Statistical theory for ferroelectrics based on triple well anharmonic potential was used for the case of structural second order phase transition in Sn 2 P 2 S 6 crystals. Parameters of effective Hamiltonian of the model were estimated using available experimental data. These findings confirm the assumption that the phase transition in these crystals is located in crossover region between order-disorder and displacive type, and very closely to tricritical point.
The paper presents the X-ray photoelectron spectra (XPS) of the valence band (VB) and of the core levels (CL) of uniaxial ferroelectric Sn 2 P 2 S 6 single crystals from different crystallographic planes in both paraelectric and ferroelectric phases. The XPS were measured with monochromatized Al Kα radiation in the energy range 0-1400 eV. The VB consists of five bands with the maxima between 3.3 eV and 14.5 eV below the Fermi level. Experimental energies of the VB and core levels are compared with the results of theoretical ab initio calculations of the molecular model of the Sn 2 P 2 S 6 crystal. The electronic structure of the VB is revealed. Ferroelectric phase transition changes the atom's charge and strength of the bonds, electronic structure of VB, width of CL lines and chemical shifts for the Sn, P and S states which are crystallographic plane-dependent.
A temperature dependence of hypersound velocities at transition from a paraelectric phase to ferroelectric phase in Sn 2 P 2 S 6 crystals was investigated by Brillouin scattering spectroscopy. Based on these data, full set of elastic constants was determined. Similar measurements were also performed for Sn 2 P 2 (Se 0.28 S 0.72 ) 6 mixed crystals in the paraelectric phase near a Lifshitz point. The sound velocity indicatrices' evolution at transition from Sn 2 P 2 S 6 to Sn 2 P 2 (Se 0.28 S 0.72 ) 6 was observed and softening of transverse acoustic phonons in the paraelectric phase near the Lifshitz point was found. An instability of the acoustic phonons is induced by an interaction with a soft optic mode which is the origin of an incommensurate phase appearance in mixed crystals Sn 2 P 2 (Se x S 1−x ) 6 with x > x LP = 0.28.
Polarizable ion model was used in describing the lattice dynamics in the Sn 2 P 2 S 6 and Sn 2 P 2 Se 6 ferroelectric crystals and their solid solutions. There has been obtained a good agreement of the calculated phonon spectra with the experimental data of Raman and Brillouin spectroscopies, neutron scattering and ultrasound experiments. Paraelectric phase instability has been modelled by negative charge transferring from the tin cations to the chalcogen ions, and by increasing the polarizabilities of the latter. The ferroelectric phase has been stabilized by tin atom displacement from centrosymmetric positions and a partial reversal recharging between tin and chalcogen ions. The effective charges decreasing by moving from Sn 2 P 2 S 6 to Sn 2 P 2 Se 6 compounds determine the shift of condensation wave vector of soft optic phonons in paraelectric phase from q = 0 in sulfur compound to q > 0 in selenium compound. Such a change of dynamical instability character is connected with the appearance of incommensurate phase in Sn 2 P 2 (SexS 1−x ) 6 solid solution under x > 0.28. The "two-mode" instability emerged as possible in the vicinity of Lifshitz point -there have been modelled the condensation of soft optic mode with q ≈ 0 and mixed optic and transversal acoustic phonons near q > 0. This fact requires further experimental and theoretical investigations.
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