Critical indices of the ferroelectric phase transition in TGS crystals
Temperature dependencies of retardation, electron susceptibility and linear thermal expansion for three crystal-physic directions are obtained by means of optical investigations of the ferroelectric phase transition in TGS crystal using the James-type interferometer. Temperature dependencies of t...
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Інститут фізики конденсованих систем НАН України
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irk-123456789-1205402017-06-13T03:03:00Z Critical indices of the ferroelectric phase transition in TGS crystals Myshchyshyn, O. Andriyevsky, B. Romanyuk, M. Temperature dependencies of retardation, electron susceptibility and linear thermal expansion for three crystal-physic directions are obtained by means of optical investigations of the ferroelectric phase transition in TGS crystal using the James-type interferometer. Temperature dependencies of the spontaneous changes of the characteristics studied in the 39–49◦ C range are fitted by the power low Y ~ τ²β with double critical indices 2β=0.87–0.95. Difference of 2β values from the unity is explained by the essential temperature dependence in the range close to the phase transition point for the coefficients of electrooptic, reversed piezoelectric and electrostriction effects. Шляхом оптичних вимірювань сегнетоелектричного фазового переходу в кристалі тригліцинсульфату за допомогою інтерферометра Жамена одержано температурні залежності оптичної рiзниці ходу, електронної сприйнятливості та лінійного розширення для трьох кристалофізичних напрямків. Температурні залежності спонтанних змін досліджуваних характеристик в області 39–49◦ C апроксимовані степеневими залежностями Y ~ τ²β з подвійними критичними індексами 2β=0.87–0.95. Відмінність 2β від одиниці пояснюється суттєвою температурною залежністю поблизу точки фазового переходу коефіцієнтів електрооптичного, оберненого п’єзоелектричного ефектів та електрострикції. 1999 Article Critical indices of the ferroelectric phase transition in TGS crystals / O. Myshchyshyn, B. Andriyevsky, M. Romanyuk // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 509-514. — Бібліогр.: 6 назв. — англ. 1607-324X DOI:10.5488/CMP.2.3.509 PACS: 77.80.Bh, 77.84.Fa, 78.20.Ci http://dspace.nbuv.gov.ua/handle/123456789/120540 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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English |
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Temperature dependencies of retardation, electron susceptibility and linear thermal expansion for three crystal-physic directions are obtained by
means of optical investigations of the ferroelectric phase transition in TGS
crystal using the James-type interferometer. Temperature dependencies of
the spontaneous changes of the characteristics studied in the 39–49◦ C
range are fitted by the power low Y ~ τ²β with double critical indices
2β=0.87–0.95. Difference of 2β values from the unity is explained by the
essential temperature dependence in the range close to the phase transition point for the coefficients of electrooptic, reversed piezoelectric and
electrostriction effects. |
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Article |
| author |
Myshchyshyn, O. Andriyevsky, B. Romanyuk, M. |
| spellingShingle |
Myshchyshyn, O. Andriyevsky, B. Romanyuk, M. Critical indices of the ferroelectric phase transition in TGS crystals Condensed Matter Physics |
| author_facet |
Myshchyshyn, O. Andriyevsky, B. Romanyuk, M. |
| author_sort |
Myshchyshyn, O. |
| title |
Critical indices of the ferroelectric phase transition in TGS crystals |
| title_short |
Critical indices of the ferroelectric phase transition in TGS crystals |
| title_full |
Critical indices of the ferroelectric phase transition in TGS crystals |
| title_fullStr |
Critical indices of the ferroelectric phase transition in TGS crystals |
| title_full_unstemmed |
Critical indices of the ferroelectric phase transition in TGS crystals |
| title_sort |
critical indices of the ferroelectric phase transition in tgs crystals |
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Інститут фізики конденсованих систем НАН України |
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1999 |
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http://dspace.nbuv.gov.ua/handle/123456789/120540 |
| citation_txt |
Critical indices of the ferroelectric phase transition in TGS crystals / O. Myshchyshyn, B. Andriyevsky, M. Romanyuk // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 509-514. — Бібліогр.: 6 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT myshchyshyno criticalindicesoftheferroelectricphasetransitionintgscrystals AT andriyevskyb criticalindicesoftheferroelectricphasetransitionintgscrystals AT romanyukm criticalindicesoftheferroelectricphasetransitionintgscrystals |
| first_indexed |
2025-07-08T18:06:07Z |
| last_indexed |
2025-07-08T18:06:07Z |
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1837103022898937856 |
| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 3(19), pp. 509–514
Critical indices of the ferroelectric
phase transition in TGS crystals
O.Myshchyshyn, B.Andriyevsky, M.Romanyuk
Ivan Franko State University of Lviv,
8 Kyryla and Mefodiya Str., 290005 Lviv, Ukraine
Received January 13, 1999
Temperature dependencies of retardation, electron susceptibility and lin-
ear thermal expansion for three crystal-physic directions are obtained by
means of optical investigations of the ferroelectric phase transition in TGS
crystal using the James-type interferometer. Temperature dependencies of
the spontaneous changes of the characteristics studied in the 39–49◦ C
range are fitted by the power low Y ∼ τ2β with double critical indices
2β=0.87–0.95. Difference of 2β values from the unity is explained by the
essential temperature dependence in the range close to the phase tran-
sition point for the coefficients of electrooptic, reversed piezoelectric and
electrostriction effects.
Key words: ferroelectrics, phase transition, optical properties, critical
indices
PACS: 77.80.Bh, 77.84.Fa, 78.20.Ci
1. Introduction
It is known, that critical behaviour of spontaneous polarization Ps at the 2nd
order phase transition (PT) in a crystal is described by the critical index β,
Ps ∼ (Tc − T )β, (1)
where Tc is the PT temperature [1].
Temperature dependencies of the refractive indices and linear thermal expansion
of TGS in the range of PT have already been studied [2–4], but the corresponding
critical indices have not been determined.
The goals of the present investigation were precise measurements of temperature
dependencies of interferometric retardation of the sample-air type for the TGS in
the range of 2nd order PT at 322K, calculating the temperature dependencies of
refractive indices and linear thermal expansion for the main crystallophysic direc-
tions of the crystal, as well as studying these dependencies using the corresponding
critical indices 2β.
c© O.Myshchyshyn, B.Andriyevsky, M.Romanyuk 509
O.Myshchyshyn, B.Andriyevsky, M.Romanyuk
2. Methods, results and discussion
20 30 40 50 60 70
-60
-40
-20
0
20
40
32
31
23
21
13
12
10
4 (
∆
D
i j
/
D
i j
)
T (oC)
Figure 1. Experimental temperature de-
pendencies of the relative changes of op-
tical thickness ∆Dij/Dij of TGS crys-
tal (indices ij indicate the corresponding
curves)
20 30 40 50 60 70
-20
0
20
40 3e
2e
1e
2
3
2
1
10
4 (∆
l i /
l i)
T (oC)
Figure 2. Calculated and experimen-
tal (e) temperature dependencies of the
geometric thickness changes ∆li/li of
TGS crystal (indices i indicate the cor-
responding curves)
Temperature dependencies of retar-
dation by the susceptibility η for two in-
terfering beams, one of which has passed
through a sample studied, and the other
one through the air, were measured us-
ing the home built Jamen type interfer-
ometer. In this case the retardation D
can be written in the form
D = l · (n− 1) = l · η, (2)
where n is the refractive index of the
sample. The laser light of the wave-
length λ=632.8 nm was used in the ex-
periments.
Proceeding from the relation (2), the
temperature changes of relative retarda-
tion ∆D/D along the three crystallo-
physic directions can be written in the
form of a system of linear equations
∆Dij
Dij
=
∆li
li
+
∆ηj
ηj
, (3)
(i, j = 1, 2, 3; i 6= j),
where index i denotes the direction of
light propagation, index j denotes the
direction of light polarization. Based
on the six temperature dependencies
∆Dij/Dij measured we have determined
the relative temperature changes of ge-
ometric thickness ∆li/li and suscepti-
bility ∆ηj/ηj [5]. Results of the com-
puter calculations have shown, that the
relative errors of determining the tem-
perature changes of geometric thick-
ness δli/li and susceptibility δηj/ηj after
solving the system (3), did not exceed
5% of the respective maximum magni-
tudes ∆li/li and ∆ηj/ηj for the case of TGS crystal. The initial li and ηj values
were measured independently at the initial temperature T0. The error of deter-
mining the interference order was δm(T ) 6 1/4, that corresponds to the errors of
δD/D ∼ δl/l ∼ δη/η ∼ 10−5 in our case (l=5 mm and n=1.5). Temperature depen-
dencies of relative changes of retardation ∆Dij/Dij for TGS crystal are shown on
figure 1.
510
Critical indices in TGS crystals
20 30 40 50 60 70
-30
-20
-10
0
10
3
1
2
10
4 (∆
η j /
η j)
T (oC)
Figure 3. Calculated temperature de-
pendencies of the refractive indices
changes ∆nj/nj of TGS crystal (indices
j indicate the corresponding curves)
35 40 45 50 55 60 65
0.00
0.01
0.02
0.03
∆ D
e3
2/
D
32
T (oC)
Figure 4. Temperature dependence of
the relative optical path difference
∆De32/D32 of TGS crystal induced by
the constant electric field of 3.5 kV/cm
magnitude along the [010]-direction
The temperature dependencies of
the changes of the geometrical thick-
ness ∆li/li and the refractive indices
∆nj/nj of the TGS crystal calculated
using the system of equations (3) are
shown in figures 2,3. The temperature
dependencies of the calculated ∆li/li pa-
rameters (figure 2) agree satisfactorily
with the results of experimental mea-
surements of thermal expansion of TGS
crystals obtained by us using a mechan-
ical quartz dilatometer. The anisotropy
of the spontaneous increases ∆ls/l cal-
culated (figure 2) agrees well with the
relationships between piezoelectric coef-
ficients of TGS: g22 > g21, |g23| > g22,
sign g22 = sign g21 = −sign g23 [6].
It follows from figures 2,3, that the
temperature dependencies of geometri-
cal thickness and refractive indices for
the same crystal physics directions are
not similar in all cases. For example,
a temperature increase of refractive in-
dex is observed for [010] direction of
spontaneous polarization in TGS and a
decrease of this parameter is observed
for [100] and [001] directions (figure 3).
The sign of the temperature changes
of the geometrical thickness ∆l/l along
the [010] direction (figure 2) is opposite
to the sign of the corresponding ∆n/n
changes (figure 3).
Based on the known relation for tem-
perature changes of the order parameter
p for 2nd order PT in the T < Tc range,
∆Ys ∼ P 2
s ∼ τ 2β =
(
Tc − T
Tc − Tmin
)2β
, (4)
we have calculated the double critical indices 2β, replacing P 2
s value by the sponta-
neous increases of ∆Ys(T )/∆Ys(Tmin) (Y=D, l and η). Here Tc=49◦C is the temper-
ature of PT, Tmin is the lower edge of the temperature range studied (Tmin=39◦C in
our case), ∆Ys(T ) and ∆Ys(Tmin) are spontaneous increments, corresponding to the
Tc and Tmin temperatures. The double critical indices 2β for TGS in the range of
39–49◦C are shown in table 1.
511
O.Myshchyshyn, B.Andriyevsky, M.Romanyuk
Table 1. Critical indices 2β, corresponding to the temperature dependencies of
spontaneous increments of ∆Ds/D, ∆ls/l and ∆ηs/η for different crystallophysic
directions (i, j=1,2,3) of TGS crystal
2β
(D)
12 2β
(D)
13 2β
(D)
21 2β
(D)
23 2β
(D)
31 2β
(D)
32
0.899 0.898 0.888 0.893 0.945 0.924
2β
(l)
1 2β
(l)
2 2β
(l)
3 2β
(η)
1 2β
(η)
2 2β
(η)
3
0.910 0.895 0.923 0.876 0.925 0.877
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
η
1
l
1
δn
s(
T
)/
δn
s(
T
m
in
)
(T
c
-T)/(T
c
-T
min
)
Figure 5. Dependencies of the nor-
malised spontaneous changes of thick-
ness (l1) and susceptibility (η1) of TGS
for the [100] direction on the normalized
temperature (Tc − T )/(Tc − Tmin) in the
range of 39–49◦C
The results obtained testify to not
exact fulfilment of functional dependen-
cies for the quadratic electrooptic effect
∆ns ∼ P 2
s and electrostriction ∆ls ∼
P 2
s . If these effects were displayed in the
form indicated, then the double criti-
cal index 2β would be equal to unity,
2β=1. Therefore we have to explain the
fact that 2β values are different from the
unity.
Analytical description of the ob-
served temperature dependence of re-
tardation ∆Ds/D induced by sponta-
neous polarization can be presented in
the most common form
∆Ds/D(τ) = a(τ)·P 2
s (τ) = a(τ)·τ, (5)
where a(τ) is temperature dependent
coefficient. It follows from the character
of experimental dependencies of sponta-
neous increases of ∆Ds/D, ∆ls/l, and
∆ηs/η, that the corresponding a(τ) coefficients are maximal in the region of PT.
To obtain additional proofs of the validity of this viewpoint, we performed an ex-
perimental study of artificially induced electrooptic effect in TGS crystal in the
temperature range of 30–65◦C. This investigation was carried out in the same ar-
rangement as was done for the same effect induced by spontaneous polarization.
External electric field of E ≈ 3.5 kV/cm magnitude was applied to the sample at
different temperatures along the [010]-direction of spontaneous polarization Ps, and
the corresponding induced increments of the retardation ∆De/D were measured.
The maximum-like ∆De/D temperature dependence obtained (figure 4) correlates
well with the temperature dependence of a(τ). This maximum-like character of the
coefficient mentioned is connected with the non-equality of 2β < 1.
The results obtained can be considered from another viewpoint. Analysis of the
512
Critical indices in TGS crystals
table 1 testifies to certain segregation of the [010] direction of spontaneous po-
larization. Among the temperature changes of spontaneous increments ∆lie and
∆ηi (i = 1, 2, 3) the dependence ∆l2(τ) is characterised by the least index 2β, but
the dependence ∆n2(τ) is characterised by the greatest one (table 1). On the other
hand, a proximity of the values 2β
(l)
2 ≈ 2β
(η)
2 (table 1) is observed on the background
of obvious inequalities of similar characteristics for the other two crystallophysic di-
rections 2β
(l)
1,3 > 2β
(
1,3η) (table 1 and figure 5).
0.0 0.2 0.4 0.6 0.8 1.0
0.5
1.0
1.5
2.0
dη
1
/dτ
dl
1
/dτ
dv
/d
τ
τ
Figure 6. Temperature dependencies of
derivatives for the curves, presented on
figure 5.
The latter features can be inter-
preted as different rate of the order-
ing of two subsystems, one of which de-
termines electron susceptibility and the
second one is connected with geomet-
ric parameters of the crystal unit cell
for the directions [100] and [001]. The
equality 2β
(l)
2 ≈ 2β
(η)
2 for the direction
of spontaneous polarization [010] can be
interpreted as high degree of correlation
of the above mentioned subsystems in
TGS crystal. From such a viewpoint,
the observable inequalities of the indices
2β
(l)
(1,3 > 2β
(η)
1,3 testify to various speeds of
temperature changes of the correspond-
ing subsystems of the crystal in the tem-
perature range (∆T ∼ 10◦C) below PT
point. It is seen from figure 6, where two
temperature dependencies of derivatives
of the values on the figure 5 are pre-
sented for two different indices β1 and β2. The crossing of the curves, corresponding
to two different indices β (figure 6), will take place in all cases, if the experimen-
tal temperature dependence of the values studied (V = ∆Ds/D, ∆ls/l, ∆ηs/η) is
described by the power like law, V ∼ τ 2β .
Such a peculiarity in the temperature dependence of different parameters can be
characteristic to the ferroelectric crystals.
3. Conclusion
1. Deviation from the unity of the double critical index 2β for the tempera-
ture dependencies of the changes of susceptibility and geometric thickness of
TGS sample induced by spontaneous polarization is explained by significant
maximum-like temperature dependencies of the coefficients of electrooptic, in-
verse piezooptic, and electrostriction effects.
2. An anisotropy of the critical indices 2β
(l)
i and 2β
(η)
i , and nonequality 2β
(l)
i 6=
2β
(η)
i testify to different rates of temperature changes of different subsystems
513
O.Myshchyshyn, B.Andriyevsky, M.Romanyuk
of the crystal studied, taking place in ferroelectric ordering in the range of
∆T ∼ 10◦C below Tc.
References
1. Lines M.E., Glass A.M. Principles and Application of Ferroelectrics and Related Ma-
terials. Oxford, Clarendon Press, 1977.
2. Sonin A.S., Vasilevskaya A.S. Electrooptical Crystals. Moscow, Atomizdat Publ., 1971
(in Russian).
3. Lomova L.G., Sonin A.S., Regulskaya T.A. Spontaneous electrooptic effect in the
triglycine sulphate single crystals. // Kristallografiya, 1968, vol. 13, No. 1, p. 90–94
(in Russian).
4. Romanyuk N.A., Kostetskii A.M., Andrievskii B.V. Dispersion of the refractive in-
dex and some characteristics of absorption spectra for the triglycine sulphate crystal’s
group. // Phys. Sol. Stat, 1977, vol. 19, No. 10, p. 1809–1812.
5. Malyshev A.N. Introduction into Calculational Linear Algebra. Novosibirsk, Nauka
Publ., 1991 (in Russian).
6. Schmidt G., Pfannschmidt P. Piezoelektrizitat und Elektrostriktion des Triglyzinsul-
fats. // Phys. Stat. Sol, 1963, vol. 3, No. 12, p. 2215–2220.
Критичні індекси сегнетоелектричного фазового
переходу в кристалі TГС
О.Мищишин, Б.Андрієвський, М.Романюк
Львівський державний университет ім. І.Франка,
290005 Львів, вул. Кирила і Мефодія, 8
Отримано 13 січня 1999 р.
Шляхом оптичних вимірювань сегнетоелектричного фазового пере-
ходу в кристалі тригліцинсульфату за допомогою інтерферометра
Жамена одержано температурні залежності оптичної рiзниці ходу,
електронної сприйнятливості та лінійного розширення для трьох кри-
сталофізичних напрямків. Температурні залежності спонтанних змін
досліджуваних характеристик в області 39–49◦ C апроксимовані сте-
пеневими залежностями Y ∼ τ2β з подвійними критичними індек-
сами 2β=0.87–0.95. Відмінність 2β від одиниці пояснюється суттєвою
температурною залежністю поблизу точки фазового переходу ко-
ефіцієнтів електрооптичного, оберненого п’єзоелектричного ефек-
тів та електрострикції.
Ключові слова: сегнетоелектрики, фазові переходи, оптичні
властивості, критичні індекси
PACS: 77.80.Bh, 77.84.Fa, 78.20.Ci
514
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