The Raman-active phonons in orthorhombic perovskitelike ${\mathrm{YMnO}}_3$ and ${\mathrm{LaMnO}}_3$ were studied by measuring Raman spectra in various scattering configurations. The experimental Raman line wave numbers and the expected shapes for the phonon modes were compared to those reported for other perovskitelike compounds with the $\mathrm{Pnma}$ structure and to the results of lattice dynamical calculations. The observed Raman lines in the spectra of ${\mathrm{YMnO}}_3$ and ${\mathrm{LaMnO}}_3$ were assigned to definite atomic motions. The much larger linewidths and strong variation of the Raman spectra with increasing laser power in the case of ${\mathrm{LaMnO}}_3$ provide evidence for a structural instability that may result in a phase transition under laser annealing.

Analytical expressions for the velocities of the longitudinal and the torsional sound waves in single-walled carbon nanotubes are derived using Born’s perturbation technique within a lattice-dynamical model. These expressions are compared to the formulas for the velocities of the sound waves in an elastic hollow cylinder from the theory of elasticity to obtain analytical expressions for the Young’s and shear moduli of nanotubes. The calculated elastic moduli for different chiral and achiral (armchair and zigzag) nanotubes using force constants of the valence force field type are compared to the existing experimental and theoretical data.

The Raman and infrared phonons of isostructural rhombohedral ${\mathrm{LaMnO}}_3$ and ${\mathrm{LaAlO}}_3$ 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 ${\mathrm{LaAlO}}_3$ and ${\mathrm{LaMnO}}_3$ (at $123\hspace{0.5em}{\mathrm{cm}}^{-1}$ and $236\hspace{0.5em}{\mathrm{cm}}^{-1},$ respectively) 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 ${\mathrm{LaMnO}}_3$ are not proper modes of the rhombohedral $R3\mathrm{}¯c$ structure, but are rather induced by the dynamic Jahn-Teller effect.

Raman-scattering and far-infrared-transmission spectra of hexagonal ${\mathrm{YMnO}}_3$ (space group ${P6\mathrm{}}_{3}cm)$ are reported and discussed. In the Raman spectra measured in several exact scattering configurations, lines of $A_1$ (at 148, 190, 257, $\sim 300$, 433, 459, and 681 cm${}^{-1})$, $E_1$ (at 376, 408, and 632 cm${}^{-1})$, and $E_2$ (at 135, and $\sim 215$ cm${}^{-1})$, symmetries have been observed. Maxima in the infrared absorption have been found at 211, 238, 265, 281, 308, 398, 428, 457, 491, 596, and 612 cm${}^{-1}$. An assignment of the phonon lines to definite atomic vibrations has been made on the basis of their symmetries in close comparison with results of lattice-dynamical calculations for ${\mathrm{YMnO}}_3$ in its ferroelectric ${(P6\mathrm{}}_{3}cm,\hspace{0.5em}Z=6)$ and high-temperature paraelectric ${(P6\mathrm{}}_3/mmc,\hspace{0.5em}Z=2)$ phases.

The dielectric response function of single-walled carbon nanotubes is calculated within tight-binding models with different levels of complexity. First, the effects of the orbital basis set of the model, the orbitals overlap, and the structural optimization on the electronic band structure and the dielectric function of three small-radius nanotubes are investigated in detail. Second, the optical transition energies for a large number of nanotubes are derived from the peak positions of the imaginary part of the dielectric function for parallel and perpendicular light polarization. These results can be useful for the assignment of absorption spectra of nanotube samples and for the determination of the conditions for resonant Raman scattering from nanotubes. The obtained results are compared to recent spectrofluorimetric data on isolated single-walled carbon nanotubes.