Phase transitions in Sn 2 P 2 S 6 ferroelectric under high pressures

The Sn2P2S6 monoclinic crystals are proper ferroelectrics, whose unit cell parameters under standard conditions are a=9.378Å, b=7.488Å, c=6.513Å and β=91.150◦ [1]. Under atmospheric pressure p = patm a temperature increase induces a phase transition (PT) T0 = 337K into a nonpolar phase with a change of symmetry from Pc to P21/c. By means of a uniform compression (p = 180MPa) we can also realize the Sn2P2S6 crystal transition from the ferroelectric state into the paraelectric state at temperature T=296K. The investigation of the p,T -diagram of the Sn2P2S6 ferroelectric showed that an external hydrostatic pressure induces a high pressure incommensurate phase in this crystal. The multicritical point of p,T -diagram, where a splitting of the commensurate p,T -line T0(p) into a line Ti(p) and a line Tc(p) bordering the incommensurate phase region occurs, is the Lifshitz point. For the purpose of further PT and critical behaviour investigation of Sn2P2S6 crystal in the vicinity of Lifshitz point, induced by external pressure, we have made pressure behaviour studies and analysis of pressure dependencies for linear and volume compressibilities in the present paper. The linear compressibilities under uniform compression were determined by the experimental pressure dependencies of the linear deformations, which were obtained by means of optical interference technique [3] proposed previously. In this case, the directions of measurements coincided with crystallographic directions [100], [010], and [001]. The test specimens for experiments were prepared from Sn2P2S6 crystals grown by Bridgeman method. The studies were performed in an optical pres-

The Sn 2 P 2 S 6 monoclinic crystals are proper ferroelectrics, whose unit cell parameters under standard conditions are a=9.378Å, b=7.488Å, c=6.513Å and β=91.150• [1].Under atmospheric pressure p = p atm a temperature increase induces a phase transition (PT) T 0 = 337K into a nonpolar phase with a change of symmetry from P c to P 2 1 /c.By means of a uniform compression (p = 180MPa) we can also realize the Sn 2 P 2 S 6 crystal transition from the ferroelectric state into the paraelectric state at temperature T=296K.
The investigation of the p,T -diagram of the Sn 2 P 2 S 6 ferroelectric showed that an external hydrostatic pressure induces a high pressure incommensurate phase in this crystal.The multicritical point of p,T -diagram, where a splitting of the commensurate p,T -line T 0 (p) into a line T i (p) and a line T c (p) bordering the incommensurate phase region occurs, is the Lifshitz point.
For the purpose of further PT and critical behaviour investigation of Sn 2 P 2 S 6 crystal in the vicinity of Lifshitz point, induced by external pressure, we have made pressure behaviour studies and analysis of pressure dependencies for linear and volume compressibilities in the present paper.
The linear compressibilities under uniform compression were determined by the experimental pressure dependencies of the linear deformations, which were obtained by means of optical interference technique [3] proposed previously.In this case, the directions of measurements coincided with crystallographic directions [100], [010], and [001].The test specimens for experiments were prepared from Sn 2 P 2 S 6 crystals grown by Bridgeman method.The studies were performed in an optical pres- sure chamber.The pressure measurement was taken by mechanical and manganin manometers with an accuracy of ±5MPa and temperature was taken by a copperconstantan thermocouple with an accuracy of ±0.1K.
In figure 1 the pressure dependencies for linear compressibilities of Sn 2 P 2 S 6 crystal are shown in various crystallographic directions.It can be seen, that in the vicinity of the PT (p=180Mpa) an anomalous behaviour of linear compressibility occurs for all three directions.The change of the χ [100] and χ [010] values at the PT is more significant, than χ [100] change.This is in agreement with the results of a dilatometric investigation of the temperature expansion coefficient of Sn 2 P 2 S 6 crystals [4] and points to the fact; that the basic structural changes at the PT take place along the crystallographic directions [100] and [010].This PT may be connected with synphase and antisynphase shifts of Sn +2 ferroactive cation.In the paraelectric phase further away from the PT the χ [100] value is closer to the χ [001] value than the χ [010] value.For the [010] direction one observes the smallest value of the thermal conductivity coefficient [5] and the linear thermal expansion coefficient [4].The anomalous part of the compressibility in the ferroelectric phase χ an = χ − χ reg (χ reg is the χ value in paraelectric phase) reveals that at p = p atm the values obey χ an [100] > χ an [100] = 0 and χ an [010] = 0.In figure 2 the pressure dependence of the volume compressibility of the Sn 2 P 2 S 6 crystal at T = 296K are given.In the insert the critical index dependence α cr of ln(τ ) (where α cr = (p − p o )/p o ) is given which characterizes an anomalous behaviour of the volume compressibility in the vicinity of the PT (p = p atm ).For −2 < ln(τ ) < 0 the α cr is close to the value of 0.30 + 0.03, which is characteristic to the Lifshitz point.With further decreasing τ the α cr value monotonically decreases to 0.20.Such a dependence of the α cr is, probably, connected with the transition from multicritical to critical behaviour.Using the results of investigations obtained for linear compressibilities of Sn 2 P 2 S 6 crystal and s 11 , s 22 , s 33 compliances values [6], the shearing components of s 11 , s In figure 3 the pressure dependencies of the χ [100] linear compressibility at different temperatures are given.These results enabled us to study the transformation of the χ(p) dependencies along the p,T -diagram.For temperatures T < 296 K the χ(p) behaviour is different from similar dependencies obtained at T > 296 K. Thus, at T = 272K the two PT, namely p c and p i , with the pressure range of ∆p = 11.6 MPa are revealed which limit the region of the incommensurate phase.With the further temperature decreasing the p c − p i pressure width increases (at T = 274.5K ∆p = 21.6 MPa).The values of p c and p i pressures at different temperatures are in good agreement with the p,T phase diagram of Sn 2 P 2 S 6 crystal (figure 3) based on the complex optical, dielectric and pyroelectric studies.For curves 4-6 in comparison with curves 1-3 (figure 3) in the pc region (ferroelectric-incommensurate phases) the maximum value of isothermic compressibility χ max increases and the pressure width of an anomalous behaviour of the χ(p) in the vicinity of the PT simultaneously decreases which is explained by the first-order character of this PT.
The PT in proper Sn 2 P 2 S 6 ferroelectric in the liquid-like crystal model approximation at one-dimensional modulation in the incommensurate phase may be described by the density expansion of the thermodynamic potential Φ in the order  parameter η = P s with the account of its spacious derivatives: where α = α 0 (T − T 0 ), β, γ, δ and g are the expansions coefficients which are generally pressure-dependent.The value α 0 = 1/ε 0 C w value, where C w -Curie-Weiss constant.
For second-order PT, that is the PT at p 0 and p i , by the ∆χ V compressibility jump and the known of α 0 , dT 0 /dp and dT i /dp and by using a common relation one may define the β coefficient in the thermodynamic potential expansion (1).In figure 4  The experimental behaviour of α 0 [9] testifies to the enhancement of ferroactive normal mode unharmonicity with approaching the Lifshitz point.The ∆ jump in the change of β in this point confirms the results of theoretical investigations [10].Thus, considering (1), and taking into account its elastic part and an additional higherorder term in the form of ( λ 2 )η 2 η′ 2 it has been shown that between homogeneous and inhomogeneous deformations the "gap" ∆ is formed, conditioned by long-range elastic forces.
So, the dilatometric investigations of the PT in Sn 2 P 2 S 6 crystal carried out at high pressures enabled us to define the change of the coefficients in the expansion of the thermodynamic potential and critical compressibility index in the vicinity of the Lifshitz point along the PT-diagram.

Figure 2 .
Figure 2. The pressure dependencies of ∆V /V value (1) and χ(p) volume compressibility (2) of the Sn 2 P 2 S 6 crystal at T = 296K (in the insert -the pressure dependencies of α cr critical compressibility index).
the pressure dependencies of ∆χ V , α 0 , β values along the p,T-diagram are shown.At the pressure p L = 180 MPa corresponding to the Lifshitz point in the p,Tdiagram an anomalous character of all three indicated values occurs.Thus, in the point of line splitting for continuous phase transitions T 0 (p) at p = p L = 180 MPa the α 0 value is the maximum value.The β > 0 coefficient undergoes a jump equal to ∆ ≈ 2.2 • 10 8 Jm 5 /Cl 4 .According to [8], under the given pressure the δ coefficient tends to 0, and the values of γ and g in the expansion (1) are practically not pressuredependent (γ ≈ 3.5 • 10 10 Jm 9 /Cl 6 , g = 2.2 • 10 −27 Jm 5 /Cl 2 ).