We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the mid-frequency range between the K and M points in the Brillouin zone, where experimental data have been unavailable so far. The existence of a Kohn anomaly at the K point is further supported. We fit a fifth-nearest neighbour force-constants model to the experimental data, making improved force-constants calculations of the phonon dispersion in both graphite and carbon nanotubes available.

The full symmetry groups for all single-and multi-wall carbon nanotubes are found. As for the single-wall tubes, the symmetries form nonabelian nonsymorphic line groups, enlarging the groups reported in literature. In the multi-wall case, any type of the line and the axial point groups can be obtained, depending on single-wall constituents and their relative position. Several other consequences are discussed: quantum numbers and related selection rules, electronic and phonon bands, and their degeneracy, application to tensor properties. 61.46.+w,02.20

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Normal vibrational modes of all possible quasi-one-dimensional systems and polymers are classified according to the line-group symmetry. The results are used to discuss the vibronic instabilities for such systems and to establish the Jahn-Teller theorem. A general, but simple method, involving only one monomer, is developed to construct the normal displacements for the concrete polymers. As an illustration, it is verified that the symmetry arguments confirm the Jahn-Teller effect in trans-polyacetylene, resulting in dimerization with alternating bond lengths.