Using first principles density functional theoretical calculations, the present paper reports a systematic study of phonon dispersion curves in pristine carbon (CNT) and silicon nanotubes (SiNT) having chirality (6,6) in the armchair configuration. Some of the phonon modes are found to have negative frequencies which leads to instability of the systems under study. The number of phonon branches has been found to be thrice as much as the number of atoms. The frequency of the higher optical bands varies from 1690 to 1957 cm~(-1) for CNT(6,6) while it is 596 to 658 cm~(-1) for SiNT.
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