Effect of Ba content on the stress-sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb,La,Ba,)(Zr,Sn,Ti)O3 ceramics

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1 Materials Science and Engineering Publications Materials Science and Engineering 2014 Effect of Ba content on the stress-sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb,La,Ba,)(Zr,Sn,Ti)O3 ceramics Yonghao Xu Iowa State University Hanzheng Guo Iowa State University Xiaoming Liu Iowa State University, Yujun Feng Xi'an Jiaotong University Xiaoli Tan Iowa Follow State this University, and additional works at: Part of the Ceramic Materials Commons, Electro-Mechanical Systems Commons, and the Other Chemical Engineering Commons The complete bibliographic information for this item can be found at mse_pubs/180. For information on how to cite this item, please visit howtocite.html. This Article is brought to you for free and open access by the Materials Science and Engineering at Iowa State University Digital Repository. It has been accepted for inclusion in Materials Science and Engineering Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact

2 Effect of Ba content on the stress-sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb,La,Ba,)(Zr,Sn,Ti)O3 ceramics Abstract The effect of Ba content on the stress sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb 0.94 x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics is investigated through monitoring electric fieldinduced polarization and longitudinal strain under compressive prestresses. It is found that incorporation of Ba significantly suppresses the stress sensitivity of the phase transition, as manifested by slight decreases under prestresses up to 100 MPa in the maximum polarization (P m ) and longitudinal strain (x m ). The energy storage density is even increased under the mechanical confinement in compositions x = 0.02 and X-ray diffraction, transmission electron microscopy, and dielectric measurements indicate that the suppressed stress sensitivity is associated with the disruption of micrometersized antiferroelectric domains into nanodomains and the transition from antiferroelectric to relaxor behavior. Keywords Antiferroelectric ceramics, phase transition, pre-stress, relaxor antiferroelectrics Disciplines Ceramic Materials Electro-Mechanical Systems Other Chemical Engineering Comments This is the accepted version of the following article: Journal of the American Ceramic Society 97, (2014). DOI: /jace.12585, which has been published in final form at doi/ /jace.12585/full. This article is available at Iowa State University Digital Repository:

3 This is the accepted version of the following article: Journal of the American Ceramic Society 97, (2014). DOI: /jace.12585, which has been published in final form at Journal of the American Ceramic Society 97, (2014). DOI: /jace Effect of Ba content on the stress-sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb,La,Ba,)(Zr,Sn,Ti)O 3 ceramics Yonghao Xu,, Hanzheng Guo, Xiaoming Liu, Yujun Feng, and Xiaoli Tan,, * Electronic Materials Research Laboratory, Xi'an Jiaotong University, Xi'an , China Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, USA This work was supported by the National Natural Science Foundation of China under Grant No. U and the National Science Foundation (NSF) of USA through Grant CMMI YHX acknowledges the financial support from the China Scholarship Council. Member, the American Ceramic Society. *Author to whom correspondence should be addressed. Electronic mail: xtan@iastate.edu 1

4 Abstract The effect of Ba content on the stress-sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics is investigated through monitoring electric field-induced polarization and longitudinal strain under compressive pre-stresses. It is found that incorporation of Ba significantly suppresses the stress-sensitivity of the phase transition, as manifested by slight decreases under pre-stresses up to 100 MPa in the maximum polarization (P m ) and longitudinal strain (x m ). The energy storage density is even increased under the mechanical confinement in compositions x = 0.02 and X-ray diffraction, transmission electron microscopy, and dielectric measurements indicate that the suppressed stress-sensitivity is associated with the disruption of micron-sized antiferroelectric domains into nanodomains and the transition from antiferroelectric to relaxor behavior. Keywords: Antiferroelectric ceramics, phase transition, pre-stress, relaxor antiferroelectrics 2

5 I. Introduction Antiferroelectric ceramics can be transformed into a ferroelectric phase with the application of an electric field; this transition is accompanied by an expansion in both longitudinal and transverse directions, making them promising in applications of actuators and transducers. 1,2 PbZrO 3 was the first reported antiferroelectric compound. 3 However, the large free energy difference between its ferroelectric phase and ground-state antiferroelectric phase prevents the electric field-induced phase transition from occurring at room temperature. For device applications, the critical electric field (E F ) should be reduced to a proper level, and the transition field hysteresis ( E, the difference between E F and the reverse transition field E A ) should be minimized to avoid heat generation. Chemical modifications of PbZrO 3 with Sn, Ti, Nb as well as La were found to be effective in reducing E F for the antiferroelectric to ferroelectric phase transition. 4-7 A particularly interesting chemical modifier is Ba. It was found that incorporating Ba to the A-site of the ABO 3 perovskite structure not only reduced E F, but also suppressed the transition field hysteresis. 8 In addition, Ba makes the antiferroelectric-paraelectric transition diffuse and shifts the transition temperature down. 8 In real transducers and actuators, the active ceramic is subject to combined pre-stresses and electrical loadings. Therefore, knowledge of how the pre-stress influences the functional properties of the active ceramic becomes essential. Recently, the compressive pre-stress dependence of dielectric and ferroelectric properties has been studied in many piezoelectric oxides including Pb(Zr,Ti)O 3, 9 (Pb,La)(Zr,Ti)O 3, 10 Pb(Mg 1/3 Nb 2/3 )O 3 PbTiO 3, 11,12 and Pb(Mg 1/3 Nb 2/3 )O 3 Pb(Zr,Ti)O These investigations reveal that the superimposed uniaxial 3

6 compressive pre-stress reduces the remnant polarization, decreases the dielectric constant, and impacts the piezoelectric properties. The changes are attributed to the suppressed domain wall motion and reduced non-180 o ferroelectric domain switching activities under the mechanical confinement. In contrast, research on the effect of pre-stresses on the antiferroelectric to ferroelectric phase transition is very limited. It was generally observed that both E F and E A in antiferroelectric ceramics were shifted to higher levels by uniaxial compressive pre-stresses. 1,14-16 Meanwhile, the electric field-induced strain showed different tendencies under different compressive pre-stress levels. 2,15,16 Ferroelasticity due to non-180 o domains and volume expansion at the transition are rendered to the interpretation of the observed stress effects. In the present study, the stress-sensitivity of the antiferroelectric to ferroelectric phase transition is investigated in (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 (PLBZST) ceramics with different Ba contents. The electric field-induced polarization and longitudinal strain were monitored under a series of uniaxial compressive pre-stresses up to 100 MPa. The microstructure and dielectric behavior of these ceramics were analyzed in order to explain the suppressed stress-sensitivity. II. Experimental Procedure Polycrystalline ceramics with a formula (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 (x = 0.00, 0.02, 0.04, and 0.06) were prepared using the solid-state reaction method. To compensate lead loss during high temperature processing, an excess 2 wt.% PbO was included. The mixed powders were ball milled with ZrO 2 media for 5 h, and the dried mixture was calcined at 850 o C 4

7 for 2 h. Sintering was carried out at 1320 o C for 3h in a lead-rich atmosphere. The surface of each as-sintered pellet was examined with scanning electron microscopy (SEM, Hitachi S2460-N VP-SEM). After the surface layer of each pellet was removed by grinding, the phase purity and crystal structure of the samples were analyzed with X-ray diffraction using Cu Kα radiation in the 2θ range from 20 o to 60 o. Specimens for transmission electron microscopy (TEM) were prepared via standard procedures including grinding, cutting, dimpling, and ion milling. The dimpled disks were annealed at 200 o C for 2 h to minimize the residual stresses introduced during mechanical thinning. Then the disks were thinned with an Ar-ion mill until a perforation was formed. TEM studies were carried out on a Phillips CM-30 microscope operated at 200 kv. The relative dielectric permittivity (ε r ) was measured with an LCR meter (HP-4284A, Hewlett-Packard) at frequencies of 1 khz, 10 khz, 100 khz, and 1 MHz during heating at a rate of 4 o C/min. For experiments under uniaxial compressive pre-stresses, cuboids 6 mm in length and width and 2 mm in thickness were prepared with silver electrodes. The sharp edges and corners of the specimen were carefully rounded to prevent stress concentration and cracking during pre-stress loading. Great care was taken to ensure the two major faces were parallel. A homebuilt test fixture was used to investigate the responses of the ceramics to applied electric fields under pre-stresses. 15,16 Electric fields in a sinusoidal waveform at 0.05 Hz with a peak level of 30 kv/cm were supplied by a Trek-model 610D high-voltage amplifier. A computerized instrument (TF analyzer 2000, aixacct, Aachen, Germany) was used to record the polarization (P) vs. electric field (E) hysteresis loops at room temperature. The longitudinal strains that developed 5

8 under the applied electric fields were measured with a MTI-2000 fotonic sensor (MTI Instruments Inc., Albany, NY). Specimens were submerged in silicone oil during the tests. The data presented here were recorded after 10 cycles of electric field application to the specimens at each pre-stress level. III. Results and Discussion Figure 1 shows the SEM micrographs of the as-sintered surfaces of PLBZST ceramics with various Ba contents. It can be seen that all the ceramics have equiaxial grains and are very dense. The average grain size, determined with the linear intercept method, for compositions x = 0.00, 0.04, and 0.06 is 2.5 μm while that for x = 0.02 is 3.4 μm. X-ray diffraction spectra of the sintered PLBZST ceramics are displayed in Fig. 2. A single perovskite phase is confirmed. For the base composition (Pb 0.94 La 0.04 )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3, a tetragonal distortion is revealed by the splitting of the (200) and (002) peaks. As shown in Fig. 2(b), the tetragonal distortion is gradually weakened with increasing Ba content. Eventually at the composition x = 0.06 becomes cubic and does not display any tetragonal distortion. The trend of the lattice distortion with changing Ba content is consistent with previous studies in similar compositions. 17 The evolution of the crystal structure is accompanied with changes in domain morphology, as revealed by TEM analysis. The base composition (x = 0.00) with the tetragonal perovskite structure displays hierarchical microstructural features, as illustrated in Fig. 3(a) and 3(b) with a representative grain along its [001] zone-axis. At low magnifications, the characteristic 6

9 checkerboard patterns of antiferroelectric domains are found in most parts of the grain. Close up examination at higher magnifications reveals two sets of incommensurate modulation stripes along orthogonal {110} planes (Fig.3 (b)). Selected area electron diffraction along the [001] zone axis shows the corresponding two sets of satellite spots surrounding fundamental reflections (inset in Fig.3 (b)). According to previous studies, 1,6 the checkerboard pattern consists of 90 o antiferroelectric domains while the modulation stripes are in fact 180 o domain slabs. Corresponding to the cubic perovskite structure revealed by X-ray diffraction, the composition of x = 0.06 displays nanodomains, see Fig. 3(c) and (d). Apparently the addition of Ba disrupts both the large 90 o antiferroelectric domains and the incommensurate modulation stripes. At higher magnifications (Fig. 3(d)), remnants of the thin 180 o domain slabs is still seen in clusters, as indicated by the bright triangles. The disruption of the modulation is also verified by the absence of satellite diffraction spots in the [001] zone axis diffraction pattern (inset in Fig. 3(d)). Therefore, Ba modification is found to suppress the long-range antiferroelectric order by breaking apart the micron-sized antiferroelectric domain into an ensemble of nanodomains. The temperature dependence of the relative dielectric permittivity (ε r ) and loss tangent (tan ) of PLBZST ceramics at different frequencies are plotted in Fig. 4. When the concentration of Ba increases from 0.00 to 0.06, the temperature at the dielectric maximum (T m ) at 1 khz decreases from 124 o C to 56 o C, and the dielectric constant at T m increases from 2082 to Only very limited frequency dispersion is observed in the dielectric response below T m in the base composition x = Ba addition gradually enhances the frequency dispersion and eventually a typical relaxor behavior is developed in x = It is interesting to note that both dielectric 7

10 constant and loss tangent above T m in the paraelectric regime do not change much upon Ba addition. However, tan at room temperature slightly increases with Ba content. The enhanced relaxor behavior may be caused by mixed cations with distinct sizes and charges sharing the same lattice sites in the ABO 3 perovskite structure. 18 The radius of Ba 2+ is bigger than that of Pb 2+, so adding Ba generates local random stress fields. In addition, the tolerance factor is also expected to increase with Ba content. This in turn will destabilize the antiferroelectric order. 8 The results in Figs. 2, 3, and 4 from complimentary measurements consistently show that Ba addition disrupts the long range antiferroelectric order and introduces a short range relaxor behavior. The observed phenomena are quite similar to the addition of La to an antiferroelectric Pb(Zr,Ti)O 3. 19,20 The competing and coexisting antiferroelectric and relaxor behaviors were also noticed in (Bi 1/2 Na 1/2 )TiO 3 -based lead-free compositions, and the term relaxor antiferroelctric was suggested to describe these ceramics The electric field-induced antiferroelectric to ferroelectric phase transition at zero pre-stress in PLBZST ceramics is revealed by the P vs. E hysteresis loops and the longitudinal strain x 33 vs. E loops shown in Fig. 5. Typical double-loops of antiferroelectric ceramics are observed. It is evident that the critical field (E F ), and the transition field hysteresis ( E) both decrease with increasing Ba content. Large strains (x 33 approaching 10-3 ) are achieved in Ba doped compositions at very low electric fields, which makes these ceramics excellent candidates for actuator devices. The effect of Ba addition on the stress-sensitivity of the antiferroelectric to ferroelectric phase transition in PLBZST ceramic is shown in Fig. 6. It is noticed that compared to the Ba 8

11 doped compositions, the base composition x = 0.00 is very sensitive to the uniaxial compressive pre-stress. Significant suppression of the hysteresis loops is observed at high compressive pre-stresses. The data displayed in Fig. 6 are further quantitatively analyzed to reveal the impact of the pre-stress, as displayed in Figs. 7, 8, and 9. As shown in Fig. 7, the critical electric field (E F ) for the antiferroelectric to ferroelectric phase transition increases with the compressive pre-stress in all the tested ceramics. However, the transition field hysteresis ( E) hardly changes with the pre-stress. The changes in the maximum polarization (P m ) and the maximum longitudinal strain (x m ) under pre-stress in the ceramics with different Ba contents are compared in Fig. 8. For the base composition x = 0.00, the reduction in P m is about 52.3% when the pre-stress increases from 0 to 100 MPa. In contrast, the reduction in P m is 23.3% and 17.3% for x = 0.02 and 0.04, respectively. The decrease in P m indicates that a smaller portion of the antiferroelectric phase is transformed to the ferroelectric phase under applied pre-stresses. In addition, when the uniaxial compressive pre-stress is applied in the direction of the electric field, the antiferroelectric domains tend to align their polar axes away from the stress direction through ferroelastic switching. 24 In the ferroelectric phase after the phase transition, the compressive pre-stress also prevents the polarization alignment, resulting in a reduced P m. Ba modification reduces the domain size and makes the pre-stress less effective in preventing the domain polarization alignment. In addition, the critical field E F is decreased in Ba doped compositions. As a result, P m in x = 0.02 and 0.04 is less sensitive to the presence of compressive pre-stresses. 9

12 The impact of pre-stress on the maximum longitudinal strain (x m ) is slightly different (Fig. 8(b)). For compositions x = 0.02 and 0.04, x m initially increases with increasing pre-stress, reaching a maximum at about 25MPa, and then gradually decreases at a slow rate upon further increase in pre-stress. A similar trend was observed before. 2,16 In contrast, x m for the base composition x = 0.00 is quite stable up to 40 MPa, abruptly decreases at 50 and 60 MPa, and then gradually decreases at higher pre-stresses. To understand the change of x m under pre-stress, the sources contributing to the change have to be clear. Considering the combined mechanical and electrical loading configurations, x m is a reflection of the following activities: the volume expansion at the electric field-induced phase transition, the linear elastic deformation under the compressive pre-stress in the antiferroelectric and ferroelectric phases, the ferroelastic deformation due to non-180 o domain switching in the antiferroelectric and ferroelectric phases, and the electrostrictive as well as the piezoelectric deformation under electric field. The addition of Ba disrupts large ferroelastic antiferroelectric domains, reduces the lattice distortion, and promotes the relaxor behavior, thus, Ba suppresses the ferroelastic contribution and boosts the electrostrictive portion in x m. Presumably, the ferroelastic strain is more sensitive to the pre-stress than the electrostrictive strain. As a result, Ba addition suppresses the sensitivity of x m to the mechanical confinement in PLBZST ceramics. Antiferroelectric ceramics are known for their high energy density for capacitor applications. 1 Energy storage density is calculated by integrating the discharge curve against the polarization axis in the first quadrant and stands for the usable energy. Efficiency is defined as the ratio of the released energy to the energy charged to the capacitor. 25 From the hysteresis 10

13 loops data measured at the peak field of 30 kv/cm, energy storage density and efficiency are calculated and shown in Fig. 9. For the base composition x = 0.00, the energy storage density increases slightly at lower stresses and then decreases considerably beyond 20 MPa. For x = 0.02, the maximum energy storage density is found at 70 MPa (a 14.8% increase). Further increase in pre-stress leads to a decrease in energy storage density. In contrast, the energy storage density in x = 0.04 shows a monotonic increase with pre-stress up to 100 MPa. It should be noted that the high energy density observed in antiferroelectric ceramics is resulted from the reversible antiferroelectric-ferroelectric phase transition. 1,25 Compressive pre-stresses act against the transition and push it to occur at higher applied electric fields (Fig. 6). For the base composition x = 0.00 under zero pre-stress, the critical electric field (E F ) is slightly below the applied peak field. When compressive stresses beyond 20 MPa are applied and E F shifts to higher levels, the applied peak field of 30 kv/cm becomes insufficient to trigger a complete phase transition. As a consequence, the energy storage density decreases dramatically beyond 20MPa. In contrast, E F is significantly reduced in compositions x = 0.02 and x = 0.04 (Fig. 5) because of the formation of nanodomains and reduced tetragonality. The same applied peak field (30 kv/cm) is still capable of completing the antiferroelectric to ferroelectric phase transition even under the pre-stress of 100MPa. Therefore, the energy storage density is very stable against pre-stresses in Ba-doped compositions. Figure 9(b) shows that the efficiency is enhanced in all three ceramics by the application of pre-stresses. This is because the area within the double hysteresis loops, representing the energy dissipated during electrical cycling, is reduced under compressive pre-stresses. The higher 11

14 efficiency observed in Ba-doped compositions than the base composition at the same pre-stress level is again due to the reduction in E F because of the formation of nanodomains. IV. Conclusions The effect of Ba content on the stress-sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 antiferroelectric ceramics is investigated. The results indicate that the phase transition in Ba-doped ceramics is less affected by the uniaxial compressive pre-stress because of the development of a relaxor behavior and nanodomains. The maximum polarization and the maximum longitudinal strain become much more stable against pre-stress with Ba addition. In addition, the energy storage density even increases considerably under uniaxial mechanical confinement. The experimental results suggest that these ceramics are very promising for actuator and capacitor applications, with uncompromised performances even under strong mechanical clamping. 12

15 References: 1 X. Tan, C. Ma, J. Frederick, S. Beckman, and K.G. Webber, The antiferroelectric ferroelectric phase transition in lead-containing and lead-free perovskite ceramics, J. Am. Ceram. Soc., 94, (2011). 2 O. Essig, P. Wang, M. Hartweg, P. Jänker, H. Näfe, and F. Aldinger, Uniaxial stress and temperature dependence of field induced strains in antiferroelectric lead zirconate titanate stannate ceramics, J. Eur. Ceram. Soc., 19, (1999). 3 E. Sawaguchi, H. Maniwa, and S. Hoshino, Antiferroelectric structure of lead zirconate, Phys. Rev., 83, 1078 (1951). 4 W. Y. Pan, C. Q. Dam, Q. M. Zhang, and L. E. Cross, Large displacement transducers based on electric field forced phase transitions in the tetragonal (Pb 0.97 La 0.02 )(Ti,Zr,Sn)O 3 family of ceramics, J. Appl. Phys., 66, (1989). 5 S. E. Park, M. J. Pan, K. Markowski, S. Yoshikawa, and L. E. Cross, Electric field induced phase transition of antiferroelectric lead lanthanum zirconate titanate stannate ceramics, J. Appl. Phys., 82, (1997). 6 H. He and X. Tan, Electric field-induced transformation of incommensurate modulations in antiferroelectric Pb 0.99 Nb 0.02 [(Zr 1-x Sn x ) 1-y Ti y ] 0.98 O 3, Phys. Rev. B, 72, (2005). 7 K. Markowski, S. E. Park, S. Yoshikawa, and L. E. Cross, Effect of compositional variations in the lead lanthanum zirconate stannate titanate system on electrical properties, J. Am. Ceram. Soc., 79, (1996). 8 S. E. Park, K. Markowski, S. Yoshikawa, and L. E. Cross, Effect on electrical properties of barium and strontium additions in the lead lanthanum zirconate stannate titanate system, J. Am. Ceram. Soc., 80, (1997). 9 R. Yimnirun, Y. Laosiritaworn, and S. Wongsaenmai, Effect of uniaxial compressive pre-stress on ferroelectric properties of soft PZT ceramics, J. Phys. D: Appl. Phys, 39, (2006). 10 A. P. Barranco and D. A. Hall, Influence of composition and pressure on the electric field-induced antiferroelectric to ferroelectric phase transformation in lanthanum modified lead zirconate titanate ceramics, IEEE T. Ultrason. FeRR., 56, (2009). 11 M. Unruan, R. Wongmaneerung, and A. Ngamjarurojana, Changes in ferroelectric properties of ceramics in lead magnesium niobate-lead titanate system with compressive stress, J. Appl. 13

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18 Fig. 1. SEM micrographs of the as-sintered surface of (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics. (a) x = 0.00, (b) x = 0.02, (c) x = 0.04, (d) x = 0.06.

19 Fig. 2. X-ray diffraction spectra of the (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics. (a) The whole pattern is indexed based on a pseudo-tetragonal unit cell. (b) The close view of the (200)/(002) peak.

20 Fig. 3. TEM analysis of the (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics along the [001] zone axis. (a) and (b) x = 0.00, (c) and (d) x = 0.06.

21 Fig. 4. Temperature dependence of the dielectric constant ( r ) and loss tangent (tan ) of (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics measured during heating at different frequencies. (a) x = 0.00, (b) x = 0.02, (c) x = 0.04, (d) x = 0.06.

22 Fig. 5. (a) The polarization vs. electric field hysteresis loops and (b) the longitudinal strain vs. electric field curves for the (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics measured at 0.05 Hz.

23 Fig. 6. The effect of compressive pre-stresses along the longitudinal direction on the electrical polarization and longitudinal strain developed under bipolar electric fields in the (Pb 0.94-x La 0.04 Ba x )[(Zr 0.60 Sn 0.40 ) 0.84 Ti 0.16 ]O 3 ceramics. (a) and (b) x = 0.00, (c) and (d) x = 0.02, (e) and (f) x = 0.04.

24 Fig. 7. Changes in the critical field (E F ) and the transition field hysteresis ( E) with the compressive pre-stress.

25 Fig. 8. Changes in the (a) maximum polarization (P m ) and (b) maximum longitudinal strain (x m ) with the compressive pre-stress.

26 Fig. 9. Changes in the (a) energy density and (b) efficiency with the compressive pre-stress.