Introduction

High-power piezoelectric applications have been indispensable for the development of our society, e.g., ultrasonic welding, cleaning, machining, and medical surgery [1,2,3]. Numerous industries benefit from these applications, including manufacturing, engineering, medical, food industries, etc. High-power piezoelectric applications usually refer to the applications operated at resonant frequencies (a few kHz to MHz) with a relatively large driving electric field for maximizing the amplitude of the acoustic wave (or the vibration velocity). Normally, piezoelectric devices are operated at an electric field on the order of a few kV/mm, depending on the electrical breakdown strengths of materials in which the strain amplitude increases almost linearly with the applied electric field [1, 4, 5]. High acoustic vibration amplitude is desirable for generating non-linear effects from the source to the medium, including radiation pressure, cavitation, streaming, etc., which are the fundamental mechanisms for applications.

Unfortunately, high-power piezoelectric applications are sometimes limited by the internal power dissipation, which is normally presented in the form of heat and consequently induces degradation of performances [6]. The internal power dissipation is inevitable due to the presence of losses inside materials, including elastic loss, electric loss, and piezoelectric loss. To minimize the power dissipation, “hard” piezoelectric materials with low losses are preferable, e.g., acceptor-doped lead zirconate titanates (abbreviated as PZT), like PZT-4 and PZT-8. These materials have been commercialized for mid-power and high-power piezoelectric applications for quite a few decades. Since PZT-based ceramics consist of a large amount of hazardous PbO (~ 60%), improper manufacturing setup and disposal during the whole-life cycle would bring serious harm to the human and ecological environment. Therefore, a growing concern over environmental protection has been raised by the governments around the world, while the first regulations arose in the European Union. Related legislation restricting the use of Pb element in electronics has been proposed, e.g., RoHS and REACH [7]. Consequently, for the replacement of lead-based piezoelectrics, lead-free piezoelectric ceramics with equivalent or even better performance are highly demanded [8]. Several promising lead-free candidates have been developed so far, including BaTiO3 (BT)-based [9], (Bi0.5Na0.5) TiO3 (BNT)-based [10,11,12], and (K0.5Na0.5)NbO3 (KNN)-based [13]. Each of these systems possesses unique characteristics, e.g., high piezoelectricity in BT, large electric-field-induced strain in BNT, and high Curie temperature in KNN. It is worth noting that, for high-power applications, BNT-based ceramics present exceptional stability at high vibration velocity, which is superior to the others. However, the low depolarization temperature in the BNT-based system limits its application. Therefore, KNN-based ceramics with high Curie temperature and satisfactory piezoelectricity have also received extensive attention from researchers [14, 15].

Mechanical quality factor (Qm) is an important property for high-power piezoelectric application as it reflects the capability of mitigating heat generation [16]. For high-power application, a high Qm is often desirable, yet another property, i.e. electromechanical coupling factor (k), should also be considered at the same time. The figure of merit (FOM) for high-power application is frequently defined as the product of k and Qm [17]. However, these properties are often inversely proportional. Namely, it is hard to achieve a high FOM with simultaneously high k and Qm. For example, a “soft” PZT usually exhibiting a high piezoelectricity but low Qm, while a “hard” PZT exhibiting an opposite combination of performances [18]. Although optimized “hard” PZT materials have been frequently used for high-power application, materials with higher FOMs are still being pursued.

This review aims to provide a comprehensive summary of the research progress of the “hardening” effect in lead-free piezoelectric ceramics. This review starts with the “hardening” mechanisms in piezoelectric ceramics and its influence on the high-power performance. Then, we comprehensively summarize the research of the hardening effect in BT-based, BNT-based, and KNN-based lead-free piezoelectric ceramics. Meanwhile, for the characterization of high-power electromechanical performance, we propose three specific techniques, i.e., the constant-voltage method, constant-current method, and transient method. Finally, we exhibit a few typical high-power piezoelectric application examples.

Hardening effect in ferroelectric materials

Loss mechanisms

According to the law of conservation of energy, the energy of an isolated system should always remain constant, which means that energy can neither be created nor destroyed. Due to the presence of losses, the interconversion between electrical and mechanical energies in a piezoelectric material is never 100% efficient. Most of the lost energy would transform into heat and later dissipate inside the material. Unfortunately, the dissipated heat can cause significant degradation to the performances of materials and devices.

Understanding the loss mechanisms is critical for improving the design of piezoelectric materials. There are three major types of losses in piezoelectric materials, including electrical (or dielectric) loss, mechanical (or elastic) loss, and piezoelectric loss. Dielectric loss and mechanical loss have been well recognized and introduced in various representative testing standards, e.g., IEEE standard and European standard. Compared to these losses, the piezoelectric loss is less known, but actually, it has been studied in numerous researches in early times [19,20,21,22]. Currently, quite a few researchers are still paying high attention and working relentlessly on this topic [23]. Mezheritsky described piezoelectric loss as “a consequence of complex piezoelectric phenomena” [24].

The loss mechanisms in piezoelectric materials have been phenomenologically explained since the late 1960s [25]. Dielectric constant and dielectric loss (often parameterized in terms of loss tangent, symbol: tanδ) reflects the capacitive and resistive properties of a dielectric material when measured in an AC electric circuit, which corresponds to the capability of storing and dissipating electrical energy, respectively. On the other hand, elastic compliance constant and elastic loss (often parameterized in terms of the tanϕ) represent the stored and dissipated mechanical strain energy, respectively. Similarly, piezoelectric loss (tanθ) is defined as the hysteresis loss in electromechanical process, including strain-electric field x(E) or electric displacement-stress D(X) curves. Damjanovic proposed an equivalent electric circuit to include the piezoelectric loss onto the standard circuit that is ubiquitously used nowadays [26]. There was experimental evidence showing that the piezoelectric loss plays a critical role at resonance frequency but could be neglected at anti-resonance frequency [27].

Surprisingly, the origin of loss mechanisms at off-resonance has been reviewed by Härdlt by the early 1980s [28]. A positive correlation between the electrical and mechanical losses was found in a series of doped PZT-based ceramics. It is worth noting that these losses decrease steeply above the Curie temperature, which is when the ferroelectricity disappears. The result is strong evidence that the losses are highly related to the ferroelectricity, to be clear, the domain-wall motion. The idea is still widely accepted at present, and many models or concepts have been built on top of it. Härdlt also pointed out three other factors associated with the losses, including lattice (e.g., polarization rotation and extension), microstructure (e.g., grain boundaries and pores), and conductivity. However, contributions of these three factors are relatively small compared to that of the domain-wall motion. A comprehensive review of the intrinsic/extrinsic contribution to losses in ferroelectric ceramics can be found elsewhere [29].

To demonstrate the significance of ferroelectricity, tanδ and Qm of various ferroelectric materials are summarized in Table 1. There are two distinctive types of ferroelectrics, i.e., “soft” ferroelectric with high tanδ and low Qm, and “hard” ferroelectric with exactly opposite performances. Compared to the hard ferroelectric, soft ferroelectric usually exhibits easier polarization switching upon the applied electric field, or namely, the soft ferroelectric normally requires a lower electric field for the polarization switching, thus exhibiting higher dielectric and piezoelectric properties. Among these materials, relaxor-ferroelectric materials show distinctively low losses but high piezoelectricity because of the high intrinsic contribution and unique domain configuration, which is different from the conventional ferroelectric materials [30]. Piezoelectric single crystals like SiO2 and LiNbO3, which possess exceptionally high Q and low loss, are widely employed in filters, surface acoustic wave devices, and electro-optics. However, these materials show lower piezoelectricity, compared to perovskite ferroelectric materials. Especially, ferroelectric materials of single-crystal form are more desirable, compared to their polycrystalline counterparts. Hard PZT polycrystalline ceramics have been an excellent and mainstream choice for high-power piezoelectric applications because growing a single-crystal PZT with a sufficiently usable size is a difficult task. In contrast, growing of single-crystal relaxor ferroelectrics, like PMN-PT, was much easier and higher performances can be obtained. Obviously, manufacturing a single crystal of high quality requires high technique and is time-consuming, thus it is more expensive. Therefore, it is common to employ single-crystal relaxor ferroelectrics in high-end piezoelectric applications only when the costs are not the first consideration. A more detailed discussion over the single-crystal relaxor ferroelectrics can be found elsewhere [31].

TABLE 1 Comparison of Different Piezoelectric Materials.
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Models of hardening effect

Hardening effect can be defined as the stabilization of domain configuration or inhibited domain-wall motion in ferroelectrics. Phenomenologically, one of the most significant characteristics of the hardening effect is the internal bias observed in the polarization–electric field P(E) loop. However, different models have been proposed to account for the hardening effect, including bulk (or volume) effect, domain-wall effect, and surface (or grain boundary) effect, as illustrated in Fig. 1. In this section, three different models will be briefly introduced. Before we start, we would like to emphasize that the universality of these models on different materials systems is highly uncertain because these models have been developed mainly based on the lead-based ferroelectrics, especially the PZT-based system.

Figure 1
figure 1

Illustration of three distinctive models of hardening effect in ferroelectrics. (a) A representative multi-domains state inside a single grain. Models of (b) bulk effect, (c) domain-wall effect, and (d) surface effect.

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Bulk effect

Defect associates, either intrinsic or extrinsic, could form a dipole moment with net polarization greater than zero and thus would align along with the spontaneous polarization of ferroelectric domains. The alignment of defect associates would cause an internal bias macroscopically inside a single grain and consequently stabilize the domain configuration or restrict the domain-wall motion, which is known as the bulk effect. Microscopically, the presence of defect dipole inside domain would restrict the rotation or switching of spontaneous polarization [47, 48]. The localization of oxygen vacancies surrounding the acceptor center has been experimentally observed. Eichel et al. implemented electron paramagnetic resonance (EPR) for characterizing the defect structure in Cu-doped PbTiO3 and found the defect dipoles align along the [001] axis, which is parallel to the direction of spontaneous polarization [49].

The impact of the bulk effect strongly depends on the short-range diffusion of the defects. Short-range diffusion is necessary to align defect dipoles along with the spontaneous polarizations within domains. Erhart et al. developed a kinetic model based on first-principles calculations to describe the switching of defect dipoles in acceptor-doped PbTiO3 [50]. Related kinetic reactions in Fe-doped PZT ceramic were investigated by Morozov and Damjanovic [51, 52] using the harmonic analysis firstly developed by Leary and Pilgrim [53]. According to the results, the diffusion process is confirmed to be responsible for the aging and de-aging processes in PZT ceramics. Meanwhile, the nature of symmetry-conforming short-range order (SC-SRO) of defect dipoles has been manipulated for creating a large and reversible electrical-field-induced strain, albeit accompanied by a huge hysteresis [54].

While the hardening effect of bulk effect has been well understood, the location and formation of defect dipoles is still an open question. Does defect dipoles form at domain walls or between domain walls? If the dipoles are found at domain walls, another question should follow: do the dipoles form naturally at domain walls or the domain walls migrate toward dipoles? The location of defect associates with respect to the domain wall was investigated by Jakes et al. [55]. In the experiment, the EPR results between a calcined powder and a sintered ceramic were compared. Compared to the fine domain configuration in the sintered ceramic, a highly reduced domain wall density could be expected in calcined powder. An indirect conclusion that defect dipoles are located inside the domain rather than the domain wall was given. Nevertheless, an opposite result suggested a favorable position of oxygen vacancies at the domain wall rather than inside domain [56]. Apparently, the location of defect dipoles is a scientifically important research topic that required further investigation. Recently, our group has been investigating the hardening effect of defect dipoles with respect to the variation of domain-wall density in acceptor-doped PZT-based ceramics [57]. A model involving interaction between defect dipoles and domain-wall density was proposed.

Domain-wall effect

Strain hardening has been a practical strengthening mechanism for structural materials, e.g. metal and alloys, where the increased number of dislocations appear after cold working play a significant role. Analogous to dislocations, lattice defects can act as a pinning center, hindering the domain-wall motion. A classic direct observation of the pinning of domain-wall motion can be found in the work done by Yang et al. [58].

Pinning effect was already considered in ferromagnetic materials prior to ferroelectric materials. Rayleigh law was later proved to be universal to describe the pinning effect in most of the ferroic materials [59]. According to the Rayleigh analysis of the hysteresis loops of soft/hard/undoped PZT ceramics, the extrinsic contribution was found strongly related to the ordering of defects [60]. For a quenched ferroelectric ceramic, the pre-existing defects should be distributed randomly; in that case, the domain-wall contribution is rarely affected. However, due to lower formation energy, these defects tend to migrate towards domain walls gradually over time [56]. Aggregation of defects into clusters along domain walls would result in a strong pinning force to the domain-wall motion and consequently leading to a significant hardening effect. The pinning strength of an oxygen vacancy was calculated by Chandrasekaran et al., using the first-principles method [61]. They also compare the pinning strength between an oxygen vacancy and a defect associate. Interestingly, the defect associate was found performing a pinning strength 3 times higher than that of the oxygen vacancy.

Surface effect

In contrast to the domain-wall effect, a long-range diffusion of mobile charged carriers, i.e., electronic charge carriers and ionic defects, to the microstructural surface boundary, e.g., grain boundaries, pores, and cracks, are considered in the model of surface effect [62]. Drifting of mobile charged carriers is necessary for compensating the depolarization field caused by the discontinuity of spontaneous polarizations at the surface boundary, but consequently exerting a significant clamping force on the domain-wall motion [63, 64].

Compared to the previous two models, the model of surface effect is mainly based on numerical calculations. Even though, this model can explain the experimental observation reasonably. For example, the internal bias observed in an aged sample can be understood as a consequence when positive charges (e.g., oxygen vacancies) and negative charges (e.g., acceptor centers) migrate towards negatively and positively charged surfaces, respectively. Then, the drifting of charges is decisive to the aging process in this model. Vorotiahin et al. [65] stated that the bulk effect itself cannot explain the saturating dependence of the internal bias or the monotonic decrease of the characteristic aging time with increasing doping concentration in PZT ceramics, while the surface effect is capable of doing so. The surface effect is versatile as the influences of concentration, temperature, and time could be considered simultaneously.

Instead of giving a conclusion on whether which models are the best, we would like to point out, even in a highly commercialized piezoelectric system like PZT, the hardening effect is perplexing. In the following section, the investigation of the hardening effect in lead-free piezoelectric ceramics would be summarized and compared.

Lead-free piezoelectric materials for high-power applications

BT-based ceramics

BT ceramics were the earliest discovered polycrystalline piezoelectrics and have been widely utilized for transducer applications [66]. However, the high-power performance of BT ceramics has always been far from satisfactory due to the large dielectric loss at high driving field. It has been pointed out that the dielectric loss is only of the order of 0.01 at low fields. But as the field is increased, the dielectric loss rises sharply, reaching about 0.1 at 1 kV/cm [67]. Baerwald and Berlincourt firstly reported that the dielectric loss at high fields can be substantially reduced by applying a positive DC bias equal to the negative peak of the driving field [68]. Soon after, Schofield et al. showed that the addition of cobalt to (Ba0.95Ca0.05)TiO3 can produce a large reduction in hysteretic loss at high electric fields without a significant reduction in piezoelectric characteristics [69]. Both high Qm- and d33 can be achieved, being on the order of ~ 800 and 150 pC/N, respectively.

In recent years, Liu et al. found that the internal bias field (Eib) derived from the defect dipoles showed a significant effect on “hard” behavior of BT ceramics [70]. Meanwhile, they provided a quantitative explanation of the relationship between ferroelectric properties and defect dipoles based on the first-principles calculation. By far, the electromechanical properties, especially Qm and d33, can be effectively optimized by defect engineering. For example, acceptor doping of Mn2+ in BT ceramics can cause the formation of defect dipoles, leading to an improvement of Qm [71,72,73]. A dramatic enhancement of Qm (> 2700) can be obtained in 1 mol % Mn-doped Ba(Ti0.96Zr0.04)O3 ceramics. Additionally, certain ionic pairs, e.g., Li+-Al+, were proposed to be able to form defect dipoles in BT ceramics, resulting in a huge Qm (~ 2000) accompanied by high d33 with good temperature stability [74]. Moreover, (Ba0.9Ca0.1)TiO3–0.5 wt% MnCO3 (BCT-0.5Mn) exhibited a relatively high Qm of 2400 and a low dielectric loss of 0.23% [42]. The investigation of high-power characteristics of BCT-0.5Mn indicated the stable Qm and fr under high-level vibrations [42]. These results notably revealed the strong potential for the utilization of BT-based ceramics in high-power applications.

KNN-based ceramics

The development of KNN-based piezoelectric ceramics has been mature, as evidenced by the on-going transfer of technology [13]. However, the large-scaling replacement for PZT has not yet occurred. There could be several reasons, e.g., cost consideration and the timing of legislation implementation. For high-power applications, one of the barriers includes the lack of practical demonstration of hard KNN-based materials.

The enhancement of Qm value has been an important task for high-power applications. It generally requires at least 800 [75,76,77]. The Qm of a pure KNN ceramic is roughly around 200 [78]. Qm value has become one of the biggest problems that KNN ceramics face in high-power applications. It should be noted that the Q value at large vibration velocity is still rarely reported and need to be further studied, especially for KNN-based ceramics. Further discussion on vibration velocity dependent Q value will be developed in Chapter 4. Limited to chapter 3.2 hereinafter the discussed Q values for various doping concentrations and compositions are measured under weak field and refer to small-signal values. Hard doping has been widely used to increase the Qm of KNN ceramics, including CuO [39, 79,80,81,82,83,84,85], K5.4Cu1.3Ta10O29 (KCT) [83, 84, 86], CuTa2O6 [87] K4CuNb8O23 (KCN) [40, 78, 88, 89], CuF2 [40, 77, 90]. Besides, co-doping of multiple compounds, together with CuO, exhibited good hardening effect, e.g., SiO2 [75], Co2O3 [91], Ni2O3 [84], B2O3 [76]. Matsubara et al. found, with the optimized addition of 0.5 mol % KCN, the Qm of KNN ceramics reached 1200 [89]. Later, they further increased the Qm of KNN ceramics to 1300 and 1400 through quantitative doping of Cu and Ta, respectively [92, 93]. Lim et al. improved the Qm value of KCN-doped KNN ceramics to 1500 by optimizing the processing of ceramics [78, 88]. Park et al. investigated the influence of Cu doping on the ferroelectric and piezoelectric properties of KCT-modified KNN ceramics. An extremely high Qm of 3053 was obtained in the sample doped with 0.5 mol % of Cu, which is by far the highest record for the KNN system, as shown in Fig. 2a [86]. Recently, Liao et al. also obtained a similar value through CuF doping [40, 77, 90].

Figure 2
figure 2

(a) Qm of KNN and CuO-doped KNN-KCT ceramics [86], (b) Polarization hysteresis (P-E) of 0.5 mol % CuO-doped KNN-KCT [83], (reproduced from Ref. [83] with permission from Copyright 2017 Elsevier), (c) Eib, tanδ, and Qm of KNN-KCT + xmol %CuO ceramics [83], (reproduced from Ref. [83] with permission from Copyright 2017 Elsevier), (d) Depolarization temperature Td and Qm(33) as a function of z in BNLKT4-100z [108], (reproduced from Ref. [108] with permission from Copyright 2008 The Japan Society of Applied Physics), (e) Coupling factor k and Qm as a function of Mn concentration in 0.88BNT-0.04BLT-0.08BKT ceramics [108], (reproduced from Ref. [108] with permission from Copyright 2008 The Japan Society of Applied Physics), and (f) variations in Qm as a function of vibration velocity v0-p for KN-0.8Mn, Sb-doped KNN-0.15CuO, BNT, 0.895BNT-0.04BLT-0.04BT-0.025Mn (BNT-BLT-BT-0.025Mn), 0.88BNT-0.04BLT-0.08BKT-0.6 wt% MnCO3 (BNT-BLT-BKT-0.6 wt% MnCO3), 0.83BNT-0.03BLT-0.084BKT-0.056BT (BNT-BLT-BKT-BT), and PZT-H (a hard PZT ceramic; NEC Tokin: N6). [12, 30, 108, 112, 113].

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In addition to Cu doping, Mn compounds are also effective doping elements for enhancing the Qm value of KNN ceramic. Hao et al. improved the Qm of KNN ceramics to around 300 through Mn doping [94]. Xu et al. also found that the doping of Mn can increase the Qm of KNN ceramics (from 85 to 330) [95]. Wang et al. prepared Mn-doped KNN ceramics with Qm of 370 [96]. In most Mn-doped KNN ceramics, it seems that the Qm does not increase significantly compared to that by Cu doping. In contrast, there are other studies proposed that doping of Mn could cause the softening effect [38, 97]. The softening or hardening effect of Mn doping in KNN ceramics seems to be different from that in PZT ceramics [97, 98]. Recently, Li et al. added a typical B-site dopant, i.e., Zn, into KNN-based ceramics and softening effect was surprisingly observed as well [99].

The explanation for the hardening effect in KNN ceramics has been confusing. Among the three aforementioned models, the bulk effect and domain-wall effect have been the most frequently used [39, 40, 80, 83, 91]. Han et al. studied the hysteresis loop of KNN ceramic doped with Cu and KCT. An Eib can be observed in the doped KNN ceramic, as shown in Fig. 2b [83]. Cu2+, as a divalent acceptor ion, will incorporate into the Nb [5]+-site and cause the formation of oxygen vacancies. The formation of defect dipoles between acceptor centers and oxygen vacancies leads to the form of Eib [39, 76, 81, 83, 91]. The increase of Eib corresponds well with the observed increase of the Qm value, as shown in Fig. 2c [83]. Similarly, Lim et al. observed Eib in doped KNN ceramics, which is proportional to the Qm value [88]. In contrast, there are researches suggesting that oxygen vacancies do not form into defect dipoles with acceptor ions, but the presence of the oxygen vacancies could inhibit the domain motion, thereby increasing Qm [80, 82, 86, 87], e.g., high Qm of 3053, shown in Fig. 2a [82].

It is known that in either bulk effect or domain-wall effect, the oxygen vacancies play a decisive role in the hardening effect. However, according to the work done by Thong et al., in which 0.95(Na0.49K0.49Li0.02)(Nb0.8Ta0.2)O3-0.05CaZrO3 ceramics were sintered at different atmospheres (air and oxygen-rich atmosphere), an obvious variation of the Eib was observed yet the Qm value does not change significantly [100]. The decreased of Eib was explained by the reduction of oxygen vacancies. A similar phenomenon was observed in KNN-based single crystal subjected to annealing [101]. Failure of using these models for explaining the variation of the Eib and the related hardening effect might imply that the current understanding of the hardening effect in KNN-based ceramics is still insufficient. Other supporting information includes the poor explanation of the softening effect observed in Mn-doped KNN ceramics [38, 97], insignificant doping impact of other typical acceptor dopants (e.g., Fe, Zn, and Ni) [84, 96, 102, 103], and sometimes inconsistent efficiency of hardening effect in different works. Therefore, it is necessary to devote much effort on the investigation of the mechanism of hardening effect in KNN-based ceramics.

BNT-based ceramics

BNT, a perovskite piezoelectric material with rhombohedral (R) symmetry at room temperature, was firstly discovered by Smolenskii in 1960. Although the d33 of pure BNT ceramic is relatively low (100 pC/N), the BNT derivatives exhibit enhanced piezoelectric performance by the construction of morphotropic phase boundary (MPB) and/or acceptor doping [104,105,106,107]. In the case of high-power application, high Qm, low tanδ, and high kij values are required. Recently, some researchers integrated the two aforementioned compositions into a solid solution with four components, i.e., x(Bi0.5Na0.5)TiO3-y(Bi0.5K0.5)TiO3-z(Bi0.5Li0.5)TiO3-pBaTiO3(BNT-BLT-BKT-BT) [30].

Hiruma et al. found that the x(Bi0.5Na0.5)TiO3–y(Bi0.5Li0.5)TiO3–z(Bi0.5K0.5)TiO3 (xBNT-yBLT-zBKT) ceramic is one of the most promising BNT-based systems for high-power applications [108]. The system is on basis of BNT-BKT, which has an R-T MPB at z = 0.18. In this case, y = 0.04 was kept and the high-power properties of different phase structures were investigated. Figure 2d shows the variation of Td and Qm(33) as a function of BKT content. It was found that Td and Qm(33) firstly increased, reaching their maxima (Td = 221 °C, Qm(33) = 200) at z = 0.08, and then decreased with further increasing z on the R side. However, Qm(33) dropped to below 90 in the region of z ≥ 0.18 on the T side. These results indicate that the R side is a suitable composition for high-power applications.

x(Bi0.5Na0.5)TiO3-y(Bi0.5K0.5)TiO3-zBaTiO3 is another suitable BNT-based system for high-power applications. Zhang et al. found that the ceramic with the composition 0.79(Bi0.5Na0.5)TiO3-0.14(Bi0.5K0.5)TiO3-0.07BaTiO3-0.8 wt% MnO2 has large Qm = 1100, k33 = 0.49, and low tanδ = 0.4% [109]. Also, a high Td = 235 °C is available in this composition, leading to the broadened operating temperature. Recently, some researchers integrated the two aforementioned compositions into a solid solution with four components, i.e., x(Bi0.5Na0.5)TiO3-y(Bi0.5K0.5)TiO3-z(Bi0.5Li0.5)TiO3-pBaTiO3(BNT-BLT-BKT-BT) [30]. The Co2O3-modified BNT-BLT-BKT-BT ceramic showed typical “hardening” characteristics, exhibiting a relatively high Qm > 800 and low dielectric loss < 0.1%, comparable to hard PZT ceramics. Lee et al. further conducted high-power characterization under constant velocity condition and minimal variation of resonance frequency shift and lower piezoelectric loss under high-level vibrations can be achieved [30]. Therefore, it is also considered as a good system for high-power materials.

MnCO3, as an effective dopant, can also further improve the high-power performance of BNT-based ceramics. Hiruma et al. [108] reported that the Qm of 0.88BNT-0.04BLT-0.08BKT was enhanced dramatically, while the kp and k31 gradually decreased as the Mn doping increased, as shown in Fig. 2e. At 0.6% Mn doping, the Qm was raised to above 700, which was twice as that of the undoped one. It is assumed that Mn2+ or Mn3+ substitutes into B-site as an acceptor dopant, and subsequently leads to the formation of oxygen vacancies. Consequently, the oxygen vacancies pinned on the ferroelectric domain and thus increased the Qm, accompanied by slight scarification of kp [110, 111]. Besides, Hejazi et al. [11] doped 1.5 mol % Mn into 0.88BNT-0.04BLT-0.08BKT and the ceramics showed a high Qm = 970 and low tanδ = 0.85%, which are comparable to that of PZT-based hard materials. Meanwhile, the ceramics exhibited the least resonant frequency shift and temperature rise, showing great potential for high-power applications [11].

As aforementioned, the stability of Qm has long been one of the important issues in high-power piezoelectric research. It represents the degradation of piezoelectric performance with increasing power demand. Figure 2f depicts the Qm of various lead-free ceramics summarized as a function of vibration velocity [12, 30, 108, 112, 113]. The variation in Qm for several hard PZT ceramics are plotted in the same figure for comparison. For all compositions, Qm decreases as the vibration velocity rises. It should be noted that the Qm of PZT-H shows a significant drop with increasing v0-p. Whereas KN and BNT-based ceramics exhibit a slower decrease than hard PZT, indicating a superior high-power applicability. That is, though the Qm value of lead-free ceramics in the low v0-p region (< 0.5 m/s) merely corresponds to half that of hard PZT, their relation quantitatively inverts in the high v0-p region (> 0.8 m/s), where KN-0.8Mn and BNT-based ceramics exhibits higher Qm. It is also noted that, by introducing another perovskite into BNT (such as BLT, BKT, and BT), the Qm of formed BNT-based solid solutions (for example, BNT-BLT-BKT and BNT-BLT-BT) can be significantly enhanced and maintain higher than 500 even at v0-p = 1.5 m/s compared with that of BNT. The degradation of Qm is possibly related to the increased losses at high vibration velocity [113]. And the stability of Qm of reported BNT-based ceramics under high-level vibration is inherently related to their high Ec, leading to higher domain stability and lower mechanical loss under high drive condition [30]. Most of the studies on the high-power performance of lead-free piezoelectric materials are concerned with the Q value as a function of vibration velocity. However, it is worth noting that Shekhani et al. proposed that the Q value of different materials should be compared with respect to the mechanical energy density, which they considered to be a more accurate evaluation method [114].

Other lead-free ceramics

In addition to KNN-based and BNT-based ceramics, the family of bismuth layer -structured ferroelectrics (BLSFs) has been attracting attention due to their exceptional high-power piezoelectric characteristics [115,116,117,118]. In these reports, the v0-p for textured BLSFs such as SrBi2Nb2-O9 and CaBi4Ti4O15 ceramics linearly reached approximately 2.5 m/s without any remarkable resonance frequency change. Meanwhile, both a high Qm and a large electromechanical coupling factor k33 can be obtained. For accessibility of manufacture, some nontextured BLSFs such as Sr0.25Bi2.75Ti0.75Ta1.25O–9 (SBTT), Bi4Ti2.98V0.02O12 (BITV) and Bi4Ti3O12-SrBi4Ti4O15 (BIT-SBTi) were recently reported to possess a high Qm value (> 2900) [118]. The stability of Qm and resonance frequency is even superior to that of hard PZT, which makes them promising candidates for lead-free high-power applications.

High-power characterization of piezoelectric materials

Vibration velocity is a parameter of interest for high-power applications. The vibration velocity is used as the high-power figure of measure instead of strain because the linear relation between strain (x) and driving electric field (E) does not sustain in the high electric field/power density and vibration velocity is independent of the sample size. The vibration modes of standard piezoelectric elements include transverse length mode (31), radial mode (p), longitudinal length mode (33), thickness extension mode and thickness shear mode. Take transverse length mode (31) for example, the vibration velocity is given by [11]:

$$v_{0} = \frac{4}{\pi }\sqrt {\frac{{\varepsilon_{33}^{T} }}{\rho }} \left( {k_{31} Q_{m} } \right)E$$
(1)

where \(\varepsilon_{33}^{T}\) is the relative permittivity, \(\rho\) is the density, \(k_{31}\) is the transverse electromechanical coupling coefficient, and \(E\) is the driving electric field.

It has been demonstrated that some of these parameters are dependent on the operating power. For example, when the vibration velocity increases from 0.05 m/s to 0.5 m/s, the Qm of PZT decreases by nearly 80% [119], as shown in Fig. 3a. The results indicate that the parameters measured at a low-power system do not represent the high-power performance. Therefore, the development of high-power characterization systems is of utmost importance. Over the past few decades, a few different characterization systems have been proposed. In the following sections, we will introduce three common techniques for high-power characterization: the constant-voltage method, the constant-current method, and the transient (or burst) method.

Figure 3
figure 3

(a) Qm of the Pb(Zrx,Ti1-x)O3 + 2.1 at. % Fe ceramics measured as a function of effective v0 = 0.05 m/s and 0.5 m/s [119], (reproduced from Ref. [119] with permission from Copyright 1993 The Japan Society of Applied Physics), (b) The 3 dB method used for calculating Qm, temperature dependences of (c) vibration velocity v0, and (d) mechanical quality factor Qm [12].

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Constant-voltage method

The constant-voltage method has been the most widely employed system in the community, due to its simplicity, which only requires a conventional impedance analyzer that could provide the impedance/admittance curves as a function of frequency. The parameters of interest can be calculated from the signals around the resonant frequency (and sometimes at the anti-resonance frequency), step-by-step according to the standards (several internationally accepted standards include the IEEE or the European standards) [120].

The 3 dB method can be used to calculate the Qm based on the impedance or admittance spectrum obtained by the constant voltage or constant-current method, as shown in Fig. 3b. The Q factor can be determined by the real part of the impedance frequency spectrum:

$$Q_{r} = \frac{{f_{1} }}{{\Delta f_{1} }}$$
(2)
$$Q_{a} = \frac{{f_{2} }}{{\Delta f_{2} }}$$
(3)

where f1, f2 are the resonance and anti-resonance frequencies, respectively, Δf1 and Δf2 correspond to the 3 dB bandwidth in the impedance curve around the resonance or anti-resonance peaks, respectively.

This characterization method works perfectly until the resonance spectrum distorts significantly with increasing applied electric field E. In some extreme cases, a large hysteresis or a jump of the peak curve could be observed upon rising and falling frequency [121], which is mainly due to the non-linear elastic properties of piezoelectric materials under high-power conditions. As demonstrated in Fig. 4a, with increasing applied voltage from 100 mV to 1500 mV, the resonance curve skewed to the left drastically, accompanied by a huge decrease of maximum admittance [1]. The asymmetry spectrum can no longer be used for calculation as the non-linear behavior is now involved [120], which is hard to be deconvoluted based on the conventional equivalent circuit models [1].

Figure 4
figure 4

The admittance spectrums measured using (a) the constant-voltage method, and (b) the constant-current method [120]. (reproduced from Ref. [120] with permission from Copyright 2009 The Japan Society of Applied Physics).

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Constant-current method

In order to avoid an asymmetry resonant curve that occurs in the constant-voltage measurement, Uchino et al. proposed the constant-current method [121]. As the vibration amplitude is proportional to the current around the resonance frequency, the constant- current condition can guarantee that the vibration amplitude is almost constant through the resonance frequency region [120]. Consequently, the electromechanical coupling parameters can be accurately determined from the perfectly symmetrical resonance spectrum, as shown in Fig. 4b.

Although the constant-current method is more suitable for high-power measurement, it is not recommended for characterizing the Q at anti-resonance frequency as it would eventually lead to a similar distortion of the anti-resonance peak, just like the measurement of resonance peak under constant-voltage condition, as shown in Fig. 4a. For determining the electromechanical coupling parameters in either the constant-voltage and the constant-current methods, it is necessary to precisely measure the vibration performance at resonance or anti-resonance frequencies. High-power measurement at such high vibration level would result in significant heat accumulation and subsequently temperature rise in samples, which could greatly affect the accuracy of the measurement. Therefore, a modified characterization method is necessary to circumvent this issue.

The transient method

The transient method was later developed by Umeda et al. to mitigate the issue of heat generation [122]. The fundamental idea is to manipulate transient driving pulses (usually < 10 ms) to stimulate a resonant oscillation of piezoelectric samples, and then determine the electromechanical coupling parameters from the decaying behavior of the stimulated oscillation, so the heat issue can be highly suppressed. As shown in Fig. 5, during measurement, the AC voltage was applied on the measured piezoelectric sample at its resonance frequency for a few cycles before turning off the applied voltage [123], then either a short-circuit or open-circuit condition is imposed during the decay. In the short-circuit condition, the oscillation of the sample will decay at its resonance frequency and the short-circuit current is proportional to the vibration amplitude; [124] while in the open-circuit condition (current amplitude is 0), the oscillation will decay at its anti-resonance frequency and the open-circuit voltage is proportional to the displacement [124], as shown in Fig. 5. The exponential decay current and voltage are used to estimate the Qm at the resonance frequency and anti-resonance frequency, respectively [123]. For example, in the short-circuit condition, Qr is calculated as:

$$Q_{r} = \frac{\omega }{{2\ln \left( {\frac{{I_{{t1}} }}{{I_{{t2}} }}} \right)/(t_{2} - t_{1} )}}$$
(4)

where It1 and It2 are the amplitudes of the current at the time t1 and t2, respectively, and ω is the angular velocity of the generated current between t1 and t2. By measuring the decay signals of amplitudes, Qm of piezoelectric ceramics at the resonance and anti-resonance frequencies can be calculated.

Figure 5
figure 5

Illustration of the transient methods, viewing from the variation of voltage, current, and vibration before and after the (a) short-circuit, and (b) open-circuit condition is applied [124]. (reproduced from Ref. [124] with permission from Copyright 2016 John Wiley & Sons).

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The transient method does not only require a very short duration for the measurement but also could collect data with a wide range of vibration velocity in one single measurement, which is a simple yet versatile characterization technique. However, the transient method still has some limitations. It is mentioned that the non-linear behavior on piezoelectrics becomes significant at high-power applications [125], yet the transient method only considers the linear behavior during analysis, which may lead to inaccuracy of results. Recently, Slabki et al. [123] developed a modified transient method to characterize the non-linear behavior of materials under high-power conditions. The modified transient method was used to investigate the electromechanical coupling properties of hard PZT piezoceramic in three different vibration modes. Anisotropy of non-linear behavior results in the strongest heat generation in the radial mode, while transverse and longitudinal length modes show a similar temperature increase [123]. The result indicates that a better understanding of non-linear behavior can help improve the performance of high-power applications.

Among the three different types of high-power characterization methods, the transient method seems to be the most promising one. Among the three different types of high-power characterization methods, the transient method seems to be the most promising one. The transient method is based on a transient signal, the loss characteristics of piezoceramic samples without heat generation are observed at high vibration velocity due to low driving times (often less than 10 ms) [124]. Therefore, we can separate the temperature-induced loss to identify the mechanism of the loss. Besides, this method can be used to calculate both resonance and anti-resonance mechanical quality factors, which cannot be achieved by the traditional constant-voltage and constant-current methods [120, 124].

As discussed above, the lead-free piezoelectric system is more stable than the lead-based system at large vibration velocity. The loss mechanism of lead-free piezoelectric ceramics seems to be different for PZT-based piezoelectric ceramics. Therefore, using the transient method to study the loss mechanism of lead-free piezoelectric ceramics will become the focus of future research.

High-power piezoelectric ultrasonic transducers

High-power piezoelectric applications include ultrasonic transducers (UT), ultrasonic motors, and piezoelectric transformers. In this section, we will introduce a few typical UT applications. Meanwhile, a few researches on utilizing the lead-free piezoelectric ceramics for UT application will be reviewed [1,2,3].

Ultrasonic transducers

An ultrasonic transducer (UT) is a device that allows the generation and detection of ultrasonic waves. There are two major types of UT, including magnetostrictive UT and piezoelectric UT. Compared with the magnetostrictive UT, the piezoelectric UT possesses numerous advantages, including the capability of providing a wider range of frequency and waveform characteristics, higher conversion efficiency, simpler structure, no electromagnetic radiation, and lower cost [126]. Therefore, piezoelectric UT has been widely used in various ultrasonic applications nowadays.

While there are several possible choices of structure, Langevin’s design has been the most popular structure [127, 128], which normally consists of a few disks of piezoelectric ceramics sandwiched between electrodes and clamped with a bolt. The geometrical dimensions of the piezoelectric ceramic disks and electrodes have to be specifically engineered according to the vibration modes, e.g., longitudinal/axial mode, radial mode, bending mode and torsional mode, and adjusted (sometimes can be auto-adjusted if a feedback loop is provided) according to the frequency constant so that the UT can be operated at the resonant frequency [129]. By operating at the resonant frequency, mechanical strain is amplified, leading to a higher vibration velocity, which corresponds to a higher acoustic wave amplitude [130].

Definition of high-power

In terms of working power, the UT can be ambiguously classified into two categories, i.e., high-intensity and low-intensity applications, which are operated at low and high frequencies, respectively [131]. By taking the example of ultrasonic cleaning application, it is evident that the lower the operating frequency, the longer are the rarefaction phases, thus cavitation bubble could be formed easier while higher intensity could be achieved [132]. The limit between low- and high-intensity is very difficult to be defined, but it can be approximately established depending on the medium, which varies between 0.1 and 1 W/cm2 [133]. Low-intensity UT has been used for exploration and detection, e.g., ultrasonic imaging for medical engineering, radar sensor for automotive. UT with higher frequencies produces higher resolution image. The frequencies are very high, typically in the megahertz and higher ranges. In contrast, the operating frequency of a high-intensity UT ranges from 20 to 100 kHz. The purpose of generating high-intensity acoustic waves is to create non-linear effects, such as wave distortion, acoustic saturation, radiation pressure, streaming, cavitation in liquids, or dislocations in solids [134]. The effects would result in a few important mechanisms, including heat generation, mechanical rupture, agitate, and chemical reaction, which can be manipulated for different applications.

High-power ultrasonic applications

The high-power UT has been widely utilized in manufacturing (welding, metal forming, machining, cleaning), food industry and pharmaceutical engineering (defoaming, drying, extraction), environmental engineering (air cleaning, sludge filtration) and medical engineering (HIFU therapy, ultrasonic surgical and cutting) [3, 135, 136]. In the following paragraphs, we will briefly introduce a few typical high-power UT applications. Unfortunately, most of them are still based on PZT materials, as the adoption of lead-free materials has just begun. Nevertheless, it is critical for materials scientist to understand how these applications work. Hopefully, more lead-free materials can be adopted into these applications for trial, from the experimental perspective.

Ultrasonic cleaning

Ultrasonic cleaning is a typical high-power UT application, which can remove contaminants on the surface of a subject immersed in liquid using high-intensity acoustic waves. The high-intensity acoustic wave was used to create cavitation bubbles for agitating the liquid, in which the bursting force of bubbles on the surface of an object could remove the contaminant efficiently. Meanwhile, the acoustic streaming generated by the acoustic waves can reduce the thickness of the hydrodynamic boundary layer on the immersed surface. Tiny particles on the surface would become more exposed to liquid streaming, which helps overcome the adhesion force between particles and surfaces [137]. Besides, it can reach blind holes, crevices, and recesses that are not easily accessible using conventional cleaning methods.

In 2009, Tou et al. developed one of the earliest lead-free piezoelectric ceramic transducers for ultrasonic cleaner [138]. A bolt-clamped Langevin-type transducers (BLT) was fabricated with the composition of (Bi0.5Na0.5)TiO3–BaTiO3–(Bi0.5Na0.5)(Mn1/3Nb2/3)O3. The lead-free ceramic was found exhibiting superior vibration velocity to that of the PZT under the identical input power. When the input voltage is increased to 25 W, the vibration velocity of lead-free BLT and hard BLT with the same frequency of 28 kHz is about 1.2 and 0.8 m/s, respectively. This indicates that the power loss in lead-free BLT is smaller than that of hard BLT. As a result, the agitation intensity of lead-free BLT is higher than that of hard BLT, as shown in Fig. 6c. As aforementioned, the efficiency of high-power applications strongly depends on the intensity. Therefore, better cleaning efficiency was achieved in the lead-free ceramic. According to the research, the Qm of lead-free ceramic was found to be highly stable against increasing vibration velocity, compared to that of PZT. The work did not only confirm the value of lead-free ceramics but also pointed out an important scientific issue, i.e., the conventional PZT ceramics materials can no longer fulfill the high-power application if a higher intensity is required.

Figure 6
figure 6

(reproduced from Ref. [138] with permission from Copyright 2009 The Japan Society of Applied Physics).

(a) The internal structure of Langevin-type transducer,139 (reproduced from Ref. [139] with permission from Copyright 2012 Elsevier), (b) Schematic view of the poling direction, clamping force direction, vibration direction, and the generation of acoustic wave, and (c) Comparison of the performance of lead-based and lead-free ceramics in the application of ultrasonic cleaner [138]

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High-intensity focused ultrasound

As an advanced medical technology, high-intensity focused ultrasound (HIFU) has been increasingly implemented in clinical practices for medical therapy. It is a non-invasive treatment technique that enables rapid heating inside tissues, causing cell death by thermal necrosis within the focal volume while leaving tissue elsewhere in the propagation path unaffected. The HIFU transducer is placed either outside the body or in the rectum, excited sinusoidally by a single frequency, f0, resulting in a monochromatic wave (Fig. 7b). When the wave propagates in a non-linear medium, the waveform becomes gradually shocked, resulting in the leakage of energy from the fundamental frequency into higher harmonics. At the higher harmonics, energy is readily absorbed and converted into heat (Fig. 7c). Finally, as the inertial cavitation occurs, the collapsed microbubbles convert part of the incident energy into broadband noise emissions, which absorbed and converted into heat rapidly (Fig. 7d). The temperature of the target tissue would be raised above 55 °C and maintained for 1 s or longer. Figure 7a shows the axial pressure distribution of HIFU transducer, the large peak defines the focal region where thermal damage occur [140].

Figure 7
figure 7

(reproduced from Ref. [140] with permission from Copyright 2007 Taylor & Francis).

(a) The axial pressure distribution of HIFU transducer, and (b-d) The frequency-content of the HIFU wave [140]

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HIFU devices are divided into extracorporeal and transrectal in approach. Extracorporeal devices have a longer focal length, so the transducers are larger, which operate at higher intensities and lower frequencies. HIFU operates at a frequency different from that of other high-power applications, usually operating at a frequency of megahertz as required for deep axial penetration of the body [141]. For example, an extracorporeal device was designed with a 12 cm diameter PZT transducer and a focal length of 9 to 16 cm. It operates at frequencies from 0.8 to 3.2 MHz and intensities up to 20,000 W/cm2 [142]. A transrectal device used to treat the prostate was built by 4 MHz PZT transducer of focal length 3.0 or 3.5 cm and the intensity at the focus is 1680 W/cm2 [143]. However, current clinical devices are still not optimal, long treatment time is one of the limitations of HIFU therapy. For example, it takes about 1 h to treat a superficial 2 cm tumor, which is longer than other minimally invasive techniques such as radiofrequency ablation [144]. Studies have shown that reducing the total number of pulses can effectively shorten the treatment time. This can be done by increasing the acoustic power and/or sonication time [145].

At present, PZT piezoelectric ceramics and 1-3 composites are the main material of high-power piezoelectric UT [146, 147]. Piezoelectric/polymer composites with 1-3 connectivity offer several advantages over monolithic piezoceramics, including high electromechanical coupling and low acoustic impedance [148, 149]. The high-power characteristics of 1-3 composites were dominated by the low elastic loss and Young’s modulus of passive polymer phase. The FOM of high-power applications is the product of k and Qm, while high k allows for increased transducer bandwidth, and high Qm reduces heat generation under high drive conditions. There are also many works about lead-free high-power UT [40, 150]. The variation of the maximum dynamic strain of BNT- and PZT-based composites with the drive field at 10% duty cycle was studied. The BNT-based composites exhibited lower dynamic strain for a given drive field due to their lower small-signal values of k·Qm. However, compared with PZT-, BNT-based composites produce higher dynamic strain under higher field drive with an isothermal temperature of 50 °C. This result indicates that the high-power performance of composites is not only related to the FOM k·Qm, but also the high-power stability of ceramics (stability of the Qm and high coercive field). In conclusion, in addition to the ultrasonic cleaning and HIFU mentioned above, lead-free piezoelectric materials are also promising candidates to many high-power applications including ultrasonic transducers for welding, ultrasonic motors and piezoelectric transformers [151,152,153,154]. Despite a wealth of researches in the field of lead-free piezoelectric ceramics, its high-power application is still in its infancy. With the further research, it seems that lead-free piezoelectric ceramics will have a great deal of high-power applications in the future.

Conclusions

This paper gives an overall review of the studies on the hardening effect in lead-free piezoelectric ceramics. Theoretically, dielectric loss, mechanical loss, and piezoelectric loss are the three major factors causing undesirable energy dissipation and resultant performance degradation of materials and devices, accompanied by a critical limitation of their practical use. Hardening effect is believed to contribute for improving the high-power performance of piezoelectric ceramics. By hardening modification, BNT-based, KNN-based as well as BT-based ceramics generally exhibit enhanced high-power piezoelectric characteristics, making them promising to replace lead-containing piezoelectric ceramics. To date, several specific techniques are developed for high-power characterization. Among them, the transient method currently draws increasing attention as it can avoid the effect of temperature rise. Finally, we reveal the versatility of ultrasonic transducers in high-power applications. Many prototype devices have been found to have comparable or even superior performances to PZT-based piezoelectric devices. Of course, there may be still a long way for lead-free piezoelectric devices to be used in practical high-power applications. Nevertheless, all these developments, in terms of theory and technology, will boost the confidence of both science and industry, subsequently leading to more investment into the development of lead-free high-power applications. We strongly believe that more progress in the extension of lead-free piezoelectric products in high-power applications will be witnessed in the next few years.