Formation energy of Stone–Wales defects in carbon nanotubes

Abstract

A Stone-Wales ͑SW͒ defect is a dipole of 5-7 ring pair in a hexagonal network, which is one of the most important defective structures in carbon nanotubes ͑CNTs͒ that will affect mechanical, chemical, and electronic properties of CNTs. Using the extended Hückel method, we calculated the formation energy of SW defects in carbon nanotubes. The formation energy of SW defects was then fitted to a simple formula as a function of the tube radius and the orientation of a SW defect in the tube. This result provides a convenient tool for the study of thermodynamics and kinetics of SW defects, as well as the interaction of SW defects with other types of defects in CNTs. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1599961͔ A carbon nanotube ͑CNT͒ was first thought of as a perfect graphene sheet wrapped up into a cylinder. However, as more experimental results became available and theoretical investigations went deeper, CNT was found to be not as perfect as it seems. Defects such as the 5-7 rings, kinks, junctions, and impurities may be presented in as-prepared CNTs. These defects can significantly change the electrical, chemical, and mechanical properties of CNTs.1-3 Therefore, it is highly desirable to gain an understanding on the energetic condition for the formation and thermodynamic behavior of defects in CNT for applications such as nanoelectronic devices, composite reinforcement, and energy storage. Unlike bulk materials, the structure of CNT has two degrees of freedom: one is the radius (r) of the tube and the other is the chiral angle ͑͒. The (r,) notation of CNT can be easily translated from the normal (n,m) notation as follows:where a is the C-C bond length, and is limited to being 0рр/6 due to the geometrical symmetry of the hexagon network. Such two degrees of freedom introduce a complexity in the description of the formation energy of a defect: with the change of radius and chiral angle of a CNT, the formation energy of a defect may also change. In addition, the orientation of the defect itself in relation to the CNT may cause variations in formation energy. The Stone-Wales ͑SW͒ defect is one of most important defective structures in CNTs. It is formed by rotating a C-C bond in the hexagonal network by 90°͑the so-called StoneWales transformation͒, 5 resulting in the creation of a dipole of a 5-7 ring pair ͓see Fig. 1͑a͔͒. Murry and co-workers 6 examined the kinetics of the SW transformation as an essential part of fullerene annealing and fragmentation. Beyond a critical level of tension, CNT releases its excessive strain via a spontaneous formation of topological defects. It was proposed that at high temperatures, a plastic response could occur due to the separation and gliding of SW defects, whereas at lower temperatures the result could be fractures. 7 The formation energy of the SW defect is sensitive to the applied strain along the axial direction of CNT.8,9 Samsonidze et al. 10 presented an analytic expression of the formation energy (E sw ) for SW defects under an applied strain . There are som...

The contribution made by lattice vacancies to the Wigner effect in radiation-damaged graphite

“…Using the PBE96-GGA instead of the LDA predicts that the barrier to eliminate a Stone-Wales defect is slightly smaller, making the estimated temperature for onset of annealing lower by about 50 K than it is with the LDA. Previous studies have found broadly similar results [44,[132][133][134][135][136][137][138], with one exception [139]. The exception (Kaxiras and Pandey) uses a model based on rhombohedral graphite instead of a single graphene sheet, which all the others use, and gives significantly higher values for the formation and activation energies.…”

Ion and electron irradiation-induced effects in nanostructured materials

“…[325][326][327] The formation energy of SW defects proved to be dependent on the tube diameter and chirality, [328][329][330] analogously to other point defects. Overall, MD simulations showed that the concentration of SW defects after impact of energetic ions 174,175,178,265 and electrons 210 is much smaller than those for adatoms and interstitials.…”

Enormous shrinkage of carbon nanotubes by supersonic stress and low-acceleration electron beam irradiation

“…It is well known that the generation of an SW defect consumes about 5 eV to eject a knock-on carbon atom from the honeycomb lattice, 13,14 where the transferred energy is almost identical to the approximate 80 keV for the perpendicularly irradiated electron beam. However, the electron energy that induced the tube shrinkage was much smaller than the threshold value, and the largest shrinkage rate was observed at 1 keV in this experiment.…”

“…10 It is well known that high energy electron irradiation induces a variety of structural changes in carbon nanotubes; perpendicularly incident electrons induce lateral ejection of carbon atoms; thus creating Stone-Wales (SW) defects on the honeycomb lattice. [11][12][13][14][15][16] The threshold energy needed to induce this so-called "knock-on mechanism" is about 86 keV, 11 and the propagation of the SW defect plays an essential role in many structural transformations, 13 because a heptagonheptagon combination cannot sustain the initial flat surface but instead generates a local curvature. Therefore, SW defects combined with local excitation of the carbon bond induces a variety of carbon nanostructures 11,[17][18][19][20][21] including the creation of fullerenes from carbon soot, 17 lattice destruction into amorphous carbon, 11,18 nanotube scissoring, 19 and the cross-linking of nanotubes and fullerenes.…”