The Formation of Haeckelite Structures Induced by Vacancy Defects in Graphene Layers of Carbon Nanotube

The formation of haeckelite structures induced by vacancy defects in graphene layers of carbon nanotube are investigated by tight-binding molecular dynamics (TBMD) simulations and by first principles total energy calculations. It is observed in the TBMD simulations that two single vacancies coalesce into a 5-8-5 double vacancy at the temperature of 3,000 K, and it is further reconstructed into a new defect structure, the 555-777 defect, by the Stone-Wales type transformation at higher temperatures. First principles calculations confirm that the 555-777 defect is energetically much more stable than two separated single vacancies, and the energy of the 555-777 defect is also slightly lower than that of the 5-8-5 double vacancy. In TBMD simulation, it is also found that the four single vacancies reconstruct into two collective 555-777 defects which is the unit for the hexagonal haeckelite structure proposed by Terrones et al. [Phys. Rev. Lett. {\bf 84}, 1716 (2000)]