Major physical characteristics of Rochelle salt: the role of thermal strains
We compare the results for the related to the shear strain ε₄ physical characteristics of Rochelle salt obtained within the recently developed modified two-sublattice Mitsui model that takes into account the strain ε₄ and the diagonal components of the strain tensor ε₁, ε₂, ε₃ with the results of th...
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Інститут фізики конденсованих систем НАН України
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| Цитувати: | Major physical characteristics of Rochelle salt: the role of thermal strains / A.P. Moina // Condensed Matter Physics. — 2012. — Т. 15, № 1. — С. 13601: 1-10. — Бібліогр.: 30 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860082271539691520 |
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| author_facet | Moina, A.P. |
| citation_txt | Major physical characteristics of Rochelle salt: the role of thermal strains / A.P. Moina // Condensed Matter Physics. — 2012. — Т. 15, № 1. — С. 13601: 1-10. — Бібліогр.: 30 назв. — англ. |
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| description | We compare the results for the related to the shear strain ε₄ physical characteristics of Rochelle salt obtained within the recently developed modified two-sublattice Mitsui model that takes into account the strain ε₄ and the diagonal components of the strain tensor ε₁, ε₂, ε₃ with the results of the previous modification of the Mitsui model with the strain ε₄ only. Within the framework of the model with the diagonal (thermal expansion) strains, we also reexamine the effects of the longitudinal electric field E₁ on the dielectric properties of Rochelle salt.
У статтi порiвнюються результати для пов’язаних зi зсувною деформацiєю ε₄ фiзичних характеристик сегнетової солi, отриманих в рамках нещодавно розвиненої модифiкованої двопiдґраткової моделi Мiцуї, що враховує деформацiю ε₄ та дiагональнi компоненти тензора деформацiй ε₁, ε₂, ε₃ , з результатами попередньої модифiкацiї моделi Мiцуї, що враховує лише ε₄. В рамках моделi з дiагональними (теплови-ми) деформацiями дослiджено вплив поздовжнього електричного поля E₁ на дiелектричнi властивостi сеґнетової солi.
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Condensed Matter Physics, 2012, Vol. 15, No 1, 13601: 1–10
DOI: 10.5488/CMP.15.13601
http://www.icmp.lviv.ua/journal
Major physical characteristics of Rochelle salt:
the role of thermal strains
A.P. Moina
Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine,
1 Svientsitskii Str., 79011 Lviv, Ukraine
Received August 29, 2011, in final form November 22, 2011
We compare the results for the related to the shear strain ε4 physical characteristics of Rochelle salt obtained
within the recently developed modified two-sublattice Mitsui model that takes into account the strain ε4 and
the diagonal components of the strain tensor ε1, ε2 , ε3 with the results of the previous modification of the
Mitsui model with the strain ε4 only. Within the framework of the model with the diagonal (thermal expansion)
strains, we also reexamine the effects of the longitudinal electric field E1 on the dielectric properties of Rochelle
salt.
Key words: Rochelle salt, thermal expansion, Mitsui model, strains, bias field
PACS: 65.40.De, 77.65.Bn, 77.22.Gm, 77.22.Ch
1. Introduction
Rochelle salt is the first known ferroelectric and a curious material, undergoing two second-order
phase transitions at TC1 = 255 K and TC2 = 297 K, with the intermediate ferroelectric phase. Spontaneous
polarization P1 is directed along the a axis and accompanied by spontaneous shear strain ε4 in the bc
plane.
Microscopic theories of Rochelle salt are usually based on the two-sublattice Mitsui model [1], which
considers motion of certain ordering units in two interpenetrating sublattices of asymmetric double-well
potentials. Deformational effects have to be included into the Mitsui model to get a proper description
of Rochelle salt behavior. Thus, only with taking into account the piezoelectric coupling with ε4 [2] it
yields the qualitatively correct behavior of the relaxation time and dynamic dielectric permittivity near
the Curie temperatures. The same modification of the Mitsui model also provides a fair description of the
major dielectric, piezoelectric, and elastic characteristics of Rochelle salt associated with the strain ε4 [2],
although some systematic discrepancies between the theory and experiment do take place.
Recently, a further modification of the Mitsui model has been proposed [3] in order to consistently
describe a number of effects associated with the diagonal components of the lattice strain tensor εi
(i = 1,2,3). Along with the shear strain ε4 included into the Mitsui model in [2], this modification takes
into account the diagonal strains in the manner suggested in [4] as well as the host lattice contribution
into the energy of thermal expansion. It has been shown [3] to be efficient in describing the effect of
hydrostatic, uniaxial, or biaxial pressure applied along the orthorhombic crystallographic axes of the
crystal, its thermal expansion, as well as related to the diagonal strains components of piezoelectric (e.g.
d1i , i = 1,2,3) and elastic (ci4) tensors, appearing in the ferroelectric phase only due to the lowered crystal
symmetry.
In the present paper we shall explore how the inclusion of thermal strains affect the agreement with
experiment for the physical characteristics of Rochelle salt related to the shear strain ε4.
It has been also shown [5] that to correctly describe the dependences of the static dielectric permittiv-
ity of Rochelle salt on the longitudinal electric field E1 at temperatures near TC2 (within the modified Mit-
sui model without the diagonal strains [2]), one has to assume that the external field is partially screened
© A.P. Moina, 2012 13601-1
http://dx.doi.org/10.5488/CMP.15.13601
http://www.icmp.lviv.ua/journal
A.P. Moina
out due to the space-charge build-up at blocking electrodes. We shall verify whether this assumption is
necessary for the model with the diagonal (thermal) strains [3].
2. ε4-strain associated physical characteristics in presence
of diagonal strains
The expressions for thermodynamic potential, polarization and strains, as well as for the observ-
able physical characteristics – second derivatives of thermodynamic potential, obtainedwithin theMitsui
model with the diagonal strains, can be found elsewhere [3]. In the present paper we shall be interested
only in the major characteristics, associated with polarization P1 and shear strain ε4. Those will be com-
pared with the results obtained within the Mitsui model without diagonal strains [2].
The characteristics we are interested in are spontaneous polarization P1 and strain ε4, dielectric sus-
ceptibility of a clamped crystal χε
11
, and the elastic constant at a constant field cE
44
, the expressions for
which are not modified by the inclusion of diagonal strains, except for renormalization of the model pa-
rameters (see [2] and [3]). On the other hand, the static dielectric susceptibility of a mechanically free
crystal χσ
11
[3, 4] and the piezoelectric constant
d14 = d0
14 −
sE0
44
µ′
1
βψ4
v
ϕ3
ϕ2 −Λϕ3
+
3
∑
j=1
sE
j 4
e1 j (1)
contain new terms (the last sum), describing the contribution of the diagonal strains. Here e1i are mon-
oclinic piezoelectric coefficients different from zero only at non-zero polarization; sE
i j
is the matrix of
elastic compliances, inverse to the matrix of elastic constants cE
i j
, the microscopic expressions for which,
as well as the notations introduced above, have been presented earlier [3]. In the paraelectric phases the
expressions for free susceptibility and d14 coincide with those obtained within the modifiedMitsui model
without thermal strains [6].
The dynamics of Rochelle salt in the presence of diagonal strains is explored [7] elsewhere. The dy-
namic dielectric permittivity of a clamped crystal relevant to the present consideration is not explicitly
dependent on the strains, apart from renormalization of the interaction constants. The expression for it
is the same as in the model without thermal strains [2, 6]
εε11(ω) = εε0
11 +
βµ2
1
2vε0
F1(αω), F1(αω) =
iαωλ1 +ϕ3
(iαω)2 + (iαω)ϕ1 +ϕ2
, (2)
where α is the parameter setting the time scale of the dynamic processes in the pseudospin subsystem
within the Glauber approach; the other notations are given in [6].
3. Numerical calculations
3.1. Model parameters
The values of the parameters of the model with diagonal strains were chosen [3] to provide as good
as possible fit of the theory to the experimental data for the following characteristics of Rochelle salt:
the Curie temperatures at ambient pressure TCk (k = 1,2) and their hydrostatic and uniaxial pressure
slopes, the temperature curves of thermal expansion strains εi , linear thermal expansion coefficients,
monoclinic piezoelectric coefficients, and elastic constants ci j and ci4 (i , j = 1,3). The adopted values of
the model parameters and the details of the fitting procedure have been given elsewhere [3].
Additionally, we need to determine the value of the parameter α that sets the time scale of the model
pseudospin dynamics. In earlier calculations [2] it was taken to be temperature independent α = 1.7 ·
10−13 s. However, the analysis [8] of the temperature dependences of the relaxation time τ and of the low-
frequency limit of the clamped dynamic permittivity (measured at 155 MHz, just above the resonances,
the experimental analog of the static clamped permittivity εε) revealed that τ is proportional to εε−ε∞
13601-2
Rochelle salt: the role of thermal strains
and to T N , with N = 1.25±0.25. In terms of our model, it means that we should take α to be temperature
dependent. The best results are obtained at α=α0 (T /TC2)1.35 , with α0 = 2.15 ·10−13 s.
The adopted set of the model parameters is not unique; there are many other sets providing the fit to
experimental data with the same error. Therefore, it is not possible to precisely establish the temperature
variation of the interaction constants. However, the overall tendency is such that an increasing temper-
ature decreases the asymmetry parameter ∆ and the constants of interactions between the pseudospins
within the same and in different sublattices J and K . In other words, increasing temperature has the
effect opposite to hydrostatic compression [3], which is understandable. The corresponding temperature
slopes at the adopted values of the model parameters are ∂ ln∆/∂T =−2 ·10−2 K−1, ∂ ln J/∂T =−6 ·10−4
K−1, and ∂ ln K /∂T =−2 ·10−2 K−1.
The number and (if any) temperature and order of the phase transitions for the Mitsui model without
thermal strains are usually analyzed in terms of dimensionless variables ā and b̄
ā =
K − J
K + J + 8
v
ψ2
4
sE0
44
, b̄ =
8∆
K + J + 8
v
ψ2
4
sE0
44
. (3)
Here, ψ4 is the parameter describing the coupling between the pseudospin subsystem and the shear
strain ε4 [2]. The phase diagram of the conventional (undeformable) Mitsui model in the (ā, b̄) plane [9–
11] shows the regions with different numbers and types of phase transitions; its topology does not change
by inclusion of the shear strain ε4.
0.64 0.65 0.66 0.67
0.28
0.30
0.32
0.34
-
-
V
II
IV
b
a
Figure 1. Part of the phase diagram of the Mitsui model.
The points corresponding to the parameters adopted in [2]
(■) and [3] (ä) are shown.
It has been found that only in a very
narrow region of the (ā, b̄) plane, the sys-
tem undergoes two second order phase tran-
sitions with the intermediate ferroelectric
phase; this region (IV) is shown in figure 1.
In the region V, the system undergoes no
phase transition, whereas in the region II the
system undergoes two second order phase
transitions with the intermediate ferroelec-
tric phase and below them — an additional
first order phase transition to another ferro-
electric phase, which persists down to 0 K.
The situation drastically changes in pres-
ence of diagonal strains, when ā and b̄ be-
come functions of temperature and pres-
sure. Here, the number and type(s) of phase
transitions are governed by more than 10
model parameters with arbitrary (physically reasonable) values. At such circumstances we think it is
impossible to construct a 2D or 3D phase diagram of the model, which would fully describe all the types
of the temperature behavior and phase transitions in the system.
In the fitting procedure we deal with the values of ā and b̄ at the upper Curie temperature and ambi-
ent pressure ā0 and b̄0. The used values of ā0 and b̄0 are from the region IV of the (ā, b̄) phase diagram
of the undeformable Mitsui model. The points (ā, b̄) = (0.3162,0.662) corresponding to the parameters
of [2] and (ā0, b̄0) = (0.295,0.648) for the parameters of [3] are shown in figure 1.
With decreasing ā0, the maximal values of the order parameter ξ and spontaneous strain ε4 increase.
In the previous model [2] we had to choose, in fact, the point almost on the boundary of the region IV,
providing the maximal possible values of ξ and ε4 in the middle of the ferroelectric phase. Neverthe-
less, the calculated spontaneous polarization and spontaneous strain were still appreciably smaller than
the experimental ones. Interestingly, at the same values of (a0,b0) for the model [3] and (a,b) for the
model [2], the maximal value of the order parameter obtained within the model with the thermal strains
is much larger. Thus, at the adopted values of the fitting parameters it is ξmax = 0.144, to be compared to
0.128 in [2].
13601-3
A.P. Moina
3.2. ε4-strain-related characteristics: role of diagonal strains
Figures 2 show that the modified Mitsui model with thermal strains [3] yields a notably larger values
of the spontaneous polarization P1 and spontaneous strain ε4 in the middle of the ferroelectric phase
and a better agreement with experimental data. The obtained improvement is explained by the increased
values of the order parameter in the center of a ferroelectric phase.
255 270 285 300
0.0
0.1
0.2
0.3
T (K)
P
1
(µC/cm2)
260 280 300
0
2
4
6
T (K)
ε
4
, 10-4
Figure 2. Temperature dependence of spontaneous polarization (left) and spontaneous strain ε4 (right) of
Rochelle salt: ◦— [12]; ■— [13]; �— [14]; ä— [15], • — ε4 = P1d14/χσ
11
[12]. Lines: a theory. Solid line:
the model of [3]; dashed line: the model of [2]. Symbols: experimental points.
The role of diagonal strains is not so apparent for the other physical characteristics of Rochelle salt
related to the shear strain ε4. In particular this concerns the static dielectric permittivities of the free εσ
11
and clamped εε
11
crystals, as well as the dynamic permittivity. Here, the differences between the obtained
results, with one exception, are caused by a different route, taken in [3] at selecting the values of the
parameters µ1 and α. The same route could be taken within the previous modification of the Mitsui
model.
240 260 280 300
0.00
0.01
0.02
1/ε
11
T (K)
Figure 3. Temperature dependence of inverse static
dielectric permittivity of a free:⋆— [16]; N— [17];
�— [14]; •— [18] and clamped:—ä— [8];◦— [19];
^ — [14]; ▽ — [20] crystals. Lines: the theory. Solid
line: the model of [3]; dashed line: the model of [2].
Symbols: experimental points.
In the previous work [2] we were not able to
simultaneously fit the free and clamped dielec-
tric permittivities in the lower paraelectric phase
with the same values of the dipolemoment µ1 (the
dashed lines in figure 3). It was chosen to provide
the best fit for the dynamic dielectric permittiv-
ity [8] at microwave frequencies and for the static
clamped permittivity at temperatures just below
TC1. Thence, the agreement with experiment for
the free permittivity at these temperatures was
unsatisfactory. Moreover, at even lower temper-
atures (below 240 K) the fit for the dynamic per-
mittivity was also bad. In the upper paraelectric
phase both free and clamped permittivities were
well described.
The problem persists after the inclusion of
diagonal strains. However, now we choose the
dipole moment µ1 to provide the best fit for the
free static permittivity in both paraelectric phases and for the dynamic dielectric permittivity [8] below
240 K. As a result, the agreement with experiment for the static clamped permittivity just below TC1 is
spoiled. This is illustrated in figure 3.
In the ferroelectric phase, there is a considerable inconsistency between the two theories and exper-
iment. This is attributed to the domain wall contributions into the static free permittivity that are not
taken into account by either modification of the Mitsui model.
13601-4
Rochelle salt: the role of thermal strains
The temperature dependences of the real ε′
11
and imaginary ε′′
11
parts of the dynamic dielectric per-
mittivity of Rochelle salt calculated within the modifications of the Mitsui model with [3] and without [2]
thermal strains are shown in figures 4 and 5.
Both models provide an excellent agreement with experimental data [8] for ε′
11
in the upper para-
electric phase. For ε′′
11
, the newest results of the model [3] are slightly better, especially for very high
frequencies (above 9 GHz).
220 240 260 280 300
50
100
150
200
250
300 '
T (K)
ε
11
220 240 260 280 300
50
100
150
200
250
300
'
T (K)
ε
11
Figure 4. The temperature dependence of the real part of dynamic dielectric permittivity at different
frequencies ν (GHz): ■ — 0.155, ◦ — 2.5, △ — 3.9, N — 5.1, ▽ — 7.05, ⊙ — 9.45, ä — 12.95. Solid lines
are calculated within the modifications of the Mitsui model without [2] (left) and with [3] (right) thermal
strains; the symbols are experimental points taken from [8].
220 240 260 280 300
0
25
50
75
100
125
150
''ε
11
T (K) 220 240 260 280 300
0
25
50
75
100
125
150
''ε
11
T (K)
Figure 5. The same for the imaginary part of the permittivity.
The domain effects are switched off at microwave frequencies. Therefore, they cannot explain the
disagreement between the theory and experiment in the ferroelectric phase for ε′
11
and ε′′
11
, which took
place in the previous modification of the Mitsui model [2]. Inclusion of thermal strains allowed us to ba-
sically solve this problem; the obtained fit using this model is quite satisfactory in the ferroelectric phase.
This improvement has the same origin as that for spontaneous polarization and spontaneous strain: the
increased maximum value of the order parameter ξ. This is the only exception when the improvement
for the permittivities could not be obtained by changing the fitting procedure for µ1 and αwithout taking
into account the diagonal strains.
None of the models can properly describe the temperature variation of ε′
11
or ε′′
11
below TC1. As we
have already mentioned, depending on the choice of µ1 we can obtain a good fit for ε′
11
either between
240 and 255 K (as was done in [2]) or below 230 K (in the model with diagonal strains). The agreement
13601-5
A.P. Moina
with experiment for ε′′
11
is only qualitatively correct at all temperatures below TC1; quantitatively it is
poor for both models.
Comparison of the piezoelectric coefficients d14 and e14 calculated within the models [3] and [2] is
given in figure 6. It can be seen that the agreement with experiment in the lower paraelectric phase for
d14 and in the upper paraelectric phase for e14 obtained within the model with the thermal strains is
better.
Inclusion of diagonal strains enhances the temperature dependence of the piezoelectric constants g14
and h14, as seen in figure 7. The theoretical curves, however, are still within the dispersion range of the
experimental data. This is the only case when we could see that the diagonal strains being taken into
account produced some qualitative changes in the calculated characteristics related to the strain ε4.
240 260 280 300
0
15
30
45
T (K)
d
14
(10-10C/N)
Figure 6. Temperature dependences of piezoelectric coefficients d14 and e14: •— [21], N— [22], H— [23],
◦— [14], ▽ — [20], △ — [24], ^— e14 = d14 · cE
44
[22, 25]. Lines: the theory. Solid line: the model of [3];
dashed line: [2]. Symbols: experimental points.
Figure 7. Temperature dependences of piezoelectric constants g14 and h14:ä— [18],△— [24],◦— [14],
▽ — h14 = e14/χε
11
and g14 = d14/(χε
11
+e14d14) [20], ^ — [12]. Lines: the theory. Solid line: the model
of [3]; dashed line: [2]. Symbols: experimental points.
No direct effect of diagonal strains on the elastic constants related to the shear strain ε4 is evident.
Due to the different value of the “seed” elastic constant cE0
44
we were able to improve the agreement with
experiment for the elastic constant at a constant field cE
44
in the lower paraelectric phase. The fit for the
elastic constant at a constant polarization cP
44
becomes a little worse, though the theoretical curve does
not fall out of the dispersion range of the experimental data.
It should be mentioned that the agreement with experiment for the free static permittivity
(figure 3), piezoelectric coefficient d14 (figure 6), and elastic constant cE
44
(figure 8) in the ferroelectric
phase is getting even worse when the diagonal strains are taken into account. The disagreement, how-
ever, is obviously caused by the domain-wall motion contributions into the mentioned characteristics,
which are not taken into account within the present [3] or previous [2] versions of the Mitsui model. On
the other hand, the dynamic dielectric permittivity at microwave frequencies (figures 4, 5) and the free
13601-6
Rochelle salt: the role of thermal strains
Figure 8. Temperature dependence of elastic constant at constant field cE
44
: × — [25], △ — [26], ^ —
[27], ◦ — 1/sE
44
[14], ▽ — 1/sE
44
[20] and constant polarization cP
44
: N — [26], ■ — [18], � — [12], • —
cP
44
= 1/sE
44
+ e14h14 [14], H— 1/sE
44
+ e2
14
/χε
11
[20]. Lines: the theory. Solid line: the model of [3]; dashed
line: [2]. Symbols: experimental points.
static permittivity in high bias fields (above at least 0.5 kV/cm, see next subsection), when the domain
contributions are switched off, are very well described by the Mitsui model with the diagonal strains.
3.3. Longitudinal electric field effects
The longitudinal electric field E1 directed along the axis of spontaneous polarization, being the field
conjugate to the order parameter, smears out the phase transitions, decreases the maximal values of per-
mittivity εm , and shifts the upper maximum temperature upward and the lower maximum temperature
downward. The phenomenological Landau-Devonshire formalism presumes that ε−1
m and the shifts of
permittivity maxima temperatures |∆Tmax(E )| are expected to vary with the external field as ∼ E 2/3 [28].
Those dependences are obtained starting with the simplified Landau expansion of the thermody-
namic potential (elastic and piezoelectric contributions not considered)
G(P1) =G0 +
α
2
P 2
1 +
β
4
P 4
1 . (4)
From (4), the equations for polarization and inverse permittivity follow
E1 =
(
∂G
∂P1
)
=αP1 +βP 3
1 , ε−1
11 = ε0
(
∂E1
∂P1
)
= ε0
(
α+3βP 2
1
)
. (5)
In the case of Rochelle salt, the expansion (4) can be performed near each of the two transitions separately,
assuming a linear temperature dependence α = αT 1(TC1 −T ) for the lower transition and α = αT 2(T −
TC2) for the upper one. Then, the field dependences of εm and ∆Tmax can be presented as [28]:
ε−1
m =
3
2
(4β)
1/3ε0E 2/3
1 = k1E 2/3
1 . (6)
|∆Tmax,i | =
3
4
(4β)1/3
αT i
E 2/3
1 = k2i E 2/3
1 , i = 1,2. (7)
The previous calculations [5] of the bias field dependences of the static free permittivity of Rochelle
salt performed within the model without the diagonal strains [3] have shown that the theory, though be-
ing qualitatively correct, strongly overestimates the field effect on temperature and magnitude of the
upper permittivity maximum. In fact, the calculated curves in the vicinity of TC2 coincided with the
experimental points obtained in much lower fields. On the other hand, the theory accorded well with
experiment in the vicinity of the lower Curie temperature.
To correctly describe the field dependences of the static dielectric permittivity of Rochelle salt at tem-
peratures near TC2, we had to use in our calculations the effective field Eeff ∼ 0.7Eext at TC2, instead of the
13601-7
A.P. Moina
values of the actually applied in the experiments field Eext, whereas Eeff = Eext below TC1. An assump-
tion has been made that the external field is partially screened out due to the space-charge build-up at
blocking electrodes [5].
250 255 260 295 300
1
2
3
4
10-3 ε
11
T (K)
Figure 9. Temperature dependences of the dielectric permittivity of Rochelle salt at different values of
external electric field E1 (kV/cm): ◦ — 0, △ — 0.05, ⊳ — 0.1, ♦ — 0.2, ä — 0.5, H — 0.96, ▽ — 1.0, • —
1.96,■— 2.46. Experimental points are taken from [29] (open symbols) and [30] (closed symbols). Lines:
the theoretical results obtained within the model of [3].
The calculations performed within the modified Mitsui model with the thermal strains [3] show that
this assumptionmay be incorrect. Indeed, as seen in figures 9 and 10, no overestimation of the field effects
on the temperature curves of the static free permittivity is obtained. In fact, the experimental permittivity
maxima are almost always lower than the theoretical ones. The field dependences of the temperature
shifts of the maxima are rather well described by the theory. The theoretical ε−1
m1,2
and |∆Tmax| vary with
the external field as ∼ E 2/3
1
, in agreement with the Landau theory.
0.1 1
100
1000
0.1 1
100
1000
0 1 2 3
-4
-2
0
2
4
εm1
E1 (kV/cm)
εm2
E1 (kV/cm)
∆Tmax (K)
E1 (kV/cm)
Figure 10. The field E1 dependences of the magnitude and temperature shifts of the dielectric permit-
tivity maxima in Rochelle salt. Experimental points are taken from [29] (open symbols) and [30] (closed
symbols). Lines: the theoretical results obtained within the model of [3].
We can now deduce the values of the coefficients of the Landau expansion. The theoretical curves in
figure 10 are well approximated by (6) and (7) dependences with
k1 = 1.03 ·10
−6
(m/V)
2/3
, k21 = 7.6 ·10
−4
K(m/V)
2/3
, k22 = 9.9 ·10
−4
K(m/V)
2/3
,
yielding
β= 1.17 ·10
14
V m
5
/C
3
, αT 1 = 7.7 ·10
7
Vm/(KC), αT 2 = 5.8 ·10
7
Vm/(KC).
Figure 11 illustrates the field effects on the microwave dynamic dielectric permittivity of Rochelle
salt. The theoretical curves were calculated within the model with the thermal strains. In zero field,
the real part of the permittivity at 8.25 GHz has shallow minima at the transition points and a pair of
13601-8
Rochelle salt: the role of thermal strains
Figure 11. (Color online) Dynamic dielectric permittivity of Rochelle salt at 8.25 GHz at different values
of the longitudinal field E1 (kV/cm): 1, ä— 0; 2, ◦— 1, 3, △ — 2; 4, ▽— 4.1. Lines: the theoretical results
obtained within the model of [3]. Symbols: experimental points taken from [8].
rounded maxima at both sides of each minimum [8]. Application of d.c. bias smears out the minima,
which shift toward the corresponding paraelectric phases, and each pair of maxima tends to coalesce.
At sufficiently high fields, the maxima merge, and the minima disappear. At temperatures far from the
transition regions, the real part of the permittivity only decreases with the bias field. This behavior is
illustrated in figure 11, and it accords qualitatively with the experimental results of [8]. The behavior
of the imaginary part of the permittivity is qualitatively the same as that of the static permittivity: it
decreases with the field at all temperatures.
4. Concluding remarks
In the present paper we compare the results obtained within two modifications ([2] and [3]) of the
two-sublattice Mitsui model for physical characteristics of Rochelle salt associated with the shear strain
ε4. The role of diagonal strains in the mentioned characteristics is explored.
It is shown that the thermal strains being taken into account bring about mostly quantitative changes
in the calculated ε4-strain-related characteristics. The only qualitative effect is the enhancement of the
temperature variation of the piezoelectric constants g14 and h14.
The agreement with experiment for spontaneous polarization, spontaneous strain ε4, and dynamic
dielectric permittivity in the ferroelectric phase, is significantly improved, as compared to that of the
modified Mitsui model without diagonal strains [2]. The obtained improvement comes not from direct
contributions into these characteristics of diagonal strains, but from the fact that the extended model
yields larger values of the order parameter ξ, resulting in a better fit to the experiment.
For the elastic constants cE ,P
44
and dielectric permittivities in the paraelectric phases, the inclusion of
diagonal strains did not result in any apparent quantitative changes. We, however, adopted a slightly
different route during the fitting procedure for the parameters µ1, cE0
44
, and α, which allowed us to some-
what improve the agreement with experiment. The same route can be taken within the model without
diagonal strains as well.
It has been also shown previously [3] that the model with diagonal strains yields a better agreement
with experimental data for small anomalies of specific heat of Rochelle salt at the Curie points than it was
obtained with the earlier model [2], especially for the magnitude of the upper anomaly. In this case, in
contrast to the above discussed cases of spontaneous polarization and spontaneous strain, the obtained
improvement is caused by taking into account the explicit contributions of diagonal strains.
We also reexamine the effect of the longitudinal bias field E1 on the dielectric characteristics of
Rochelle salt. The model with thermal strains yields a fair agreement with experiment; its results also
accord with the prediction of the Landau-Devonshire theory. In contrast to the calculations within the
model without thermal strains [5], there is no need to assume that the external electric field is screened
out by the space charge buildup at the blocking electrodes.
13601-9
A.P. Moina
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Основнi фiзичнi характеристики сеґнетової солi: вплив
теплових деформацiй
А.П. Моїна
Iнститут фiзики конденсованих систем НАН України, вул. Свєнцiцького, 1, 79011 Львiв
У статтi порiвнюються результати для пов’язаних зi зсувною деформацiєю ε4 фiзичних характеристик се-
гнетової солi, отриманих в рамках нещодавно розвиненої модифiкованої двопiдґраткової моделi Мiцуї,
що враховує деформацiю ε4 та дiагональнi компоненти тензора деформацiй ε1, ε2 , ε3, з результатами
попередньої модифiкацiї моделi Мiцуї, що враховує лише ε4 . В рамках моделi з дiагональними (теплови-
ми) деформацiями дослiджено вплив поздовжнього електричного поля E1 на дiелектричнi властивостi
сеґнетової солi.
Ключовi слова: сеґнетова сiль, теплове розширення, модель Мiцуї, деформацiї, електричне поле
PACS: 65.40.De, 77.65.Bn, 77.22.Gm, 77.22.Ch
13601-10
http://dx.doi.org/10.1103/PhysRev.111.1259
http://dx.doi.org/10.1103/PhysRevB.67.174112
http://dx.doi.org/10.5488/CMP.14.43602
http://dx.doi.org/10.1002/pssb.200541436
http://dx.doi.org/10.1103/PhysRevB.71.134108
http://dx.doi.org/10.1103/PhysRev.168.481
http://dx.doi.org/10.5488/CMP.14.23603
http://dx.doi.org/10.1103/PhysRev.47.175
http://dx.doi.org/10.1098/rspa.1946.0030
http://dx.doi.org/10.1080/00150190008228404
http://dx.doi.org/10.1088/0022-3719/17/20/017
http://dx.doi.org/10.1103/PhysRev.55.775
http://dx.doi.org/10.1103/PhysRev.72.854
http://dx.doi.org/10.1002/pssa.2210840211
http://dx.doi.org/10.1103/PhysRev.72.492
http://dx.doi.org/10.1103/PhysRev.75.946
http://dx.doi.org/10.1143/JPSJ.61.4589
Introduction
4-strain associated physical characteristics in presence of diagonal strains
Numerical calculations
Model parameters
4-strain-related characteristics: role of diagonal strains
Longitudinal electric field effects
Concluding remarks
|
| id | nasplib_isofts_kiev_ua-123456789-120146 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T17:17:36Z |
| publishDate | 2012 |
| publisher | Інститут фізики конденсованих систем НАН України |
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| spelling | Moina, A.P. 2017-06-11T07:34:12Z 2017-06-11T07:34:12Z 2012 Major physical characteristics of Rochelle salt: the role of thermal strains / A.P. Moina // Condensed Matter Physics. — 2012. — Т. 15, № 1. — С. 13601: 1-10. — Бібліогр.: 30 назв. — англ. 1607-324X PACS: 65.40.De, 77.65.Bn, 77.22.Gm, 77.22.Ch DOI:10.5488/CMP.15.13601 arXiv:1204.5819 https://nasplib.isofts.kiev.ua/handle/123456789/120146 We compare the results for the related to the shear strain ε₄ physical characteristics of Rochelle salt obtained within the recently developed modified two-sublattice Mitsui model that takes into account the strain ε₄ and the diagonal components of the strain tensor ε₁, ε₂, ε₃ with the results of the previous modification of the Mitsui model with the strain ε₄ only. Within the framework of the model with the diagonal (thermal expansion) strains, we also reexamine the effects of the longitudinal electric field E₁ on the dielectric properties of Rochelle salt. У статтi порiвнюються результати для пов’язаних зi зсувною деформацiєю ε₄ фiзичних характеристик сегнетової солi, отриманих в рамках нещодавно розвиненої модифiкованої двопiдґраткової моделi Мiцуї, що враховує деформацiю ε₄ та дiагональнi компоненти тензора деформацiй ε₁, ε₂, ε₃ , з результатами попередньої модифiкацiї моделi Мiцуї, що враховує лише ε₄. В рамках моделi з дiагональними (теплови-ми) деформацiями дослiджено вплив поздовжнього електричного поля E₁ на дiелектричнi властивостi сеґнетової солi. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Major physical characteristics of Rochelle salt: the role of thermal strains Основнi фiзичнi характеристики сеґнетової солi: вплив теплових деформацiй Article published earlier |
| spellingShingle | Major physical characteristics of Rochelle salt: the role of thermal strains Moina, A.P. |
| title | Major physical characteristics of Rochelle salt: the role of thermal strains |
| title_alt | Основнi фiзичнi характеристики сеґнетової солi: вплив теплових деформацiй |
| title_full | Major physical characteristics of Rochelle salt: the role of thermal strains |
| title_fullStr | Major physical characteristics of Rochelle salt: the role of thermal strains |
| title_full_unstemmed | Major physical characteristics of Rochelle salt: the role of thermal strains |
| title_short | Major physical characteristics of Rochelle salt: the role of thermal strains |
| title_sort | major physical characteristics of rochelle salt: the role of thermal strains |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/120146 |
| work_keys_str_mv | AT moinaap majorphysicalcharacteristicsofrochellesalttheroleofthermalstrains AT moinaap osnovnifizičniharakteristikisegnetovoísolivplivteplovihdeformacii |