The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field
The effect of external factors, such as dessicating/wetting, thermal annealing, uniaxial and hydrostatic pressure, on the dielectric permittivity of Rochelle salt crystals is investigated. The obtained results are compared with the available literature data and analyzed within the phenomenologica...
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Інститут фізики конденсованих систем НАН України
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| Цитувати: | The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field / A.G. Slivka, V.M. Kedyulich, R.R. Levitskii, A.P. Moina, M.O. Romanyuk, A.M. Guivan // Condensed Matter Physics. — 2005. — Т. 8, № 3(43). — С. 623–638. — Бібліогр.: 29 назв. — англ. |
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irk-123456789-1197442017-06-09T03:02:48Z The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field Slivka, A.G. Kedyulich, V.M. Levitskii, R.R. Moina, A.P. Romanyuk, M.O. Guivan, A.M. The effect of external factors, such as dessicating/wetting, thermal annealing, uniaxial and hydrostatic pressure, on the dielectric permittivity of Rochelle salt crystals is investigated. The obtained results are compared with the available literature data and analyzed within the phenomenological Landau approach. A significant effect of the internal polar point defects in crystals and storage conditions on the dielectric permittivity is shown. Робота містить результати експериментальних досліджень впливу зовнішніх факторів таких, як, висушування/зволоження, термічний відпал, електричне поле, одновісні тиски, гідростатичний тиск, на діелектричну проникність кристалів сегнетової солі. Отримані результати порівнюються з відомим літературними даними та аналізуються в рамках феноменологічного підходу. Показано, що умови зберігання та внутрішні полярні точкові дефекти суттєво впливають на діелектричну проникність кристалів. 2005 Article The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field / A.G. Slivka, V.M. Kedyulich, R.R. Levitskii, A.P. Moina, M.O. Romanyuk, A.M. Guivan // Condensed Matter Physics. — 2005. — Т. 8, № 3(43). — С. 623–638. — Бібліогр.: 29 назв. — англ. 1607-324X PACS: 77.80.Bh, 77.22.Ch DOI:10.5488/CMP.8.3.623 http://dspace.nbuv.gov.ua/handle/123456789/119744 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 |
The effect of external factors, such as dessicating/wetting, thermal annealing,
uniaxial and hydrostatic pressure, on the dielectric permittivity of
Rochelle salt crystals is investigated. The obtained results are compared
with the available literature data and analyzed within the phenomenological
Landau approach. A significant effect of the internal polar point defects in
crystals and storage conditions on the dielectric permittivity is shown. |
| format |
Article |
| author |
Slivka, A.G. Kedyulich, V.M. Levitskii, R.R. Moina, A.P. Romanyuk, M.O. Guivan, A.M. |
| spellingShingle |
Slivka, A.G. Kedyulich, V.M. Levitskii, R.R. Moina, A.P. Romanyuk, M.O. Guivan, A.M. The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field Condensed Matter Physics |
| author_facet |
Slivka, A.G. Kedyulich, V.M. Levitskii, R.R. Moina, A.P. Romanyuk, M.O. Guivan, A.M. |
| author_sort |
Slivka, A.G. |
| title |
The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field |
| title_short |
The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field |
| title_full |
The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field |
| title_fullStr |
The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field |
| title_full_unstemmed |
The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field |
| title_sort |
effect of external factors on dielectric permittivity of rochelle salt: humidity, annealing, stresses, electric field |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119744 |
| citation_txt |
The effect of external factors on dielectric permittivity of Rochelle salt: humidity, annealing, stresses, electric field / A.G. Slivka, V.M. Kedyulich, R.R. Levitskii, A.P. Moina, M.O. Romanyuk, A.M. Guivan // Condensed Matter Physics. — 2005. — Т. 8, № 3(43). — С. 623–638. — Бібліогр.: 29 назв. — англ. |
| series |
Condensed Matter Physics |
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Condensed Matter Physics, 2005, Vol. 8, No. 3(43), pp. 623–638
The effect of external factors on
dielectric permittivity of Rochelle salt:
humidity, annealing, stresses, electric
field
A.G.Slivka 1 , V.M.Kedyulich 1 , R.R.Levitskii 2 , A.P.Moina 2 ,
M.O.Romanyuk 3 , A.M.Guivan 1
1 Uzhgorod National University,
54 Voloshin Street, 88000 Uzhgorod, Ukraine
2 Institute for Condensed Matter Physics,
1 Svientsitskii Street, 79011 Lviv, Ukraine
3 Ivan Franko Lviv National University,
8 Kyryla and Mefodiya Street, 79005 Lviv, Ukraine
Received May 18, 2005
The effect of external factors, such as dessicating/wetting, thermal an-
nealing, uniaxial and hydrostatic pressure, on the dielectric permittivity of
Rochelle salt crystals is investigated. The obtained results are compared
with the available literature data and analyzed within the phenomenological
Landau approach. A significant effect of the internal polar point defects in
crystals and storage conditions on the dielectric permittivity is shown.
Key words: Rochelle salt, pressure, electric field, defects, annealing,
humidity
PACS: 77.80.Bh, 77.22.Ch
1. Introduction
A useful information about ferroelectric crystals can be obtained by exploring
their behavior under the influence of various external factors, such as high pressure
or electric field. For hydrogen bonded crystals the external pressures are the only way
to continuously vary geometric parameters of bonds, to break their equivalence, etc,
which permits to investigate the role of hydrogen bonds, their parameters and sym-
metry the phase transition and dielectric response of the crystals. Many ferroelectrics
are piezoelectric in the paraelectric phase; application of shear stresses and the con-
jugate electric fields allows one to explore the role of piezoelectric interactions in the
phase transitions and in the formation of physical characteristics of the crystals.
c© A.G.Slivka, V.M.Kedyulich, R.R.Levitskii, A.P.Moina, M.O.Romanyuk, A.M.Guivan 623
A.G.Slivka et al.
These possibilities were fully used for the investigation of the KH2PO4 family
crystals. Theoretical description of pressure and field effects in these crystals is
usually performed within the proton ordering model (see e.g. [1–6] and references
therein); a quantitative agreement with the experiment is obtained. It was shown,
in particular, that pressures of different symmetries produce qualitatively different
changes in the phase transition: lower its temperature down (hydrostatic), raise it
up and smear out the transition (shear stress σ6), induce a new phase of monoclinic
symmetry (as σ1 − σ2).
In contrast to the KH2PO4 family crystals, the data concerning the influence
of external factors on Rochelle salt are less extensive. The data, in particular, are
available on hydrostatic pressure [7–9] and electric field [10–12] effects on the elastic
constant and dielectric permittivity of the crystals. Uniaxial stress effects on the
phase transitions in Rochelle salt were explored in [13] from the measurements of
thermoelastic effect. Theoretically the effect of the shear stress σ4 was studied in
[14] within the modified Mitsui model.
Usually, physical characteristics of ferroelectric crystals in the vicinity of phase
transitions (especially of the second order ones) are affected by crystal defects and
internal bias electric fields and mechanical stresses, which act as the external ones.
The role of such factors as crystal defectness and the processes in the sample pre-
history that may affect the physical properties of the crystals via relaxation of the
defects such as thermal annealing, previous action of electromagnetic fields and me-
chanical stresses should be explored. High pressure and electric field studies make it
possible to explore the intrinsic field and pressure dependences of the crystal char-
acteristics, reveal the internal bias fields and stresses, and study the residual effects
of the internal defects.
For Rochelle salt, whose efflorescence (loss of crystallization water) and deli-
quescence (uptake of water) are well known, such a factor as storage air humidity
is important and should be monitored during measurements. For instance, a sig-
nificant dispersion of experimental data for the dielectric permittivity of Rochelle
salt (see the systematization in [15]), which exceeds the measurement error, takes
place. Apparently, the dispersion is due to different internal states of the samples
uncontrolled during measurements.
In the present work, the effect of the above mentioned external factors (pressure,
electric field, humidity, thermal annealing) on the dielectric permittivity of Rochelle
salt crystals in the vicinity of the structural phase transitions are explored.
2. Experimental setup
Dielectric permittivity ε11 of the crystals at 1 kHz was determined by measuring
the capacity of the samples by means of an a.c. bridge. Measurement error was
0.2 ÷ 0.4%. Samples were prepared in the form of parallellepipeds, with the faces
perpendicular to the crystallographic axes of the orthorhombic (paraelectric) unit
cell. Silver paste and copper wires, 0.08 ÷ 0.12 mm diameter, were used as electric
contacts. After partial drying of the paste, the contacts were covered by an alcohol
624
The influence of external factors on dielectric permittivity of Rochelle salt
solution of a glue with addition of silver paste. This method provided a necessary
mechanical stability of the contacts and made a free deformation of the crystals
possible.
A uniaxial pressure was created by a spring dynamometer and was transmitted
to samples via a punch with floating heads, thus securing a uniform pressure even
at possibly non-parallel faces of the sample. The pressure was set with an accuracy
of ±5%. Temperature was measured using a copper-constantan thermocouple with
an accuracy ±0.1 . Samples with the thermocouple were covered with silicone oil,
in order to enhance heat transmission and prevent direct contact with the air.
3. Model approach
Theoretical description of the physical properties of Rochelle salt is usually per-
formed within a two-sublattice Ising model with asymmetric double well potential
(Mitsui model). Hereinafter we present the expression for the dielectric permittivity
of Rochelle salt obtained within the modified Mitsui model with taking into account
the piezoelectric coupling [15] with the Hamiltonian
Ĥ =
N
2
vcE0
44 ε2
4 − Nve0
14ε4E1 −
N
2
vχ0
11E
2
1 −
1
2
∑
qq′
2∑
ff ′=1
Rqq′(ff ′)
σqf
2
σq′f ′
2
−∆
∑
q
(σq1
2
−
σq2
2
)
− (µ1E1 − 2ψ4ε4)
∑
q
2∑
f=1
σqf
2
. (3.1)
Three first terms in (3.1) correspond to a “seed” energy of the crystal lattice which
forms the asymmetric double-well potential for pseudospins. Rqq′(11) = Rqq′(22) =
Jqq′ and Rqq′(12) = Rqq′(21) = Kqq′ are constants of interaction between pseudospins
belonging to the same and to different sublattices, respectively. The parameter ∆
describes the asymmetry of the double well potential; µ1 is the effective dipole
moment. The last term is the internal field created by the piezoelectric coupling
with the shear strain ε4; the quantity ψ4 describing this coupling is treated as a
model parameter.
Within a mean field approximation the static dielectric permittivity of a free
crystal was obtained in the form [15]
χσ
11 = χσ0
11 +
β(µ′
1)
2
2v
F2. (3.2)
The following notations are used
F2 =
ϕ3
ϕ2 − Λϕ3
,
ϕ2 = 1 − βJ
2
λ1 − β2 K2
−J2
16
(λ2
1 − λ2
2), ϕ3 = λ1 + β K−J
4
(λ2
1 − λ2
2), Λ =
2βψ2
4
vcE0
44
,
λ1 = 1 − ξ2 − σ2, λ2 = 2ξσ,
χσ0
11 = χε0
11 + e0
14d
0
14, µ′
1 = µ1 − 2ψ4d
0
14, d0
14 =
e0
14
cE0
44
,
625
A.G.Slivka et al.
ξ, σ are the parameters of ferroelectric and antiferroelectric ordering.
Values of the model parameters providing the best fit to the permittivity are
given in table 1.
Table 1. Model parameters for Rochelle salt [15].
J/kB K/kB ∆/kB ψ4/kB cE0
44 d0
14 χσ0
11
K dyn/cm2 esu/dyn
797.36 1468.83 737.33 –760 12.8 · 1010 1.9 · 10−8 0.363
v = 0.5219[1+0.00013(T −190)] ·10−21 cm3, µ1 = [2.52+0.0066(297−T )] ·10−18 esu cm.
4. The effect of sample prehistory
4.1. Humidity
In [16] it was found that crystals of Rochelle salt at 25◦ and at relative humidity
below 40% lose the crystallization water, whereas at relative humidity above 85%
they absorb water from the air. Significant changes of the piezoelectric properties of
Rochelle salt were observed in the samples kept in the air with a high concentration
of ethanol vapor [17]. An essential effect of humidity on the relaxation times of the
dielectric permittivity of Rochelle salt was also observed in [18] and attributed to
the concentration changes of water vacancies in the lattice.
Experimental data for susceptibility of Rochelle salt (see figure 1) are strong-
ly dispersed, even in the paraelectric phases. This cannot be accounted for by the
differences in the measurement regimes. Thus it was interesting to explore the tem-
perature dependences of Rochelle salt crystals with different water content in order
to verify whether this dispersion can be attributed, at least partially, to it.
Figure 1. Temperature dependences of inverse susceptibility of Rochelle salt. Left:
solid lines – experimental data of this work, obtained for dessicated (1) and wet
(2) samples. Right: solid line – theoretical curve, calculated with equation (3.2).
¥ – [19]; N – [20]; ¨ – [21]; • – [22]; H – [23]; + – [24].
626
The influence of external factors on dielectric permittivity of Rochelle salt
The obtained results are presented in figure 1 (left). Along with the literature da-
ta, here we show the temperature dependences of the inverse dielectric susceptibility
χ−1
11 (solid curves 1 and 2), obtained in this work for the same sample with different
water content. The curve 1 was obtained for a sample, kept for a long time (2–3
days) at room temperature in a closed volume, filled with a dessicator (silicagel).
The curve 2 corresponds to the same sample, kept for 10 hours in the air with rela-
tive humidity ∼90%. As one can see, keeping the sample in a wet air increases the
dielectric susceptibility in the entire temperature range studied. The changes are
particularly prominent in the middle of the ferroelectric phase T ∼ 275 K and in
the high-temperature paraelectric phase.
Comparison of the obtained results with literature data shows that the dispersion
in the values of the susceptibility can be caused by the different water content in the
samples used in different experiments. It should be also noted that for the wet sample
(curve 2, figure 1), a linear temperature dependence of the inverse susceptibility is
observed with the Curie-Weiss constant CW = 1.95·103 K. For the dessicated sample,
this dependence is non-linear in both paraelectric phases.
Comparison of literature experimental data with the theoretical curve ([15] and
equation (3.2)), is given in figure 1 (right). Theoretical values of permittivity are
adjusted by the value of the effective dipole moment µ1. In [15] µ1 was chosen such
that the best agreement with the data of [23] as well as of the dynamic microwave
permittivity should be obtained. However, we failed to get an adequate agreement
with the experiment for susceptibility in the low-temperature paraelectric phase [15].
4.2. Thermal annealing
Figure 2 illustrates the temperature dependences of dielectric permittivity of
Rochelle salt near the upper Curie point for samples annealed at 308 K. On in-
creasing the annealing time, the value of the dielectric permittivity at the transition
point increases, and the maximum temperature decreases. Such changes are ap-
Figure 2. Temperature dependences of dielectric permittivity of Rochelle salt
near the upper transition point at different times of annealing in the paraelectric
phase at 308 K (min): 1 – 0, 2 – 5, 3 – 20, 4 – 60. Inset: dependences of the
maximal value of permittivity and maximum temperature on annealing time.
627
A.G.Slivka et al.
parently caused by internal electrical bias fields whose magnitude is decreased by
annealing.
Keeping the samples in the ferroelectric phase for a long term the internal bias
fields caused by polar defects [25] participate in screening the spontaneous polariza-
tion and reflect the corresponding domain structure. The action of the internal bias
field is analogous to the action of external field, that is, the temperature of the upper
maximum of permittivity increases, and the maximum magnitude decreases. In the
next section we shall estimate the magnitudes of internal bias fields in non-annealed
and annealed samples.
5. The effect of external electric field
In figure 3 we show the measured temperature dependences of dielectric per-
mittivity ε11 of Rochelle salt crystals near the upper and lower transition points at
different values of external d.c. electric field E = E1 applied along the ferroelectric
axis (conjugate to polarization). The insets contain the field dependences of the
dielectric permittivity maxima εm and their temperatures ∆Tm = Tm(E) − Tm(0).
The data are obtained by cooling samples for the upper maximum and by heating
for the lower one (from the corresponding paraelectric phase towards the ferroelec-
tric phase). As expected, the external field, conjugate to polarization, decreases the
εm and shifts the maxima temperatures ∆Tm in a non-linear way. For the upper
maximum ∆Tm2 > 0, whereas for the lower one ∆Tm1 < 0.
Figure 3. Temperature dependences of dielectric permittivity of Rochelle salt
crystals near upper and lower transition points at different values of external
electric field E1 (kV/cm): 1 – 0, 2 – 0.05, 3 – 0.1, 4 – 0.2, 5 – 0.3, 6 – 0.5, 7 –
0.75, 8 – 1. Lines are guide to the eyes.
These results are compared in figure 4 with literature data [26]. The field de-
pendences of the permittivity maxima magnitudes ε−1
m (E) obtained in this work are
the same for the two maxima (see figure 4) and well accord with the data of [26].
However, a perceptible disagreement is observed for the shift of permittivity maxima
temperatures. Our data yield very close changes of |∆Tm| with the field for the two
628
The influence of external factors on dielectric permittivity of Rochelle salt
0.01 0.1
1
10
4
3
2
1
∆T
m
i ,
K
E , MV/m
Figure 4. Field dependences of the permittivity maxima magnitudes (left) and
temperature shifts (right). Upper maximum: line 1 (•) – this work, line 3 (H) –
[17]. Lower maximum – line 2 (◦) – this work, line 4 (M) – [17].
maxima. On the contrary, the field dependence of the upper maximum temperature
obtained in [26] is much stronger than of the lower one.
For uniaxial ferroelectrics such as Rochelle salt, the phenomenological Landau
expansion of thermodynamic potential can be presented as (elastic and piezoelectric
contributions not considered)
Φ(P1) = Φ0 +
α
2
P 2
1 +
β
4
P 4
1 , (5.1)
where P1 is the crystal polarization, α, β are the expansion coefficients. The electric
field E1 is applied along the axis of spontaneous polarization [100].
From (5.1) the following equations for polarization and inverse permittivity follow
E1 =
(
∂Φ
∂P1
)
= αP1 + βP 3
1 , ε−1
11 = ε0
(
∂E1
∂P1
)
= ε0(α + 3βP 2
1 ), (5.2)
ε0 is the dielectric permittivity of vacuum.
For Rochelle salt there are two possible ways to model the temperature depen-
dence of the coefficient α.
1. The expansion (5.1) is performed near each of the two transitions separately,
assuming a linear temperature dependence α = αT1(TC1 − T ) for the lower
transition and α = αT2(T −TC2) for the upper one. Then the field dependences
of εm(E1) and ∆Tm(E1) can be presented as [25]:
ε−1
m =
3
2
(4β)1/3ε0E
2/3
1 = k1E
2/3
1 . (5.3)
|∆Tmi| =
3
4
(4β)1/3
αTi
E
2/3
1 = k2E
2/3
1 , i = 1, 2. (5.4)
2. Within the second approach, the coefficient α is chosen in the form
α = α1 + α2(T − T0)
2, (5.5)
629
A.G.Slivka et al.
where T0 = TC1+TC2
2
, and TC1,2 = T0 ∓
√
−α1
α2
. Such a choice is supported by
the fact that the phase transitions in Rochelle salt are close to a double critical
point [10,27], realized at partial substitution of potassium atoms with ammo-
nia NH4 [11,28]. In [10,27] the temperature dependences of several physical
characteristics of Rochelle salt were successfully described within the Landau
approach with (5.5).
In this case, the field dependences of ∆Tm(E1) are
∆Tm1,2 = ±A ∓
√
3
4
(4β)1/3
αT2
E
2/3
1 + A2, (5.6)
where A2 = −α1/α2. The field dependence of εm(E1) in this case is the same
as in the first approach and described by (5.3).
Figure 5. Field dependence of the upper permittivity maximum temperature
shift. Line is calculated with (5.4). Symbols are experimental data of this work.
The experimental dependences of ε−1
m (E1) of this work are well described by
equation (5.3) with k1 = 10.2 · 10−7(m/V)2/3 and β = 11.34 · 1013 V·m5/C3. Fitting
to the experimental data for ∆Tm(E1) with equation (5.4), shown in figure 5, yields
the values of k2 and αT1, αT2 for the upper and lower maxima:
for TC1 : k2 = 9.9 · 10−4 K(m/V)2/3 and αT1 = 5.82 · 107 V · m · (K · C)−1;
for TC2 : k2 = 10.5 · 10−4 K(m/V)2/3 and αT2 = 5.49 · 107 V · m · (K · C)−1.
The agreement with experiment for ∆Tm(E1), obtained with formulas (5.6) is
not any better than with (5.4). We found that
α1 = −5.82 · 108 V·m·C−1, α2 = 1.32 · 106 V·m·C−1·−2.
The second approach is advantageous only at describing the physical characteris-
tics of Rochelle salt in a sufficiently wide temperature range in paraelectric phases,
where the non-linear temperature dependence of the inverse permittivity should be
essential. For the description of the ∆Tm(E1) dependences considered here, the non-
linearity of the coefficient α within a few Kelvins near the transition points does not
play any significant role.
630
The influence of external factors on dielectric permittivity of Rochelle salt
Description of field dependences of dielectric permittivity of Rochelle salt within
a modified Mitsui model with piezoeffect will be given elsewhere.
Using the above results, we can estimate the magnitude of internal bias fields
existing in crystals without annealing as well as after 60 min of annealing. In the
former and latter cases, the values of the permittivity at the upper transition point
are about 3500 and 5100 (see figure 2). Therefore, using (5.3) and the found values
of k2, we get that at the upper Curie point Ebias = 0.055 kV/cm for a non-annealed
sample and Ebias = 0.027 kV/cm for the sample annealed for 60 min.
6. External pressures
6.1. Uniaxial stresses
The temperature dependences of dielectric permittivity ε11 of Rochelle salt were
measured at different values of mechanical stresses applied along the main crystal-
lographic directions of unit cell: [100] – σ1, [010] – σ2, [001] – σ3 and along [011] –
σ̃4. In the reference system with axes along the main crystallographic directions, the
stress σ̃4 can be presented as
σ̃4 = σ4 +
1
2
(σ2 + σ3), (6.1)
where σ4 is the shear strain, which for the Rochelle salt symmetry is the external
field conjugate to the order parameter and acts similarly to the electric field E1.
Figure 6. Temperature dependences of dielectric permittivities of Rochelle salt at
different values of mechanical stress σ1 and the stress dependences of permittivity
maxima temperatures.
Figures 6–9 contain the obtained temperature dependences of dielectric permit-
tivities at different values of uniaxial stresses and the corresponding stress depen-
dences of the permittivity maxima temperatures. The data, as in the case of electric
631
A.G.Slivka et al.
field study, were obtained at cooling for the upper maximum and at heating for the
lower maximum (on going from the corresponding paraelectric phase towards the
ferroelectric phase).
Figure 7. Same for the stress σ̃4.
Figure 8. Same for the stress σ2.
All the explored uniaxial stresses decrease the maximal values of dielectric per-
mittivity and change their temperatures Tm1 and Tm2. The action of the stresses σ1
and σ̃4 on Tm1 and Tm2 is non-linear and similar to the action of the electric field
632
The influence of external factors on dielectric permittivity of Rochelle salt
E1: dTm1/dσi < 0; dTm2/dσi > 0 (i = 1 and 4̃). The change of the upper maxi-
mum temperature with the stress σ̃4 is much larger than of the lower maximum. Let
us remind that the changes of the maxima temperatures with the electric field E1
obtained in this work are almost the same for the two maxima (see figures 4, 5).
Figure 9. Same for the stress σ3.
In section 6.3 we shall compare our results with the corresponding literature
data [13] obtained from the thermoelastic effect studies and with the data of the
phenomenological analysis. As we shall see, our data qualitatively agree with the
literature, except for the case of stress σ3. However, the quantitative agreement is
rather poor, our data for |∆TCi| being a few times smaller.
6.2. Hydrostatic pressure
Figure 10 contains the temperature dependences of the dielectric permittivity of
Rochelle salt at different hydrostatic pressures. In contrast to electric field or uniaxial
stresses, the hydrostatic pressure increases the both transition temperatures (see the
inset with the p, T -diagram). The pressure coefficients of transition temperatures are
dTC1/dp = 3.54 K/kbar and dTC2/dp = 10.92 K/kbar, in perfect agreement with
the data of [7,8]. On increasing the hydrostatic pressure, the value of εm at the lower
transition point TC1 monotonously decreases but remains unchanged at TC2.
633
A.G.Slivka et al.
Figure 10. Temperature dependence of the dielectric permittivity of Rochelle salt
at different values of hydrostatic pressure p, MPa: 1 – 0; 2 – 50; 3 – 120; 4 – 200;
5 – 320. (Inset: the p, T phase diagram. Dashed lines and ◦ – data of [7].)
6.3. Phenomenological description of pressure effects
For phenomenological description of external pressure effects on the phase tran-
sitions in Rochelle salt, let us modify the expansion (5.1) in the following way
Φ(P1, σi) = Φ0 +
α
2
P 2
1 +
β
4
P 4
1 +
3∑
i=1
qi1σiP
2
1 + g14P1σ4 −
1
2
4∑
ij=1
sP
ijσiσj. (6.2)
For the sake of simplicity we changed here the signs of the stresses σi as compared
to the standard notations, so that the uniaxial compression stresses are positive,
and for the hydrostatic pressure we have p = σ1 = σ2 = σ3. In standard notations
−p = σ1 = σ2 = σ3 and the values of the compression stress are negative.
The quantities qi1 are the electrostriction coefficients; sP
ij are the elastic com-
pliances at constant polarization. Let us note that sP
ij for i = 1, 2, 3 and sP
44 are
practically temperature independent, whereas sP
i4 ∼ P1, that is, they are different
from zero only in the ferroelectric phase or in the presence of electric field (possibly
internal bias field Ebias due to polar defects) or stress σ4.
From (6.2) the equations for polarization and lattice strains follow
E1 = g14σ4 + (α + 2
3∑
i=1
qi1σi)P1 + βP 3
1 −
3∑
i=1
sP
i4
P1
σiσ4, (6.3)
ui =
∂Φ
∂σi
= −
4∑
j=1
sP
ijσj + qi1P
2
1 , i = 1, 2, 3, (6.4)
u4 = g14P1 −
4∑
j=1
sP
ijσj. (6.5)
Assuming a linear dependence of the coefficient α = αT1(TC1−T ) for the lower tran-
sition and α = αT2(T −TC2) for the upper one, we get for the transition temperature
634
The influence of external factors on dielectric permittivity of Rochelle salt
shift and the inverse values of permittivity of a free crystal (at constant stress)
∆TC1,2 = ±
2
αT1,2
3∑
i=1
qi1σi ∓ k1(Ebias − g14σ4)
2/3 , (6.6)
ε−1
m1,2 = k2(Ebias − g14σ4 +
3∑
i=1
sP
i4
P1
σiσ4)
2/3. (6.7)
Experimental data for g14 are rather dispersive (see the systematization in [15]).
We used here the theoretical data for g14 of [15], that agree overall with the experi-
ment. The electrostriction coefficients have been determined in [29]. We adjust here
their values, in order to get a good fit to the hydrostatic pressure dependences of
transition temperatures. The values of qi1, g14 at lower and upper transition points
are given in table 2.
Table 2. The data for qi1 (in m4/C2) and g14 (in m2/C).
q11 q21 q31 g14
TC1 –7.5 4 4.5 0.174
TC2 –10 4.3 2.5 0.195
First we consider the case of a perfect crystal (Ebias = 0). The calculated shifts
of transition temperatures (permittivity maxima temperatures) with uniaxial and
hydrostatic pressures are presented in table 3. As one can see, a very good agreement
is obtained with the hydrostatic pressure data, as well as the data of [13] for the
uniaxial stresses. The agreement with the data for σ̃4 is completely unsatisfactory.
Here we used an assumption that, according to (6.1), σ̃4 = 100 bar corresponds to
a sum of σ4 = 50 bar, σ2 = 50 bar, σ3 = 50 bar. Our data for the uniaxial stresses
σ1, σ2, σ3 are also in poor agreement with the phenomenology and with the literature
data; however, the calculations agree with [13] fairly well.
Table 3. Shifts of the transition temperatures with uniaxial stresses (per 100 bar)
and with hydrostatic pressure (per 1 kbar).
σ1 σ2 σ3 σ̃4 hydrostatic
exp. [13] calc. exp. [13] calc. exp. [13] calc. exp. calc. exp. calc.
TC1 –1.2 –2.9 –2.73 0.4 1.5 1.46 0 1.7 1.63 –1.0 –8.8 3.43 3.64
TC2 2.0 3.5 3.44 –0.6 –1.6 –1.48 0.5 –0.8 –0.86 2.2 9.1 10.92 10.99
It seems likely that the disagreement between the experimental data of this work
and of [13] should be attributed to the effect of sample defects. We recalculated the
shifts of the maxima temperature with uniaxial pressure taking into account the role
of internal bias field, determining them from (6.7). A much better agreement was
635
A.G.Slivka et al.
obtained for the stresses σ2 and σ3: |∆TCi| decrease by several times with increas-
ing Ebias = 0. However, for the stress σ1, the presence of the bias field has further
enhanced the theoretical values |∆TCi|, only worsening the agreement with the ex-
perimental data of this work. At the moment, we have no satisfactory explanation
of the disagreement between our experimental data and the data of [13] and of the
calculations, especially in view of the fact that for hydrostatic pressure a complete
coincidence with the literature data and with phenomenology has been obtained.
The origin of a strong decrease of permittivity maxima magnitude with diagonal
stresses σi, i = 1, 2, 3 is not quite clear either. As it follows from (6.7), such a decrease
can be accounted for by the increase of the internal bias field Ebias or of the coefficient
k2 ∼ β1/3. Such an increase of k2 can be obtained if we take into account the terms
of the fourth order of the
∑3
i=1 q
(4)
i1 σiP
4
1 type in the expansion (6.2). Effectively it
would lead to renormalization of the coefficient β → β + 4
∑3
i=1 q
(4)
i1 σi.
7. Concluding remarks
– Strong dependence of dielectric permittivity of Rochelle salt on humidity of
the storage air is shown. We believe that the dispersion of experimental data
of different literature sources can be caused by the uncontrolled water content
during and prior to the measurements.
– The dependence of the permittivity value at the transition points on the dura-
tion of thermal annealing in high-temperature paraelectric phase indicates the
existence of internal electric bias fields in the crystals due to the point polar
defects.
– The effect of external electric field, uniaxial stresses, and hydrostatic pressure
on the dielectric permittivity has been studied. The results are compared with
the available literature data. The analysis of the obtained results is performed
within the phenomenological Landau approach. Possible reasons for discrep-
ancies in the data are discussed.
Acknowledgement
The authors acknowledge support of Fundamental Researches State Fund of
Ukraine, project No. 02.07/00310.
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A.G.Slivka et al.
Вплив зовнішніх факторів на діелектричну
проникність сегнетової солі: вологість, відпал,
тиски, електричне поле
О.Г.Сливка 1 , В.М.Кедюлич 1 , Р.Р.Левицький 2 ,
А.П.Моїна 2 , М.О.Романюк 3 , Г.М.Гуйван 1
1 Ужгородський національний університет,
Ужгород 88000, вул. Волошина, 54
2 Інститут фізики конденсованих систем,
Львів 79011, вул. Свєнціцького, 1
3 Львівський національний університет ім. І.Франка,
Львів 79005, вул. Кирила і Мефодія, 8
Отримано 18 травня 2005 р.
Робота містить результати експериментальних досліджень впливу
зовнішніх факторів таких, як, висушування/зволоження, термічний
відпал, електричне поле, одновісні тиски, гідростатичний тиск, на
діелектричну проникність кристалів сегнетової солі. Отримані ре-
зультати порівнюються з відомим літературними даними та аналі-
зуються в рамках феноменологічного підходу. Показано, що умови
зберігання та внутрішні полярні точкові дефекти суттєво впливають
на діелектричну проникність кристалів.
Ключові слова: сегнетова сіль, тиск, електричне поле, дефекти,
відпал, вологість
PACS: 77.80.Bh, 77.22.Ch
638
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