Structural and dielectric properties of BaTiO3-CaTiO 3-SrTiO3 ternary system ceramics

Article abstract of DOI:10.1111/j.1551-2916.2009.03493.x

Ba_1-x-ySr_yCa_xTiO₃ (BSCT, y=0, x=0-1; y=0.05, x=0-0.95; y=0.1, x=0-0.9; y=0.13, x=0-0.87; and y=0-0.20, x=0.5-y/2) ceramics were prepared using the solid-state reaction method in this paper. Their structural and dielectric properties were characterized. The results of refined X-ray diffractometer analysis showed that in the Ba-rich area, the solubility limits of Ba_1-xCa_xTiO₃, Ba_0.95-xSr_0.05Ca_xTiO₃, Ba _0.90-xSr_0.10Ca_xTiO₃, and Ba _0.87-xSr_0.13Ca_xTiO₃ lay around x=0.24, x=0.30, x=0.34, and x=0.36, respectively. In the Ca-rich area, the solubility limits of Ba_1-xCa_xTiO₃, Ba _0.95-xSr_0.05Ca_xTiO₃, and Ba _0.90-xSr_0.10Ca_xTiO₃ lay around x=0.92, x=0.84, and x=0.70, respectively. The dielectric constant and the tunability decreased with Ca addition, except for the solubility limit areas, near which the dielectric constant and tunability increased drastically. For the BSCT series ceramics with a 15-20 mol% Sr content, the electrostrictive strain of the samples was still around 0.15%.

Full text of DOI:10.1111/j.1551-2916.2009.03493.x

J. Am. Ceram. Soc., 93 [4] 1049–1055 (2010)
DOI: 10.1111/j.1551-2916.2009.03493.x
r 2009 The American Ceramic Society
ournal
J
Structural and Dielectric Properties of BaTiO3–CaTiO3–SrTiO3
Ternary System Ceramics
Lingling Zhang, Xusheng Wang,w Hong Liu, and Xi Yao
Functional Materials Research Laboratory, Tongji University, Shanghai 200092, China
Ba1ꢀxꢀySryCaxTiO3 (BSCT, y 5 0, x 5 0–1; y 5 0.05, x 5 0–
0.95; y 5 0.1, x 5 0–0.9; y 5 0.13, x 5 0–0.87; and y 5 0–0.20,
x 5 0.5ꢀy/2) ceramics were prepared using the solid-state
reaction method in this paper. Their structural and dielectric
properties were characterized. The results of refined X-ray
diffractometer analysis showed that in the Ba-rich area, the
solubility limits of Ba1ꢀxCaxTiO3, Ba0.95ꢀxSr0.05CaxTiO3,
Ba0.90ꢀxSr0.10CaxTiO3, and Ba0.87ꢀxSr0.13CaxTiO3 lay around
x 5 0.24, x 5 0.30, x 5 0.34, and x 5 0.36, respectively. In
the Ca-rich area, the solubility limits of Ba1ꢀxCaxTiO3,
Ba0.95ꢀxSr0.05CaxTiO3, and Ba0.90ꢀxSr0.10CaxTiO3 lay around
x 5 0.92, x 5 0.84, and x 5 0.70, respectively. The dielectric
constant and the tunability decreased with Ca addition, except
for the solubility limit areas, near which the dielectric constant
and tunability increased drastically. For the BSCT series
ceramics with a 15–20 mol% Sr content, the electrostrictive
strain of the samples was still around 0.15%.
ferroelectric phase transition from a cubic to a tetragonal
structure at 1301C and two more ferroelectric polymorphic
transitions: tetragonal to orthorhombic at 01C and orthorhom-
bic to rhombohedral at ꢀ901C, respectively. CaTiO3 and SrTiO3
are incipient ferroelectrics or quantum paraelectrics with a high
dielectric constant.19,20 The binary systems (1ꢀx)BaTiO3–
xSrTiO3 and (1ꢀx)CaTiO3–xSrTiO3 are solid solutions
throughout the x range from 0 to 1. The former is a ferroelectric
whose Tc decreases with Sr addition and it has been intensively
studied for high dielectric constant and relaxor ferroelectric
applications,4–6,21 and the latter is used for microwave dielectric
applications.20,22 (1ꢀx)BaTiO3–xCaTiO3 is a solid solution with
x up to 0.21, which causes a negligible change of the Curie point,
but strongly shifts the tetragonal–orthorhombic transition point
to substantially lower temperatures, and hence shows great
potential in improving the temperature stability of ferroelectric
and piezoelectric properties for many practical applications that
have been well discussed.6,23 Above the solubility limit
(x 5 0.21), (1ꢀx)BaTiO3–xCaTiO3 has an insolubility or a
diphasic region extending to x 5 0.9, which has been seldom
studied because of its nonpure phase and dielectric degrada-
tion.6,24 In the BaTiO3–CaTiO3–SrTiO3 (denoted as BSCT)
ternary system, a diphasic region lies in an area around 21–90
mol% CaTiO3 and 0–18 mol% SrTiO3.25 Similar to the above
binary systems, the ternary system has been widely studied in the
solid solution region10,26,27 but was neglected in the insolubility
region. Recently, it was reported that Ba1ꢀxCaxTiO3 ceramics
showed a large piezoelectric/electrostrictive strain18,28 and multi-
ple functions18,29 near its solubility limit. Our previous research
also obtained good dielectric and tunable properties in the
insoluble region of the ternary system ceramics.30,31 This paper
reports our findings of the (1ꢀxꢀy)BaTiO3–xCaTiO3–ySrTiO3
(x 5 0–1.0, y 5 0B0.2) ternary system ceramics for structural
and dielectric properties.
I. Introduction
ERROELECTRIC materials, having multiple functions of piezo-
F
electric, pyroelectric, electro-optic, and dielectric effects,1,2
have been intensively studied and widely used for electronics,
optics, sensors, and actuator applications.3–5 Barium titanate
(BaTiO3) was the first perovskite-type ferroelectric and piezo-
electric material developed in the 1940s and used extensively for
piezoelectric applications because of its higher coupling factors,
which are more chemically stable than those of any previously
known materials.6 Later, it was replaced by a more excellent
material series, lead titanate zirconate solid solutions
[Pb(Zr,Ti)O3, PZT],6,7 which have since dominated the piezo-
electric materials and devices. In recent years, with the demand
for global environmental protection, the restriction of the use of
certain hazardous substances in the electrical and electronic
equipment (RoHS) Directive banned the placing on the EU
market of new electrical and electronic equipment with a lead
content exceeding the agreed levels on July 1, 2006,8 and so lead-
free piezoelectric materials of good quality are urgently needed.
Many researchers focused mainly on BaTiO3-based,9–13
(K,Na)NbO3-based,13–16 and bismuth layer-structured ferro-
electrics (BLSF).13,17 Among these materials, the ternary system
formed by the compounds barium titanate, calcium titanate,
and strontium titanate (BaTiO3–CaTiO3–SrTiO3) in the
BaTiO3-based ferroelectrics showed great potential in the
piezoelectric and related applications for their giant electro-
strain10 and multiple functions.18
II. Experimental Procedures
The phase diagrams of the ternary system BaTiO3 (denoted as
BT)–CaTiO3 (denoted as CT)–SrTiO3 (denoted as ST) reported
earlier25,32 are shown in Fig. 1. Our ceramic compositions were
designed around the solubility limit in the Ba- and Ca-rich areas.
The ceramics were prepared according to the stoichiometric
composition of Ba1ꢀxꢀySryCaxTiO3 located on the broken lines:
(1) y 5 0, x 5 0–1; (2) y 5 0.05, x 5 0–0.95; (3) y 5 0.1, x 5 0–0.9;
(4) y 5 0.13, x 5 0–0.87; and (5) y 5 0–0.20, x 5 0.5ꢀy/2 using a
solid-state reaction method. Raw materials of BaTiO3 and
SrTiO3 (99.9%, hydrothermally synthesized by Shandong Guo-
teng Materials Co. Ltd., Shangdong Province, China), CaCO3
(99.99%, Sinopharm Chemical Reagent Co. Ltd., Shanghai,
China), and TiO2 (99.9%, Nanhai High-Tech Inorganic Materi-
als Co. Ltd., Hanan Province, China) were mixed with alcohol,
then dried and heated at 9001C for 4 h in air. Thereafter, the raw
materials were pulverized with an 8 wt% polyvinyl alcohol
binder and pressed into 10mm diameter pellets and sintered at
14001C for 4 h in air. All samples had densities 490% of their
theoretical limits. The sample crystallization behavior was ex-
amined using an X-ray diffractometer (XRD, D8 Advance;
BaTiO3 is a ferroelectric with a Curie temperature (Tc) of
1301C.6 As the temperature declines, it undergoes a paraelectric–
T. Vanderah—contributing editor
Manuscript No. 26584. Received July 22, 2009; approved October 11, 2009.
This work was supported by the Natural Science Foundation of China (No. 50672067),
Scientific and Technical Innovation Program of Shanghai (No. 08JC1419100) and Specia-
lized Research Fund for the Doctoral Program of Higher Education (No.20070247010).
wAuthor to whom correspondence should be addressed. e-mail: xs-wang@tongji.edu.cn
1049

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Journal of the American Ceramic Society—Zhang et al.
Vol. 93, No. 4
BCT ceramics shifted to a larger 2y1, showing that the lattice
constant decreased with Ca addition. Because the ionic radius of
33
˚
˚
the Ca ion (1.34 A) is smaller than that of the Ba ion (1.61 A),
the Ca ion may enter into A sites of the perovskite structure,
replacing Ba21 ions, which was consistent with the result of
Krishna et al.34
Because our interest was mainly in the solubility limit of the
BSCT ternary ceramics, with its indepth understanding , the
tetragonal strongest peak (110) [denoted as T(110)] and orthor-
hombic strongest peak (121) [denoted as O(121)] were selected
for consideration. As the T(110) and O(121) peaks for BaTiO3
and CaTiO3 are 2y 5 31.51 and 2y 5 32.911, respectively, the 2y
range from 301 to 341 was chosen for XRD refinement. Figure
3 shows the refined peaks from 2y 5 301 to 341 near T(110) and
O(121) for (a) Ba1ꢀxCaxTiO3, (b) Ba0.95ꢀxSr0.05CaxTiO3 (de-
noted as BS5CT), (c) Ba0.9ꢀxSr0.1CaxTiO3 (denoted as
BS510CT), and (d) Ba0.87ꢀxSr0.13CaxTiO3 (denoted as
BS13CT) ceramics sintered at 14001C in the Ba-rich area. It
can be seen from Fig. 3(a) that the structures of the BCT series
ceramics were determined to be a pure tetragonal phase for
x 5 0–0.23, and there was a coexistence of the tetragonal and the
orthorhombic phase for x 5 0.24–0.50, which was in accordance
with previous reports.6,28 The refined XRD pattern BS5CT
[Fig. 3(b)] showed a pure tetragonal phase for x 5 0–0.30, and
tetragonal–orthorhombic phase coexistence for x 5 0.30–0.50,
respectively. Similarly, the solubility limits lay around x 5 0.34
and 0.36 for BS10CT [Fig. 3(c)] and BS13CT [Fig. 3(d)],
respectively.
Fig. 1. Phase diagram of the ternary system BaTiO3 (BT)–CaTiO3
(CT)–SrTiO3 (ST)25 showing the compositions investigated.
Bruker AXS GmbH, Karlsruhe, Germany) and scanning elec-
tron microscopy (SEM, JSM-5510; JEOL). The sintered pellets
were polished to about 1.0 mm thickness for normal dielectric
measurement, 0.3 mm thickness for bias field dependence
measurement, and 0.5 mm thickness for P–E loop measurement.
Silver electrodes were fired on both surfaces of the specimens for
electric measurement. Dielectric properties were characterized
using a high-precision LCR meter (HP 4284A; Hewlett Packard
Co., Santa Clara, CA). Bias field dependence measurement was
carried out using a lab-established and computer-controlled e–E
analyzer system, which included an LCR meter, a high-voltage
generator, and a sample chamber. P–E and S–E loops were
measured by a precision ferroelectric/piezoelectric analyzer (Pre-
mier II, Radiant Technologies Inc., Albuquerque, NM).
The Ca fraction dependence of the related interplanar dis-
tance d110 for Ba1ꢀxCaxTiO3, Ba0.95ꢀxSr0.05CaxTiO3,
Ba0.9ꢀxSr0.1CaxTiO3, and Ba0.87ꢀxSr0.13CaxTiO3 ceramics cal-
culated by the refined XRD patterns is shown in Figs. 3(e)–(h).
From these four figures, we can see that the related interplaner
III. Results and Discussion
Figure 2 shows the XRD patterns of Ba1ꢀxCaxTiO3 (denoted as
BCT) (x 5 0.0, 0.20, 0.50, 0.90, and 1.00) ceramics sintered at
14001C. The XRD patterns revealed that all the ceramics had a
polycrystalline perovskite nature without impurity phases. The
evolution of the secondary phase can be observed in Fig. 2. The
Ã
peaks marked ‘‘ ’’ represent orthorhombic Ca-rich phases
and the ones marked ‘‘ꢁ’’ indicate tetragonal phases. In the
Ba0.5Ca0.5TiO3 ceramic, the tetragonal and orthorhombic
phases coexisted. With increasing x, the XRD peaks of the
Fig. 3. Refined X-ray diffraction peaks near the tetragonal (110) and
orthorhombic (121) for Ba1ꢀxCaxTiO3 (a), Ba0.95ꢀxSr0.05CaxTiO3 (b),
Ba0.9ꢀxSr0.1CaxTiO3 (c), and Ba0.87ꢀxSr0.13CaxTiO3 (d) ceramics in the
Ba-rich area, and related interplanar distance d110 versus Ca fraction for
these four series, respectively.
Fig. 2. X-ray diffraction patterns of Ba1ꢀxCaxTiO3 (x 5 0.0, 0.20, 0.50,
0.90, and 1.00) ceramics sintered at 14001C.

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Properties of BaTiO3–CaTiO3–SrTiO3 Ternary System Ceramics
1051
distance d110 decreased linearly with an increase of the Ca
content in the solid solution region. This might be attributed
to the fact that Ca21 entered the A site of the perovskite, which
changed the lattice constant of the samples. The interaction of
ions led to a decrease of the related interplaner distance of
T(110), whereas in the insolubility area, with increasing x, there
was a negligible change in the related interplaner distance d110
.
Considering BS5CT as an example, all samples in the diphasic
region (0.24oxo0.90) coexisted and comprised of tetragonal
Ba0.65Ca0.30Sr0.05TiO3 solid solutions and orthorhombic Ba0.11
Ca0.84Sr0.05TiO3 solid solutions [see Fig. 4(e)]. Therefore, the
interplaner distance d110 remained unchanged in the insolubility
area. This result was also consistent with the analysis of the
solubility limits we discussed above.
The refined XRD peaks from 2y 5 301 to 341 near the
tetragonal (110) and orthorhombic (121) for (a) Ba1ꢀxCaxTiO3,
(b) Ba0.95ꢀxSr0.05CaxTiO3, and (c) Ba0.9ꢀxSr0.1CaxTiO3 ceramics
sintered at 1400oC in the Ca-rich area are shown in Fig. 4. The
refined XRD pattern of the BCT showed tetragonal—orthor-
hombic phase coexistence for x 5 0.80–0.91, and a pure orthor-
hombic phase for x 5 0.92–1.00. The solubility limits of BS5CT
and BS10CT series ceramics were also determined at x 5 0.84
and 0.72, respectively.
Figure 4 also illustrates the Ca fraction dependence of the
related interplanar distance d121 for (d) Ba1ꢀxCaxTiO3, (e)
Ba0.95ꢀxSr0.05CaxTiO3, and (f) Ba0.9ꢀxSr0.1CaxTiO3 ceramics
calculated using the refined XRD patterns. The reason for the
linear change in the slope of the interplanar distance of O(121)
in these three figures was that the Ca ions substituted for Ba ions
in the solid solution, similar to what was discussed above.
Figure 5 shows the refined XRD peaks near the tetragonal
(110) and orthorhombic (121) for Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3
(denoted as BSyCTꢀx) with (a) y 5 0.05, (b) y 5 0.13, (c)
y 5 0.16, (d) y 5 0.17, and (e) y 5 0.19, respectively. From the
figures, two peaks could be seen for BS5CT-50 and BS13CT-
43.5, which corresponded to T(110) and O(121), but only one
peak for BS16CT-42, BS17CT-41.5, and BS19CT-40.5. It was
not easy for us to find the solubility limit directly, and so the Fit
Gaussian analysis was used to separate the strongest peaks
T(110) and O(121). The black lines represent the refined peaks
Fig. 5. Refined X-ray diffraction peaks near the tetragonal (110) and
orthorhombic (121) for Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3 samples. From the
bottom to the top: y 50.05, y 50.13, y 50.16, y 50.17, and y 5 0.19.
The red and green lines indicate the Gaussian Fit analysis.
and the red and green ones indicate the Gaussian Fit result.
Using Fit Gaussian analysis, for the BS16CT-42, we could
obtain two peaks for the green line, which indicated that this
peak was composed of overlapping peaks: tetragonal (110) and
orthorhombic (121). According to the analysis, the solubility
limits were determined at y 5 0.16 for Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3
variation along line (5) in Fig. 1.
From the above-mentioned result, we can infer that the
solubility limits of the BSCT series ceramics, by presenting the
firing procedure, lay around x 5 0.24, x 5 0.30, x 5 0.34, and
x 5 0.36 for BCT, BS5CT, BS10CT, and BS13CT in the Ba-rich
area, respectively. The solubility limits of BCT, BS5CT, and
BS10CT series ceramics were determined at x 5 0.92, x 5 0.84,
and x 5 0.70 in the Ca-rich area, respectively. The solubility
limit of Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3 ceramics lay around y 5 0.16.
Additional structural and shape analysis of the BSCT series
ceramics was carried out with SEM images. Figure 6 shows the
surface SEM micrographs of Ba0.9ꢀxSr0.1CaxTiO3 (a) x 5 0.10,
(b) x 5 0.45, and (c) x 5 0.85, and Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3 (d)
y 5 0.00, (b) y 5 0.10, and (e) y 5 0.20 samples. It could be seen
that all the samples exhibited dense grain structures. SEM
images were taken from randomly selected areas of the samples,
and as such, these were representative of the overall sizes and
shapes of BSCT ceramics. With an increase in the strontium
content, the average grain size from Ba0.50Ca0.50TiO3 [Fig. 6(d)]
to Ba0.40Sr0.20Ca0.40TiO3 [Fig. 6(e)] was decreased from 4.4 to
3.4 mm.
As is known, the grain size was influenced by the relative
values of the rate of nucleation N and the rate of growth G. If
the ratio of N was larger than that of G, the final grain size
would be small. Both rates depend heavily on processing para-
meters such as the composition and temperature.35 In Figs. 6(d)
and (e), because addition of Sr caused a high nucleation rate,36
the grain size of BSCT ceramics would be decreased with
increasing Sr. In Figs. 6(a) and (c), with the increase in the
calcium content, from Ba0.80Sr0.10Ca0.10TiO3 to Ba0.05Sr0.10
Ca0.85TiO3, the average grain size obviously decreased from
13.7 to 6.4 mm, which was similar to the effect caused by
increasing Sr content. Notably, there was a difference in
Fig. 6(b); the abnormal average grain size of Ba0.45Sr0.10Ca0.45
TiO3 was around 1.3 mm, which was remarkably smaller than
the other four samples. The reason for the abnormal grain size
was that the ferroelectric tetragonal and dielectric orthorhombic
coexisted and inhibited the growth of the grain size in the
diphasic region.37
Fig. 4. Refined X-ray diffraction peaks near the tetragonal (110) and
orthorhombic (121) for Ba1ꢀxCaxTiO3 (a), Ba0.95ꢀxSr0.05CaxTiO3 (b),
and Ba0.9ꢀxSr0.1CaxTiO3 (c) ceramics in the Ca-rich area, and related
interplanar distance d121 versus Ca fraction for these three series,
respectively.

1052
Journal of the American Ceramic Society—Zhang et al.
Vol. 93, No. 4
Fig. 6. Scanning electron microscopic micrographs of Ba0.9ꢀxSr0.1CaxTiO3 (a) x 5 0.10, (b) x 5 0.45, (c) x 50.85, and Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3,
(d) y 50.00, (b) y 5 0.10, and (e) y 5 0.20 samples.
In order to investigate the dielectric properties of BaTiO3–
CaTiO3–SrTiO3 ternary system’s solubility limit, we determined
the effect of composition. Figure 7 illustrates the Ca fraction
dependence of dielectric constant and loss for the ceramics (a)
Ba1ꢀxCaxTiO3, (b) Ba0.95ꢀxSr0.05CaxTiO3, (c) Ba0.9ꢀxSr0.1Cax
TiO3, and (d) Ba0.87ꢀxSr0.13CaxTiO3 measured at room tem-
perature and 10 kHz. It could be seen that for each of these four
sample series, the dielectric constant was decreased with Ca
addition, except for the solubility limit, near which the dielectric
constant increased drastically. The dielectric constant and loss
tangent had peaks near the solubility limit at around x 5 0.24
and x 5 0.92 for BCT, x 5 0.30 and x 5 0.84 for BS5CT,
x 5 0.34 and x 5 0.70 for BS10CT, and x 5 0.36 and x 5 0.64
for BS13CT, respectively, which was in accordance with our
Fig. 7. Ca fraction dependence of dielectric constant and loss for the ceramics measured at room temperature and 10 kHz. (a) Ba1ꢀxCaxTiO3,
(b) Ba0.95ꢀxSr0.05CaxTiO3, (c) Ba0.9ꢀxSr0.1CaxTiO3, and (d) Ba0.87ꢀxSr0.13CaxTiO3.

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Properties of BaTiO3–CaTiO3–SrTiO3 Ternary System Ceramics
1053
Fig. 8. The dielectric constant–electric field (e–E) relations of (a) Ba0.9ꢀxSr0.1CaxTiO3 and (b) Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3 samples at room temperature
and 10 kHz.
previous discussion on refined XRD patterns. It was considered
that this phenomenon resulted from the solubility limit effect or
coupling of the ionic polarization in the Ca-rich dielectric phase
and the ferroelectric domain in the Ba-rich ferroelectric phase,
and it was reasonable that a larger dielectric constant produced
higher dielectric loss.
strain–electric field butterfly curves for various Ca fractions are
illustrated in Fig. 9. Because these four series samples had the
same characteristic, we took Ba0.87ꢀxSr0.13CaxTiO3 (BS13CT) as
an example. Under an applied electric field of 80 kV/cm, the
polarization–electric field hysteresis loops were flattened and the
remnant polarization decreased with the increase in Ca fraction
x. For specimens of x 5 0.00, 0.20, and 0.36, the values of
remnant polarization were 20, 18, and 13 mC/cm2 and those of
electrostrictive strain were about 0.22, 0.18, and 0.14% at 780
kV/cm driving field, respectively, and the curves showed hyster-
esis because of the ferroelectric nature. For BS13CT-38, non-
linear P–E curves (with almost no hysteresis) were observed and
quite a large value of electrostrictive strain was obtained around
0.08% at 780 kV/cm driving field, though this sample was
composed of ferroelectric and normal dielectric materials.
For the BSCT series ceramics with a 15–20 mol% Sr content,
even though the remnant polarization and electrostrictive strain
decreased when the Ca content increased, the electrostrictive
strain of the samples was still around 0.15% with no delay. Such
materials, under the temperature around Tc, may be useful for
various electromechanical applications and should be studied
further.
From Fig. 8(a), it can be seen that the tunability was
suppressed with increasing Ca content. This may be attributed
to the fact that the bonding force between the A-site ion and the
oxygen ion of the ABO3 perovskite structure was stronger
because of the replacement of Ba21 and Sr21 ions by a smaller
Ca21 ion. Therefore, the bonding force of Ti–O–Ti bands of
BS10CT was weakened, which resulted in a larger distance
between the center ion and its nearest neighbors of the octahe-
dron. This weakened the anharmonic effect,40 and consequently,
the tunability was decreased with increasing Ca.
For further understanding of the dielectric properties of the
BSCT ceramics, we could explore their ability to adjust the
dielectric constant via dc electric field. This ability, with an
emphasis on room temperature, has been studied and discussed
in this section. The dc field dependences of the dielectric con-
stant e for the four samples of Ba0.9ꢀxSr0.1CaxTiO3 (BS10CT)
series ceramics are shown in Fig. 8(a). The dielectric constant
decreased with increasing downward and upward field, revealing
the field-tunable dielectric constant of BS10CT. Dielectric con-
stant tunability T of a ferroelectric ceramics was defined as:
T 5 [e(0)ꢀe(E)]/e(0), where e(0) is the zero-field dielectric con-
stant and e(E) is the dielectric constant measured at an applied
dc electric field of E. At an applied voltage of 25 kV/cm and a
frequency of 10 kHz, tunability values of the BS10CT-00
(x 5 0.00), BS10CT-10 (x 5 0.10), BS10CT-34 (x 5 0.34), and
BS10CT-45 (x 5 0.45) were 32.2%, 23.5%, 26.0%, and 17.4%,
respectively.
Figure 8(b) shows the dc electric field dependence of the
dielectric constant e for the Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3 series
ceramics at the room temperature. At an applied voltage of 30
kV/cm and frequency of 10 kHz, tunability values of the
BS16CT-42, BS17CT-42.5, BS18CT-41, and BS19CT-40.5
were 33.6%, 30.0%, 45.5%, and 54.1%, respectively. The
tunability values increased with an increase in the Sr content,
because the tunability in the soluble area was higher than that in
the diphasic region. Slight hysteresis windows were observed for
all of these four samples, which was a typical relaxor ferro-
electric (already approved in our previous paper30), owing to the
existence of microregions and the domain wall motion during
the switching of polarization.38,39
Notably, from Fig. 8(a), we can also see that the BS10CT-34
ceramics showed an abnormally high tunability. We could
explain this phenomenon using a model of a strong interaction
between the ferroelectric domain in Ba0.56Ca0.34Sr0.10TiO3 and
ionic polarization in Ba0.20Ca0.70Sr0.10TiO3. The former was a
ferroelectric, while the latter was a normal dielectric. Via a high
To reveal the ferroelectric feature of BSCT ceramics, the
polarization–electric field hysteresis loops and electroinduced
Fig. 9. (a) Polarization versus electric field and (b) Electric-field-induced strain-electric field butterfly curves for the Ba0.87ꢀxSr0.13CaxTiO3 samples
(x 5 0.0, 0.20, 0.36, and 0.38) with 780 kV/cm driving field at room temperature.

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Journal of the American Ceramic Society—Zhang et al.
Vol. 93, No. 4
Fig. 10. The dielectric constant–electric field (e–E) relations of Ba0.9ꢀxSr0.1CaxTiO3 (a) x 5 0.0 and (b) x 5 0.34 samples. The symbols indicate
experimental data and the solid lines indicate Johnson’s equation and multipolarization-mechanism model fit, respectively.
external field, a domain and its motion were affected by
surrounding domains, domain walls, and defects, which were
finally exhibited in the form of an internal field. This local
internal field overlapped on the external field and improved or
depressed the piezoelectric properties depending on whether
there was a plus or a minus interaction.18 In the present case,
BS10CT ceramics were comprised of tetragonal Ba0.56
Ca0.34Sr0.10TiO3 and orthorhombic Ba0.20Ca0.70Sr0.10TiO3 solid
solutions. In the composite ceramics, Ba0.20Ca0.70Sr0.10TiO3
grains dispersed among the ceramics; their ionic polarization
couples with the non-1801 domains in surrounding ferroelectric
Ba0.56Ca0.34Sr0.10TiO3 grains. The polarization enhanced the
polarizability and non-1801 domain rotation ability of the
ceramics when the external electric field was imposed.28,41 There-
fore, in the soluble area, the polarization mechanism related to
the ferroelectric domain wall contribution was dominant, while
near the solubility limit, it might be that domain wall motions,
defects, and phase boundary polarization contributed to the
tunability. Here, we could use the Landau–Ginzburg–Devon-
shire (LGD) theory and the multipolarization-mechanism model
to verify these deductions.
The experimental data of BS10CT-34 could be better fitted
with a statistical correlation of 0.999, which is shown in
Fig. 10(b). Therefore, we can infer that not only the polarization
mechanism but also the domain rotation ability of the samples
contributed to the related parameters like dielectric constant and
tunability of the ceramics increased in the solubility limit.
IV. Conclusions
In summary, the ternary system barium–calcium–strontium
titanate of Sr (0, 5, 10, and 13 mol %) were prepared using
the solid-state reaction technique. It was found by refined XRD
analysis that in the Ba-rich area, the solubility limit of Ba1ꢀx
CaxTiO3, Ba0.95ꢀxSr0.05CaxTiO3, Ba0.90ꢀxSr0.10CaxTiO3, and
Ba0.87ꢀxSr0.13CaxTiO3 lay around x 5 0.24, x 5 0.30, x 5 0.34,
and x 5 0.36, respectively. In the Ca-rich area, the solubility
limit of Ba1ꢀxCaxTiO3, Ba0.95ꢀxSr0.05CaxTiO3, and Ba0.90ꢀx
Sr0.10CaxTiO3 lay around x 5 0.92, x 5 0.84, and x 5 0.70,
respectively. The solubility limit of Ba0.5ꢀy/2SryCa0.5ꢀy/2TiO3
ceramics was determined at y 5 0.16. The average grain sizes
of BSCT ceramics decreased with an increase in the Ca and Sr
contents, and the coexistence of ferroelectric tetragonal and
dielectric orthorhombic inhibited the growth of the grain size
in the diphasic region. The dielectric constants and the tunability
decreased with Ca addition, except for the solubility limit, near
which the dielectric constant and tunability increased drastically.
Near the solubility limit, the polarization mechanism, such as
domain wall motions, defects, and phase boundary polarization
was attributed to the enhancement in the dielectric properties.
For the BSCT series ceramics with a 15–20 mol% Sr content,
the samples’ electrostrictive strain still had quite a large value of
around 0.15% with no delay, even though the remnant polar-
ization and electrostrictive strain decreased with an increase in
the Ca content. Such materials will be useful for various
electromechanical applications.
Johnson’s relationship of the LGD theory42,43 was applied to
explain the tunability in the soluble area:
eð0Þ
eðEÞ ¼
(1)
3
1=3
f1 þ l½e0eð0Þꢂ E2g
where l is generally a temperature-independent coefficient, e0 is
the permittivity of space, e(0) is the zero-field dielectric constant,
and e(E) is the dielectric constant measured at an applied dc
electric field of E. Using Johnson’s equation, for the Ba0.90Sr0.10
TiO3 (BS10CT-00), we found that the experimental data fitted
well with Johnson’s equation with a correlation coefficient of
0.998 [Fig. 10(a)], which suggested that the ferroelectric domain
wall was the main factor in the ferroelectric state, and it had
already been shown to be valid for (Sr,Ba)TiO3.42 For the
sample BS10CT-34, this model cannot explain the abnormal
tunability, the correlation being rather poor (0.98). The ‘‘multi-
polarization-mechanism model’’ (Eq. (2)) could be used to
describe not only the intrinsic polarization mechanism but
also extrinsic polarization contributions, such as domain wall
motions, defects, and phase boundary polarization. This model
was described as Johnson’s relationship plus a Langevin term:
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