Structural Evolving Sequence and Porous Ba6Zr2Nb8O30 FerroelectricCeramics with Ultrahigh Breakdown Field and Zero Strain

Shan-Tao Zhang,‡,† Guoliang Yuan,§,† Jun Chen,¶ Zheng-Bin Gu,‡ Bin Yang,k

Jiang Yin,‡ and Wenwu Caok

‡National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering,Nanjing University, Nanjing 210093, China

§School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

¶Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, China

kCondensed Matter Science and Technology Institute, Harbin Institute of Technology, Harbin 150001, China

Microstructural evolving sequence of relaxor ferroelectric

Ba6Zr2Nb8O30 (BZN) ceramics has been investigated and dis-

cussed. Porous BZN, which has an irregular grain networkwith pores, can be obtained within a narrow sintering window

(sintering temperature of ~1250°C and dwelling time of ~5 h in

our experiments). X-ray diffraction-based structure refinements

determine the atomic positions and confirm that the porousceramics has tetragonal tungsten bronze structure with P4bmspace group symmetry. It is found that the most porous cera-

mic has the lowest dielectric constant, highest electric fieldbreakdown strength, and nearly zero macroscopic electric field-

induced strain. These features can be related to the porous

microstructures by comparing with the denser counterparts and

can be well understood by using brick-wall model. Our resultsmay provide useful information for the understanding of micro-

structure evolving sequence of BZN during sintering and the

structural effects on electric properties of ceramics. Our work

may also provide a reliable way for developing porous ferro-electric ceramics with special properties.

I. Introduction

POROUS materials are very important for fundamentalresearch as well as practical applications because many

porous materials have unique microstructures and/or tunableelectric, magnetic, optical, and mechanical properties, whichmake porous materials indispensable in daily life as adsor-bents, catalysts, etc. Up to now, the development of porousmaterials has been mainly based on organic materials andsome simple inorganic materials such as Si, Al2O3, MoO3,etc.1–5 On the other hand, complex oxides such as perovskiteABO3 ferroelectrics have been widely applied in many fieldssuch as transducer, actuator, and memory, etc. Some artifi-cial porous ferroelectric ceramics and films have beenreported as porous microstructure can improve the break-down voltage, mechanical strength, electromechanical, andpyroelectric properties, and can also make the dielectricconstant more uniform.6–10 In general, it is relatively difficult

to get porous microstructures in ferroelectrics due to theircomplex structures. To produce porous microstructure inferroelectric ceramics/films, some carbon-based pore-formingadditives, such as carbon nanotubes and polymethylmethac-rylate (PMMA) are necessary.7–11 For many ferroelectricceramics prepared with starting carbonate raw materials, therelease of CO2 and other gases during sintering may havesimilar effect with the pore-forming additives. This methodhas not been well investigated due to the complexity ofrelated sintering process, and this process involves the devel-opment of pores formed by the release of gases and theinherent pores, which act as interparticle voids in compactpowders at the primary stage.12 As all well-sintered ferroelec-tric ceramics have dense microstructures with independentgrains, porous microstructures might be formed only at acritical stage with shorter sintering time. To clarify this point,systematical investigation on the microstructural evolutionsequence during sintering is necessary, which, althoughimportant for understanding sintering kinetic and process,has not attracted enough attentions in ferroelectric ceramics.

On the other hand, as one of the disordered systems,relaxor ferroelectrics have some unique properties, andhence, continue to be one of the attractive topics in both sci-entific research and practical applications.13–17 At present,lead-based ferroelectrics such as perovskite solid solutions Pb(Mg,Nb)O3–PbTiO3, show higher degree of relaxor behaviorthan lead-free perovskite counterparts, particularly, in thetemperature range above room temperature.13,16,17 As relaxorbehavior often increases functionality of materials, it wouldbe useful to develop lead-free ferroelectrics with high degreeof relaxor behavior, which might be also helpful for thedevelopment of lead-free piezoelectric materials. Tungstenbronze oxide has the formula of (A1)2(A2)4C4(B1)2(B2)8O30,and the smallest triangular C interstice is generally empty.These type of oxides, in single crystal, ceramic and thin filmforms, have attracted much attention because of the follow-ing: (1) They have unique physical properties, such as sec-ond-order nonlinear optical, normal/relaxor ferroelectric,piezoelectric, and pyroelectric properties that are importantfor many technical applications18–21; (2) They are goodobjects to investigate mechanism for ferroelectric relaxorbehavior22–24; (3) Their complex structure, for example, thecrystallographically nonequivalent A, B, and C sites, allowsartificial manipulation of the structure and thus, provides theflexibility to design the properties by chemical substitution,doping, etc.23 Tungsten bronze oxides have variable Curietemperature, such as ~ �100°C for Sr6Ti2Ta8O30 and 230°CBa6Ti2Nb8O30,

25 and diverse structures and properties, e.g.,tetragonal, orthorhombic structures and relaxor ferroelectric

S. Zhang—contributing editor

Manuscript No. 31809. Received July 25, 2012; approved October 11, 2012.†Authors to whom correspondence should be addressed. e-mails: stzhang@nju.edu.

cn and yuanguoliang@njust.edu.cn

555

J. Am. Ceram. Soc., 96 [2] 555–560 (2013)

DOI: 10.1111/jace.12082

© 2012 The American Ceramic Society

Journal

nature.18,24,26–29 It is generally accepted that ionic type/radiusin this tungsten bronze oxide family is one of the key factorsfor determining the structures and macroscopic proper-ties.28,29 Up to now, reported Ba6Ti2Nb8O30 and its ana-logues have the same characteristics, i.e., the B sites areoccupied by ferroelectrically active ions, such as Ti4+ andNb5+,18,26–29 whereas only few reports on analogues substi-tuted by nonferroelectrically active ions, such as Ga3+, Sc3+,and In3+ in B-sites (Ba6M

3+Nb9O30). This is due to the factthat such non-ferroelectrically active ions substitution notonly changes the ionic ratio of the host compound but alsobrings some second phases.24,30 Ba6Zr2Nb8O30 (BZN), whichcan be considered as a natural equal-valence B-site substitu-tion of non-ferroelectrically active Zr4+ for ferroelectricallyactive Ti4+, is an isostructural analogue of Ba6Ti2Nb8O30.Although BZN is mentioned briefly to be a relaxor ferroelec-tric material,25 its detailed structural parameters and electri-cal properties have not been investigated intensively.

In this article, tungsten bronze BZN ceramics have beenprepared with starting raw materials of BaCO3, ZrO2, andNb2O5 and it is found that single-phase porous BZN ceram-ics can be obtained without any additive within a criticalsintering stage. The microstructure evolution sequence hasbeen investigated systematically. The porous ceramics havehigh degree relaxor behavior. More interestingly, uniqueproperties of the porous ceramics are obtained: the porousceramics have low dielectric constant of 550, negligible mac-roscopic electric field-induced strain and can endure ultrahighelectric field of 15 kV/mm. All these features can be relatedto the porous structure by comparing with the results ofdense structure counterparts.

II. Experimental Procedure

By conventional ceramic fabrication method using BaCO3

BZN ceramics were prepared (99.8%; Alfa Aesar, MA),ZrO2 (99.9%; Alfa Aesar), and Nb2O5 (99.9%; ChemPur,Karlsruhe, Germany) as starting raw materials. They wereweighed according to the stoichiometric formula and ball-milled for 24 h in ethanol. The dried slurries were grounded,calcined at 750°C for 3 h, grounded again, and ball-milledagain in ethanol for 24 h. The powders were subsequentlydried, grounded and pressed into green disks with a diameterof 10 mm under 70 MPa pressure. The samples were sinteredin covered alumina crucibles at 1150°C for 5 h (S-1), 1250°Cfor 2 h (S-2), 1250°C for 5 h (S-3), 1250°C for 10 h (S-4),and 1350°C for 5 h (S-5), respectively. It is noted that withnaked eye examination, S-1 has white color because it is notwell sintered, other well-sintered samples have brown color,but S-2 and S-3 samples have some scattered dark dots.

The density was determined by the Archimedes method.The crystal structures of the ceramics were characterized bypowder X-ray diffraction (XRD; Rigaku Ultima III, RigakuCorporation, Tokyo, Japan) using crushed and unpoled sin-tered samples. Structure refinements were carried out by meansof XRD Rietveld method. For the microstructure observation,a scanning electron microscopy (SEM; XL 30 Philips, Philips,lnc., Amsterdam, The Netherlands) analysis was performed onfractured samples. To evaluate the reaction process, thermo-gravimetric and differential scanning calorimetric (TG-DSC;NETZSCH GmbH, Selb, Germany) measurements were car-ried out on the calcined powders with a heating rate of 10°C/min.

Electric measurements were carried out on sintered diskswith a typical radius of ~6 mm and thickness of ~0.4 mm.The circular surfaces of the disks were covered with a thinlayer of silver paste and fired at 550°C for 30 min. Dielectricconstant (er) and loss tangent (tand) of unpoled ceramicswere measured using an impedance analyzer (HP4294A,Hewlett-Packard Company, Palo Alto, CA) at differentfrequencies in the temperature range from �120°C to200°C. Electric measurements were carried out at room

temperature in silicone oil. Both polarization-electric field(P–E) and strain-electric field (S–E) curves were measured at1 Hz using TF analyzer 1000 (AixACCT, Aachen,Germany).

III. Results and Discussion

The phase evolution of ceramics during sintering process hasbeen studied through XRD patterns as shown in Fig. 1(a).After the mixed powders have been calcined at 750°C for3 h, the BZN phase begins to form with considerable inter-mediate phases being detected, typically indicated by thestrongest diffraction peak located at 2h = 30.5° which corre-sponds to Ba5Nb4O15, as indicated by the red star. Withhigher sintering temperatures of 1150°C and 1250°C, butshort dwelling time of 0.5 h, the BZN phase become domi-nant as the intermediate phases show dramatically decreaseddiffraction intensity. The above results suggest that the chem-ical reaction mainly happened within the initial sinteringstage.

The S-1 and S-2 ceramics, which have been sintered at1150°C for 5 h, 1250°C for 2 h, respectively, show tungstenbronze BZN structure although a very small diffraction peak

(a)

(b)

Fig. 1. (a) The XRD patterns of all calcined powder (750°C, 3 h),and the ceramics sintered at 1150°C for 0.5 h, 1250°C for 0.5 h,1150°C for 5 h (S-1), 1250°C for 2 h (S-2), 1250°C for 5 h (S-3),1250°C for 10 h (S-4), and 1350°C for 5 h. (b) Structure refinementof the S-3, where the corresponding structural sketch is also shown.

556 Journal of the American Ceramic Society—Zhang et al. Vol. 96, No. 2

indicated by the red star exists, suggesting tiny residual inter-mediate phases while S-3, S-4, and S-5, which have been sin-tered at 1250°C for 5 h, 1250°C for 10 h, and 1350°C for5 h, respectively, are single-phase tungsten bronze BZNceramics without any detectable secondary phases within theresolution of our XRD. Obviously, sintering at 1250°C for5 h is enough to allow the formation of single-phase BZN.The detailed structures of the single-phase ceramics (S-3, S-4,and S-5) have been further analyzed by using structuralrefinement, typical result of S-3 is shown in Fig. 1(b) andTable I. There are eight large (Zr/Nb)O6 oxide octahedra at8d sites and two small (Zr/Nb)O6 oxide octahedra at 2b sitesin a Ba6Zr2Nb8O30 crystal cell, as shown in inset of Fig. 1(b).The large Ba2+ cation imparts rigidity to the metal oxide

framework, resulting in a tetragonal structure with P4bmsymmetry, consistent with previous report on BZN25 S-4 andS-5 have the same crystal structure.

The microstructure evolution sequence can be clearly seenfrom the SEM measurements shown in Figs. 2(a)–(e). ForS-1, which has been sintered at 1150°C for 5 h, its micro-structure is shown in Fig. 2(a). One can see that theconnected irregular-shaped grains are formed within ahomogeneous compact background, and the grain bound-aries are not clearly defined. Some intergranular pores can bedetected, which may come from the release of gases fromresidual BaCO3/intermediate phases. In addition, S-1 has ahigh relative density of 91.5% (Fig. 3) and is not well crystal-lized. Actually, S-1 is white in color, similar to the greenbody, whereas S-2, S-3, S-4, and S-5 are brown in color. Webelieve that at the initial sintering stage [Fig. 2(a)], single-phase BZT are nearly formed and the gas are releasedsmoothly when residual BaCO3/intermediate phases decom-pose, leading to intergranular pores. For S-2 sample, a lot ofCO2 gases have been fast released from intermediate phasedecomposition and the S-2 ceramic also shrinks faster at1250°C than that of S-1 at 1150°C. When a part of interme-diate phase is rigorously embraced by a big grain or manygrains, the CO2 gas cannot be released smoothly similar tothat of S-1 and thus it may form many close intergranularpores with high pressure. When the pressure of these closedpores is high enough to erupt, it destroys the shrinking pro-cess and creates many bigger intragranular pores so that CO2

can be released to air. All these processes decreasethe relative density to 87.8% of S-2 (Fig. 3). When S-3 issintered at 1250°C for 5 h, the trend discussed in S-2

Table I. Structure Parameters of the Porous BZT Ceramics (S-3)

Tetragonal P4bm

Atomic position

Atomic Site x y z

Ba1 2a 0.0 0.0 0.35047(8)Ba2 4c 0.17236(2) 0.67236(2) 0.36380(4)Zr/Nb1 2b 0.0 0.5 0.85312(9)Zr/Nb2 8d 0.07577(2) 0.21 272(9) 0.84830(2)O1 2b 0.0 0.5 0.35555 (9)O2 4c 0.22820(9) 0.72820(9) 0.82399(2)O3 8d 0.07261(4) 0.20648(7) 0.34981(7)O4 8d 0.34563(3) 0.01554(5) 0.85407(9)O5 8d 0.14804(4) 0.07300(8) 0.85457(2)

Lattice parameter: a = 12.6507(1) A, c = 4.0027(8) A, V = 640.604 A3

R-value of Rietveld refinements: Rwp = 8.5%

(a) (b)

(d)(c)

(e)

Fig. 2. The SEM images of (a) S-1, (b) S-2, (c) S-3, (d) S-4, and (e)S-5 showing the structural evolving sequence of the BZN ceramics.Clearly, S-2 and S-3 show porous microstructures.

Fig. 3. The relative densities of all ceramics.

February 2013 Porous Ba6Zr2Nb8O30 Ceramics 557

continues: More high-pressure pores and closed pores areformed and then erupt at the first stage of 1250°C, sothat the relative density of S-3 decreases further to 81.8%(Fig. 3). The porous microstructure and the correspondingproperties of S-3 can be well explained based on brick-wall model, as will be discussed subsequently. Figures 2(b)and (c) show the sintering stage described above. WhenS-4 is sintered at 1250°C for 10 h [Fig. 2(d)], condition issufficient for intragranular and intergranular pores toevolve, which pushes the majority of pores outside of theceramics, so that the connected grains tend to be discon-nected, and independent rectangle/cubic-shaped grains areformed. At this stage, the porous structure recrystallizes,the density recovers to a high level of 91.2% (Fig. 3).When S-5 is sintered at 1350°C for 5 h [Fig. 2(e)], temper-ature/time is high/long enough to push most of poresoutside of ceramics and then densify the ceramics, andincrease the relative density to 92.5% (Fig. 3); therefore,after the final stage dense ceramics with well-shaped inde-pendent grains can be obtained.

The microstructure difference between the S-4 and S-5should be mentioned. For S-4, the distribution of grains isnot homogeneous. The tiny grains are connected together toform grain groups, which distribute randomly with voidsbetween them. However, this is not the case for S-5, whichhas a relatively independent and homogeneous grain distribu-tion. In other words, S-4 has an intergrading microstructurebetween porous and dense ceramics.

The above described process is further confirmed by theTG-DSC measurements shown in Fig. 4. From room temper-ature to 800°C, the weight loss is only 0.7%, accompaniedby a flat DSC curve, which implies continuous formation ofintermediate phases, decomposition of residual raw materials,and release of CO2. This is consistent with the XRD resultsof calcined powders shown in Fig. 1(a). From 800°C to1300°C, a significant weight loss of 3.7% is observed. Fur-thermore, there is a broad exothermic peak near 1030°C,indicating that the reaction to form BZN phase and therelease of CO2 primarily occur around this temperature.

It might be concluded that the process of ceramic expand-ing and then shrinking is a common phenomenon when car-bonates, e.g., BaCO3, are used as raw materials on conditionthat the sintering temperature and time is delicately balanced.For oxide ceramics sintered with BaCO3, for example, theintermediate phases could be formed, and CO2 gas should becreated and released during sintering as starting raw materi-als have a similar structural evolving sequence because forsuch ceramics. The releasing process will create releasingpath, which can lead to cross-linked porous structures asshown in Figs. 2(b) and (c). Although the CO2 gases arereleased completely, the shrinking process will break thecross-linked porous structures and result in independentgrains as shown in Figs. 2(d) and (e). It is noted that S-3 hasthe lowest relative density of ~ 81.8% (Fig. 3), significantlylower than that of other samples and reported well-densifiedferroelectric ceramics.31,32 By assuming P=(q0�q)/q, where

q0 and q are the measured and theoretical densities, respec-tively,11 the S-3 sample has the highest volume fraction ofpores P~18.2%, which is comparable with that reportedBi0.5Na0.5TiO3-based porous thick films.11

Scanning Electron Microscopy images showing thedetailed microstructure of porous S-3 sample are given inFigs. 5(a) and (b), respectively, in different scales. It can beseen that irregular grains are connected together to form anetwork with connecting pores, i.e., the pores and grainsform a 3-3 type composite structure.11 In addition to theconnecting irregular pores, some intragranular bowl-shapedpores of different sizes can be observed on grain surfaces, astypically indicated by the green circles in Fig. 5(b), which arerelated to the residual gases in grains.

It is found that porous BZN ceramics can only beobtained in a narrow sintering window (1250°C, 2–5 h in ourexperiments). At a critical intermediate sintering condition(1250°C, 5 h), the ceramics have the most porous structure.Therefore, our discussions will mainly focus on porousceramics sintered at 1250°C for 2 and 5 h (S-2 and S-3), andsome data of well-sintered dense ceramics (S-4 and S-5) willbe used for comparison. It should be mentioned that the S-1ceramic has high leakage current for electrical measurementsdue to the poor crystalline quality.

The typical temperature-dependent dielectric constant (er)and loss tangent (tand) of the most porous ceramics (S-3) areplotted in Figs. 6(a) and (b), respectively. As can be seen, theer and tand show significant frequency dependence withbroad peaks. With increasing frequency, both the maximumer and tand shift to higher temperature. This means that theporous BZN ceramics have a typical relaxor ferroelectricnature.13 An empirical relation can be used to determine thedegree relaxor nature:

lnð1=erÞ � ð1=er;maxÞ ¼ c lnðT� TmÞ þ C

where ɛr,maxis the maximum ɛr value at T = Tm, c(1 � c � 2) is the diffuse exponent, and C is a constant.

Fig. 4. TG-DSC curves of the calcined powders.

(a)

(b)

Fig. 5. Detailed porous microstructure of the S-3, showing the 3-3typed spatial intergranular arrangement of pores and grains (a), andthe intragranular pores (b).

558 Journal of the American Ceramic Society—Zhang et al. Vol. 96, No. 2

Generally, c = 1 corresponds to normal ferroelectric naturewhile c = 2 to a complete disorder system.21 As shown inFig. 6(c), porous BZN ceramics show an ultrahigh relaxordegree of 1.87 at 100 kHz, significantly higher than otherreported tungsten bronze oxide ceramics.21,29 It is also foundthat S-2, S-3, S-3, and S-5 samples have similar relaxorbehaviors, which indicates that the relaxor is almost micro-structure-independent. The ɛr,maxof S-2, S-3, S-4, and S-5 at100 kHz are plotted in Fig. 6(d). Clearly, S-3 has the lowestɛr,max. This is because the dielectric constant of air is verylow (~1) and S-3 has the most porous microstructure so thatthe 3-3 composite has the lowest dielectric constant. Thisresult is understood by using brick-wall model. Based on thismodel, the pores and grain are simplified to have seriescapacitance geometry if neglecting the different dielectricconstants between grains and grain boundaries, so

e�1eff ¼ Pe�1

air þ ð1� PÞe�1grain where P is the volume fraction of

pores, eeff is the effective dielectric constant, ɛair is the dielec-tric constant of pore (air), and ɛgrain is the dielectric constantof grains. Therefore, in a simplified model by assuming theegrain is constant and eair = 1, there is eeff ¼ egrain

1þPðegrain�1Þ. As

confirmed by both experimental results and theoretical calcula-tions, more pores will generally reduce the dielectric constantof high dielectric constant materials.33,34 Actually, a similardecrease in the dielectric constant has been reported in porouslow dielectric constant materials with porous structure.2

Polarization-electric field (P–E) hysteresis loops have beenmeasured with 1 Hz frequency. It is found that S-1 has highleakage and will electrically breakdown with field higher than6 kV/mm. Fig. 7(a) represents the room temperature P–Ehysteresis loops of the porous BZN ceramics (S-2 and S-3).For comparison, well-sintered dense ceramics (S-4 and S-5)are also potted in the same figure. There are some interestingfeatures about the P–E loops. Firstly, the well-sinteredceramics (S-2, S-3, S-4, and S-5) have very slim P–E loops,slimmer than that of other reported tungsten bronze oxideceramics,19–21,27 which is an indication of strong relaxorcharacter of BZN.28 Secondly, for each sample, the appliedfield shown in Fig. 7(a) is close to the electrical breakdownfield. For example, for S-3, the applied field for mea-surements is 15 kV/mm, and very close to the electricalbreakdown field level. Hence, the figure also shows the other fea-ture that ceramics with more porous microstructure have higherbreakdown strength. The highest endurable electric field for eachsample is 6, 11, 15, 10, and 10 kV/mm, respectively, for S1-S5samples as plotted in Fig. 7(b). Clearly, the most porous sample(S-3) has the highest breakdown field of 15 kV/mm, which isalso significantly higher than other reported tungsten bronzeoxide ceramics.18–20,25 According to the brick-wall model, porescan induce strong depolarizing field,33 which is opposite to theapplied electric field. In addition, as similar analysis of the abovepore-induced decrease in effective dielectric constant, pores candecrease the effective field on grains. So it is reasonable that por-ous ceramics can endure relatively higher applied electric fieldthan dense counterparts.

As shown in Fig. 8, all porous ceramics show a weak but-terfly-shaped strain-electric field (S–E) curve. However, themacroscopic field-induced strain is almost negligible (with thevalue of ~0.015% for S-3 at an applied field of 15 kV/mm),while the well-sintered, densest sample (S-5) has the muchdistinct butterfly-shaped S–E curves with improved strainvalue. The field-induced strain can be relaxed by pores,which is responsible for the near negligible strain of porousceramics of S-2 and S-3. The connected pores provide con-nected space in microstructure scale for the field-induceddimension change in the grains, and the space is largeenough to relax the field-induced dimension change. There-fore, the macroscopic strain is almost negligible for porous

(a)

(b)

Fig. 7. (a) P–E ferroelectric loops of all samples. (b) The highestendurable field of samples.

Fig. 8. Porous ceramics show almost zero field-induced strain,whereas the dense counterpart shows butterfly-shaped S–E curvewith improved strain value.

(a) (b)

(c) (d)

Fig. 6. The temperature-dependent relative dielectric constant (a)and loss tangent (b) of the most porous S-3. (c) S-3 has high relaxorcharacterization. (d) The er,max of all ceramics, the most porousceramics have the lowest er,max.

February 2013 Porous Ba6Zr2Nb8O30 Ceramics 559

ceramics of S-2 and S-3. Although S-4 is relatively dense, italso shows negligible strain, which is different from thatfound for dense S-5. This fact might be due to the fact thatS-4 has intergrading microstructure between porous anddense ceramics whereas S-5 has dense microstructure.

IV. Summary

In conclusion, we have investigated the microstructure evolv-ing sequence of BZN ceramics and found that porous micro-structures can be formed within a narrow sintering window(1250°C for 2–5 h) without any additives. The ceramics showtypical relaxor characteristics of broad dielectric peak withstrong frequency dispersion and very slim ferroelectric P–Eloop. Furthermore, the observed features that the mostporous ceramics have the lowest dielectric constant, endurehighest electric field of 15 kV/mm, and have nearly zeromacroscopic electric field-induced strain can be attributed tothe porous structures and be well understood based on brick-wall model. Our results may provide detailed informationabout microstructure evolving process and the influence ofmicrostructure on electric properties of ceramics. This studyalso shows an effective way to make porous ferroelectricmaterials with special properties, such as low dielectricconstant, ultrahigh breakdown field strength and nearly zerofield-induced macroscopic strain.

Acknowledgments

This study was supported by the State Key Program for Basic Research ofChina (2013CB632900, 2012CB619406), the National Nature Science Founda-tion of China (11 174 127), the Doctoral Fund of Ministry of Education ofChina (20 110 091 110 014).

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