Abstract
Dense microstructure BaTiO₃ (BT) ceramic with c/a ~1.0144 and average grain size ~7.8 μmis developed by achieving the ferroelectric parameters Psat. = 24.13 μC/cm2 and Pr = 10.42 μC/cm2 with lower coercive field of Ec = 2.047 kV/cm. For BT ceramic, the “sprout” shape nature is observed for strain-electric field measurements with remnant strain ~ 0.212%, converse piezoelectric constant ~376.35 pm/V and electrostrictive coefficient Q33~ 0.03493 m4/C2. To tune the piezoelectric properties of BT ceramic, the substitutions of Ca2+ and Sn4+, Zr4+ are done for Ba2+ and Ti4+ sites respectively. The Ba0.7Ca0.3Ti1-xSnxO3 (x = 0.00, 0.025, 0.050, 0.075, and 0.1, BCST) system was studied with ferroelectric, piezoelectric and electrostrictive properties. The electrostrictive coefficient (Q33) ~ 0.0667 m4/C2 was observed for x = 0.075 and it is higher than the lead-based electrostrictive materials. Another (1-X) Ba0.95Ca0.05Ti0.92Sn0.08O3 (BCST) – (X) Ba0.95Ca0.05Ti0.92Zr0.08O3 (BCZT), ceramics (x = 0.00, 0.25, 0.50, 0.75, and 1) is studied. The BCST-BCZT ceramic system shows the increase of polymorphic phase transition temperatures toward the room temperature by Ca2+, Sn4+ and Zr4+ substitution. For BCST-BCZT system the composition x = 0.75 exhibits the d33, and Q33 values of 310 pC/N, 385 pm/V and 0.089 m4/C2 respectively which is greater than BT ceramics.
Keywords
- lead-free piezoelectric
- BaTiO3
- ferroelectric
- curie temperature
- electrostrictive coefficient
1. Introduction
Currently, most of the electronic devices and naval departments use the materials that are based on interconversion of mechanical and electrical energies i.e. piezoelectric effect for actuator/transducer/energy harvester applications. The examples of these devices include ink-jet printers, fuel injection actuators in cars, transducers for ultrasonic imaging and therapy in medicine, sensors and actuators for vibration control, and sonars. In many of devices, (PbZr1 − xTixO3, PZT) based piezoelectric materials are mainly employed due to its excellent piezoelectric properties viz. piezoelectric charge coefficient (
Barium titanate, BaTiO3 (BT) is the first polycrystalline ceramic ever discovered that exhibits the stable piezoelectric and dielectric properties; hence considered as a promising lead-free ferroelectric ceramic with perovskite ABO3 structure [2]. BT is one of the promising ferroelectric materials specifically known for its wide range of applications from dielectric capacitor to non-linear optic devices. For BT ceramic, below Curie temperature (120°C), the vector of the spontaneous polarization points in the [001] direction (tetragonal phase), below 5°C it reorients in the [011] (orthorhombic phase), and below −90°C in [111] direction (rhombohedral phase) [3, 4, 5]. The present scenario of BT based electroceramics is to bring the polymorphic phase transition (PPT) i.e. Rhombohedral to orthorhombic (TR-O) and Orthorhombic to Tetragonal (TO-T) close to room temperature to achieve the phase coexistence at 300 K and hence shows the enhanced piezoelectric properties [6]. For Zr4+, Sn4+, and Hf4+ substitution at Ti4+ site in BaTiO3 increases PPT temperatures from low temperatures (0°C and −90°C) to room temperature [6]. Recently, high performance BT-based ceramics such as (Ba,Ca)(Ti,Zr)O3 (BCZT) and (Ba,Ca)(Ti,Sn)O3 (BCST) prepared by substitution of Ca2+ at A-site and Zr4+/Sn4+ at B-site showed the properties comparable to that of soft PZT materials [7, 8, 9, 10, 11, 12]. Furthermore, the substitution of Ca2+at Ba2+ in BaTiO3-CaTiO3 system (i.e. to form Ba1−xCaxTiO3 (BCT) ceramics) results in a slight increase in the Curie temperature (TC) and on the other hand suppresses the orthorhombic to tetragonal (TO-T) transition temperature. This is one of the important considerations in developing the temperature stability of piezoelectric properties for various practical applications [13]. Many research groups have reported the dielectric, diffused phase transition, ferroelectric and piezoelectric properties of BCZT and BCST ceramics [6, 7, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22]. However, there is a need of detailed investigation of electrostrictive properties of BT based lead free electroceramics which are correlated with the structure–property-composition having the phase coexistence of orthorhombic-tetragonal (O-T), Rhombohedral-Orthorhombic (R-O) and Rhombohedral-Tetragonal (R-T) lattice symmetries, at room temperature. Thus, in view of the above, we have investigated the ferroelectric, piezoelectric and electrostrictive properties of Ca2+, Sn4+ and Zr4+ modified BaTiO3 ceramics and tried to correlate the observed results with the phase coexistence of noncentrosymmetric lattice symmetries achieved at room temperature.
2. Experimental details
2.1. Synthesis
2.1.1. BaTiO3 (BT) synthesis
Barium titanate, BaTiO3 polycrystalline electroceramic was synthesized by conventional solid-state reaction method. Staring raw materials barium carbonate (BaCO3, ≥ 99%) and titanium dioxide (TiO2, ≥ 99%) (from Sigma Aldrich) were weighted and mixed in stoichiometric proportions and ball-milled for 15 h in the ethanol medium. After ball milling slurry were dried at 100°C overnight and dried powder grounded well. Then the powder pressed into pellets of 2 cm in diameter and 4–5 mm in thickness and calcined at 1260°C for 5 h. The calcined pellets were crushed and grounded well to form the fine powder. Thereafter, pellets with 10 mm diameter and 0.6–1 mm in thickness were prepared from calcined powder by using poly vinyl alcohol (PVA) as a binder. Finally, the prepared pellets were sintered at 1300°C for 5 h.
2.1.2. Ba0.7Ca0.3Ti1−xSnxO3 (BCST) synthesis
Ba0.7Ca0.3Ti1−xSnxO3 (BCST) ceramics with
2.1.3. (1−x) Ba0.95Ca0.05Ti0.92Sn0.08O3-xBa0.95Ca0.05Ti0.92Zr0.08O3 [(1−x)BCST-xBCZT] synthesis
The (1−x) Ba0.95Ca0.05Ti0.92Sn0.08O3-xBa0.95Ca0.05Ti0.92Zr0.08O3 [(1−x)BCST-xBCZT] lead-free piezoelectric ceramics with x = 0, 0.25, 0.50, 0.75, 1 were prepared by mixed oxide solid state reaction. High purity analytical grade BaCO3, CaCO3, TiO2, SnO2, and ZrO2 (Hi Media; purity ≥99%) chemicals were mixed in stoichiometric proportion and ball milled for 24 h using ethanol medium. Thereafter solutions were dried and calcined at 1200°C for 10 h in air. Calcined powders were grounded well and pressed into pellets of 1 cm in diameter and ~ 0.7–0.8 mm in thickness using 5 wt% polyvinyl alcohol (PVA) as a binder. After burning out PVA at 600°C the samples were sintered at 1350°C for 10 h.
All ferroelectric materials system investigated in this book chapter was prepared and characterized for structural information at functional ceramics laboratory, Savitribai Phule Pune University.
2.2. Characterizations
The phase formation, crystal lattice symmetry and microstructural features of the samples were examined using the X-ray diffraction (XRD) with a CuKα radiation (λ = 1.5406 Å; D8 Advance, Bruker Inc., Germany) and the scanning electron microscopy (JEOL-JSM 6306A, Japan). The relative density of sintered pellets was estimated from the ratio of the apparent density measured by Archimedes’ principle and the theoretical density calculated using crystal cell parameters. For electrical property measurements, silver paste was applied on both sides of the polished surfaces of pellet and then the sample was cured at 200°C for overnight to dry out the moisture prior to any measurements. Dielectric constant (εr) and loss tangent (tanδ) were measured as a function of temperature from −100 to 150°C at 100 kHz using inductance-capacitance-resistance (LCR) meter (HIOKI- 3532-50, Japan), connected to a computer-controlled furnace. Polarization (
3. Results and discussion
3.1. High dense BaTiO3 ceramic with their ferroelectric and piezoelectric properties
X-ray diffraction study confirmed the tetragonal crystal structure having c/a ~ 1.0144. The dense microstructure was evidenced from morphological studies with an average grain size ~ 7.8 μm as shown in Figure 1(a). Figure 1(b) shows the temperature dependent variation of the dielectric permittivity (εr) in the range of 25–160°C at fixed frequencies viz. 1, 25, 50, 75 and100 kHz for BT ceramic sintered at 1300°C. The phase transition from ferroelectric to paraelectric was observed at Curie temperature (Tc ~ 125°C) with εr = 5617 [23]. Figure 1(c) shows the polarization-electric field (P-E) hysteresis loops for BaTiO3 ceramic measured at 0.1 Hz and room temperature. Typical hysteresis loop confirms the ferroelectric nature of the sample at room temperature. The hysteresis loop is well saturated and fully developed, indicate that external field has enough energy to switch and rotate the ferroelectric domain of BT ceramic. The saturation and remnant polarization, Psat = 24.13 μC/cm2 and Pr = 10.42 μC/cm2 was observed at the electric field strength of 57.14 kV/cm having lower coercive field of Ec = 2.047 kV/cm. The reason for achieving improved ferroelectric properties in the present work may be attributed to the high value of c/a ratio ~1.014 and dense microstructure with average grain size 7.8 μm. The lower Ec indicate that low energy loss during electric field sweep having low energy barriers for polarization rotation i.e. soft ferroelectric nature. Low energy barrier can greatly promote the polarization rotation and effectively enhance the piezoelectric properties [3]. Figure 1(d) shows variation of polarization current density with respect to applied electric field. Current density exhibits the peaking behavior for both positive and negative cycle of applied electric field. The peaking behavior is a characteristic feature of the good ferroelectric ceramic having saturation polarization. Therefore, in present work we are successful to obtain the high-quality BT ceramic having saturated polarization states [23]. Thus, the observed ferroelectric properties are promising for ferroelectric memory device applications with larger
Figure 1(e) shows the bipolar electric field induced strain curves measured for BT sample at frequency of 0.1 Hz with respect to bipolar electric fields. Sample revealed the “sprout” shape loop instead of “butterfly” loop which confirms the improved piezoelectric behavior [4]. Which indicates that the BT ceramic is not showing negative strain behavior, therefore here we should note that the enhancement of strain (S) is due to the sprout shape of bipolar electric field induced strain curve [4]. For electric field E = 57.14 kV/cm, better value of remnant strain 0.212% and higher value of the converse piezoelectric coefficient d*33 = 376 pm/V were observed. Unfortunately, practical implementations of BT-based ceramics for commercial actuator applications are still limited by their inferior electromechanical properties as compare to those of their conventional PZT counterparts. In the present study, it is worth pointing out that the strain reaches 0.212% at E = 57.14 kV/cm which is a promising value for lead-free piezoelectric ceramic. Large value of strain output of BaTiO3 is accompanied by small strain hysteresis which enabling the materials to be a promising potential for actuator applications. It is well known that domain switching and domain wall motion of BaTiO3 ceramic could contribute to field-induced strain as an extrinsic effect. Since the extrinsic contribution is sensitive to external excitation, the large electric field in strain measurement may be responsible for a larger d*33 = 376 pm/V [23]. Here for BaTiO3 ceramic the strain-electric field hysteresis loop, which resembles the “sprout” shape loop, is may be due to the three types of effects; one is the normal converse piezoelectric effect of the lattice and other two are due to switching and movement of domain walls of BaTiO3 [24]. The electrostriction coefficients Q is a four-rank tensor property that describes the relationship between polarization-induced strain (S) which proportional to the square of polarization (P) and is given by
3.2. Tune the ferroelectric and piezoelectric properties of BaTiO3 by Ca2+ and Sn4+ substitution
The phase formation, microstructural aspects and dielectric properties for Ba0.7Ca0.3Ti1−xSnxO3 (BCST) ceramics with
Figure 3(a-e), shows the polarization-electric field (
An observation made from Figure 3(a-e) reveals that the compositions with
The bipolar strain (S) versus electric field (E) behavior was investigated for all the BCST samples and is shown in Figure 4(a-e). They exhibit a typical butterfly loop, which is a feature of piezoelectric system for biaxial field. It is well-known that the butterfly loop is observed due to the normal converse piezoelectric effect of the lattice along with the switching and movement of domain walls. Here, all the BCST ceramics show the hysteretic strain behavior which may be associated with the domain reorientation. The converse piezoelectric constant is defined as
The average value of
3.3. Tune the ferroelectric and piezoelectric properties of BaTiO3 by Ca2+, Sn4+ and Zr4+ substitution
Figure 6(a) shows the XRD patterns of the (1−x) Ba0.95Ca0.05Ti0.92Sn0.08O3 (BCST) – (X)Ba0.95Ca0.05Ti0.92Zr0.08O3 (BCZT) i.e. (1−x) BCST-xBCZT ceramics with x = 0.00, 0.25, 0.50, 0.75, and 1 measured at room temperature. All the ceramics possess the single-phase perovskite structure, and no secondary phases are detected, showing the formation of a stable solid solution between BCST and BCZT. The standard diffraction peaks cited from the tetragonal (T) BaTiO3 (PDF#81-2205), the orthorhombic (O) (PDF#81–2200) and rhombohedral (R) (PDF#85–0368) are indicated by vertical lines for comparison. Sample with x = 0.00, shows the phase coexistence of O and T phases [34]. The diffraction peaks for 0.25 ≤ x ≥ 0.5 well matches with PDF#81–2200, suggesting that the crystalline structure of samples is of orthorhombic symmetry. The composition x = 1 reveals the rhombohedral phase according to PDF#85–0368. The composition x = 0.75 showed the phase coexistence of orthorhombic and rhombohedral lattice symmetries. The change in diffraction peak around 45° as shown in Figure 6(b) the gradual transitions from orthorhombic to mixed phase to rhombohedral symmetry of the unit cell at room temperature, due to the increase of x content that can be favorable to enhance the piezoelectric properties. Figure 7 shows the temperature dependence of dielectric constant (
The micrograph images for (1−x) BCST-xBCZT system is shown in Figure 8, well densified and pore-free microstructure, consisting of irregular grains in which the large one is approximately 35 μm and the small is only about 6 μm with well-defined grain boundaries were observed. Clear grain boundary observed for ceramics samples could enhance the density and helps to improve the electrical properties of the BaTiO3 based ceramics [42, 43]. All the obtained ceramics are well sintered and acquires the relative densities in the range of 93–95% with average grain size 19.4–25 μm. Figure 9 shows the polarization versus electric field hysteresis loops of (1−x) BCST-xBCZT ceramics with different x content measured with an applied electric field up to 30–40 kV/cm at 0.1 Hz. All samples possess a typical ferroelectric polarization hysteresis loop with remnant polarization (Pr), saturation polarization (Ps) and coercive field (Ec). The ferroelectric properties, i.e. the Pr and the coercive field Ec are observed in the range of 4.7–6.6 μC/cm2 and 2.6–3.6 kV/cm respectively. Remnant polarization increases with increase in BCZT content. Sample with x = 0.75 shows superior value of remnant polarization 6.3 μC/cm2 with lower value of Ec = 2.9 kV/cm this can be attributed to the dipole moments of the compositions near the R-O phase coexistence being able to reorient dipoles more completely [34]. The decrease of
Figure 10 shows the bipolar field-induced strain (S-E) curves for (1−x) BCST-xBCZT ceramics measured with an applied electric field up to 30–40 kV/cm at 0.1 Hz. All samples reveal the butterfly shaped S-E loops that are typical feature of ferroelectric materials. A prominent enhancement in the maximum positive strain response from 0.086% at x = 0.00 to 0.122% at x = 0.75 is observed. In ferroelectric, electric field induced butterfly like hysteresis strain loops are occurs fundamentally due to the intrinsic and extrinsic contribution [41]. By modifying the chemical composition of BaTiO3 based masteries one can achieve phase coexistence that facilitated the polarization rotation and enhance the intrinsic contribution (lattice strain) [10, 34, 41]. In ferroelectric materials the domain switching provides the extrinsic contribution, it happens when ferroelectric materials change the spontaneous polarized state along the applied electric field direction. Therefore, the higher strain S = 0.122 observed for x = 0.75 is attributed to the R-O phase coexistence. However, the extrinsic contribution is attributed to the lower value of Ec which supports to easy domain switching and contributes to achieve the superior piezoelectric properties. Figure 10 shows variation of direct piezoelectric coefficient
4. Future scope and implications
The search of lead-free piezoelectric ceramics has significantly improved over the last two decades. The deep research in ferroelectric materials can develop better ferroelectric and electrostrictive ceramics. It is necessary to develop lead free ceramic materials having morphotropic phase boundary like PZT and improve the temperature dependence of piezoelectric properties of lead free ceramics. Lower Curie temperature of BT based ceramics hinders their use in practical applications. Improvement in this regime is most welcome in the future. The improvement in piezoelectric properties of BT based ceramics has done in last few years which are attractive for various applications; though need to improve other basic properties such as Curie temperature and temperature dependent piezoelectric properties to accelerate the use of BT based materials in piezoelectric applications. It is difficult to replace the PZT by single lead free piezoelectric material. Therefore, need to develop different lead-free materials which can fulfill the different challenges and can useful for various piezoelectric applications. The BT based polycrystalline electroceramics possess inferior properties than BT based single crystal materials. In future this gap can be fulfilled by textured piezoceramics. The textured piezoelectric ceramics have potential to fulfill the gap between polycrystalline and single crystal piezoelectric ceramics. In conventional polycrystalline ceramics grains are randomly oriented while in the textured polycrystalline ceramics grain structure is oriented along one of the crystallographic direction. Due to the orientation of grain structure in specific crystallographic direction, the textured piezoelectric materials give higher performance characteristics close to single crystal materials. Also, as compare to single crystal materials the textured polycrystalline ceramics do not suffer from fracture toughness issues. In future textured BT based piezoelectric materials can become potential materials to replace the lead based piezoelectric materials.
5. Conclusions
We have successfully developed the superior quality high dense microstructure BaTiO3 (BT) electroceramic material with
Acknowledgments
RCK thankfully acknowledge the Science and Engineering Research Board (SERB)-DST, Government of India (File No. EMR/2016/001750) for providing the research funds under Extra Mural Research Funding (Individual Centric) scheme.
References
- 1.
Rödel J, Webber KG, Dittmer R, Jo W, Kimura M, Damjanovic D. Transferring lead-free piezoelectric ceramics into application. Journal of the European Ceramic Society. 2015; 35 :1659-1681 - 2.
Mahesh MLV, Bhanu Prasad VV, James AR. Effect of sintering temperature on the microstructure and electrical properties of zirconium doped barium titanate ceramics. Journal of Materials Science: Materials in Electronics. 2013; 24 :4684-4692 - 3.
Acosta M, Novak N, Rojas V, Patel S, Vaish R, Koruza J, Rossetti GA, Rödel J. BaTiO3-based piezoelectrics: Fundamentals, current status, and perspectives. Applied Physics Reviews. 2017; 4 :041305 - 4.
Wang JJ, Meng FY, Ma XQ, Xu MX, Chen LQ. Lattice, elastic, polarization, and electrostrictive properties of BaTiO3 from first-principles. Journal of Applied Physics. 2010; 108 :034107 - 5.
Li YL, Cross LE, Chen LQ. A phenomenological thermodynamic potential for single crystals. Journal of Applied Physics. 2005; 98 :064101 - 6.
Kalyani AK, Brajesh K, Senyshyn A, et al. Orthorhombic-tetragonal phase coexistence and enhanced piezo-response at room temperature in Zr, Sn, and Hf modified BaTiO3. Applied Physics Letters. 2014; 104 :252906 - 7.
Liu W, Ren X. Large piezoelectric effect in Pb-free ceramics. Physical Review Letters. 2009; 103 :257602 - 8.
Deluca M, Stoleriu L, Curecheriu LP, et al. High-field dielectric properties and Raman spectroscopic investigation of the ferroelectric-to-relaxor crossover in BaSnxTi1−xO3 ceramics. Journal of Applied Physics. 2012; 111 :084102 - 9.
Zhao L, Zhang BP, Zhou PF, et al. Phase structure and property evaluation of (Ba,Ca)(Ti,Sn)O3 sintered with Li2CO3 addition at low temperature. Journal of the American Ceramic Society. 2014; 97 :2164-2169 - 10.
Zhu LF, Zhang BP, Zhao L, et al. High piezoelectricity of BaTiO3-CaTiO3- BaSnO3 lead-free ceramics. Journal of Materials Chemistry C. 2014; 2 :4764 - 11.
Mahesh MLV, Bhanu Prasad VV, James AR. Enhanced dielectric and ferroelectric properties of lead-free Ba(Zr0.15Ti0.85)O3 ceramics compacted by cold isostatic pressing. Journal of Alloys and Compounds. 2014; 611 :43-49 - 12.
Shen ZY, Li JF. Enhancement of piezoelectric constant d33 in BaTiO3 ceramics due to nano-domain structure. Journal of the Ceramic Society of Japan. 2010; 118 :940-943 - 13.
Zhu XN, Zhang W, Chen XM. Enhanced dielectric and ferroelectric characteristics in Ca-modified BaTiO3 ceramics. AIP Advances. 2013; 3 . DOI: 082125 - 14.
Wei XY, Feng YJ, Yao X. Dielectric relaxation behavior in barium stannate titanate ferroelectric ceramics with diffused phase transition. Applied Physics Letters. 2003; 83 :2031-2033 - 15.
Lu SG, Xu ZK, Chen H. Tunability and relaxor properties of ferroelectric barium stannate titanate ceramics. Applied Physics Letters. 2004; 85 :5319-5321 - 16.
Singh KC, Nath AK, Thakur OP. Structural, electrical and piezoelectric properties of nanocrystalline tin-substituted barium titanate ceramics. Journal of Alloys and Compounds. 2011; 509 :2597-2601 - 17.
Cai W, Fan Y, Gao J, et al. Microstructure, dielectric properties and diffuse phase transition of barium stannate titanate ceramics. Journal of Materials Science: Materials in Electronics. 2011; 22 :265-272 - 18.
Horchidan N, Ianculescu AC, Vasilescu CA, et al. Multiscale study of ferroelectric-relaxor crossover in BaSnxTi1−xO3 ceramics. Journal of the European Ceramic Society. 2014; 34 :3661-3674 - 19.
Yasuda N, Ohwa H, Asano SH. Dielectric properties and phase transitions of Ba(Ti1−xSnx)O3 solid solution. Japanese Journal of Applied Physics. 1996; 35 :5099 - 20.
Jonker GH. Philips Technical Review. 1955; 17 :129 - 21.
Smolenskii GA, Isupov VA. Phase transitions in some solid solutions with ferroelectric properties. Doklady Akademii Nauk SSSR. 1954; 97 :653 - 22.
Shvartsman VV, Kleemann W, Dec J, et al. Diffuse phase transition in BaTi1−xSnxO3 ceramics: An intermediate state between ferroelectric and relaxor behavior. Journal of Applied Physics. 2006; 99 :124111 - 23.
Baraskar BG, Kakade SG, James AR, Kambale RC, Kolekar YD. Improved ferroelectric, piezoelectric and electrostrictive properties of dense BaTiO3 ceramic. AIP Conference Proceedings. 2016; 1731 :140066 - 24.
Weaver PM, Cain MG, Stewart M. Temperature dependence of strain-polarization coupling in ferroelectric ceramics. Applied Physics Letters. 2010; 96 :142905 - 25.
Uchino K, Nomura S, Cross LE, Newnham RE, Jang SJ. Electrostrictive effect in perovs-kites and its transducer applications. Journal of Materials Science. 1981; 16 :569-578 - 26.
Baraskar BG, Kambale RC, James AR, Mahesh MLV, Ramana CV, Kokelar YD. Ferroelectric, piezoelectric and electrostrictive properties of Sn4+-modified Ba0.7Ca0.3TiO3 lead-free electroceramics. Journal of the American Ceramic Society. 2017; 100 :5755-5765 - 27.
Viola G, Saunders T, Wei X, et al. Contribution of piezoelectric effect, electrostriction and ferroelectric/ferroelastic switching to strain-electric field response of dielectrics. Journal of Advanced Dielectrics. 2013; 3 :1350007 - 28.
Yan H, Inam F, Viola G, et al. The contribution of electrical conductivity, dielectric permittivity and domain switching in ferroelectric hysteresis loops. Journal of Advanced Dielectrics. 2011; 1 :107-118 - 29.
Kumar A, Prasad VVB, Raju KCJ, et al. Poling electric field dependent domain switching and piezoelectric properties of mechanically activated (Pb0.92La0.08)(Zr0.60Ti0.40)O3 ceramics. Journal of Materials Science: Materials in Electronics. 2015; 26 :3757-3765 - 30.
Fan L, Chen J, Li S, et al. Enhanced piezoelectric and ferroelectric properties in the BaZrO3 substituted BiFeO3-PbTiO3. Applied Physics Letters 2013; 102 :022905 - 31.
Fu D, Itoh M, Koshihara S. Invariant lattice strain and polarization in BaTiO3-CaTiO3 ferroelectric alloys. Journal of Physics. Condensed Matter 2010; 22 :052204 - 32.
Horchidan N, Ianculescu AC, Curecheriu LP, et al. Preparation and characterization of barium titanate stannate solid solutions. Journal of Alloys and Compounds. 2011; 509 :4731-4737 - 33.
Xue DZ, Zhou YM, Bao HX, et al. Large piezoelectric effect in Pb-free Ba(Ti,Sn)O3-x(Ba,ca)TiO3 ceramics. Applied Physics Letters. 2011; 99 :122901 - 34.
Zhu LF, Zhang BP, Zhao XK, et al. Enhanced piezoelectric properties of (Ba1−xCax)(Ti0.92Sn0.08)O3 lead-free ceramics. Journal of the American Ceramic Society. 2013; 96 :241-245 - 35.
Lupascu DC. Fatigue in Ferroelectric Ceramics and Related Issues. New York: Springer; 2004 - 36.
Nath AK, Medhi N. Density variation and piezoelectric properties of Ba(Ti1−xSnx)O3 ceramics prepared from nanocrystalline powders. Bulletin of Materials Science. 2012; 35 :847-852 - 37.
Furuta A, Uchino K. Dynamic observation of crack propagation in piezoelectric multilayer actuators. Journal of the American Ceramic Society. 1993; 76 :1615 - 38.
Li F, Jin L, Xu Z, et al. Electrostrictive effect in ferroelectrics: An alternative approach to improve piezoelectricity. Applied Physics Reviews. 2014; 1 :011103 - 39.
Ang C, Yu Z. High, purely electrostrictive strain in lead-free dielectrics. Advanced Materials. 2006; 18 :103 - 40.
Zhang ST, Kounga AB, Jo W, et al. High-strain lead-free antiferroelectric electrostrictors. Advanced Materials. 2009; 21 :4716 - 41.
Zhu L-F, Zhang B-P, Zhao X-K, Zhao L, Yao F-Z, Han X, Zhou P-F, Li J-F. Phase transition and high piezoelectricity in (Ba,ca)(Ti1−xSnx)O3 lead-free ceramics. Applied Physics Letters. 2013; 103 :072905 - 42.
Li W, Xu Z, Chu R, Fu P, Zang G. Enhanced ferroelectric properties in (Ba1−xCax)(Ti0.94Sn0.06)O3 lead-free ceramics. Journal of European Ceramic Society. 2012; 32 :517-520 - 43.
Wu J, Xiao D, Wu B, Wu W, Zhu J, Yang Z, Wang J. Sintering temperature-induced electrical properties of (Ba0.90Ca0.10)(Ti0.85Zr0.15)O3 lead-free ceramics. Materials Research Bulletin. 2012; 47 :1281-1284 - 44.
Xu C, Yao Z, Lu K, Hao H, Yu Z, Cao M, Liu H. Enhanced piezoelectric properties and thermal stability in tetragonal-structured (Ba,ca)(Zr,Ti)O3 piezoelectrics substituted with trace amount of Mn. Ceramics International. 2016; 42 :16109-16115