Dielectric properties of CuInP 2 S 6 crystals under high pressure

Monoclinic CuInP2S6 crystals undergo a phase transition from paraelectric (C2/c) to ferrielectric (Cc) phase. The studies of ferrielectric phase transition in the layered CuInP2S6 crystals at atmospheric pressure have shown [1,2] that polarization in these crystals arises at the first-order phase transition, normally to the layers, and results from anticollinear contributions due to copper ion ordering and indium ion displacement. The sponatneous polarization value is Ps = 2.5 μC·cm . While physical properties at high hydrostatic pressures of “3–D” Sn2P2S6-type crystals have been well investigated earlier [3,4] the studies of “2–D” (layered) hypothiodiphosphates under high pressure are at the initial stage. The only paper devoted to this problem reported on a pressureinduced first-order phase transition from the monoclinic to the trigonal phase observed in CuInP2S6 crystals at p = 4.0 GPa at room temperature from Raman measurements [5]. The present paper is devoted to the study of the hydrostatic pressure effect (patm < p < 0.4 GPa) on the dielectric properties of CuInP2S6 crystals and to the determination of their (p, T ) phase diagram.


Introduction
Monoclinic CuInP 2 S 6 crystals undergo a phase transition from paraelectric (C2/c) to ferrielectric (Cc) phase.The studies of ferrielectric phase transition in the layered CuInP 2 S 6 crystals at atmospheric pressure have shown [1,2] that polarization in these crystals arises at the first-order phase transition, normally to the layers, and results from anticollinear contributions due to copper ion ordering and indium ion displacement.The sponatneous polarization value is P s = 2.5 µC•cm −2 .
While physical properties at high hydrostatic pressures of "3-D" Sn 2 P 2 S 6 -type crystals have been well investigated earlier [3,4] the studies of "2-D" (layered) hypothiodiphosphates under high pressure are at the initial stage.The only paper devoted to this problem reported on a pressureinduced first-order phase transition from the monoclinic to the trigonal phase observed in CuInP 2 S 6 crystals at p = 4.0 GPa at room temperature from Raman measurements [5].
The present paper is devoted to the study of the hydrostatic pressure effect (p atm < p < 0.4 GPa) on the dielectric properties of CuInP 2 S 6 crystals and to the determination of their (p, T ) phase diagram.

Experimental
The crystals were grown using the Bridgman techniques.The samples were the plates 0.2 to 1.6 mm thick with the silver paste or aquadag electrodes applied to their surfaces.The complex dielectric permeability was measured in the temperature range from 77 to 450 K with temperature variation rate of 1 K/min, using an AC bridge at frequencies of 1 kHz and 1 MHz.

Results and discussion
Figure 1 presents temperature dependences of dielectric permeability of CuInP 2 S 6 crystals obtained at the measuring field frequencies of 1 kHz and 1 MHz.At atmospheric pressure the maximum of dielectric permeability, corresponding to the phase transition temperature in the crystals under investigation is observed at the temperature T c ≈ 315 K.The increase of dielectric permeability at 1 kHz (curve 1 in figure 1) in the temperature range above 330 K is due to ionic conductivity of Cu atoms [1].It should be noted that for the investigated samples, a temperature hystheresis ∆T ≈ 1.7 K of the phase transition is observed.This value is much lower than those observed for CuInP 2 S 6 crystals in [1] and is in good agreement with the results of [2].The studies of dielectric properties of CuInP 2 S 6 crystals at atmospheric pressure have shown a considerable dependence of the dielectric permeability on the sample thickness.In our opinion, it can be responsible for the difference in the dielectric permeability maximum values (140 < ε max < 900) obtained by different authors [1,2].Temperature dependences of dielectric permeability of CuInP 2 S 6 crystals ware measured for the samples of the same cross-section (S ≈ 12 mm 2 ) but of different thickness.As seen in figure 2, the dielectric properties essentially depend on the crystal thickness in the whole temperature range under study.The coefficient of the dielectric permeability maximum value variation with thickness is ∂ε max /∂D = 220 mm −1 .A similar dependence of dielectric permeability on the sample thickness in the phase transition vicinity was observed earlier for a number of ferroelectrics: TGS [6], Pb 5 GeO 11 [7], Sn 2 P 2 S 6 [8].In particular, in Sn 2 P 2 S 6 crystals it is related to the existence of subsurface layers with small ε due to the presence of near-electrode spatial charges.Besides, in CuInP 2 S 6 crystals we have revealed the increase of the dielectric loss angle tangent in both phases with the decrease of the crystal sample thickness as well as the increase of the Curie-Weiss constant C W from 2 • 10 3 K to 7.5 • 10 3 K at the sample thickness increase from 0.2 to 1.6 mm.Evidently, the dependence of dielectric properties on thickness in layered CuInP 2 S 6 crystals is much more complicated than in Sn 2 P 2 S 6 and is determined by more factors, e.g. the defects in the interlayer spaces.
The results quoted below were obtained for the 1.6-mm thick CuInP 2 S 6 crystal.Figure 3 shows the temperature dependences of CuInP 2 S 6 crystal dielectric permeability obtained at the measuring field frequency f = 1 kHz.With the increase of the hydrostatic pressure the curves shift towards higher temperatures.As seen from figure 3, the pressure increase has practically no effect on the character of the temperature dependence of ionic conductivity in the paraelectric phase.The pressure increase is accompanied by the increase of the step at the phase transition.This is due to the absence of ionic conductivity contribution to the dielectric permeability.According to our calculations, in the pressure range of p 400 MPa, the anomaly of the dielectric permeability will be completely masked by copper ion conductivity.Figure 4 illustrates the results of the hydrostatic pressure effect on the temperature dependences of CuInP 2 S 6 crystal dielectric permeability and dielectric loss angle tangent obtained at the measuring field frequency f = 1 MHz.The shift of anomalies is accompanied by the decrease of its maximum values at the constant value of the phase transition thermal hystheresis.This is the evidence for the phase transition character remaining the same.The Curie-Weiss constant which is equal to 7.5 • 10 3 K at the atmospheric pressure in paraelectric phase, decreases with pressure.The pressure coefficient ∂C W /∂p = −2.8K/MPa.The phase transition also corresponds to the maximum of the tgδ value (figure 4b).The temperature of tgδ maximum exactly coincides with the dielectric permeability maximum temperature.The loss increase in the high-temperature range is determined by copper ion conductivity.The pressure increase causes a considerable increase of dielectric loss in both phases as well as changes the temperature behaviour at the phase transition.
Figure 5 shows the corresponding (p, T ) diagram built based on the studies of temperature and pressure dependences of CuInP 2 S 6 crystal dielectric properties.In the pressure interval under study the increase of p causes a linear increase of the phase transition temperature with a coefficient of ∂T c /∂p = 210 K/GPa.This coefficient is positive which is typical of the order/disorder phase transitions and its value is high enough in comparison with other materials possessing this type of phase transitions [9].

Conclusions
Dielectric properties of CuInP 2 S 6 crystals at high hydrostatic pressures are studied.The pressure behaviour of Curie-Weiss constant, dielectric permeability maximum and phase transition temperature are studied.The dependence of dielectric parameters on the sample size is revealed.The pressure behaviour of the phase transition temperature confirms the phase transition in these crystals to be of the order/disorder type.The (p, T ) phase diagram of CuInP 2 S 6 crystals has been constructed.

Figure 1 .
Figure 1.Temperature dependences of CuInP2S6 crystals dielectric permeability in the heating mode at the measuring field frequencies of 1 kHz (1) and 1 MHz (2).

Figure 2 .
Figure 2. Temperature dependences of CuInP2S6 crystal dielectric permeability at different values of the crystal thickness D: 0.2 mm (1); 0.4 mm (2); 1.1 mm (3); 1.3 mm (4) at the measuring field frequency of 1 MHz.The insert shows the dependence of the dielectric permeability maximum value on the crystal thickness.

Figure 3 .
Figure 3. Temperature dependences of CuInP2S6 crystal dielectric permeability at the measuring field frequency of 1 kHz at atmospheric pressure (1) and at hydrostatic pressure values of 128 MPa (2) and 248 MPa (3).