Origin of composition-insensitive electrostrictive coefficient and continuous decrease of domain wall density in (1-x)NaNbO3-xBaTiO3 lead-free ferroelectrics

Accepted Manuscript Title: Origin of composition-insensitive electrostrictive coefficient and continuous decrease of domain wall density in (1-x)NaNbO3 -xBaTiO3 lead-free ferroelectrics Authors: Xu Lu, Lei Hou, Li Jin, Dawei Wang, Qingyuan Hu, D.O. Alikin, A. Pu. Turygin, Liang Wang, Lin Zhang, Xiaoyong Wei PII: DOI: Reference:

S0955-2219(18)30163-8 https://doi.org/10.1016/j.jeurceramsoc.2018.03.026 JECS 11783

To appear in:

Journal of the European Ceramic Society

Received date: Revised date: Accepted date:

3-1-2018 16-3-2018 17-3-2018

Please cite this article as: Lu X, Hou L, Jin L, Wang D, Hu Q, Alikin DO, Turygin AP, Wang L, Zhang L, Wei X, Origin of composition-insensitive electrostrictive coefficient and continuous decrease of domain wall density in (1-x)NaNbO3 xBaTiO3 lead-free ferroelectrics, Journal of The European Ceramic Society (2010), https://doi.org/10.1016/j.jeurceramsoc.2018.03.026 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.

Origin of composition-insensitive electrostrictive coefficient and continuous decrease of domain wall density in (1-x)NaNbO3-xBaTiO3 lead-free ferroe-

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lectrics

Xu Lua,*, Lei Houa, Li Jinb,*, Dawei Wangc,*, Qingyuan Hud, D. O. Alikind, A. Pu. Turygind,

Laboratory of Functional Films, School of Materials Science and Engineering, Xi'an University of

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a

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Liang Wanga, Lin Zhangb, Xiaoyong Weib

Electronic Materials Research Laboratory, School of the Electronic and Information Engineering,

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Xi'an Jiaotong University, Xi'an 710049, China

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b

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Technology, Xi'an 710048, China

School of Microelectronics & State Key Laboratory for Mechanical Behavior of Materials, Xi'an

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c

School of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg 620000, Russia

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d

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Jiaotong University, Xi'an 710049, China

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*Corresponding authors. E-mail addresses: [email protected] (X. Lu), [email protected] (L. Jin), [email protected] (D. Wang)

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Perovskite ferroelectric ceramics with giant electrostrictive coefficient Q33 have attracted much attention due to their high strain response with ultralow hysteresis. In this work, the electrostrictive properties as well as domain morphology of the lead-free (1−x)NaNbO3-xBaTiO3 (NN-xBT) (0.10≤x≤0.27) system were investigated systematically. A composition-insen-

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sitive Q33 of 0.0406 m4/C2 is identified in the NN-xBT ceramics (0.15≤x≤0.27). An ab initio computation indicates that transverse Q12 would play an important role in understanding of

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the composition-insensitive Q33. Furthermore, distinctively banding domains and inhomoge-

neous distribution of nanodomains were observed in NN-xBT by piezoresponse force micros-

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copy. A continuous decrease of domain wall density was identified with respect to the in-

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crease of x. This study would not only deepen our understanding of the origin of composi-

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tion-insensitive Q33 in NN-BT and other related systems, but also provide a way to enhance

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the Q33, i.e., by forming the solid solutions with end members, which possess high Q12.

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Keywords: Lead-free; Electrostrictive coefficient; Ferroelectric; Domain

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1. Introduction

Recently, electrostrictive effect in perovskite ferroelectric ceramics has attracted much

attention due to their small hysteresis or hysteresis-free in strain response with respect to ex-

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ternal electric stimuli [1-19]. A large hysteresis in strain-electric field (S-E) curves would not only affect the design of actuators, but also result in a large energy dissipation and subsequent degradation of the materials [20-22]. Therefore, electrostrictive ceramics are very important to actuators from the point view of practical application. Compared with piezoelectric effect,

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which is linear effect between input electric field and induced strain, electrostrictive effect can also convert electric field (or polarization) into mechanical signal (i.e., strain or displacement) with high resolution and low hysteresis [21]. However, the strain generated based on electrostrictive effect is proportion to the square of electric field or polarization. This relation-

𝑆3 = 𝑄33 ∙ 𝑃32 ,

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ship is expressed by Eq. (1) [21], (1)

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where S3, P3 and Q33 are mechanical strain, polarization, and electrostrictive coefficient, respectively. Note that here the subscript 3 indicates that strain and polarization are along the

direction of the electric field stead of the direction of crystal axis. In piezoelectric ceramics,

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on the one hand inherently extrinsic domain wall (DW) motion makes up a large proportion

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of dielectric and piezoelectric properties [23-30]. On the other hand, a large extrinsic DW

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motion also results in a large hysteresis in polarization and strain with respect to external electric stimuli [31-36]. In contrast, in electrostrictive ceramics, without the serious interfer-

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ences by DW motion near their Curie temperatures and in their paraelectric phase, the hyste-

21].

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resis is subsequently decreased to a large extent or even removed completely [8, 11, 13, 14,

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The first generation of electrostrictive ceramics is based on Pb(Mg1/3Nb2/3)O3 (PMN) re-

laxor ferroelectric ceramics [37-39]. High strain response (~0.1%) with ultra-low hysteresis

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in S-E curves has been reported. The corresponding Q33 is about 0.023 m4/C2 [38]. However, from environmental and policy consideration, hazardous substances used in electronic equipments have been limited rigorously [40-49]. In such a circumstance, developing lead-free electrostrictive alternative becomes an important challenge from both fundamental researches and industry applications. Although (Bi0.5Na0.5)TiO3 (BNT)-based ferroelectrics have been 3

studied extensively, recent investigations of the electrostrictive properties in BaTiO3 (BT)based ferroelectrics suggest that BT-based systems would possess superior electrostrictive performance over the BNT-based systems. The Q33 of BNT-based systems is reported between 0.02 and 0.03 m4/C2 [1-7, 9, 10, 14, 15, 17], which is about 20-30% higher than that in

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PMN. In contrast, Li et al. [8] and Jin et al. [11] first reported a giant Q33 (0.04~0.05 m4/C2) in (1-x)Ba(Zr0.2Ti0.8)O3-x(Ba0.7Ca0.3)TiO3 (BZT-xBCT). They attributed the high piezoelec-

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tricity in the BZT-xBCT to such a giant Q33. Then in (Ba1-xGd2x/3)Zr0.3Ti0.7O3, and (1-

x)NaNbO3-xBaTiO3 (NN-xBT), similar Q33 values as high as 0.054 m4/C2 and 0.046 m4/C2,

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were also reported by Ghosh et al. [12] and Zuo et al. [13], respectively. These values of Q33

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is about twice as big as the Q33 in PMN. A comprehensive summary of the Q33 for electro-

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strictive ceramics has been given by Jin et al. [11]. In addition, Lu et al. [50] reported excep-

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tionally ultra-low hysteresis unipolar electric field-induced strain in the NN-xBT system,

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which is highly correlated to the electrostrictive effect. Although the ferroelectric and electrostrictive properties of NN-BT systems have been

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studied by several groups, a comprehensive explanation of its composition-insensitive Q33 is

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not well developed. Jiang et al. used ab initio techniques to exploit the electrostriction of ferroelectric materials and found that in ABO3 perovskite ferroelectrics relative displacements (for example, the B-Oǁ bond length) at a given polarization could be a good indicator of lon-

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gitudinal electrostrictive coefficient Q11 [51]. According to their computation, BT should possess a much larger Q11 than that of BaZrO3. It should be noted that here Jiang et al. only calculated the Q coefficient in a unit cell, the complexity of Q coefficient in polycrystalline ceramics has not been explored. Moreover, Zuo et al. have studied the electrostriction in the

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̅ ∗2 , where q is the charge of cations and NN-xBT system [13] and correlated Q33 to ∑ 𝑞 2 /𝑍33 ̅ ∗ is the average Born effective charge. They suggested that BT would have a lower Q33 𝑍33 than that of BaZrO3 and PbTiO3. However, this result contradicts the computation by Jiang et al. and experimental data [21]. Therefore the origin of the composition-insensitive Q33 is still

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an open question needed to answer. Furthermore, although it is well accepted that the domains and their response with respect to external stimuli is very important to their functional

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properties [25, 31, 52-56], heretofore, there is no report on the domain morphology of the NN-xBT ceramics.

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In this work, we conducted a systematic investigation of the NN-xBT system for compo-

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sitions from 0.10 to 0.27 with emphasis on its electrostrictive property as well as domain

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morphology evolution. A composition- insensitive electrostrictive coefficient Q33 of 0.04

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m4/C2 for the NN-xBT system (0.22≤x≤0.27) suggests that the Q33 of pure NN would possess

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similar value, which has not been verified in pure NN ceramics by electrostrictive characterization. The underlying mechanism governing such a composition-insensitive Q33 was pro-

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posed based an ab initio computation. We found that the longitudinal Q11 of NN is lower than

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other simple perovskite compounds, however, its transverse Q12 shows the largest value among other studied compounds. It is suggested not only the Q11, but also the Q12, should also be taken into account to explain the origin of the composition-independent Q33 in NN-

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xBT ceramics. Domain morphology evolution was revealed by piezoresponse force microscopy. With respect to the increase of BT content, domain wall density decrease continuously from ferroelectric to relaxor state. This work not only shows a promising material which is potential to high-precision actuators, more importantly, but also paves a new path to enhance

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the Q33 in ferroelectric ceramics, i.e., by designing a novel compound with high Q12. 2. Experimental Conventional solid state reaction method was used to prepare NN-xBT ceramic samples. The x was set as 0.10, 0.15, 0.20, 0.22, 0.23, 0.24, 0.25 and 0.27. High purity of Na2CO3

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(99.8%), Nb2O5 (99.5%), BaCO3 (99%) and TiO2 (98%) powders (Sinopharm Chemical Reagent Co., Ltd, Shanghai, China) were used as raw materials. They were calcined at 1250 oC

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for 4 h and sintered at 1450 oC for 6 h in sealed crucibles. The details of the synthesis process can be found in Ref. [50]. X-ray diffraction (XRD, PANalytical, Cambridge, UK) analysis

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suggests pure perovskite structures. Polarization-electric field (P-E) loops, current-electric

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field curves (I-E) and strain-strain electric field curves (S-E) were collected simultaneously

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using a Sawyer-Tower circuit based on a commercial ferroelectric testing system (TF ana-

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lyzer 2000, aixACCT, Aachen, Germany). The strain was determined by a laser interferome-

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ter vibrometer (SP-S 120, SIOS Meβtechnik GmbH, Germany) and the measurement frequency is 1 Hz.

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Ceramic samples for scanning electron microscope (SEM) and piezoresponse force mi-

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croscopy (PFM) characterization were first polished with a gradual decrease of diamond abrasive (down to 0.25 μm), and then by a mechanochemical polishing with colloidal silica, by which the particle size is decreased below 100 nm. The investigated samples were sliced

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with a wire cutter and polished to 1-mm-thick pellets. For SEM measurement, the polishing surfaces were etched in an acid solution of hydrochloric acid (37%) and hydrofluoric acid (40%) with a volume ratio of 1:1 for 25 to 40 seconds. Then the acid etched morphologies were taken by a SEM (SU-1510, Hitachi, Japan). PFM investigations were performed with

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NTEGRA Aura (NT-MDT, Russia) and MFP-3D (Asylum Research, Oxford Instruments, UK). Asylum ASYELEC-01 commercial tips with Ti/Ir coating were used. A typical value of the curvature radius of the coated tips was about 28 nm as specified by the manufacturer. The spring constant and the resonance frequency of the cantilevers used were ~2 N/m and ~70

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kHz, respectively. The sample was attached to a polished metal disc by a conductive silver paint used also as a bottom electrode. The PFM signal was acquired by the application of an

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ac modulated voltage (5 V in amplitude) at low frequency (20 kHz) and near the resonance frequency (280 kHz).

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3. Results and discussion

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3.1 Ferroelectric properties

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According to our previous work [50], there is a tetragonal-to-cubic phase transition,

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which was revealed by XRD structure refinement at room temperature, at x=0.22 composi-

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tion. Therefore, we chose the compositions at both sides of this composition. Furthermore, because the ferroelectric properties of x = 0.23 and 0.25 compositions are very close to these

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ing section.

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with x = 0.22 and 0.24, their ferroelectric properties are only used to extract the Q33 in follow-

Fig. 1 presents room temperature P-E hysteresis loops for NN-xBT ceramics measured

at 1 Hz. For the x=0.10 sample, square P-E loops suggests a typical ferroelectric DW

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switching at coercive feild Ec [22]. With increasing x, P-E loops become slanted and slim. Finally, very slim and nonlinear P-E loops are observed in the x=0.27 composition. The general evolution of the P-E loops is consistent with a crossover from classical ferroelectrics to re-

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laxor-like ferroelectrics [13, 46, 47]. As discussed in Ref. [50], with increasing the BT content, the Tm decreased gradually from 225 oC to −6.9 oC. In this case, when the measuring temperature approaches the Tm for each composition, both the maximum polarization (Pmax) and remnant polarization (Pr) would decrease gradually, due to thermal fluctuation to the

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long-range order of the polarization [22]. The corresponding I-E curves for the compositions from x=0.1 to 0.27 are shown in Fig. 2. It is clear that only one single positive current peak

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(indicated by the black arrow) is observed in compositions with x=0.10, 0.15, and 0.20. These sharp current peaks are attributed to a typical domain switching process [22]. For x=0.22, two

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positive current peaks are detected from Fig. 2(d), as indicated by the arrows, although the

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distance between these two peaks is not large enough. Normally two current peaks are fre-

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quently observed in antiferroelectrics or ferroelectrics with pinning defect dipoles [29, 31, 57-

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59]. To present studied NN-xBT system, antiparallel arrangement of the dipoles (i.e., the anti-

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ferroelectricity) cannot be verified, and defect dipoles were not introduced into the crystal lattices by means of doping. Zuo et al. ascribed the pinched P-E loops to the coexistence of

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nonergodic and ergodic states of relaxor ferroelectrics [13, 60]. For x=0.24 and 0.27 composi-

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tions, single and broad current peaks are observed. This feature is related to the nature of relaxor ferroelectrics [39, 61-63]. Since polar nano regions (PNRs) switching does not happen in a relatively narrow electric field but in a broad region, a broad current peak can be ex-

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pected.

Fig. 3(a)-(f) present P-E hysteresis loops for the NN-xBT ceramics as a function of temperature. For each composition, its P-E loops become slim as temperature increases. To x=0.10 composition, the Pmax is almost temperature-independent. In contrast, the Pmax of

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other compositions shows degradation as temperature increases. In order to trace the evolution of the P-E hysteresis loops with respect to temperature quantitatively, we present Pmax, Pr and coercive field (Ec) as a function of temperature in Fig. 3(g)-(i). It is clear that the variation of Pmax, Pr and Ec is highly dependent of the TC. A composition possessing a higher TC

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would show higher temperature-stable properties. It is interesting to note that the Pmax and Pr for x=0.10 have a very small variation with respect to temperature (less than 5%). A large

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change of the trend of Pmax and Pr is observed between x=0.15 and 0.20 compositions. The Ec for x=0.10 and 0.15 decrease linearly with respect to the temperature. While for other compo-

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sitions, the Ec almost approaches zero when temperature increases, due to the nature of re-

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laxor ferroelectrics [13, 61-63]. The increase of both Pr and Ec for x=0.27 at high temperature

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region is attributed the increase of the ac conductivity, which is thermally activated at ele-

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vated temperatures [64, 65] and has already been revealed by dielectric property characteriza-

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tion [45]. It is interesting to note that in x=0.22 and 0.24 compositions, very slim P-E loops suggest their potential application in energy storage application [66-72]. A ferroelectric mate-

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rials with slim and slanted hysteresis loops would possess large Pmax and small Pr simultane-

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ously, resulting in a high energy storage efficiency [22]. Fig. 4 presents bipolar S-E curves for the NN-xBT ceramics as a function of tempera-

ture. For x=0.10 and 0.15 compositions, typical butterfly S-E curves, including both positive

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and negative strains, are observed. The large hysteresis and negative strains in the S-E curves are ascribed to the domain switching. Normally both positive and negative strains can be observed in piezoelectric ceramics once the direction of electric field is reversed. In contrast,

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only positive strain can be observed in electrostrictive ceramics, since the strain is proportional to the square of the electric field or polarization [11, 21]. For x=0.20 composition, butterfly S-E curves are observed at lower temperatures (30 oC~60 oC), while hysteresis-free S-E curves without negative strains are observed at higher temperatures (>60 oC). These features

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suggest a piezoelectric-to-electrostrictive crossover [73]. For x=0.22, 0.24, and 0.27 compositions, only pure (positive) electrostrictive strains are observed in all measuring temperatures.

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Fig. 5 shows positive strain Spos (determined at +Emax), negative strain Sneg [determined as indicated in Fig. 4(a)], and phase diagram for the piezoelectric/electrostrictive strain with re-

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spect to composition and temperature. It can be seen that the Spos in bipolar mode is very sim-

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ilar to the Smax in unipolar mode. However, as shown in Fig. 5(b), only in three compositions

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(x=0.10, 0.15 and 0.20), negative strain are observed. The missing of the negative strain in

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other compositions suggests a pure electrostrictive effect dominates the strain response.

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Therefore a crossover from the piezoelectric to electrostrictive transition can be identified through the negative strain with respect to the temperature and composition. In Fig. 5(c), the

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boundary between the piezoelectric and electrostrictive strains is very close to the boundary

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determined by the dielectric spectrum. It is noted that to x=0.20 composition, pure electrostrictive can be obtained at 90 oC, while is around 30 oC higher than the Tm of this composition.

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3.2 Electrostrictive properties Fig. 6 presents the S-P curves for the NN-xBT ceramics as a function of temperature, and the data are obtained from Figs. 3 and 4. In principle, a parabolic relationship between the S and P as expressed by Eq. (1) can be expected in an electrostrictive material [8, 11, 21].

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For x=0.10 [Fig. 6(a)], it is clear that the S-P curves deviate from the parabolic relationship, and a large hysteresis due to the interference by the domain switching is observed from 30 oC to 120 oC. For x=0.15 [Fig. 6(b)], although its S-P curves still deviate from the parabolic relationship, the hysteresis becomes smaller gradually as temperature increases. For other com-

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positions [Fig. 6(c)-(f)], a parabolic relationship is identified 30 oC to 120 oC by the quadratic fittings. These results suggest that a pure electrostrictive effect governs the electric field-in-

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duced strain in these four compositions. In order to obtain real and accurate Q33, the P-E

loops and S-E curves should be measured at higher temperatures and electric field. Note that

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even the measuring temperature and electric field are increased to 180 oC and 60 kV/cm, re-

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spectively, the hysteresis still exists in x=0.10, and decreases to a large extent in x=0.15 (see

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Figs. S1 and S2). Therefore the Q33 for x=0.15 was determined accurately using high temper-

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ature data.

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The Q33 as a function of temperature for x=0.15~0.27 compositions are shown in Fig. 7(a). Fig. 7(b) shows the Q33 as a function of composition for x=0.15~0.27. Even though the x

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is increased from 0.15 to 0.27, the variation of Q33 is also rather small, giving an average Q33

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as 0.0406 m4/C2. This value is a little bit smaller than the value reported by Zuo et al. (0.046 m4/C2) [13], but is still in a high value region for perovskite ferroelectrics [11, 21]. Based on these observations, we conjecture that pure NN might possess a similar Q33 value around 0.04

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m4/C2, although the Q33 for pure NN is still not available up to present. In order to explore the origin of the composition-insensitive Q33 in NN-xBT system, we performed an ab initio computation using an open-source ABINIT software package to study the effect of a given polari-

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zation on the relative displacement of pure NN, which direction is along (c axis) and perpendicular to (a axis) the direction of polarization. The details of the computation was reported in Ref. [51]. The strains along (x3) and perpendicular to (x1) the polarization is calculated using x3=(c−ac0)/ac0 and x1=(a−ac0)/ac0, where c and a are the displacements from a cubic lattice

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with respect to the increase of polarization, and ac0 is the relaxed cubic lattice constant. As shown in Fig. 7(c), the x3 elongates with respect to the increases of polarization, while x1 con-

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tracts at the same time. Both x3 and x1 versus polarization are quadratic (as proven by the fitting), suggesting that electrostrictive effect dominates the mechanical response with respect

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to the polarization. The longitudinal Q11 and transverse Q12 for NN are 0.0659 m4/C2 and

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−0.0434 m4/C2, respectively. For BT, the Q11 and Q12 are 0.137 m4/C2 and −0.026 m4/C2. The

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comparison of Q11 and Q12 for some typical perovskite-structure compounds, including NN,

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BT, KN (kNbO3), ST (SrTiO3), BZ (BaZrO3) and PT (PbTiO3), is shown in Fig. 7(d). Among

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these compounds, NN has the lowest Q11. In contrast, it also has the largest Q12 (absolute value). Our calculation is performed on a cubic crystal lattice. As we know, for polycrystal-

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line ceramics, the physical properties of polycrystalline ceramics are always average of the

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properties along different crystal direction (i.e., anisotropy of the physical properties). In principle, if we learn the distribution of gains with respect to the external stimuli, we could calculate the average properties of ceramics from its crystal properties. The average Q33 for

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ceramic sample can be expressed as f(Q11,Q12), where f is the function related to the distribution of the grains. Although the specific expression of f function is not derived at present, our calculation suggests that Q12 may play an important role to the average Q33. 3.3 Domain structures

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Fig. 8 shows the etched surfaces of the NN-xBT ceramics taken by SEM. After etching in acid solution, grain boundaries are well revealed and some of domain structures (strip-like structures) can also be recognized especially in the compositions with less BT content (x<0.22). The grain size of compositions with x=0.10 is around 5 m, and then it is drasti-

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cally decreased to 1~2 m as the x increases to 0.27. Since the electromechanical properties of ferroelectric ceramics are highly corrected to their domain structures, in this section, we

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would to study the domain structures of NN-xBT ceramics mainly by means of PFM. Both

the surface topography and domain structure of the NN-xBT ceramics were revealed by the

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in-phase (IP) PFM images in amplitude mode are shown in Fig. 9. It can be seen that domain

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walls are observed clearly. Domain size becomes smaller gradually as x increases, suggesting

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that long-range order is disturbed by BT. This feature is consistent with decreases of the TC

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for NN-xBT ceramics [13, 50]. In the samples with lower x content, bending domain struc-

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tures with obvious contrast are found in the whole scanning areas [Fig. 9(a) and (b)]. According to previous report [50], a tetragonal P4mm symmetry is verified for the compositions

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from 0.10 to 0.20. Normally, straight banded-like domains are often reported in tetragonal

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phase ferroelectric materials, for example BT and Pb(Zr0.45Ti0.55)O3 [74, 75]. However, the bending domains observed in the NN-BT systems are totally different from these observations. In contrast, domain structures are well depicted only in few grains in the samples with

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high x content [Fig. 9(c)-(f)]. For these samples with high x, the corresponding TC has been shifted to or below room temperature [50], only residual nanodomains can be detected. In addition, the distribution of these residual domain structures is inhomogeneous. To identify conjecture, we performed a selected area PFM measurement in x=0.22 composition. As shown in

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Fig. 10(a), two points (A and B) in one grain were scanned by PFM with the same voltage amplitude. In point A area, where clear domain walls are reveled, a large hysteresis is observed [Fig. 10(b)]. In contract, in point B area, almost no domain walls can be detected and the corresponding PFM signal shows very small hysteresis compared with that of point A

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[Fig. 10(c)]. These observations verified the inhomogeneity of the domain distribution. Furthermore, In order to clarify the relationship between the domain structures and BT

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content x, we used vector PFM (VPFM) analysis to extract the domain wall density [76, 77]. As shown in Fig. S3, the 2D VPFM images show higher contract than these in IP PFM. The

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domain walls can be well depicted by the blue lines. Since the domain walls distribute inho-

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mogeneously in the whole scanning region, we performed the statistics only in selected re-

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gion (indicated by the yellow square frames). Domain wall density as a function of x is

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shown in Fig. 11. In x=0.1 composition, a domain wall density around 10 m−1. Then the

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density decreases gradually as x increases. When x is large 0.22, the scattering distribution of density around 6 m−1 suggests the saturated value of the domain wall density. Although in

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these compositions, large domains cannot be developed due to the disturbance by the BT con-

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tent to the long-range order, domain wall density is also not increased with respect to the decrease of the domain size.

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4. Conclusions

In this work, the electrostrictive properties and domain morphology in lead-free NN-xBT solid solution (0.1≤x≤0.27) have been investigated systematically. As x increases, a piezoelectric-to-electrostrictive crossover is identified by bipolar S-E curves. Pure electrostrictive effect is revealed by the hysteresis-free strain response, which are observed in compositions 14

with x>0.22. A composition-insensitive Q33 around 0.0406 m4/C2 is verified in the NN-BT system. The ab initio computation shows that NN has the lowest Q11 but highest Q12 among several studied perovskite-structure ferroelectrics. We suggest that not only the Q11 but also the Q12 should be taken into account to explain the composition-insensitive Q33 in this system.

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Bending domain structures and nanodomains are observed in compositions with tetragonal and cubic symmetries, respectively. The inhomogeneity of the domain wall distribution as

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well as continuous decrease of domain wall density with respect to the increase of x are also revealed by PFM.

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Acknowledgments

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This work was supported by the National Nature Science Foundation of China (Grant

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Nos. 51772239, 61404106 and 51761145024), the Natural Science Basis Research Plan in

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Shaanxi Province of China (Grant Nos. 2015JM5199, and 2017JM5016), the Fundamental

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Research Funds for the Central Universities (XJTU), and the doctoral starting fund of Xi'an University of Technology under Grant No. 101-256211306. We thank the Science-IT Project

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and TRITON of Aalto University for providing computational resources. The SEM work was

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done at International Center for Dielectric Research (ICDR), Xi’an Jiaotong University,

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Xi’an, China. We also thank Mr. Kun Yu for his help in using SEM.

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Figure captions Fig. 1. Room temperature P-E hysteresis loops for NN-xBT ceramics measured at 1 Hz: (a) x=0.10, (b) x=0.15, (c) x=0.20, (d) x=0.22, (e) x=0.24, and (f) x=0.27.

Fig. 2. Room temperature I-E curves for NN-xBT ceramics measured at 1 Hz: (a) x=0.10, (b)

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x=0.15, (c) x=0.20, (d) x=0.22, (e) x=0.24, and (f) x=0.27. The arrows indicate the positive

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current peak positions.

Fig. 3. P-E hysteresis loops for NN-xBT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the maximum electric field is 40

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kV/cm. (a) x=0.10, (b) x=0.15, (c) x=0.20, (d) x=0.22, (e) x=0.24, and (f) x=0.27. (g) Pmax, (h)

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Pr and (i) Ec as function of temperature for NN-xBT ceramics extracted from P-E loops [(a)-

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(f)].

Fig. 4. Bipolar S-E curves for NN-xBT ceramics measured from 30 oC to 120 oC with a tem-

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perature step of 10 oC. The measuring frequency is 1 Hz and the maximum electric field is 40

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kV/cm. (a) x=0.10; (b) x=0.15, (c) x=0.20, (d) x=0.22, (e) x=0.24, and (f) x=0.27.

Fig. 5. (a) Positive strain Spos and (b) negative strain Sneg as function of temperature for NN-

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xBT ceramics extracted from bipolar S-E curves. (c) A composition-temperature phase diagram of the piezoelectric and electrostrictive properties determined by the S-E curves and di-

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electric properties.

Fig. 6. Bipolar S-P curves for NN-xBT ceramics measured from 30 oC to 120 oC with a temperature step of 10 oC. The measuring frequency is 1 Hz and the maximum electric field is 40 kV/cm. (a) x=0.10; (b) x=0.15, (c) x=0.20, (d) x=0.22, (e) x=0.24, and (f) x=0.27. Open circles connected by the thin lines represent the experimental data, while the solid bold lines are 23

the fitting curves based on Eq. (1).

Fig. 7. (a) Q33 as a function of temperature for NN-xBT ceramics. (b) Q33 as a function of composition for NN-xBT ceramics. (c) Out-of-plane strain x3 and in-plane strain x1 as a function of polarization. The solid lines are the fitting curves based on Eq. (1). (d) Longitudinal

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electrostrictive Q11 and transverse electrostrictive −Q12 of NN, BT, KN (kNbO3), ST (SrTiO3), BZ (BaZrO3) and PT (PbTiO3). In principle Q12 possesses negative value, indicat-

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ing a contraction with respect to the external stimuli. Here we used –Q12 to denote its absolute value to compare with Q11 for convenience.

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Fig. 8. SEM images of acid etched surfaces for NN-xBT ceramics. (a) x=0.10; (b) x=0.15, (c)

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x=0.20, (d) x=0.22, (e) x=0.24, and (f) x=0.27.

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Fig. 9. PFM images in amplitude mode for NN-xBT ceramics. (a) x=0.10; (b) x=0.15, (c)

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x=0.20, (d) x=0.22, (e) x=0.24, and (f) x=0.27.

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Fig. 10. (a) PFM image in amplitude mode for x=0.22 composition. The amplitude as function of voltage was measured at point A (b) and point B (c), which are indicated by the white

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hollow circles in (a).

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Fig. 11. Domain wall density as a function of x. The straight dash line is a guide for the eye.

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