We study the acoustic-phonon transmission spectra in periodic and quasiperiodic (Fibonacci type) superlattices made up from the III-V nitride materials AlN and GaN. The phonon dynamics is described by a coupled elastic and electromagnetic equations within the static field approximation model, stressing the importance of the piezoelectric polarization field in a strained condition. We use a transfermatrix treatment to simplify the algebra, which would be otherwise quite complicated, allowing a neat analytical expressions for the phonon transmission coefficients. Numerical results, for the normal incidence case, show a strike self-similar pattern for both hexagonal (class 6 mm) and cubic symmetries crystalizations of the nitrides.

CdSnO(3) ilmenite and perovskite crystals were investigated using both the local density and generalized gradient approximations, LDA and GGA, respectively, of the density functional theory (DFT). The electronic band structures, densities of states, dielectric functions, optical absorption and reflectivity spectra related to electronic transitions were obtained, as well as the infrared absorption spectra after computing the vibrational modes of the crystals at q = 0. Dielectric optical permittivities and polarizabilities at ω = 0 and ∞ were also calculated. The results show that GGA-optimized geometries are more accurate than LDA ones, and the Kohn-Sham band structures obtained for the CdSnO(3) polymorphs confirm that ilmenite has an indirect band gap, while perovskite has a direct band gap, both being semiconductors. Effective masses for both crystals are obtained for the first time, being highly isotropic for electrons and anisotropic for holes. The optical properties reveal a very small degree of anisotropy of both crystals with respect to different polarization planes of incident light. The phonon calculation at q = 0 for perovskite CdSnO(3) does not show any imaginary frequencies, in contrast to a previous report suggesting the existence of a more stable crystal of perovskite CdSnO(3) with ferroelectric properties.

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