Dielectric Properties of Ca0.7Bi0.3Ti0.7Cr0.3O3 (CBTC)–CaCu3Ti4O12 (CCTO) Composite

Abstract

The main object of this work is to study two materials with giant dielectric constants: CaCu3Ti4O12 (CCTO) and Ca0.7Bi0.3Ti0.7Cr0.3O3 (CBTC). CBTC1−x
–CCTO
x
composites were also obtained to create a new dielectric material with dielectric properties between these two phases. Structural properties were studied by x-ray powder diffraction (XRPD), Fourier transform infrared spectroscopy (FT-IR), Raman spectroscopy and dielectric measurements. CCTO showed a cubic phase and CBTC an orthorhombic phase. An interesting result was that the dielectric constant (K) did not follow the rule of the mixture of Lichtnecker, and this happened due to the presence of other phases of its crystalline structure, which decreases the value of K when compared to the predicted values of Lichtnecker. It was also found that the dielectric properties of the composite are very promising for use in microelectronics, according to the miniaturization factor, which is crucial for those applications.

Full text

Dielectric Properties of Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
(CBTC)–
CaCu
3
Ti
4
O
12
(CCTO) Composite
E.J.J. MALLMANN,
1
M.A.S. SILVA,
2
A.S.B. SOMBRA,
2
M.A. BOTELHO,
3
S.E. MAZZETTO,
1
A.S. DE MENEZES,
4
A.F.L. ALMEIDA,
5
and P.B.A. FECHINE
1,6
1.—Grupo de Quı
´mica de Materiais Avanc¸ados (GQMAT) – Departamento de Quı
´mica Analı
´tica e
Fı
´sico-Quı
´mica, Universidade Federal do Ceara
´– UFC, Campus do Pici, CP 12100, Fortaleza,
CE CEP 60451-970, Brazil. 2.—Laborato
´rio de Telecomunicac¸o
˜es e Cie
ˆncia e Engenharia de
Materiais (LOCEM) – Departamento de Fı
´sica, Universidade Federal do Ceara
´, Fortaleza, Brazil.
3.—Post-Graduation Program in Biotechnology, University Potiguar, Natal, RN 59060-010,
Brazil. 4.—Departamento de Fı
´sica, CCET, Universidade Federal do Maranha
˜o, Campus do
Bacanga, Sa
˜o Luı
´s, MA 65085-580, Brazil. 5.—Departamento de Engenharia Meca
ˆnica e de
Produc¸a
˜o (DEMP), Centro de Tecnologia, Universidade Federal do Ceara
´, Fortaleza , Brazil.
6.—e-mail: fechine@ufc.br
The main object of this work is to study two materials with giant dielectric
constants: CaCu
3
Ti
4
O
12
(CCTO) and Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
(CBTC). CBTC
1x
–
CCTO
x
composites were also obtained to create a new dielectric material with
dielectric properties between these two phases. Structural properties were
studied by x-ray powder diffraction (XRPD), Fourier transform infrared
spectroscopy (FT-IR), Raman spectroscopy and dielectric measurements.
CCTO showed a cubic phase and CBTC an orthorhombic phase. An interesting
result was that the dielectric constant (K) did not follow the rule of the mixture
of Lichtnecker, and this happened due to the presence of other phases of its
crystalline structure, which decreases the value of Kwhen compared to the
predicted values of Lichtnecker. It was also found that the dielectric properties
of the composite are very promising for use in microelectronics, according to
the miniaturization factor, which is crucial for those applications.
Key words: CaCu
3
Ti
4
O
12
, dielectric measurements, ceramics, composite,
microdevice
INTRODUTION
A ceramic disk capacitor is one of the simplest forms
of capacitor; it consists essentially of a pair of parallel
metal plates separated by an electrically insulating
material, a dielectric. Capacitors are essential com-
ponents of most electronic circuits, not only to store
electrical energy but these devices can also be used for
filtering out electronic noise and for high-frequency
tuning as well as many other purposes.
1
For capacitor-
type applications,
2
the primary requirements are the
high dielectric constant (K) characteristicsand a small
temperature variation of Kover a wide temperature
region. High Kceramic makes possible a noticeable
miniaturization of passive microwave devices. Their
size can typically be reduced in comparison with
classical resonators andfilters by a factor of ffiffiffiffi
K
p.
3
Such
material is very promising for capacitor applications
and certainly for microelectronics, microwave devices
(for example, cell phones), where the miniaturization
of the devices is crucial.
Perovskite and perovskite-related materials are
important crystal structures due to their diverse
physical/chemistry properties over a wide tempera-
ture range. An ideal perovskite structure has an
ABX
3
stoichiometry and a cubic crystal structure.
4
It
can be considered flexible, and most of the distortion
on this structure is based on tilting of TiO
6
octahedra
which causes a displacement in the 180 angles of
O–Ti–O bonds.
5
The disordered structure of the
perovskite contributes to photoluminescence
(Received April 25, 2014; accepted October 8, 2014)
Journal of ELECTRONIC MATERIALS
DOI: 10.1007/s11664-014-3464-z
2014 The Minerals, Metals & Materials Society

emission at room temperature. This effect can be
observed by exciting the material with wavelengths
of higher energy than the band gap.
6
Recently, there
has been considerable interest in the dielectric
properties of the CaCu
3
Ti
4
O
12
(CCTO) cubic perov-
skite-related phase.
3,5,7–9
This complex perovskite
(CCTO) has been reported as a material having the
largest K(16,000–18,000) ever measured in the lab-
oratory at room temperature and remains constant
during the temperature range of 100–600 K, sug-
gesting that it is very desirable for practical appli-
cations.
9,10
Subramanian et al.
8
discovered that the
static Kof CCTO at room temperature has a very
large value of 10
4
. The high Kvalue of the CCTO has
been attributed to intrinsic
10,11
and extrinsic mech-
anisms.
9–11
Explaining the anomalous Khas been an
intriguing issue, and many models have been pro-
posed. A combined study of both crystal structure and
electrophysical properties of new compounds and
solid solutions are necessary for the development of
new ceramic materials. A refinement of stoichiome-
tric compositions and homogeneity regions of new
materials is desirable.
12
Recently, extensive studies
of the formation of perovskite oxides of the systems
Ca
1x
M
x
Ti
1x
M¢O
3
(M = Y, Sr, Ba, Pb; M¢= Co, Al,
Fe, Cr) were performed. Chung and coworkers
13
investigated the stability of the perovskite phase and
the dielectric properties in the Ca
1x
Bi
x
Ti
1x
Cr
x
O
3
system (CaTiO
3
and BiCrO
3
perovskites). The value
of Kwas about 150,000 when x= 0.3 (Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
–CBTC). In an analogous previous work, Al-
meida and coworkers
14
investigated the properties of
the composite BTO–CCTO and its potential use as
antennas and microdevices.
In this work, we report the effect of the presence of
the CCBTC on the dielectric properties of the CCTO.
We compare the dielectric properties of the CBTC
1x
–
CCTO
x
composites. The produced samples were also
studied using x-ray powder diffraction (XRPD), Fou-
rier transform infrared spectroscopy (FT-IR), Raman
spectroscopy and dielectric measurements.
EXPERIMENTAL
Commercial Ca(OH)
2
(97% with 3% of CaCO
3
,
Vetec), titanium oxide (TiO
2
) (99%, Aldrich), CuO
(99%, Aldrich) were used to obtain the CCTO. The
materials were ground on a Fritsch Pulverisette 6
planetary mill with the ratio of 1 Ca(OH)
2
to 3 CuO-
4TiO
2
. Milling was performed in sealed stainless
steel vials and balls under air. Mechanical alloying
was performed for 30 min of milling. In this case,
the milling was used only to give a good homoge-
neity of the powder. However, the literature shows
that complete production of CCTO is possible after
100 h of milling.
7
The reaction occurring during
milling can be summarized as:
CaðOHÞ2þ3CuO þ4TiO2!
IMPACTS CaCu3
Ti4O12 þH2O(1)
The compounds were also prepared by the con-
ventional powder-sintering technique using the
same starting materials. The ceramic was submit-
ted to sintering and calcination in air in the range of
900C/12 h and 1100C/24 h, respectively.
5
This
ceramic was called CCTO (calcination + sintering).
We also prepared solid solution oxides according to
formula Ca
1y
Bi
y
Ti
1y
Cr
y
O
3
(CBTC sample). Chung
and coworkers
13
used y= 0.01, 0.03, 0.05, 0.1, 0.3,
and 0.5. However, we only prepared samples when
y= 0.3 (Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
) due to the highest
value of Kobtained for this composition. The raw
material, CaCO
3
(99%, Aldrich), Bi
2
O
3
(99.9%,
Aldrich), Cr
2
O
3
(99.8% with 0.01% of CrO
3
and 0.02%
of SO
4
, Reagen) and TiO
2
(99.9%, Aldrich) were
mixed in a ball mill in air for 30 min (to also give a
good homogeneity). The mixed powders were calcined
in the air at 1000C for 10 h. This process is similar to
the one proposed by Chung and coworkers.
13
In this paper, we had five composites of the kind
CBTC
1x
–CCTO
x
(x= 0.3, 0.5 and 0.7), in which x
corresponds to the percentage in weight (%) of each
component, besides CCTO and CBTC pure ceramics.
These mixed powders were compacted in a cylindrical
mold into disc format of 1.7 cm in diameter and sub-
mitted to a pressure of 111.0 MPa. The disks were
sintered in air at 1100C for 24 h at a rate of 3C/min.
XRPD measurements were performed at room
temperature in a Rigaku x-ray powder diffractom-
Fig. 1. XRPD pattern of CBTC
1x
–CCTO
x
system with Rietveld
refinement.
Mallmann, Silva, Sombra, Botelho, Mazzetto, de Menezes, Almeida, and Fechine

eter operating at 40 kV/25 mA, using CuKa radia-
tion. The diffraction patterns were carried out using
Bragg–Brentano geometry in continuous mode with
a speed of 0.5/min and step size of 0.02(2h).
Rietveld refinement was performed in the diffrac-
tion patterns using the GSAS program
15
in order to
confirm the phases present in the samples and to
obtain the concentrations of each phase.
Raman spectroscopy of the powder samples was
carried out in a T64000 JobinYvon SPEX spec-
trometer using an Ar laser (k= 514.5 nm). The
spectra were obtained in a back-scattering geome-
try, between 100 and 2000 cm
1
.The FT-IR was
measured using circular pellets, made from the
mixture of KBr (potassium bromide) and the powder
of each sample, in a ratio of KBr/sample powder
close to 100. This mixture was pressed with 6 tons
for 15 min, in vacuum, and all the pellets obtained
had a thickness of c.1.5 mm. The FT-IR was
recorded in the 4000–400 cm
1
range with a Matt-
son 7000 (FT-IR) spectrometer, although the
selected range was 750–400 cm
1
.
The dielectric measurements (loss (D)andK)were
obtained from a Solartron Model 1260A Impedance/
Gain-phase Analyzer. In this study, we measured in
the frequency region from 1 Hz until 10 MHz.
RESULTS AND DISCUSSION
Figure 1shows XRPD patterns together with
Ritveld refinement of the CBTC
1x
–CCTO
x
(x= 0.0,
0.3, 0.5, 0.7 and 1.0) system sintered at 1100C
during 24 h. The crystalline phases obtained from
the composite were identified by comparison of the
diffractograms with the ICDD data bank. The blue
lines represent the relative differences between the
experimental (I
Exp
) and the calculated (I
Calc
) inten-
sities obtained by the refinement. The XRPD pat-
terns show that the CCTO sample presents only the
CaCu
3
Ti
4
O
12
(ICDD/PDF–01-075-2188) cubic phase
and the CBTC presents a single phase of the
orthorhombic Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
(ICDD/PDF–01-
082-0229). However, samples with x= 0.7 and 0.5
presented two phases (CuCrO
2
and TiO
2
) beyond
the desired level, while, for the samples with
x= 0.3, the pattern shows three phases (CuCrO
2
,
Fig. 2. Analysis of FT-IR of the CBTC
1x
–CCTO
x
system.
Table I. Phases and its concentration, according to the XRPD
Samples
Phase concentrations (%)
R
wp
(%)
CaCu
3
Ti
4
O
12
Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
CuCrO
2
TiO
2
CaCO
3
CCTO 100 – – – – 9.8
CCTO
0.7
-CBTC
0.3
52.7 (3) 32.6 (3) 3.9 (2) 10.8 (4) – 11.7
CCTO
0.5
-CBTC
0.5
45.1 (4) 43.1 (3) 5.4 (5) 6.4 (2) – 13.7
CCTO
0.3-
CBTC
0.7
10.0 (5) 53.2 (3) 8.4 (3) 6.2 (7) 22.2 (5) 15.5
CBTC – 100 – – – 12.3
Samples
Lattice parameters
a(A
˚)b(A
˚)c(A
˚)
CCTO 7.39141 (7) 7.39141 (7) 7.39141 (7)
CBTC 5.4008 (4) 5.4626 (4) 7.6793 (7)
Dielectric Properties of Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
(CBTC)-CaCu
3
Ti
4
O
12
(CCTO) Composite

TiO
2
and CaCO
3
). All the phases and their respec-
tive concentrations are listed in Table I, where one
can also see the lattice parameters of the CCTO and
CBTC single phase samples and the R
wp
(residual
error) values of the Rietveld refinement. This
knowledge of the phase concentrations contributes
to a better understanding of the dielectric properties
of the composites.
The FT-IR spectra of the ceramics CBTC and
CCTO, together with the spectra of the CBTC
1x
–
CCTO
x
composites, are shown in Fig. 2. The CCTO
phase presented absorptions at 559, 515 and
440 cm
1
. Several authors
7,15,16
have assigned this
region of absorptions to the titanium ion. These
bands were associated to m
Ti-O
= 653–550 cm
1
and
m
Ti-O-Ti
= 495–436 cm
1
. The only absorption asso-
ciated to CBTC in the frequency range studied is a
very broad absorption in the region of 400–450 cm
1
with a maximum at 427 cm
1
, the characteristic
absorption mode of the titanium ion. One can also
notice the presence of these modes in the solid
solutions of CBTC
1–x
–CCTO
x
. For the FT-IR spectra
of the CBTC
0.7
–CCTO
0.3
sample, the presence of
modes from CCTO was not seen.
In a previous work, Valim and co-workers
17
eluci-
dated that CCTO hasa body-center cubic primitive cell
that contains 20 atoms and belongs to the centro-
symmetric T
h
(Im3) group. The standard group theory
analysis predicts that the Raman active modes are
distributed among the irreducible representation as
2A
g
+2E
g
+4F
g.18
CCTO is a weak scatter and only
five of the eight predicted modes are observed at
around 444 cm
1
, 453 cm
1
, 510 cm
1
, 576 cm
1
,and
761 cm
1
, as shown in Fig. 3. Based on lattice
dynamics studies
19,20
and polarized Raman mea-
surements,
17
the mode symmetries are identified as
A
g
(1)(444 cm
1
), F
g
(2)(453 cm
1
), A
g
(2)(510 cm
1
),
F
g
(3)(576 cm
1
), and F
g
(4)(761 cm
1
). Following lat-
tice dynamics calculations, 444 cm
1
, 453 cm
1
,and
510 cm
1
are TiO
6
rotation-like modes. The band at
576 cm
1
is assigned to the Ti–O–Ti anti-stretching
mode of the TiO
6
octahedra.
17
The F
g
(4) mode has been
predicted to be observed at about 710 cm
1
. The mode
761 cm
1
is assigned to the symmetric stretching
breathing of the TiO
6
octahedra. Its low intensity is
typical of the structures containing shared units in
which the neighboring octahedral damps the
symmetric vibrations.
17
CBTC
1-x
–CCTO
x
composites were compacted in
pellets and measured the dielectric properties, such as K
Fig. 3. Raman spectra of the CBTC
1x
–CCTO
x
system.
Fig. 4. Kas a function of frequency of the CBTC
1x
–CCTO
x
system.
Fig. 5. Das a function of frequency of theCBTC
1x
–CCTO
x
system.
Mallmann, Silva, Sombra, Botelho, Mazzetto, de Menezes, Almeida, and Fechine

and D,asshowninFigs.4and 5,respectively.Both
crystalline phases (CCTO and CBTC) presented high
values of Kat radio-frequency ranges with values higher
than 1 910
4
at 100 Hz for CBTC. One can observe that
CBTC presents a larger decrease of dielectric permit-
tivity values than other samples, which suggests a
dielectric relaxation as also evidenced in D(Fig. 5),
where a maximum of Dwas observed. This behavior
happens because, during the polarization or depolar-
ization process, a relaxation phenomenon occurs due to
thetimerequiredforthechargecarrierstoovercomethe
inertia arising from the surrounding medium in order to
proceed in their movement.
21
A previous study has col-
lected data about dielectric relaxation from BTO–CCTO,
and similar results were found.
22
Thus, this involves the
movement of charges either by orientation or through
the migration of charge carriers. The same process was
observed for other ceramics in the lowest frequencies.
The relaxation processes from CBTC and CCTO are
strongly temperature-dependent.
13,23
ThedecreaseofK
with the increase of frequency for all samples are shown
in Fig. 4. However, the CCTO decreases more than other
samples. The dielectric properties were estimated by the
law of Lichtenecker.
24
This dielectric mixture model is
an empirical logarithmic rule for the Kand the dielectric
constants (K
i
) of the individual phases. It is given by:
ln K¼Xixiln Ki(2)
where x
i
is the percentage in weight of each com-
ponent. Therefore, fractional mass (x
i
) and K
i
of
each constituent are the main parameters used in
calculating the effective Kof the mixture.
Figure 6shows that Kdid not follow the expected
profile by the rule of the mixture of Lichtnecker.
This may be explained by the results of XRPD,
which shows the presence of other phases (CuCrO
2
,
Fig. 6. Kas a function of the composition of the CBTC
1x
–CCTO
x
.
Fig. 7. Nyquist plot for composites CCTO–CBTC at room temperature.
Table II. Dielectric constant of CCTO, CBTC and composites at function of frequency
%CCTO 10 Hz 100 Hz 1 kHz 10 kHz 1 MHz
1 35,179.77 25,065.59 16,270.64 11,154.92 5042.43
0.7 24,435.87 10,682.35 4833.76 2223.26 714.38
0.5 28,828.65 7551.10 2519.61 904.28 167.72
0.3 33,371.25 10,561.65 4047.15 1721.82 473.94
0 187,752.02 18,581.64 4616.38 1258.13 137.43
Dielectric Properties of Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
(CBTC)-CaCu
3
Ti
4
O
12
(CCTO) Composite

TiO
2
and CaCO
3
) from the reaction of CCTO with
CBTC. The presence of these phases causes the
decrease of Kof the composite to smaller values as
predicted by the rule of mixtures (Table II).
The impedances for CCTO, CBTC and composites
were plotted in the Nyquist diagram
25
for identifying
which model theory was more representative and
which phenomenon occurs in the material. The
frequency response of a real polycrystalline ceramic
carrying metallic electrodes may yield three
well-defined semicircles representing, respectively,
polarization processes associated with the interior of
the grains, with the grain boundary regions and with
the electrode–ceramic interfacial region.
24
Figure 7
shows just one phenomenon occurring in the electrical
measuring at the CCTO and CBTC
1x
–CCTO
x
system.
Arcs for all measurements were observed and they
were associated with the process described above. One
arc can represent one or various phenomena which can
be explained by the overlap, or not, of the arcs.
Figure 8a shows the equivalent circuit analysis
for the CCTO sample. The arc was represented for
one circuit composed of three elements in series.
The first one is an element of constant phase, while
the second and third ones comprised the capacitor in
parallel with a resistor. The equivalent circuit used
for CBTC
0.3
–CCTO
0.7
(Fig. 8b) was similar to
CCTO. However, CBTC
0.5
–CCTO
0.5
(Fig. 8c) was a
Fig. 8. Fitting of impedance measurements for CCTO (a), CBTC
0.3
–CCTO
0.7
(b), CBTC
0.5
–CCTO
0.5
(c), CBTC
0.7
–CCTO
0.3
(d), and CBTC (e)
composites and their equivalent circuits, respectively.
Mallmann, Silva, Sombra, Botelho, Mazzetto, de Menezes, Almeida, and Fechine

combination of five constant phase elements (CPE)
distributed in series with the CPE2–CPE3 and
CPE4–CPE5 disposed in parallel. CBTC
0.7
–CCTO
0.3
(Fig. 8d) had a similar equivalent circuit used for
CCTO, with the substitution of C1 by CPE2. CBTC
was fitted with an equivalent circuit formed by one
association in series of the RC (parallel resistors and
capacitors), as shown in Fig. 8e. The values for each
circuit element are shown in Table III. Each polar-
ization process was described in the equivalent
circuits utilized as grain, grain boundary and
ceramic–electrode interface.
The use of CPE in the fitting of impedances for
CCTO, CBTC and composites is shown in Fig. 9.
Where the AC conductivity presented high values,
the ceramics are not presented as one ideal capaci-
tor. The CPE is described by two parameters, ‘‘P’’ is
a quantity value and ‘‘n’’ gives the deviation of the
capacitor feature, i.e., when the n value is close to
unity, the CPE resembles a capacitor, while for zero
it has the characteristics of a resistor. The values of
P and n for CBTC
1x
–CCTO
x
composites are listed
in Table III. Although the impedance measure-
ments do not reveal arcs associated with the polar-
ization processes of the grain, grain boundary and
electrode–ceramic interface, the equivalent circuits
utilized for the fittings showed groups of elements
that justify this process, i.e., these three processes
overlapped. There are some errors or measurement
deviation that can be associated with extra phases
present in the composites, as shown in the XPRD
results.
CONCLUSION
The evaluated CBTC
1–x
–CCTO
x
had shown
interesting dielectric properties, in which we can
see that the phase concentrations contribute to
understanding the dielectric properties. The char-
acterization methods and equivalent circuit ana-
lysis were important for knowledge of the behavior
of the samples. The obtained composite had a giant
Kvalue due to the CBTC and CCTO phases. These
dielectric properties of the system can be attractive
for capacitor applications and certainly for
microelectronics, microwave devices (for example,
cell mobile phones), in which the miniaturization of
the devices is desirable.
ACKNOWLEDGEMENTS
We gratefully acknowledge the financial support
of Brazilian Agencies for Scientific and Technologi-
cal Development CAPES, Funcap, FAPEMA, IPDI
and CNPq.
REFERENCES
1. I. Burn, Ceramic Capacitor Dielectric. In: Engineered
Materials Handbook

-Ceramics and Glasses, vol. 4 (ASM
International, The Materials Information Society, 1991).
Table III. Circuit element values of the composites
Samples
Element CCTO CBTC
0.3
–CCTO
0.7
CBTC
0.5
–CCTO
0.5
CBTC
0.7
–CCTO
0.3
CBTC
R1 (Ohms) 9.12 910
5
2.48 910
5
– 6.03 910
5
4367
R2 (Ohms) 6.67 910
5
9.90 910
4
– 1.21 910
4
12,139
R3 (Ohms) – – – – 13,484
C1 (Farad) 9.88 910
8
2.30 910
7
– 4.89 910
8
3.32 910
5
C2 (Farad) 1.35 910
7
7.87 910
8
–––
CPE1 (P) 1.40 910
7
8.26 910
7
1.53 910
4
1.52 910
6
1.97 910
5
CPE2 (P) – – 1.36 910
6
3.26 910
7
4.70 910
7
CPE3 (P) – – 3.22 910
7
––
CPE4 (P) – – 3.01 910
26
––
CPE5 (P) – – 2.96 910
6
––
CPE1 (n) 0.74 0.48 0.95 1.00 0.79
CPE2 (n) – – 1.00 0.56 0.50
CPE3 (n) – – 0.51
CPE4 (n) – – 0.87
CPE5 (n) – – 0.001
Fig. 9. AC conductivity for CBTC, CCTO and composites.
Dielectric Properties of Ca
0.7
Bi
0.3
Ti
0.7
Cr
0.3
O
3
(CBTC)-CaCu
3
Ti
4
O
12
(CCTO) Composite

2. V. Mitic
´, Z. Nikolic
´, and L. Zivkovic
´,Electr. Energy 9, 255
(1996).
3. A.F.L. Almeida, P.B.A. Fechine, J.C. Go
´es, M.A. Valente,
M.A.R. Miranda, and A.S.B. Sombra, Mater. Sci. Eng. B 111,
113 (2004).
4. C. Li, K.C.K. Soh, and P. Wu, J. Alloy. Compd. 372, 40 (2004).
5. M.A. Subramanian and A.W. Sleight, Solid State Sci. 4, 347
(2002).
6. L.S. Cavalcante, M.A. Santos, J.C. Sczancoski, L.G.P.
Simo
˜es, M.R.M.C. Santos, J.A. Varela, P.S. Pizani, and E.
Longo, J. Phys. Chem. Solids 69, 1782 (2008).
7. A.F.L. Almeida, R.S. de Oliveira, J.C. Go
´es, J.M. Sasaki, J.M.
Filho, and A.S.B. Sombra, Mater. Sci. Eng. B 96, 275 (2002).
8. M.A. Subramanian, D. Li, N. Duran, B.A. Reisner, and A.W.
Sleight, J. Solid State Chem. 323, 151 (2000).
9. A.P. Ramirez, M.A. Subramanian, M. Gardel, G. Blumberg,
D. Li, T. Vogt, and S.M. Shapiro, Solid State Comm. 115,
217 (2000).
10. C.C. Homes, T. Vogt, S.M. Shapiro, S. Wakimoto, and A.P.
Ramirez, Science 293, 673 (2001).
11. M.A. Subramanian, D. Li, N. Duan, B.A. Reisner, and A.W.
Sleight, J. Solid State Chem. 151, 323 (2000).
12. E.A. Nenasheva and N.F. Kartenko, J. Eur. Ceram. Soc. 21,
2697 (2001).
13. C.Y. Chung, Y.H. Chang, Y.S. Chang, and G.J. Chen,
J. Alloy. Compd 385, 298 (2004).
14. A.F.L. Almeida, P.B.A. Fechine, L.C. Kretly, and A.S.B.
Sombra, J. Mater. Sci. 41, 4623 (2006).
15. A.C. Larson and R.B. Von Dreele, GSAS, LAUR 86, 748
(2004).
16. S. Music, M. Gotic, M. Ivanda, S. Popovic, A. Turkovic, R.
Trojko, A. Sekulic, and K. Furic, Mater. Sci. Eng. B 47, 33
(1997).
17. D. Valim, A.G.S. Filho, P.T.C. Freire, S.B. Fagan, A.P.
Ayala, J.M. Filho, A.F.L. Almeida, P.B.A. Fechine, A.S.B.
Sombra,J.Staun,andL.Olsen,Phys. Rev. B 70, 132103 (2004).
18. N. Kolev, et al., Phys. Rev. B 66, 132102 (2002).
19. L. He, et al., Phys. Rev. B 65, 214112 (2002).
20. L. He, et al., Phys. Rev. B 67, 012103 (2003).
21. K.C. Kao, Dielectric Phenomena in Solids (San Diego:
Elsevier, 2004).
22. P.B.A. Fechine, A.F.L. Almeida, F.N.A. Freire, M.R.P.
Santos, F.M.M. Pereira, R. Jimenez, J. Mendiola, and A.S.B.
Sombra, Mater. Chem. Phys. 96, 402 (2006).
23. A.F.L. Almeida, P.B.A. Fechine, J.M. Sasaki, A.P. Ayala,
J.C. Go
´es, D.L. Pontes, W. Margulis, and A.S.B. Sombra,
Solid State Sci. 6, 267 (2004).
24. A.J. Moulson and J.M. Herbert, Electroceramics: Materials,
Properties, Applications (Chichester: Wiley, 2003).
25. E. Barsoukov and J.R. Macdonald, Impedance Spectroscopy:
Theory, Experiment, and Applications, 2nd ed. (New Jersey:
Wiley, 2005).
Mallmann, Silva, Sombra, Botelho, Mazzetto, de Menezes, Almeida, and Fechine