Vacancy-hole and vacancy-tube migration in multiwall carbon nanotubes

Evidence is presented that vacancy-hole or vacancy-tube (similar to vacancy loops in crystalline materials) migration constitutes an important self-diffusion mechanism in multiwall carbon nanotubes (MWCNTs) when they were irradiated by an electron beam at about $2000°\text{C}$. Isolated vacancies agglomerated to form vacancy holes/tubes with lengths from 3 to 16 nm and widths from 1 to 4 basal planes in the intermediate layers of the MWCNTs. The formation of vacancy holes/tubes is attributed to the high mobility of vacancies at high temperatures and the confinement of the intermediate layers posed by the top and bottom layers. The vacancy holes/tubes were mobile and could migrate along the axial, radial, or circumferential directions of the nanotubes. Driven by the temperature gradient and the thermal fluctuation, the migration velocity of the holes varies from a few to 80 nm/s. The results demonstrate that a carbon nanotube is a perfect system for studying vacancy properties in a quasi-one-dimensional system.

Figure 1

(Color online) (a)–(f) Formation and migration of two vacancy holes/tubes (outlined by two sets of dotted lines near the hollow and surface of the MWCNT, respectively) in a MWCNT irradiated by electron beam at about $2000°\text{C}$. Note both the shape and position changes of the holes. In (c) the upper hole extended through the entire circumference, forming a vacancy tube. The length and width of the upper hole are 6 nm and three-wall thickness, respectively, and those of the lower hole are 4 nm and three-wall thickness, respectively. (g)–(l) Schematic drawing showing how a vacancy hole/tube is formed due to removal of C atoms.

Figure 2

(Color online) (a)–(c) Formation and migration of two vacancy loops (outlined by two sets of dotted lines on top and bottom of the figure, respectively) in a MWCNT irradiated by an electron beam at about $2000°\text{C}$. Note both the shape and position changes of the loops. In (c) the upper loop extended through the entire circumference, forming a vacancy tube with the same axis as the nanotube. The nanotube was joule heated at 2.26 V and $111\mu \text{A}$. (d)–(e) and (g)–(j) are schematic drawings showing how the lower vacancy hole in Figs. 2a, 2b, 2c migrated along the circumferential and the radial directions of the tube, respectively.

Figure 3

(Color online) Growth and migration of a vacancy hole on the surface wall of a MWCNT. The dotted lines outline the shape and size of the holes.

Figure 4

(Color online) Migration of a vacancy hole (outlined by dotted lines and arrowheads) with a velocity of 5 nm/min downward the tube axis when the nanotube was irradiated at $2000°\text{C}$ (Ref. 29) (movie M1). While the hole moved downward, it also expanded along the circumferential direction. The bias voltage applied to the nanotube was 2.55 V. The length and width of the vacancy hole are 10 nm and two-wall thickness, respectively. Note that the innermost two walls were detached from the rest of the walls, which was caused by the diameter shrinkage of the nanotube induced by vacancy generation and reconstruction.

Figure 5

(Color online) MD simulation of vacancy aggregation $\left[\left(\text{a}\right)\to \left(\text{c}\right)\right]$ and interstitial diffusion along the edge of a vacancy hole $\left[\left(\text{d}\right)\to \left(\text{f}\right)\right]$. The migration barriers were calculated by the semiempirical PM3 method and the MD simulation was done with a density-functional-based tight-binding (DFTB) method (Refs. 33, 34). In the MD simulation, a graphene described by a periodic boundary condition was used to model a wall in the middle of a MWCNT, which cannot shrink as a SWCNT due to the confinement of the inner walls. The simulation starts with six single vacancies. At 3500 K, the six vacancies evolve into a vacancy hole [$\left(\text{a})\to (\text{b})\to (\text{c})\right)$] by vacancy aggregation. The arrows mark an atom migrating along an atom edge of a hole [$(\text{d})\to (\text{e})\to (\text{f})$]. The MD time step is 0.5 fs. (g),(h) C atoms are evaporated from the upper edge of the hole and deposited at the lower edge, causing the hole to move upward. (i),(j) Potential barrier for a C atom to migrate along the armchair and zigzag edges of a graphene.