Abstract
Universite´Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris Cedex 05, France~Received 14 May 1998!In this paper, the theory of lattice dynamics of single-walled carbon nanotubes is presented. The screwsymmetry of the system is used to reduce the rank of the dynamical matrix to six, independent of the numberof atoms in the unit cell. Calculations of the lattice dynamics are carried out within a valence force field modeland of the Raman intensity—within a bond-polarizability model. It is found that the breathing mode frequencyis inversely proportional to the radius of the tube that can be used for the characterization of the samples on thebasis of Raman-scattering data. The results for the Raman intensity are compared to available Raman spectra.@S0163-1829~98!06434-0#
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