Dinámica de redes y el modelo del ión rígido en cristales del tipo R2MX6

Abstract

The theory of lattice dynamics in the harmonic approximation and the Born and Huang's rigid-ion model are used to study ionic crystals of R2MX6 type with antifluorite structure. The rigid-ion model expresses the potential energy as the sum of long-range coulomb interactions and repulsive short-range interactions between ions in the unitary cell. A function of axially symmetric type is used to approximate the short-range part; the number of force constants arising were reduced by working out the stability conditions according to Katiyar. The remainder constants were determined by a nonlinear least-squares analysis of some experimental frequencies in the critical point. The long-range contributions were calculated by using the Ewald transformation and the method described by Cowley. The phonon frequencies and the normal modes of vibrations in the zone-center were obtained; of particular interest was the resulting lowest librational frequency for each crystal. Excellent concordance between the calculated and observed frequencies was obtained. The resulting effective charge parameters indicate that these crystals are partially ionic. In general, the results offer a better understanding of the possible structural phase transition mechanism involving the rotational mode T1g. In this paper we make a theoretical study of crystals K2SnCl6, K2PtBr6, Cs2SnBr6, Rb2SnCl6, Cs2TeCl6, and Rb2SnBr6 in the cubic phase.