Monte-Carlo simulation of the phase diagrams in Ising model of [Sn(Pb)]2P2[S(Se)]6 crystals

In Sn2P2S6 crystals ferroelectric second order phase transition (PT) occurs. In this case the number of formula units in elementary cell stays unchanged. In Sn2P2Se6 crystals the intermediate incommensurate phase exists. A dipole Ising model of Sn2P2[S(Se)]6 ferroelectrics has been developed. To consider the dipole long-range interaction around the dipole an area of simple form is singled out. Within this area the interaction between the dipoles is calculated precisely. The interaction with the other dipoles is considered by introduction of a local field. For better accordance with the real experiment an amendment on the short-range interaction with two nearest neighbours has been introduced. As a result of calculations made by Monte-Carlo method it has been found that when a certain short-range interaction coefficient in Sn2P2S6 is selected the intermediate modulated phase disappears. In this case the temperatures of PTs are as follows: for Sn2P2S6 model T*o ∼ 10.3; for Sn2P2Se6 model T*c ∼ 8.7, T*i ∼ 9.7 (in the effective temperatures). These data are in satisfactory agreement with the results of the real experiment. The concentration dependences of temperatures of PTs in Sn2P2(SxSe1-x)6 crystals are simulated and the Lifshitz point was observed. In mixed (PbySn1-y)2P2S6 and (PbySn1-y)2 P2Se6 crystals increase of Pb concentration causes reduction of temperatures of PTs to 0K. In this case the character of PTs stays unchanged. By the method of diluted Ising lattice the concentration dependences of temperatures of PTs in this crystals are simulated.

Keywords:

• Sn₂P₂[S(Se)]₆
• (Pb _y Sn_1-y)₂P₂[S(Se)]₆
• ferroelectrics
• phase transition
• Monte-Carlo procedure
• Ising lattice