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Wenfeng Liu, [Xiaobing Ren](https://orcid.org/0000-0002-4973-2486)

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[Large Piezoelectric Effect in Pb-Free Ceramics](https://mdr.nims.go.jp/datasets/512ed635-dce3-456e-9531-6117ddfaa501)

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untitledLarge Piezoelectric Effect in Pb-Free CeramicsWenfeng Liu1,2 and Xiaobing Ren2,*1Multi-disciplinary Materials Research Center and State Key Lab of Electrical Insulation and Power Equipment,Xi’an Jiaotong University, 710049, China2Ferroic Physics Group, National Institute for Materials Science, Tsukuba, 305-0047, Ibaraki, Japan(Received 25 July 2009; published 15 December 2009)We report a non-Pb piezoelectric ceramic system BaðTi0:8Zr0:2ÞO3-ðBa0:7Ca0:3ÞTiO3 which shows asurprisingly high piezoelectric coefficient of d33 � 620 pC=N at optimal composition. Its phase diagramshows a morphortropic phase boundary (MPB) starting from a tricritical triple point of a cubic paraelectricphase (C), ferroelectric rhombohedral (R), and tetragonal (T) phases. The high piezoelectricity of theMPB compositions stems from the composition proximity of the MPB to the tricritical triple point, whichleads to a nearly vanishing polarization anisotropy and thus facilitates polarization rotation betweenh001iT and h111iR states. We predict that the single-crystal form of the MPB composition of the presentsystem may reach a giant d33 ¼ 1500–2000 pC=N. Our work may provide a new recipe for designinghighly piezoelectric materials (both Pb-free and Pb-containing) by searching MPBs starting from a TCP.DOI: 10.1103/PhysRevLett.103.257602 PACS numbers: 77.65.Bn, 77.80.BhFor half a century, the PZT (lead zirconate titanate)family has been the icon of a large class of technologicallyimportant materials—piezoelectrics, which convert be-tween mechanical stress (strain) and electrical voltage(charge) [1,2]. Despite its outstanding piezoelectric prop-erty, PZT is currently facing global restrictions due to itsPb toxicity; thus, there is an urgent need to develop anon-Pb substitute that can compete with PZT, in particular,with the most important high-end PZT (with d33 ¼500–600 pC=N) [3–6]. However, non-Pb piezoelectric ce-ramics generally have inferior piezoelectricity (d33 <150 pC=N in most cases) compared with PZT. Recently,their limit has been pushed to a higher level of d33 �300 pC=N [3] but is still halfway to the most-desiredhigh-end PZT property. It remains a mystery why non-Pbpiezoelectric materials do not exhibit very highpiezoelectricity.The basic approach to achieving high piezoelectricity isto place the composition of the material to the proximity ofa composition-induced phase transition between two fer-roelectric phases. Such a transition has been known as the‘‘morphotropic phase boundary (MPB)’’ in the phase dia-gram [1,2]. The composition-induced ferro-ferro transitionat MPB causes the instability of the polarization state sothat the polarization direction can be easily rotated byexternal stress or electric field [7,8], thereby resulting ina high piezoelectricity and permittivity [9–13]. Recentstudies further pointed out the importance of a field-induced critical behavior [14,15] and of the miniaturizationof domains [16] due to vanishing polarization anisotropy atMPB [17,18]. Although these mechanisms of high piezo-electricity at MPB have so far been discussed mainly forPb-based systems, there seems to be no particular reasonthat they are inapplicable to non-Pb systems. However, theMPB in non-Pb ferroelectric systems [3–5] exhibits sig-nificantly lower piezoelectricity (typically d33 �100–300 pC=N) than that of Pb-based systems(300–600 pC=N) [4]. It is unclear why the MPB of non-Pb systems is ‘‘inferior’’ to that of the Pb-based systemsfrom the existing theories.We designed a non-Pb pseudobinary ferroelectric sys-tem BaðZr0:2Ti0:8ÞO3-xðBa0:7Ca0:3ÞTiO3, or BZT-xBCT,where x is the molar percent of BCT. The samples werefabricated with a conventional solid-state reaction methodwith starting chemicals of BaZrO3 (98%), CaCO3 (99.9%),BaCO3 (99.95%), and TiO2 (99.9%). The calcining wasperformed at 1350 �C, and sintering was done at1450 �C–1500 �C in air.Figure 1(a) shows the phase diagram of this non-PbBZT-xBCT system, determined by measuring dielectricpermittivity (") versus temperature curves (T), a few typi-cal ones shown in Figs. 1(b)–1(d). The structures of differ-ent phases were determined by x-ray diffractometry. Thephase diagram is characterized by a MPB separating aferroelectric R (BZT side) and T (BCT side) phases. Themost important feature of the BZT-BCT system, beingdifferent from other non-Pb systems, is the existence of aC-R-T triple point in the phase diagram locating at x�32% and at T � 57 �C. It is noted that the existence ofC-R-T triple point characterizes many highly piezoelectricPb-based systems such as PZT and PMN-PT [19].Figures 2(a) and 2(b) reveal the composition depen-dence of ferroelectric, dielectric, and piezoelectric proper-ties of this new system at room temperature (20 �C), inrelation to theMPB composition BZT-50BCT (abbreviatedas 50BCT hereafter), which has a Tc ¼ 93 �C. FromFigs. 2(b)1, 2(b)2, 2(b)3, 2(b)4, 2(b)5, and 2(b)6, it is foundthat MPB composition 50BCT exhibits anomaly in all ofthe properties such as the highest spontaneous polariza-tion Pm [Fig. 2(b)1], highest remnant polarization PrPRL 103, 257602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending18 DECEMBER 20090031-9007=09=103(25)=257602(4) 257602-1 � 2009 The American Physical Societyhttp://dx.doi.org/10.1103/PhysRevLett.103.257602[Fig. 2(b)2], lowest coercive field Ec [Fig. 2(b)3], andhighest dielectric permittivity " [Fig. 2(b)4]. 50BCT seemsto be extraordinarily ‘‘soft,’’ as manifested by a very lowcoercive field Ec of 168 V=mm and a very high permittiv-ity "� 3060. The permittivity value is comparable withsoft PZT materials (2000–3500) and significantly higherthan other nonlead piezoelectrics (290–1740).Figure 2(b)5 shows the most interesting result: the com-position dependence of the piezoelectric coefficient d33,measured by a commercial Berlingcourt-type d33 meter(ZJ-3A). Being consistent with the anomaly in other prop-erties, d33 shows a maximum also at 50BCT, which ex-hibits a surprisingly high value of 560–620 pC=Ndepending on poling condition. This high d33 value evenexceeds that of many soft PZTs. The d33 value lowers withdeviating from 50BCT, but still maintains a high value of�350 pC=N for 45BCT and 55BCT. Figure 2(b)6 showsthat 50BCT also exhibits the maximum converse piezo-electric coefficient dS=dE with a very high value ofdS=dE ¼ 1140 pm=V, exceeding that of all PZT ceramics(with dS=dE ¼ 360–900 pm=V). The property anomaly atMPB of the BZT-BCT system is analogous to a similarphenomenon found in PZT and PMN-PT systems.Figure 2(c) shows a comparison in the room temperatured33 of 50BCTwith other non-Pb piezoelectrics and severaltypical PZT piezoelectrics. The d33 (620 pC=N) of 50BCTis about twice that the alkaline-niobate-based ceramics(currently the best non-Pb material) and several timeshigher than other non-Pb piezoelectrics, mostly with d33 <150 pC=N. When compared with the PZT family, 50BCTexhibits similar piezoelectricity with the ultrasoft PZT-5H(d33 � 590 pC=N). This is unusual for a non-Pb material.Figure 2(d) shows that 50BCT (after poling) exhibits ahigher electrostrain (0.057%) than the ultrasoft PZT-5H(�0:045%) and well exceeds unmodified PZT and PZT-4.Figures 2(e)1 and 2(e)2 show the temperature dependenceof d33 for the MPB composition 50BCT and for an off-MPB composition 45BCT, respectively. It is found that themaximum d33 appears at the temperature at which thesample passes the MPB line along the temperature axis.It should be pointed out that the high d33 (�620 pC=N)of the non-Pb BZT-50BCT cannot be explained just byits relatively low Tc (�93 �C), because the existingnon-Pb materials of similar Tc can show much lower d33values [4].As the MPB is tilted, it is possible to approach the MPBnot only by changing composition, but also by changingtemperature. This provides a chance to understand whathappens at MPB. Figures 3(a)–3(d) show the results ofin situ x-ray diffractometry for a 50BCT sample duringcooling from its tetragonal (T) state (32 �C) through MPBstate (14 �C) to rhombohedral (R) state (�63 �C). Thediffraction profiles at 32 �C and �63 �C correspond to atetragonal symmetry [Fig. 3(b)] and a rhombohedral sym-metry [Fig. 3(d)], respectively. At the MPB state of 14 �C,FIG. 1 (color). (a) Phase diagram of pseudobinary ferroelectricsystem BaðZr0:2Ti0:8ÞO3-ðBa0:7Ca0:3ÞTiO3, abbreviated as BZT-BCT. (b)–(d) Dielectric permittivity curves for 20BCT, 50BCT,and 90BCT, respectively.FIG. 2 (color). (a) Hysteresis loops of 40BCT, 40BCT,and 60BCT. (b1) Saturation polarization Pm, (b2) remnantpolarization Pr, (b3) coercive field Ec, (b4) permittivity ",(b5) piezoelectric coefficients d33, and (b6) converse piezo-electric coefficient dS=dE. Values of various PZTs are alsoshown as a reference. (c) Comparison of d33 among BZT-50BCT and other non-Pb piezoelectrics and PZT family. Thenon-Pb systems include Bi-layer (bismuth-layered ferroelec-trics), TBSF (tungsten bronze structured ferroelectrics), BNT-BT ½ðBi0:5Na0:5ÞTiO3-BaTiO3�, BT (BaTiO3-based ceramics),and KNN-LT-LS [ðK;Na;LiÞðNb;Ta;SbÞO3 ceramics].(d) Electric-field-induced strain of BZT-50BCT in comparisonwith several typical PZT ceramics. (e1), (e2) show the tempera-ture variation of d33 for 50BCT and 45BCT, respectively.PRL 103, 257602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending18 DECEMBER 2009257602-2being close to the permittivity maximum in Fig. 3(a), thepeak profiles are consistent with a superposition of T and Rprofiles [Fig. 3(c)]. This suggests that MPB corresponds tothe coexistence of R and T phases; thus, the polarizationrotation from h001iT to h111iR must be a first ordertransition.Figure 3(e) shows that the three transitions in this sys-tem, C-T, C-R, and T-R, are all first order transitions, asmanifested by the existence of transition hysteresis forthem (see the inset). However, the hysteresis of the threefirst order transitions seems to gradually converge to zeroat the triple point. The vanishing hysteresis for the threefirst order transitions at the triple point suggests that thetriple point corresponds to a crossover from a discontinu-ous to a continuous transition and thus it is a tricriticalpoint (TCP), which is characterized by the absence ofenergy barrier among the three states [20]. Figure 3(f)shows that the 30BCT, a near-tricritical composition, ex-hibits the highest permittivity peak at Tc compared withthat of the off-triple-point compositions. This anomalyfurther supports that the triple point is a TCP.With the knowledge that the triple point is a TCP,Figs. 4(a)1, 4(a)2, 4(a)3, 4(a)4, and 4(a)5 explain whythe MPB of the present non-Pb system (BZT-BCT) canexhibit a very high piezoelectricity. The schematic phasediagram in Fig. 4(a)1 reproduces the key feature of theBZT-BCT system—a triple-point-type (or tricritical-type)MPB between T and R phases, which starts from a TCP.Following the approach by Rossetti et al. [18] and Haunet al. [21], the free energy (F) of the system, being afunction of composition x and temperature T, can bewritten as a symmetry-adapted Landau polynomial withrespect to the magnitude of polarization P and its direction(unit vector n),Fðx; T;n; PÞ ¼ Aðx; TÞP2 þ Bðx;nÞP4 þ Cðx;nÞP6; (1)where Aðx; TÞ, Bðx;nÞ, and Cðx;nÞ are the coefficients ofsecond, fourth, and sixth order terms, respectively. For anideally vertical MPB starting from a TCP (i.e.,xMPB ¼xTCP), tricriticality requires BðxMPB;nÞ ¼ BðxTCP;nÞ ¼ 0[20], and the equilibrium between T (n ¼ h0; 0; 1i and R(n ¼ h1; 1; 1i= ffiffiffi3p) phases demands that CðxMPB;nÞ ¼CðxTCP;nÞ ¼ CðxTCPÞ. Therefore, an important conclusioncan be drawn: the free energy of the MPB compositionxMPBð¼ xTCRÞ is isotropic, being independent of polariza-tion direction. The vanishing polarization anisotropy leadsto an important consequence: no energy barrier exists forpolarization rotation from h001iT state to h111iR state [18].This is the fundamental reason why the triple-point-typeMPB has very high piezoelectric and dielectric properties.Real MPBs are always tilted to some extent likeFig. 4(a)1, i.e., xMPB � xTCP but xMPB � xTCP. Such a situ-ation cannot make a zero polarization anisotropy at MPBas the above ideal case {except for the TCP [Figs. 4(a)2and 4(a)3]}, but it can make a very weak polarizationanisotropy. This weak polarization anisotropy yields alow barrier between h001iT and h111iR polarization states[Figs. 4(a)4 and 4(a)5], which explains the observed firstorder T-R transition but still enables an easy polarizationrotation and thus gives rise to high dielectric and piezo-electric properties. The above mechanism may also beapplicable to Pb-based systems (like PZT and PMN-PT),as these systems are also characterized by a triple-point-type MPB. A rigorous modeling of the triple-point-typeMPB will appear elsewhere [22].By contrast, existing non-Pb piezoelectric systems donot seem to show a triple-point-type MPB like Fig. 4(a)1.Many of them (like alkaline niobate) show a polymorphic-type MPB, which starts from a polymorphic point of aterminal composition like Fig. 4(b)1. Polymorphic transi-tion has also been shown to enhance piezoelectric proper-ties by the instability with respective to polarizationrotation [11]. However, unlike the triple-point situation,for a first order polymorphic transition, there is no thermo-dynamic restriction to the anisotropy of Bðx;nÞð<0Þ andCðx;nÞð>0Þ terms. Thus, they are quite anisotropicalong the whole polymorphic boundary line, as shown inFigs. 4(b)2, 4(b)3, 4(b)3, 4(b)4, and 4(b)5. This results in alarger energy barrier (compared with the case of triple-point MPB) between the two polarization states (T andO).As a result, the property enhancement by polymorphictransition is not as significant as in the triple-point-typeMPB systems. This can explain why such non-Pb materialshave a lower piezoelectric and dielectric property com-pared with that of triple-point MPB systems.Finally, it should be noted that strictly speaking highpiezoelectricity not only requires a low polarization an-FIG. 3 (color). (a)–(d) In situ x-ray diffraction (XRD) profilesof 50BCT during cooling. (a) Permittivity versus temperaturerelation of the sample. (b) XRD profiles at 32 �C. (c) XRDprofiles at 14 �C (MPB). (d) XRD profiles at �63 �C. (e) Attriple point (�32BCT), the transition hysteresis (as defined in theinset) of the three first order transitions (C-T, C-R, and T-R)vanishes. (f) Highest permittivity peak appears for a near-tricritical composition, 30BCT.PRL 103, 257602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending18 DECEMBER 2009257602-3isotropy but also a softening of the lattice [23]. Fortunately,low polarization anisotropy and elastic softening go handin hand, both contributing to a high piezoelectricity.In summary, we report a non-Pb piezoelectric systemBZT-BCT, which exhibits a very high piezoelectric coef-ficient of 620 pC=N at MPB, which is comparable evenwith high-end PZT. The high piezoelectricity stems froman MPB starting from a triple point, which is a TCP andcauses a very low energy barrier for polarization rotationand lattice distortion. Our work indicates that there is nospecial reason that non-Pb piezoelectric materials shouldalways be inferior to Pb-based systems; if a suitable TCP-type MPB is designed, non-Pb systems may exhibit equallyexcellent or even better piezoelectricity as Pb-based ones.For the MPB composition (50BCT) of the BZT-BCT sys-tem, we predict a 3–4 times larger piezoelectricity (d33 ¼1500–2000 pC=N) in single-crystal form, similar single-crystal enhancement having been empirically known inPMN-PT [24].The authors are grateful to D. Z. Xue, H. X. Bao,C. Zhou, and Y.M. Zhou for the contribution toFigs. 3(e), 3(f), and 4. W. F. Liu acknowledges the supportof the National Natural Science Foundation of China(Grants No. 50720145101 and No. 50702042), theNational Basic Research Program of China (GrantsNo. 2004CB619303 and No. 2010CB631003), and 111project of China.*Ren.Xiaobing@nims.go.jp[1] K. Uchino, Ferroelectric Devices (Marcel Dekker, NewYork, 2000), Chap. 7.[2] B. Jaffe, Piezoelectric Ceramics (Academic Press, India,1971), Chap. 7.[3] Y. Saito et al., Nature (London) 432, 84 (2004).[4] T. R. Shrout and S. J. Zhang, J. Electroceram. 19, 113(2007).[5] T. Takenaka and H. Nagata, J. Eur. Ceram. Soc. 25, 2693(2005).[6] X. B. Ren, Nature Mater. 3, 91 (2004).[7] H. X. Fu and R. E. Cohen, Nature (London) 403, 281(2000).[8] M. Ahart et al., Nature (London) 451, 545 (2008).[9] B. Noheda et al., Phys. Rev. Lett. 86, 3891 (2001).[10] L. Bellaiche, A. Garcia, and D. Vanderbilt, Phys. Rev.Lett. 84, 5427 (2000).[11] S. Wada et al., Jpn. J. Appl. Phys. 38, 5505 (1999).[12] R. Ahluwalia, T. Lookman, A. Saxena, and W. Cao, Phys.Rev. B 72, 014112 (2005).[13] D. Damjanovic, J. Am. Ceram. Soc. 88, 2663 (2005).[14] Z. Kutnjak, J. Petzelt, and R. Blinc, Nature (London) 441,956 (2006).[15] Z. Kutnjak, R. Blinc, and Y. Ishibashi, Phys. Rev. B 76,104102 (2007).[16] Y.M. Jin et al., Phys. Rev. Lett. 91, 197601 (2003).[17] Y. Ishibashi and M. Iwata, Jpn. J. Appl. Phys. 37, L985(1998).[18] G. A. Rossetti, A. G. Khachaturyan, G. Akcay, and Y. Ni,J. Appl. Phys. 103, 114113 (2008).[19] D. E. Cox et al., Appl. Phys. Lett. 79, 400 (2001).[20] E. K. H. Salje, Phase Transitions in Ferroelastic and Co-Elastic Crystals (Cambridge University Press, Cambridge,1990).[21] M. J. Haun, E. Furman, S. J. Jang, and L. E. Cross,Ferroelectrics 99, 13 (1989).[22] X. B. Ren (to be published).[23] M. Iwata, H. Orihara, and Y. Ishibashi, Ferroelectrics 266,57 (2002).[24] S.-E. Park and T. R. Shrout, J. Appl. Phys. 82, 1804(1997).FIG. 4 (color). (a1) Schematic of a tricritical-type MPB be-tween tetragonal (T) and rhombohedral (R) phases. (a2),(a3) Isotropic free energy surface for tricritical point. (a4),(a5) Nearly isotropic free energy surface of MPB compositionat room temperature. (b1) Schematic of a polymorphic-typeMPB between tetragonal (T) and orthorhombic (O) phases.(b2), (b3) Schematic anisotropic free energy surface for poly-morphic point. (b4), (b5) Schematic anisotropic free energysurface for polymorphic MPB (room temperature). The 1Dfree energy plots in (a3), (a5) and (b3), (b5) show the freeenergy barrier along the polarization rotation path [fromPTh001i or PRh111i (or POh110i)].PRL 103, 257602 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending18 DECEMBER 2009257602-4