Stability and electronic structure of Si, Ge, and Ti substituted single walled carbon nanotubes

Si, Ge, and Ti substituted nanotubes have been theoretically investigated. We employed a mixed approach for the computation of the electronic structure of these systems under periodic conditions. Band energy methods were then employed at a pseudopotential and all-electron schemes. The optimized geometries, binding, and atom-substitution energies have been computed along with the details of the electronic structure and bonding characteristics. Our results indicate the feasibility of up to now hypothetical Ge and Ti large substitutions in single walled carbon nanotubes. We also discuss the electronic behavior and the nature of the bonding in this class of materials.

Figure 1

(Color online) Optimized geometries of (5,5) nanotubes substituted with two silicon atoms.

Figure 2

(Color online) Optimized geometries of selected substituted tubes, showing the number of $X$ atom per unitary cell.

Figure 3

(Color online) Optimized structures of substituted carbon nanotubes at $X=50\%$ and their approximated diameters.

Figure 4

Binding energies per atom (eV) for different $X∕\mathrm{C}$ ratios. Solid lines (dark symbols) were obtained at GGA/PW91/DND, and dashed lines (open symbols) at LDA/PWC/DND theory levels.

Figure 5

(Color online) Structure volume $\left({\mathrm{\AA }}^3\right)$ computed with van der Waals radii of the elements for different substituted nanotubes as a function of the substitution percentage.

Figure 6

(Color online) (a) Total DOS (states/eV 40-atom cell) for the 2.5% Si-substituted (5,5) carbon nanotube, and the corresponding (5,5) pristine nanotube, (b) partial DOS (states/eV atom) at the Si and adjacent C sites. (c) Partial DOS differences $({\mathrm{C}}_{\mathit{adj}}-{\mathrm{C}}_{\mathit{far}})$. Fermi energy was set to zero. Results obtained at LAPW theory level.

Figure 7

(Color online) (a) Partial DOS (states/eV atom) at the Si and adjacent C sites for the 5% Si-substituted (5,5) carbon nanotube (ortho configuration). In inset, the total DOS (states/eV 80-atom cell) and (b) partial DOS differences $({\mathrm{C}}_{\mathit{adj}}-{\mathrm{C}}_{\mathit{far}})$. Fermi energy was set to zero. Results obtained at LAPW theory level.

Figure 8

(a) Partial DOS (states/eV atom) at the Si site for the 50% Si-substituted (5,5) carbon nanotube. In inset, the total DOS (states/eV 20-atom cell) and (b) partial DOS (states/eV atom) at the C site. Fermi energy was set to zero. Results obtained at LAPW theory level.

Figure 9

(Color online) (a) Partial DOS (states/eV atom) at the Ge and adjacent C sites for the 5% Ge-substituted (5,5) carbon nanotube (ortho configuration). In inset, the total DOS (states/eV 80-atom cell) and (b) partial DOS differences $({\mathrm{C}}_{\mathit{adj}}-{\mathrm{C}}_{\mathit{far}})$. Fermi energy was set to zero. Results obtained at LAPW theory level.

Figure 10

(Color online) (a) Partial DOS (states/eV atom) at the Ti site for the 2.5% Ti-substituted (5,5) carbon nanotube. In inset, the total DOS (states/eV 80-atom cell) and (b) partial DOS (states/eV atom) at the C site. Fermi energy was set to zero. Results obtained at LAPW theory level.