Valence fluctuations in Sn(Pb)₂P₂S₆ ferroelectrics

Abstract

The valence fluctuations which are related to the charge disproportionation of phosphorous ions P⁴⁺+P⁴⁺→P³⁺+P⁺⁵ are the origin of ferroelectric and quantum paraelectric states in Sn(Pb)₂P₂S₆ semiconductors. They involve recharging of SnPS ₃ or PbPS ₃ structural groups which can be represented as half-filled sites in the crystal lattice. Temperature–pressure phase diagram for Sn ₂P ₂S ₆ compound and temperature-composition phase diagram for (Pb ySn ₁– y) ₂P ₂S ₆ mixed crystals, which include tricritical points and where a temperature of phase transitions decrease to 0 K, together with the data about some softening of low energy optic phonons and rise of dielectric susceptibility at cooling in quantum paraelectric state of Pb₂P₂S₆ are analyzed by GGA electron and phonon calculations and compared with electronic correlations models. The anharmonic quantum oscillators model is developed for description of phase diagrams and temperature dependence of dielectric susceptibility.