Chemical capacitance proposed for manganite-based ceramics
The measured value of effective electric permittivity ϵeff of several compounds, e.g., (BiNa)(MnNb)O₃, (BiPb)(MnNb)O₃, and BiMnO₃ increases from a value ≅10÷100 at the low temperature range (100÷300 K) up to the high value reaching the value 10⁵ at high temperature range, e.g., 500÷800 K. Such featu...
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irk-123456789-1208282017-06-14T03:04:13Z Chemical capacitance proposed for manganite-based ceramics Molak, A. The measured value of effective electric permittivity ϵeff of several compounds, e.g., (BiNa)(MnNb)O₃, (BiPb)(MnNb)O₃, and BiMnO₃ increases from a value ≅10÷100 at the low temperature range (100÷300 K) up to the high value reaching the value 10⁵ at high temperature range, e.g., 500÷800 K. Such features suggest the manifestation of thermally activated space charge carriers, which effect the measured capacitance. The measured high-value effective permittivity of several manganite compounds can be ascribed to the chemical capacitance Cμ=e² ∂Ni/∂μi expressed in terms of the chemical potential μ. The chemical capacitance Cμ(cb)=e² nC/kBT depends on temperature when the conduction electrons with density nC=NCexp(μn-EC)/kBT are considered. The experimental results obtained for the manganite compounds, at high temperature range, are discussed in the framework of the chemical capacitance model. However, the measured capacitance dependence on geometrical factors is analysed for BiMnO3 indicating that the non-homogeneous electrostatic capacitor model is valid in 300÷500 K range. Вимiряне значення ефективної електричної проникностi εeff декiлькох сполук, а саме, (BiNa)(MnNb)O₃, (BiPb)(MnNb)O₃, i BiMnO₃ збiльшилося iз значення ≈ 10÷100 в низькотемпературнiй областi (100÷300 K) до високого значення, досягаючи значення 10⁵ у високотемпературнiй областi, а саме, 500 ÷ 800 K. Такi риси є виявом термiчно активованих носiїв просторового заряду, якi впливають на вимiрювану ємнiсть. Вимiряне високе значення ефективної проникностi декiлькох магнiтних сполук може бути приписане хiмiчнiй ємностi Cµ = e²∂Ni /∂µi , вираженiй в термiнах хiмiчного потенцiалу µ. Хiмiчна ємнiсть C(cb) µ = e²nC/kBT залежить вiд температури, при якiй розглядаються електрони провiдностi з густиною nC = NC exp¡µn −EC¢/kBT. Експериментальнi результати, отриманi для сполук манганiту у високотемпературнiй областi, обговорюються в рамках моделi хiмiчної ємностi. Проте, вимiряна ємнiсна залежнiсть вiд геометричних факторiв, що аналiзується для BiMnO3, вказує, що неоднорiдна електростатична ємнiсна модель є справедливою в областi 300÷500 K. 2013 Article Chemical capacitance proposed for manganite-based ceramics / A. Molak // Condensed Matter Physics. — 2013. — Т. 16, № 3. — С. 31801:1-10. — Бібліогр.: 20 назв. — англ. 1607-324X PACS: 82.45.Un, 77.22.Ch DOI:10.5488/CMP.16.31801 arXiv:1309.6127 http://dspace.nbuv.gov.ua/handle/123456789/120828 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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The measured value of effective electric permittivity ϵeff of several compounds, e.g., (BiNa)(MnNb)O₃, (BiPb)(MnNb)O₃, and BiMnO₃ increases from a value ≅10÷100 at the low temperature range (100÷300 K) up to the high value reaching the value 10⁵ at high temperature range, e.g., 500÷800 K. Such features suggest the manifestation of thermally activated space charge carriers, which effect the measured capacitance. The measured high-value effective permittivity of several manganite compounds can be ascribed to the chemical capacitance Cμ=e² ∂Ni/∂μi expressed in terms of the chemical potential μ. The chemical capacitance Cμ(cb)=e² nC/kBT depends on temperature when the conduction electrons with density nC=NCexp(μn-EC)/kBT are considered. The experimental results obtained for the manganite compounds, at high temperature range, are discussed in the framework of the chemical capacitance model. However, the measured capacitance dependence on geometrical factors is analysed for BiMnO3 indicating that the non-homogeneous electrostatic capacitor model is valid in 300÷500 K range. |
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Molak, A. Chemical capacitance proposed for manganite-based ceramics Condensed Matter Physics |
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Molak, A. |
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Molak, A. |
| title |
Chemical capacitance proposed for manganite-based ceramics |
| title_short |
Chemical capacitance proposed for manganite-based ceramics |
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Chemical capacitance proposed for manganite-based ceramics |
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Chemical capacitance proposed for manganite-based ceramics |
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Chemical capacitance proposed for manganite-based ceramics |
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chemical capacitance proposed for manganite-based ceramics |
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Інститут фізики конденсованих систем НАН України |
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Chemical capacitance proposed for manganite-based ceramics / A. Molak // Condensed Matter Physics. — 2013. — Т. 16, № 3. — С. 31801:1-10. — Бібліогр.: 20 назв. — англ. |
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Condensed Matter Physics |
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AT molaka chemicalcapacitanceproposedformanganitebasedceramics |
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2025-07-08T18:41:34Z |
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| fulltext |
Condensed Matter Physics, 2013, Vol. 16, No 3, 31801: 1–10
DOI: 10.5488/CMP.16.31801
http://www.icmp.lviv.ua/journal
Proceedings Paper
Chemical capacitance proposed for
manganite-based ceramics
A. Molak
Institute of Physics, University of Silesia, 4 Uniwersytecka St., 40–007 Katowice, Poland
Received November 7, 2012
The measured value of effective electric permittivity εeff of several compounds, e.g., (BiNa)(MnNb)O3,
(BiPb)(MnNb)O3, and BiMnO3 increases from a value ≈ 10÷100 at the low temperature range (100÷300 K)
up to the high value reaching the value 105 at high temperature range, e.g., 500÷800 K. Such features sug-
gest the manifestation of thermally activated space charge carriers, which effect the measured capacitance. The
measured high-value effective permittivity of several manganite compounds can be ascribed to the chemical ca-
pacitance Cµ = e2∂Ni /∂µi expressed in terms of the chemical potential µ. The chemical capacitance C
(cb)
µ =
e2nC/kBT depends on temperature when the conduction electrons with density nC = NC exp
(
µn −EC
)
/kBT
are considered. The experimental results obtained for the manganite compounds, at high temperature range,
are discussed in the framework of the chemical capacitance model. However, the measured capacitance de-
pendence on geometrical factors is analysed for BiMnO3 indicating that the non-homogeneous electrostatic
capacitor model is valid in 300÷500 K range.
Key words: chemical capacitance, electric permittivity, perovskite, defects
PACS: 82.45.Un, 77.22.Ch
1. Introduction
Recently, scientists have turned their attention to the development of high power electrical energy
storage devices. Such a system includes electrochemical and electrostatic capacitors. The promising ma-
terials are oxides and composites of oxides, e.g., MnO2, RuO2, Fe2O3 [1]. The occurrence of defects pro-
duces an effect on the electric properties of a sample. Primarily, they affect the electronic structure and
thus the conductivity. However, due to the relation ε∗ = iσ∗, the effective value of electric permittivity is
usually measured in case of the materials with perovskite structure that contain defects. In such a case,
contribution of the lattice and the space charge or charge carrier responses ought to be considered [2]
ε∗(ω)= ε∗(ω)lattice+ε∗(ω)carries . (1.1)
The concept of a capacitance is usually related to an electrostatic geometric capacitor determined
by the electric field E between two metal electrodes storing opposite charges. When a dielectric fills the
capacitor, the electric field is modified due to the appearance of induced and ordered dipoles. Hence, the
capacitance of such a system can be modified in accord with the dielectric material properties
Celectrostatic = εr ε0
A
d
. (1.2)
However, the excess charge is confined to the thin region close to the interface between dielectric mate-
rial and the electrode, and the sub-electrode layer can be considered. The contribution of defects can be
considered basing on a multi-layer condenser [3]. In such a case, the space charge effects are ascribed to
the sub-electrode layers whose properties are different from those of the bulk.
© A. Molak, 2013 31801-1
http://dx.doi.org/10.5488/CMP.16.31801
http://www.icmp.lviv.ua/journal
A. Molak
The perovskite stoichiometric ABO3 compounds, e.g., niobates, tantalates and titanates, show a large
gap Eg ∼ 3 eV in the electronic structure. Hence, their dielectric properties are described using the electro-
static geometric capacitance [equation (1.2)]. However, several perovskites that contain the 3d transition
metal ions in the B sublattice, e.g., BiMnO3, (BiNa)(MnNb)O3 [4, 5], (BiPb)(MnNb)O3 [6], have a narrow
gap Eg < 1 eV. Therefore, they show a marked conductivity at temperature ranges above the room tem-
perature. It was reported that these perovskite materials (see also references in [4–6] for other materials)
exhibit the effective permittivity which reaches high values εeff ∼ 105
÷ 106 at high temperature when
measured at radio-frequencies. This effect can be ascribed to the occurrence of defects, not only to elec-
tric current charges and to oxygen vacancies but also to chemical and structural non-homogeneity. Such
features correspond to the semiconductor behaviour of the electric conduction. The reported activation
energy values varied within 0.2÷1.0 eV range [4–6].
It seems worthwhile to discuss whether the electric properties of the non-homogeneous perovskite
compounds can be considered in terms of the chemical capacitance. Such an approach would be lim-
ited, e.g., to the manganite-based compounds, their solid solutions, and to compounds containing a high
amount of oxygen vacancies.
The electrochemical capacitance includes electrical and chemical contributions
Celectrochem∝
(
∂φ
∂Q
+
∂µ∗
∂Q
)−1
∝
(
1
Celectro
+
1
Cchem
)−1
, (1.3)
where Q denotes the charge, φ — the electric potential at the electrode, µ∗
= (1/ez)µ denotes the nor-
malized chemical potential, e — the elementary charge, and z — charge number (the notation which
discriminates the type of the charge carriers and non-homogeneity of the material is omitted here for
simplicity) [7].
The general electrochemical capacitance has been defined for mesoscopic systems [8]. The capaci-
tance relates to the density of states
CDOS = e2 dN
dE
, (1.4)
where N denotes the density of charges. The other definition of the chemical capacitance is related to the
carriers density c, since µ= µ∗
+kBT ln(c/N ),
Cchem = (ez)2
(
∂µ
∂c
)−1
Ad =
[
(ez)2
kBT
]
c Ad . (1.5)
Therefore, the chemical capacitance is proportional to the volume, V = Ad , which contains the charge
carriers. Correspondingly, the electrochemical resistor can be defined and the electric current density
was obtained [7]
I (r, t) = ze J =−σ(r )∇
(
µ∗
+φ
)
. (1.6)
This idea of the chemical capacitance was proposed e.g., for the solar cells based on TiO2 nanocom-
posites working on the redox processes [8, 9] and (La,Sr)(Co,Fe)O3−δ electrodes applied for solid oxide fuel
cells [10]. In such cases, the modification of the electrochemical potential dV produces a change in the
chemical potential dµn of electrons, associated both with the variation of free electron density dnC and
the variation of a localized electron density in band gap states dnL. The chemical capacitance defined lo-
cally for a small volume element, reflects the capability of a system to accept or release additional charge
carriers with the density Ni due to a change in their chemical potential µi = µ0
i
+ kBT . The chemical
capacitance per unit volume is formulated as follows:
C (i)
µ = e2 ∂Ni
∂µi
=
e2Ni
kBT
. (1.7)
Hence, when both free and localized electrons are considered, one obtains the chemical capacitance de-
pendent on temperature
Cµ = e2 ∂(nC +nL)
∂µn
=C (cb)
µ +C
(trap)
µ , (1.8)
31801-2
Chemical capacitance for manganite based ceramics
where
C
(trap)
µ = e2 ∂nL
∂µn
= e2g (µn) . (1.9)
The density of localized states in the band gap, at energy E and for exponential distribution is [8, 11, 12]
g (E )=
(
NL
kBT0
)
exp
(
E −EC
kBT0
)
, (1.10)
where NL is the total density below the conductivity band and T0 is a parameter with temperature units
that determines the depth of distribution. Similarly, for electrons placed in a conduction band
C (cb)
µ =
e2nC
kB T
, (1.11)
where in accord with the Boltzmann distribution function
nC = NC exp
[
µn −EC
kB T
]
. (1.12)
Therefore, the occurrence of the free charge carriers offers a thermally activated contribution to the
chemical capacitance.
2. Experimental
Several compounds were chosen for analysis, i.e., BiMnO3, (BiNa)(MnNb)O3, (BiPb)(MnNb)O3, and
NaNbO3. The ceramic samples of the (BiNa)(MnNb)O3 and (BiPb)(MnNb)O3 compounds were prepared
by high-temperature sintering. The details have been described in the former papers [4–6]. Standard
electrical properties, e.g., electric permittivity, dielectric loss coefficient, electric conductivity temper-
ature and frequency dependencies of the (BiNa)(MnNb)O3, (BiPb)(MnNb)O3 compounds have been al-
ready published. High values of the effective permittivity were observed for a series of BiMnO3-NaNbO3
compounds. Therefore, the analysis of the end members of this series, i.e., BiMnO3 and NaNbO3, was
conducted as well.
The geometrical dependence of the capacitance was measured for BiMnO3 and NaNbO3. Several ce-
ramics BiMnO3 samples with different thickness d and surface area A were prepared. Moreover, one
chosen sample of BiMnO3 ceramics was polished step by step to obtain a series with d varying from
3.7 mm to 0.833 mm while the surface A = 0.72 mm was constant. The capacitance C and conductance G
of the BiMnO3 samples were measured using a HP 4263B LCR meter in a parallel mode.
The results obtained for the NaNbO3 and NaNbO3−x crystals were analyzed for comparison. The crys-
tals have been obtained from the solution of melted salts [13]. The amount of the oxygen vacancies was
increased by the electrochemical procedure conducted at high temperature (950 K). The samples were
reduced at a chamber in the air at a pressure lowered to 0.1 Pa. The concentration of the space charge
was estimated from depolarization currents. The electric measurements of sodium niobate crystals were
conducted using a Tesla BM 595 capacitance meter at f = 1 MHz.
3. Results
3.1. Capacitance dependence on temperature
The former studies conducted for the (BiNa)(MnNb)O3 and (BiPb)(MnNb)O3 compounds showed their
chemical and structural disorder. The XRD test showed the coexistence of long range electric order and
short-range disorder related to defects [14]. The microanalysis carried out with the SEM tests showed
a chemical non-homogeneity in the micro-scale [4–6, 15]. The analysis of the electric conductivity and
the effective permittivity was consistent with these features of the materials. The electric conductivity
temperature dependences were described within the small polaron model with the activation energy
varying in the 0.2÷0.5 eV range. Themodel of a small variable hopping polaron, which has been proposed
31801-3
A. Molak
for these compounds, indicated that a distribution of traps with different energies takes place in the
(BiNa)(MnNb)O3 and (BiPb)(MnNb)O3 ceramics.
The effective permittivity εeff( f ,T ) estimated from the geometrical formula (1.2) showed a steep in-
crease in the high temperature range, above 500 K. Moreover, a marked dispersion in εeff took place.
The permittivity estimated at the measuring frequency f = 100 kHz, showed moderate values between
εeff ⋍ 100÷1000. On the other hand, the permittivity at the frequency of 100 Hz reached high values about
εeff ⋍ 105
÷106 in the high temperature range 600÷800 K. This effect was ascribed to the mutual effect of
the conductivity and the capacitance in accord with the general dependence ε∗ = iσ∗.
However, another approach, based on the chemical capacitance concept is considered herein. This
model includes the participation of defects and electric current carriers [7–12]. The occurrence of the
point defects, which form the traps, consecutively enables the participation of thermally activated charge
carriers in the measured capacitance of the samples.
The Arrhenius-type dependences of the measured capacitance C on temperature T were plotted to
check the contribution of the defect subsystem (figure 1 and 2). It turned out that the C (T, f ) dependences
can be described in accord with the chemical capacitance model [equations (1.7), (1.8), (1.9), (1.10),
(1.11), (1.12)] within the high temperature range. The local peaks or anomalies caused by a phase
transition are also visible, e.g., the structural phase transition at Tph.tr. = 474 K manifests itself in case of
BiMnO3 [16, 17].
The parameter ∆E =
(
µn −EC
)
would be estimated, using a numerical fitting in accord with nC =
NC exp[(µn −EC)/kBT ] [equation (1.12)], from the slope of straight-line segments discerned in the ε′
eff
vs.
T −1 plot. The ∆E value varies from 0.06 eV in the temperature range in the vicinity of room temperature
up to 2.61 eV in the 765÷773 K range depending on the compound (see figures 1 and 2, table 1). One can
notice that the effective permittivity can be described in such cases within the chemical capacitance C (cb)
µ
model [equations (1.11), (1.12)] [7–12].
3.2. The effect of the concentration of oxygen vacancies on capacitance
The effect of the concentration of oxygen vacancies on the capacitance is shown for the case of sodium
niobate crystals. The estimated concentration of the space chargewas equal to NQ ∈ (1·1017
÷6·1017) cm−3
in case of the as-grown crystals. The estimated concentration of the charge carriers was one order higher,
and it can be ascribed to the appearance of the oxygen vacancies NQ ⋍ N(VO) ∈ (2 ·1017
÷1 ·1018) cm−3.
Figure 1. (Color online) The Arrhenius plots of the effective electric permittivity ε′
eff
drawn
in accord with the chemical capacitance model obtained for (Bi0.5Na0.5)(Mn0.5Nb0.5)O3 (a) and
(Na0.5Pb0.5)(Mn0.5Nb0.5)O3 (b) ceramics. The parameter ∆E value and the straight-line segment denote
the proposed applicability of the chemical capacitance model.
31801-4
Chemical capacitance for manganite based ceramics
Figure 2. (Color online) The plots obtained for BiMnO3 ceramics. (a) The effective electric permittivity
temperature dependence ε′
eff
vs. T. (b) The Arrhenius plot of the electric conductivity σ vs. T−1. (c) The
Arrhenius plot of the effective electric permittivity ε′
eff
obtained for a wide temperature range 250÷800 K.
(d) The Arrhenius plot of effective electric permittivity ε′
eff
shown in the high temperature range.
The ε′eff(T ) plots obtained at frequency f = 1 MHz are shown in figure 3. A higher amount of the oxygen
vacancies resulted in an increase of the actual capacitance, and thus in an increase of the estimated
effective permittivity ε′eff. This effect corresponded to a similar increase of the ac conductivity σac(T ).
3.3. The effect of Mn addition on capacitance
Amarked dispersion in the electric properties of the (BixNa1−x )(MnyNb1−y )O3 ceramics series is visi-
ble in the real part of the effective electric permittivity εeff( f ,T ) diagram [figure 4 (a) and (b)]. Moderate
values measured at f = 100 kHz were obtained for the electric permittivity i.e., εeff(T,100 kHz) < 2000
within the range 300÷900 K, even for the samples with high Bi-Mn content. The Bi and Mn co-doping
caused a steep increase of the εeff(T,100 kHz) value at a high temperature range. This effect corre-
sponded to the increase in the loss factor tanδ with temperature and it was ascribed to a thermally
activated effect. The electric permittivity εeff(T ) of the lightly doped ceramics (x = 0.015, y = 0.01), mea-
sured at f = 100 Hz, exhibited the values close to the values measured for the crystal εeff(T,100 Hz) < 103.
31801-5
A. Molak
Table 1. Data obtained for the ceramics compounds. The parameter ∆E value estimated in the chosen
temperature ranges ∆T from numerical fit in accord with the chemical capacitance model. The ε′
eff
vs.
reciprocal temperature T−1 plots are shown in figures 1 and 2.
Compound f = 100 kHz f = 1 kHz
∆E (eV) ∆T (K) ∆E (eV) ∆T (K)
BiMnO3 2.52 765–773 2.61 765–773
1.82 730–760 1.16 650–740
0.22 650–670
0.07 260–400
(Bi0.5Na0.5)(Mn0.5Nb0.5)O3 0.40 600–690 0.40 600–710
0.21 310–400 0.37 360–520
(Na0.5Pb0.5)(Mn0.5Nb0.5)O3 0.26 530–690 0.36 530–690
0.06 270–430 0.08 220–340
However, it markedly increased with temperature and the Mn ion content, reaching the high value ≃ 105
for the (Bi0.24Na0.76)(Mn0.16Nb0.84)O3 and (Bi0.50Na0.50)(Mn0.33Nb0.67)O3 compounds at high temperature
[figure 4 (b)].
Hence, the addition of Bi and Mn ions to the sodium niobate host induced the high value effective
permittivity when measured at low frequency and at high temperature.
3.4. Capacitance dependence on geometrical factors
The electrostatic and the chemical capacitance show different dependences on the geometrical fac-
tors. The electrostatic capacitance is proportional to the ratio A/d [equation (1.1)], while the chemical
capacitance is proportional to the volume V = Ad of the sample [equation (1.5)]. In case of sodium nio-
bate, the contribution εbulk from the antiferroelectric bulk can be discerned from the contribution εL of
the space charge formed at the sub-electrode layers. Since the Curie-Weiss dependence is valid for an
antiferroelectric phase transition, the effective electric permittivity is [figure 5 (a)]
εeff = εbulk+εL =
C
T −Tafe
+εL . (3.1)
Figure 3. The electric permittivity ε′
eff
dependence on temperature obtained for the as-grown NaNbO3
and the oxygen vacancies containing reduced NaNbO3−x crystals.
31801-6
Chemical capacitance for manganite based ceramics
Figure 4. Electric effective permittivity ε′
eff
measured on heating at f = 100 kHz (a) and at f = 100 Hz
(b) for (BixNa1−x )(MnyNb1−y )O3 ceramics. The ε′
eff
(T ) obtained for a non-doped NaNbO3 single crystal
is plotted for comparison. The arrows point the temperatures of structural phase transitions occurring
in pure sodium niobate between AFE and PE phases. The content of the Bi and Mn ions, x and y , in the
ceramics is noted in the diagram.
When a non-homogeneous multi-layer model of a condenser is assumed [3, 18], the thickness L of sub-
electrode layers can be estimated from the formula
ε−1
eff = ε−1
bulk
(
1−
2L
d
)
+ε−1
L
2L
d
≈ ε−1
B +ε−1
L
2L
d
, (3.2)
Figure 5. (a) The electric permittivity ε′
eff
dependence on the sample thickness d obtained for the NaNbO3
crystals at several temperatures at f = 1 MHz. Tafe ≈ 620 K denotes an antiferroelectric phase transition.
(b) The reciprocal effective electric permittivity vs. reciprocal thickness of the samples. (c) The scheme of
a non-homogeneous condenser where the sub-electrode layer with thickness L is assumed.
31801-7
A. Molak
Figure 6. (Color online) (a) Geometrical dependencies of the capacitance C obtained for the BiMnO3 ce-
ramics measured at f = 100 kHz at several temperatures. (a) The dependence of C on the ratio A/d . (b)
The dependence of C on the sample volume V = Ad .
where d is the thickness of the sample, L is the thickness of the sub-electrode layer [figure 5 (c)]. The
thickness L = (1/2)εL tanα of the sub-electrode layer in NaNbO3 crystal was estimated as L = 40±10 µm
(numerical fit for plots in figure 5 (b), correlation coefficient 0.964÷0.990). The εL contribution varied
from ≃ 300 to ≃ 1000. Therefore, the crystal lattice contribution dominated in case of NaNbO3 crystals,
when measured at a frequency f = 1 MHz.
The dependence of capacitance on the geometrical factors, obtained for the BiMnO3 ceramics, is
shown in figure 6. It turned out that the capacitance measured at f = 100 kHz increased with the A/d
ratio [figure 6 (a)]. The C dependence on the volume of the samples was not clear. However, a decreas-
ing tendency can be deduced from the data obtained for the sample whose thickness was decreased by
polishing step by step when V ∈ (0.59÷2.68) mm3. Similar results were obtained at f = 1 kHz. Hence,
the model of electrostatic capacitance [see equations (1.3), (3.1), and (3.2)] is consistent with the data
presented in figure 6. It should be noted that they were obtained in the 300÷ 500 K range, where the
dependence of the measured capacitance on temperature is weak (compare figure 2).
Figure 7. (Color online) (a) The effective electric permittivity ε′
eff
dependence on the sample thickness d
obtained for the BiMnO3 ceramics at several temperatures at f = 100 kHz. (b) The reciprocal effective
electric permittivity vs. reciprocal thickness of the samples.
31801-8
Chemical capacitance for manganite based ceramics
In case of bismuth manganite, the thickness L of sub-electrode layers was estimated using the data
presented in figure 7 fitted with the equation (3.2). Assuming the value εL ∼ 200, extrapolated for thin
samples, and the slope tanα = 4.5 ·10−4 mm, the sub-electrode thickness L = (1/2)εL tanα = 50±30 µm
was estimated.
4. Discussion
The studied ceramics BiMnO3, (BiNa)(MnNb)O3, and (BiPb)(MnNb)O3 show thermally activated ca-
pacitance in a high temperature range. Such a behaviour corresponds to the semiconductor-type fea-
tures of the electric conductivity. When the contribution of thermally activated charges to the measured
capacitance is assumed, the chemical capacitancemodel can be applied. In accordwith thismodel, the ex-
ponential dependence on temperature C (cb)
µ = e2nC/kBT = (e2NC/kBT )exp[(∆E )/kBT ] [equation (1.12)]
describes the capacitance temperature dependence. One can notice that the estimated values of param-
eter ∆E ∈ 0.06÷2.52 eV correspond to the activation energy Ea obtained from the electric conductivity
temperature dependence since the Ea value varies within 0.2÷ 1.1 eV range. Moreover, in case of the
BiMnO3, the values of the ∆E can be compared to the energy gap Eg obtained from optical absorption
measurements 1.1 eV and 1.6 eV [19] as well as to the result obtained from ab initio calculations of the
electronic structure where Eg = 0.33 eV [20].
In case of the perovskite structure, the crystal lattice component is usually on the ε′
lattice
∼ 100 and
higher values ≃ 103
÷104 occur in the vicinity of structural phase transitions. From this point of view,
the common origin for higher values of conduction and the capacitance temperature dependence, apart
from the narrow energy gap, would be the occurrence of defects. Such a deduction is consistent with the
results of former studies which proved the occurrence of a local structural disorder and chemical non-
homogeneity in these materials by XRD and EPMA tests. The estimated density of states in the vicinity of
the Fermi energy was ∼ 1018
÷1020 eV−1cm−3 [4–6, 14, 15]. Hence, the high value of the measured capac-
itance and thus the estimated effective electric permittivity are consistent with the high concentration of
defects in the samples studied, since Cchem = [(ez)2/kBT ]c Ad [equation (1.5)].
On the other hand, the chemical capacitance and the electrostatic capacitance show different depen-
dences on the geometrical factors. Therefore, the test was conducted for the end members of the studied
series of compounds, i.e., for NaNbO3 and BiMnO3.
In case of the stoichiometric sodium niobate crystals, the chemical capacitance contribution was not
expected. The dielectric permittivity did not increase with temperature increase. However, a low con-
centration of the space charge was determined ∼ 1017 cm−3. Hence, the model of electrostatic, non-
homogeneous, multi-layer condenser was used to estimate the participation of the space charge in the
effective permittivity. The thickness of sub-electrode layers was of the order of several tenth of µm.
In case of sodium niobate and bismuth manganite, one can expect a correlation of the capacitance
with the volume of the samples, in accord with the chemical capacitance model. However, it turned out
that the capacitance was not proportional to the volume of the samples when they were measured and
analysed in the temperature range 300÷500 K. Instead, it was proportional to the A/d ratio which in-
dicated that the electrostatic, non-homogeneous model is appropriate for bismuth manganite. The esti-
mated thickness of sub-electrode layers was also of the order of several tenth of µm.
Hence, in case of BiMnO3, contradictory results were obtained from the analysis of the geometrical
factor dependence and from the high temperature dependence of the capacitance. One can notice that the
geometrical factors analysis was carried out in the 300÷500 K range where the capacitance dependence
on temperature was weak.
Nevertheless, the chemical capacitance model should be used for high temperature ranges for
(Bi0.5Na0.5)(Mn0.5Nb0.5)O3, (Na0.5Pb0.5)(Mn0.5Nb0.5)O3, BiMnO3 compounds (see figure 1 and 2) where
a steep increase in C (T ) took place. The thermal generation of the charge carriers, which contribute to
the capacitance and induce its high value, is likely to occur only in a part of the volume of the samples.
Therefore, it seems that further studies conducted at T > 600 K would be quite useful in order to discern
the ambiguities.
31801-9
A. Molak
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Хiмiчна ємнiсть, запропонована для керамiк на основi
манганiту
А. Моляк
Iнститут фiзики, Сiлезький унiверситет, Катовiце, Польща
Вимiряне значення ефективної електричної проникностi εeff декiлькох сполук, а саме, (BiNa)(MnNb)O3,
(BiPb)(MnNb)O3, i BiMnO3 збiльшилося iз значення ≈ 10÷100 в низькотемпературнiй областi (100÷300 K)
до високого значення, досягаючи значення 105 у високотемпературнiй областi, а саме, 500÷800 K. Та-
кi риси є виявом термiчно активованих носiїв просторового заряду, якi впливають на вимiрювану єм-
нiсть. Вимiряне високе значення ефективної проникностi декiлькох магнiтних сполук може бути припи-
сане хiмiчнiй ємностi Cµ = e2∂Ni /∂µi , вираженiй в термiнах хiмiчного потенцiалу µ. Хiмiчна ємнiсть
C
(cb)
µ = e2nC/kBT залежить вiд температури, при якiй розглядаються електрони провiдностi з густиною
nC = NC exp
(
µn −EC
)
/kBT . Експериментальнi результати, отриманi для сполук манганiту у високотем-
пературнiй областi, обговорюються в рамках моделi хiмiчної ємностi. Проте, вимiряна ємнiсна залежнiсть
вiд геометричних факторiв, що аналiзується для BiMnO3, вказує, що неоднорiдна електростатична ємнi-
сна модель є справедливою в областi 300÷500 K.
Ключовi слова: хiмiчна ємнiсть, електрична проникнiсть, перовскiти, дефекти
31801-10
http://dx.doi.org/10.1039/C1CP22659B
http://dx.doi.org/ 10.1080/01411590903341155
http://dx.doi.org/10.1088/0022-3727/38/9/019
http://dx.doi.org/10.1080/01411590600892336
http://dx.doi.org/10.1016/j.ssi.2005.03.013
http://dx.doi.org/10.1039/b100180i
http://dx.doi.org/10.1039/b310907k
http://dx.doi.org/10.1039/c0cp02249g
http://dx.doi.org/10.1016/j.ssi.2006.07.057
http://dx.doi.org/10.1103/PhysRevB.77.235203
http://dx.doi.org/10.1039/b709316k
http://dx.doi.org/10.1080/00150190802375417
http://dx.doi.org/10.1016/j.sab.2005.03.013
http://dx.doi.org/10.1021/ja0664032
http://dx.doi.org/10.1103/PhysRevB.67.180401
http://dx.doi.org/10.1080/00150199608223629
http://dx.doi.org/10.1063/1.3457786
http://dx.doi.org/10.1103/PhysRevB.81.144103
Introduction
Experimental
Results
Capacitance dependence on temperature
The effect of the concentration of oxygen vacancies on capacitance
The effect of Mn addition on capacitance
Capacitance dependence on geometrical factors
Discussion
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