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The ideal nanotube structure can be obtained from a graphene sheet by rolling it up along the straight line connecting two lattice points into a seamless cylinder in such a way that the two points coincide. 11,19,20 The tube is uniquely

The Raman and infrared phonons of isostructural rhombohedral LaMnO 3 and LaAlO 3 are studied at room temperature. The experimental spectra are compared with the prediction of lattice-dynamical calculations and the lines observed are assigned to definite atomic vibrations. It is shown that the Raman mode of A 1g symmetry in LaAlO 3 and LaMnO 3 ͑at 123 cm Ϫ1 and 236 cm Ϫ1 , respectively͒ involves atomic motions that cause the rhombohedral distortion, i.e., it is a ''soft'' mode, and its position could be used as a measure of the degree of the distortion. It is also argued that the broad Raman bands in the high-frequency range of LaMnO 3 are not proper modes of the rhombohedral R3 c structure, but are rather induced by the dynamic Jahn-Teller effect.

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The breathinglike phonon modes of multiwalled carbon nanotubes are studied within a valence force field model for nanotubes with two and three layers of armchair type and within a continuum model for nanotubes with a large number of layers. A bond-polarizability model is used to calculate the nonresonant Raman intensity of the breathinglike modes. It is obtained that among all breathinglike modes of a given multiwalled tube, the in-phase one has a maximal intensity. The predicted intensity of the breathinglike modes is compared to available low-frequency experimental Raman data. Special attention is given to the comparison with Raman data on double-walled carbon nanotubes.

The analysis of the Raman scattering cross section of the radial breathing modes of double-wall carbon nanotubes allowed to determine the optical transitions of the inner tubes. The Raman lines are found to cluster into species with similar resonance behavior. The lowest components of the clusters correspond well to SDS wrapped HiPco tubes. Each cluster represents one particular inner tube inside different outer tubes and each member of the clusters represents one well defined pair of inner and outer tubes. The number of components in one cluster increases with decreasing of the inner tube diameter and can be as high as 14.

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