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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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