Ab initio calculations were applied to the study of phonon frequencies and the corresponding eigenmodes for zig-zag C nanotubes with single vacancies. Two types of vibrational mode were found that served as fingerprints of the single vacancy, and could be detected by using the Raman spectra technique. The calculations revealed that these vibrational frequencies exhibited a weak size-dependence upon the diameters of tubes. It was found that the frequencies of the radial breathing modes of the defective tubes were quite close to those of the related perfect ones.

Characteristic Vibrational Modes of a Single Vacancy in a Zig-zag Carbon Nanotube. H.Y.He, B.C.Pan: Physical Review B, 2008, 77[7], 073410 (4pp)