LATTICE-DYNAMICS, STRUCTURAL STABILITY, AND PHASE-TRANSITIONS IN INCOMMENSURATE AND COMMENSURATE A2BX4 MATERIALS

Numerous materials with the general formula A 2BX4, where A and B are cations and X is the anion, are isomorphous to beta-K2SO4 (space group Pnam) at high temperatures. A considerable number of them exhibit a structural instability leading to an incommensurately modulated phase with identical superspace symmetry. K2SeO4 is the archetypical example. From the analysis of the incommensurate structures, the polarization vector of the unstable frozen mode can be determined, being similar in all investigated compounds. We report here a comparative energetic study and lattice-dynamics analysis of a set of compounds in this family. The set of materials K2SO4, Rb2SeO4, CS2SeO4, CS2ZnCl4, CS2ZnBr4, K2CrO4, K2SeO4, K2ZnCl4, Rb2ZnCl4, and Rb2ZnBr4, includes compounds with and without an incommensurate phase. An empirical rigid-ion force model has been used with only three adjustable parameters, the tetrahedral BX4 groups being reduced to rigid bodies. The adjusted force model, optimized for each compound with use of only static structural data, is sufficient to explain the eventual presence of an incommensurate lattice instability at lower temperatures. The calculated phonon dispersion curves of those compounds with an incommensurate phase include an unstable SIGMA-2 phonon branch with a minimum close to 1/3a*. In the simulations, the unstable or soft-mode branch is always an optical branch in the extended zone scheme or the consequence of an anticrossing of an optical branch with the SIGMA-3-SIGMA-2 acoustic branch; this result discredits any attempt to explain the soft-mode mechanism in terms of a one-dimensional model with an acoustic soft branch. The polarization vectors of the soft or unstable modes obtained in the simulations fairly agree with the experimental ones. They are rather insensitive to the details of the interactions, explaining their strong similarities. On the other hand, the form of the soft branch depends strongly on the material, and clearly distinguishes those materials having the BX4 groups disordered in the normal phase, from those having a soft-mode mechanism. The simulations indicate that the static and dynamic features of potassium chromate are similar to those of potassium selenate, raising the possibility that potassium chromate could exhibit a similar mode softening at low temperatures. The existence of an incommensurate lattice instability in these compounds depends basically on the effective volume of the A cations compared with the size of the BX4 tetrahedra. The charge distribution within the tetrahedral anion groups also plays a significant secondary role; smaller values of the charge of B tend to stabilize the Pnam structure. The static energy of some of the compounds has been investigated in a restricted configuration subspace, which includes the order-parameter distortion. The energy maps obtained show a clear "multiple-well" structure, that can be quantitatively related with the transition temperatures by means of a local-mode model.