The phonon spectra of calcium, strontium, barium, radium, cadmium, zinc, magnesium, germanium, tin, and lead titanates with the perovskite structure are calculated from first principles within the density functional theory. By analyzing the unstable modes in the phonon spectra, the possible lattice distortions are determined and the energies of the corresponding phases are calculated. From analyzing the phonon spectra, force constants, and eigenvectors of TO phonons, a conclusion is drawn on the origin of the ferroelectricity in considered crystals. It is shown that the main factors determining the possible off-centering of atoms in the A position are the geometric size and electronic configuration of these atoms.

Phonon spectra of CdSe nanoplatelets (2-6 ML) with the zinc-blende structure were calculated from first principles within the density-functional theory. It turned out that the Lamb modes in nanoplatelets are in fact optical rather than acoustic vibrations. Phonon spectra of the nanoplatelets show the appearance of a large number of low-frequency modes inherited from TA phonons in bulk CdSe. Calculations of the Raman spectra indicate a need to revise the interpretation of available experimental data. The largest contribution to the Raman spectra is provided by the quasi-Lamb modes with the A1 symmetry. The B2 modes whose frequencies depend on the environment of nanoplatelets and whose properties are closest to the properties of LO phonons explain the results obtained in the "nanoparticle-on-mirror" geometry. The features in Raman spectra previously attributed to surface optical (SO) modes should be interpreted as a manifestation of lower-order quasi-Lamb A1 modes. Calculations of the infrared spectra find, in addition to the TO phonon line, the appearance of intense lines from surface modes originating from terminating F(Cl) atoms on the surface of nanoplatelets and true SO-modes.

Semiconductor nanoparticles of cadmium chalcogenides are known to exhibit pronounced thickness-dependent E0 series of exciton transitions at the Γ point of the Brillouin zone (BZ). In this work, we report an experimental evidence for high-energy series of exciton transitions, which originates from BZ points different from the Γ point, in the family of cadmium chalcogenide quasi-2D nanoplatelets (NPLs). Intensive UV absorption bands demonstrating a pronounced size effect are observed for CdTe, CdSe, and CdS NPLs in addition to the E0 exciton bands in the visible region. These new bands are attributed to transitions analogous to the E1, E1 + ∆1, and E2 series observed in bulk crystals. First-principles DFT calculations of the electronic structure and absorption spectra support this explanation and show that the main contribution to these optical transitions comes from X and M points of the 2D BZ, which originate from L and X points of the 3D BZ. At the same time, the E0 series of transitions at the Γ point is well described by the multiband effective-mass model. The observation of the UV exciton bands reveals tunable optical properties of cadmium chalcogenide NPLs in UV spectral region, which may be interesting for practical applications.

Phonon spectrum of cubic barium zirconate is calculated from first principles using the density functional theory. Unstable phonon mode with the R25 symmetry in the phonon spectrum indicates an instability of the cubic structure with respect to rotations of the oxygen octahedra. It is shown that the ground-state structure of the crystal is I4/mcm. In order to find the manifestations of the predicted instability, EXAFS measurements at the Ba LIII-edge are used to study the local structure of BaZrO3 at 300 K. An enhanced value of the Debye-Waller factor for the Ba-O atomic pair (σ 2 1 ∼ 0.015Å2 ) revealed in the experiment is associated with the predicted structural instability. The average amplitude of the thermal octahedra rotation estimated from the measured σ 2 1 value is ∼4 degrees at 300 K. The closeness of the calculated energies of different distorted phases resulting from the condensation of the R25 mode suggests a possible structural glass formation in BaZrO3 when lowering temperature, which explains the cause of the discrepancy between the calculations and experiment.

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The vibrational spectroscopy of semiconductor nanostructures can provide important information on their structure. In this work, experimental Raman and infrared spectra are compared with vibrational spectra of CdSe/CdS core/shell nanoplatelets calculated from first principles using the density functional theory. The calculations confirm the two-mode behavior of phonon spectra of nanostructures. An analysis of the experimental spectra reveals the absence of modes with a high amplitude of vibrations of surface atoms, which indicates their strong damping. Taking into account the difference in the damping of different modes and their calculated intensities, all bands in the spectra are unambiguously identified. It is found that the frequencies of longitudinal optical modes in heterostructures are close to the frequencies of LO phonons in bulk strained constituents, whereas the frequencies of transverse modes can differ significantly from those of the corresponding TO phonons. It is shown that an anomalous thickness dependence of CdS TO mode is due to a noticeable surface relaxation of the outer Cd layer in the nanostructure.

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