}\]  
where \(E_{\text{X}}\) and \(E_{\text{X/slab}}\) are energies of an isolated X (X = C, N, and Si) atom and the slab with X atoms absorbed on its surfaces, respectively. Table 2 shows that among the three absorption atoms, the C atoms show the strongest absorption energy on the W (100) surface (\(-\)11.12 eV). This indicates that the C atom has a priority to sink to the nanometer catalysts grain of W, and the pre-sunk C atom could react with a Si atom to form NWs.