Investigation of the Soft Mode of SbSBr_xI_1−x Crystals

Abstract

The behaviour of the potential energy V(z) of the B _1u (A ₁ ) symmetry soft mode vibrations of atoms in the direction of the z(c) axis of SbSBr_xI _1−x crystals (x = 0, 0.2, 0.75, 1) upon the normal coordinate (relative displacements of atoms) was investigated in the region of the phase transition temperatures. For this B _1u (A ₁ ) symmetry soft mode, the potential energy barrier height ΔV, the potential energy V(z), its harmonic and anharmonic terms were studied as functions of the mixture composition x and temperature T. The dependence of the soft mode frequency ω_S upon the composition x and temperature has been established assuming the double-well shape of the potential energy (per atom) V(z). By employing A _1u (A ₂ ) symmetry coordinates, the force constants C of interaction between molecular chains have been obtained. The type of the phase transition has been established by calculating the Rhodes–Wohlfarth factor R. To calculate this factor, the ratio /ΔV depending upon the mixture composition was employed. It has been found that for mixed crystals with x < 0.8, the phase transition is intermediate between order–disorder and displacive types, and for crystals with x > 0.8, the phase transition is of displacive type.

Keywords:

• SbSI
• SbSBr
• SbSBr _x I_1−x
• potential energy
• soft mode
• phase transition
• semiconductors ferroelectrics

Acknowledgements

This work was supported, in part, by a grant from the Soros Foundation awarded by the American Physical Society.

The authors are also grateful to the anonymous referee for his comments which helped to improve this work.