Piezoelectric Activity in Perovskite Ferroelectric Crystals - IEEE Xplore

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IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control ,

vol. 62, no. 1,

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2015

Piezoelectric Activity in Perovskite Ferroelectric Crystals Fei Li, Linghang Wang, Li Jin, Dabin Lin, Jinglei Li, Zhenrong Li, Zhuo Xu, and Shujun Zhang Abstract—Perovskite ferroelectrics (PFs) have been the dominant piezoelectric materials for various electromechanical applications, such as ultrasonic transducers, sensors, and actuators, to name a few. In this review article, the development of PF crystals is introduced, focusing on the crystal growth and piezoelectric activity. The critical factors responsible for the high piezoelectric activity of PFs (i.e., phase transition, monoclinic phase, domain size, relaxor component, dopants, and piezoelectric anisotropy) are surveyed and discussed. A general picture of the present understanding on the high piezoelectricity of PFs is described. At the end of this review, potential approaches to further improve the piezoelectricity of PFs are proposed.

I. Introduction

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ased on the principle of crystallographic symmetry, piezoelectricity may present in dielectric crystals which are non-centrosymmetric. There are 20 point-groups that are piezoelectric active, in which the point-groups 1, 2, m, mm2, 4, 4mm, 3, 3m, 6, and 6mm are found to possess unipolar axis and exhibit spontaneous polarization and pyroelectricity. The crystals with these point-groups are referred to pyroelectric crystals. Ferroelectric crystal is one type of the pyroelectric crystals, where the spontaneous polarization can be reversed by the application of an external electric field. The multi-functional properties, including piezoelectric, pyroelectric, and dielectric effects, make the ferroelectrics “smart” materials. Among ferroelectric materials, perovskite ferroelectrics (PFs) have been received considerable attentions in last 60 years because of their outstanding multi-functional properties, being actively studied for various applications, such as ultrasonic transducers, sensors, actuators, energy harvesting devices, multilayer ceramic capacitors, infrared sensors, and ferroelectric memories, to name a few [1]–[4]. In addition to state-of-the-art applications, PFs have recently attracted attention as promising candidates for photovoltaic and electrocaloric applications [5]–[9]. Manuscript received July 27, 2014; accepted September 29, 2014. This work was supported by the National Nature Science Foundation of China (grant no. 51102193, 51202183, and 51372196), the China Postdoctoral Science Foundation and the Fundamental Research Funds for the Central Universities. F. Li, L. Wang, L. Jin, D. Lin, J. Li, Z. Li, and Z. Xu are with the Electronic Materials Research Laboratory, Key Laboratory of Ministry of Education and International Center for Dielectric Research, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, China (e-mail: [email protected]). D. Lin is also with the Laboratory of Thin Film Techniques and Optical Test, Xi’an Technological University, Xi’an, China. S. Zhang is with the Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania (e-mail: [email protected]). DOI http://dx.doi.org/10.1109/TUFFC.2014.006660

PFs have dominated the area of transducer and actuator applications since the 1950s, including barium titanate (BT), lead zirconate titanate (PZT) ceramics, and recently developed relaxor-PbTiO3 single crystals. The piezoelectric effect in PFs is much stronger than that in nonferroelectric materials, due to the fact that the PFs exhibit different ferroelectric phases with minimal energy discrepancies, leading to a high dielectric permittivity in a strong polar lattice on the proximity of the phase boundary. In addition, PFs are piezoelectric active in both single crystals and randomly oriented polycrystalline ceramics (poling can break the inversion symmetry of ferroelectric ceramics), whereas the non-ferroelectric ceramics (e.g., ZnO ceramics) show macroscopic symmetry of inversion, exhibiting no piezoelectricity [10]. The formula of perovskite structure is ABO3, where A and B represent cation elements or mixture of two or more such elements. The ideal perovskite structure is the high-temperature paraelectric phase, whose space group is Pm3m, where the A atom takes at the corner of the cube, whereas the B atom is at the body center and the oxygen atom is at the face center, as shown in Fig. 1. PFs are generally recognized as displacive ferroelectrics. With cooling a PF material through its Curie temperature, paraelectric to ferroelectric phase transition occurs, which is accompanied with a specific strain, being induced by a small atomic displacement (especially by the displacement of the B cation relative to the oxygen octahedron network). It should be noted here that some PFs are also considered to be order-disorder ferroelectrics [11], [12], leading to the open questions of the origin and type of ferroelectricity. In this article, the concept of displacive ferroelectrics is adopted for the discussion of ferroelectric phase transition. The tetragonal, rhombohedral, and orthorhombic phases are three general ferroelectric phases observed in PFs, with the spontaneous polarization along 〈100〉, 〈111〉, and 〈110〉 crystallographic directions, respectively. Based on a sixth-order free-energy expansion, the existence of these three ferroelectric phases was explained by the Devonshire theory in 1949 [13]. With the development of PFs, however, the monoclinic phase, whose polar vector lies in (110) or (010) mirror plane, was observed in Pb(Zn1/3Nb2/3)– PbTiO3 (PZN-PT), Pb(Mg1/3Nb2/3)–PbTiO3 (PMN-PT), and PZT solid solutions [14], [15]. Meanwhile, Vanderbilt and Cohen confirmed that the monoclinic phases are permissible in PFs by extending the free energy to eighth order [16]. In addition to the normal ferroelectric phases, improper ferroelectricity and ferrielectricity were observed in perovskite materials. The improper ferroelectricity was reported in PbTiO3/SrTiO3 (2/3) artificial superlattices,

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li et al.: perovskite ferroelectric crystals

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Fig. 1. Schematic of perovskite structure.

where the electric polarization is driven by two coupled octahedral-rotation lattice modes [17]. The PbTiO3/SrTiO3 (2/3) thin film exhibits higher values of the spontaneous polarization and dielectric permittivity (PS = 11 μC/cm2 and εr = 600) when compared with the typical improper ferroelectrics (in gadolinium molybdate, PS = 0.2 μC/ cm2 and εr = 10) [17]. In some perovskite materials, on the other hand, multiple distortions of perovskite structure can occur. These distortions may create local dipole moments of different magnitudes but in opposite directions, so there is an overall polarization being smaller than that which is produced by each distortion on its own. Such materials are described as ferrielectrics [18]. Examples of these perovskite materials are AgNbO3, Na0.5Bi0.5TiO3 [19]–[21], ABO3/A’BO3 superlattices [22], etc. In perovskite structure, the microscopic/atomic-scale characteristics, such as tolerance factor and electronic structure, are important for the ferroelectricity and other physical properties. Tolerance factor, as given in (1), represents the stability and distortion of the pervoskite structure [23], [24].

t =

rA + rO , (1) 2(rB +rO )

where rA, rB, and rO represent the ionic radii of A, B, and oxygen ions, respectively. It is generally accepted that the perovskite structure is formed when the factor is close to unity (0.9 < t < 1.1). In PFs, the tetragonal distortion is generally favored as t > 1, whereas the rhombohedral and orthorhombic distortions are generally favored as t < 1 [25], [26]. Tolerance factor is also associated with the Curie temperature for PFs. In solid solution system ABO3– PbTiO3, low tolerance factor of ABO3 is proposed to have high Curie temperature, as given in Fig. 2 [27]. Based on this notion, Eitel et al. explored a BiScO3–PbTiO3 solid solution system for high temperature piezoelectric applications [28]. The electronic structure of A-site cations is inherently associated with the strength level of ferroelectricity. Two typical PFs, PbTiO3, and BaTiO3, are generally used for comparison. The remarkable feature of Pb2+ cation is the two electrons in the outermost filled 6 s2 subshell, forming the lone pair electrons. Compared with the outermost 5p subshell of Ba2+, the 6s subshell is more easily hybridized with the orbitals of other ions, leading to high stability of ferroelectric state and large distortion of unit cell in

Fig. 2. Curie temperature (TC) of PbTiO3-based solid solution (at MPB compositions) versus tolerance factor of the end member. Data are from [27].

PbTiO3 [29]. Based on this consideration, searching for proper A-site cation with lone pair electronic structure is believed to be very important for lead-free PF systems, such as Bi3+ [26]. II. Growth of PF Crystals High-quality PF crystals are required in terms of both fundamental research and practical applications. For fundamental research, the information achieved from single crystals will help us to establish the relation between physical properties and crystal structure. On the other hand, the performance of devices will benefit greatly from the strong anisotropy of crystal. Attempts to grow PF crystals, including BT, PZT, relaxor-PT (PMN-PT, PZN-PT, etc.), (Na1/2Bi1/2)TiO3 (NBT), and (K1/2Na1/2)NbO3 crystals, have been made by numerous institutes around the world. BT is the first grown crystal with PF structure; however, the piezoelectric properties of BT crystal do not show obvious advantages over its ceramic counterpart. Meanwhile, the BT crystal is easy to crack because the tetragonal-orthorhombic phase transition is close to room temperature. Therefore, the application of BT crystals is very limited. PZT-based polycrystalline ceramics have been the mainstay piezoelectric materials since their discovery; unfortunately, no high-quality and large-size crystals are available due to the incongruent melting feature of the solid solution and the refractory zirconate, with recently reported millimeter-size PZT crystals being grown for fundamental studies [30]–[32]. A breakthrough in crystal growth occurred in 1990s, when Park and Shrout reported that the solid solutions of relaxor (PMN or PZN) and ferroelectric PT can be readily grown in single crystal form following the earlier work of Kuwata et al. in 1982 [33]. In general, lots of Pb(B1,B2)O3–PT crystals can be grown by high temperature solution method using Pb-based flux, but with limited size [34], [35]. In last two decades, Pb(B1,B2)

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O3-PT crystals have been grown by different techniques, such as Bridgman, top-seeded solution, and solid-state conversion methods, etc. [34]–[36]. Currently, PMN-PT and Pb(In1/2Nb1/2)–Pb(Mg1/3Nb2/3)–PbTiO3 (PIN-PMNPT) crystals have been successfully grown along the 〈100〉 crystallographic direction, with 50 to 100 mm in diameter and 100 to 200 mm in length, by using the modified Bridgman method [37]. Fig. 3 shows the PIN-PMN-PT crystals grown by Xi’an Jiaotong University. PMN-xPT (x = 0.28~0.33) crystals with morphotropic phase boundary (MPB) compositions exhibit ultrahigh piezoelectric coefficients (d33 = 1500 to 2500 pC/N) and electromechanical coupling factors (k33 > 0.9), far outperform PZT-based ceramics with d33 = 200 to 700 pC/N and k33 = 0.6 to 0.75. Because of these outstanding electromechanical properties, the PMN-PT crystals have been commercialized for medical transducers by various companies around the world, such as Philips, GE, Siemens, Hitachi, and Humanscan, to name a few. Due to the regulations against hazardous substances, lead-free perovskite ferroelectrics have been actively studied in last 10 years. The KNN and NBT-BT based materials are thought to be potential lead-free piezoelectric materials to replace the Pb-based counterparts. The growth of KNN- and NBT-BT-based crystals were reported [38]– [44]. However, some issues were presented in the lead-free crystals, where small size and high leakage current have been reported for KNN crystals. The maximum size of KNN crystals is around 10 × 10 × 10 mm3, because of the high volatility of K/Na and the incongruent melting nature. The high leakage current of KNN crystals is attributed to the oxygen vacancies. For NBT-BT-based crystals, on the other hand, the piezoelectric properties generally exhibited large discrepancy, being attributed to the influence of growth technique and crystal composition [41]. As discussed in this section, attempts to grow highquality PF crystals have been made by numerous researchers, which will benefit the understanding of the structureproperty relationship. Further efforts are still required to grow various PF crystals from both academic and industrial viewpoints. III. Piezoelectric Coefficients: Definition, Measurement, and Anisotropy A. Definition of Piezoelectric Coefficients Piezoelectricity refers to the linear coupling between mechanical stress and electrical polarization and/or between mechanical strain and applied electric field [45]. Based on the selection of independent electrical and mechanical variables, there are four sets of piezoelectric coefficients. At constant electric field (E) and mechanical stress (T), the piezoelectric strain (or charge) coefficient d can be formulated as

 ∂S   ∂D  d =  =    . (2)   ∂E T  ∂T E

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Fig. 3. Photographs for PIN-PMN-PT crystals grown by Xi’an Jiaotong University. The crystal rings are shown at the bottom.

The piezoelectric voltage coefficient g is related to the voltage response to an applied stress when the electrical displacement (D) and mechanical stress (T) are selected as independent variables. The coefficient g can be written as follows:

 ∂E   ∂S  g =  −  =  ∂D  . (3)  ∂T D  T

As the electric field (E) and strain (S) are selected as independent variables, the piezoelectric stress coefficients e can be written as follows:

 ∂T   ∂D  e =  −  =  ∂S  . (4)  ∂E S  E

The piezoelectric clamped voltage (or stiffness) coefficients h can be derived when the independent variables are S and D, according to (5).

 ∂T   ∂E  h =  −  =  − ∂S  . (5) ∂ D  S  D

The four sets of piezoelectric coefficients are interrelated as follows:

 d iλ   e iλ  g iλ   h iλ

E = εTij g j λ = e i µs µλ E = εijSh j λ = d i µc µλ , (6) D = β ijTd j λ = h i µs µλ D = β ijSe j λ = g i µc µλ

where β is the dielectric impermeability and s/c are the elastic constants. The superscripts E, T, S, and D indicate different boundary conditions. i, j = 1, 2, 3; μ, λ = 1, 2, 3, 4, 5, 6.


B. Measurement of Piezoelectric Coefficients Three measurements are generally accepted to determine piezoelectric coefficients, i.e., Berlincourt d33-meter, the slope of strain-electric field and electrical impedance methods [46]. The Berlincourt and strain-electric field methods are quasi-static, where the testing frequency is much lower than the fundamental resonance frequency of the sample, being generally used to determine the piezoelectric coefficient d33, d31, and d32 for piezoelectric crystals and ceramics. The electrical impedance method is based on the theory of acoustic vibration, which can be used to determine full matrix of piezoelectric and elastic constants. To obtain a certain vibration mode, the sample geometry must meet the required aspect ratio [46]. C. Anisotropy of Piezoelectric Coefficients PF crystals show strong piezoelectric anisotropy, investigations on which could benefit both scientific researches and practical applications. The orientation dependence of piezoelectric coefficients can be analyzed by transforming the coordinate system, as given in the following:

* d ijk =

∑a ila jma kndlmn, (7)

where dlmn are the piezoelectric coefficients measured in the standard coordinate system, dijk* are the piezoelectric coefficients in the new rotated coordinate system, and ail, ajm, and akn are the components of the transformation matrix. The standard coordinate systems of single domain rhombohedral, orthorhombic, and tetragonal PF crystal are (X: [110], Y: [112], Z: [111]), (X: [011], Y: [100], Z: [011]), and (X: [100], Y: [010], Z: [001]), respectively. By transforming the coordinate system, the orientation dependence of d33* for PF crystals can be plotted, as shown in section V. IV. Electric-Field-Induced Strain and Piezoelectricity in PFs Piezoelectric activity of PFs can be divided into two parts: intrinsic (lattice deformation) and extrinsic contributions (domain wall motion). Although extrinsic contribution may account for 20 to 60% of the piezoelectricity in ferroelectric ceramics, the intrinsic contribution is the dominant factor for improving the piezoelectric activity of PFs. In this section, these two contributions will be discussed separately. A. Intrinsic Contribution The intrinsic contribution of piezoelectric activity means that the electric-field-induced strain originates from the distortion of the lattice. From intrinsic respect, the relationship between the strain and polarization can be conventionally written as

S = g ⋅ P ( E ) + Q ⋅ P 2 ( E ) + ..., (8)

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where the first and second terms represent the piezoelectric and electrostrictive strains, respectively, P(E) is the electric-field-induced polarization, g is the piezoelectric voltage coefficient, Q is the electrostrictive coefficient. The strain related to the high order of P was ignored in (8). For piezoelectric crystals without spontaneous polarization, the strain induced via piezoelectric effect (first order) is usually much higher than the electrostrictive strain (second order), such as in quartz crystals. The electricfield-induced strain in ferroelectrics with centrosymmetric parent phases, on the other hand, is only induced by the electrostriction [47]. These ferroelectrics include lithium niobate and perovskite ferroelectrics. Thus, (8) can be expressed in the following form: S = QP 2 ( E ) . (9)

The piezoelectric coefficient d, which is a derivative of strain to electric field, can be expressed as follows:

d =

∂S E =0 ∼ Q εP(E )  →Q εPS, (10) ∂E

where ε is the dielectric constant and PS is the spontaneous polarization. Eq. (10) indicates that the piezoelectric activity of PFs is associated with the electrostrictive effect, spontaneous polarization, and dielectric constant. From experimental results, the electrostrictive coefficient Q was found to be closely related to the dielectric and elastic constants. Using a simple atomistic model, Newnham et al. [48] proposed the relationship between dielectric/elastic and the electrostrictive coefficients, as shown in Q ∼

s , (11) ε

where s is the elastic compliance constant. Taking (11) to (10), the piezoelectric coefficient can be written as

d ∼

s εP ∼ sPS . (12) ε S

Eq. (12) indicates that the high level of elastic compliance constant and spontaneous polarization may result in a high piezoelectric coefficient d. In conclusion, the intrinsic piezoelectric response in PFs is actually based on the electrostrictive effect. To qualitatively evaluate the piezoelectric activity in PFs, the electrostrictive coefficient, dielectric constant, elastic constant, and spontaneous polarization have to be considered [49]. B. Extrinsic Contribution Extrinsic contributions to the piezoelectric effect can be defined as the contributions that do not originate from E-field-/stress-induced variation of the lattice parameter. Extrinsic contribution in PFs is dominated by the displacement of domain walls [50]. The electric-field-induced

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Fig. 4. (a) Electric-field-induced strain for [111] and [720] oriented BT crystals; (b) Possible domain vectors for [111] and [720] poled BT crystals. It can be seen that as the electric field is applied along [720] direction, [010] domains will transform to [100] domains, resulting in high E-field-induced strain and large hysteresis. Reprinted by permission from Li F. et al., Appl. Phys. Lett., 93, 192904 (2008). Copyright© 2008, the American Institute of Physics.

strain from extrinsic contribution is generally nonlinear and hysteretic, which may induce high dielectric and mechanical losses [51]. In PFs, the contribution of domain wall motion to the strain is much larger than that to the small signal piezoelectric coefficient, due to the fact that both irreversible and reversible domain wall motions can contribute to electric-field-induced strain, whereas only the reversible part of domain wall motion contributes to the piezoelectric coefficient measured under small electric/ stress stimuli. An example about BT crystal is given to illustrate this issue. Fig. 4 gives the strain and piezoelectric coefficient of [111] and [720] oriented BT crystals [52]. For [111] oriented BT crystal, the electric field along [111] direction will induce “3T” engineered domain configuration, in which the domain wall motion cannot contribute to the strain and piezoelectric coefficient, because the spontaneous strains of the six possible tetragonal domains are equal to the [111] direction. On the contrary, the electricfield-induced strain of [720] oriented BT was found to be about eight times larger than that of the [111] oriented one, due to the large contribution of the irreversible domain wall motion, whereas the piezoelectric coefficients (measured by small signal) are comparable in these two crystals (230 pC/N and 180 pC/N for [720] and [111] oriented BT crystals, respectively). V. Factors Responsible for High Piezoelectric Activity in PFs The piezoelectricity is associated with the output strain to external electric stimuli. Generally speaking, high piezoelectricity can be expected in ferroelectrics with high instability of crystal structure or domain configuration. In this section, the remarkable findings responsible for the high piezoelectric response of PFs will be surveyed and discussed.

A. Phase Transition Point As ferroelectric materials approach the phase transition points, no matter it is induced by composition, temperature, or stress, the phase will lose its stability due to the flattening of the free-energy profile [53]–[56]. At phase transition point, the functionality of ferroelectrics, including the dielectric and piezoelectric coefficients, may exhibit maximum values, as shown in Fig. 5 [53], [57]. In ferroelectric materials, the phase transition can be categorized as ferroelectric-ferroelectric [i.e., rhombohedral (R)-tetragonal (T), orthorhombic (O)-T, and R-O] and ferroelectric-nonpolar [i.e., R-cubic (C), T-C, T-antiferro, etc.] phase transitions. With approaching the ferroelectricferroelectric phase transition point, the rotation of polar vector is facilitated under external stimuli, leading to high transverse dielectric permittivity ε11 or ε22 and high piezoelectric shear coefficient d15 or d24, as illustrated in Fig. 6(a). On the other hand, as the ferroelectric materials approach ferrolelectric-nonpolar phase transition, the magnitude of polarization is easier to be changed under external stimuli, giving rise to the increased longitudinal dielectric permittivity ε33 and piezoelectric coefficient d33, as illustrated in Fig. 6(b). Based on these two mechanisms, Davis et al. proposed that the enhancement of piezoelectric response can be divided to two contributions: polarization rotation and polarization extension [54]. Morphotropic phase boundary (MPB), which is a composition induced ferroelectric-ferroelectric phase transition, has been generally used to enhance the piezoelectric response in PFs since its discovery in the PZT system. By selecting proper ferroelectric solid solution with MPB composition, the contribution of polarization rotation to piezoelectric activity can be greatly enhanced. Similar to MPB, the temperature-induced phase transition points (polymorphic phase transitions, PPT) were also employed to enhance the piezoelectricity in PFs, such as KNN and


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Fig. 5. (a) Dielectric permittivity versus composition of PZT; the data are from [57]. (b) The piezoelectric coefficients versus temperature for barium titanate crystal calculated by LGD theory. Reprinted with permission from [53].

(Ba,Ca)TiO3-(Ba,Zr)TiO3 (BCT-BZT) systems (moving the phase transition temperature to the vicinity of room temperature) [58]–[60]. In general, by utilizing the MPB or PPT, the piezoelectric response can be only induced from the polarization rotation contribution. To further enhance the piezoelectric activity, the combinatory contributions of polarization rotation and extension are desired. High piezoelectric activity was reported in BCT-BZT lead-free ceramics (~650 pC/N), in which both the R-T and T-C phase transition points are close to the room temperature, thus polarization rotation and extension can cooperatively contribute to the piezoelectricity [59]. However, due to the low phase transition temperature (~60°C), the usage temperature range of BCT-BZT is considerably restricted. To address this issue, Damjanovic proposed a new phase diagram for ferroelectric solid solutions, by which the piezoelectric activity can be enhanced from both polarization rotation and extension without sacrificing the temperature usage range [61]. Unfortunately, this new type phase diagram has not yet been realized in real materials. Nowadays, therefore, seeking new ways to enhance the contribution of both polarization rotation and extension to piezoelectricity is still a valuable research direction. In

this respect, thin film is ahead of bulk materials. Because of the development of artificial superlattices, improper ferroelectric and ferrielectric phases can be achieved in PF thin films, and thus more types of phase transition can be used to enhance the piezoelectricity in perovskite thin films [17], [22]. For example, Gou et al. showed the possibility of enhancing polarization switching and piezoelectricity by utilizing ferri-to-ferroelectric transition in LaScO3/BiScO3 and LaInO3/BiInO3 superlattices [22]. As discussed above, the phase transition can enhance the intrinsic piezoelectricity, due to the decreased phase stability. It should be noted here that the domain wall stability may also be decreased near phase transition points, resulting in the enhancement of extrinsic piezoelectricity. Around phase transition points, the free energy of various ferroelectric phases are similar, and the possible number of stable states is increased. Thus, domain switching from one stable state to another may be facilitated. B. Monoclinic Phase In late 1990s, the monoclinic phases were observed in lead-based PFs, including PZT, PMN-PT and PZN-PT

Fig. 6. Schematic for polarization rotation and extension, where the red arrows represent the directions of polarization. (a) Polarization rotation corresponds to a shear deformation, which occurs more easily at ferroelectric-ferroelectric phase transition points; (b) polarization extension corresponds to a tensile deformation of lattice, which is facilitated at the ferroelectric-nonpolar phase transition points.

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solid solutions. The various types of monoclinic phases, namely, MA, MB, and MC, have been confirmed by different research groups using in situ high energy x-ray/ neutron, Micro-Raman spectroscopy, and polarized light microscopy [14], [15], [62]–[64]. Fig. 7 presents the polar directions for the M phases, where polar vectors of MA, MB, and MC phases lie in (110), (101), and (010) planes, respectively. Due to the discovery of M phases, the high piezoelectric activity of lead-based PFs was believed to be closely associated with the “new” phases, and several mechanisms were proposed based on the M phase. Noheda et al. demonstrated that the M phase was a structural bridge between tetragonal, orthorhombic, and/or rhombohedral phases; thus, M phase may facilitate the polarization rotation and result in an enhanced piezoelectricity [14]. Jin et al. proposed that the observed monoclinic was an adaptive phase, which was formed by tetragonal micro-domains with very low domain wall energy [65]. In this model, 90° nano-domain wall motion was thought to be the dominant factor for high piezoelectricity. However, several researchers hold critical opinions on the understanding of the high piezoelectricity based on monoclinic phases. Kisi et al. proposed that it was the high piezoelectricity that induces the monoclinic phase in PZN-PT crystals, other than the monoclinic phase contributing to the high piezoelectricity [66]. Thus, a monoclinic phase can be recognized as a monoclinic distortion induced by the strong piezoelectric anisotropy in relaxor-PT crystals. Based on experimental results, Li et al. observed that the maximum piezoelectric coefficient d33 of PMN-PT crystals was located in the rhombohedral side with composition on proximity of R-M phase boundary, rather than in the M phase [67]. Thus, Li et al. proposed that the monoclinic phase did not directly contribute to the ultrahigh piezoelectric, the role of M phase was to form MPBs with R and/or T phases. Up to now, the role of monoclinic phases on piezoelectricity is still a controversial issue. To resolve this debate, the structure of monoclinic phase should be ascertained in consensus. For example, is the monoclinic phase composed of micro-twined domains? C. Domain Size/Domain Wall Density Size effect, including the materials size (dimension), grain size, and domain size, plays an important role in the functionality of ferroelectrics. In general, the stability of ferroelectric phase is decreased with decreasing grain and domain sizes. Below a critical size, ferroelectric phase may transform to the paraelectric phase [68]–[72]. Analogous to composition and temperature, therefore, size effect can also induce the phase transition. It is reasonable to expect that the piezoelectricity of ferroelectrics can be enhanced by controlling the grain/domain size. Takahashi et al. and Karaki et al. reported that the fine domains in BaTiO3 ceramics could largely enhance piezoelectric activity (d33 = 350 pC/N [73] and 460 pC/N [74]). Wada et al. reported that grain-oriented BaTiO3 ceramics with an average do-

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Fig. 7. Schematic of the polar directions of MA, MB, and MC phases, respectively. The directions of spontaneous polarization of MA, MB, and MC phases are given by red arrows.

main size of 800 nm had a piezoelectric coefficient d33 of 788 pC/N [75]. In addition, the piezoelectric properties of domain-engineered BaTiO3 crystals were studied as a function of domain size, revealing that the piezoelectricity was enhanced with decreasing the domain size (or increasing domain wall density), as shown in Fig. 8(a) [76]. Following Wada’s work, Lin et al. studied the domain size dependent piezoelectric property in domain-engineered tetragonal PIN-PMN-PT crystals, where the similar tendency was observed, as given in Fig. 8(b) [77]. Ahluwalia et al. reported that the phase transition electric-field was decreased with decreasing the domain size based on a continuum Ginzburg-Landau model, accounting for the enhancement of piezoelectric activity in BT crystal with fine domain size [78]. On the other hand, Sluka et al. proposed a charged-domain-wall model to explain the domain-wall density effect, where the electric field built by the charges in domain walls was thought to be responsible for the enhancement of piezoelectricity [79]. Although the effect of domain size has been experimentally identified in tetragonal BaTiO3 and PIN-PMNPT crystals, this effect cannot be regarded as a universal effect in perovskite ferroelectrics. More confirmative evidences are yet required for various ferroelectric phases (e.g., rhombohedral, orthorhombic, etc.) and material systems (e.g., KNN, NBT, etc.). D. Relaxor Component Glass-like phenomena, such as spin glass in magnetic system [80], strain glass in metallic system [81], and relaxor ferroelectrics in dielectrics [82], have received considerable attention from the viewpoint of both scientific and application respects. PMN and PZN are typical relaxor ferroelectrics with complex B-site cations. The disordered B-site heterovalent cations and the polar nano-regions (PNRs) are important characteristics of perovskite relaxors. It is generally accepted that the relaxor component can destroy the stability of long-range-ordered ferroelectric state, when it forms solid-solution with normal ferroelectrics, such as PT. Therefore, the relaxor component was thought to play an important role in high piezoelec-


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Fig. 8. Relationship between d33 and domain size for (a) [111] poled BT and (b) tetragonal PIN-PMN-PT crystals. (a) Reprinted with permission from [76]. (b) Data are from [77].

tric activity for relaxor-ferroelectric solid-solutions, where the relaxor component reduces the stability of ferroelectric phase [83]–[86]. Furthermore, the switching and dynamic properties of PNRs may also have a great impact on the electromechanical properties of relaxor ferroelectrics. From the respect of application, relaxor-based ferroelectrics, such as PMN-xPT and PZN-xPT, indeed show larger piezoelectric coefficients d and electromechanical coupling factors k when compared with the non-relaxor PZT. Recently, the electric-field-induced strain was reported to be greatly enhanced in lead-free ceramics by designing a relaxor/ferroelectric composite [87]. Some models have been proposed to illustrate the effect of relaxor component on electromechanical properties in PF systems. Kutnjak et al. reported a line of critical end points of the liquid-vapor type in the E-T-x phase diagram of the PMN-xPT system [83]. On the proximity of the critical end points, the electric fields being necessary for the polarization rotations were found to significantly decrease. Consequently, the critical end points existing in relaxor ferroelectrics were thought to be responsible for the giant electromechanical response. Xu et al. studied relaxor-PT crystals by neutron inelastic scattering experiments and observed that the transverse acoustic (TA) mode was softened due to the existence of polar nano-regions [84]. This softened TA mode indicates high elastic shear compliance in relaxor-PT crystals. As expressed in (12), high elastic compliance may result in high piezoelectricity. Pirc et al. analyzed the effect of PNRs on electrostriction and piezoelectricity in relaxor ferroelectrics by the spherical random bond-random-field model, demonstrating that the interactions between PNRs play an important role on the electrostriction and piezoelectricity of relaxors [85]. Phelan et al. made comparative studies on PMN-xPT and PZT crystals and proposed that the underlying nanometer-scale, static, polar order in relaxors played an influential role on the greatly enhanced piezoelectric response when compared with the non-relaxor PZT [86]. Although consensus of the effect of relaxors on piezoelectricity has not been reached, it is believed that the PNRs and random fields in

relaxors should be the most important factors responsible for the high piezoelectricity. In future, the local structure and structural transition of PNRs under external fields need to be carefully studied by in situ Raman [88], [89], TEM [90], [91], etc., to provide exact structural information of PNR. E. Dopant Strategy Chemically modifying a material (dopants and defects), as a well-known approach for piezoelectricity control, has been widely used in PFs, especially in the PZT solid solution. PZT can be modified either “hard” or “soft” by adding suitable dopants [1]. In general, the donor dopants (e.g., Nb, Ta on B-site or La, Y, Nd on A-site of PZT) lead to “soft” PZT materials (high dielectric and piezoelectric coefficients, square ferroelectric hysteresis loops, high dielectric and mechanical loss, and no obvious aging phenomenon), whereas the acceptor dopants (e.g., Fe, Mn, Al on B-site of PZT or K, Cu on A-site of PZT) lead to “hard” PZT materials (low dielectric and piezoelectric coefficients, low dissipation factors, pinched hysteresis loops, and strong aging effect) [1]. Fig. 9 gives the typical electric-field-induced strain for soft and hard PZT ceramics, where large strain and accompanied nonlinear and hysteretic behaviors in soft PZT materials can be observed. It should be noted here that the nonlinear and hysteretic behaviors are undesirable for most of the piezoelectric applications. Even though the doping level is very low (less than 5 mol %), the physical property divergences between the hard and soft PZT ceramics are impressively large. Interestingly, it has been observed in doped PZT ceramics (with the same Zr/Ti ratio) that the difference of the properties vanished at very high frequency (above GHz) [92]–[94] and/or very low temperature (below few K) [95], [96], revealing that the intrinsic properties from the crystalline lattices in soft and hard PZTs are almost the same, because the intrinsic properties are thought to be controlled by the crystalline structures (governed by the Zr/

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As discussed in this section, dopant strategy is a generally accepted approach to modify the piezoelectricity for PZT-based ceramics. The mechanisms of dopant strategy, however, are not clear, which inhibits the utilization of this strategy to other perovskite ferroelectrics. For example, soft effect was only demonstrated in the PZT-based ceramics, which is not evident in BT, KNN-, and NBTbased ferroelectric materials [110]. F. Piezoelectric Anisotropy

Fig. 9. Electric-field-induced strains for soft and hard PZT ceramics.

Ti ratio) instead of the dopant types and concentration. Therefore the difference of the properties at room temperature and low frequency region are naturally attributed to the extrinsic domain wall motion. According to the Landau-Ginsburg-Devonshire phenomenological theory, it is suggested that the extrinsic domain wall movement contributes more than 40% to the piezoelectric and dielectric properties in soft PF ceramics [93], [97]. The effects of dopants are thought to be associated with the mobility of domain wall [98], [99], where the donor dopants can enhance the mobility of domain wall, whereas the acceptor dopants can decrease the mobility of the domain wall. The hardening mechanism was reported to be associated with the internal bias field induced by the existence of defect dipoles/defect complexes (acceptor dopants and oxygen vacancies), though the locations and orientations of these defect dipoles are still controversial [100]–[105]. Compared with hardening mechanisms, the softening mechanism of PZT ceramics has not been well understood until now, and it is still a “hand waving” topic [98]. It suggested that the donor dopants in soft PZT would prevent the formation of oxygen vacancies and facilitate the formation of lead vacancies [1]. The lead vacancies might reduce the internal stresses and make domain wall mobility easier [106]. Furthermore, electron transfer between defects in soft PZT could minimize the space charge in domain walls and thus increase the domain wall mobility [107]. Even though the domain wall mobility (extrinsic contribution) has attracted much attention with respect to the origin of the hardening and softening mechanisms for PZT ceramics, we should not ignore the intrinsic contribution from crystal lattice to properties. For example, the internal bias field induced by defect dipoles may affect the properties of crystalline lattice, as analyzed by Landau– Ginzburg–Devonshire theory [79], [108], [109]. Therefore, a lot of work still needs to be done to understand the “hard” and “soft” mechanisms.

The above five factors are available for both PF polycrystalline ceramics and single crystals. In contrast to the ceramics with randomly oriented grains, the piezoelectricity of single crystals and textured ceramics can benefit from the crystal anisotropy. Selecting the proper orientation is an effective way to optimize the physical properties of single crystals. The piezoelectric properties of PFs show strong orientation-dependent behaviors, taking tetragonal 4mm crystal as an example, the longitudinal piezoelectric coefficient d33* with respect to orientation can be expressed in the following equation:

* T d 33 = d T31 cos θ sin 2 θ + d 15 cos θ sin 2 θ + d T33 cos θ, (13)

T where d T33, d 15 , and d T31 are single domain piezoelectric coefficients measured along principal crystallographic axes of tetragonal crystal. θ is the angle between the measurement direction and the [001] polar direction. It can be T observed that the piezoelectric shear coefficient d 15 contributes to the value of d33* as θ deviates from polar direction (θ≠0). Thus, if the shear coefficient is large enough, the maximum d33* may lie along the direction away from the polar axis [54]. Based on the feature of piezoelectric anisotropy, the PF crystals can be divided into the following two types. Type 1: the crystals with maximum piezoelectric coefficient d33* along the polar direction (e.g., the PT and tetragonal PZT crystals). Type 2: the crystals with maximum piezoelectric coefficient d33* along the nonpolar direction (e.g., the BT and relaxor-PT crystals). Fig. 10 gives the orientation dependence of d33* for BT and PT crystals, where the maximum d33* of PT is along the [001] polar direction, whereas for BT crystals it is along the [111] nonpolar direction. It should be noted that the piezoelectric anisotropy in PFs could be changed with composition variation, temperature, or stress [54], [111]. The PF crystals show the Type 1 characteristic when approaching the ferroelectric-paraelectric phase transition point (e.g., Curie temperature), while exhibiting the Type 2 feature when approaching the ferroelectric-ferroelectric phase transition point (e.g., MPB or PPT). This is due to the fact that the single domain d33 is enhanced at ferroelectric-paraelectric phase transition point whereas single domain d15 is increased at ferroelectric-ferroelectric phase transition point, as discussed in Section V.A. In general, if single domain coefficient d33 is much higher than d15, the maximum d33* is along the polar direction; otherwise, the maximum d33* is along the nonpolar direction. As re-


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Fig. 10. Orientation dependence of piezoelectric coefficient d33* for (a) BT and (b) PT crystals at room temperature. To obtain the d33* value of one direction, a line along this direction should be plotted from the origin to surface of 3-D figure. An intersection point can be found between the line and surface of 3-D figure. The distance between this intersection point and the origin indicates the value of d33* along this direction.

ported, the PZT, relaxor-PT, and NBT-BT crystals with MPB compositions exhibit maximum longitudinal piezoelectric coefficient d33* along their respective nonpolar directions [2], [38], [112]–[114]. Of particular significance is that the maximum d33* of rhombohedral relaxor-PT crystals (being along [001] nonpolar direction) is about 12 times higher than that along its [111] polar direction, as shown in Fig. 11(a). For tetragonal relaxor-PT crystals with composition on proximity of MPB, however, the maximum d33* (being along [011] nonpolar direction) is only 2 times higher than that along its [001] polar direction, as given in Fig. 11(b). This feature can be explained by the anisotropic electrostrictive coefficient Q33*, which exhibits the maximum value along 〈100〉 directions for perovskite crystals [49]. To utilize the piezoelectricity of nonpolar direction, the PF crystals are required to be poled along the specific nonpolar directions. Various ferroelectric domain configurations may occur in the crystals poled along their nonpolar directions, and these crystals are called domain engineered crystals. Of particular interest is that not only is the piezoelectric activity enhanced but also the hysteresis is decreased in the domain engineered crystals, as shown in Fig. 12, due to the fact that all domains are energetically equivalent in [001] poled rhombohedral crystals with applying electric field along [001] direction, leading to the minimal contribution of domain wall motion to the strain. G. Short Summary The critical factors responsible for high piezoelectric activity of PFs have been discussed in this section. The factors discussed in section V.A. to V.E. are associated with the instability of crystalline lattice (ferroelectric phase) and domain wall, whereas the anisotropic factor discussed in section V. F. accounts for the high piezoelectric activity in PF single crystals and textured ceramics. Fig. 13 gives the development history of perovskite ferroelectrics and

the milestones related to enhanced piezoelectricity. It can be seen from Fig. 13 that the combination of more factors (V.A.-V.F.) in PFs will lead to a higher piezoelectric activity. VI. Future Trends In this review article, the piezoelectric behaviors of PFs and the critical factors responsible for the high piezoelectricity were surveyed. The piezoelectric coefficients of PFs have been enhanced from 100 pC/N for BaTiO3 to 1500– 2800 pC/N for relaxor-PT crystals in last 60 years. These developments have benefited various piezoelectric devices, including ultrasonic transducers, sensors, and actuators. Nowadays, improving the piezoelectricity of PFs is still a valuable and desirable research direction from the viewpoint of applications, especially for the following three respects. (1) Next-generation ferroelectric single crystals (high piezoelectric coefficients, low losses, high TC and EC) are required to improve the efficiency and bandwidth of ultrasonic transducers. (2) PFs with high piezoelectric properties on micro- and nano-meter scales are required to meet the future miniaturization goals and MEMS/NEMS applications (micro and nano-electromechanical systems). (3) Piezoelectricity of lead-free ferroelectrics needs to be enhanced with the aim to replace the state-of-the-art lead-based perovskite ferroelectrics to alleviate the environmental concerns. To fulfill these requirements, some important issues involved in the PFs should be addressed; meanwhile, new approaches to enhance the piezoelectricity should be explored. Some queries and potential approaches to further improve the piezoelectricity of PFs are listed. 1) Tuning the electrostrictive coefficient Q in PFs. As presented in section IV, the piezoelectric response in ferroelectrics is based on the electrostrictive effect,

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Fig. 11. Orientation dependence of piezoelectric coefficient d33* for (a) rhombohedral and (b) tetragonal PIN-PMN-PT crystals. Input data are from [113] and [114]. One can plot a line from the origin to the contour of the 2-D figure. An intersection point can be found between the line and contour of the figure. The distance between this intersection point and the origin indicates the value of d33* along the direction of this line.

investigations on which will benefit the exploration of next-generation high-performance piezoelectrics. The electrostrictive coefficients Q of PFs show minimal variations with respect to the temperature; thus, improving the piezoelectricity via electrostricitive coefficient Q will not sacrifice the temperature stability. This is an attractive advantage when compared with the piezoelectricity improvement via the phase transition. The electrostrictive effect originates from the anharmonicity of ion-pair potential and is highly associated with the crystal structure, including the electronic structure of ions, the tolerance factor, the ordering of A- and B-site cations in perovskite materials ([49] and references therein). Thus, establishment of the relationship between electrostrictive effect and crystal structure will be valuable. 2) Exploring the mechanism of dopant strategy. Thanks to the dopant strategy, we have large family of PZT ceramics with various properties to meet the requirements of different applications. However, the mechanism of dopant strategy is yet uncertain. For example, is the dopant only related to the extrinsic contribution (domain wall motion) without any im-

pact on the intrinsic one? To answer this question, two approaches are proposed. One is to study the high frequency (from GHz to THz region) or low temperature (from 10 k to 100 k) electromechanical properties of the PZT ceramics. Due to the domain wall relaxation, we could approach the intrinsic lattice response of PZT ceramics at high frequency or low temperature. The other approach is to analyze the properties extracted from both doped and undoped single domain PZT crystals, where the extrinsic contribution can be excluded. 3) The role of relaxor and how to utilize the relaxor component in PFs. Numbers of investigations show that relaxors or polar nanoregions may play an important role in ultrahigh piezoelectricity of PMNPT and PZN-PT crystals. To illustrate the effect of relaxors, tetragonal PMN-PT and PZT crystals were generally used to compare with rhombohedral PMN-PT crystals, because tetragonal PMN-PT (PT content is higher than 38%) and PZT crystals do not possess polar nanoregions and other relaxor characteristics [84], [86]. The piezoelectric coefficients d33* of domain engineered tetragonal PMN-PT and PZT

Fig. 12. The electric-field-induced strain for rhombohedral relaxor-PT crystals. (a) [111] poled PZN crystal, reprinted by permission from Park S. E. and Shrout T. R., J. Appl. Phys., 82, 1804 (1997). Copyright© 1997, the American Institute of Physics; (b) [001] poled PMN-0.28PT crystal, where the electric field is applied along nonpolar direction.


Fig. 13. The development of perovskite ferroelectrics with respect to the piezoelectric coefficient d33. The factors responsible for the enhancement of piezoelectric activity are listed by red characters.

crystals are