Stability of carbon nanotubes under electron irradiation: Role of tube diameter and chirality

Abstract

As recent experiments demonstrate, the inner shells of multiwalled carbon nanotubes are more sensitive to electron irradiation than the outer shells. To understand the origin of such counterintuitive behavior, we employ a density-functional-theory based tight-binding method and calculate the displacement threshold energies for carbon atoms in single-walled nanotubes with different diameters and chiralities. We show that the displacement energy and the defect production rate strongly depend on the diameter of the nanotube and its chirality, with the displacement energy being lower, but saturating towards the value for graphite when the tube diameter increases. This implies that the threshold electron energies to produce damage in nanotubes with diameters smaller than 1 nm are less than the commonly accepted value for graphitic nanoparticles. We also calculate the displacement energies for carbon atoms near defects and show that if a single vacancy is formed, it will likely be transformed to a double vacancy, as the nanotube atomic network with double vacancies has no energetically unfavorable undercoordinated atoms.

Ion and electron irradiation-induced effects in nanostructured materials

“…This value ͑perpendicular direction͒ was very close to the corresponding value for graphite ͑15-20 eV͒. 72 Later calculations 46,210 showed that for small nanotubes with diameters less than 1 nm, T d indeed depends on the tube diameter and chirality. Figure 13 shows T d as a function of tube diameter for armchair nanotubes.…”

“…A nonorthogonal self-consistent charge TB method 208,209 in which the parameters of the Hamiltonian were derived from DFT calculations ͑a second-order expansion of the KohnSham total energy in DFT with respect to charge density fluctuations͒ has been widely used for simulations of impacts of energetic electrons onto C, 46,210,211 BN, 212 and SiC ͑Ref. 213͒ nanosystems.…”

“…Such a setup has been successfully used to calculate the displacement energies of atoms from graphene and carbon nanotubes, 46,210,212 as well as from SiC nanotubes, 213 see Sec. V A 5.…”

“…II, the electron-atom collision time is extremely short ͑10 −21 s, Ref. 72͒, so that the impacts of energetic electrons onto carbon nanosystems can be modeled 43,46,210,212,271,289 by assigning some kinetic energy to a carbon atom in the atomic network and then by using the MD method to simulate the subsequent atom motion to understand if the impact gave rise to the formation of a defect. The orientation of the initial velocity vector can be chosen either randomly if the main goal is to simulate the response of the system to a prolonged irradiation or in the direction, 43 which will more likely result in the formation of a defect, if the defect formation energy is the quantity of interest.…”

Quasi first-principles Monte Carlo modeling of energy dissipation by low-energy electron beams in multi-walled carbon nanotube materials

“…10,11 In the present energy range, energy dissipation in matter by electron beams is almost exclusively due to inelastic electron-electron scattering. Elastic electron scattering by target nuclei, well-known to be responsible for irradiation damage via knock-on atomic displacement at high beam energies (above about 80 keV for CNTs), 12,13 results in significant momentum transfer (or equivalent, angular deflection) but practically zero energy loss. 14 Contrary to the continuous energy-loss models (e.g., from stopping power theory) widely used for studying irradiation effects in bulk solids, MC models of materials with restricted dimensions (e.g., CNTs and nanodevices in general) must account for secondary-electron cascade generation through the use of discrete (or single-scattering) energy-loss models.…”