Excellent stability and low dielectric loss of Ba(Fe0.5Nb0.5)O3 synthesized by a solution precipitation method

Article abstract of DOI:10.1016/j.jallcom.2015.09.169

A solution precipitation method was applied to prepare Ba(Fe_0.5Nb_0.5)O₃ powders. Nano-size BFN powders with uniform particles size (～40 nm) were synthesized by solution precipitation method, which is beneficial to calcine at low temperature (1223 K). The sintering sample with dense microstructure and uniform grain size (15 μm) was obtained at 1673 K, which exhibits enhanced dielectric properties. The dielectric loss of BFN ceramic could be significantly reduced by solution precipitation method. The frequency and temperature stability of BFN ceramics could also be improved. The complex impedance spectroscopy analysis results suggested that the obtained Ba(Fe_0.5Nb_0.5)O₃ ceramics, consisting of semiconducting grains and insulating grain boundaries, were electrically heterogeneous. The grain boundary effect was responsible for such a high value of dielectric constant.

Full text of DOI:10.1016/j.jallcom.2015.09.169

Accepted Manuscript
Excellent stability and low dielectric loss of Ba(Fe Nb )O synthesized by a
.5 0.5
0
3
solution precipitation method
Zhuo Wang, Yong Fei Wen, Hai Juan Li, Ming Rui Fang, Chun Wang, Yong Ping Pu
PII:
S0925-8388(15)31145-2
10.1016/j.jallcom.2015.09.169
JALCOM 35444
DOI:
Reference:
To appear in: Journal of Alloys and Compounds
Received Date: 17 February 2015
Revised Date: 16 September 2015
Accepted Date: 18 September 2015
Please cite this article as: Z. Wang, Y.F. Wen, H.J. Li, M.R. Fang, C. Wang, Y.P. Pu, Excellent stability
and low dielectric loss of Ba(Fe Nb )O synthesized by a solution precipitation method, Journal of
.5 0.5
0
3
Alloys and Compounds (2015), doi: 10.1016/j.jallcom.2015.09.169.
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ACCEPTED MANUSCRIPT
Abstract:
A solution precipitation method was applied to prepare Ba(Fe Nb )O powders. Nano-size BFN
0.5
0.5
3
powders with uniform particles size (~40 nm) can be obtained by solution precipitation method at low
calcinations temperature (1223 K for 2 h). Microstructure analysis shows dense microstructure and
uniform of the grain size (15 µm) in 1673 K sintered sample exhibiting enhanced dielectric properties.
The solution precipitation method could significantly reduce the dielectric loss of BFN ceramic. The
frequency stability and temperature stability of BFN ceramics could also be improved by solution
precipitation method. The complex impedance spectroscopy analysis suggested that the obtained
Ba(Fe Nb )O ceramics were electrically heterogeneous, consisting of semiconducting grains and
0
.5
0.5
3
insulating grain boundaries. The grain boundary effect (barrier layer formation) is responsible for such
a high value of dielectric constant.
Fig. 6. Frequency dependence of dielectric constant and dielectric loss for BFN ceramics prepared by
the solution precipitation method and solid-state reaction method between 100 Hz and 1 MHz.
The low dielectric loss and high dielectric constants of BFN ceramics could be obtained by
solution precipitation method.

ACCEPTED MANUSCRIPT
Excellent stability and low dielectric loss of Ba(Fe Nb )O synthesized by a
0
.5
0.5
3
solution precipitation method
Zhuo Wang*, Yong Fei Wen, Hai Juan Li, Ming Rui Fang, Chun Wang, Yong Ping Pu
School of Materials Science and Engineering, Shaanxi University of Science and Technology, Xi’an
7
10021, China
Abstract:
A solution precipitation method was applied to prepare Ba(Fe Nb )O powders. Nano-size BFN
0.5
0.5
3
powders with uniform particles size (~40 nm) were synthesized by solution precipitation method,
which is beneficial to calcine at low temperature (1223 K). The sintering sample with dense
microstructure and uniform grain size (15 µm) was obtained at 1673 K, which exhibits enhanced
dielectric properties. The dielectric loss of BFN ceramic could be significantly reduced by solution
precipitation method. The frequency and temperature stability of BFN ceramics could also be improved.
The complex impedance spectroscopy analysis results suggested that the obtained Ba(Fe Nb )O
0.5
0.5
3
ceramics, consisting of semiconducting grains and insulating grain boundaries, were electrically
heterogeneous. The grain boundary effect was responsible for such a high value of dielectric constant.
Keywords: A. Solution Precipitation Method; C. Dielectric Loss; C. Temperature Stability; C. Electrical
Heterogeneous
1
. Introduction
Recently, giant dielectric constant compounds with perovskite structures (ABO ) have been
3
contributed greatly to research because of the diversity of their physical properties. Many applications
of these compounds have been found in several industrial fileds, such as high density capacitors,
memory devices, actuators et al [1-4]. Most high dielectric constant materials with perovskite structures
*Corresponding author. Tel: +86 29 86168688.
E-mail address: wangzhuo@sust.edu.cn (Zhuo Wang)

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contain lead [5-6], which pollutes the envirenment. Therefore, it is necessary to search alternative
lead-free compounds for such applications, which should have either comparable or superior dielectric
properties. A kind of lead-free perovskite oxide, CaCu Ti O (CCTO) [7-12], which has an
3
4
12
5
extraordinarily high static dielectric constant ε'~10 but also high dielectric loss at room temperature
and 1 kHz, has been reported recently. Li and Ti-doped NiO is a new oxide with a high dielectric
4
5
constant (ε'~10 -10 at room temperature and 1 kHz) [13-16], which does not have a good temperature
stability and is nonferroelectric. Ba(Fe Nb )O (BFN), which generally exhibit a very high dielectric
0
.5
0.5
3
3
5
constant step ( in the order of 10 - 10 ) over a broad temperature and frequency interval, is a
relaxor-type material with partially disordered perovskite structure [17-20]. This kind of material has
excellent potential application in microelectronics and energy storage components. In general,
Ba(Fe Nb )O ceramics could be synthesized by the solid-state reaction method [21-23]. However, it
0
.5
0.5
3
requires synthesis temperature higher than 1473 K, and the particle sizes are relatively large with a
non-stoichiometric, which causes that the ceramics have high dielectric loss. To overcome these
shortcomings and fabricate small sizes ceramic powders, wet chemical method is considered to be
effective way to prepare BFN ceramic powders. Microwave synthesis of BFN ceramics was reported
by Charoenthai et al, which exhibited rather high dielectric constant (~300,000 at 527 K for 1 kHz) and
low dielectric loss (less than 0.6) [24]. Chung et al studied the dielectric properties of BFN ceramics
synthesized by sol-gel method. The average grain size increased with heating temperature (from 20 nm
to 30 nm), a dielectric constant of 20,000 and dielectric loss of ~0.2 were obtained at room temperature
and 1 kHz [25]. Piyush et al also synthesized BFN ceramics whose average particle size was found to
be 20 - 25 nm by sol-gel method and studied their dielectric properties. And the dielectric constant and
dielectric loss of BFN ceramics turned out to be ~33,000 and 0.45 at room temperatures and 100 Hz

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frequency [26]. However, each of these methods has both disadvantages and advantages which requires
an application of specific technological conditions and accuracy of the process performance. Solution
precipitation method has been considered to be the most efficient wet chemical method to obtain BFN
ceramics with lower dielectric loss, which have considerable advantages including excellent chemical
stoichiometry, compositional homogeneity and lower crystallization temperature [27-29]. The method
is considered to be efficient to obtain BFN ceramics with lower dielectric loss. It is known that the
nano-powders is difficult to form the dense ceramics due to nanometer size effect. It is reported that
two-step sintering method can act as a sintering method for various nano-powders to promote grain
growth and ceramic densification owe to its liquid-phase effect [30]. Therefore, the two-step sintering
method was applied to obtain BFN ceramics and the liquid-phase appear in more than 1723 K in
sinterring process.
In this work, a novel solution precipitation method was used to synthesis the BFN powders. The
effects of synthesis temperature on the phase of BFN precursor powders were investigated. BFN
ceramics have been prepared by two-step sintering method. The microstructure and dielectric
properties of the BFN ceramics were also investigated. The dielectric relaxation behavior was
analysised. The possible origin of giant permittivity was also discussed based on the complex
impedance spectroscopy.
2
.
Experimental procedure
Ba(Fe Nb )O powders was synthesized by the solution precipitation method. The starting
0
.5
0.5
3
materials were niobium oxide (Nb O ), potassium hydroxide (KOH), barium nitrate (Ba(NO ) ) and
2
5
3 2
iron nitrate nonahydrate (Fe(NO ) •9H O), oxalic acid ((COOH) •2H O) and aqueous ammonia
3
3
2
2
2
(
NH •H O). At first, Nb O and KOH were mixed and calcined at 633 K for 2 h to form a soluble
3 2 2 5

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potassium niobate. Potassium niobate was dissolved into distilled water and titrated by nitric acid to
form a precipitate of niobium hydroxide (Nb(OH) ). The freshly precipitated niobium hydroxide was
5
dissolved into a solution by chelation of oxalic acid to obtain the niobium precursor solution. Then
according to the chemical stoichiometry of BFN, the as-prepared niobium precursor solution was
mixed with iron nitrate and barium nitrate. Thereafter, aqueous ammonia was used to adjust pH value
2+
3+
5+
of the solution to be 10 to realize the coprecipitation of Ba , Fe and Nb ions. After drying, the
precipitates were calcined for 2h at 623-1223 K to produce BFN powders. Thermal analysis was
conducted on a TG-DTA thermoanalyzer (STA409PC) in the nitrogen atmosphere in the temperature
range 308-1273 K with a heating rate of 10 K/min. In order to study phase formation of the calcined
powders, X-ray diffraction (XRD) analysis was performed using a diffractrometer with CuKα radiation
(
D/max-2200PC). Powders of the optimum calcined condition were then pressed into a pellet and
sintered at 1673 K for 3 h. The sintering method that we report here used two steps in the heating
schedule. The sample was first heated to a higher temperature (1773 K) to achieve an intermediate
density, then cooled down and held at a relatively lower temperature (sintering temperature 1673 K)
until it was fully dense. Microstructure of calcined powders and sintered samples were examined using
scanning electron microscopy (S-4800). For the dielectric investigation, silver paste was painted on
both sides of the samples. The samples with silver paste were fired at 823 K for 15 min. Dielectric and
complex impedance measurements were carried out by a dielectric measurement system
(
Agilent-E4980A). In addition, the BFN ceramic was sintered at 1673 K for 3h by solid-state reaction
method.
3
3
.
Results and discussions
.1 Synthesis of BFN precursor powders

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The XRD patterns of the BFN precursor powders calcined at different temperature are displayed
in Fig. 1. The XRD results reveal that the as-dried precipitates present the feature of metal-organics.
The diffraction peaks of the BaCO are found when the calcination temperature increases to 623 K.
3
Further, as the temperature rises to 823 K, the largest amount of BaCO crystal phase can be found. The
3
diffraction of the perovskite BFN appears when the calcination temperature reaches to 1023 K. Further
increasing the temperature gradually leads to the increment of BFN phase, small amount of impurity
phase (BaCO ) is discovered in our samples calcinated at 1123 K. Lastly, when the temperature reaches
3
to 1223 K, pure perovskite phase BFN is obtained. In general, the pure phase of BFN can be obtained
at the calcination temperature over 1473 K using the conventional method [19]. These results suggest
that the synthesis temperature of BFN powders prepared by solution precipitation method is lower than
that by solid-state reaction method (from 1473 K drop to 1223 K).
The thermal analysis on BFN precursor powders is shown in Fig. 2. There are three weight loss
regions in the TGA curve. The first region (308-473 K) corresponds to the evaporation of remnant
water or solvents [31]. In the second region (473-1123 K) two exothermal peaks are appeared at 791 K
and 1023 K, respectively, which could be due to the pyrolysis of organic materials or the formation of
BaCO phase [31]. The weak exothermic peak at 1189 K could be attributed to the transition from
3
amorphous to crystalline phase [26]. The weight loss near 1189 K in the TG curve is related to the
release of CO with small amount BaCO phase transformed to Ba(Fe Nb )O phase at high
2
3
0.5
0.5
3
temperature. The thermal analysis behavior agrees well with the results of XRD patterns of BFN
powders calcined at various temperatures as shown in Fig. 1.
The morphology of BFN powders calcined at 1023 K, 1123 K and 1223 K for 2 h is illustrated in
Fig. 3. Nano-sized BFN powder with average diameter of about 20 nm, consisting of fine elements

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joined in to the bigger agglomerates, are observed at 1023 K. The particle size of the BFN powders
increases with the increase of the calcinations temperature. Very fine particles with average diameter of
about 40 nm are observed in the powders calcined at 1223 K. Therefore, nano-sized BFN powders with
uniform particles size (~40 nm) can be obtained by solution precipitation method at low calcination
temperature (1223 K).
3
.2 Phase structure and microstructure of BFN ceramics
Fig. 4 reveals XRD patterns of BFN ceramics synthesized by solution precipitation method and
solid-state reaction method, respectiyely. As shown in Fig. 4, all the diffraction peaks in the XRD
patterans can be indexed as the body-centered cubic with the space group pm3m (221) according to
JCPDS #89-2967. Fig. 5 shows the SEM photographs of the surface of BFN ceramic. The BFN
ceramic shows well-grown and dense microstructure in all samples. Fig. 5(a) shows the microstructure
of BFN ceramic synthesized by solution precipitation method with grain sizes around 15 µm and a
3
density of 6.533 g/cm . Fig. 5(b) presents the morphology of BFN ceramic synthesized by solid-state
reaction method. The sample shows a microstructure with grain sizes around 20 µm and a density of
3
6
.203 g/cm . The uniform grain sizes of BFN ceramics are obtained by solution precipitation method.
Comparing with the microstructure and density of the ceramics prepared by the two methods, it can
concluded that the small grain size and high density of the ceramic prepared by solution precipitation
method are attributed to high surface energy of nano-powders and the two-step sintering method.
3
.3 Dielectric properties of BFN ceramics.
Fig. 6 shows the frequency dependence of dielectric constant and dielectric loss of the BFN
ceramics prepared by two methods. As shown in Fig 6(a), the dielectric constant of BFN ceramics
decreases with increasing frequency, which is a normal behavior of dielectrics. The high values of

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permittivity are associated with heterogeneous conduction in the grain and grain boundary of the
compounds [32]. When further increasing the frequency to a certain value, the dielectric constant
shows a step decrease and the dielectric loss shows a relaxation peak, which indicates that BFN
ceramic has a Debye-like relaxation [33]. As shown in Fig 6(b), dielectric loss of BFN ceramics is
obviously frequency dependent, and dielectric loss peak is observed at high frequency where
Debye-like relaxations occur. It is worth noting that the dielectric loss of BFN ceramics prepared by
solution precipitation method is lower compared with that by solid-state reaction method. The low
dielectric loss is related to the uniform grain size and the dense microstructure of BFN ceramics. The
dielectric constant and dielectric loss of the BFN ceramic prepared by solution precipitation method at
1
0 kHz are about 36,639 and 0.45, respectively. However, the dielectric constant and dielectric loss of
the BFN ceramic prepared by solid-state reaction method are about 13,645 and 2.42, respectively. It
indicates that the dielectric loss of BFN ceramic can be significantly reduced by the solution
precipitation method. In the process of sintering, the small size of the BFN powders is beneficial to
grain growth and porosity elimination. Therefore, the BFN ceramics prepared by the solution
precipitation method is denser than that by solid-state reaction method, which leads to lower dielectric
loss. To discuss the frequency stability of BFN ceramics prepared by two methods, the Eq. (1) is used
to calculate the data shown in Table 1 [34],
1
′( f0 )
ε
′( f ) −
ε
′( f0 )
α ε − f
=
×
(1)
ε
( f − f0 )
where, ε' is the dielectric constant, f is measured frequency, f is the low-frequency (generally, 1 kHz),
0
αε−f indicates the frequency dependence of dielectric constant for BFN ceramics. As shown in Table 1,
it turns out that the solution precipitation method can improve the frequency stability of BFN ceramics.
Table. 1. Comparison of the frequency stability of BFN ceramics prepared by two methods

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-1
Parameters
ε' (f =100 Hz) ε' (f =1 kHz) ε' (f =10 kHz)
αε−f (Hz )
1
0
2
-
5
-5
-3
solution precipitation method
solid-state reaction method
55,771
51,564
36,639
-3.4×10 ~-9.1×10
-5
372,818
72,910
11,748
-9.3×10 ~-4.6×10
Fig. 7(a) demonstrates the temperature dependence of dielectric constant of BFN ceramics
synthesized by solution precipitation method at 500 Hz - 1 MHz. A dielectric relaxation is observed in
the present ceramics at room temperature to ~573 K and the critical temperature of dielectric relaxation
4
increases with the increase of frequency. A giant dielectric constant step (in the order of 10 ) is
observed in the as-sintered BFN ceramics. Fig. 7(b) reveals temperature dependence of dielectric
constant of BFN ceramics synthesized by solid-state reaction method at 100 Hz - 100 kHz. A dielectric
relaxation is observed in the present ceramics from room temperature to ~450 K. There is an obvious
change in dielectric constant dependence on temperature for the BFN ceramics synthesized by
solid-state reaction method compared with that by solution precipitation method. Fig. 7(c) and (d) show
the temperature dependence of dielectric constant and dielectric loss for BFN ceramics prepared by two
methods at 1 kHz, respectively. It is found that the dielectric constant of BFN ceramic prepared by
solution precipitation method is less dependence on temperature in the range of 300 - 475 K. Notably,
the dielectric loss (0.11) of BFN ceramics synthesized by solution precipitation method was much
lower than that (3.21) by solid-state reaction method at room temperature, which is consistent with the
Fig. 6.
To discuss the temperature stability of BFN ceramics prepared by the solution precipitation
method and solid-state reaction method, the Eq. (2) is used to calculate the data shown in Table 2 [34],
1
′(T0 )
ε
′(T) −
ε
′(T0 )
α ε −T
=
×
(2)
ε
(T −T0 )
where, ε' is the dielectric constant, T is measured temperature, T is the room temperature (generally,
0

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3
00 K), αε−T indicates the temperature dependence of dielectric constant of BFN ceramics.
Table. 2. Comparison of the temperature stability of BFN ceramics prepared by two methods,
respectively.
1
Parameters
ε' (T =300 K)
ε' (T=425 K)
55,314
αε−T (K- )
0
-
4
2
solution precipitation method
solid-state reaction method
51,341
67,045
6.2×10
3.1×10
-
324,406
It can be calculated that the αε−T of BFN ceramics prepared by the solution precipitation method
-4
1
(
αε−T= 6.2×10 K- ) is much lower than that prepared by the solid-state reaction method (αε−T=3.1×
-2
1
1
0 K- ) in the temperature range from 300 to 425 K. These results indicate that the BFN ceramics
prepared by solution precipitation method can significantly improve the temperature stability. As show
in Fig. 7 (a), a dielectric anomaly is observed in the present ceramics at near room temperature, another
dielectric anomaly appears in more than 573 K. At the same time, Fig. 7 (b) shows that the low
temperature dielectric anomaly is observed in near room temperature and the high temperature
dielectric anomaly is discovered in 425~475 K. Compared with BFN ceramics prepared by solid-state
reaction method, the low-temperature dielectric abnormity of BFN ceramics prepared by the solution
precipitation method could be detected at lower temperature and the high-temperature dielectric
abnormity, detected at higher temperature, which leads to higher temperature stability of BFN ceramics.
There is a universal case in the analog giant dielectric constant materials. The giant dielectric constant
step in the ceramics is just a competing balance result of the low- and high-temperature dielectric
relaxations.
To understand the physical nature of the dielectric abnormities of BFN ceramics that synthesized
using solution precipitation method, the frequency dependen of dielectric constant is plotted form 303

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K to 403 K. As shown in Fig. 8, these data are also consistent with the modified Debye Equation [23],
*
1−α
ε
=
ε
′ − i
ε
′′ = ε∞ + (εs
−
ε∞ ) /[1+ (iωτ ) ]
(3)
where, ω is the frequency, τ is the relaxation time, εs is the low-frequency values of ε',
ε
ꢀ
is the
high-frequency values of ε', α is a measure of the distribution of relaxation time. The variation of
τ
with 1/T is consistent with the Arrhenius law [19], as Eq. (4):
τ
=
τ 0 exp(E / k T)
(4)
a
B
where, τ0 is the Debye relaxation time, E is the activation energy, and k is Boltzmann constant. As
a
B
shown in Fig. 8, a nearly monodispersive nature of dielectric relaxation is indicated in the present
ceramics with a very small
α parameter: 0.16531~ 0.23976. The relaxation time follows the Arrhenius
law with the fitting parameters: τ0=0.584 ns, E =0.24 eV. It indicates that the dielectric relaxation,
a
which a thermal activation process, is a Debye-like relaxation. The activation energy (E =0.24 eV) of
a
dielectric relaxation is very similar to 0.38 eV, which is activation energy of Sr(Fe Nb )O prepared
0.5
0.5
3
by solid-state reaction method [35]. It is worth noting that the activation energy (E =0.24 eV) of
a
Ba(Fe Nb )O ceramics is lower than that of Sr(Fe Nb )O ceramics (E =0.38 eV) at low
0
.5
0.5
3
0.5
0.5
3
a
temperature. It suggests that the temperature of low temperature dielectric relaxation of BFN ceramics
synthesized by the solution precipitation method becomes lower compared with solid-state reaction
method. The result demonstrates the above discussed inference.
In general, a high dielectric constant can be explained by barrier layer capacitance effect. In order
to confirm the formation of barrier layers in BFN ceramics, complex impedance is analyzed using
Cole-Cole plots. Fig. 9(a-e) show the variation of imaginary part of impedance (Z”) as a function of
real part (Z’) (Cole–Cole plots) at 313K, 353K, 393K, 433K and 473K for the BFN ceramics
synthesized by solution precipitation method. The inset of (a) show the complex impedance spectra of

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BFN ceramics synthesize by solid-state reaction method at 313 K. The observed data is modelled on an
equivalent circuit with series combination of two parallel resistor-capacitor elements is shown in the
inset of Fig. 9(b). The real (Z’) and imaginary (Z”) part of total impedance of the equivalent circuit are
defined as [26]:
Rg
Rgb
Z′ =
+
(5)
(6)
2
2
1
+ (
ω
R C ) 1+ (
ω
R C )
g
g
gb gb
ω
R Cg
ωR C
gb gb
g
Z′′ = Rg [
]+ Rgb[
]
2
2
1
+ (ω
R C )
1+ (ωR C )
gb gb
g
g
where R and C are the grain resistance and grain capacitance, R and Cgb are the grain boundary
g
g
gb
resistance and grain boundary capacitance at the interfacial region, and
ω is the angular frequency. This
plot shows one semicircular arcs with its centre lying below the real axis. The semicircular arcs and the
extent of their intercept on the real axis give information about the electrical behaviour of the
compound. The arc at the lower frequency corresponds to grain boundary which is mainly due to space
charge polarization, while the arc at the higher frequency corresponds to grain which is due to
orientational polarization. Least-mean-square analysis can be performed on these arcs, and the results
are shown as the solid line in plots (see Fig.9). The intercepts of semicircles on the Z’ axis give the Rg
in high frequency range and Rgb in low frequency range. The value of R is about 140 Ω, 42 Ω, 18 Ω, 9
g
Ω and 5 Ω, and grain boundary resistance Rgb is about 168.3 kΩ, 70.5 kΩ, 31.1 kΩ, 11.5 kΩ, and 3.0
kΩ at 313 K, 353 K, 393 K, 433 K and 473 K respectively. Both R and Rgb obtained from fitting the
g
Cole-Cole plots obey the Arrhenius law are shown in Fig. 9(f). Activation energy of grain and grain
boundary is found to be 0.27 eV and 0.31 eV respectively. The grain and grain boundary resistance of
BFN ceramics synthesized by solid-state reaction method can also be obtained at 313 K, which is 440
Ω and 8.7 kΩ, respectively. Comparing with the grain resistance and grain boundary resistance of the

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ceramics prepared by the two methods, it shows that the obtaining of small grain resistance and large
grain boundary resistance at 313 K is related to the decrease of grain size and the increase of grain
boundary. This analysis confirms that the grain boundaries are more resistive than grains in BFN
ceramic. It reveals that the BFN ceramics have a electrically inhomogeneous microstructure because of
grain is surrounded by insulating grain boundary regions. The difference of the ceramic resistance can
be understood according to the mechanism of barrier layer formation. This difference of the resistance
arises from the loss of oxygen during sintering at high temperature in accordance with the reaction
[
36]:
1
•
O
•
O ↔ O +V + 2e′
(7)
(8)
o
2
2
3
+
2+
Fe + e′ → Fe
During cooling, reoxidation takes place after sintering. But due to insufficient time, as temperature falls
rapidly, the reoxidation is limited to the grain boundaries. Thus, the grain boundaries become more
insulating as compared to grains. It gives rise to Schottky barriers at the grain-grain boundary interfaces
and produces a large polarization across the grain boundaries, which lead to a high dielectric constant.
4
.
Conclusion
A solution precipitation method was proposed for the preparation of BFN powders. Pure
perovskite phase with cubic symmetry was obtained in 1223 K for 2 h and the BFN powders exhibited
nano-size particles (~40 nm) with a uniform size distribution. The solution precipitation method could
reduce the calcination temperature of the BFN powders to a low temperature (1223 K). The BFN
ceramics with small and uniform grain size was obtained by the solution precipitation method. The
solution precipitation method could significantly reduce the dielectric loss of BFN ceramic. The
frequency and temperature stability can also be significantly improved, which was related to the

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competitive balance result of the low- and high-temperature dielectric relaxations. The complex
impedance analysis provides more effective evidence of the high dielectric constant that supported by
the grain boundary barrier layer capactior model. Activation energy was found to be 0.27 eV and 0.31
eV corresponding to grain and grain boundary respectively, which proves that the grain boundaries are
more resistive than grains. It confirms that barrier layers create the heterogeneity in the ceramics,
which is responsible for the giant dielectric constant.

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Acknowledgments
The present work was supported by National Science Foundation of China (51572160, 51372144),
the China Postdoctoral Science Foundation (2015M572516), the Special Foundation of Educational
Department of Shaanxi Province (14JK1080) and Graduate Innovation Fund of Shaanxi University of
Science and Technology.

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Appendices
Eq :
1
′( f0 )
ε
′( f ) −
ε
′( f0 )
α ε − f
=
=
×
×
(1)
ε
ε
( f − f0 )
1
′(T0 )
ε
′(T) −
ε
′(T0 )
α ε −T
(2)
(T −T0 )
*
1−α
ε
τ
=
ε
′ − i
ε
′′ = ε∞ + ( s
ε
−
ε∞ ) /[1+ (iωτ ) ]
(3)
(4)
=
τ 0 exp(E / k T)
a
B
Rg
Rgb
Z′ =
+
(5)
(6)
2
2
1
+ (
ω
R C ) 1+ (
ω
R C )
g
g
gb gb
ω
R Cg
ωR C
gb gb
g
Z′′ = Rg [
]+ Rgb[
]
2
2
1
+ (
ω
R C )
1+ (ωR C )
gb gb
g
g
1
•
O
•
O ↔ O +V + 2e′
(7)
(8)
o
2
2
3
+
2+
Fe + e′ → Fe

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Table Captions:
Table. 1. Comparison of the frequency stability of BFN ceramics prepared by two methods
Table. 2. Comparison of the temperature stability of BFN ceramics prepared by two methods,
respectively.
Table. 1. Comparison of the frequency stability of BFN ceramics prepared by two methods
-1
Parameters
ε' (f =100 Hz) ε' (f =1 kHz) ε' (f =10 kHz)
αε−f (Hz )
1
0
2
-
5
-5
-3
solution precipitation method
solid-state reaction method
55,771
51,564
36,639
-3.4×10 ~-9.1×10
-5
372,818
72,910
11,748
-9.3×10 ~-4.6×10
Table. 2. Comparison of the temperature stability of BFN ceramics prepared by two methods,
respectively.
1
Parameters
ε' (T =300 K)
ε' (T=425 K)
55,314
αε−T (K- )
0
-
4
2
solution precipitation method
solid-state reaction method
51,341
67,045
6.2×10
3.1×10
-
324,406

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Figures Captions::
Fig. 1. XRD patterns of BFN powders calicined at various temperatures.
Fig. 2. TG-DSC curves of the BFN precursor powders.
Fig. 3. SEM micrographs of BFN powders calcined at (a) 1023 K, (b) 1123 K and (c) 1223 K for 2 h.
Fig. 4. XRD patterns of BFN ceramics respectively prepared by (a) the solution precipitation method
and (b) solid-state reaction method.
Fig. 5. Micrographs of BFN ceramics: (a) prepared by solution precipitation method, and (b) prepared
by solid-state reaction method.
Fig. 6. Frequency dependence of dielectric constant and dielectric loss for BFN ceramics prepared by
the solution precipitation method and solid-state reaction method between 100 Hz and 1 MHz.
Fig. 7. Temperature dependence of dielectric constant for BFN ceramics synthesized by (a) solution
precipitation method and (b) solid-state reaction method at various frequencies; Temperature
dependence of (c) dielectric constant and (d) dielectric loss of BFN ceramics prepared by two methods
at 1 kHz.
Fig. 8. (a) Frequency dependence of dielectric constant for BFN ceramics synthesized by solution
precipitation method at various temperatures. The solid lines represent the calculated values, assuming
a Debye model. (b) The log of the relaxation time
solid lines are the Arrhenius fit.
τ vs 1/T. Symbols are the experimental points and
Fig. 9. (a)-(e) Complex impedance spectra of BFN ceramics synthesized by solution precipitation
method at various temperatures. The symbols are experimental data and the solid lines are determined
by the least-mean-square analyses. (f) Arrhenius plots of R and R of the BFN ceramic along with
g
gb
equivalent circuit representation of grain and grain boundary contributions in the inset of (b). The inset

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of (a) show the complex impedance spectra of BFN ceramics synthesized by solid-state reaction
method at 313 K.

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Fig. 1. XRD patterns of BFN powders calicined at various temperatures.

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Fig. 2. TG-DSC curves of the BFN precursor powders.

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Fig. 3. SEM micrographs of BFN powders calcined at (a) 1023 K, (b) 1123 K and (c) 1223 K for 2 h.

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Fig. 4. XRD patterns of BFN ceramics respectively prepared by (a) the solution precipitation method
and (b) solid-state reaction method.

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Fig. 5. Micrographs of BFN ceramics: (a) prepared by solution precipitation method, and (b) prepared
by solid-state reaction method.

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Fig. 6. Frequency dependence of dielectric constant and dielectric loss for BFN ceramics prepared by
the solution precipitation method and solid-state reaction method between 100 Hz and 1 MHz.