Lattice dynamics of K2NaAlF6, K3AlF6, and Na3AlF6 crystals with the elpasolite structure

This paper presents the results of a nonempirical calculation of the static and dynamic properties of K 2 NaAlF 6 , K 3 AlF 6 , and Na 3 AlF 6 crystals with the elpasolite structure. The calculation is based on a microscopic model of an ionic crystal that allows for the deformability and polarizability of the ions. The deformability parameters of the ions are determined by minimizing the total energy of the crystal. The total energy is regarded as a functional of the electron density, using the local Thomas-Fermi approximation and taking into account exchange (correlation) effects. The results of the calculations of the equilibrium lattice parameters and of the permittivities are in good agreement with the experimental data. Unstable vibrational modes are found in the spectrum of the lattice vibrations, with these modes occupying the phase space in the entire Brillouin zone.