We present the results of room-and low-temperature measurements of second-order Raman scattering for perfect GaN and AlN crystals as well as the Raman-scattering data for strongly disordered samples. A complete group-theory analysis of phonon symmetry throughout the Brillouin zone and symmetry behavior of phonon branches, including the analysis of critical points, has been performed. The combined treatment of these results and the lattice dynamical calculations based on the phenomenological interatomic potential model allowed us to obtain the reliable data on the phonon dispersion curves and phonon density-of-states functions in bulk GaN and AlN. ͓S0163-1829͑98͒06840-4͔

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We report the results of experimental and theoretical studies of phonon modes in GaN/AlN superlattices (SLs) with a period of several atomic layers, grown by submonolayer digital plasma-assisted molecular-beam epitaxy, which have a great potential for use in quantum and stress engineering. Using detailed group-theoretical analysis, the genesis of the SL vibrational modes from the modes of bulk AlN and GaN crystals is established. Ab initio calculations in the framework of the density functional theory, aimed at studying the phonon states, are performed for SLs with both equal and unequal layer thicknesses. The frequencies of the vibrational modes are calculated, and atomic displacement patterns are obtained. Raman spectra are calculated and compared with the experimental ones. The results of the ab initio calculations are in good agreement with the experimental Raman spectra and the results of the group-theoretical analysis. As a result of comprehensive studies, the correlations between the parameters of acoustic and optical phonons and the structure of SLs are obtained. This opens up new possibilities for the analysis of the structural characteristics of short-period GaN/AlN SLs using Raman spectroscopy. The results obtained can be used to optimize the growth technologies aimed to form structurally perfect short-period GaN/AlN SLs.

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Using the method of induced band representations of space groups, we have performed a complete group-theory analysis of electron state symmetries in superlattices grown along the [001] direction. The spin - orbit interaction has been taken into account. The selection rules for both direct and phonon-assisted optical transitions have been derived. Using both the results of our group-theory analysis and data on the various electronic-structure calculations which have appeared in the literature, we predict some variations in the optical transitions when m and/or n are varied. We also propose optical experiments to decide among the numerous and sometimes contradictory results of those band calculations.

A group‐theory analysis of temperature‐induced phase transitions in ZrO2 has been performed in the framework of the group–subgroup relationship tree (Bärnighausen tree) with the computer tools of the Bilbao Crystallographic Server. The transition paths including symmetry‐allowed intermediate phases have been established. The active irreducible representations corresponding to soft phonon modes and spontaneous deformation strains responsible for the phase transitions have been determined. The phonon mode frequencies at the symmetry points of the Brillouin zones of cubic, tetragonal and monoclinic phases have been calculated using the ab initio density functional theory method. As a result, the soft modes and their symmetries have been revealed, which are in a complete agreement with the group‐theoretical predictions.