Incommensurate Structural Instability and Lattice Dynamics of A2BX4 Materials

Abstract

Some isomorhous materials of the type A2BX4 (K2SeO4 being the archetypical example) exhibit a structural instability leading to an incommensurate phase with common superspace symmetry. A clear soft-mode mechanism has only been observed in potassium selenate, other compounds having probably an order-disorder mechanism. From the analysis of the incommensurate structures, the eigenvector of the unstable frozen mode can be determined in each case, being similar in all investigated compounds. After revising some structural features of these materials, the results of a lattice dynamics analysis, within an empirical rigid-ion model, are reported. The model of interatomic forces used has only three adjustable parameters and was optimized using only static structural data for each compound. The tetrahedral BX4 groups are reduced to rigid bodies. The model is sufficient to reproduce the incommensurate lattice instability. The calculated eigenvectors of the soft or unstable modes fairly agree with the experimental ones, being rather unsensitive to the details of the interactions and explaining their strong similarities in most compounds. On the other hand, the form of the soft branch strongly depends on the material, and clearly distinguish those materials having the BX4 groups disordered in the normal phase, from those having a soft-mode mechanism. The results indicate that any empirical model consistent with the structural data easily reproduces the essential features of the incommensurate instability, indicating that its origin is to be directly connected with structural fearutes, the relative size of the cations playing an essential role.