External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure
Experimental studies of the effect of temperature, external pressure and electric eld on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals are performed. The experimental data on the effect of electric field and pressure on the dielectric permeability of Rochelle sa...
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| Zitieren: | External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure / A.G. Slivka, V.M. Kedyulich, H.M. Guyvan // Condensed Matter Physics. — 2008. — Т. 11, № 3(55). — С. 571-581. — Бібліогр.: 17 назв. — англ. |
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irk-123456789-1193832017-06-07T03:02:33Z External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure Slivka, A.G. Kedyulich, V.M. Guyvan, H.M. Experimental studies of the effect of temperature, external pressure and electric eld on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals are performed. The experimental data on the effect of electric field and pressure on the dielectric permeability of Rochelle salt are analyzed in the framework of phenomenological theory with the account of the vicinity of the phase transitions to the double critical point. Coefficients of thermodynamic potential expansion over the order parameter are determined as well as its pressure behaviour is described. The hydrostatic pressure increase is shown to shift the phase transitions in Rochelle salt away from the double critical point. Проведено експериментальнi дослiдження впливу температури, зовнiшнього тиску та електричного поля на анiзотропiю дiелектричної проникностi кристалiв KH₂PO₄ та NaKC₄H4O₆· 4H₂O. У рамках феноменологiчної теорiї та з врахуванням близькостi фазових переходiв до подвiйної критичної точки проведено аналiз експериментальних результатiв по впливу електричного поля та тиску на дiелектричну проникнiсть сегнетової солi. Визначено коефiцiєнти розкладу термодинамiчного потенцiалу по параметру порядку i їх баричну поведiнку. Показано, що збiльшення гiдростатичного тиску вiддаляє фазовi переходи в сегнетовiй солi вiд подвiйної критичної точки. 2008 Article External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure / A.G. Slivka, V.M. Kedyulich, H.M. Guyvan // Condensed Matter Physics. — 2008. — Т. 11, № 3(55). — С. 571-581. — Бібліогр.: 17 назв. — англ. 1607-324X PACS: 77.80.Bh, 77.22.Ch, 77.84.Fa DOI:10.5488/CMP.11.3.571 http://dspace.nbuv.gov.ua/handle/123456789/119383 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
Experimental studies of the effect of temperature, external pressure and electric eld on the anisotropy of
dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals are performed. The experimental data
on the effect of electric field and pressure on the dielectric permeability of Rochelle salt are analyzed in the
framework of phenomenological theory with the account of the vicinity of the phase transitions to the double
critical point. Coefficients of thermodynamic potential expansion over the order parameter are determined as
well as its pressure behaviour is described. The hydrostatic pressure increase is shown to shift the phase
transitions in Rochelle salt away from the double critical point. |
| format |
Article |
| author |
Slivka, A.G. Kedyulich, V.M. Guyvan, H.M. |
| spellingShingle |
Slivka, A.G. Kedyulich, V.M. Guyvan, H.M. External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure Condensed Matter Physics |
| author_facet |
Slivka, A.G. Kedyulich, V.M. Guyvan, H.M. |
| author_sort |
Slivka, A.G. |
| title |
External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure |
| title_short |
External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure |
| title_full |
External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure |
| title_fullStr |
External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure |
| title_full_unstemmed |
External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure |
| title_sort |
external field effect on the anisotropy of dielectric permeability of kh₂po₄ and nakc₄h4o₆· 4h₂o crystals under high pressure |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119383 |
| citation_txt |
External field effect on the anisotropy of dielectric permeability of KH₂PO₄ and NaKC₄H4O₆· 4H₂O crystals under high pressure / A.G. Slivka, V.M. Kedyulich, H.M. Guyvan // Condensed Matter Physics. — 2008. — Т. 11, № 3(55). — С. 571-581. — Бібліогр.: 17 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT slivkaag externalfieldeffectontheanisotropyofdielectricpermeabilityofkh2po4andnakc4h4o64h2ocrystalsunderhighpressure AT kedyulichvm externalfieldeffectontheanisotropyofdielectricpermeabilityofkh2po4andnakc4h4o64h2ocrystalsunderhighpressure AT guyvanhm externalfieldeffectontheanisotropyofdielectricpermeabilityofkh2po4andnakc4h4o64h2ocrystalsunderhighpressure |
| first_indexed |
2025-07-08T15:46:09Z |
| last_indexed |
2025-07-08T15:46:09Z |
| _version_ |
1837094259176505344 |
| fulltext |
Condensed Matter Physics 2008, Vol. 11, No 3(55), pp. 571–581
External field effect on the anisotropy of dielectric
permeability of KH2PO4 and NaKC4H4O6 · 4H2O crystals
under high pressure
A.G.Slivka, V.M.Kedyulich, H.M.Guyvan
Uzhhorod National University, Department of Optics, 54 Voloshyn Str., 88000, Uzhhorod, Ukraine
Received June 5, 2008, in final form July 15, 2008
Experimental studies of the effect of temperature, external pressure and electric field on the anisotropy of
dielectric permeability of KH2PO4 and NaKC4H4O6 · 4H2O crystals are performed. The experimental data
on the effect of electric field and pressure on the dielectric permeability of Rochelle salt are analyzed in the
framework of phenomenological theory with the account of the vicinity of the phase transitions to the double
critical point. Coefficients of thermodynamic potential expansion over the order parameter are determined as
well as its pressure behaviour is described. The hydrostatic pressure increase is shown to shift the phase
transitions in Rochelle salt away from the double critical point.
Key words: ferroelectrics, phase transition, dielectric permeability, pressure, electric field
PACS: 77.80.Bh, 77.22.Ch, 77.84.Fa
1. Introduction
Long time has passed since the discovery of ferroelectric activity in KH2PO4 (KDP) and
NaKC4H4O6 · 4H2O (Rochelle salt) crystals. However, these materials still attract keen attention
of researchers due to their specific physical properties related to a system of structural hydro-
gen bonds and their changes at phase transformations. Another common feature of these crystals
consists in their piezoelectric properties revealed in the paraelectric phase.
Experimental studies of the anisotropy of physical properties and its variation under external
pressure and electric field play an important role in understanding the microscopic mechanisms
of phase transitions in ferroelectric crystals with hydrogen bonds. This is due to the fact that by
applying external pressure once can continuously vary geometrical parameters of hydrogen bonds
and violate their equivalence, which provides a unique possibility to study the role of hydrogen
bonds in the mechanisms of structural phase transformations and dielectric response of crystals.
Applying uniaxial strain as well as electric fields enables one to investigate the role of piezoelec-
tric interactions in the phase transitions and in the formation of physical characteristics of these
crystals.
In the 1990s the keypoint for further investigations of the KDP family crystals was related
to theoretical studies by Stasyuk and Biletsky [1,2] which gave an impetus to another series of
theoretical studies of these crystals and subsequently of other ferroelectric materials with hydrogen
bonds including Rochelle salt crystals. The effective Hamiltonian for KDP crystals was obtained
ab initio with the account of piezoelectric interaction within the framework of a modified model of
proton ordering. This enabled a proper description of a number of available physical characteristics
of crystals of this group as well as made it possible to predict some physical effects due to external
fields which had not been experimentally studied before. Similarly, Stasyuk and Levitskii [3–5] have
taken into account the piezoelectric interaction within the framework of a modified Mitsui model
for theoretical description of experimental data for Rochelle salt. The results of these theoretical
studies required experimental investigations of a number of key issues which led to more active
experimental studies.
c© A.G.Slivka, V.M.Kedyulich, H.M.Guyvan 571
A.G.Slivka, V.M.Kedyulich, H.M.Guyvan
Here we report on the results of experimental studies of the effect of external pressure and
electric field on the anisotropy of dielectric properties of KDP and Rochelle salt crystals. These
results were obtained in a series of studies starting from 1999, having been initiated by the above
mentioned theoretical papers.
2. Anisotropy of dielectric permeability of KDP and Rochelle salt crystals
Figure 1 shows the temperature dependences of longitudinal dielectric permeability of KDP
crystals at atmospheric pressure and at the measuring field frequency of 1 kHz (curve 1) and 1 MHz
(curve 2). No dispersion of transverse dielectric permeability has been revealed at these frequencies
(curve 3). At the frequency of 1 kHz the dependence of longitudinal dielectric permeability is
characterized by two anomalies: a maximum of εc(T ) at the phase transition temperature TC =
122 K and a shoulder in the ferroelectric phase in the temperature range from 91 to 122 K, related
to the domain wall dynamics [6]. At the measuring field frequency of 1 MHz a number of extrema
is observed in the εc(T ) plot in the vicinity of the phase transition point (curve 2). This feature is
related to the piezoelectric resonance in KDP crystal [7]. It cannot be related to the trend of the
order parameter relaxation time in an order/disorder ferroelectric to the infinity, since in this case
a single minimum in the temperature dependence of dielectric permeability at the phase transition
temperature should be observed.
Figure 1. Temperature dependences of longitudinal dielectric permeability of KDP crystal at
the frequency of 1 kHz (curve 1) and 1 MHz (curve 2) and transverse dielectric permeability
(curve 3).
The temperature behaviour of dielectric permeability of Rochelle salt in different crystallo-
graphic directions at different measuring field frequencies (f = 1 kHz and f = 1 MHz) is shown
in figures 2 and 3. The anomalous behaviour of ε(T ) in the vicinity of the phase transitions at
f = 1 kHz is observed only along the a direction. Two characteristic maxima are observed at
the phase transition temperatures −18◦C and +24◦C (figure 2) in the temperature dependence
ε(T ) along the polar axis. The dielectric permeability values at the phase transition tempera-
tures are different: 2200 and 4300, respectively. Along the c and b directions (f = 1 kHz) the
dielectric permeability values are practically the same in the whole temperature range under in-
vestigation, except the high-temperature phase (T > 25◦C). The temperature dependences of εb
and εc reveal a monotonous increase of the dielectric permeability in the ferroelectric phase and in
the high-temperature paraelectric phase. Since practically no anomalies are observed at the phase
transition temperatures, this indicates that the main changes in the crystal structure, resulting
in the appearance of spontaneous polarization, occur along the a direction. At the temperatures
T > 25◦C, the features in the temperature dependences of εb and εc are revealed, evidently related
to the crystal lattice destruction and, as a consequence, an increase of the crystal ionic conduc-
tivity. These processes are irreversible and at temperatures above 50◦C they result in a loss of the
Rochelle salt ferroelectric properties.
572
External field effect on the anisotropy...
Figure 2. Temperature dependences of the dielectric permeability of Rochelle salt crystals for
different crystallographic directions at the measuring field frequency f = 1 kHz.
In the temperature dependence of εa at the measuring field frequency f = 1 MHz a number of
extrema is observed in the vicinity of the phase transition points (figure 3) which is related to the
piezoelectric resonance, since the measuring field frequency is close to the resonance frequency of
the crystal. The study of anisotropy of the crystal dielectric permeability consists in determining
the orientation of the main ellipsoid axes along the crystallographic directions. It is also important
to determine the variation of these parameters under temperature and external pressure. The
orientational dependence of dielectric permeability which is a tensor in anisotropic crystals, is
given by ε = εij lilj , where εij are the dielectric permeability tensor components, li and lj are the
cosines of the angles between the direction, in which the dielectric permeability is being determined,
and the Cartesian coordinate axes, in which the tensor is written.
Figure 3. Temperature dependences of dielectric permeability of Rochelle salt crystals for dif-
ferent crystallographic directions at the measuring field frequency f = 1 MHz.
In the KDP crystal at room temperature the transverse dielectric permeability value is higher
than the longitudinal one (see figure 1). The temperature decrease results in an increase of both
values; however, the longitudinal dielectric permeability undergoes essential anomalous changes,
its value sharply increasing with the approach to the phase transition point. Therefore, at the
temperature Ti = 186 K (f = 1 kHz) the longitudinal and transverse dielectric permeability values
become equal. The temperature of the isotropic point at the measuring field frequency of 1 MHz
is Ti = 176 K (see the insert to figure 1). At the temperatures T < Ti the longitudinal dielectric
permeability value exceeds the transverse one.
573
A.G.Slivka, V.M.Kedyulich, H.M.Guyvan
Sections of the indicating surface of the dielectric permeability tensor for the KDP crystal
at atmospheric pressure and different temperatures are shown in figure 4. The results of angular
dependence of dielectric permeability of KDP crystals in the (010) plane show that the main axes of
the εij tensor clearly coincide with the crystallographic axes of the crystal. At room temperature,
the semi-major axis is directed along the a direction, while the semi-minor axis is along the c
direction. The decrease of temperature at first results in the decrease of anisotropy of the crystal
dielectric permeability. At Ti = 186 K the section of the indicating surface is a circle, which means
that dielectric permeability ε is isotropic at this temperature. A further decrease of temperature
again results in the anisotropy of dielectric permeability, its value being maximal at ferroelectric
phase transition temperature. In this case the semi-major axis is oriented along the c direction
while the semi-minor one – along the a direction. In the ferroelectric phase (T < TC) the values
of dielectric permeability along the c direction are by an order of magnitude higher than for the
a direction. Thus, in KDP crystal at the temperature Ti an isotropic point is achieved, where the
temperature inversion of the sign of dielectric permeability difference ∆ε = εa − εc is observed.
Figure 4. Temperature transformation of the section of dielectric permeability indicating surface
by the ac plane of the KDP crystal, 1: T = 275 K, 2: T = 186 K, 3: T = 150 K.
We have also performed direct measurements of the ε value along different crystallographic
directions for the NaKC4H4O6 · 4H2O crystal. The angular dependence of dielectric permeability
of Rochelle salt in the (010) symmetry plane at atmospheric pressure and at different temperatures
is shown in figure 5.
The obtained results show that the specific features of temperature transformation of sections
of the indicating surface of dielectric permeability for KH2PO4 and NaKC4H4O6 · 4H2O crystals
are caused by the anomalous temperature behaviour of dielectric permeability along the polar
direction in the crystals. The orientation of the main axes is independent of temperature.
3. High-temperature anomaly of dielectric permeability in KDP
The temperature dependence of dielectric permeability εa of KDP crystal at atmospheric pressure
at the measuring field frequency of 1 MHz is shown in figure 6. Three characteristic features can
be seen in this dependence: a step of dielectric permeability at the phase transition temperature
TC = 122 K, a maximum in the εa(T ) dependence at the temperature Tmax = 130 K, and an
inflection point at Tf = 172 K. The existence of a maximum of dielectric permeability at T > TC
was registered in KMnF3 and NH4H2AsO4 antiferroelectric crystals [8]. In our earlier papers [9–
11] the first experimental studies of the effect of external hydrostatic pressure on the temperature
dependence of transverse dielectric permeability εa for KDP crystal were described. The hydrostatic
574
External field effect on the anisotropy...
Figure 5. Temperature transformation of the section of the dielectric permeability indicating
surface by the (010) plane of Rochelle salt crystal. Curve 5 shows the theoretical calculation
data.
pressure increase to 6.5 kbar results in a shift of the εa(T ) curves towards lower temperatures, the
TC , Tmax, and Tf values varying linearly with pressure with the following coefficients: dTC/dp =
−4.8 · 10−2 K/MPa; dTmax/dp = −5.4 · 10−2 K/MPa; dTf/dp = −5.4 · 10−2 K/MPa. It was also
shown that the temperature interval Tmax − TC becomes narrower with pressure.
Figure 6. Specific features of the temperature dependence of transverse dielectric permeability
for KDP crystal.
Figure 7 shows the temperature dependences of dielectric permeability of KH2PO4 crystal along
the a side at the measuring field frequency f = 1 kHz (curve 1 – cooling, curve 2 – heating) and
f = 1 MHz (curve 3 – heating). In the temperature range 250–300 K at f = 1 kHz an anomaly
(a maximum) is observed, which is not revealed in the temperature dependence of dielectric per-
meability at f = 1 MHz, but is observed in the temperature dependence of dielectric loss angle
tangent tan δ(T ). Temperature cycling (heating-cooling) leads to an increase of the temperature
of maximum of dielectric permeability for the high-temperature anomaly (figure 8).
The change of the measuring field frequency results in considerable transformations of the
high-temperature anomalies of transverse dielectric permeability in the paraelectric phase. While
for KH2PO4 crystal at the measuring field frequency of 1 kHz the anomalies are observed both
on ε(T ), and tan δ(T ) curves at the frequency of 1 MHz they are revealed only in the tan δ(T )
dependence. An increase of the hydrostatic pressure results in the suppression of high-temperature
anomalies and their shift towards higher temperatures.
Low-frequency internal friction and shear modulus of KDP crystal in the paraelectric phase at
575
A.G.Slivka, V.M.Kedyulich, H.M.Guyvan
Figure 7. Temperature dependences of dielectric permeability of KDP crystal along the a side at
the measuring field frequency f = 1 kHz (curves 1,2) and at the frequency f = 1 MHz (curve 3).
Figure 8. Temperature dependences of dielectric permeability of KDP crystal along the a side
at the temperature cycling.
various external effects was studied in [12]. In the temperature range under investigation 80–325 K
two distinct anomalies at the temperatures TC and T ∗ are observed in the Q−1(T ) and G(T )
dependences. Measurements of Q−1(T ), G(T ), and ϕ(T ) (ϕ being the spontaneous torsion angle)
were carried out at various rates of temperature, external mechanical strain, etc. The results of these
studies have shown that the mechanism of the appearance of the high-temperature anomalies in the
temperature interval 250–320 K is common for the KH2PO4 family crystals and practically does not
depend on deuteration and isomorphic ion substitution which affect only the temperature position
and magnitude of the anomalies revealed. The anomalies in high-temperature phase depend on
the sample orientation, i. e. they are revealed not at an arbitrary orientation of the sample with
respect to the crystallographic axes. Studies of temperature dependences of Q−1 [12] at different
frequencies in the range from 6 Hz to 150 kHz have shown that the peak height at T ∗ varies
inverse proportionally to the frequency, the shift of the Q−1 maximum along the temperature scale
being insignificant. Such a behaviour of the internal friction maximum is typical of low-frequency
relaxational processes related to phase transformations.
According to [13], in KDP-type crystals the role of impurities can be played by phosphate
complexes (HPO−2
4 , H5P2O
−
8 , H3PO4), present even in thoroughly purified solutions. Besides,
the presence of a small concentration of uncontrollable impurities (Fe3+, Cr3+, Ca2+, Al3+) is
assumed [14], responsible for local deformations which, in turn, lead to local symmetry distortion
of the crystal matrix.
576
External field effect on the anisotropy...
Since the volume fraction of inclusions is small (the average size of impurities is within 500–
4500 Å and the total inclusion volume is from 1.5 to 5% in different crystals [13]), the dielectric
permeability of such microheterogeneous system is determined mostly by the dielectric properties
of the matrix, rather than the inclusions, which explains the absence of dielectric anomalies at the
temperature T ∗ at certain experimental studies.
The data showing the anomalous behaviour of ε(T ) and tan δ(T ) dependences for KH2PO4
crystals obtained here agree with the results of low-frequency measurements of internal friction
and shear modulus [12], related to a first-order phase transitions (4̄2m−→mm2), occuring in the
inclusions of another phase whose formation is due to the uncontrollable defects.
4. Effect of external electric field and pressure on dielectric permeability of
Rochelle salt
Temperature behaviour of dielectric permeability of Rochelle salt has been studied by many
authors. The analysis of the available reference data shows a noticeable spread of the experimental
values of dielectric permeability in different structural phases of Rochelle salt crystals [15]. Be-
sides, variable character of the temperature dependence of inverse dielectric permeability in the
paraelectric phase of these crystals is reported. These discrepancies, evidently, result from a dif-
ferent prehistory and quality of the samples as well as from different experimental conditions. In
order to find possible reasons for such a situation, we have performed experimental studies of the
effect of external factors (temperature, mechanical and electric fields, environment humidity) and
experimental measurement conditions (temperature variation rate, preliminary thermal annealing,
temperature mode of the measurements) on the dielectric properties of Rochelle salt crystals.
The value of ε and the character of its temperature dependence in the paraelectric phases
most essentially depends on durable storage of Rochelle salt crystals in a humid air or on thermal
annealing [17]. A crystal having not undergone thermal annealing, in the low-temperature phase is
characterized by linear ε−1(T ) dependence with the Curie-Weiss constant CW = 1.95 ·103 K. After
preliminary thermal annealing the ε−1(T ) dependence is nonlinear in both paraelectric phases and
can be described by a single relationship ε−1(T ) = −0.006−0.01t+1.05t2 where t = (T −Tm)/T0,
Tm = 275 K, T0 = (TC2 − TC1)/2 = 276 K which is in agreement with the results of [15] where
the nonlinear dependence ε−1(T ) in the paraelectric phases is explained within the framework
of a phenomenological approach with the account of the vicinity of the phase transitions to the
double critical point. Using the basic idea of [15], we have analyzed the obtained experimental
data regarding the external electric field effect on the temperature dependences for Rochelle salt
crystals. These results are illustrated in figures 9 and 10.
Figure 9. Temperature dependences of the dielectric permeability of Rochelle salt crystals in the
vicinity of the upper Curie point at different values of the longitudinal electric field E, kV/cm:
0 (1), 0.05 (2), 0.1 (3), 0.2 (4), 0.3 (5), 0.5 (6), 0.75 (7), 1 (8).
577
A.G.Slivka, V.M.Kedyulich, H.M.Guyvan
Figure 10. Temperature dependences of dielectric permeability of Rochelle salt crystals in the
vicinity of the lower Curie point at different values of the longitudinal electric field E, kV/cm:
0 (1), 0.05 (2), 0.1 (3), 0.2 (4), 0.3 (5), 0.5 (6), 0.75 (7), 1 (8).
Within the framework of thermodynamic theory for a second-order phase transition, the ex-
pansion of thermodynamic potential in a series over the powers of the order parameter P is given
by
F = F0 +
α
2
P 2 +
β
4
P 4
− PE, (1)
where F0 is the paraelectric phase energy, E is the electric field, α and β are the expansion
coefficients. The α coefficient depends on temperature and changes its sign at the phase transition
point. The β coefficient should be positive for a second-order phase transition. By minimizing the
expression in equation (1) one obtains the equation of state of a unit volume of a ferroelectric
αP + βP 3 = E. (2)
Inverse dielectric permeability
ε−1 =
∂E
∂P
= α + 3βP 2 (3)
is a function of temperature and of the applied field magnitude. The extremum of this function
with respect to temperature can be found as follows:
∂ε−1
∂α
= 1 + 6βP
∂P
∂α
= 0. (4)
The ∂P
∂α value can be found from equation (2), taking into account the fact of the applied field
being independent of temperature:
∂E
∂α
= P + α
∂P
∂α
+ 3βP 2 ∂P
∂α
= 0. (5)
Hence
∂P
∂α
= −
P
α + 3βP 2
. (6)
By substituting equation (6) into equation (5), one obtains the value of polarization, at which the
extremum of the temperature dependence of dielectric permeability is observed:
P 2 =
α
3β
. (7)
Using equations (7) and (2), one can obtain
α = 1.19β1/3E2/3. (8)
578
External field effect on the anisotropy...
The α coefficient in the vicinity of the upper and lower phase transitions for Rochelle salt crystals
can be given by
α = αT (T − T2), α = αT (T1 − T ), (9)
where T1 and T2 are the temperatures of the lower and the upper phase transitions, respectively. By
substitution of equation (9) into equation (8), one arrives at the expressions for the temperatures
of dielectric permeability maximum under an electric field:
Tm1 = T1 − 1.19α−1
T β1/3E2/3, Tm2 = T2 + 1.19α−1
T β1/3E2/3. (10)
In order to find the dielectric permeability value at the maximum point substitute equations (7)
and (8) into equation (3):
εm = 0.42ε−1
0 β−1/3E−2/3. (11)
Taking into account the vicinity of the phase transitions in Rochelle salt to the double critical
point [16], the coefficient of expansion of thermodynamic potential can be written in the form
α = αT1 + αT2(T − T0)
2, (12)
where T0 = (T1−T2) is the midpoint of the temperature interval of the ferroelectric phase existence.
By substituting equation (12) into equation (8), one can obtain different expressions for the shift
of the temperatures of the dielectric permeability maxima for Rochelle salt crystals:
∆Tm1 = A −
√
1, 19α−1
T2
β1/3E2/3 + A2 , ∆Tm2 = −A +
√
1, 19α−1
T2
β1/3E2/3 + A2 , (13)
where A =
√
−αT1/αT2 . Contrary to equations (10), in which according to equation (9) the αT
coefficients can be different, in equations (13) for Rochelle salt crystals the shifts of the temperatures
of dielectric permeability maxima are the same in the absolute value and opposite in sign for the
upper and for the lower phase transitions. Exactly this situation that was observed in [17] where the
variation of the ∆Tm absolute value under the electric field for both phase transitions is practically
the same within the error limits. Using the experimental data of the discussed paper, we have found
the coefficients of expansion of thermodynamic potential in equation (1): αT1 = −7.4·108 J·m·C−2,
αT2 = 1.58 · 106 J · m · C−2K−2, β = 11.34 · 1013 J · m5
· C−4.
Using the experimental data of the studies of hydrostatic pressure effect on the Rochelle salt
crystal dielectric permeability, carried out in our earlier paper [17], we have obtained the pressure
dependences of αT1 and αT2 coefficients within the framework of phenomenological theory with
the account of the phase transition vicinity to the double critical point. These dependences are
shown in figure 11. With the pressure increase, an increase of the αT1 value is observed which
indicates the phase transition shift away from the double critical point which in the Rochelle salt
crystal corresponds to the negative hydrostatic pressure p = −240 MPa.
While studying the effect of transverse electric field on the upper phase transition in Rochelle
salt crystals we found that the reproducibility of the experimental data for different samples is
poor. Such a situation is a consequence of a non-uniform distribution of potentials between the
sample plates which results in the formation of a longitudinal electric field as well. The experimen-
tal results of [16] enable the effect of this field to be estimated and the dependence of the transition
temperature on the transverse electric field strength to be found. The recalculated values of the
transition temperature shift due to the electric field are shown in figure 12. As one can see, the effect
of transverse electric field, contrary to the longitudinal one, results in the phase transition temper-
ature decrease for all Rochelle salt samples with a coefficient ∆T (E)/∆E = −0.5± 0.1 K·cm/kV.
Theoretical calculations of the transverse electric field effect on the Rochelle salt dielectric proper-
ties performed within the framework of the Mitsui model [5], show that transverse external fields
make the ferroelectric phase existence interval narrower. This is confirmed by our experimental
data.
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A.G.Slivka, V.M.Kedyulich, H.M.Guyvan
Figure 11. Pressure dependence of the thermodynamic potential expansion coefficients αT1 and
αT2 of Rochelle salt crystals.
Figure 12. Dependence of the upper phase transition temperature on the transverse electric field
strength for different Rochelle salt samples.
5. Conclusions
Based on the experimental studies performed, we discuss the regularities of variation of anisotropy
of dielectric permeability of KH2PO4 and NaKC4H4O6·4H2O crystals due to temperature, pressure,
and electric field. In KDP crystals we experimentally observed new high-temperature anomalies
(250–300 K) in the temperature dependences of transverse dielectric permeability and dielectric loss
angle tangent which are due to the phase transition that occurs in local domains of nanometric size
with the 4̄2m−→mm2 symmetry change. Under external hydrostatic pressure, the temperatures
of these phase transitions increase. Within the framework of Landau phenomenological theory, the
experimental results for temperature dependences of longitudinal dielectric permeability of Rochelle
salt crystals under external longitudinal and transverse electric field are analyzed. The coefficients
αT1 and αT2 of thermodynamic potential expansion over the order parameter are calculated with
the account of the vicinity of phase transitions in Rochelle salt to the double critical point. The
increase of the αT1 absolute value with hydrostatic pressure p shows that the phase transitions in
Rochelle salt shift away from the double critical point which corresponds to p = −240 MPa. It is
shown experimentally that the effect of transverse electric field, contrary to the longitudinal one,
results in the upper phase transition decrease with a coefficient ∆T (E)/∆E = −0.5±0.1 K·cm/kV.
580
External field effect on the anisotropy...
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Matter Phys., 2005, 8, No. 3(43), 623.
Вплив зовнiшнiх полiв на анiзотропiю дiелектричної
проникностi кристалiв KH2PO4 та NaKC4H4O6 · 4H2O
О.Г.Сливка, В.М.Кедюлич, Г.М.Гуйван
Ужгородський нацiональний унiверситет, кафедра оптики Вул.Волошина, 54, 88000, Ужгород,
Україна
Отримано 5 червня 2008 р., в остаточному виглядi – 15 липня 2008 р.
Проведено експериментальнi дослiдження впливу температури, зовнiшнього тиску та електричного
поля на анiзотропiю дiелектричної проникностi кристалiв KH2PO4 та NaKC4H4O6 ·4H2O. У рамках фе-
номенологiчної теорiї та з врахуванням близькостi фазових переходiв до подвiйної критичної точки
проведено аналiз експериментальних результатiв по впливу електричного поля та тиску на дiеле-
ктричну проникнiсть сегнетової солi. Визначено коефiцiєнти розкладу термодинамiчного потенцiалу
по параметру порядку i їх баричну поведiнку. Показано, що збiльшення гiдростатичного тиску вiдда-
ляє фазовi переходи в сегнетовiй солi вiд подвiйної критичної точки.
Ключовi слова: сегнетоелектрики, фазовий перехiд, дiелектрична проникнiсть, температура,
тиск, електричне поле
PACS: 77.80.Bh, 77.22.Ch, 77.84.Fa
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