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Ultra-low hysteresis electric field-induced strain with high electrostrictive coefficient in lead-free Ba(ZrxTi1-x)O3 ferroelectrics
Accepted Manuscript Ultra-low hysteresis electric field-induced strain with high electrostrictive coefficient in lead-free Ba(ZrxTi1-x)O3 ferroelectrics Li Jin, Jun Qiao, Liang Wang, Lei Hou, Ruiyi Jing, Jing Pang, Lin Zhang, Xu Lu, Xiaoyong Wei, Gang Liu, Yan Yan PII:
S0925-8388(19)30114-8
DOI:
https://doi.org/10.1016/j.jallcom.2019.01.106
Reference:
JALCOM 49144
To appear in:
Journal of Alloys and Compounds
Received Date: 25 August 2018 Revised Date:
6 January 2019
Accepted Date: 10 January 2019
Please cite this article as: L. Jin, J. Qiao, L. Wang, L. Hou, R. Jing, J. Pang, L. Zhang, X. Lu, X. Wei, G. Liu, Y. Yan, Ultra-low hysteresis electric field-induced strain with high electrostrictive coefficient in leadfree Ba(ZrxTi1-x)O3 ferroelectrics, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/ j.jallcom.2019.01.106. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Ultra-low hysteresis electric field-induced strain with high electrostrictive coefficient in lead-free Ba(ZrxTi1-x)O3 ferroelectrics
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Li Jin a,*, Jun Qiao a, Liang Wang a, Lei Hou a, Ruiyi Jing a, Jing Pang a, Lin Zhang a,**, Xu Lu , Xiaoyong Wei a, Gang Liu b, Yan Yan b,***
a
Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education &
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a
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International Center for Dielectric Research, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Faculty of Materials and Energy, Southwest University, Chongqing 400715, China
*Corresponding author. **Corresponding author.
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***Corresponding author.
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b
E-mail addresses: [email protected] (L. Jin), [email protected] (L. Zhang),
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[email protected] (Y. Yan).
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ACCEPTED MANUSCRIPT ABSTRACT From the application point of view, high electric field-induced strain with ultra-low hysteresis or hysteresis-free characteristic is highly desired in high-precision displacement actuators. In
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this work, lead-free Ba(ZrxTi1-x)O3 (BZT) ferroelectrics with x in the range between 0.02 and 0.1 were fabricated by a conventional solid state reaction method. The structural evolution and electrical properties were investigated systematically with an emphasis on electrostrictive
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effect. As x increases from 0.02 to 0.1, the crystal lattice parameters (a and c axes) increase
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while the tetragonality (c/a-1) goes down. In addition, the Curie temperature (TC) of BZT decreases gradually, while the temperatures corresponding to tetragonal-to-orthorhombic (T-O) and orthorhombic-to-rhombohedral (O-R) phase transitions increase. Ultra-low hysteresis (<8%) and high electric field-induced strains (>0.15% at 60 kV/cm) are observed
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in all studied compositions. Most importantly, a high longitudinal electrostrictive coefficient Q33 (0.0453 m4/C2) was also identified in x=0.1 composition. This work not only reports high
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electric field-induced strains with ultra-low hysteresis and high Q33 in lead-free BZT ferroelectrics, but also indicates a potential application for BZT ceramics in high-precision
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displacement actuators.
Keywords: Lead-free; Electrostriction; Ferroelectric; Electric field induced strain; BZT
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ACCEPTED MANUSCRIPT 1. Introduction The electric field-induced strains in ferroelectric ceramics have been extensively investigated during the past decades due to their applications in high-precision displacement
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actuators [1-13]. From the application point of view, the strain level should be as high as possible. It is found that high strain responses can be obtained in ferroelectrics near the phase boundaries (either morphotropic phase boundary [14-17] or polymorphic phase transition
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[18-21]) or enhanced based on electric field-induced phase transitions [22-29]. However,
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coherent domain wall motion or switching in ferroelectrics would lead to a high hysteresis in strain-electric field (S-E) curves. To actuator devices, the hysteresis in S-E curves should be lowered as much as possible. A high hysteresis would not only result in a high energy dissipation during electric field loading, but also affect the design and performance of
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actuators. Therefore, hysteresis is taken into account as an important figure of merit to evaluate the electric field-induced strain in ferroelectric materials [2]. It was suggested that the strain generated based on electrostrictive effect would possess a hysteresis-free
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characteristic, since this characteristic originates from intrinsic lattice instead of extrinsic
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domain wall motion [30]. The electrostrictive effect is described by Eq. (1) [30], ܵଷ = ܳଷଷ ∙ ܲଷଶ ,
(1)
where S3, P3 and Q33 are strain, polarization, and longitudinal electrostrictive coefficient, respectively. According to Eq. (1), we can see that the electrostrictive strain is positive and hysteresis-free. In ferroelectrics, the hysteresis-free characteristic cannot be obtained in their ferroelectric states, since both domain wall motion and electrostrictive effect coexist. When temperature approaches Curie temperature (TC), the interference by domain wall motion
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ACCEPTED MANUSCRIPT would be eliminated drastically due to the thermal disturbance to the long-range ordered polarization [30]. Thus, the hysteresis is decreased obviously. Therefore, to make use of the electrostrictive effect to generate a hysteresis-free strain at room temperature, the TC of
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ferroelectric materials should be shifted to around or below room temperature. As a representative electrostrictive material, Pb(Mg1/3Nb2/3)O3 (PMN) relaxor ferroelectric ceramic shows a high strain of around 0.1% with hysteresis-free characteristic at
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room temperature with a Q33 of 0.023 m4/C2 [31]. However, because of the regulations to
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restrict the usage of lead and other harmful elements in electronic devices issued by European Union and other countries, developing lead-free alternatives becomes an attractive research topic in ferroelectric materials [14, 15, 18, 32-34]. Similarly, the electrostrictive effect was also extensively investigated in lead-free (Bi0.5Na0.5)TiO3 (BNT)-based systems. These include,
Bi0.5Na0.5TiO3-BaTiO3-K0.5Na0.5NbO3
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systems
(Bi0.5Na0.5)TiO3-(Bi0.5K0.5)TiO3-(K0.5Na0.5)NbO3 (0.935−x)Bi0.5Na0.5TiO3-0.065BaTiO3-xSrTiO3
(BNT-BT-KNN)
(BNT-BKT-KNN) (BNBSTx)
[22], [35], [36],
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0.99Bi0.505(Na0.8K0.2)0.5-xTiO3-0.01SrTiO3 [BNKST(0.5−x)] [37], (Sr1-y-xNayBix)TiO3 (SNBT)
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[38], (1−x)(Bi0.5Na0.5)TiO3-xBa0.85Ca0.15Ti0.9Zr0.1O3 (BNT-BCZT) [39], etc. The Q33 in such a kind of ferroelectric materials ranges from ~0.02 m4/C2 to ~0.03 m4/C2. Compare to the Q33 value in PMN, the Q33 of BNT-based ferroelectrics was enhanced by a certain degree. Later, Li et al. [40] and Jin et al. [41] reported a high Q33 of ~0.04-0.05 m4/C2 in (1−x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 (BZT-xBCT) ceramics. In addition, a high Q33 of 0.046 m4/C2 was reported in (1−x)NaNbO3-xBaTiO3 (NN-xBT) ferroelectric ceramics [42, 43]. These works indicate that BT-based systems might possess a higher electrostrictive effect
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ACCEPTED MANUSCRIPT than that in BNT-based and PMN ceramics. This conjecture later was supported by an ab initio computation [44]. Although a high electrostrictive coefficient was reported in BT single crystal above their
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TC [45], its high TC (120 oC) of BT limits its electrostrictive application at room temperature [46]. The TC of the BT-based ferroelectrics should be around room temperature in order to obtain a pure electrostrictive response. Doping is a common method used to tailor the TC of
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ferroelectrics. It was reported that Zr4+ can substitute the B-site Ti4+ ion and form a
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Ba(ZrxTi1−x)O3 (BZT) solid solution, accompanying with a shift of TC to lower temperature [47, 48]. Since BaZrO3 is a nonferroelectric material [49], substituting the Ti4+ ion by the Zr4+ ion would disturb the long-range order of polarization and weaken the ferroelectricity in BT, thus leading to a decrease of the TC. Although diffuse phase transitions [47, 48], structures
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[49], piezoelectric properties [50], dielectric tunability [51, 52], dielectric properties [53-56] as well as grain size effect [57] of BT ceramics were investigated in detail during past decades, the electrostrictive effect in BZT system is still not well explored.
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In this paper, we investigate the electric field-induced strains of BZT ferroelectric
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ceramics with an emphasis on the hysteresis and electrostrictive coefficient. Interestingly, high electric field-induced strains (>0.15%) with an ultra-low hysteresis (<8%) are observed in BZT ceramics with x from 0.02 to 0.1. In addition, a high electrostrictive coefficient (~0.0453 m4/C2) is also obtained in x=0.1 composition. These results suggest that BZT ceramics can be considered as potential electrostrictive materials for the application in high-precision displacement actuators. 2. Experimental procedures
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ACCEPTED MANUSCRIPT Lead-free Ba(ZrxT1−x)O3 (BZT) ferroelectric ceramics with x=0.02, 0.04, 0.06, 0.08 and 0.1 were fabricated by means of a conventional solid state reaction method using BaCO3 (99 %), TiO2 (99 %) and ZrO2 (99.96 %) high purity oxide powders (Sinopharm Chemical
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Reagent Co., Ltd, Shanghai, China) as starting materials. These precursor powders were weighted in stoichiometric ratio and mixed by a planetary ball milling in alcohol for 6 h, and then calcined at 1250 oC for 4 h. After a second ball milling for 12 h, the milled powders
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were uniaxially pressed at 10 MPa to form thin disks with 1 mm in thickness and 10 mm in
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diameter. These thin disks were condensed by a cold isostatic pressing (CIP) with a maximum pressure of 250 MPa for 15 min. Finally they were sintered at 1400 oC for 4 h in air. The heating rate was set as 5 oC/min.
X-ray diffraction (XRD, PANalytical, Cambridge, UK) analysis in a θ-2θ scanning
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mode using a CuKα radiation was used to identify the crystal structures of ceramics samples. The scanning angle was set from 20o to 60o. To remove any residual stress, crushed ceramics powders were annealed at 500 oC for 2 h before XRD measurement. Dielectric properties
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were measured using thin disk samples. The main surfaces of these samples were polished by
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silica papers and coated by silver pastes, which were burnt out at 600 oC for 15 min. Temperature-dependent relative dielectric permittivity (εr) and loss (tanδ) were determined at 0.1, 1, 10 and 100 kHz by a multi-frequency LCR meter (E4980A, Agilent, Palo Alto, USA) from −120 oC to 160 oC during heating. The heating rate was set as 2 oC/min. Bipolar polarization-electric field (P-E) hysteresis loops and corresponding strain-electric field (S-E) curves were collected using a ferroelectric testing system (TF analyzer 2000, aixACCT, Aachen, Germany) combining with a laser interferometer vibrometer (SP-S 120, SIOS
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ACCEPTED MANUSCRIPT Meβtechnik GmbH, Germany) at a frequency of 1 Hz. The maximum electric field (Emax) applied to the samples was set as 60 kV/cm.
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3. Results and discussion Fig. 1(a) shows the room temperature XRD patterns of BZT ceramics with x from 0.02 to 0.1. The scanning angle is from 20o to 60o. It is clear that six groups of diffraction peaks
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can be indexed in Fig. 1(a). These diffraction peaks suggest a pure perovskite structure. No
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diffraction peaks correlated to a second phase can be detected. To further reveal the phase structure, enlarged XRD patterns from 44.6o to 45.8o are shown in Fig. 1(b). In such a scanning region, it can be seen that the two diffraction peaks denoted as (002) and (200) shift to lower angle gradually with respect to the increase of x. This is mainly attributed to the
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relatively large ionic radius of Zr4+ compared to that of Ti4+. The ionic radii of Zr4+ and Ti4+ are 72 pm and 60.5 pm, respectively (at a coordinate number of 6) [58]. Therefore the substitution of Ti4+ ion by Zr4+ ion would result in an increase of crystal lattice and thus a
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shift of the diffraction peaks to lower angle direction. Most importantly, the (200) peak
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moves closer to the (002) peak gradually as x increases, suggesting an increase of crystal lattice parameters (a and c axes) and a decrease of tetragonality, i.e., the (c/a-1). When x increases to 0.08, the splitting of (200) peaks almost disappear completely, suggesting an involvement of a phase transition. In order to reveal the structural evolution in BZT ceramics directly, we measured the εr and tanδ as a function of temperature from −120 oC to 160 oC at 0.1, 1, 10 and 100 kHz, as shown in Fig. 2(a)-(e). In Fig. 2(a), three dielectric anomalies are observed in εr when
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ACCEPTED MANUSCRIPT temperature decreases. The temperatures corresponding to these anomalies are denoted as TC, T1, and T2, respectively. According to the phase transition sequence revealed in BT ceramics, four phases, i.e., cubic (C) paraelectric phase, tetragonal (T) ferroelectric phase,
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orthorhombic (O) ferroelectric phase and rhombohedral (R) ferroelectric phase, emerge during cooling [59]. Therefore, the TC, T1, and T2 are the phase transition temperatures separating these phases. With respect to the increase of x, TC goes down, while both T1, and
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T2 increase to higher temperature and come close to each other. Note that in x=0.08
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composition, due to broadness of the dielectric peak, T2 cannot be identified in εr. Similarly, in x=0.1 composition, only a broad and asymmetrical dielectric peak is observed at 95 oC. The temperature corresponding to this peak is often correlated to the TC [47, 50]. In x=0.02~0.06 compositions, three dielectric anomalies are also observed in tanδ at
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temperatures around TC, T1, and T2. However, in x=0.08 and 0.1, only a monotonous decrease of tanδ is observed. Fig. 2(f) shows the phase diagram of BZT ceramics based on TC, T1, and T2 determined from Fig. 2(a)-(e). This phase diagram is very similar to previous reports in
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BZT [47, 50] and other BT-based systems, including (Ba,Sr)TiO3 [59] and Ba(Ti,Sn)O3 [60],
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suggesting that the Zr4+ has entered into the lattice as we expect. It should be noted that x=0.1 composition shows a diffuse phase transition characteristic, which is reflected clearly by a broad dielectric peak. The εr measured at different frequencies show very small dispersion in our compositions, suggesting an absence of a typical relaxor behavior [61, 62]. It was suggested by Shvartsmann and Lupascu [63] that diffuse phase transition is an intermediate state between relaxor and normal ferroelectric states. In the present study, it seems that a small amount of Zr4+ (0.02≤ x ≤0.10) substitution cannot induce a strong relaxor state in BZT
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ACCEPTED MANUSCRIPT system due to similar radii and the same valence between Zr4+ and Ti4+ ions. Fig. 3(a)-(d) present bipolar P-E hysteresis loops of BZT ceramics measured from 30 oC to 120 oC at an Emax of 60 kV/cm. In x=0.02, normal hysteresis loops are observed at low
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temperatures [64]. Once the external electric field is larger than the coercive field (Ec), domains in BZT are rearranged or switched along the direction of the field. With respect to the increase of temperature, hysteresis loops become slanted and slim due to the thermal
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disturbance to the long-range order in BZT. When x increases from 0.02 to 0.1, the P-E loops
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become even slimmer. This trend is well revealed by the evolutions of maximum polarization (Pmax), remnant polarization (Pr) and Ec. As summarized in Fig. 4, the Pmax, Pr and Ec for all studied compositions decrease when temperature increases. Generally the Pmax, Pr and Ec in x=0.02 at 30 oC possess the highest values. They decrease with respect to the increase of x
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and temperature. Most importantly, the Ec in all studied samples show very small values. This means that the domain reversal process happens at a relatively small electric field compared to the Emax. Such a characteristic would be beneficial to lower the hysteresis in P-E hysteresis
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loops and S-E curves.
o
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Fig. 5 shows the corresponding bipolar S-E curves of BZT ceramics measured from 30 C to 120 oC at an Emax of 60 kV/cm. It can be seen that butterfly-shape S-E curves are
observed at low temperatures. The negative strains are mainly attributed to the contribution by non-180o domain reveal around Ec [65, 66]. A large negative strain represents a large contribution by non-180o domain reveal. As temperature increases, these butterfly-shape S-E curves transform into V-shape S-E curves gradually, suggesting that electrostrictive effect dominates the electric field-induced strain responses. From the application point of view, the
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ACCEPTED MANUSCRIPT maximum strain (Smax) obtained at Emax is of interest. Fig. 6(a) shows the Smax as a function of temperature for BZT ceramics. At 30 oC, the Smax in all studied compositions show similar values around 0.152 % to 0.173 %. The corresponding equivalent piezoelectric coefficient
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∗ ݀ଷଷ , which is defined as Smax/Emax, is around 253 pm/V to 288 pm/V. Except in x=0.02 and
0.06, the Smax in other three compositions shows a monotonous decrease when temperature ∗ can exceed 300 pm/V by making use increases. Note that in piezoelectric ceramics, the ݀ଷଷ
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of phase boundary engineering or phase transition engineering [27]. However, the high strain
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∗ or ݀ଷଷ of these systems is mainly due to the extrinsic domain wall motion and other
extrinsic mechanisms, which inherently lead to a high hysteresis in S-E curves [4, 7-12]. Without the assistance by extrinsic domain wall motion, the electric field-induced strain based on purely electrostrictive effect becomes much smaller. For example, strains of 0.102%
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and 0.13% at 80 kV/cm with low hysteresis were reported in SBNT [38] and BNT-KN-ST ∗ of these two systems are only 128 pm/V [22] ceramics, respectively. The corresponding ݀ଷଷ
and 163 pm/V. Hysteresis η is calculated using ∆SE/2/Smax×100%, where ∆SE/2 is the
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difference of the strain measured at Emax/2. As shown in Fig. 6(c), the η in all studied
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compositions maintains a rather small level. Even though the highest η is less than 8%. The maximum negative strain is observed near the Ec. When external electric field exceeds the Ec, the electric field-induced strain is mainly governed by the electrostrictive effect. The ultra-low η in BZT ceramics is also attributed to such an intrinsic electrostrictive effect. To evaluate the electrostrictive effect in BZT ceramics, we plot the strain as a function of polarization. The bipolar S-P curves of BZT ceramics measured from 30 oC to 120 oC are shown in Fig. 7. In principle, the S-P curves can be described by Eq. (1), if the electric
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ACCEPTED MANUSCRIPT field-induced strain is governed by the electrostrictive effect. As shown in Fig. 7, the S-P curves can be well fitted by the solid bold lines, which are generated based on Eq. (1), confirming the dominating role of the electrostrictive effect. However, due to the negative
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strain induced by domain reversal, there are some deviations from the solid lines especially at low field region (below the Ec). These deviations affect the accuracy of the fitting results. Here, only the fitting results with an R>98 % are used to evaluate the electrostrictive effect.
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Fig. 8(a) shows the Q33 as a function of temperature for BZT ceramics. The Q33 ranges from
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0.0344 m4/C2 to 0.0462 m4/C2. It can be seen that the Q33 in each composition shows a relatively small variation from 30 oC to 120 oC, revealing a temperature-insensitive characteristic. Such a characteristic was suggested by a thermodynamic calculation [67] and also verified in many ferroelectric materials, including Pb(Mg1/3Nb2/3)O3-PbTiO3 [68], [40,
41],
NN-xBT
[42,
43],
and
BNT-BKT-KNN
[35],
and
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BZT-xBCT
(1−x)Bi0.5(Na0.78K0.22)0.5TiO3-xBi(Ni0.5Ti0.5)O3 [69]. Fig. 8(b) shows the average Q33 as a function of x. The error bars are extracted from the standard deviation of Q33. It is evident that
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the error bars are a little bit higher in x=0.02 and 0.08 due to their relatively high variations
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with respect to temperature. In contrast, relatively small error bars in other compositions reveal a temperature-independent characteristic. It seems that the average Q33 of BZT is enhanced at a certain level when x increases from 0.02 to 0.1, as suggested by the red straight line, which is obtained based on a linear fitting. Although composition-insensitive characteristic of Q33 is often observed in ferroelectric materials [5, 40, 42, 68, 70], a composition-dependent Q33 was also reported in some ferroelectric systems, including BNT-BKT-KNN [35], BNT-BT-KNN [22], and Bi0.5Na0.5TiO3-BaTiO3-(Sr0.7Bi0.18Er0.02)TiO3
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ACCEPTED MANUSCRIPT [71]. A highest Q33 of 0.0452 m4/C2 is observed in x=0.1 composition. Note that a Q33 ranging from 0.0276 m4/C2 to 0.0312 m4/C2 was observed in BaZr0.05Ti0.95O3 ceramics [72]. In contrast, the Q33 in x=0.04 and 0.06 is 0.0387 m4/C2 and 0.0429 m4/C2, respectively. The
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properties of ferroelectric ceramics are highly sensitive to relative density, grain size and processing parameters. Therefore the difference of the Q33 between our results and that in Ref. [72] might be attributed to any one of these factors. Compare to the Q33 in lead-based
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ferroelectrics (~0.015-0.029 m4/C2 [73-75]) and BNT-based ferroelectrics (~0.020-0.0354
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m4/C2 [35, 38, 76-79]), the Q33 in BZT ferroelectrics shows much higher values.
4. Conclusions
In this work, BZT ceramics with x from 0.02 to 0.1 were fabricated by means of a solid
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state reaction method. The structures of BZT ceramics were investigated by XRD and temperature-dependent dielectric properties. The TC of BZT ceramics goes down, while T1
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and T2 increase and come close to each other gradually. High electric field-induced strain (0.152%-0.173%) with ultra-low hysteresis (<8%) and high electrostrictive coefficient Q33
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(0.0452 m4/C2) were observed in studied samples. These results suggest that x=0.1 BZT composition possesses high electrostrictive properties at room temperature, and would find its potential application in high-precision displacement actuators.
Acknowledgments This work was supported by the National Nature Science Foundation of China (Grant Nos. 51772239 and 51761145024), the Joint Fund of the Ministry of Education under Grant 12
ACCEPTED MANUSCRIPT No. 6141A02033210, the fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201709), the Fundamental Research Funds for the Central Universities (XJTU), the National Basic Research Program of China (973 Program) under
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Grant No. 2015CB654602, the Key Scientific and Technological Innovation Team of Shannxi Province (Grant No. 2018TD-024) and “111” Project (Grant No. B14040). The SEM work was done at International Center for Dielectric Research (ICDR), Xi’an Jiaotong University,
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Figures
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Fig. 1. (a) Room temperature XRD patterns for BZT ceramics with a scanning angle from 20o
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to 60o. (b) Enlarged XRD patterns for BZT ceramics from 44.6o to 45.8o.
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Fig. 2. (a) Dielectric permittivity εr measured at 0.1, 1, 10 and 100 Hz as a function of
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temperature from −120 oC to 160 oC for BZT ceramics with a heating rate of 2 oC/min. TC, T1 and T2 corresponding three phase transition temperatures during cooling from high temperature. (a) x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1. (f) Phase diagram of BZT ceramics structured based on the dielectric properties.
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Fig. 3. Bipolar P-E curves of BZT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the Emax is 60 kV/cm. (a)
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x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1.
Fig. 4. (a) Pmax, (b) Pr and (c) Ec as function of temperature of BZT ceramics.
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Fig. 5. Bipolar S-E curves of BZT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the Emax is 60 kV/cm. (a)
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x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1.
∗ Fig. 6. (a) Smax, (b) ݀ଷଷ and (c) hysteresis η as function of temperature of BZT ceramics.
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Fig. 7. Bipolar S-P curves of BZT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the Emax is 60 kV/cm. (a)
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x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1. Open circles represent the
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experimental data, while the solid bold lines are the fitting curves based on Eq. (1).
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Fig. 8. Q33 as a function of temperature from 30 oC to 120 oC of BZT ceramics. (b) Average
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Q33 as a function of x.
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ACCEPTED MANUSCRIPT A high electrostrictive effect is reported in Ba(ZrxTi1-x)O3 (BZT).
High electrostrictive strain larger than 0.15% at 60 kV/cm is observed.
Ultra-low hysteresis less than 8% is observed.
High electrostrictive coefficient Q33 (0.0452 m4/C2) is obtained in x=0.10.
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S0925-8388(19)30114-8
DOI:
https://doi.org/10.1016/j.jallcom.2019.01.106
Reference:
JALCOM 49144
To appear in:
Journal of Alloys and Compounds
Received Date: 25 August 2018 Revised Date:
6 January 2019
Accepted Date: 10 January 2019
Please cite this article as: L. Jin, J. Qiao, L. Wang, L. Hou, R. Jing, J. Pang, L. Zhang, X. Lu, X. Wei, G. Liu, Y. Yan, Ultra-low hysteresis electric field-induced strain with high electrostrictive coefficient in leadfree Ba(ZrxTi1-x)O3 ferroelectrics, Journal of Alloys and Compounds (2019), doi: https://doi.org/10.1016/ j.jallcom.2019.01.106. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Ultra-low hysteresis electric field-induced strain with high electrostrictive coefficient in lead-free Ba(ZrxTi1-x)O3 ferroelectrics
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Li Jin a,*, Jun Qiao a, Liang Wang a, Lei Hou a, Ruiyi Jing a, Jing Pang a, Lin Zhang a,**, Xu Lu , Xiaoyong Wei a, Gang Liu b, Yan Yan b,***
a
Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education &
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a
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International Center for Dielectric Research, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Faculty of Materials and Energy, Southwest University, Chongqing 400715, China
*Corresponding author. **Corresponding author.
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***Corresponding author.
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b
E-mail addresses: [email protected] (L. Jin), [email protected] (L. Zhang),
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[email protected] (Y. Yan).
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ACCEPTED MANUSCRIPT ABSTRACT From the application point of view, high electric field-induced strain with ultra-low hysteresis or hysteresis-free characteristic is highly desired in high-precision displacement actuators. In
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this work, lead-free Ba(ZrxTi1-x)O3 (BZT) ferroelectrics with x in the range between 0.02 and 0.1 were fabricated by a conventional solid state reaction method. The structural evolution and electrical properties were investigated systematically with an emphasis on electrostrictive
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effect. As x increases from 0.02 to 0.1, the crystal lattice parameters (a and c axes) increase
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while the tetragonality (c/a-1) goes down. In addition, the Curie temperature (TC) of BZT decreases gradually, while the temperatures corresponding to tetragonal-to-orthorhombic (T-O) and orthorhombic-to-rhombohedral (O-R) phase transitions increase. Ultra-low hysteresis (<8%) and high electric field-induced strains (>0.15% at 60 kV/cm) are observed
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in all studied compositions. Most importantly, a high longitudinal electrostrictive coefficient Q33 (0.0453 m4/C2) was also identified in x=0.1 composition. This work not only reports high
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electric field-induced strains with ultra-low hysteresis and high Q33 in lead-free BZT ferroelectrics, but also indicates a potential application for BZT ceramics in high-precision
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displacement actuators.
Keywords: Lead-free; Electrostriction; Ferroelectric; Electric field induced strain; BZT
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ACCEPTED MANUSCRIPT 1. Introduction The electric field-induced strains in ferroelectric ceramics have been extensively investigated during the past decades due to their applications in high-precision displacement
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actuators [1-13]. From the application point of view, the strain level should be as high as possible. It is found that high strain responses can be obtained in ferroelectrics near the phase boundaries (either morphotropic phase boundary [14-17] or polymorphic phase transition
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[18-21]) or enhanced based on electric field-induced phase transitions [22-29]. However,
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coherent domain wall motion or switching in ferroelectrics would lead to a high hysteresis in strain-electric field (S-E) curves. To actuator devices, the hysteresis in S-E curves should be lowered as much as possible. A high hysteresis would not only result in a high energy dissipation during electric field loading, but also affect the design and performance of
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actuators. Therefore, hysteresis is taken into account as an important figure of merit to evaluate the electric field-induced strain in ferroelectric materials [2]. It was suggested that the strain generated based on electrostrictive effect would possess a hysteresis-free
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characteristic, since this characteristic originates from intrinsic lattice instead of extrinsic
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domain wall motion [30]. The electrostrictive effect is described by Eq. (1) [30], ܵଷ = ܳଷଷ ∙ ܲଷଶ ,
(1)
where S3, P3 and Q33 are strain, polarization, and longitudinal electrostrictive coefficient, respectively. According to Eq. (1), we can see that the electrostrictive strain is positive and hysteresis-free. In ferroelectrics, the hysteresis-free characteristic cannot be obtained in their ferroelectric states, since both domain wall motion and electrostrictive effect coexist. When temperature approaches Curie temperature (TC), the interference by domain wall motion
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ferroelectric materials should be shifted to around or below room temperature. As a representative electrostrictive material, Pb(Mg1/3Nb2/3)O3 (PMN) relaxor ferroelectric ceramic shows a high strain of around 0.1% with hysteresis-free characteristic at
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room temperature with a Q33 of 0.023 m4/C2 [31]. However, because of the regulations to
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restrict the usage of lead and other harmful elements in electronic devices issued by European Union and other countries, developing lead-free alternatives becomes an attractive research topic in ferroelectric materials [14, 15, 18, 32-34]. Similarly, the electrostrictive effect was also extensively investigated in lead-free (Bi0.5Na0.5)TiO3 (BNT)-based systems. These include,
Bi0.5Na0.5TiO3-BaTiO3-K0.5Na0.5NbO3
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systems
(Bi0.5Na0.5)TiO3-(Bi0.5K0.5)TiO3-(K0.5Na0.5)NbO3 (0.935−x)Bi0.5Na0.5TiO3-0.065BaTiO3-xSrTiO3
(BNT-BT-KNN)
(BNT-BKT-KNN) (BNBSTx)
[22], [35], [36],
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0.99Bi0.505(Na0.8K0.2)0.5-xTiO3-0.01SrTiO3 [BNKST(0.5−x)] [37], (Sr1-y-xNayBix)TiO3 (SNBT)
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[38], (1−x)(Bi0.5Na0.5)TiO3-xBa0.85Ca0.15Ti0.9Zr0.1O3 (BNT-BCZT) [39], etc. The Q33 in such a kind of ferroelectric materials ranges from ~0.02 m4/C2 to ~0.03 m4/C2. Compare to the Q33 value in PMN, the Q33 of BNT-based ferroelectrics was enhanced by a certain degree. Later, Li et al. [40] and Jin et al. [41] reported a high Q33 of ~0.04-0.05 m4/C2 in (1−x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 (BZT-xBCT) ceramics. In addition, a high Q33 of 0.046 m4/C2 was reported in (1−x)NaNbO3-xBaTiO3 (NN-xBT) ferroelectric ceramics [42, 43]. These works indicate that BT-based systems might possess a higher electrostrictive effect
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TC [45], its high TC (120 oC) of BT limits its electrostrictive application at room temperature [46]. The TC of the BT-based ferroelectrics should be around room temperature in order to obtain a pure electrostrictive response. Doping is a common method used to tailor the TC of
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ferroelectrics. It was reported that Zr4+ can substitute the B-site Ti4+ ion and form a
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Ba(ZrxTi1−x)O3 (BZT) solid solution, accompanying with a shift of TC to lower temperature [47, 48]. Since BaZrO3 is a nonferroelectric material [49], substituting the Ti4+ ion by the Zr4+ ion would disturb the long-range order of polarization and weaken the ferroelectricity in BT, thus leading to a decrease of the TC. Although diffuse phase transitions [47, 48], structures
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[49], piezoelectric properties [50], dielectric tunability [51, 52], dielectric properties [53-56] as well as grain size effect [57] of BT ceramics were investigated in detail during past decades, the electrostrictive effect in BZT system is still not well explored.
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In this paper, we investigate the electric field-induced strains of BZT ferroelectric
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ceramics with an emphasis on the hysteresis and electrostrictive coefficient. Interestingly, high electric field-induced strains (>0.15%) with an ultra-low hysteresis (<8%) are observed in BZT ceramics with x from 0.02 to 0.1. In addition, a high electrostrictive coefficient (~0.0453 m4/C2) is also obtained in x=0.1 composition. These results suggest that BZT ceramics can be considered as potential electrostrictive materials for the application in high-precision displacement actuators. 2. Experimental procedures
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ACCEPTED MANUSCRIPT Lead-free Ba(ZrxT1−x)O3 (BZT) ferroelectric ceramics with x=0.02, 0.04, 0.06, 0.08 and 0.1 were fabricated by means of a conventional solid state reaction method using BaCO3 (99 %), TiO2 (99 %) and ZrO2 (99.96 %) high purity oxide powders (Sinopharm Chemical
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Reagent Co., Ltd, Shanghai, China) as starting materials. These precursor powders were weighted in stoichiometric ratio and mixed by a planetary ball milling in alcohol for 6 h, and then calcined at 1250 oC for 4 h. After a second ball milling for 12 h, the milled powders
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were uniaxially pressed at 10 MPa to form thin disks with 1 mm in thickness and 10 mm in
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diameter. These thin disks were condensed by a cold isostatic pressing (CIP) with a maximum pressure of 250 MPa for 15 min. Finally they were sintered at 1400 oC for 4 h in air. The heating rate was set as 5 oC/min.
X-ray diffraction (XRD, PANalytical, Cambridge, UK) analysis in a θ-2θ scanning
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mode using a CuKα radiation was used to identify the crystal structures of ceramics samples. The scanning angle was set from 20o to 60o. To remove any residual stress, crushed ceramics powders were annealed at 500 oC for 2 h before XRD measurement. Dielectric properties
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were measured using thin disk samples. The main surfaces of these samples were polished by
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silica papers and coated by silver pastes, which were burnt out at 600 oC for 15 min. Temperature-dependent relative dielectric permittivity (εr) and loss (tanδ) were determined at 0.1, 1, 10 and 100 kHz by a multi-frequency LCR meter (E4980A, Agilent, Palo Alto, USA) from −120 oC to 160 oC during heating. The heating rate was set as 2 oC/min. Bipolar polarization-electric field (P-E) hysteresis loops and corresponding strain-electric field (S-E) curves were collected using a ferroelectric testing system (TF analyzer 2000, aixACCT, Aachen, Germany) combining with a laser interferometer vibrometer (SP-S 120, SIOS
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ACCEPTED MANUSCRIPT Meβtechnik GmbH, Germany) at a frequency of 1 Hz. The maximum electric field (Emax) applied to the samples was set as 60 kV/cm.
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3. Results and discussion Fig. 1(a) shows the room temperature XRD patterns of BZT ceramics with x from 0.02 to 0.1. The scanning angle is from 20o to 60o. It is clear that six groups of diffraction peaks
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can be indexed in Fig. 1(a). These diffraction peaks suggest a pure perovskite structure. No
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diffraction peaks correlated to a second phase can be detected. To further reveal the phase structure, enlarged XRD patterns from 44.6o to 45.8o are shown in Fig. 1(b). In such a scanning region, it can be seen that the two diffraction peaks denoted as (002) and (200) shift to lower angle gradually with respect to the increase of x. This is mainly attributed to the
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relatively large ionic radius of Zr4+ compared to that of Ti4+. The ionic radii of Zr4+ and Ti4+ are 72 pm and 60.5 pm, respectively (at a coordinate number of 6) [58]. Therefore the substitution of Ti4+ ion by Zr4+ ion would result in an increase of crystal lattice and thus a
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shift of the diffraction peaks to lower angle direction. Most importantly, the (200) peak
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moves closer to the (002) peak gradually as x increases, suggesting an increase of crystal lattice parameters (a and c axes) and a decrease of tetragonality, i.e., the (c/a-1). When x increases to 0.08, the splitting of (200) peaks almost disappear completely, suggesting an involvement of a phase transition. In order to reveal the structural evolution in BZT ceramics directly, we measured the εr and tanδ as a function of temperature from −120 oC to 160 oC at 0.1, 1, 10 and 100 kHz, as shown in Fig. 2(a)-(e). In Fig. 2(a), three dielectric anomalies are observed in εr when
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ACCEPTED MANUSCRIPT temperature decreases. The temperatures corresponding to these anomalies are denoted as TC, T1, and T2, respectively. According to the phase transition sequence revealed in BT ceramics, four phases, i.e., cubic (C) paraelectric phase, tetragonal (T) ferroelectric phase,
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orthorhombic (O) ferroelectric phase and rhombohedral (R) ferroelectric phase, emerge during cooling [59]. Therefore, the TC, T1, and T2 are the phase transition temperatures separating these phases. With respect to the increase of x, TC goes down, while both T1, and
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T2 increase to higher temperature and come close to each other. Note that in x=0.08
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composition, due to broadness of the dielectric peak, T2 cannot be identified in εr. Similarly, in x=0.1 composition, only a broad and asymmetrical dielectric peak is observed at 95 oC. The temperature corresponding to this peak is often correlated to the TC [47, 50]. In x=0.02~0.06 compositions, three dielectric anomalies are also observed in tanδ at
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temperatures around TC, T1, and T2. However, in x=0.08 and 0.1, only a monotonous decrease of tanδ is observed. Fig. 2(f) shows the phase diagram of BZT ceramics based on TC, T1, and T2 determined from Fig. 2(a)-(e). This phase diagram is very similar to previous reports in
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BZT [47, 50] and other BT-based systems, including (Ba,Sr)TiO3 [59] and Ba(Ti,Sn)O3 [60],
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suggesting that the Zr4+ has entered into the lattice as we expect. It should be noted that x=0.1 composition shows a diffuse phase transition characteristic, which is reflected clearly by a broad dielectric peak. The εr measured at different frequencies show very small dispersion in our compositions, suggesting an absence of a typical relaxor behavior [61, 62]. It was suggested by Shvartsmann and Lupascu [63] that diffuse phase transition is an intermediate state between relaxor and normal ferroelectric states. In the present study, it seems that a small amount of Zr4+ (0.02≤ x ≤0.10) substitution cannot induce a strong relaxor state in BZT
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ACCEPTED MANUSCRIPT system due to similar radii and the same valence between Zr4+ and Ti4+ ions. Fig. 3(a)-(d) present bipolar P-E hysteresis loops of BZT ceramics measured from 30 oC to 120 oC at an Emax of 60 kV/cm. In x=0.02, normal hysteresis loops are observed at low
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temperatures [64]. Once the external electric field is larger than the coercive field (Ec), domains in BZT are rearranged or switched along the direction of the field. With respect to the increase of temperature, hysteresis loops become slanted and slim due to the thermal
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disturbance to the long-range order in BZT. When x increases from 0.02 to 0.1, the P-E loops
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become even slimmer. This trend is well revealed by the evolutions of maximum polarization (Pmax), remnant polarization (Pr) and Ec. As summarized in Fig. 4, the Pmax, Pr and Ec for all studied compositions decrease when temperature increases. Generally the Pmax, Pr and Ec in x=0.02 at 30 oC possess the highest values. They decrease with respect to the increase of x
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and temperature. Most importantly, the Ec in all studied samples show very small values. This means that the domain reversal process happens at a relatively small electric field compared to the Emax. Such a characteristic would be beneficial to lower the hysteresis in P-E hysteresis
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loops and S-E curves.
o
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Fig. 5 shows the corresponding bipolar S-E curves of BZT ceramics measured from 30 C to 120 oC at an Emax of 60 kV/cm. It can be seen that butterfly-shape S-E curves are
observed at low temperatures. The negative strains are mainly attributed to the contribution by non-180o domain reveal around Ec [65, 66]. A large negative strain represents a large contribution by non-180o domain reveal. As temperature increases, these butterfly-shape S-E curves transform into V-shape S-E curves gradually, suggesting that electrostrictive effect dominates the electric field-induced strain responses. From the application point of view, the
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ACCEPTED MANUSCRIPT maximum strain (Smax) obtained at Emax is of interest. Fig. 6(a) shows the Smax as a function of temperature for BZT ceramics. At 30 oC, the Smax in all studied compositions show similar values around 0.152 % to 0.173 %. The corresponding equivalent piezoelectric coefficient
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∗ ݀ଷଷ , which is defined as Smax/Emax, is around 253 pm/V to 288 pm/V. Except in x=0.02 and
0.06, the Smax in other three compositions shows a monotonous decrease when temperature ∗ can exceed 300 pm/V by making use increases. Note that in piezoelectric ceramics, the ݀ଷଷ
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of phase boundary engineering or phase transition engineering [27]. However, the high strain
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∗ or ݀ଷଷ of these systems is mainly due to the extrinsic domain wall motion and other
extrinsic mechanisms, which inherently lead to a high hysteresis in S-E curves [4, 7-12]. Without the assistance by extrinsic domain wall motion, the electric field-induced strain based on purely electrostrictive effect becomes much smaller. For example, strains of 0.102%
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and 0.13% at 80 kV/cm with low hysteresis were reported in SBNT [38] and BNT-KN-ST ∗ of these two systems are only 128 pm/V [22] ceramics, respectively. The corresponding ݀ଷଷ
and 163 pm/V. Hysteresis η is calculated using ∆SE/2/Smax×100%, where ∆SE/2 is the
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difference of the strain measured at Emax/2. As shown in Fig. 6(c), the η in all studied
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compositions maintains a rather small level. Even though the highest η is less than 8%. The maximum negative strain is observed near the Ec. When external electric field exceeds the Ec, the electric field-induced strain is mainly governed by the electrostrictive effect. The ultra-low η in BZT ceramics is also attributed to such an intrinsic electrostrictive effect. To evaluate the electrostrictive effect in BZT ceramics, we plot the strain as a function of polarization. The bipolar S-P curves of BZT ceramics measured from 30 oC to 120 oC are shown in Fig. 7. In principle, the S-P curves can be described by Eq. (1), if the electric
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ACCEPTED MANUSCRIPT field-induced strain is governed by the electrostrictive effect. As shown in Fig. 7, the S-P curves can be well fitted by the solid bold lines, which are generated based on Eq. (1), confirming the dominating role of the electrostrictive effect. However, due to the negative
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strain induced by domain reversal, there are some deviations from the solid lines especially at low field region (below the Ec). These deviations affect the accuracy of the fitting results. Here, only the fitting results with an R>98 % are used to evaluate the electrostrictive effect.
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Fig. 8(a) shows the Q33 as a function of temperature for BZT ceramics. The Q33 ranges from
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0.0344 m4/C2 to 0.0462 m4/C2. It can be seen that the Q33 in each composition shows a relatively small variation from 30 oC to 120 oC, revealing a temperature-insensitive characteristic. Such a characteristic was suggested by a thermodynamic calculation [67] and also verified in many ferroelectric materials, including Pb(Mg1/3Nb2/3)O3-PbTiO3 [68], [40,
41],
NN-xBT
[42,
43],
and
BNT-BKT-KNN
[35],
and
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BZT-xBCT
(1−x)Bi0.5(Na0.78K0.22)0.5TiO3-xBi(Ni0.5Ti0.5)O3 [69]. Fig. 8(b) shows the average Q33 as a function of x. The error bars are extracted from the standard deviation of Q33. It is evident that
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the error bars are a little bit higher in x=0.02 and 0.08 due to their relatively high variations
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with respect to temperature. In contrast, relatively small error bars in other compositions reveal a temperature-independent characteristic. It seems that the average Q33 of BZT is enhanced at a certain level when x increases from 0.02 to 0.1, as suggested by the red straight line, which is obtained based on a linear fitting. Although composition-insensitive characteristic of Q33 is often observed in ferroelectric materials [5, 40, 42, 68, 70], a composition-dependent Q33 was also reported in some ferroelectric systems, including BNT-BKT-KNN [35], BNT-BT-KNN [22], and Bi0.5Na0.5TiO3-BaTiO3-(Sr0.7Bi0.18Er0.02)TiO3
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ACCEPTED MANUSCRIPT [71]. A highest Q33 of 0.0452 m4/C2 is observed in x=0.1 composition. Note that a Q33 ranging from 0.0276 m4/C2 to 0.0312 m4/C2 was observed in BaZr0.05Ti0.95O3 ceramics [72]. In contrast, the Q33 in x=0.04 and 0.06 is 0.0387 m4/C2 and 0.0429 m4/C2, respectively. The
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properties of ferroelectric ceramics are highly sensitive to relative density, grain size and processing parameters. Therefore the difference of the Q33 between our results and that in Ref. [72] might be attributed to any one of these factors. Compare to the Q33 in lead-based
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ferroelectrics (~0.015-0.029 m4/C2 [73-75]) and BNT-based ferroelectrics (~0.020-0.0354
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m4/C2 [35, 38, 76-79]), the Q33 in BZT ferroelectrics shows much higher values.
4. Conclusions
In this work, BZT ceramics with x from 0.02 to 0.1 were fabricated by means of a solid
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state reaction method. The structures of BZT ceramics were investigated by XRD and temperature-dependent dielectric properties. The TC of BZT ceramics goes down, while T1
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and T2 increase and come close to each other gradually. High electric field-induced strain (0.152%-0.173%) with ultra-low hysteresis (<8%) and high electrostrictive coefficient Q33
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(0.0452 m4/C2) were observed in studied samples. These results suggest that x=0.1 BZT composition possesses high electrostrictive properties at room temperature, and would find its potential application in high-precision displacement actuators.
Acknowledgments This work was supported by the National Nature Science Foundation of China (Grant Nos. 51772239 and 51761145024), the Joint Fund of the Ministry of Education under Grant 12
ACCEPTED MANUSCRIPT No. 6141A02033210, the fund of the State Key Laboratory of Solidification Processing in NWPU (Grant No. SKLSP201709), the Fundamental Research Funds for the Central Universities (XJTU), the National Basic Research Program of China (973 Program) under
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Grant No. 2015CB654602, the Key Scientific and Technological Innovation Team of Shannxi Province (Grant No. 2018TD-024) and “111” Project (Grant No. B14040). The SEM work was done at International Center for Dielectric Research (ICDR), Xi’an Jiaotong University,
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Xi’an, China.
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[52] X.G. Tang, J. Wang, X.X. Wang, H.L.W. Chan, Effects of grain size on the dielectric properties and tunabilities of sol-gel derived Ba(Zr0.2Ti0.8)O3 ceramics, Solid State Commun. 131 (2004) 163-168. [53] P.S. Dobal, A. Dixit, R.S. Katiyar, Z. Yu, R. Guo, A.S. Bhalla, Micro-Raman scattering and dielectric investigations of phase transition behavior in the BaTiO3-BaZrO3 system, J. Appl. Phys. 89 (2001) 8085-8091. [54] Z. Yu, R. Guo, A.S. Bhalla, Dielectric behavior of Ba(Ti1-xZrx)O3 single crystals, J. Appl. Phys. 88 (2000) 410-415. [55] F. Moura, A.Z. Simões, B.D. Stojanovic, M.A. Zaghete, E. Longo, J.A. Varela, Dielectric and ferroelectric characteristics of barium zirconate titanate ceramics prepared from mixed oxide method, J. Alloy. Compd. 462 (2008) 129-134. [56] Q. Xu, D. Zhan, H.-X. Liu, W. Chen, D.-P. Huang, F. Zhang, Evolution of dielectric properties
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Figures
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Fig. 1. (a) Room temperature XRD patterns for BZT ceramics with a scanning angle from 20o
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to 60o. (b) Enlarged XRD patterns for BZT ceramics from 44.6o to 45.8o.
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Fig. 2. (a) Dielectric permittivity εr measured at 0.1, 1, 10 and 100 Hz as a function of
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temperature from −120 oC to 160 oC for BZT ceramics with a heating rate of 2 oC/min. TC, T1 and T2 corresponding three phase transition temperatures during cooling from high temperature. (a) x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1. (f) Phase diagram of BZT ceramics structured based on the dielectric properties.
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Fig. 3. Bipolar P-E curves of BZT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the Emax is 60 kV/cm. (a)
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x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1.
Fig. 4. (a) Pmax, (b) Pr and (c) Ec as function of temperature of BZT ceramics.
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Fig. 5. Bipolar S-E curves of BZT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the Emax is 60 kV/cm. (a)
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x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1.
∗ Fig. 6. (a) Smax, (b) ݀ଷଷ and (c) hysteresis η as function of temperature of BZT ceramics.
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Fig. 7. Bipolar S-P curves of BZT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the Emax is 60 kV/cm. (a)
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x=0.02, (b) x=0.04, (c) x=0.06, (d) x=0.08 and (e) x=0.1. Open circles represent the
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experimental data, while the solid bold lines are the fitting curves based on Eq. (1).
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Fig. 8. Q33 as a function of temperature from 30 oC to 120 oC of BZT ceramics. (b) Average
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Q33 as a function of x.
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High electrostrictive strain larger than 0.15% at 60 kV/cm is observed.
Ultra-low hysteresis less than 8% is observed.
High electrostrictive coefficient Q33 (0.0452 m4/C2) is obtained in x=0.10.
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