Six representative isotope-labeled samples of titanium dioxide were synthesized: Ti¹⁶O₂, Ti¹⁷O₂ and Ti¹⁸O₂, each in anatase and rutile forms. Their Raman scattering was analyzed at temperatures down to 5 K. Spectral assignment was supported by numerical simulation using DFT calculations. The combination of experimental and theoretical Raman frequencies with the corresponding isotopic shifts allowed us to address various still-open questions about the second-order Raman scattering in rutile, and the analysis of overlapping features in the anatase spectrum.

The radial breathing mode is a promising candidate for the analysis of conformational and electronic properties of carbon nanotubes. The paper presents calculations based on the local density approximation to determine the radial breathing mode (RBM) frequency of various zigzag and armchair tubes with radii between 3.5 and 8.1 Å. The frequencies are derived from both frozen phonon calculations for nanotubes and from the elastic constants of the flat graphene sheet. The RBM frequency of the (10,10) armchair tube is found to be $175{\mathrm{cm}}^{\mathrm{-}1}$ and $174{\mathrm{cm}}^{\mathrm{-}1}$ for the two techniques, respectively. These values are in very good agreement with one of the strongest components in the structured Raman band of the radial breathing modes observed at $177{\mathrm{cm}}^{\mathrm{-}1}.$ Since the RBM frequency turns out to scale with $1/R$ the calculations also allow one to evaluate the frequency of this mode for tubes with arbitrary chirality.

Photoselective resonance Raman scattering from laser ablation grown single-wall carbon nanotubes is demonstrated to be consistent with a response from tubes with all geometrically allowed helicities. This information is drawn from an analysis of the resonance scattering by combining ab initio calculations for the mode frequencies with evaluations of the resonance cross sections for isolated tubes. The resonance excitation was found to exhibit an oscillatory behavior. To match the experiments and the calculations, the frequencies obtained from the latter must be up-shifted by $8.5\%$ on the average. This stiffening is ascribed to the tube-tube interaction in the carbon nanotube bundles.

We review the key aspects of Raman spectroscopy of graphite and graphene, focusing on the double resonant Raman modes such as the D, D* (also known as G' or 2D), and D' bands. We discuss the practical significance of Raman spectroscopy for the study of single‐ and multi‐layer graphene.