Phys. Rev. B 78, 155436 (2008)   J.Y. Huang, F. Ding, B.I. Yakobson

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 °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.