Original scientific paper
Journal of Microelectronics,
Electronic Components and Materials
Vol. 53, No. 4(2023), 233 – 238

https://doi.org/10.33180/InfMIDEM2023.403

Linear Thermal Expansion of 0.5Ba(Zr0.2Ti0.8)O30.5(Ba0.7Ca0.3)TiO3 Bulk Ceramic
Sabi William Konsago1,2, Andrej Debevec1, Jena Cilenšek1, Brigita Kmet1,2, Barbara Malič1,2
Electronic Ceramics Department, Jožef Stefan Institute, Ljubljana, Slovenia
Jožef Stefan International Postgraduate School, Ljubljana, Slovenia

1
1

Abstract: We report the linear thermal expansion coefficient of lead-free ferroelectric ceramic barium zirconate titanate - barium
calcium titanate 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 (BZT-BCT). The material was prepared by solid-state synthesis and consolidated by
sintering at 1450°C. BZT-BCT crystallizes in the perovskite phase. The microstructure of the ceramic with about 95 % relative density
consists of about 10 mm-sized grains. The contact dilatometry of the ceramic specimen reveals the change of slope of the linear
thermal expansion curve at 84°C. This is in good agreement with the peak of the dielectric permittivity versus temperature at about
85°C indicating the transition from the low-temperature polar ferroelectric phase to a high-temperature nonpolar phase or Curie
temperature. The thermal expansion coefficients of the polar tetragonal and nonpolar cubic phases of BZT-BCT are 7.69×10-6 K-1 (40°C
– 80°C) and 12.39×10-6 K-1 (100°C – 600°C), respectively. The thermal expansion data are among the material data needed in the design
of thin- and thick-film structures for energy-harvesting and energy-storage applications.
Keywords: 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 (BZT-BCT), lead-free, ferroelectric ceramic, linear thermal expansion

Linearni temperaturni raztezek volumenske
keramike 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3
Izvleček: V delu poročamo o linearnem temperaturnem raztezku volumenske keramike barijevega cirkonata titanata - barijevega
kalcijevega titanata 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 (BZT-BCT). Material smo pripravili s sintezo v trdnem stanju in sintranjem pri
1450°C. BZT-BCT kristalizira v perovskitni fazi. Mikrostrukturo keramike s ≈95% relativno gostoto sestavljajo zrna velikosti okrog 10
mm. Linearni temperaturni raztezek keramike smo izmerili s kontaktno dilatometrijo od sobne temperature do 600°C. Pri temperaturi
84°C opazimo spremembo naklona krivulje raztezka. Ta podatek se ujema s temperaturo maksimuma dielektričnosti v odvisnosti
od temperature, ki označuje prehod nizkotemperaturne polarne feroelektrične faze v visokotemperaturno nepolarno fazo oziroma
Curiejevo temperaturo. Vrednosti linearnega temperaturnega raztezka polarne in nepolarne faze BZT-BCT sta 7.69×10-6 K-1 (40°C – 80°C)
in 12.39×10-6 K-1 (100°C – 600°C). Podatke o temperaturnem raztezku keramike potrebujemo pri načrtovanju tanko- in debeloplastnih
struktur, namenjenih zbiranju in shranjevanju energije.
Ključne besede: 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 (BZT-BCT), brez svinca, feroelektrična keramika, linearni temperaturni raztezek
* Corresponding Author’s e-mail: barbara.malic@ijs.si

1 Introduction

made of BZT-BCT has been prototyped [4]. It is also being studied as a promising biocompatible material for
bone regeneration [5], [6]. BZT-BCT has gained the attention of the ferroelectric/piezoelectric communities
as one of the most promising environment-friendly
alternatives to commercially widely spread lead-based
piezoelectric ceramic materials such as Pb(Zr,Ti)O3
(PZT) due to the Restriction of Hazardous Substances

The discovery of the high piezoelectric properties of
the barium zirconate titanate - barium calcium titanate
solid solution 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 (BZTBCT) bulk ceramic has revealed its great potential for
many piezoelectric applications including actuators,
transducers, and energy harvesting devices [1] - [3].
As an example, an intravascular ultrasound transducer

How to cite:
S. W. Konsago et al., “Linear Thermal Expansion of 0.5Ba(Zr0.2Ti0.8)O3-0.5(Ba0.7Ca0.3)TiO3 Bulk Ceramic", Inf. Midem-J. Microelectron. Electron.
Compon. Mater., Vol. 53, No. 3(2023), pp. 233–238
233

S. W. Konsago et al.; Informacije Midem, Vol. 53, No. 4(2023), 233 – 238

(RoHS) regulations [7] - [9]. Recently it has been reported that it possesses promising energy storage properties [10], [11].

oxides (TiO2, 99.8% also from Alfa Aesar, Karlsruhe, Germany and ZrO2, 99.8% from Tosoh, Japan). The metal
content was checked gravimetrically. The 25 g batches
of stoichiometric fractions of the reagents were homogenized using isopropanol in a planetary mill (PM
400, Retsch) with yttria-stabilized zirconia milling bodies (3 mm, Tosoh, Japan) for 2 h at 200 rpm. The median
particle size of the milled powder was 0.45 mm as determined by laser granulometry (Microtrac S3500 Particle
Size Analyzer) using isopropanol as a dispersion liquid.
The calcination of the loosely pressed reagent mixture
(P = 50 MPa) took place at 1300 °C for 4 hours in the air
with heating and cooling rates of 5 K/min. The powder
was again milled for 2h at 200 rpm in a planetary mill,
dried at 120 °C and sieved. The powder was shaped
into pellets (diameter: 8 mm) or bars (40 mm x ≈7 mm x
≈5 mm) by uniaxial (P = 50 MPa) and isostatic pressing
(P = 300 MPa). The powder compacts were sintered at
1450 °C for 4 hours in the air with heating and cooling
rates of 5 K/min.

BZT-BCT exhibits a Curie temperature of about 85-90 °C.
In the proximity of room temperature, the coexistence
of rhombohedral, orthorhombic, and tetragonal phases of solid solutions of Ba(Zr0.2Ti0.8)O3 and (Ba0.7Ca0.3)TiO3
with the molar ratios close to unity contributes to enhanced piezoelectric properties [12], [13]. It was shown
that the grain size strongly influences the piezoelectric
properties and the phase transitional behaviour of BZTBCT bulk ceramic; the enhanced piezoelectric response
was characteristic for grain sizes exceeding 10 mm [14].
In numerous miniature devices, such as microelectromechanical systems (MEMS) or energy harvesters, the
space constraints favour the use of piezoelectric ceramic elements in the form of thin or thick films [15],
[16]. One of the key parameters for designing such
devices includes the thermal expansion coefficients
of the constituent materials. In case of a large difference in thermal expansion coefficients of the film and
the substrate, the induced stresses may contribute to
lowering the piezoelectric response [17] - [19]. Clamping the screen-printed thick film by the substrate results in poor densification during sintering [20]. Tensile
stresses in the film that arise due to the thermal expansion coefficient mismatch may lead to the evolution of
cracks [19]. Various effects of stresses generated by the
thermal expansion mismatch also affect other functional properties, such as breakdown strength [21],
[22], which is important in energy storage applications.

The phase composition of the calcined powders and
crushed sintered specimens was analyzed by X-ray diffraction (XRD, X’Pert PRO MPD, PANanalytical, CuKa1 radiation, time/step: 100 s, interval between data points:
0.0016°). The density of the sintered samples was determined pycnometrically (Micromeritics, AccuPyc III
1340 Pycnometer).
The ceramic samples were ground and polished using
standard ceramographic techniques. Thermal etching
of the polished sections at 1350 °C for a few minutes revealed the grain boundaries. A field-emission scanning
electron microscope (FE-SEM JEOL JSM-7600) with an
energy-dispersive X-ray spectrometer (EDXS, INCA Oxford 350 EDS SDD) was used for the analysis of the microstructure. The grain size was determined using the
Image Tool software.

There are some publications on the thermal expansion coefficient of Ca- and Zr-modified barium titanate
ceramics [23] - [26] but to our knowledge, there is no
reported study on the linear thermal expansion coefficient of BZT-BCT ceramic. Such data would contribute
to efficiently designing the processing of dense and
crack-free BZT-BCT thick films where the powder slurry
is screen-printed on a platinized alumina substrate.
Such films could find applications in energy harvesting.

For low- and high-field dielectric measurements, the
disks were cut to the thickness of 0.5 mm and polished.
An annealing step to 600 °C for 1 h followed by a slow
cooling (1 K/min) was used to release the stresses of
mechanical operations. The Au electrodes with a diameter of 3 mm were RF-magnetron sputtered on the faces of the disks (5 Pascal). The dielectric permittivity (e)
and losses (tan d) were measured between +150 °C and
-40°C with a cooling rate of 1 K/min (Agilent E4980A
Precision LCR meter, 1V). The polarization-electric field
hysteresis loops were measured at room temperature
with a sine voltage at the frequency of 50 Hz (Aixacct
TF analyzer 2000).

Our study aims to prepare perovskite BZT-BCT ceramic
with a high relative density, uniform microstructure,
and adequate low- and high-field dielectric properties.
The linear thermal expansion coefficient from room
temperature to 600 °C is measured.

2 Materials and methods

For the measurement of the thermal expansion, the
ceramic bars were cut to the dimensions of 25 mm x
5 mm x 4 mm. The faces of the bars were plan-parallel

BZT-BCT powder was prepared using alkaline earth carbonates ((BaCO3, 99.8% and CaCO3, 99,95% both from
Alfa Aesar, Karlsruhe, Germany) and transition metal
234

S. W. Konsago et al.; Informacije Midem, Vol. 53, No. 4(2023), 233 – 238

polished. Thermal stresses were released as described
above. The dimensional changes of the specimen
upon heating and cooling were measured with a contact dilatometer with a corundum measuring system
(Netzsch DIL 402 PC) between room temperature and
600 °C with the heating and cooling rates of 5 K/min
in air.

3 Results and discussion
Figure 1 contains the XRD patterns of BZT-BCT powder after the calcination at 1300 °C (a) and the ceramic
sintered at 1450 °C (b). The XRD patterns of both samples reveal a perovskite phase without any noticeable
secondary phases. The unit cell distortion could not be
determined using a standard X-ray diffractometer, synchrotron radiation would be needed to obtain a deeper
insight into the phase composition of the material, c.f.
[13], [27] - [29]. According to the phase diagram [13],
the coexistence of the orthorhombic phase cannot
be excluded at room temperature besides rhombohedral and tetragonal phases in the morphotropic phase
boundary region.
The relative density of BZT-BCT ceramic is 95.4 %. The
microstructure shown in Figure 2 a) is uniform, with a
unimodal grain size distribution and a mean grain size
of 9.66 ± 4.84 μm (Figure 2 b)). EDXS analysis confirmed
a uniform distribution of elements within and between
individual grains (EDXS spectra are not shown). Trace
amounts of a secondary phase were observed at some
grain junctions (see the inset of Figure 2 a)) but due to
their small size, their chemical composition could not
be reliably determined on the level of FE-SEM.

Figure 2: a) SEM micrograph of the microstructure of
BZT-BCT ceramic and b) grain size distribution. Inset
in panel a) reveals an intergranular phase located at a
grain junction.
Figure 3 shows the temperature dependence of the dielectric permittivity and losses as a function of temperature in the frequency range from 100 Hz to 100 kHz.
Dielectric permittivity and losses at room temperature
and 1 kHz are 3165 and 0.029 in agreement with reported values for ceramics with similar grain sizes [14].
There is no significant change in the dielectric permittivity in the frequency range from 100 Hz to 100 kHz in
the measured temperature range. The change of slope
at about 40 °C is attributed to the rhombohedral–tetragonal phase transition, and the dielectric permittivity peak at about 85 °C to transition to the cubic
phase or Curie temperature. The grain size influences
both phase transition temperatures; for the ceramic
with about 10 mm-sized grains, the respective values
were 87 °C and 35 °C [14]. Broadening of the permittivity peak, characteristic of polycrystalline ferroelectrics, is related to the micron size of the crystallites and
the presence of two cations on each cation sublattice

Figure 1: XRD patterns of BZT-BCT powder calcined at
1300 °C and ceramic sintered at 1450 °C. The peaks are
indexed according to the BaTiO3 cubic phase (PDF 01074-4539).
235

S. W. Konsago et al.; Informacije Midem, Vol. 53, No. 4(2023), 233 – 238

site. We do not observe any noticeable frequency peak
shifting in the measured frequency range supporting
the ferroelectric nature of the BZT-BCT ceramic. It has
been shown that processing conditions and grain size
strongly influence the ferroelectric or relaxor nature of
BZT-BCT [14], [27].

value of TEC and the TEC-inflexion point’s temperature
depended on the studied materials’ chemical composition[31], [32]. Our results are in good agreement with
these latter dilatometric studies of the (Ba,Ca)TiO3Ba(Zr,Ti)O3 solid solutions.

Figure 4 shows the room temperature polarization–
electric field (P–E) hysteresis loops measured at 50 Hz.
The sample survived the maximum applied field of 70
kV/cm, indicating its good dielectric breakdown resistance. The remnant polarization Pr and coercive field Ec
are about 13 μC/cm2 and 5.9 kV/cm, respectively, indicating a good ferroelectric response of BZT-BCT. Hao et
al obtained similar Pr and Ec values for the ceramic with
10 mm-sized grains [14].
Figure 5 shows the dilatometric curves of BZT-BCT ceramic, revealing linear thermal expansion or contraction upon heating or cooling. There is not much difference between the heating and cooling curves. Two
main slopes are discerned in both cases with the inflexion point at 84.0 °C. The thermal hysteresis between
the heating and cooling runs is quite small. We note
that the inflexion temperature corresponds well to the
dielectric permittivity peak temperature, cf. Figure 3.
The thermal expansion coefficient (TEC = (DL/L0)/DT),
determined from the cooling curve in the temperature range from 40 °C to 80 °C, is 7.69×10-6 K-1. In this
temperature range the tetragonal phase prevails [13],
but the coexistence of a rhombohedral phase cannot
be excluded judging from the evident change of slope
at about 40 °C in the dielectric permittivity curve (cf.
Figure 3). As the temperature increases, the TEC progressively increases as well. From 100 °C to the final
temperature of 600 °C, in the temperature range of the
cubic phase, the TEC is 12.39×10-6 K-1.

Figure 3: The dielectric permittivity and losses as a
function of the temperature of BZT-BCT ceramic.

Figure 4: Polarization - electric field- loops of BZT-BCT
ceramic measured at 50 Hz and room temperature.

As explained earlier we could not find the thermal
expansion data for BZT-BCT. The TEC of the base formulation of BZT-BCT solid solution, the prototype ferroelectric BaTiO3, is 6.5×10-6 K-1 in the tetragonal phase
and 9.8×10-6 K-1 in the cubic phase (125 °C – 200 °C)
measured by contact dilatometry [30]. It is noted that
the change in the slope of the thermal expansion of BaTiO3 at the phase transition temperature is sharp and
accompanied by a noticeable shrinkage which is a fingerprint of a first-order phase transition and is not the
case with BZT-BCT. Here, we observe only the change in
the slope of the thermal expansion. Tian et al. studied
(Ba,Ca)TiO3-Ba(Zr,Ti)O3 with slightly different molar ratios of cations compared to BZT-BCT formulation, and
they incorporated various rare-earth dopants. They
measured a TEC of about 5×10-6 K-1 at lower temperatures and a TEC of about 11×10-6 K-1 at higher temperatures, the final temperature being 400 °C. The exact

Figure 5: The linear thermal expansion of BZT-BCT ceramic measured between room temperature and 600
°C. The inflexion point and TEC were determined from
the cooling curve.
236

S. W. Konsago et al.; Informacije Midem, Vol. 53, No. 4(2023), 233 – 238

4 Conclusions
4.

In conclusion, this study focused on determining
the thermal expansion behavior of 0.5Ba(Zr0.2Ti0.8)O305(Ba0.7Ca0.3)TiO3 (BZT-BCT) bulk ceramic. The powder,
prepared by solid-state synthesis, was compacted and
sintered to a high relative density at 1450 °C for 4 hours.
The ceramic crystallized in the perovskite phase. The microstructure consisted of about 10 mm sized grains. The
measurement of the dielectric permittivity versus temperature revealed two anomalies which could be related
to the phase transitions of the predominantly rhombohedral to tetragonal phase at about 40 °C and to cubic
phase at about 90 °C. The hysteretic dependence of the
polarization versus the electric field confirmed the ferroelectric nature of the ceramic. The dilatometric measurements revealed the thermal expansion coefficients of the
polar and cubic phases of 7.69×10-6 K-1 (40 °C – 80 °C) and
12.39×10-6 K-1 (100 °C – 600 °C). The study results contribute to the design of thick and thin-film structures based
on BZT-BCT in various energy-harvesting and/or energystorage applications.

5.

6.

7.

8.

5 Acknowledgments
The authors acknowledge the advice and technical
support of Silvo Drnovšek, Electronic Ceramics Department, Jožef Stefan Institute.

9.

6 Conflict of interest

10.

The authors declare no conflict of interest.
The authors acknowledge the financial support of the
Slovenian Research Agency (core funding P2-0105).

11.

7 References
1.

2.

3.

W. Liu and X. Ren, “Large piezoelectric effect in
Pb-free ceramics,” Phys Rev Lett, vol. 103, no. 25,
257602, Dec. 2009,
https://doi.org/10.1103/PhysRevLett.103.257602.
M. Acosta, N. Novak, W. Jo, and J. Rödel, “Relationship between electromechanical properties and
phase diagram in the Ba(Zr0.2Ti0.8)O3-x (Ba0.7Ca0.3)
TiO3 lead-free piezoceramic,” Acta Mater, vol. 80,
pp. 48–55, 2014,
https://doi.org/10.1016/j.actamat.2014.07.058.
J. Rödel, K. G. Webber, R. Dittmer, W. Jo, M. Kimura,
and D. Damjanovic, “Transferring lead-free piezoelectric ceramics into application,” J Eur Ceram

12.

13.

237

Soc, vol. 35, no. 6, pp. 1659–1681, Jun. 2015,
https://doi.org/10.1016/j.jeurceramsoc.2014.12.013.
X. Yan et al., “Correspondence: Lead-free intravascular ultrasound transducer using BZT-50BCT ceramics,” IEEE Trans Ultrason Ferroelectr Freq Control,
vol. 60, no. 6, pp. 1272–1276, 2013,
https://doi.org/10.1109/TUFFC.2013.2692.
K. K. Poon, M. C. Wurm, D. M. Evans, M. Einarsrud,
R. Lutz, and J. Glaum, “Biocompatibility of (Ba,Ca)
(Zr,Ti)O3 piezoelectric ceramics for bone replacement materials,” J Biomed Mater Res B Appl Biomater, vol. 108, no. 4, pp. 1295–1303, May 2020,
https://doi.org/10.1002/jbm.b.34477.
C. S. Manohar et al., “Novel Lead-free biocompatible piezoelectric Hydroxyapatite (HA) – BCZT
(Ba0.85Ca0.15Zr0.1Ti0.9O3) nanocrystal composites for
bone regeneration,” Nanotechnol Rev, vol. 8, no. 1,
pp. 61–78, May 2019,
https://doi.org/10.1515/ntrev-2019-0006.
“DIRECTIVE 2002/95/EC OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 27 January
2003 on the restriction of the use of certain hazardous substances in electrical and electronic
equipment.”
“JIS-C-0950: 2005 (E), ‘The marking for presence of
the specific chemical substances for electrical and
electronic equipment’, Japanese Standards Association, 2005”.
L. M. Benson and K. K. Reczek, “A guide to United
States electrical and electronic equipment compliance requirements,” Jun. 2021.
https://doi.org/10.6028/NIST.IR.8118r2.
V. S. Puli et al., “Structure, dielectric, ferroelectric,
and energy density properties of (1 − x)BZT–xBCT
ceramic capacitors for energy storage applications,” J Mater Sci, vol. 48, no. 5, pp. 2151–2157,
Mar. 2013,
https://doi.org/10.1007/s10853-012-6990-1.
Neha, R. Pandey, M. Bhatnagar, P. Kumar, R. K.
Malik, and C. Prakash, “Improved dielectric and
energy storage properties in (1-x)BaTi0.80Zr0.20O3xBa0.70Ca0.30Ti0.99Fe0.01O3 ceramics near morphotropic phase boundary,” Mater Lett, vol. 318,
132126, Jul. 2022,
https://doi.org/10.1016/j.matlet.2022.132126.
M. Acosta, N. Novak, G. A. Rossetti, and J. Rödel,
“Mechanisms of electromechanical response in (1
- X)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 ceramics,” Appl
Phys Lett, vol. 107, no. 14, 142906, Oct. 2015,
https://doi.org/10.1063/1.4932654.
D. S. Keeble, F. Benabdallah, P. A. Thomas, M. Maglione, and J. Kreisel, “Revised structural phase diagram of (Ba0.7Ca0.3TiO3)-(BaZr0.2Ti0.8O3),” Appl Phys
Lett, vol. 102, no. 9, 092903, Mar. 2013,
https://doi.org/10.1063/1.4793400.

S. W. Konsago et al.; Informacije Midem, Vol. 53, No. 4(2023), 233 – 238

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

J. Hao, W. Bai, W. Li, and J. Zhai, “Correlation between
the microstructure and electrical properties in highperformance (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 lead-free piezoelectric ceramics,” Journal of the American Ceramic
Society, vol. 95, no. 6, pp. 1998–2006, Jun. 2012,
https://doi.org/10.1111/j.1551-2916.2012.05146.x.
L. Song, S. Glinsek, S. Drnovsek, V. Kovacova, B.
Malic, and E. Defay, “Piezoelectric thick film for
power-efficient haptic actuator,” Appl Phys Lett,
vol. 121, no. 21, 212901, Nov. 2022,
https://doi.org/10.1063/5.0106174.
P. Muralt, “Polar oxide thin films for MEMS applications,” T. Schneller, R. Waser, M. Kosec and D. Payne
(Eds.), Chemical Solution Deposition of Functional
Oxide Thin Films, Wien, Austria, Springer-Verlag,
2013, Ch. 24, pp. 593-620.
https://doi.org/10.1007/978-3-211-99311-8_24.
T. A. Berfield, R. J. Ong, D. A. Payne, and N. R. Sottos,
“Residual stress effects on piezoelectric response
of sol-gel derived lead zirconate titanate thin films,”
J Appl Phys, vol. 101, no. 2, 024102, Jan. 2007,
https://doi.org/10.1063/1.2422778.
L. Lian and N. R. Sottos, “Effects of thickness on
the piezoelectric and dielectric properties of lead
zirconate titanate thin films,” J Appl Phys, vol. 87,
no. 8, pp. 3941–3949, Apr. 2000,
https://doi.org/10.1063/1.372439.
K. Coleman, J. Walker, T. Beechem, and S. TrolierMcKinstry, “Effect of stresses on the dielectric and
piezoelectric properties of Pb(Zr0.52Ti0.48)O3 thin
films,” J Appl Phys, vol. 126, no. 3, 034101, Jul. 2019,
https://doi.org/10.1063/1.5095765.
R. K. BORDIA and R. RAJ, “Sintering Behavior of
Ceramic Films Constrained by a Rigid Substrate,”
Journal of the American Ceramic Society, vol. 68,
no. 6, pp. 287–292, Jun. 1985,
https://doi.org/10.1111/j.1151-2916.1985.tb15227.x.
A. M. Pashaev, A. Kh. Dzhanakhmedov, and A. A.
Aliyev, “Effect of Tensile Stresses on the Breakdown Voltage of Thin Films,” Technical Physics, vol.
65, no. 1, pp. 54–56, Jan. 2020,
https://doi.org/10.1134/S1063784220010211.
Y.-N. Bie et al., “Effect of Source Field Plate Cracks on
the Electrical Performance of AlGaN/GaN HEMT Devices,” Crystals (Basel), vol. 12, no. 9, 1195, Aug. 2022,
https://doi.org/10.3390/cryst12091195.
Y. Tian et al., “Diversiform electrical and thermal expansion properties of (1 − x)Ba0.95Ca0.05Ti0.94Zr0.06O3–
(x)Dy lead-free piezoelectric ceramics influenced
by defect complexes,” J Mater Sci, vol. 53, no. 16,
pp. 11228–11241, Aug. 2018,
https://doi.org/10.1007/s10853-018-2428-8.
Y. Tian et al., “Electrical Properties and Thermal Expansion Characteristics of (1– x )Ba 0.948
Ca0.05Er0.002Ti0.94Zr0.06O3 –( x )Pr Lead‐Free Piezoelectric
Ceramics Sintered at a Low‐Temperature,” physica

25.

26.

27.

28.

29.

30.

31.

32.

status solidi (a), vol. 216, no. 2, 1800622, Jan. 2019,
https://doi.org/10.1002/pssa.201800622.
Y. Tian et al., “Temperature-dependent ferroelectric and piezoelectric response of Yb3+ and Tm3+
co-doped Ba0.95Ca0.05Ti0.90Zr0.10O3 lead-free ceramic,” Journal of Ceramic Processing Research, vol. 23,
no. 4, pp. 430–435, Aug. 2022,
https://doi.org/10.36410/jcpr.2022.23.4.430.
Y. Tian et al., “Piezoelectricity and Thermophysical Properties of Ba0.90Ca0.10Ti0.96Zr0.04O3 Ceramics
Modified with Amphoteric Nd3+ and Y3+ Dopants,” Materials, vol. 16, no. 6, 2369, Mar. 2023,
https://doi.org/10.3390/ma16062369.
F. Benabdallah et al., “Structure–microstructure–
property relationships in lead-free BCTZ piezoceramics processed by conventional sintering and
spark plasma sintering,” J Eur Ceram Soc, vol. 35,
no. 15, pp. 4153–4161, Dec. 2015,
https://doi.org/10.1016/j.jeurceramsoc.2015.06.030.
H. Amorín et al., “Insights into the Early Size Effects
of Lead‐Free Piezoelectric Ba0.85Ca0.15Zr0.1Ti0.9O3,”
Adv Electron Mater,
https://doi.org/10.1002/aelm.202300556.
S. López-Blanco, D. A. Ochoa, H. Amorín, A. Castro, M. Algueró, and J. E. García, “Fine-grained high-performance
Ba0.85Ca0.15Zr0.1Ti0.9O3 piezoceramics obtained by currentcontrolled flash sintering of nanopowders,” J Eur Ceram
Soc, vol. 43, no. 16, pp. 7440–7445, Dec. 2023,
https://doi.org/10.1016/j.jeurceramsoc.2023.08.012.
G. Shirane and A. Takeda, “Volume Change at
Three Transitions in BaTiO3 Ceramics,” J Physical
Soc Japan, vol. 6, no. 2, pp. 128–129, Mar. 1951,
https://doi.org/10.1143/JPSJ.6.128.
Y. Tian et al., “Diversiform electrical and thermal expansion properties of (1 − x)Ba0.95Ca0.05Ti0.94Zr0.06O3–
(x)Dy lead-free piezoelectric ceramics influenced
by defect complexes,” J Mater Sci, vol. 53, no. 16,
pp. 11228–11241, Aug. 2018,
https://doi.org/10.1007/s10853-018-2428-8.
Y. Tian et al., “Temperature-dependent ferroelectric and piezoelectric response of Yb3+ and Tm3+
co-doped Ba0.95Ca0.05Ti0.90Zr0.10O3 lead-free ceramic,” Journal of Ceramic Processing Research, vol. 23,
no. 4, pp. 430–435, Aug. 2022,
https://doi.org/10.36410/jcpr.2022.23.4.430.

Copyright © 2023 by the Authors.
This is an open access article distributed under the Creative Commons Attribution (CC BY) License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted
use, distribution, and reproduction in any medium,
provided the original work is properly cited.
Arrived: 09. 01. 2024
Accepted: 13. 02. 2024
238