Application of the sublattice method to the investigation of phonon spectra and frequency density of fluorite-structure crystals

Phonon spectra and state densities of MeF₂ (Me = Ca, Sr, Cd, Ba, or Pb) crystals are calculated in the basis of sublattice state vectors using the Born–Mayer model. The phonon spectra and the sublattice state densities are calculated in the field of the second frozen sublattice. It is demonstrated that optical crystal branches are mainly due to oscillations of fluorine ions; moreover, the topology of optical branches in the spectrum and the crystal state densities are close to the topology of the spectra and state densities of the fluorine sublattice in the frozen metal sublattice. Exception is CaF₂ whose ion and cation masses are close in values.     

Electronic Structure of Alkali Metal Sulfates

A calculation of the band structure, state density, valence and difference densities of Na₂SO₄, LiKSO₄, NaKSO₄ is carried out within the framework of the theory of local electron density by the pseudo-potential method based on numerical sp ³ d ⁵- pseudo-orbitals. The absorption edge of these crystals is found to be circuitous. The partial composition of the valence band is analyzed, and the contribution from non-equivalent oxygen atoms in individual sub-bands is revealed to be different. The band structure of LiKSO₄ is shown to essentially differ from that of Na₂SO₄ and NaKSO₄ in the number of isolated band bunches and state density structure. It is shown that the polarizing effects of cations on anions gives rise to considerable changes in electric charge distribution, which, in particular, results in the formation of a tetrahedral complex LiO₄.