Lattice dynamics, structural stability, and phase transitions in incommensurate and commensurateA2BX4

Abstract

Numerous materials with the general formula A2BX4, where A and B are cations and X is the anion, are isomorphous to Il-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. K&Se04 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, R12Se04, Cs2Se04, Cs2ZnC14, Cs2ZnBr4, K2Cr04, K2Se04, K~ZnC14, Rb&ZnC14, and Rb~ZnBr4, 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 X2 phonon branch with a minimum close to -, ' a*. 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 X3 X2 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.

Size criterion for amorphization of molecular ionic solids

“…This view is consistent with the explanation provided for the incommensurate lattice instabil- ity exhibited by several of these compounds at ambient pressure. [13][14][15]26 It was found that the presence of large anionic BX 4 groups in relation to the size of the A cations induces increased stresses in the backbone lattice resulting in an incommensurate modulation and strict loss of translational periodicity along a particular crystallographic axis.…”

“…They consist of anionic BX 4 tetrahedral groups which are separated from each other by interstitial A cations. [11][12][13][14][15][16] The essential way in which these systems differ from each other is via the ratios of the sizes of the anionic BX 4 tetrahedral units to that of their interstitial A cations (ZnCl 4 /K ϩ ϭ1.69, ZnBr 4 / Rb ϩ ϭ1.62, ZnCl 4 /Rb ϩ ϭ1.52, ZnBr 4 /Cs ϩ ϭ1.43, ZnCl 4 /Cs ϩ ϭ1.35, SeO 4 /K ϩ ϭ1.23). Therefore we can directly examine the importance of this size ratio in influencing crystalline to noncrystalline transitions within this family.…”

Disorder in the Crystal Structure of Cs2HgCl4 Studied by the Maximum Entropy Method

“…Experimentally, a softening of the optic phonon branch with AE 2 symmetry has been found in K 2 SeO 4 . Landau theory did lead to a symmetry of the a* modulation equal to the AE 2 normal mode also and the superstructures of Rb 2 ZnCl 4 , Rb 2 ZnBr 4 and K 2 ZnCl 4 have been found to form according to this mode (Etxebarria et al, 1992).…”

Long-range order in the high-temperature phase ofK2ZnCl4

“…24,25 This size criterion should also be responsible for the existence of the incommensurate lattice instability in the A 2 BX 4 compounds. This phenomenon is in agreement with the hypothesis that the ordered phase is due to the softening of modes that were soft in the prototypic hexagonal high-temperature phase.…”