p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase

The investigations on the temperature change in dielectric permeability of Sn₂P₂S₆ crystal at different misaligning electric ﬁelds and hydrostatic pressures have been carried out to establish the form of p, T, E-diagram for this crystal. Based on the investigations on dielectric permeability anoma...

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Datum:	2000
Hauptverfasser:	Kedyulich, V.M., Slivka, A.G., Gerzanich, E.I., Shusta, V.S.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Інститут фізики конденсованих систем НАН України 2000
Schriftenreihe:	Condensed Matter Physics
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/120986
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Zitieren:	p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase / V.M. Kedyulich, A.G. Slivka, E.I. Gerzanich, V.S. Shusta // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 851-856. — Бібліогр.: 5 назв. — англ.

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spelling	irk-123456789-1209862017-06-14T03:04:44Z p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Shusta, V.S. The investigations on the temperature change in dielectric permeability of Sn₂P₂S₆ crystal at different misaligning electric ﬁelds and hydrostatic pressures have been carried out to establish the form of p, T, E-diagram for this crystal. Based on the investigations on dielectric permeability anomalies, the E, T -diagrams at different magnitudes of hydrostatic pressure and p, T, E-diagram of Sn₂P₂S₆ crystal have been constructed. The magnitudes of coefﬁcients in the thermodynamic potential expansion have been estimated and coordinates of critical points in E, T -diagrams have been deﬁned. Проведено дослідження температурної зміни діелектричної проникності кристала Sn₂P₂S₆ при різних зміщуючих електричних полях та гідростатичних тисках з метою встановлення виду p, T, E-діаграми цього кристала. На основі досліджень аномалій діелектричної проникності побудовано E, T -діаграми при різних величинах гідростатичного тиску та p, T, E-діаграму кристала Sn₂P₂S₆. Проведено оцінку величин коефіцієнтів у розкладі термодинамічного потенціалу та визначено координати критичних точок на E, T -діаграмах. 2000 Article p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase / V.M. Kedyulich, A.G. Slivka, E.I. Gerzanich, V.S. Shusta // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 851-856. — Бібліогр.: 5 назв. — англ. 1607-324X DOI:10.5488/CMP.3.4.851 PACS: 77.80.Bh, 64.70.Rh http://dspace.nbuv.gov.ua/handle/123456789/120986 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	The investigations on the temperature change in dielectric permeability of Sn₂P₂S₆ crystal at different misaligning electric ﬁelds and hydrostatic pressures have been carried out to establish the form of p, T, E-diagram for this crystal. Based on the investigations on dielectric permeability anomalies, the E, T -diagrams at different magnitudes of hydrostatic pressure and p, T, E-diagram of Sn₂P₂S₆ crystal have been constructed. The magnitudes of coefﬁcients in the thermodynamic potential expansion have been estimated and coordinates of critical points in E, T -diagrams have been deﬁned.
format	Article
author	Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Shusta, V.S.
spellingShingle	Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Shusta, V.S. p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase Condensed Matter Physics
author_facet	Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Shusta, V.S.
author_sort	Kedyulich, V.M.
title	p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase
title_short	p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase
title_full	p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase
title_fullStr	p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase
title_full_unstemmed	p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase
title_sort	p, t, e-diagram of sn₂p₂s₆ ferroelectric with high-pressure incommensurate phase
publisher	Інститут фізики конденсованих систем НАН України
publishDate	2000
url	http://dspace.nbuv.gov.ua/handle/123456789/120986
citation_txt	p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase / V.M. Kedyulich, A.G. Slivka, E.I. Gerzanich, V.S. Shusta // Condensed Matter Physics. — 2000. — Т. 3, № 4(24). — С. 851-856. — Бібліогр.: 5 назв. — англ.
series	Condensed Matter Physics
work_keys_str_mv	AT kedyulichvm ptediagramofsn2p2s6ferroelectricwithhighpressureincommensuratephase AT slivkaag ptediagramofsn2p2s6ferroelectricwithhighpressureincommensuratephase AT gerzanichei ptediagramofsn2p2s6ferroelectricwithhighpressureincommensuratephase AT shustavs ptediagramofsn2p2s6ferroelectricwithhighpressureincommensuratephase
first_indexed	2025-07-08T18:58:26Z
last_indexed	2025-07-08T18:58:26Z
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fulltext	Condensed Matter Physics, 2000, Vol. 3, No. 4(24), pp. 851–856 p, T, E-diagram of Sn2P2S6 ferroelectric with high-pressure incommensurate phase V.M.Kedyulich, A.G.Slivka, E.I.Gerzanich, V.S.Shusta Uzhgorod State University, 34 Voloshin Str., 294000 Uzhgorod, Ukraine Received November 1, 1999 The investigations on the temperature change in dielectric permeability of Sn2P2S6 crystal at different misaligning electric fields and hydrostatic pres- sures have been carried out to establish the form of p, T, E-diagram for this crystal. Based on the investigations on dielectric permeability anoma- lies, the E, T -diagrams at different magnitudes of hydrostatic pressure and p, T, E-diagram of Sn2P2S6 crystal have been constructed. The magni- tudes of coefficients in the thermodynamic potential expansion have been estimated and coordinates of critical points in E, T -diagrams have been defined. Key words: ferroelectrics, phase transitions, electric field, hydrostatic pressure PACS: 77.80.Bh, 64.70.Rh It is known that under the action of external hydrostatic pressure an incommen- surate (IC) phase and, respectively, Lifshitz point (LP) [1] are induced in the proper Sn2P2S6 ferroelectric. To obtain additional information on the character of PT and the peculiarities of a pressure behaviour of the thermodynamic potential expansion coefficients in this crystal it was of great importance to investigate the effect of ex- ternal electric fields on phase transitions along p,T -diagram. In the given work the results of experimental investigations on the effect of electric field and hydrostatic pressure on temperature dependences of the dielectric permeability of Sn2P2S6 crys- tal are given which were conducted to establish the form of p,T ,E-diagram of this crystal. In figure 1 the E,T -diagrams of Sn2P2S6 crystal at different hydrostatic pressures are given. The temperature of phase transition polar-incommensurate phase Tc was defined from the maximum of temperature dependence of the dielectric permeability and the temperature of phase transition symmetric-IC phase Ti was defined from the break in the dependence ε−1(T ). It should be mentioned that in the fields in which c© V.M.Kedyulich, A.G.Slivka, E.I.Gerzanich, V.S.Shusta 851 V.M.Kedyulich et al. �� Figure 1. Phase E,T -diagrams of Sn2P2S6 crystal at different values of hydro- static pressure. IC phase exists the temperature of dielectric permeability maximum Tm coincides with the temperature of phase transition Tc. As it is seen, the temperature of PT Tc rises linearly with the increasing field, and the temperature Ti falls non-linearly. So, the temperature interval of IC phase existence decreases with the increasing intensity of electric field and at some value of E = Ecr it becomes equal to zero. In the fields E > Ecr an incommensurate phase is not realized. Based on E,T -diagrams of Sn2P2S6 crystal obtained at different values of hy- drostatic pressures the p,T ,E-diagram of this crystal is constructed (figure 2). As the hydrostatic pressure causes considerable changes in PT temperatures (approxi- mately 220 K/GPa [1]), and the electric field changes these temperatures for some degrees, the p,T ,E-diagram of Sn2P2S6 crystals is constructed in respect to the temperature of PT incommensurate-ferroelectric phase Tc. The first-order PT from incommensurate into polar phase is shown by solid lines. The second-order PT from symmetric into polar phase is shown by dashed lines. The line of AB critical points smoothly enters Lifshitz point. The lines of the dielectric permeability maximum at E > Ecr are shown by dash-dot lines that are not assigned to phase transitions. Let us estimate the magnitudes of coefficients in the thermodynamic potential expansion 852 p, T, E-diagram of Sn2P2S6 ferroelectric. . . A B Figure 2. p,T ,E-diagram of Sn2P2S6 crystal. Φ = Φ0 + α 2 P 2 + β 4 P 4 + δ 2 ( ∂P ∂z )2 + g 2 ( ∂2P ∂z2 )2 + χ 2 P 2 ( ∂P ∂z )2 − PE , (1) where α = αT (T − T0), αT = 1/(ε0Cw), ε0 is the electric constant, Cw is Curie- Weiss constant. At pressures p < pL the field dependence of dielectric permeability maximum temperature is given by the expression Tm(E) = T0 + 1.19α−1 T β1/3E2/3 . (2) From experimental dependences Tm(E) for pressures p < pL, coefficient β in the thermodynamic potential expansion was found. For pressures patm, 100 MPa, 160 MPa its value was (8,0± 0,9) · 109, (8,3± 0,9) · 109, (8,4± 0,9) · 109 J ·m5 ·C−4, respectively. The results of investigations of volume compressibility also testify to the increase of β while approaching LP in p,T -diagram from the side of commensurate PT [2]. However, the values of β defined on the basis of the analysis of experimental dependences Tm(E) are by an order of magnitude greater than the analogous results of dilatometric investigations [2]. In case β > 0, the superposition of external electric field causes the decrease of the temperature of PT paraelectric-IC phase in accordance with quadratic law [3] Ti(E) = Ti(0)− 48βg αT δ4 E2 . (3) The temperature of PT ferroelectric-IC phase linearly increases Tc(E) = Tc(0) + 3 αT ( βg 2δ2 )1/2 E . (4) 853 V.M.Kedyulich et al. ! "!! #!! $!! %!! &!! ! " # $ ' () * + , -. / 010 2 3 456 788 988 : ;< =: > ? @ ABA C D EFG 8 7 9 Figure 3. Pressure dependence of the value of critical field for Sn2P2S6 crystal. On the insert — a pressure dependence of a critical temperature. By solid lines the calculated values are shown, by points — the experimental values. Taking in the first approximation a linear dependence of δ coefficient of pressure and taking into account that at p = pL the value δ = 0 we have δ(p) = δ(0) + ∂δ ∂p p , (5) where δ(0) = 1 · 10−10 J ·m3 · C−2 [4], (∂δ/∂p) = −5,55 · 10−13 J · m3 · C−2 MPa−1. The temperature interval of IC phase existence in the absence of the electric field is given by the expression Ti − Tc = 0,375 αTg ( ∂δ ∂p )2 (p− pL) (6) and from the known values ∂δ/∂p and αT we determine the numerical value of the coefficient g = (1,3± 0,2) · 10−27 J ·m5 · C−2. From expression (3), (4) it is seen that the increase in absolute value δ with the increasing pressure has to cause the decrease in coefficients of field shifts of temperatures Tc and Ti while moving away from Lifshitz point. However, within the error of the experiment the change in these coefficients along p,T -diagram of Sn2P2S6 crystal is not noticed. A similar situation is also observed along x,T -diagram of Sn2P2(S1−xSex)6 compounds [5]. Probably, this is connected with the supposition that coefficient g at the change of pressure and concentration Se is constant. 854 p, T, E-diagram of Sn2P2S6 ferroelectric. . . The coordinates of critical point (Ecr, Tcr) in E,T -diagram higher of which IC phase is not realized, are found from the condition Ti(E)− Tc(E) = 0. Taking into account (3), (4) we get Ecr = δ3 16β1/2g3/2 , Tcr = T0 + δ2 16αTg , (7) where T0 = 1 3 (Ti(0) − 2Tc(0)) [3]. In figure 3 theoretically calculated and experi- mentally defined values for Ecr, Tcr are given. It is seen, that experimental values of Ecr are rather well described by the expression (7), but a pressure change in Tcr about three times exceeds the calculated one that may be caused by the stability of coefficients of field shifts for temperatures Tc and Ti along p,T -diagram. References 1. Guranich P.P., Gerzanich E.I., Slivka A.G., Shusta V.S. Compressibility in the vicinity of polycritical point in p,T -diagram of Sn2P2S6 crystals. // Ukr. Fiz. Zhurn., 1996, vol. 41, No. 9, p. 858–861 (in Ukrainian). 2. Slivka A.G., Gerzanich E.I., Guranich P.P., Shusta V.S., Kedyulich V.M. Pres- sure behaviour of compressibility in Sn2P2S6 ferroelectric. // Fiz. Tv. Tela, 1996, vol. 38, No. 27, p. 2155–2158 (in Russian). 3. Levanyuk A.P., Sannikov D.G. Thermodynamic theory of phase transitions with the formation of incommensurate superstructure in NaNO2 ferroelectrics. // Fiz. Tv. Tela, 1976, vol. 18, No. 7, p. 1927–1932 (in Russian). 4. Vysochanskiy Yu.M., Slivka V.Yu. Ferroelectrics of Sn2P2S6 family. The properties in the vicinity of Lifshitz point. Lviv, Nauchnoe izdanie, 1994 (in Ukrainian). 5. Mayor M.M., Khoma M.M., Vysocanskiy Yu.M. et al. The influence of electric field on phase diagram of proper ferroelectrics Sn2P2(S1−xSex)6 in the vicinity of Lifshitz point. // Kristallografiya, 1988, vol. 33, No. 1, p. 158–162 (in Ukrainian). 855 V.M.Kedyulich et al. p, T, E-діаграма сегнетоелектрика Sn2P2S6 з неспіврозмірною фазою високого тиску Кедюлич В.М., Сливка О.Г., Герзанич О.І., Шуста В.С. Ужгородський державний університет, 294000 Ужгород, вул. Волошина, 34 Отримано 1 листопада 1999 р. Проведено дослідження температурної зміни діелектричної проник- ності кристала Sn2P2S6 при різних зміщуючих електричних полях та гідростатичних тисках з метою встановлення виду p, T, E-діаграми цього кристала. На основі досліджень аномалій діелектричної про- никності побудовано E, T -діаграми при різних величинах гідроста- тичного тиску та p, T, E-діаграму кристала Sn2P2S6. Проведено оцін- ку величин коефіцієнтів у розкладі термодинамічного потенціалу та визначено координати критичних точок на E, T -діаграмах. Ключові слова: сегнетоелектрики, фазові переходи, електричне поле, гідростатичний тиск PACS: 77.80.Bh, 64.70.Rh 856

p, T, E-diagram of Sn₂P₂S₆ ferroelectric with high-pressure incommensurate phase

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