The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals
Temperature dependences of transverse dielectric permeability of KH₂PO₄ crystals under different values of hydrostatic pressure have been investigated. Within the framework of a tunnelling mode model, the dipole interaction energy and the tunnelling energy are suggested to be determined using the...
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Інститут фізики конденсованих систем НАН України
2002
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| Цитувати: | The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals / V.M. Kedyulich, A.G. Slivka, E.I. Gerzanich, A.M. Guivan // Condensed Matter Physics. — 2002. — Т. 5, № 4(32). — С. 761-767. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1206882017-06-13T03:05:03Z The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Guivan, A.M. Temperature dependences of transverse dielectric permeability of KH₂PO₄ crystals under different values of hydrostatic pressure have been investigated. Within the framework of a tunnelling mode model, the dipole interaction energy and the tunnelling energy are suggested to be determined using the temperature position of the dielectric permeability kinking point. From the temperature dependences of the dielectric permeability εa(T) under various pressures, the pressure dependences of these values are derived. Досліджено температурні залежності поперечної діелектричної проникності кристала КН₂Р0₄ при різних величинах гідростатичного тиску. В рамках моделі тунельної моди запропоновано спосіб визначення енергії дипольної взаємодії та енергії тунелювання з використанням температурного положення точки перегину діелектричної проникності. За результатами експериментальних досліджень залежностей ε(Т) при різних тисках отримано баричні залежності вказаних величин. 2002 Article The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals / V.M. Kedyulich, A.G. Slivka, E.I. Gerzanich, A.M. Guivan // Condensed Matter Physics. — 2002. — Т. 5, № 4(32). — С. 761-767. — Бібліогр.: 13 назв. — англ. 1607-324X PACS: 77.80.Bh, 77.22.Ch, 77.84.Fa DOI:10.5488/CMP.5.4.761 http://dspace.nbuv.gov.ua/handle/123456789/120688 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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DSpace DC |
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English |
| description |
Temperature dependences of transverse dielectric permeability of KH₂PO₄
crystals under different values of hydrostatic pressure have been investigated.
Within the framework of a tunnelling mode model, the dipole interaction
energy and the tunnelling energy are suggested to be determined using the
temperature position of the dielectric permeability kinking point. From the
temperature dependences of the dielectric permeability εa(T) under various
pressures, the pressure dependences of these values are derived. |
| format |
Article |
| author |
Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Guivan, A.M. |
| spellingShingle |
Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Guivan, A.M. The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals Condensed Matter Physics |
| author_facet |
Kedyulich, V.M. Slivka, A.G. Gerzanich, E.I. Guivan, A.M. |
| author_sort |
Kedyulich, V.M. |
| title |
The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals |
| title_short |
The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals |
| title_full |
The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals |
| title_fullStr |
The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals |
| title_full_unstemmed |
The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals |
| title_sort |
effect of hydrostatic pressure on transverse dielectric permeability of kh₂po₄ crystals |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2002 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120688 |
| citation_txt |
The effect of hydrostatic pressure on transverse dielectric permeability of KH₂PO₄ crystals / V.M. Kedyulich, A.G. Slivka, E.I. Gerzanich, A.M. Guivan // Condensed Matter Physics. — 2002. — Т. 5, № 4(32). — С. 761-767. — Бібліогр.: 13 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
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| first_indexed |
2025-07-08T18:24:27Z |
| last_indexed |
2025-07-08T18:24:27Z |
| _version_ |
1837104178856460288 |
| fulltext |
Condensed Matter Physics, 2002, Vol. 5, No. 4(32), pp. 761–767
The effect of hydrostatic pressure on
transverse dielectric permeability of
KH2PO4 crystals
V.M.Kedyulich, A.G.Slivka, E.I.Gerzanich, A.M.Guivan
Uzhgorod National University, 32 Voloshin Str., 88000 Uzhgorod, Ukraine
Received September 30, 2002
Temperature dependences of transverse dielectric permeability of KH2PO4
crystals under different values of hydrostatic pressure have been investigat-
ed. Within the framework of a tunnelling mode model, the dipole interaction
energy and the tunnelling energy are suggested to be determined using the
temperature position of the dielectric permeability kinking point. From the
temperature dependences of the dielectric permeability εa(T ) under vari-
ous pressures, the pressure dependences of these values are derived.
Key words: ferroelectrics, dielectric permeability, hydrostatic pressure
PACS: 77.80.Bh, 77.22.Ch, 77.84.Fa
1. Introduction
The first-order phase transition of the order-disorder type in KH2PO4 (KDP) crys-
tals is related to proton ordering in hydrogen bonds lying in the ab plane of the
tetragonal lattice structure [1]. Spontaneous polarization along the crystallograph-
ic orientation c is caused by ion displacements normal to the plane, in which the
hydrogen bonds lie. Thus, the structure of KDP crystal at the phase transition is
changed both along the orientation of spontaneous polarization and normal to it.
The studies of the behaviour of longitudinal dielectric permeability along the
orientation of spontaneous polarization show that in the paraelectric phase the de-
pendence εa(T ) obeys the Curie-Weiss law with the constant Cw = 2.91 · 103 K
[2]. The temperature dependence of the dielectric permeability under atmospheric
pressure with the orientation normal to Ps, was investigated in [3,4]. The εa(T ) de-
pendence was observed to undergo a step at the phase transition temperature. It
was shown [4] that from the studies of the transverse dielectric susceptibility one
can obtain information on the main parameters of Blinc – de Gennes [5] microscopic
model for this crystal: the values of the dipole interaction energy J(0) and tun-
nelling energy Γ which at the atmospheric pressure for KDP crystals are 204 K and
185 K, respectively. Here we report the studies of the effect of hydrostatic pressure
c© V.M.Kedyulich, A.G.Slivka, E.I.Gerzanich, A.M.Guivan 761
V.M.Kedyulich et al.
on the transverse dielectric permeability of KDP crystals and the derived pressure
dependences of the tunnelling energy and the dipole interaction energy.
2. Results
The temperature dependence of dielectric permeability εa of KDP crystal under
atmospheric pressure at the measuring field frequency 1 kHz is shown in figure 1.
This dependence possesses three characteristic features: a step of dielectric perme-
ability at the phase transition temperature Tc = 122 K, a maximum at the tem-
perature Tmax = 130 K (see the insert to figure 1) and a kinking point of dielectric
permeability at Tf = 172 K. The temperature dependences of transverse dielectric
permeability under various hydrostatic pressure values are shown in figure 2. With
the pressure increase, the εa(T ) dependence shifts to lower temperatures. The pres-
sure dependences of the values Tc, Tmax, Tf are shown in figure 3. The pressure
increase to 6.5 kbar causes a linear decrease of these temperatures with the coeffi-
cients: ∂Tc/∂p = −4.8 K/kbar, ∂Tmax/∂p = −5.4 K/kbar, ∂Tf/∂p = −5.4 K/kbar.
The existence of a maximum of dielectric permeability at T > Tc was also ob-
served in other antiferroelectric crystals such as KMnF3, NH4H2AsO4 [6]. However,
in NH4H2AsO4 crystals, the increase of the external pressure value causes the broad-
ening of the temperature range between Tc and Tmax, while for KDP, the difference
in the pressure coefficients of the phase transition temperature Tc and the temper-
ature of maximal dielectric permeability Tmax causes the decrease of the Tmax − Tc
difference with pressure.
Figure 1. The temperature dependence of transverse dielectric permeability of
KDP crystal under atmospheric pressure.
762
The effect of hydrostatic pressure on KH2PO4
Figure 2. The temperature dependences of transverse dielectric permeability of
KDP crystal under various hydrostatic pressures.
Figure 3. The pressure dependences of the Tc, Tmax, Tf values.
763
V.M.Kedyulich et al.
3. Discussion
A relation, describing the temperature dependence of transverse dielectric sus-
ceptibility for KDP-type crystals in the paraelectric phase was obtained in [4]:
χa =
Nµ2
2
Γ
tanh (Γ/T )
1 + J(0)
3Γ
tanh (Γ/T )
, (1)
where J(0) is the dipole interaction energy in the mean-field approximation, N is
hydrogen bond concentration, µ2 is the dipole moment along the a-axis. Based on
equation (1) and using the relationship between J(0), Γ and the phase transition
temperature Tc
tanh
(
Γ
Tc
)
=
Γ
J(0)
, (2)
the authors of [4] suggested that the unknown values of J(0) and Γ can be determined
using the experimental dependences of εa(T ). At T � Tc equation (1) can be given
by
χ−1
a =
kT
Nµ2
2
, (3)
which permits the value of µ2 to be found from the slope of the experimental curve.
But the nonlinear character of this dependence causes the ambiguity of the derived
µ2 value. The highest accuracy can be achieved from the µ2 phase transition tem-
perature. However, at high temperatures, the conductivity of the samples increases,
which induces additional uncertainty to the determination.
From the known value of µ2 and transverse dielectric susceptibility at the phase
transition temperature χ−1
a (Tc) using a relationship [4]
χ−1
a =
3
4
J(0)
Nµ2
2
(4)
the dipole interaction energy J(0) was derived. However, as shown in the insert
in figure 1, the dependence εa(T ) has an anomalous character at Tmax > Tc, not
being described by equation (1). Therefore, the value χ−1
a (Tc) and, hence, the dipole
interaction energy J(0) are also derived with some approximation.
The analysis of equation (1) shows that the dependence has a kink in the para-
electric phase, being clearly revealed in the experimental curves. This feature of
the temperature behaviour of the transverse dielectric permeability can be used for
deriving J(0) and Γ energies in the simplest way. The position of the kinking point
can be found from the condition ∂2χa/∂T 2 = 0:
tanh
(
Γ
Tf
)
=
(3Tf − J(0))Γ
3Γ2 − J(0)Tf
. (5)
From equations (5) and (2), one can determine the unknown values of tunnelling
energy and dipole interaction energy, using the temperatures of the phase transition
764
The effect of hydrostatic pressure on KH2PO4
Figure 4. The pressure dependences of tunnelling energy Γ and dipole interaction
energy J(0).
and the kinking point of εa(T ) dependence, which can be easily derived from the
experimental data.
The approach proposed to obtain the parameters of the Blinc – de Gennes theory
for KDP crystals has a number of advantages. First, there is no necessity to use the
εa(T ) dependences far from the transition temperature, where, besides the increase
of the sample conductivity, high-temperature anomalies of the dielectric permeability
can be observed [7,8]. Second, the knowledge of the dielectric permeability value at
the transition temperature and the dipole moment value µ2 is not required. Third,
the temperature positions of the phase transition and the kinking point of the εa(T )
plot are independent of the accuracy of determining the absolute value of dielectric
permeability.
Thus, based on the experimental studies of εa(T ) dependences, the values of
tunnelling and dipole interaction energies were derived, their values at atmospheric
pressure being J(0) = 207 K and Γ = 190 K, respectively, which are close to those
derived in [4]. The pressure dependence of these values is shown in figure 4. The
increase of the external hydrostatic pressure causes the decrease of both values with
the coefficients ∂J(0)/∂p = −6.8 K/kbar, ∂Γ/∂p = −5.9 K/kbar.
The values of the tunnelling energy and the dipole interaction energy depend on
the distance between two potential minima along the hydrogen bonds, along which
protons move. Since the pressure increase causes the decrease of this distance, the
tunnelling energy value should increase and the dipole interaction energy should
765
V.M.Kedyulich et al.
decrease [9]. It was expected that the pressure change of the tunnelling energy should
essentially exceed the pressure change of the dipole interaction energy. However,
Raman studies [10] have shown that the decrease of the dipole interaction energy
with pressure is three times greater than the tunnelling energy increase. Such a
behaviour of these parameters was related to the pressure-induced rotation of PO4-
groups around the fourth-order axis and to the temperature change of the tunnelling
energy [11].
As follows from figure 4, the pressure behaviour of the dipole interaction energy,
deduced from transverse dielectric permeability studies, confirms the theory. How-
ever, the tunnelling energy value decreases with pressure. This situation may be
related to the unsatisfactory description of the experimental temperature behaviour
of the transverse dielectric permeability by equation (1). The fact that the tem-
perature dependence of the tunnelling energy has been neglected is very important
as follows from [11]. Hence, further experimental studies of KDP-type crystals are
required in order to elucidate the role of the hydrogen bond length in the phase
transition mechanism as well as the role of piezoelectric effect and electrostriction,
which is significant for the crystals of this group [12,13]. Having this in view, the
experimental studies of the effect of hydrostatic as well as of uniaxial stresses in var-
ious directions on the anisotropy of fundamental physical properties for KDP-type
crystals are important indeed.
4. Conclusion
From the studies of the temperature dependences of transverse dielectric per-
meability in KDP crystals under various hydrostatic pressures, the pressure depen-
dences of the phase transition temperature, the temperature of maximal dielectric
permeability and the temperature of the of εa(T ) plot kinking point are derived.
The increase of the hydrostatic pressure causes the decrease of these parameters.
The difference of the pressure coefficients of the phase transition temperature and
the temperature of maximal dielectric permeability causes the decrease of the dif-
ference Tmax − Tc. The values of the tunnelling energy and the dipole interaction
energy are suggested to be determined using the temperature position of the kinking
point of the εa(T ) dependence. The calculation results show the decrease of the tun-
nelling energy and of the dipole interaction energy with pressure, while the earlier
investigations show the increase of Γ value with pressure [10]. This discrepancy is
related to the difference in the theoretically calculated and experimental behaviour
of the transverse dielectric permeability in the vicinity of the phase transition in
the paraelectric phase as well as to the fact that the temperature dependence of the
tunnelling energy has been neglected.
5. Acknowledgements
The authors are grateful to Professor R.R.Levitskii for having involved us in the
studies and for showing a permanent interest in this study.
766
The effect of hydrostatic pressure on KH2PO4
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9. Samara G.A. // Phys. Rev. Lett., 1971, vol. 27, No. 103
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vol. 4, No. 3(27), p. 553.
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