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PII: S0022-3697(98)00049-3
Pergamon
J. Phys. Chem Solids Vol 59, No. 8, pp. 1255–1258, 1998
0022–3697/98/$ – see front matter
q 1998 Elsevier Science Ltd. All rights reserved
TEMPERATURE DEPENDENCE OF ELECTRIC PERMITTIVITY OF LINEAR
DIELECTRICS WITH IONIC AND POLAR COVALENT BONDS
M. LJ. NAPIJALO*, Z. NIKOLIĆ, J. DOJČILOVIĆ, M. M. NAPIJALO and L. NOVAKOVIĆ
Faculty of Physics, University of Belgrade, Studentski Trg 12, P.O. Box 550, 11000 Beograd, Minor Yugoslavia
(Received 20 February 1997; accepted 11 March 1998)
Abstract—Results are presented of experimental verification of the relation describing temperature dependence
of permittivity of linear dielectrics with ionic and polar covalent bonds. The relation has been derived by means of
the thermodynamic method [1]. The verification has been realized on sodium chloride, sulfates, phosphates and
arsenates of magnesium and cobalt, as well on barium titanate in paraelectric phase. The experimental results
confirm the theoretical relation and, at the same time, indicate the possibility of determining the linearity region of
properties of these dielectrics. q 1998 Elsevier Science Ltd. All rights reserved
Keywords: A. inorganic compounds, D. dielectric properties
er (T ¼ 0) ¼ 1 þ
1. INTRODUCTION
In [1] it was shown that applications of classical thermodynamics of equilibrium processes enable equation of
state of dielectrics (paraelectrics) to be deduced. From
that equation it is possible to deduce relations that
describe temperature dependence of the electric susceptibility (x e) of linear solid dielectrics.
One of those relations is:
xe ¼
Ce
ve ¹ T
(1)
where C e and v e are constants characteristic of the dielectrics and T is the temperature of the sample. This relation
determines x e as an increasing function of temperature,
which, by comparison with experimental data, means that
it should correspond to dielectrics with ionic and polar
covalent bonds (induction or displacement polarizing
mechanism).
This thermodynamic approach, in this case as in
the case of other systems, does not enable the
constants C e and v e to be determined as functions of
microscopic parameters characterizing the dielectric.
This can be accomplished by means of corresponding
microscopic theories (which do not exist for dielectrics of
this type).
From relation (1) it follows for the relative electrical
permittivity (e r):
er ¼ 1 þ xe ¼ 1 þ
Ce
ve ¹ t
and for the absolute zero of temperature:
*Corresponding author
(2)
Ce
ve
(3)
The type of temperature dependence of e r may be determined experimentally and compared with the theoretical
relations (2). This is done in the present paper for a number of dielectrics; the values of the constants C e and v e
were also determined.
It should be noted that there are numerous examples for
the increase of e r with temperature. We shall only mention some newer results. These are data for thallous
halides [2], alkali halides and alkaline earth oxides [3],
alkaline earth fluorides and lead fluoride [4], potassium
chloride [5], barium molibdate [6], sodium chlorate and
sodium bromate [7], ammonium sulphate [8] etc. It
should also be mentioned that these dielectrics were
examined and described in earlier papers as well.
In addition to this, there are several papers dealing with
numerical treatment of experimental data (in narrower
temperature intervals). We shall only mention a series of
papers by Shanker et al. (e.g. [9], where the other papers
of the same author are cited).
2. THE EXPERIMENT
Here we present results of determination of e r(T) for a
number of dielectrics; the results are employed to prove
relation (2).
All experiments were carried out on polycrystalline
samples—pellets which were made out of originally
powered substances by compression at 70 b. The pellets
were 13 mm in diameter and 2 mm thickness. The
measurements were performed at a frequency of 1 MHz
by means of Hewlett-Packard Model 1721B OPT101
1 MHz Digital LCR Meter. A specially designed thermostat was used which allowed measurements in the
1255
1256
M. LJ. NAPIJALO et al.
Fig. 1. Temperature dependence of relative permittivity for
NaCl: 1, experimental data; 2, curve which corresponds to
relation (2).
temperature range 290–1300 K, while the temperature of
the sample was defined within an error of 0.3%.
2.1. Electrical permittivity of NaCl
The temperature dependence of e r(T) for NaCl is
shown in Fig. 1 (curve 1). The measurement was performed with a sample of high purity (99.99%) in the
temperature region up to 970 K, to achieve premelting
(melting point at T M ¼ 1074 K [10]).
A complex form of dependence was found for a small
number of dielectrics. As an example we mention double
arsenate of sodium and cobalt, MgCoAsO 4, which we
have examined [11].
The complex, non-monotonic shape of dependence of
e r(T) in the higher temperature region may be explained
by competition of a series of electron and ion processes at
these temperatures. These processes have been described
in a detailed but fragmentary manner in the literature (e.g.
[12–15] and also in [16–25]).
We limit our attention to the lower temperature region.
Dependence e r(T) in this region is well represented by
relation (2). Numerical tests resulted in curve 2 in Fig. 1.
The following numerical values of the parameters correspond to this curve:
Ce ¼ 3720 K, ve ¼ 964 K
while the errors are less than 1%.
Using these values, we get from relation (3):
er (T ¼ 0) ¼ 4:86
It should be noted that the theoretical curve agrees well
with the experimental data within the region T # 560 K,
which therefore determines the linearity region for NaCl
as paraelectrics.
2.2. Electrical permittivity of MgSO 4 and CoSO 4
Fig. 2(a) and Fig. 2(b) show the results of determinations of the temperature dependence of permittivity of
magnesium sulfate MgSO 4 and cobalt sulfate CoSo 4.
Sulfates are obtained by dehydration of commercial
sulfate heptahydrates (purity 99.5%). The temperature
Fig. 2. Temperature dependence of relative permittivity for
(a) MgSO 4 and (b) CaSO 4: 1, experimental data; 2, curve
which corresponds to relation (2).
of dehydration of MgSO 4 is T d ¼ 473 K and of CoSO 4 is
T d ¼ 693 K [26]. In the temperature region below T ¼
800 K both substances are isostructural [26]; at the higher
temperatures structural phase transitions occur [27].
It is seen from the figures that a monotonous increase
of e r(T) exists in the temperature region examined.
Table 1 presents characteristic parameters of these dielectrics, which were obtained by numerical analysis.
From the figures it is seen that MgSO 4 may be
considered linear in the region T # 620 K while for
CoSO 4 the linearity region is T # 650 K.
2.3. Electrical permittivity of Mg 3(PO 4) 2 and
Co 3(PO 4) 2
Fig. 3(a) and Fig. 3(b) present temperature dependence
of permittivity of magnesium orthophosphate Mg 3(PO 4) 2
and cobalt orthophosphate Co 3(PO 4) 2. The synthesis of
these compounds was realized by the procedure
described in [28–31], starting with chemicals of 99.5%
purity. These phosphates are isostructural within the
examined temperature interval [28–31]. On the grounds
of experimental data presented in the figures, characteristic parameters of these phosphates were determined by
Table 1. Characteristic parameters of
Mg and Co sulfates
ve
e r(T ¼ 0)
MgSO 4
CoSO 4
2491 K
1098 K
3.27
3308 K
1191 K
3.78
Temperature dependence of permitticity of linear dielctrics
1257
Fig. 3. Temperature dependence of relative permittivity for (a)
Mg 3(PO 4) 2 and (b) CO 3(PO 4) 2: 1, experimental data; 2, curve
which corresponds to relation (2).
means of numerical analysis. The corresponding data are
given in Table 2.
The figures show that both the dielectrics are linear in
the region T # 560 K.
2.4. Electrical permittivity of Mg 3(AsO 4) 2 and
Co 3(AsO 4) 2
Fig. 4(a) and Fig. 4(b) present temperature dependence
of permittivity of magnesium arsenate Mg 3(AsO 4) 2 and
cobalt arsenate Co 3(AsO 4) 2. These arsenates are synthesized by a procedure analogous to those described in [30].
Their examination is in progress in our laboratory since
they are not sufficiently known. The figures indicate an
analogous form of the dependence of e r(T) for the
arsenates and the phosphates, which could have been
expected on the grounds of general characteristics of
these compounds (e.g. [32–34]).
Numerical analysis of the data enabled determination
of characteristic parameters of these dielectrics, which
are given in Table 3.
From the figures it is seen that the linearity region for
both dielectrics is T # 850 K.
Fig. 4. Temperature dependence of relative permittivity for (a)
Mg 3(AsO 4) 2 and (b) CO 3(AsO 4) 2: 1, experimental data; 2, curve
which corresponds to relation (2).
Table 3. Characteristic parameters of Mg and
Co arsenates
Mg 3(AsO 4) 2 Co 3(AsO 4) 2
Ce
ve
e r(T ¼ 0)
1136 K
797 K
2.42
1394 K
974 K
2.43
2.5. Electrical permittivity of BaTiO 3
Fig. 5 shows the temperature dependence of electrical
permittivity of barium titanate BaTiO 3 in the paraelectric
phase. As far as we know, this well known ferroelectric
Table 2. Characteristic parameters of
Mg and Co phosphates
Ce
ve
e r(T ¼ 0)
Mg 3(PO 4) 2
Co 3(PO 4) 2
1046 K
867 K
2.21
1811 K
1067 K
2.70
Fig. 5. Temperature dependence of relative permittivity for
BaTiO 3: 1, experimental data; 2, curve which corresponds to
relation (2).
1258
M. LJ. NAPIJALO et al.
has not been studied in the paraelectric phase. Our
measurements were performed with the substance
synthesized at the Institute ‘M.Pupin’ in Belgrade.
For this ferroelectric the temperature of transition into
paraelectric phase is T c ¼ 393 K [35]. Our measurements
covered the temperature interval from 400 to 1000 K. The
upper limit of the interval is considerably lower than
the melting point of BaTiO 3 (T M ¼ 1893 K, [36]). The
characteristic parameters for the linearity region,
obtained from numerical analysis, are
Ce ¼ 5217K, ve ¼ 1346 K
It may be seen from the figure that the linearity region for
BaTiO 3 lies above T ¼ 600 K.
3. CONCLUSION
Experimental investigation of the temperature behaviour
of the permittivity e r of a number of dielectrics, presented
in this paper, confirms the applicability of relation (2) to
linear dielectrics with ionic and polar covalent bonds.
Numerical analysis of the experimental data enable the
characteristic parameters in relation (2) to be determined
for these dielectrics. The estimated uncertainty of the
parameters is 1%.
In our laboratory, relation (2) has also been tested on a
number of salts of oxo-acids of various transition metals.
The data will be published later.
We conclude that the thermodynamically deduced
relation (2) well represents the temperature dependence
of permittivity of paraelectrics and, at the same time,
enables a simple determination of the linearity region for
these materials to be carried out.
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