DISORDER AND MODULATIONS IN CRYSTAL CS₂HGCL₄

B. Sh. Bagautdinov¹, I. D. Brown², J. Luedecke³, M. Schneider³, Sander van Smaalen³, M. S. Novikova⁴

¹ Institute of Solid State Physics, Russian Academy of the Sciences, Chernogolovka, Moscow district, Russia.
² Institute for Materials Research, McMaster University, Hamilton, Canada.
³ Laboratory of Crystallography, University of Bayreuth, Bayreuth, Germany.
⁴ Institute of Crystallography RAS, Moscow

Keywords: incommensurate crystals, maximum entropy method

Cs₂HgCl₄ belongs to the family of A₂BX₄ compounds and, like many of them, shows ferroelectric and ferroelastic phase transitions at cooling [1]. The high resolution x-ray diffraction study of Cs₂HgCl₄ in the range 4.2-300K shows the series phase transitions with incommensurately and commensurately forms of modulation, first, along the pseudohexagonal a* axis, and then along c* axis (Pnma setting) :

normal Pnma

incommensurate q = (1/5 + d)a* ( 221 - 195K )
commensurate q = 1/5 a* ( 195 - 178K )
commensurate q = 1/3 c* ( 185.2 - 179K)
incommensurate q= (1/5 + d)c* ( 179 - 172 K )
commensurate q = 1/5 c* ( 172 - 163 K )
commensurate q = 1/2 c* ( 163 - 4.2 K )

To find the correlation of the low temperature modulations with features of prototype structure the accurate structural determinations of the normal Pnma at room temperature and commensurate ferroelectric q=1/5a* (187K) phases are performed using laboratory X-ray (Nonius-Mach3-CAD4 diffractometer) and DESY synchrotron radiation, respectively.

The data were processed in both ordinary and superspace group formlism in frame of the program system JANA. The structure models are analyzed by the Bond-Valence Method and Maximum Entropy Method.

Like many b-K2SO4 -type structure Cs₂HgCl₄ exhibits large amplitude anharmonic displacements at room temperature. For study of the disorder the Maximum Entropy Method applied to the Bragg intensity data.

Applying this metod allows to show that the atoms which involved in unphysically short distances exhibit strong anharmonic displacements out of the mirror plane. The relation between the soft phonons at room temperature and the static modulations at low tempeatures is found.

1. Dmitriev V.P Yuzyuk Yu.I., et al. Sov. Phys. Solid State (1988) 30, 704.