#
Ferroelectric, Dielectric and Electromechanical Performance of Ba_{0.92}Ca_{0.08}Ti_{0.95}Zr_{0.05}O_{3} Ceramics with an Enhanced Curie Temperature

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

_{0.92}Ca

_{0.08}Ti

_{0.95}Zr

_{0.05}O

_{3}(BCZT8-5) ceramic materials have been scarcely studied as lead-free piezo/ferroelectrics despite their enhanced Curie temperature (>100 °C) with respect to most studied BCZT compositions. In this work, homogeneous dense BCZT8-5 ceramics with grain size in the range of 20 μm, and optimum ferroelectric, dielectric, and electromechanical performance, were prepared by the mixed oxides route using moderate synthesis (1250 °C-2 h) and sintering (1400 °C-2 h) conditions. Thickness-poled thin disks and monomodal shear plate resonators were used for the determination of piezoelectric coefficients, coupling factors, elastic, and dielectric permittivity coefficients, including all losses, by iterative analysis of impedance curves at resonance. Furthermore, the thermal evolution of the piezoelectric characteristics at resonance was determined to assess the enhanced working range of the ceramics (≈100 °C). Ferroelectric hysteresis loops and strains vs. electric-field butterfly loops were also measured and showed soft behavior with E

_{c}= 2 kV/cm, P

_{r}= 12 μC/cm

^{2}after a maximum applied field of 3 kV was used. The ceramics showed a high endurance of P-E cycles to electrical fatigue up to 10

^{7}cycles. Moreover, dielectric properties as a function of temperature were also accomplished and showed nearly normal ferroelectric behavior, characteristic of samples with low crystallographic disorder. Overall, these ceramics showed high sensitivity and higher stability than other currently studied BCZT compositions.

## 1. Introduction

_{3}(KNN), (Na,Bi)TiO

_{3}(BNT), Ba(Zr,Ti)O

_{3}(BZT), and (Ba,Ca)TiO

_{3}(BCT) [6,7,8], have been under study as ecological and practical alternatives to lead-based systems, mostly based on Lead Zirconate Titanate (Pb(Zr,Ti)O

_{3}). In this regard, a modified BaTiO

_{3}ceramic, named (Ba,Ca)(Ti,Zr)O

_{3}(BCTZ), has been widely reported because of its notable electrical properties.

^{4+}, at the B-site, and Ca

^{2+}, at the A-site, adjusts the properties of BaTiO

_{3}manyfold [10]; while the incorporation of Zr

^{4+}increases material densification and piezo/ferroelectric activity, the addition of Ca

^{2+}enhances the dielectric properties of BCTZ materials [11,12]. Moreover, the phase coexistence temperature region is defined by the proper doping amount of Ca and Zr cations [13,14,15], and the Curie temperature of the material is directly influenced by the saturation of the B-site of the perovskite [16]. Additionally, doping induces microstructural characteristics that are required for integrated devices (i.e., miniaturization, lightweight, and integration). Therefore, the performance of BCTZ is largely dependent on the porosity, stoichiometry, and grain size of the sintered ceramics [17].

_{ij}), induced polarization per unit of stress applied (d

_{i}

_{j}), an optimum degree of damping (low mechanical quality factor “Q”), and high ability of the material to store charge (dielectric permittivity “ε”). All of these must be accompanied by thermal and mechanical stability as well as endurance to fatigue.

_{0.92}Ca

_{0.08}Ti

_{0.95}Zr

_{0.05}O

_{3}(BCZT8-5) ceramic materials have been scarcely studied [23] as a lead-free piezo/ferroelectric, despite their enhanced Curie temperature (>100 °C) with respect to most studied BCZT compositions, namely BCZT1010 [24] and BCZT1510 [25]. In this work, Ba

_{0.92}Ca

_{0.08}Ti

_{0.95}Zr

_{0.05}O

_{3}(BCZT8-5) ceramics were fabricated using a conventional mixed oxide route using a moderate synthesis schedule. Their structure and microstructure, as well as the electrical properties, were determined. Additionally, their stability was analyzed.

## 2. Materials and Methods

_{3}(99.0%, Analytica), CaCO

_{3}(99.0%, Fluka), ZrO

_{2}(99.0%, Riedel-deHaën), and TiO

_{2}(99.5%, Sigma-Aldrich). Stoichiometric amounts of reagents were weighted and mixed with the addition of acetone in an agate mortar for 30 min. The powder was then dried and calcined at 1250 °C for 2 h. Thereafter, the powders were grounded (using a Zirconia grinding media) for at least 6 h (at 350 rpm) in a planetary mill (Fritsch Pulverisette 6) to avoid agglomeration and reduce and homogenize the particle size. Then, the ceramic powder was pressed into pellets, and sintered at 1400 °C for 2 h in air. For both the synthesis/sintering processes a heating/cooling ramp rate of 5 °C/min was used. The bulk density of the sintered ceramics was measured by the Archimedes method using distilled water as a medium. The relative density was obtained from a theoretical density value of 5.82 g/cm

^{3}.

_{33}was measured quasi-statically 24 h after the poling process (15 kV/cm for 30 min at room temperature) using a d

_{33}-meter (APC International, Mackeyville, PA, USA). One piezoelectric, one elastic, and one dielectric parameter of the material were directly determined using the resonance method from the analysis of the complex impedance vs. frequency curves of each of the studied electrically induced, electromechanical resonances of the ceramic resonators. These were measured with a the precision impedance analyzer. The interested reader can find the principles of resonance measurement and definitions of the material coefficients in the classical literature [26]. An automatic iterative method was used for the analysis of the radial and thickness modes of thin ceramic disks [26,27]. Furthermore, parameters obtained from the shear resonance mode of a rectangular plate (thickness poled) [28,29] were calculated using the same method. For this purpose, alternative plots to the conventional representation of the complex impedance as modulus and phase angle were used. Instead, the peaks of the Resistance (R) and Conductance (G), the real part of the complex impedance and its inverse (complex admittance), were used. Not only the frequencies of the maximum values of R and G, but also the measured values of these, were used to determine the piezoelectric, dielectric, and elastic complex parameters as complex quantities (P* = P′ + iP″), thus including losses for each parameter. Losses are currently expressed in two alternative ways, as quality factors and as loss tangents. Mechanical losses are currently given by the quality factors (Q = P′/P″) of each elastic coefficient. The lower the losses the higher the Q. Dielectric losses are currently given by the loss factors (tan δ = P″/P′), which are higher, the higher the losses. Piezoelectric losses are less commonly reported and there is no convention about them. From well-known relations with the directly calculated parameters at resonance [26,27,28,29], the other parameters and also the electromechanical coupling factors (k

_{x}, with x = planar(p), thickness(t), 31 and 15) were determined:

_{33}must be replaced by h

_{15}, ε

_{33}

^{S}by ε

_{15}

^{S}and c

_{33}

^{D}by c

_{55}

^{D}, and k

_{t}by k

_{15}.

_{x}) were determined as the product of the vibrating dimension (in mm) and the resonance frequency (in kHz). It was noticeable that only by using this methodology, can the k

_{31}coupling be obtained from the planar mode of the disk and without the use of another resonator, namely the thickness poled long bar at its longitudinal extension resonance mode.

_{33}-meter.

## 3. Results

#### 3.1. Structural and Morphological Characterization

^{2+}and Zr

^{4+}ions were incorporated into the BaTiO

_{3}, lattice forming a complete solid solution. Figure 1b shows the SEM micrograph of the fractured surface of the BCTZ8-5 sintered ceramic. The micrograph indicates that there was a small amount of closed porosity and showed homogeneity of grain size in the range above 20 µm. Furthermore, it showed a transgranular fracture, which indicated that the grains were well soldered, and the sintering process was accomplished. The grains did not show intragranular porosity or inclusions of any kind. The obtained ceramic pellets revealed a highly dense microstructure (~97%).

#### 3.2. Dielectric Permittivity Analysis

_{0}is the Curie–Weiss temperature and C is the Curie–Weiss constant. Figure 2b shows the plots of inverse dielectric permittivity vs. temperature fitted to the Curie–Weiss law from a temperature (T

_{CW}) higher than that of the maximum permittivity (T

_{m}). ΔT

_{m}describes the degree of the deviation from the Curie–Weiss law: ΔT = T

_{CW}− T

_{m}. For the BCTZ8-5 ceramic, T

_{0}= 104 °C and C = 1.23 × 10

^{5}were calculated. The C value was close to that reported in the literature for BaTiO

_{3}(~10

^{5}), indicating a displacive-type phase transition for this type of ferroelectric material [32]. To evaluate this phase transition diffusiveness, a modified empirical expression proposed by Uchino and Nomura [33] was used:

_{m}, corresponds to the ferroelectric-paraelectric phase transition temperature.

^{2+}and Zr

^{4+}cations were incorporated into the BaTiO

_{3}lattice, it was possible to locate a Morphotropic Phase Boundary (at Ca = 0.15, Zr = 0.10), achieving a high permittivity response with a reduced Curie temperature. Moreover, it was possible to observe that the ferroelectric phase transition (Rhombohedral to Tetragonal) shifted to a higher temperature. Nevertheless, despite different stoichiometric compositions, the dielectric losses remained lower than 10%, up to 200 °C for BCZT8-5. In comparison with previous results [34,35], the composition under study had a noticeably higher transition temperature, with a moderate reduction of the permittivity with respect to the most widely studied compositions in the literature. This can be compared with one recently obtained by additional doping with Sm in BCZT [36].

#### 3.3. Piezoelectric and Ferroelectric Properties

_{ij}), voltage coefficients (g

_{ij}), as well as h

_{ij}and e

_{ij}coefficients) are given as real and imaginary parts. Finally, the d

_{33}-meter piezoelectric coefficient measured at the Berlincourt piezo-meter, the regression factors for the iterative method, the electromechanical coupling factors, and the frequency numbers of all considered resonances, are given as real parameters.

^{2}) close to 1 (Table 1) for the experimental data (symbols) to the recalculated ones (doted lines) after the material coefficients were determined. These curves were the alternative plot of the complex impedance, more commonly represented by the plot of its modulus (|Z|) and the phase angle (θ) for using the iterative method for the analysis of complex impedance curves. Decoupling from the overtones of the planar mode was achieved for the thickness resonance of the thin disk by separating the frequencies of the radial and thickness resonances using samples with a high diameter-to-thickness ratio. However, this is a mode that is always affected by many other shear or more complex modes [37]. This is observed in the R and G curves of Figure 4b. The shear coefficients were scarcely reported as the in-plane poled shear plates involved complex poling and preparation as they required very high lateral dimensions of the plate-to-thickness ratios. The use of the thickness-poled shear plate allowed for effective decoupling of modes by tuning the thickness of the plate once it was thickness poled and re-electroded for measurement [35]. This can be observed in Figure 4c.

_{33}, d

_{31}and d

_{15}) and electromechanical coupling factors (k

_{p}, k

_{15}) values did not vanish completely until 120 °C. After 100 °C, the depolarization process and vanishing of the piezoelectric activity in BCTZ8-5 ceramics took place abruptly for the piezoelectric coefficients and coupling factors. There are no reports of this extended working range as an ultrasonic generator for a pure BCZT ceramic. The one reported here extended by some 20 °C that recently reported for an Sm-modified BCZT1510 system [29].

_{c}) of some 2 kV/cm when most of the easily switchable ferroelectric 180° domains in a tetragonally distorted perovskite were already aligned with the field, it increased at a lower rate as this involved the orientation of the ferroelectric-ferroelastic 90°-domains. The loops became well-saturated without conductivity contributions. Remanent polarization (P

_{r}) increases up to 12 μC/cm

^{2}when a maximum applied field of 3 kV was used. Furthermore, the mentioned coercive field value indicated the easy polarization mechanism of the material, here related to a low tetragonal distortion, which is typically observed in “soft” type ceramics. Figure 6b shows a comparison between the best ferroelectric cycles for BCTZ1010, BCTZ1510, and BCTZ8-5 ceramics carried out at the same frequency (1Hz). Higher E

_{c}and P

_{r}values were achieved for BCTZ8-5 ceramics. Figure 6c displays the applied field dependence of the piezoelectric response for BCTZ8-5. The obtained displacement was achieved by applying a DC voltage from −2.4 to 2.4 kV while the strain signal was recorded. Therefore, a typical well-shaped strain-electric field (S-E) “butterfly” curve was obtained with a maximum displacement of 0.09%. Both the S-E and P-E loops presented a slightly asymmetric shape. Some reports suggest that the asymmetry of the loops can be related to internal fields resulting from microstructural defects, such as grain boundaries, pores, or dopant effects [38,39]. Moreover, the hysteresis of the butterfly loop was expected due to the normal ferroelectric character of the BCZT8-5. However, due to the soft ferroelectric behavior, it was not very pronounced.

^{5}, and 10

^{7}cycles, respectively. Figure 7d describes three different changes of the remanent polarization. In Stage A, from the beginning until 10

^{3}cycles, P

_{r}was nearly constant, determining a domain switching stability at small cycle numbers. In Stage B, between 10

^{3}to 10

^{5}cycles showed a fast decrease of up to 89%. Finally, in Stage C, the P

_{r}dropped off slightly and slowly to 81% after 10

^{7}cycles applied by less speed. Table 2 lists the average of remanent polarization, coercive field, and current at 1, 10

^{5}, and 10

^{7}cycles. Ferroelectric properties degradation has been associated with intrinsic defects, redistributions of imperfection after switching the dipole process, and punctual defects by doping [40]. Therefore, BCTZ8-5 showed a high electrical fatigue resistance, which makes it a promising candidate for actuator or nonvolatile random-access memory applications when prepared in thin film form [41].

## 4. Conclusions

^{7}cycles.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Reyes-Montero, A.; Castañeda-Guzmán, R.; Villafuerte-Castrejón, M.E.; Chávez-Carvayar, J.A.; Pardo, L. Perovskite-like structure ceramic materials and their design for electrical applications, Chapter 10. In Perovskite Ceramics: Recent Advances and Emerging Applications; Huaman, J., García-Rivera, V., Eds.; Elsevier: Amsterdam, The Netherlands, 2023. [Google Scholar]
- McCabe, E.E.; Bousquet, E.; Stockdale, C.P.J.; Deacon, C.A.; Tran, T.T.; Halasyamani, P.S.; Stennett, M.C.; Hyatt, N.C. Proper Ferroelectricity in the Dion-Jacobson Material CsBi
_{2}Ti_{2}NbO_{10}: Experiment and Theory. Chem. Mater.**2015**, 27, 8298–8309. [Google Scholar] [CrossRef] - Zheng, W.; Wang, X.; Zhang, X.; Chen, B.; Suo, H.; Xing, Z.; Wang, Y.; Wei, H.; Chen, J.; Guo, Y.; et al. Emerging Halide Perovskite Ferroelectrics. Adv. Mater.
**2023**. [Google Scholar] [CrossRef] - Weyland, F.; Acosta, M.; Koruza, J.; Breckner, P.; Rödel, J.; Kovak, N. Criticality: Concept to Enhance the Piezoelectric and Electrocaloric Properties of Ferroelectrics. Adv. Funct. Mater.
**2016**, 26, 7326–7333. [Google Scholar] [CrossRef] - Wang, H.; Gou, G.; Li, J. Ruddlesden-Popper perovskite sulfides A3B2S7: A new family of ferroelectric photovoltaic materials for the visible spectrum. Nano Energy
**2016**, 22, 507–513. [Google Scholar] [CrossRef] - Villafuerte-Castrejón, M.E.; Morán, E.; Reyes-Montero, A.; Vivar-Ocampo, R.; Peña-Jiménez, J.; Rea-López, S.; Pardo, L. Towards Lead-Free Piezoceramics: Facing a Synthesis Challenge. Materials
**2016**, 9, 21. [Google Scholar] [CrossRef] - Wei, H.; Wang, H.; Xia, Y.; Cui, D.; Shi, Y.; Dong, M.; Liu, C.; Ding, T.; Zhang, J.; Ma, Y.; et al. An overview of lead-free piezoelectric materials and devices. J. Mater. Chem. C
**2018**, 6, 12446. [Google Scholar] [CrossRef] - Wu, J. Perovskite lead-free piezoelectric ceramics. J. Appl. Phys.
**2020**, 127, 190901. [Google Scholar] [CrossRef] - Wang, D.; Fan, Z.; Rao, G.; Wang, G.; Liu, Y.; Yuan, C.; Ma, T.; Li, D.; Tan, X.; Lu, Z.; et al. Ultrahigh piezoelectricity in lead-free piezoceramics by synergistic design. Nano Energy
**2020**, 76, 104944. [Google Scholar] [CrossRef] - Verma, R.; Chauhan, A.; Batoo, K.; Jasrotia, R.; Sharma, A.; Kumar, R.; Hadi, M.; Raslan, E.; Labis, J.; Imran, A. Review—Modulation of Dielectric, Ferroelectric, and Piezoelectric Properties of Lead-Free BCZT Ceramics by Doping. ECS J. Solid State Sci. Technol.
**2021**, 10, 073004. [Google Scholar] [CrossRef] - Wang, H.; Wu, J. Phase transition, microstructure, and electrical properties of Ca, Zr, and Sn-modified BaTiO
_{3}lead-free ceramics. J. Alloys Compd.**2014**, 615, 969–974. [Google Scholar] [CrossRef] - Reyes-Montero, A.; Ramos-Alvarez, P.; González, A.; López-Juárez, R.; Villafuerte-Castrejón, M.E. Dielectric and Impedance Analysis on the Electrical Response of Lead-Free Ba
_{1−x}Ca_{x}Ti_{0.9}Zr_{0.1}O_{3}Ceramics at High Temperature Range. Appl. Sci.**2017**, 7, 214. [Google Scholar] [CrossRef] - Zhang, Y.; Glaum, J.; Groh, C.; Ehmke, M.; Blendell, J.; Bowman, K.; Hoffman, M.J. Correlation Between Piezoelectric Properties and Phase Coexistence in (Ba,Ca)(Ti,Zr)O
_{3}Ceramics. J. Am. Ceram. Soc.**2014**, 97, 2885–2891. [Google Scholar] [CrossRef] - Keeble, D.S.; Benabdallah, F.; Thomas, P.; Maglione, M.; Kreisel, J. Revised structural phase diagram of (Ba
_{0.7}Ca_{0.3}TiO_{3})-(BaZr_{0.2}Ti_{0.8}O_{3}). Appl. Phys. Lett.**2013**, 102, 092903. [Google Scholar] [CrossRef] - Zhang, L.; Zhang, M.; Wang, L.; Zhou, C.; Zhang, Z.; Yao, Y.; Zhang, L.; Xue, D.; Lou, X.; Ren, X. Phase transitions and the piezoelectricity around morphotropic phase boundary in Ba(Zr
_{0.2}Ti_{0.8})O_{3}-x(Ba_{0.7}Ca_{0.3})TiO_{3}lead-free solid solution. Appl. Phys. Lett.**2014**, 105, 162908. [Google Scholar] [CrossRef] - Park, J.G.; Oh, T.; Kim, Y.H. Dielectric properties and microstructural behaviour of B-site calcium-doped barium titanate ceramics. J. Mater. Sci.
**1992**, 27, 5713–5719. [Google Scholar] [CrossRef] - Bai, Y.; Matousek, A.; Tofel, P.; Bijalwan, V.; Nan, B.; Hughes, H.; Button, T.W. (Ba,Ca)(Zr,Ti)O
_{3}lead-free piezoelectric ceramics—The critical role of processing on properties. J. Eur. Ceram. Soc.**2015**, 35, 3445–3456. [Google Scholar] [CrossRef] - Adak, M.K.; Dhak, D. Perovskite lead-free dielectric ceramics: Highly promising materials for energy storage applications. In Perovskites Ceramics: Recent Advances and Emerging Applications; Elsevier: Amsterdam, The Netherlands, 2023; pp. 295–316. [Google Scholar]
- Abraham, K.M. Prospects and Limits of Energy Storage in Batteries. J. Phys. Chem. Lett.
**2015**, 6, 830–844. [Google Scholar] [CrossRef] - Sezer, N.; Koç, M. A comprehensive review on the state-of-the-art of piezoelectric energy harvesting. Nano Energy
**2021**, 80, 105567. [Google Scholar] [CrossRef] - Muhammad, R.; Ali, A.; Camargo, J.; Castro, M.; Lei, W.; Song, K.; Wang, D. Enhanced Thermal Stability in Dielectric Properties of NaNbO
_{3}-Modified BaTiO_{3}-BiMg_{1/2}Ti_{1/2}O_{3}Ceramics for X9R.MLCC Applications. Crystals**2022**, 12, 141. [Google Scholar] [CrossRef] - Sarker, M.R.; Julai, S.; Sabri, M.; Said, S.; Islam, M.; Tahir, M. Review of piezoelectric energy harvesting system and application of optimization techniques to enhance the performance of the harvesting system. Sens. Actuator A Phys.
**2019**, 300, 111634. [Google Scholar] [CrossRef] - Li, W.; Xu, Z.; Chu, R.; Fu, P.; Zang, G. Piezoelectric and Dielectric Properties of (Ba
_{1−x}Ca_{x})(Ti_{0.95}Zr_{0.05})O_{3}Lead-Free Ceramics. J. Am. Ceram. Soc.**2010**, 93, 2942–2944. [Google Scholar] [CrossRef] - Reyes-Montero, A.; Rubio-Marcos, F.; Pardo, L.; del Campo, A.; López-Juárez, R.; Villafuerte-Castrejón, M.E. Electric field effect on the microstructure and properties of Ba
_{0.9}Ca_{0.1}Ti_{0.9}Zr_{0.1}O_{3}. J. Mater. Chem. A**2018**, 6, 5419–5429. [Google Scholar] [CrossRef] - Reyes-Montero, A.; Rubio-Marcos, F.; Fuentes-Cobas, L.; del Campo, A.; Castañeda-Guzmán, R.; Villafuerte-Castrejón, M.E. Confocal Raman Microscopy, Synchrotron X-ray Diffraction, and Photoacoustic Study of Ba
_{0.85}Ca_{0.15}Ti_{0.90}Zr_{0.10}O_{3}: Understanding Structural and Microstructural Response to the Electric Field. ACS Appl. Electron. Mater.**2021**, 3, 2966–2976. [Google Scholar] [CrossRef] - Alemany, C.; Pardo, L.; Jiménez, B.; Carmona, F.; Mendiola, J.; González, A.M. Automatic iterative evaluation of complex material constants in piezoelectric ceramics. J. Phys. D Appl. Phys.
**1994**, 27, 148–155. [Google Scholar] [CrossRef] - Alemany, C.; González, A.; Pardo, L.; Jiménez, B.; Carmona, F.; Mendiola, J. Automatic determination of complex constants of piezoelectric lossy materials in the radial mode. J. Phys. D Appl. Phys.
**1995**, 28, 945–956. [Google Scholar] [CrossRef] - Pardo, L.; de Espinosa, F.M.; García, A.; Brebøl, K. Choosing the best geometries for the linear characterization of lossy piezoceramics: Study of the thickness-poled shear plate. Appl. Phys. Lett.
**2008**, 92, 172907. [Google Scholar] [CrossRef] - Sherrit, S.; Masys, T.; Wiederick, H.; Mukherjee, B.K. Determination of the reduced matrix of the piezoelectric, dielectric, and elastic material constants for a piezoelectric material with C∞ symmetry. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2011**, 58, 1714–1720. [Google Scholar] [CrossRef] - Betancourt-Cantera, L.G.; Bolarín-Miró, A.; Cortés-Escobedo, C.; Hernández-Cruz, L.; Jesús, F.S.-D. Structural transitions and multiferroic properties of high Ni-doped BiFeO
_{3}. J. Magn. Magn. Mater.**2018**, 456, 381–389. [Google Scholar] [CrossRef] - Tian, Y.; Gong, Y.; Zhang, Z.; Meng, D. Phase evolutions and electric properties of BaTiO
_{3}ceramics by a low-temperature sinterign process. J. Mater. Sci. Mater. Electron.**2014**, 25, 5467–5474. [Google Scholar] [CrossRef] - Bharathi, P.; Varma, K.B.R. Grain and the concomitant ferroelectric domain size dependent physical properties of Ba
_{0.85}Ca_{0.15}Zr_{0.1}Ti_{0.9}O_{3}ceramics fabricated using powders derived from oxalate precursor route. J. Appl. Phys.**2014**, 116, 164107. [Google Scholar] [CrossRef] - Uchino, K.; Nomura, S. Critical exponents of the dielectric constants in diffused-phase-transition crystals. Ferroelectrics
**1982**, 44, 55–61. [Google Scholar] [CrossRef] - Reyes-Montero, A.; Pardo, L.; López-Juárez, R.; González, A.; Rea-López, S.; Cruz, M.; Villafuerte-Castrejón, M.E. Sub-10 μm grain size, Ba
_{1−x}Ca_{x}Ti_{0.9}Zr_{0.1}O_{3}(x = 0.10 and x = 0.15) piezoceramics processed using a reduced thermal treatment. Smart Mater. Struct.**2015**, 24, 065033. [Google Scholar] [CrossRef] - Reyes-Montero, A.; Pardo, L.; García, A.; González, A.; Villafuerte-Castrejón, M.E. Ba
_{1-x}Ca_{x}Ti_{0.90}Zr_{0.10}O_{3}shear properties and their frequency dependence determined from ceramic plates by an effective method for resonance decoupling. J. Alloys Compd.**2019**, 806, 428–438. [Google Scholar] [CrossRef] - Xiao, A.; Xie, X.; He, L.; Yang, Y.; Ji, Y. Enhanced Piezoelectric Properties in a Single-Phase Region of Sm-Modified Lead-Free (Ba,Ca)(Zr,Ti)O
_{3}Ceramics. Materials**2022**, 15, 7839. [Google Scholar] [CrossRef] [PubMed] - Pardo, L.; García, A.; Shubert, F.; Kynast, A.; Scholehwar, T.; Jacas, A.; Bartolomé, J.F. Determination of the PIC700 Ceramic’s Complex Piezo-Dielectric and Elastic Matrices from Manageable Aspect Ratio Resonators. Materials
**2021**, 14, 4076. [Google Scholar] [CrossRef] [PubMed] - Schenk, T.; Yurchuk, E.; Muller, S.; Schroeder, U.; Starschich, S.; Böttger, U.; Mikilajick, T. About the deformation of ferroelectric hystereses. Appl. Phys. Rev.
**2014**, 1, 041103. [Google Scholar] [CrossRef] - Jin, L.; Li, F.; Zhang, S. Decoding the Fingerprint of Ferroelectric Loops: Comprehension of the Material Properties and Structures. J. Am. Ceram. Soc.
**2014**, 97, 1–27. [Google Scholar] [CrossRef] - Wang, C.; He, C.; Wang, Z.; Li, X.; Yang, X.; Liu, Y.; Long, X. Fatigue endurance enhancement of Sn-doped Pb(Lu
_{1/2}Nb_{1/2})O_{3}-PbTiO_{3}ceramics. RCS Adv.**2018**, 8, 11633–11642. [Google Scholar] [CrossRef] - Namsar, O.; Pojprapai, S.; Watcharapasorn, A.; Jiansirisomboon, S. Polarization fatigue in ferroelectric Pb(Zr
_{0.52}Ti_{0.48})O_{3}-SrBi_{2}Nb_{2}O_{9}ceramics. Electron. Mater. Lett.**2015**, 11, 881–889. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) XRD patterns of BCTZ8-5 powder and sintered ceramic obtained by conventional solid-state reaction. (

**b**) SEM micrograph of the fracture surface of the sintered pellet.

**Figure 2.**(

**a**) Temperature-dependence of dielectric permittivity and losses for BCTZ8-5 sintered ceramics. (

**b**) Curie–Weiss fitting curve for BCTZ8-5; the inset shows the plot of log (1/ε − 1/ε

_{r}) vs. log (T − T

_{m}).

**Figure 3.**A comparison of the dielectric permittivity and losses of BCTZ8-5 against another two important BCTZ compositions: Ba

_{0.85}Ca

_{0.15}Ti

_{0.90}Zr

_{0.10}O

_{3}(BCTZ1510) and Ba

_{0.90}Ca

_{0.10}Ti

_{0.90}Zr

_{0.10}O

_{3}(BCTZ1010) calculated at 1 kHz.

**Figure 4.**Impedance spectra as R and G plots of the: (

**a**) planar resonance of a thin disk, thickness poled and excited, (

**b**) thickness resonance mode of the same disk, and (

**c**) shear resonance mode of thickness poled and longitudinally excited plates of BCZT8-5. The symbols are the experimental data, and the dotted lines are the reconstructed peaks after the calculation of the material coefficients.

**Figure 5.**Thermal stability analysis of (

**a**) piezoelectric coefficients and (

**b**) the electromechanical coupling factors of BCTZ8-5 ceramics obtained from the radial and shear resonances of thickness-poled thin disks and plates of BCTZ8-5 ceramics.

**Figure 6.**(

**a**) Ferroelectric hysteresis loop at 1 Hz of BCTZ8-5 ceramics for the maximum applied field of 30 kV/cm. (

**b**) Ferroelectric loops at 1 Hz for BCTZ8-5 ceramic in comparison with BCZT1510 and BCTZ1010 ceramics. (

**c**) S-E loop for BCTZ8-5 ceramic.

**Figure 7.**The changes of (

**a**) polarization, (

**c**) current, and (

**d**) remanent polarization of the BCTZ8-5 sample during different fatigue cycling analyses. (

**b**) A magnification of the polarization axis with the different obtained P

_{r}values at 1, 10

^{5}, and 10

^{7}cycles.

**Table 1.**Piezoelectric, dielectric, and elastic complex coefficients at resonance of BCZT8-5 ceramics (ρ = 5.65 g/cm

^{3}) from resonances of thickness-poled thin disks and plates measured at 25 °C. Electromechanical coupling factors and frequency numbers are also shown.

Elastic stiffness coefficients (c_{ij}* _{=} (c_{ij})_{real} + i(c_{ij})_{img}) (10^{10} N/m^{2}) | ||||||||||

${c}_{11}^{D}$ | ${c}_{33}^{D}$ | ${c}_{55}^{D}$ | ${c}_{11}^{E}$ | ${c}_{33}^{E}$ | ${c}_{55}^{E}$ | |||||

real | 11.15 | 12.39 | 3.81 | 10.05 | 11.97 | 3.49 | ||||

Q_{m} | 150 | 51 | 65 | 102 | 75 | 43 | ||||

Elastic compliance coefficients (s_{ij}* _{=} (s_{ij})_{real} + i(s_{ij})_{img}) (10^{−12} m^{2}/N) | ||||||||||

${s}_{11}^{D}$ | ${s}_{12}^{D}$ | ${s}_{55}^{D}$ | ${s}_{11}^{E}$ | ${s}_{12}^{E}$ | ${s}_{55}^{E}$ | ${s}_{66}^{E}$ | ||||

real | 11.31 | −5.15 | 22.35 | 11.80 | −4.67 | 24.32 | 32.93 | |||

Q_{m} | 117 | 83 | 65 | 103 | 106 | 43 | 104 | |||

Piezoelectric coefficients | ||||||||||

d_{ij}*_{=} (d_{ij})_{real} + i(d_{ij})_{img}(10 ^{−12} C/N) | e_{ij}*_{=} (e_{ij})_{real} + i(e_{ij})_{img}(C/m ^{2}) | g_{ij}*_{=} (g_{ij})_{real} + i(g_{ij})_{img}(10 ^{−3} Vm/N) | h_{ij}*_{=} (h_{ij})_{real} + i(h_{ij})_{img}(10 ^{8} V/m) | |||||||

^{d}${d}_{33}$ | ${d}_{31}$ | ${d}_{15}$ | ${e}_{33}$ | ${e}_{15}$ | ^{d}${g}_{33}$ | ${g}_{31}$ | ${g}_{15}$ | ${h}_{33}$ | ${h}_{15}$ | |

real | 320 | −99.06 | 175.72 | 15.91 | 5.14 | 14 | −4.90 | 9.21 | 5.95 | 3.61 |

imaginary | 3.40 | −14.31 | 0.23 | −0.39 | 0.02 | −0.36 | 0.55 | −0.09 | ||

(d) measured in a d_{33}-meterElectromechanical coupling factors (%) and frequency numbers (N (kHz.mm)) | ||||||||||

${k}_{31}$ | ${k}_{15}$ | ${N}_{15}$ | ${k}_{t}$ | ${N}_{t}$ | ${k}_{p}$ | ${N}_{p}$ | ||||

28.2 | 27.4 | 1294 | 30.4 | 2514 | 36.9 | 2829 | ||||

Dielectric permittivity and regression factors of the iterative method | ||||||||||

${\epsilon}_{33}^{T}$ | ${\epsilon}_{33}^{S}$ | ${\epsilon}_{11}^{T}$ | ${\epsilon}_{11}^{S}$ | $\mathcal{R}$^{2} | ||||||

real | 2286 | 2330 | 2023 | 1873 | Radial | Thickness | Shear | |||

tanδ | 0.03 | 0.09 | 0.04 | 0.03 | 0.9929 | 0.9001 | 0.9593 |

Cycles [n] | E_{c}[kV/cm] | P_{r}[μC/cm ^{2}] | I [mA] |
---|---|---|---|

1 | 3.5 ± 0.2 | 9.5 ± 0.3 | 0.46 ± 0.01 |

10^{5} | 3.1 ± 0.1 | 8.5 ± 0.2 | 0.45 ± 0.01 |

10^{7} | 3.3 ± 0.1 | 7.7 ± 0.1 | 0.41 ± 0.01 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hernández-Moreno, A.C.; Reyes-Montero, A.; Carreño-Jiménez, B.; Acuautla, M.; Pardo, L.
Ferroelectric, Dielectric and Electromechanical Performance of Ba_{0.92}Ca_{0.08}Ti_{0.95}Zr_{0.05}O_{3} Ceramics with an Enhanced Curie Temperature. *Materials* **2023**, *16*, 2268.
https://doi.org/10.3390/ma16062268

**AMA Style**

Hernández-Moreno AC, Reyes-Montero A, Carreño-Jiménez B, Acuautla M, Pardo L.
Ferroelectric, Dielectric and Electromechanical Performance of Ba_{0.92}Ca_{0.08}Ti_{0.95}Zr_{0.05}O_{3} Ceramics with an Enhanced Curie Temperature. *Materials*. 2023; 16(6):2268.
https://doi.org/10.3390/ma16062268

**Chicago/Turabian Style**

Hernández-Moreno, Ana Cristina, Armando Reyes-Montero, Brenda Carreño-Jiménez, Mónica Acuautla, and Lorena Pardo.
2023. "Ferroelectric, Dielectric and Electromechanical Performance of Ba_{0.92}Ca_{0.08}Ti_{0.95}Zr_{0.05}O_{3} Ceramics with an Enhanced Curie Temperature" *Materials* 16, no. 6: 2268.
https://doi.org/10.3390/ma16062268