Phonon modes in carbon nanotubules

The relationship between the phonon modes in carbon nanotubules and those in a graphene sheet is studied by use of the zone-folding method. The modes identified with pure translations and rotations are identified. General results relating to the symmetry properties of the Raman and infrared activity...

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Bibliographic Details
Published in:Chemical physics letters 1993-06, Vol.209 (1), p.77-82
Main Authors: Jishi, R.A., Venkataraman, L., Dresselhaus, M.S., Dresselhaus, G.
Format: Article
Language:English
Subjects:
Condensed matter: structure, mechanical and thermal properties
Exact sciences and technology
Lattice dynamics
Phonon states and bands, normal modes, and phonon dispersion
Phonons and vibrations in crystal lattices
Physics
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Summary:The relationship between the phonon modes in carbon nanotubules and those in a graphene sheet is studied by use of the zone-folding method. The modes identified with pure translations and rotations are identified. General results relating to the symmetry properties of the Raman and infrared activity of the phonon modes are deduced. It is shown that as the diameter of a tubule increases, the number of Raman and infrared active modes is essentially unchanged despite the increase in the number of atoms per unit cell. Explicit phonon dispersion curves are presented for a small diameter armchair carbon tubule.
ISSN:0009-2614
1873-4448
DOI:10.1016/0009-2614(93)87205-H