A New Class of Scandium Carbide Nanosheet

A new class of two-dimensional scandium carbide nanosheet has been identified by using first-principles density functional theory. It has a primitive cell of Sc3C10, in which there are two pentagonal carbon rings surrounded by one scandium octagon. Being as the precussor of Volleyballene Sc20C60 and ScC nanotubes, the Sc3C10 nanosheet is exceptionally stable. By rolling up this Sc3C10 sheet, a series of stable ScC nanotubes have been obtained. All the nanotubes studied have been found to be metallic. Furthermore, the hydrogen storage capacity of the ScC nanotubes has been explored. The calculated results show that one unit of the (0,3) ScC nanotube can adsorb a maximum of 51 hydrogen molecules, reaching up to a 6.25 wt% hydrogen gravimetric density with an average binding energy of 0.23 eV/H2.

, as well as the ScC nanotubes. Over the last several years, carbon-based nanomaterials, including carbon nanotube 23 , graphene 24 , and fullerene 25 have been widely studied for the H 2 storage applications due to their low weight and high specific surface area. However, the adsorption of H 2 molecule is dominated by weak Van der Waals force, and only a small amount can be stored under ambient conditions. A possible way to enhance the interaction is by importing heteroatoms to synthesis novel carbon-based materials with large surface areas and pores [26][27][28][29] . BN nanotubes have been tested to be a better hydrogen storage medium than pure carbon nanotubes 28,29 . In this way, the hydrogen storage of this novel ScC nanotubes has been studied. It has been found that one unit of the (0,3) ScC nanotube can adsorb 51 hydrogen molecules and the hydrogen gravimetric density can reach up to 6.25 wt%. Figure 1a shows the configuration of the most stable Sc 3 C 10 sheet obtained in the structural search. The primitive cell contains 3 scandium atoms and 10 carbons with the chemical formula of Sc 3 C 10 . The lattice parameters are a 1 = a 2 = 8.855 Å and α = 142°, respectively. A unit cell (b 1 , b 2 ), twice the size of the primitive cell, is also given in Fig. 1a. In the Sc 3 C 10 nanosheet, there is a basic structure, the Sc 8 C 10 subunit, highlighted in the top left corner of Fig. 1a. In the Sc 8 C 10 subunit, there are two carbon pentagons (C-pentagon) and one scandium octagon (Sc-octagon). It may be seen that each group of two C-pentagons is surrounded by one Sc-octagon, as the case of Sc 20 C 60 Volleyballene 19 . This new scandium carbide sheet may thus be viewed as consisting of Sc 8 C 10 subunits set in a crisscross pattern. The average Sc-Sc bond length is 3.340 Å with two distinct Sc-Sc bond lengths: 3.351 Å along the horizontal direction (b 1 in Fig. 1) and 3.328 Å for the other cases. For the C-pentagons, there are three C-C double bonds (1.428 Å), two C-C single bonds (1.466 Å), and one C-C bond of 1.437 Å connecting the two C-pentagons. Thus, the average C-C bond is 1.443 Å. For the Sc-C bond, the average value is 2.299 Å.

Results and Discussion
The stability of the Sc 3 C 10 nanosheet was studied by analyzing the bond characteristics, and confirmed using ab initio molecular dynamics simulations. Figure 2 shows the deformation electron density, which reveals electron transfer from Sc atoms to carbons. Mülliken population analysis shows a charge transfer of ~0.6e for one Sc atom, mainly from Sc 3d state. On C atoms, it has obvious sp 2 -like hybridization. For Sc atoms, there are obvious d orbital characteristics. The Sc atom in the middle of the primitive cell bonds, through its d orbital, with the neighboring carbons. For the remaining two Sc atoms of the primitive cell, each Sc interacts with the two C atoms which are more centrally located than are the other six carbons. Close examination of the partial density of states (PDOS), as shown in Fig. 3, further confirms the hybrid characteristics between Sc d orbitals and C s-p orbitals. This is of great importance in stabilizing the planar Sc 3 C 10 nanosheet.
Next, ab initio molecular dynamics simulations with an NVE ensemble were carried out with a time step of 1.0 fs. Here, a relatively large 2 × 2 supercell was used. The calculated results indicated that the Sc 3 C 10 sheet retained its original topological structure and was not disrupted over a 5.0 ps dynamic simulation at a ~801 K  www.nature.com/scientificreports www.nature.com/scientificreports/ effective temperature (also see Section I of the Supplementary Information). The snapshots of the geometries at the end of 5 ps simulations were given in Section I of the Supplementary Information. All the results indicate that the Sc 3 C 10 naosheet has good thermodynamic stability. Finally, some typical variants of the Sc 3 C 10 monolayer, consisting of the bilayer, trilayer, and bulk forms, were simulated at the same theoretical level and the calculated results were listed in Section II of the Supplementary Information. Furthermore, the mechanical property and the electric structure have been analysed at the GGA/PBE level. It is found that the elastic constants of Sc 3 C 10 sheet are 83. 34, 70.27, and 23.71 N/m for C 11 , C 22 , and C 12 , respectively. According to the the equations of 2D system 30 , the Young's modulus is obtained and the results are Y [10] = 75.34 and Y [01] = 63.54 N/m. The analysis of band structure (see Fig. 3) shows a direct band gap ~0.62 eV for the Sc 3 C 10 nanosheet.
Just as graphene is the precursor of carbon nanotubes, a series of ScC nanotubes with different diameters and chiralities could be constructed based on the Sc 3 C 10 nanosheet. We first specify how to describe these ScC nanotubes. Due to the low symmetry of this Sc 3 C 10 nanosheet, it seems not appropriate to classify the ScC nanotubes by using the primary vectors (a 1 , a 2 ) of the orthorhombic lattice. The lattice vectors of the rectangular lattice, b 1 and b 2 (as shown in Fig. 1a), seem to be more appropriate and convenient for labelling ScC nanotubes with integer multiples of the rectangular lattice vectors. Here we considered two kinds of tubes: (p, 0) and (0, q), where p and q are integers. The pb 1 and qb 2 represent the vectors of a strip which will be rolled up to a nanotube.
Calculations were performed on these tubes. After geometry optimization, it was found that the (p, 0) tubes with p = 1, 2, 3 had all collapsed. Only the (0, q) nanotubes with q = 2, 3, 4, 5 were stable. For these (0, q) nanotubes, the diameters are in the range 1.83-4.53 Å, and the stabilities and electronic properties have been explored.  www.nature.com/scientificreports www.nature.com/scientificreports/ Figure 4 lists the binding energy per atom of the (0, q) nanotubes vs the diameter. It can be seen that with the increase of diameter the binding energy approaches the value of the corresponding Sc 3 C 10 nanosheet. The (0, q) ScC nanotubes of large diameter have relatively high stability. Analysis of the electronic structures of the (0, q) ScC nanotubes indicates that all four (0, q) tubes rolled from the Sc 3 C 10 nanosheet are metallic. The band structures and densities of states (DOS) of the (0, q) ScC nanotubes are shown in Fig. 5. Close examination of the band structures indicates that the (0, 2) nanotube is different from the other three examined. For the latter cases, all of the (0, 3), (0, 4), and (0, 5) nanotubes exhibit a gap slightly above the fermi level. All three band gaps are direct band gaps at the Г-point and the gap sizes increase as the diameter increases. The band gaps are ~0.60, 0.64, and 0.71 eV for the (0, 3), (0, 4), and (0, 5) nanotubes, respectively. The band structure of the (0, 2) tube, on the other hand, shows several bands in the vicinity of the fermi level, which ensures a large carrier density. The above results indicate that these ScC nanotubes may have potential applications in metallic connections of electronic devices.
Then, the hydrogen adsorption of (0,3) ScC nanotube was discussed. As we known that the van der Waals (vdW) interactions are important for the formation and stability of molecules. The hybrid semiempirical dispersion-correction approach of the Tkatchenko-Scheffler (TS) scheme 31 was employed during the optimization.
We first considered the interaction between Sc atom and hydrogen molecules, and the Sc lying in the middle of the unit of the (0,3) ScC nanotube was selected. Figure 6(a,b) shows the configurations of H 2 adsorption on the selected Sc atom, as well as the average adsorption energy of hydrogen molecule (E a ) and the average distance between hydrogen molecule and Sc atom (d). The first hydrogen molecule tend to the site right above the Sc atom and lies parallel to the axis of the tube. The adsorption energy of the first adsorbed H 2 is 0.377 eV lying in the range 0.1-0.6 eV, which was a suggested criterion for the H 2 storage medium. The distance of the hydrogen molecule to Sc atom is 2.229 Å indicating a strong van der Waals interaction between hydrogen molecule and the ScC nanotube. When adsorbed two hydrogen molecules, the H 2 molecules prefer to form a line vertical to the axis of the ScC nanotube. It has only a small change for the distance between hydrogen and Sc atom (2.325 and 2.406 Å). For the second hydrogen molecule, the adsorption energy is 0.155 eV smaller than that of the first one. When the third H 2 were added, the energy minimization indicated that the third H 2 molecule prefers to the neighbor Sc atoms. It may due to the limited Sc-Sc distance (3.356 Å) of the (0, 3) ScC nanotube.
Thus, we take the neighboring three Sc atoms, which lie on a line parallel to the axis of the tube, as a group to consider the situation of their hydrogen adsorption. It is found that the three Sc atoms can adsorb eight H 2 molecules in maximum. Besides each Sc atom can adsorb two H 2 , just as the case of one Sc atom, one more H 2 can adsorb by the side Sc atoms arranging along the axis of the tube, as shown in Fig. 6(c). The average distance, d,

conclusions
In conclusion, our first-principles investigations have proposed a stable Sc 3 C 10 nanosheet using both static and dynamic ab initio calculations. The new scandium carbide nanosheet may be viewed as consisting of Sc 8 C 10 units arranged in a crisscross pattern. Hybridization between Sc d orbitals and C s-p orbitals is essential for stabilizing the Sc 3 C 10 nanosheet. Furthermore, all the stable ScC nanotubes rolled from this Sc 3 C 10 nanosheet were found to be metallic within the scope of the approximations used in our research. The hydrogen storage property of ScC nanotube has also been explored. For one unit of (0,3) ScC nanotube, the number of adsorbed hydrogen molecules can reach up to 51, corresponding to a 6.25 wt% hydrogen uptake with Ec = 0.230 eV/H 2 . All these prediction are expected to motivate experimental efforts in view of the fundamental value and potential applications of ScC nanostructures.