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

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 $1\mathrm{nm}$ 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.

Figure 1

Morphological evolution of a multiwalled carbon nanotube under electron irradiation. An electron beam with $300\mathrm{keV}$ and beam current density of approximately $450\mathrm{A}∕\mathrm{cm}$ was focused onto an area of $10–20\mathrm{nm}$ over the central part of the tube. The sequence (a)–(e) shows the evolution of a typical tube during some minutes of irradiation. In (d) and (e) only two shells or one shell are left, respectively. Specimen temperature: $600°\mathrm{C}$. The solid arrows indicate the position of the beam center where the shells successively break.

Figure 2

(Color online) (a) The simulation setup used (side view). (b) Several snapshots showing the atom positions after electron impact onto a zigzag nanotube. The initial energy of the recoil atom is just above the threshold for defect production. (c) The atomic networks of armchair and zigzag nanotubes (top view). The arrows show the most probable directions of the recoil atom motion (projection to the tube surface) when the original recoil atom velocity is perpendicular to the tube surface.

Figure 3

(Color online) Threshold energy $T_d$ needed to displace a carbon atom from armchair and zigzag single-walled carbon nanotubes and graphene calculated dynamically as a function of tube diameter. The solid lines are guides for the eye.

Figure 4

(Color online) Formation energy of an interstitial-vacancy pair in carbon nanotubes as a function of tube diameter. The lines are guides for the eye. The inset schematically shows the simulation setup used to calculate the formation energy.

Figure 5

(Color online) The atomic network of a (8,8) armchair nanotube and the energies needed to knock out the atom (marked with a circle) from the intact tube (a), nanotube with a vacancy (b), and a double vacancy (c).