Stone-Wales-type transformations in carbon nanostructures driven by electron irradiation

Observations of topological defects associated with Stone-Wales-type transformations (i.e., bond rotations) in high-resolution transmission electron microscopy (HRTEM) images of carbon nanostructures are at odds with the equilibrium thermodynamics of these systems. Here, by combining aberration-corrected HRTEM experiments and atomistic simulations, we show that such defects can be formed by single electron impacts and, remarkably, at electron energies below the threshold for atomic displacements. We further study the mechanisms of irradiation-driven bond rotations and explain why electron irradiation at moderate electron energies ($~$100 keV) tends to amorphize rather than perforate graphene. We also show via simulations that Stone-Wales defects can appear in curved graphitic structures due to incomplete recombination of irradiation-induced Frenkel defects, similar to formation of Wigner-type defects in silicon.

Figure 1

HRTEM images of an initially pristine graphene sample (a), followed by an SW(55-77) (b). Frame (c) shows the same image with a structure overlay. SW(55-77) disappears in the following frame (d). Scale bar is 1 nm. (See also video S1 in Ref. 29.)

Figure 2

Relative displacement threshold $T_d^{\varphi ,\theta }/T_d^{\theta =0}$ as a function of the displacement space angle ($\theta$,$\varphi$). Crosses mark the angles for which we observed impact-induced SW transformations.

Figure 3

Typical SW transformation processes for low out-of-plane displacement angles ($\theta ⩽{25}^{°}$): (a) The “circle” process and (b) the “nudge” process. The black spheres correspond to the recoil (displaced) atoms, and the monovacancy structure is highlighted with numbered carbon rings in the second panels. The last panel shows schematically the route of the displaced atom. (See also videos S8 and S9 in Ref. 29.)

Figure 4

Experimental image sequence of a vacancy annihilation. Panel (a) shows a $V_1$(5-9) monovacancy, with an overlay in the inset, and (b) shows the same region in a later exposure, with no defect visible. Scale bar is 1 nm. (See also video S7 in Ref. 29.)

Figure 5

(a) SW(55-77) creation process as an outcome of a vacancy-adatom annihilation in a (6,6) armchair nanotube. (b) Carbon dimer sputtering process in a (10,0) zigzag nanotube. The black spheres stand for adatoms and the gray ones denote the dimer to be sputtered [marked in the first panel of (b)]. The nanotube structures are shown from inside the tube. The tube axis is in the horizontal direction. (See also videos S10 and S11 in Ref. 29.)

Figure 6

Experimental images illustrating SW transformations in the atomic structure of divacancies and migration of these defects. Panels (a)–(d) show sequential HRTEM images of the same defect (in the lower row with structure overlay). (a) $V_2$(5555-6-7777) transforming into $V_2$(555-777) (b) and $V_2$(5-8-5) (c). Each of these transitions can be explained by a single bond rotation. In the later frame (d), the defect is again a $V_2$(5555-6-7777), but shifted by one lattice parameter. Scale bar is 1 nm. (See also videos S2–S4 in Ref. 29.)

Figure 7

Changes in the atomic structures of reconstructed divacancy defects through SW transformations upon atom displacements perpendicular to the graphene sheet ($\theta =0^{°}$); (a) $V_2$(5-8-5)$\to V_2$(555-777) and (b) $V_2$(555-777)$\to V_2$(5555-6-7777). The black spheres indicate the recoil (displaced) atoms. Structurally equivalent atoms to the displaced ones are marked with circles in first panels. In the last panels, the circled atoms are those which could cause a backward transformation upon displacement in addition to the recoil atom. (See also videos S12–S14 in Ref. 29.)