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We perform transmission electron microscopy, electron diffraction, and Raman scattering experiments on an individual suspended double-walled carbon nanotube (DWCNT). The first two techniques allow the unambiguous determination of the DWCNT structure: (12,8)@(16,14). However, the low-frequency features in the Raman spectra cannot be connected to the derived layer diameters d by means of the 1/d power law, widely used for the diameter dependence of the radial-breathing mode of single-walled nanotubes. We discuss this disagreement in terms of mechanical coupling between the layers of the DWCNT, which results in collective vibrational modes. Theoretical predictions for the breathing-like modes of the DWCNT, originating from the radial-breathing modes of the layers, are in a very good agreement with the observed Raman spectra. Moreover, the mechanical coupling qualitatively explains the observation of Raman lines of breathing-like modes, whenever only one of the layers is in resonance with the laser energy.

Lattice dynamics for five ordered PbMg 1/3 Nb 2/3 O3 supercells were calculated from first principles by the frozen phonon method. Maximal symmetries of all supercells are reduced by structural instabilities. Lattice modes corresponding to these instabilities, equilibrium ionic positions, and infrared reflectivity spectra were computed for all supercells. Results are compared with our experimental data for a chemically disordered PMN single crystal.states (GS) with symmetries that are lower than those dictated by chemical ordering]. ( 2) to compute the lattice dynamics for the same set of ordered PMN supercells, and to compare the results with experimental data, e.g. by comparing simulated IR reflectivity spectra with the experimental one. The goal is to find which ordered supercell most closely approximates the experimental case of local 1:1 order.

Raman spectra of sodium niobate (NaNbO 3 ) were obtained in all phases and revealed a significant disorder in the high-temperature U, T2 and T1 phases and a complicated folding of the Brillouin zone at the transitions into modulated S, R, P and N phases associated with the competitive zone-boundary soft modes (in-phase and out-of phase octahedral tilts) along the M-T-R line. An extensive Raman study combined with x-ray diffraction (XRD) and dielectric measurements confirmed the presence of the incommensurate (INC) phase in sodium niobate. XRD experiments revealed the invar effect in the temperature interval 410-460 K corresponding to the INC phase associated with rotations of the NbO 6 octahedra modulated along the b-direction. Our experiments suggest that the phase P consists of three phases: monoclinic (P m ) between 250 and 410 K, INC between 410 and 460 K, and orthorhombic (P o ) between 460 and 633 K. At the low-temperature transition to the ferroelectric rhombohedral N phase all folded modes originating from the M-and T-points of the Brillouin zone abruptly disappear, Raman spectra in the N phase become much simpler and all peaks were assigned.

We develop a phenomenological thermodynamic theory of ferroelectric BaTiO3 (BT) thin films epitaxially grown on cubic substrates using the Landau-Devonshire eight-order potential. The constructed "misfit-temperature" phase diagram is asymmetrical. We found that, overall view of the phase diagram depends on the values of compliances used in calculations and provide two qualitatively different diagrams. A thermodynamic path for BT film grown onto a particular substrate can be found using a plot of the room-temperature tetragonal distortion (c − a)/a as a function of misfit strain.