The Antiferroelectric Ferroelectric Phase Transition in Lead-Containing and Lead-Free Perovskite Ceramics

Transcription

1 Materials Science and Engineering Publications Materials Science and Engineering 2011 The Antiferroelectric Ferroelectric Phase Transition in Lead-Containing and Lead-Free Perovskite Ceramics Xiaoli Tan Iowa State University, Cheng Ma Iowa State University Joshua Frederick Iowa State University Sarah Beckman Iowa State University Kyle G. Webber Follow this and additional works at: Technische Universitat Darmstadt Part of the Ceramic Materials Commons, Electromagnetics and Photonics Commons, and the Metallurgy Commons The complete bibliographic information for this item can be found at mse_pubs/190. 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 The Antiferroelectric Ferroelectric Phase Transition in Lead- Containing and Lead-Free Perovskite Ceramics Abstract A comprehensive review on the latest development of the antiferroelectric ferroelectric phase transition is presented. The abrupt volume expansion and sudden development of polarization at the phase transition has been extensively investigated in PbZrO 3 -based perovskite ceramics. New research developments in these compositions, including the incommensurate domain structure, the auxetic behavior under electric fields in the induced ferroelectric phase, the ferroelastic behavior of the multicell cubic phase, the impact of radial compression, the unexpected electric field-induced ferroelectric-to-antiferroelectric transition, and the phase transition mechanical toughening effect have been summarized. Due to their significance to lead-free piezoelectric ceramics, compounds with antiferroelectric phases, including NaNbO 3, AgNbO 3, and (Bi 1/ 2Na 1/2 )TiO 3, are also critically reviewed. Focus has been placed on the (Bi 1/2 Na 1/2 )TiO 3 BaTiO 3 solid solution where the electric field-induced ferroelectric phase remains even after the applied field is removed at room temperature. Therefore, the electric field-induced antiferroelectric-to-ferroelectric phase transition is a key to the poling process to develop piezoelectricity in morphotropic phase boundary (MPB) compositions. The competing phase transition and domain switching processes in 0.93(Bi 1/2 Na 1/2 )TiO BaTiO 3 are directly imaged with nanometer resolution using the unique in situ transmission electron microscopy (TEM) technique. Keywords Antiferroelectric ceramics, phase transition, domain structure, polarization and strain, ferroelastic deformation, lead-free piezoelectrics, in situ TEM Disciplines Ceramic Materials Electromagnetics and Photonics Metallurgy Comments This is the peer reviewed version of the following article: Journal of the American Ceramic Society 94, (2011). DOI: /j x. which has been published in final form at Rights This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving. This article is available at Iowa State University Digital Repository:

3 This is the peer reviewed version of the following article: Journal of the American Ceramic Society 94, (2011). DOI: / j x. which has been published in final form at This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving. The Antiferroelectric Ferroelectric Phase Transition in Lead- Containing and Lead-Free Perovskite Ceramics Xiaoli Tan*, Cheng Ma, Joshua Frederick, and Sarah Beckman Department of Materials Science and Engineering, Iowa State University, Ames, IA 50011, USA Kyle G. Webber Institute of Materials Science, Technische Universität Darmstadt, Darmstadt 64287, Germany This work was supported by the National Science Foundation (NSF) through Grants CMMI and DMR *Member, the American Ceramic Society. Author to whom correspondence should be addressed. Electronic mail: 1

4 Abstract A comprehensive review of the latest development on the antiferroelectric ferroelectric phase transition is presented. The abrupt volume expansion and sudden development of polarization at the phase transition has been extensively investigated in PbZrO3- based perovskite ceramics. New research developments in these compositions, including the incommensurate domain structure, the auxetic behavior under electric fields in the induced ferroelectric phase, the ferroelastic behavior of the multicell cubic phase, the impact of radial compression, the unexpected electric field-induced ferroelectric-to-antiferroelectric transition, and the phase transition mechanical toughening effect have been summarized. Due to their significance to lead-free piezoelectric ceramics, compounds with antiferroelectric phases, including NaNbO3, AgNbO3, and (Bi1/2Na1/2)TiO3, are also critically reviewed. Focus has been placed on the (Bi1/2Na1/2)TiO3 BaTiO3 solid solution where the electric field-induced ferroelectric phase remains even after the applied field is removed at room temperature. Therefore, the electric field-induced antiferroelectric-to-ferroelectric phase transition is key to the poling process to develop piezoelectricity in morphotropic phase boundary (MPB) compositions. The competing phase transition and domain switching processes in 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3 are directly imaged with nanometer resolution using the unique in situ transmission electron microscopy (TEM) technique. Keywords: Antiferroelectric ceramics, phase transition, domain structure, polarization and strain, ferroelastic deformation, lead-free piezoelectrics, in situ TEM 2

5 I. Introduction The concept of antiferroelectricity was proposed by Kittel in It describes a state where chains of ions in the crystal are spontaneously polarized, but with neighboring chains polarized in antiparallel directions. As a result, the crystal does not display spontaneous macroscopic polarization or the piezoelectric effect. PbZrO3 was the first compound identified as an antiferroelectric crystal. 2,3 Later, the antiferroelectric state was observed in other perovskite compounds such as PbHfO3, 4,5 Pb(B'1/2B"1/2)O3, 6,7 (Bi1/2Na1/2)TiO3, 8,9 NaNbO3, AgNbO3, 13 and order-disorder compounds NH4H2PO4 14 and Cu(HCOO)2 4H2O 15. About twenty years ago, the antiferroelectric concept was found applicable to describe the new phase in polymeric liquid crystals. 16 In the antiferroelectric phase of these crystals, the antiparallel dipoles originate from the cation displacements in perovskite compounds, 2 the ordering of H + in order-disorder transition compounds, 17 and the opposite tilting of rod-like polar molecules in neighboring layers in smectic liquid crystals 18,19. When an antiferroelectric crystal is subjected to electric fields, the antiparallel dipoles can be flipped and forced to be parallel, corresponding to an electric field-induced antiferroelectric-to-ferroelectric phase transition. 1,20 This phase transition manifests itself by the signature double-hysteresis loops as the electric polarization P is monitored as a function of applied field E. 3 In addition to the abrupt change in polarization, significant changes in other quantities, such as linear dimensions and optical properties 16, also accompany the phase transition. These changes at the phase transition provide the physics foundation for important engineering applications of antiferroelectric materials in digital displacement transducers, energy storage capacitors, 27 electrocaloric cooling devices, and flat panel displays 18,19. For most device applications, antiferroelectric materials in the thin film form are required. As a result, films with various antiferroelectric compositions have been deposited and characterized Because of the importance of antiferroelectric crystals to engineering applications, comprehensive reviews have been made on inorganic compounds 6,7,36 as well as liquid crystals 18,19. The present work will first review the recent research findings on bulk ceramics of PbZrO3-based antiferroelectric oxides. Then the results in the literature on lead-free 3

6 antiferroelectric perovskites will be summarized and compared with lead-containing compounds. Focus will be placed on (Bi1/2Na1/2)TiO3, NaNbO3, and AgNbO3 since they are the most commonly used end members for lead-free piezoelectric solid solutions Most importantly, recent measurements suggest that the electric field-induced antiferroelectric-to-ferroelectric phase transition plays a decisive role in the poling process and the resulting piezoelectric properties in (Bi1/2Na1/2)TiO3-based compositions With the electric field in situ transmission electron microscopy (TEM) technique, 43 the latest results on the evolution of domain morphology and crystal structure during this phase transition will be presented. II. Lead-Containing Antiferrolectric Perovskite Oxides (1) Materials and microstructures Before the discovery of its antiferroelectric behavior, PbZrO3 was initially determined to be a perovskite with tetragonal distortions at room temperature. 44 With the knowledge of the antiferroelectric order, Sawaguchi et al. 2 used X-ray analysis and optical polar microscopy of single crystal PbZrO3 to determine that the crystal structure was orthorhombic. The unit cell was found to contain eight formula units and the centrosymmetric space group Pbam was suggested. 2 Later in 1957, Jona et al. 45 published X-ray and neutron diffraction data of single crystal PbZrO3 and confirmed orthorhombic distortions but assigned the non-centrosymmetric space group Pba2. The space group Pbam was reclaimed in 1993 by Glazer et al. with lattice parameters a = Å, b = Å, and c = Å at 24 C. 46 Although historically there has been dispute on the superstructure of the PbZrO3 crystal and the assignment of a space group, all the reports are consistent on the unit cell parameters and the Pb 2+ cation displacement. With respect to the pseudocubic perovskite primitive unit cell that contains one PbZrO3 molecule with lattice parameter ac, the dimensions of the orthorhombic cell are 4 a 2ac, b 2 2ac, c 2ac primary structural feature that accounts for the antiferroelectricity is the antiparallel. The displacements of Pb 2+ along the pseudocubic <110> direction, as schematically shown in Fig. 1(a). At room temperature, the average displacement of Pb 2+ is ~0.25 Å. 2,45,46 Early researchers were puzzled by the fact that the electric field-induced antiferroelectricto-ferroelectric phase transition was not observed in PbZrO3 polycrystalline ceramics at room

7 temperature. The signature double P ~ E loop can only be recorded at temperatures slightly below the Curie point, which was measured to be 233 C. 3,47 A linear extrapolation of the critical electric field necessary to induce the ferroelectric phase (EF) to 25 C indicates that an electric field of ~360 kv/cm is needed to trigger the antiferroelectric-to-ferroelectric transition. This value exceeds the breakdown strength of conventionally sintered PbZrO3 ceramics and hence the sample exhibits dielectric breakdown instead of phase transition at room temperature. With highquality PbZrO3 single crystals, Fesenko et al. 48 were able to systematically investigate the complex phase transitions with optical microscopy under electric fields up to 1400 kv/cm in the temperature range of -170 ~ 160 C. At 25 C, a transition from the antiferroelectric orthorhombic to a ferroelectric orthorhombic phase was detected at ~220 kv/cm. Further increase in the electric field was observed to trigger two ferroelectric-to-ferroelectric transitions: orthorhombic to rhombohedral at ~330 kv/cm and rhombohedral to rhombohedral at ~400 kv/cm. Also with high quality PbZrO3 single crystals, Xu et al. 49 discovered a ferroelectric rhombohedral phase characterized by micrometer-sized domains and strong 110 c diffraction spots within a narrow temperature range around 220 C. 1 2 superlattice To utilize the antiferroelectric-to-ferroelectric transition in polycrystalline PbZrO3 ceramics for engineering devices, the critical electric field EF has to be reduced and other properties need to be optimized. The most effective way to achieve this is through chemical modification with Sn, Ti, and Nb or La ,36,50-65 As expected, the change in properties traces its origins to the change in microstructures. Micrometer-sized antiferroelectric 60, 90, as well as 180 domains are typical subgrain features in undoped PbZrO3. 66,67 In chemically modified PbZrO3 ceramics, the room temperature antiferroelectric phase takes a tetragonal symmetry. 21,36 Furthermore, a checkerboard pattern formed by 90 antiferroelectric domains becomes dominant and incommensurate modulations are observed within each 90 domain Under TEM, these modulations manifest themselves as fine fringes with a wavelength around 2 nm in diffraction- 1 contrast images and c n 110 satellite diffraction spots in selected area electron diffraction patterns, where n is a non-integer. The value of n seems to be in the range between 6 and 15 for PbZrO3-based antiferroelectrics In our previous work, 60 we proposed a structural model for 5

8 the incommensurate modulation. We suggested that the observed incommensurate modulation is actually an average effect over an ensemble of stripes of commensurate modulations, as schematically shown in Fig. 1(b). In this illustration, the periodicity of the incommensurate modulation lies somewhere between 7 and 8 pseudocubic {110}c planes. Such an incommensurate modulation is composed of stripes of periodicities of n = 7 and 8, which are commensurate to the underlying lattice. In the electron diffraction pattern, the satellite spots appear to be incommensurate due to an average effect. In contrast, undoped PbZrO3 consists of stripes of the commensurate modulation of Pb 2+ displacements with periodicity of 4 pseudocubic {110}c planes [Fig. 1(a)]. 2 Obviously, these stripes can be considered as 180 ferroelectric domains. Therefore, adding chemical dopants to PbZrO3 increases the thickness of the 180 ferroelectric domains (as well as the modulation wavelength and the n value). It has been suggested that the frustration from the competing long-range ferroelectric and antiferroelectric orderings is responsible for the presence of the incommensurate structure. 55 The modulation wavelength has been found to increase with temperature and Ti content in Sn- and/or Ti-modified PbZrO3 ceramics Since PbTiO3 is a compound with strong ferroelectricity, 7,36,67 increase in Ti content promotes long-range ferroelectric ordering. Compromise is then shifted toward the ferroelectric side and the thickness of 180 ferroelectric domains increases. In contrast, the wavelength (or the n value) is very stable against applied electric fields until the modulation disappears during the antiferroelectric-to-ferroeletric phase transition (Figs. 2 and 3). 58,60 It is speculated that the electric field-induced antiferroelectric-to-ferroelectric phase transition starts with the alignment of Pb 2+ displacements. The aligning process may be initiated preferentially from sites such as grain boundaries and 90 antiferroelectric domain walls. The volume with aligned cation displacement no longer contributes to the satellite spots. As this volume increases with increasing electric field, the intensity of the satellite diffraction spots decreases. At the antiferroelectric-to-ferroelectric phase transition, the antiparallel Pb 2+ displacement becomes parallel. The above description implies that the electric field-induced antiferroelectric-to-ferroelectric transition essentially takes place through the 180 ferroelectric domain polarization reversal. The relative stability between the antiferroelectric and the ferroelectric phases correlates well with the thickness of 180 ferroelectric domains. The thinner the domains are, the more stable the antiferroelectric phase is. The 180 domains in the parent 6

9 PbZrO3 have a thickness of 2 layers of the {110}c plane, which appears to be the lower limit of thickness in perovskite oxides. Accordingly, the antiferroelectric phase in PbZrO3 is stable and EF is extremely high. 47,48 In chemically modified PbZrO3 ceramics with incommensurate modulations, the stability of the ferroelectric phase is enhanced and the 180 domains are thickened to 3~8 layers of the {110}c plane. On the thick side of this range, the original configuration of the 180 domains may not be resumed upon the release of applied electric fields in antiferroelectric crystals. In this case, the induced ferroelectric phase remains even after the applied field is removed. Other ferroelectric domain configurations will become dominant and a ferroelectric phase will be stable in the virgin state when the thickness of the 180 domains is further increased. Therefore, the model in Fig. 1(b) relates the antiferroelectric and the ferroelectric phases through 180 ferroelectric domains. 1 In addition to the disappearance of c n response of the ooo c satellite spots, Fig. 3 also reveals the (o stands for odd Miller indices) superlattice diffraction spots to the applied electric field. These superlattice spots were observed previously in the antiferroelectric, ferroelectric, and even cubic paraelectric phases in many PbZrO3-based compositions. 51 The structural origin for these superlattice spots is the oxygen octahedron tilting in the perovskite lattice. 51,68,69 It is clear in Fig. 3 that the intensity of the ooo c antiferroelectric ceramics through characterization of dielectric constant, electric polarization, spots does not change with the applied electric field during the antiferroelectric-to-ferroelectric phase transition, implying that the oxygen octahedron tilts are not as responsive to applied fields as cation displacements. There are indications that the induced ferroelectric phase immediately after the transition is rhombohedral. 62,63 The results in Fig. 3 confirmed this and further suggest that the space group is likely to be R3c. (2) The macroscopic behavior The dielectric behavior and volume change Many macroscopic behavior studies have been performed on PbZrO3-based perovskite

10 and mechanical strain. For undoped PbZrO3, the dielectric constant displays a sharp peak at the Curie point, 233 C, marking the first order antiferroelectric-to-paraelectric transition. 3 In Snand Ti-modified ceramics, the sharp peak is truncated by an intermediate paraelectric multiple cell cubic phase. 36,51,52 The intermediate phase displays a much higher thermal expansion rate, eliminating the volume discontinuity between the antiferroelectric and the cubic paraelectric phase. Therefore, the first order transition is replaced by two second order transitions. 36 We recently prepared Pb0.99Nb0.02[(Zr0.57Sn0.43)1-yTiy]0.98O3 (abbreviated PNZST43/100y/2) ceramics with y = 0.060, 0.063, 0.067, 0.069, 0.071, and and reported detailed data on dielectric constant, electric polarization, and longitudinal and transverse strains obtained from bulk specimens. 65 In this composition series, the multiple cell cubic paraelectric phase appears from ~170 C to ~120 C during cooling and from ~150 C to ~200 C during heating. The ferroelectric phase that is induced from the antiferroelectric phase by electric field in PbZrO3-based ceramics is generally signaled by a dramatic increase in electric polarization and an abrupt expansion in volume. The volume change in bulk specimens is a reflection of the change in unit cell dimensions. For PbZrO3-based perovskite compositions at a phase transition, the size of the primitive unit cell varies in descending order as follows: high-temperature ferroelectric rhombohedral (R3m), low-temperature ferroelectric rhombohedral (R3c), paraelectric cubic (single/multiple cell), antiferroelectric tetragonal (with incommensurate modulations), antiferroelectric orthorhombic (isostructural to PbZrO3). 36 In the literature, most PbZrO3-based antiferroelectric oxides were modified with Sn and Ti and are in the tetragonal phase with incommensurate modulations ,50-65 The electric field-induced antiferroelectric-toferroelectric dielectric phase transition corresponds to a tetragonal to rhombohedral structural phase transition. 58,62,63 Because the primitive cell gets larger, the bulk specimen expands not only in the direction the electric field is applied (longitudinal direction), but also in directions that are orthogonal to the field (transverse direction). 70 The auxetic behavior After the phase transition, it was believed that the electric field-induced ferroelectric phase would behave like a normal ferroelectric, 63 which expand in the field direction (positive longitudinal strain x33) and contract in orthogonal directions (negative transverse strain x11) with 8

11 applied electric field. 36 However, a recent study on the composition PNZST43/6.0/2 suggests otherwise: The expansion occurs in both the longitudinal and transverse directions in the induced ferroelectric phase after the transition. 70 The antiferroelectric phase is stable in this composition at room temperature. It transforms to a ferroelectric phase at a field ~30 kv/cm (EF) and the antiferroelctric phase is resumed at 25 kv/cm (EA) during unloading of electric field. To focus on the electric field-induced ferroelectric phase, electric fields with a profile shown in Fig. 4(a) were applied. Both x33 and x11 were measured between 60 and 140 kv/cm, far away from the phase transition between 20 and 40kV/cm. The applied field above 60 kv/cm consisted of segments A, B, C, and D. When the strains are calculated against the specimen dimensions at 60 kv/cm (under conditions represented by point Z in Fig. 4(a)), the field-induced deformation above 60 kv/cm in the four segments is no longer associated with the antiferroelectric ferroelectric transition. The deformation in segments A and B represents the first full ferroelectric cycle immediately after the transition from the antiferroelectric phase, while the deformation in segments C and D represents the second ferroelectric cycle, i.e. after the ferroelectric domain structure has been exposed to high fields. The strains x33 and x11 with respect to the new origin are plotted in Fig. 4(b) for the four segments. The longitudinal strain x33 responds almost instantaneously to the applied electric field. In contrast, the transverse strain x11 appears to decouple from the longitudinal strain with a time delay with respect to the applied electric field. Another striking feature in Fig. 4(b) is the significant difference in both x33 and x11 between segments A and C, indicating different domain structures between the two successive cycles of unipolar fields in the induced ferroelectric phase. The most important feature that Fig. 4(b) reveals is the positive sign of x11, i.e. the expansion in the transverse direction under electric fields far above EF. Such a behavior is analogous to a negative Poisson s ratio in elastic deformation under mechanical stresses. 71,72 The mechanism for this unexpected auxetic behavior under electric fields is suggested to be related to the corner-linked oxygen octahedra, which resemble at the molecular level the hinge-like structure that has been shown to result in auxetic behavior in organic polymers. 70 The induced ferroelectric phase immediately after the transition was suggested to be in space group R3c with antiphase tilting of oxygen octahedra. 58,62,63 In PbZrO3-based ceramics, the tilt angle in the R3c phase about the pseudocubic <111>c orientation lies in the range of 1~6 degrees. 73 When 9

12 an electric field of increasing magnitude is applied, the tilted oxygen octahedra may straighten if certain conditions are met. This will produce a transverse expansion, i.e. the auxetic behavior. The scenario described above is a ferroelectric R3c to ferroelectric R3m phase transition after the electric field-induced antiferroelectric-to-ferroelectric transition. The R3c R3m transition mechanism is supported by the following facts: First, the unit cell of R3m is larger than the primitive cell of R3c. 36 Second, further electric field-induced ferroelectric-to-ferroelectric phase transitions after the antiferroelectric-to-ferroelectric transition were observed in PbZrO3. 48 In addition, the R3c phase is characterized by the presence of ooo c 1 2 superlattice diffraction spots because of the oxygen octahedral tilting. 68,69 It has been shown in a similar composition 1 2 ooo (Pb0.98Nb0.02Zr0.95Ti0.05) that the c superlattice spots disappear under applied electric field, 74 indicating the removal of the tilts of oxygen octahedra. It should also be noted that the de-tilting of oxygen octahedra under electric loadings as a mechanism for the auxetic behavior shares similarity with the rigid unit model for the negative thermal expansion in ZrW2O8. 75 The observed auxetic behavior under electric field through de-tilting of oxygen octahedra may be unique to the antiferroelectric ceramics with hierarchical subgrain structure. Figure 5 displays the transverse strain x11 during electric field loading in a series of compositions. The antiferroelectric-to-ferroelectric phase transition is characterized by the abrupt increase in x11 at 25~30 kv/cm. It is evident that after this phase transition there is a maximum point (marked by solid triangles) on each of these x11 vs. E curves. The induced ferroelectric phase in these ceramics displays the auxetic behavior up to this maximum point. Beyond this point, x11 decreases with increasing E, indicating the expected behavior in a normal ferroelectric ceramic. These ceramics contain large antiferroelectric 90 domains with a checkerboard-like morphology and thin 180 domain slabs (the incommensurate modulations) within each 90 domain. 60,76 As Ti content increases in these compositions, such a hierarchical subgrain structure becomes less prominent and ferroelectric domains start to emerge. 76 Correspondingly, the maximum point shifts to lower fields on the x11 vs. E curves, indicating that the auxetic behavior diminishes as the incommensurate structure becomes less dominant. 10

13 (3) The electric and mechanical cross coupling The ferroelastic behavior 1 2 The strain resulted from domain morphology change and phase transition in antiferroelectric crystals makes them responsive to mechanical stress in addition to electric field; hence, the 60 and 90 antiferroelectric domains in PbZrO3-based compositions are also ferroelastic domains. 66,77 Under uniaxial compression in an antiferroelectric composition Pb0.97La0.02(Zr0.64Sn0.27Ti0.09)O3 at room temperature, appreciable nonlinear deformation due to ferroelastic domain switching was observed at stresses between 20 and 100 MPa. 78 The initial tangent modulus is ~130 GPa and beyond 500 MPa is ~160 GPa. Poisson s ratio decreases from its initial value of ~0.35 to a final value of ~ We performed uniaxial compressive experiments on antiferroelectric PNZST43/6.0/2 ceramic at 25, 175, and 250 C. According the dielectric characterization, this ceramic is in the antiferroelectric phase at 25 C, the multiple cell cubic paraelectric phase at 175 C, and the cubic paraelectric phase at 250 C. 65 As expected, excessive nonlinear deformation is seen between 20 and 100 MPa at room temperature in the tetragonal antiferroelectric phase (Fig. 6). Surprisingly, excessive nonlinear deformation persists at 175 C in the multiple cell cubic paraelectric phase of the ceramic. At 250 C in the single cell cubic paraelectric phase, the ceramic shows an almost linear elastic behavior beyond 25 MPa. Residual strains of 0.12%, 0.02%, 0.01% and elastic moduli of 128, 125, 105 GPa were recorded at 25, 175 and 250 C, respectively. The elastic modulus was determined from the slope of the unloading curves between 350 and 280 MPa. The ferroelastic behavior at 175 and 250 C appears to be supported by a previous hotstage TEM study. 51 The ooo c C and additional ooe c superlattice spots were observed from room temperature up to (e stands for even Miller indices) superlattice spots were present in the intermediate multiple cell cubic phase. 51 The presence of these superlattice spots is indicative of distortions of the cubic cell and the deviation from the ideal perovskite structure. At room temperature, the 60 and 90 antiferroelectric domains are simultaneously ferroelastic domains. At 175 and 250 C, those domains disappear. At the same time, new ferroelastic 11

14 domains (but not antiferroelectric) emerge. The change in their configurations under applied compressive stresses contributes to the nonlinear deformation observed up to 25 MPa. It is interesting to notice that the existence of ferroelastic domains in the paraelectric phase has also been reported in the lead-free compound (Bi1/2Na1/2)TiO3. 79 The impact of mechanical pre-stresses Both the longitudinal strain x33 and the transverse strain x11 from domain switching are small when compared to the strains resulted from the antiferroelectric ferroelectric phase switching. Because this phase switching also involves an abrupt change in electric polarization, the strains x33 and x11 serve as the mediator for the electric and mechanical cross coupling in antiferroelectric ceramics. Uniaxial compressive pre-stresses applied in the direction of the applied electric field act against x33 and push both EF and EA to higher magnitudes Applying a compressive pre-stress to act against x11 along all radial directions of a cylindrical antiferroelectric specimen requires a special loading fixture The results are shown in Fig. 7 for PNZST43/6.0/2. 82 Under a uniaxial compressive stress up to 90 MPa, the pre-stress delays the phase transition to higher critical fields while it maintains the maximum polarization largely unchanged. At the pre-stress of 100 MPa, the phase transition is significantly suppressed. Further increase in the pre-stress to 250 MPa completely prevents the phase transition from occurring. The radial compressive pre-stress acting against x11 appears to have a distinctly different influence on the field-induced phase transition. As can be seen in Fig. 7(b), the maximum polarization progressively decreases as the radial pre-stress increases. This indicates that only a fraction of the ceramic sample experiences the phase transition and this fraction gradually becomes smaller as the pre-stress increases. The critical field EF also increases with the radial pre-stress. To interpret the observed results, one has to consider the ferroelastic domain switching in the antiferroelectric phase due to the pre-stress, ferroelastic domain switching in the induced ferroelectric phase, as well as the transition itself because of the significant volume expansion. 82 The ferroelectric-to-antiferroelectric phase transition For the same reason that compressive mechanical stresses suppress the electric fieldinduced antiferroelectric-to-ferroelectric phase transition in PbZrO3-based antiferroelectric 12

15 ceramics, they drive the ferroelectric-to-antiferroelectric phase transition to occur in ferroelectric compositions close to the phase boundary. This has been experimentally confirmed with uniaxial compressive stresses as well as hydrostatic pressures 21, It has been generalized that a symmetric external stimulus (such as hydrostatic pressure) stabilizes the antiferroelectric phase while an asymmetric stimulus (such as electric field) stabilizes only the ferroelectric phase in Sn- and Ti-modified PbZrO3-based ceramics. 88 However, a recent experimental investigation indicates it is possible for an external electric field to recover the antiferroelectric phase from the induced metastable ferroelectric one. 92 In the PNZST43/100y/2 composition series, the antiferroelectric order is weakened while the ferroelectric order is strengthened with increase in y (Ti content). At room temperature (25 C), the antiferroelectric/ferroelectric phase boundary is around y = ,65 It was observed that the induced ferroelectric phase remained and the antiferroelectric phase was not resumed during unloading of electric field to zero in the composition PNZST43/7.1/2. 65,92 Measurements on electric field induced strains (x33 and x11) indicated that the critical field EA was in opposite sign with EF within a given half-cycle. Hence, the metastable ferroelectric phase induced by the electric field in the first quarter cycle was transformed back to the antiferroelectric phase when a field with opposite polarity was applied. This is the situation where an external electric field assists the formation of the antiferroelectric phase from the ferroelectric one. The unexpected phenomenon was further verified by in situ X-ray diffraction analysis, 92 as shown in Fig. 8. The composition PNZST43/6.0/2, which exhibits a stable antiferroelectric phase at room temperature, 64,65 was used as a reference. Figures 8(a) and 8(b) indicate that the as-sintered ceramic displays a tetragonal (T) symmetry in the virgin state. The induced ferroelectric phase under electric fields displays a rhombohedral (R) distortion of the perovskite structure as confirmed by the disappearance of the T(200)/T(002) splitting (2θ ~ 44º) and the presence of splitting of R(222)/R( 222 ) (2θ ~ 81º) at -40 kv/cm in the third quarter of the first cycle of electric field application. The calculated volume of the primitive cell (containing one ABO3 formula unit) is Å 3 for the tetragonal phase at virgin state and Å 3 for the rhombohedral phase at -40 kv/cm. The primitive cell volume expansion of 0.6% agrees well with the macroscopic strain measurement. At the end of the first cycle where the electric field returns to zero, the antiferroelectric phase with tetragonal distortion is resumed. The 13

16 disappearance of the R(222) peak shown in Fig. 8(b) indicates a complete return to the antiferroelectric tetragonal phase while the weaker intensity of the T(002) peak relative to that of the virgin state suggests a texture has developed. 63,92 Obviously the reappearance of the T(002) peak can be considered as the signature for the antiferroelectric tetragonal phase. As such, this peak is highlighted by the dashed box in Fig. 8(a). Figures 8(c) and 8(d) display the results of the in situ X-ray diffraction experiment on PNZST43/7.1/2. Similar to that in PNZST43/6.0/2, a tetragonal distortion of the perovskite lattice with antiferroelectric order is seen in the virgin state while the ferroelectric phase with a rhombohedral structure is found under strong electric fields. When the electric field reaches zero at the end of the very first cycle, the rhombohedral ferroelectric phase is preserved. However, when an electric field with reversed polarity at a magnitude of 5 kv/cm is applied, the T(002) signature peak reappears [highlighted by the dashed box in Fig. 8(c)], conclusively verifying the occurrence of the electric field-induced ferroelectricto-antiferroelectric phase transition. From strain measurement data, the field 5 kv/cm is almost identical to the coercive field Ec of the induced ferroelectric phase. It is suggested that the key factors for the seemingly unlikely electric field-induced ferroelectric-to-antiferroelectric phase transition are the chemical composition and the process of exposing the ceramic to an intense electric field. The composition has to be in the range where the energy barrier between the antiferroelectric and ferroelectric phases is low so that either one can be preserved at ambient conditions in the absence of any applied electric fields or mechanical stresses. 25,93 When the ceramic is exposed to an intense electric field, not only can the metastable ferroelectric phase be realized, but also the electric dipoles in the induced ferroelectric phase are forced to align along the field direction and the induced ferroelectric phase becomes piezoelectric. 63 Under the electric field with reversed polarity, there is a volume contraction from the converse piezoelectric effect. It is this volume contraction that produces a similar effect as compressive stresses and triggers the transition to the antiferroelectric phase. 92 With this mechanism, a recent experimental observation on Pb0.99Nb0.02(Zr0.75Sn0.20Ti0.05)0.98O3 can be easily explained. 90 Similar to PNZST43/7.1/2, the induced ferroelectric phase is metastable and returns to the original antiferroelectric phase under hydrostatic pressure. It was found that the critical pressure needed increases under positive electric fields while it decreases 14

17 under negative fields. 90 Obviously the field with reversed polarity assisted the ferroelectric-toantiferroelectric phase transition. The phase transition toughening effect The fracture behavior of antiferroelectric ceramics has received little attention in the literature. 94 The volume expansion during the antiferroelectric-to-ferroelectric phase transition may toughen the ceramic by helping to close the crack and stop propagation via localized volume expansion. 76 For the phase transition toughening effect to work, the phase transition has to be localized at the crack tip and the transition has to generate a volume expansion. 95,96 The volume expansion at the phase transition has been verified extensively. 26,65 Recently experimental evidence was found for the transition to occur only at a localized zone at a crack tip. 76 With micro Raman spectroscopy, it was shown that the Raman shift at 86 cm -1 (antiferroelectric mode) was strong in an as-sintered PNZST 43/7/2 ceramic. At a nominal applied electric field of 15 kv/cm, this mode was weakened and the ferroelectric mode at 122 cm -1 started to emerge for most areas between the two electrodes. However, at a spot in the close vicinity of a crack tip, the antiferroelectric mode almost completely disappeared and the ferroelectric mode became evident. To fully establish the phase transition toughening effect in PbZrO3-based antiferroelectric ceramics, direct fracture mechanics tests under tensile stresses are still needed. III. Lead-Free Antiferroelectric Perovskite Oxides Although the lead-containing antiferroelectric oxides discussed above display superior performance in engineering devices, the toxicity of lead raises serious environmental concerns. 39 Driven by the current intensive research interest on lead-free piezoelectric ceramics, research on lead-free antiferroelectric perovskite compounds is expected to prosper. Such research has been primarily focused on (Bi1/2Na1/2)TiO3, NaNbO3, and AgNbO3. 7 The antiferroelectric characteristics of these lead-free compounds vary from each other, and are also quite different from PbZrO3-based compositions. Most importantly, these compounds are major end members in lead-free piezoelectric solid solutions ,97 This section will first discuss the structure and properties of NaNbO3, AgNbO3, and (Bi1/2Na1/2)TiO3 compounds. Then the dictating role that 15

18 the electric field-induced antiferroelectric-to-ferroelectric transition plays in the (Bi1/2Na1/2)TiO3 BaTiO3 lead-free piezoelectric ceramics will be explained in detail. (1) Lead-free antiferroelectric perovskite compounds NaNbO3 NaNbO3 is a well-documented antiferroelectric perovskite compound with a complex sequence of temperature-induced structural phase transitions , In addition to temperature, pressure 113,114, particle size 115,116, and electric field can also trigger phase transitions in NaNbO3. The complex temperature-induced transitions have been extensively studied by various methods, including X-ray diffraction, neutron diffraction, dielectric analysis, 11,102,108,109 and Raman spectroscopy. 102, Despite extensive structural analysis with various tools, controversy still remains in the literature regarding the symmetry and transition temperatures of NaNbO3. Table I summarizes the phase transition sequence determined with different characterization methods. It is generally agreed that the N phase is ferroelectric, P and R phases are antiferroelectric, and S, T1, T2, and U phases are paraelectric ,106 As evident from Table I, the controversy is primarily regarding the antiferroelectric P phase and the ferroelectric N phase. The latest neutron diffraction study reveals wide temperature windows for phase coexistence (-258 ~ 7 ºC for N and P phases while 360 ~ 407 ºC for P and R phases during heating). 107 In addition, a huge thermal hysteresis of the P N phase transition is noticed (The N phase starts to form at -193 ºC during cooling). 107 In contrast, a recent Raman spectroscopy study, in combination with synchrotron X-ray diffraction and dielectric analysis, suggests that the temperature region where the P phase is stable actually consists of three different phase regions. 102 The antiferroelectric P phase has been reported to be monoclinic at room temperature in some studies, 102,103 but it is most commonly assigned as orthorhombic Pbcm, which is sometimes equivalently referred to as Pbma , This structure possesses two crystallographically distinct Na sites and exhibits an unusual oxygen octahedra tilting leading to a 2ac 2ac 4ac supercell consisting of primitive cells of the cubic perovskite structure. 98 The antiferroelectric phase with the Pbcm space group is non-polar by symmetry and the dipole moments from 16

19 antiparallel Nb 5+ displacements are completely cancelled within the unit cell. 98 At room temperature, 90º and 60º antiferroelectric domains were observed in NaNbO The 90º antiferroelectric domains are of micrometer size. Most of them take the wedged shape, but the rectangular-shaped ones were also observed. The 60º domains, with the walls along the {110}c 1 plane, were observed in the dark field image formed with the ( 1 0) superlattice diffraction spot 4 along the [001]c zone axis. 123 Although NaNbO3 exhibits at least seven polymorphic phases and a complex sequence of phase transitions, only three dielectric anomalies were observed in the temperature dependent dielectric characterization of the ceramic at -183, 7, and 377 ºC. 108,109 While the anomalies at and 377 ºC have been unambiguously attributed to the N/P and P/R phase transitions, respectively, the origin of the one at 7 ºC is still unclear for ceramic NaNbO3. The intermediate dielectric anomaly is shifted to 137 ºC in NaNbO3 single crystals and was attributed to the transition from a monoclinic phase (Pm) to an incommensurate phase. 102 It should be noted that frequency dispersion in dielectric constant was observed at the -183 and 7 ºC transitions in ceramic samples in the frequency range between 1 khz and 100 khz. 108,109 However, the microstructure origin for the dielectric relaxation in NaNbO3 ceramic has not yet been found. The signature double P~E hysteresis loops, marking the electric field-induced antiferroelectric-to-ferroelectric phase transition, were only observed in high-quality NaNbO3 single crystals with electric fields applied perpendicular to the orthorhombic c axis. The critical field EF is around 90 kv/cm at room temperature and increases with decreasing temperature. 117,118 Apparently chemical modification has a profound impact on the antiferroelectric-to-ferroelectric phase transition in NaNbO3. Only 0.6 mol.% K substitution of Na reduces the EF to 20 kv/cm and the induced ferroelectric phase remains after electric field unloading. 118 It is believed that a new ferroelectric phase (Q phase with space group P21ma) is resulted from the electric field-induced transition at room temperature Detailed structural study indicated that this electric field-induced P Q phase transition occurs between -100 and at least 257 C. 121 According to the lattice parameters at room temperature, 120 the electric fieldinduced P Q transition may lead to a maximum volume expansion of ~0.2%. Compared to the 17

20 antiferroelectric-to-ferroelectric transition in PbZrO3-based compositions, 26 such an expansion is small. Between -173 and -100 ºC, instead of transforming to the Q phase, the antiferroelectric P phase with Pbcm space group transforms to the ferroelectric N phase with the R3c space group. 121 In contrast, the EF decreases with decreasing temperature and eventually the ferroelectric N phase becomes stable without application of electric fields. 121 It was shown that at low temperatures, the unit cell volume of the ferroelectric N phase is ~2.5% bigger than the antiferroelectric P phase. 106 Therefore, a significant volume expansion should be expected at the low-temperature electric field-induced antiferroelectric-to-ferroelectric phase transition in NaNbO3. AgNbO3 AgNbO3 has been more widely studied as a microwave ceramic and photocatalytic material rather than a lead-free antiferroelectric. 124 This is probably due to the long-existing controversy regarding the antiferroelectricity in AgNbO3 at room temperature The first study on AgNbO3 indicated weak ferroelectricity at room temperature based on the small remanent polarization obtained from hysteresis loops and the pyroelectric effect. 125 The small remanent polarization was later confirmed to persist from room temperature up to around 75 ºC. 126 However, the observed weak ferroelectricity contradicted the centrosymmetric Pbcm space group, which forbids the presence of ferroelectricity but rather suggests antiferroelectricity. 127 This discrepancy was not resolved until recently. In 2007, Fu et al. 128 successfully prepared highquality AgNbO3 ceramic samples and applied high electric fields (up to 220 kv/cm) for P~E loop measurements. The electric field-dependent polarization measurement clearly revealed the characteristic double hysteresis loops with a saturation polarization of 52 C/cm 2 and a critical field EF of ~110 kv/cm. The confirmation of the electric field-induced antiferroelectric-toferroelectric transition seemed to support the claim that AgNbO3 adopts the Pbcm crystal structure in the virgin state. 127 However, a weak but non-zero remanent polarization was still recorded. 128 In 2011, a detailed structural analysis updated the space group of AgNbO3 at room temperature as the polar Pmc21 group. 129 Furthermore, this study revealed a ferrielectric order, where the cation displacements are still antiparallel to each other as in a normal antiferroelectric crystal but the associated dipole moments do not cancel each other completely. The ferrielectric 18

21 (uncompensated antiferroelectric) phase in AgNbO3 explains the observed non-zero remanent polarization and the abrupt increase in polarization at ~110 kv/cm. Under high electric fields, the uncompensated antiferroelectric state of AgNbO3 transforms to a ferroelectric one. Similar to NaNbO3, AgNbO3 exhibits a number of other phases with deviations from room temperature. With the latest data in the literature, the complex phase transition sequence of AgNbO3 is summarized in Table II. When heated, the room-temperature uncompensated antiferroelectric (ferrielectric) M1 phase with the Pmc21 space group 129 transforms to the antiferroelectric M2 and M3 phases at 67 and 267 ºC, respectively. 127 The crystal structures of the M1, M2 and M3 phases are very close to each other and belong to the same oxygen octahedra tilting system. Both M2 and M3 phases exhibit the same Pbcm space group, and only the amplitude of atomic displacement decreases appreciably from the M2 phase to the M3 phase. 127 When further heated, the M3 phase transforms to the paraelectric O1, O2, T and C phases in sequence. 127 While the O1 phase is stable only in a very small temperature window of 8 ºC (thus preventing a decent structural analysis), the space groups of the other three paraelectric phases have been determined, as listed in Table II. 127 There are very limited reports in the literature on the domain structure of AgNbO3. Optical microscopy with polarized light was employed to characterize the structural change during the temperature-induced phase transitions. 130,131 TEM was also used to form a dark field image with the (241) diffraction spot in the antiphase domain walls aligned perpendicular to the [ 210] o zone axis, where a high incidence of 19 [ 001] o direction was observed. 132 The relationship between the dielectric and structural phase transitions of AgNbO3 is similar to that of NaNbO3. Upon cooling, the dielectric constant of AgNbO3 obeys the Curie- Weiss law without any anomaly in the temperature region where the paraelectric C, T, O2, and O1 phases are stable. 133 With further cooling, the dielectric constant exhibits a frequencyindependent sharp drop at the temperature where the structural transition from O1 to the M3 phase takes place (~353 ºC). 133 At lower temperatures, the M2-M3 and M1-M2 structural transitions are associated with two diffuse maxima of dielectric constant. 133,134 The dielectric anomaly associated with the M1-M2 transition exhibits typical features of relaxor ferroelectrics in

22 the 1 ~ 100 khz frequency range: with increasing frequency, the real part of the dielectric constant decreases, and Tm (where the dielectric constant peaks) increases. 133 Two possible mechanisms for the relaxor-like behavior in the M1 phase were proposed: it could be a result of the freezing of the non-equilibrated disordered antiferroelectric state, or a result of another type of correlated ion displacements within nanoregions. 133 However, neither of them has been experimentally confirmed. The application of axial pressure was observed to increase the dielectric constant, shift the dielectric transition temperatures, make the dielectric anomalies more diffused, and decrease the thermal hysteresis of the transitions. 135 Similar to PbZrO3-based antiferroelectric ceramics, 65 the AgNbO3 ceramic abruptly develops a longitudinal strain x33 up to 0.15% at the electric field-induced antiferroelectric-toferroelectric phase transition at room temperature. 128 During unloading of electric field, a sudden decrease in x33 was noticed at around 60 kv/cm, suggesting that the induced ferroelectric phase transforms back to the uncompensated antiferroelectric phase. However, since the transverse strain x11 was not measured and the crystal structure of the induced ferroelectric phase was not determined, the volume change associated with the electric field-induced phase transition is not clear. (Bi1/2Na1/2)TiO3 (Bi1/2Na1/2)TiO3 was first synthesized by Smolenskii et al. 50 year ago. 8 It is ferroelectric up to 200 C and paraelectric above ~320 C. In the paraelectric regime, there is a ferroelasticparaelastic transition at ~520 C. 7 The intermediate phase between 200 and 320 C was suggested to be antiferroelectric based on the presence of double P~E hysteresis loops and the absence of spontaneous polarization in the (Bi1/2Na1/2)TiO3 SrTiO3 solid solution. 9 Recently, double P~E hysteresis loops were recorded in undoped (Bi1/2Na1/2)TiO3 ceramics at temperatures around 200 C. 136,137 Compared to PbZrO3-based antiferroelectric ceramics, a much larger polarization is developed under electric field prior to the antiferroelectric-to-ferroelectric transition and an apparent remanent polarization is recorded. The temperature for the ferroelectric-to-antiferroelectric transition [~200 C for (Bi1/2Na1/2)TiO3] has been widely referred to as the depolarization temperature Td, while that for the antiferroelectric-to-paraelectric transition [~320 C for (Bi1/2Na1/2)TiO3] as Tm. 37,136 The 20

23 transition at Td is characterized by a hump in the loss tangent vs. temperature curve and a steep increase in the dielectric constant vs. temperature curve. Tm situates at the major peak on the dielectric constant vs. temperature curve. 37,136 The dielectric constant in the low temperature phases displays a strong frequency dependence. The behavior is very similar to that in Pb(Mg1/3Nb2/3)O3 with a diffused phase transition In contrast, there is no frequency dispersion in the major peak accounting for the antiferroelectric-paraelectric transition. 9 The ferroelastic-paraelastic transition does not produce an anomaly in the dielectric constant measured with frequency higher than 1 khz, but manifests itself as a huge frequency-dependent peak (dielectric constant approaches 10,000) with lower frequencies. 141 The structural phase transition sequence in (Bi1/2Na1/2)TiO3 as a function of temperature was examined by X-ray 142 and neutron 143,144 diffraction techniques. Early X-ray diffraction tests observed two first order structural phase transitions during cooling: from cubic to tetragonal at 520 C and then to rhombohedral at 260 C. 142 The cubic-to-tetragonal transition shows a very small volume contraction (~0.02%) and no temperature hysteresis. In sharp contrast, the tetragonal-to-rhombohedral transition displays no volume change and exhibits a remarkable temperature hysteresis of ~60 C. 142 A recent comprehensive neutron diffraction study 144 revealed that a pure rhombohedral R3c phase exists from 255 down to -268 C, a pure tetragonal P4bm phase exists between 400 and 500 C, and a pure cubic Pm3 m phase forms at temperatures above 540 C. Coexisting R3c/P4bm phases and P4bm/ Pm3 m phases were detected in the temperature regimes from 255~400 C and 500~540 C, respectively. The R3c phase is obviously ferroelectric with Bi 3+ /Na + and Ti 4+ cations displaced parallel to each other along <111>c directions and with the oxygen octahedra tilted about the <111>c direction. It has been suggested that the tetragonal phase of (Bi1/2Na1/2)TiO3 is antiferroelectric 142,143 and a special term low-temperature non-polar phase 143 was proposed for it. However, Jones and Thomas 144 assigned the polar P4bm space group to the tetragonal phase. The displacements of Ti 4+ cations are antiparallel to that of Bi 3+ /Na + cations and both are along the polar [001] direction. The structure also exhibits in-phase (a 0 a 0 c + ) tilts of oxygen octahedra. Similar to AgNbO3, 129 the intermediate phase of (Bi1/2Na1/2)TiO3 is actually an uncompensated antiferroelectric, i.e. a ferrielectric phase. If we assume only cation displacements contribute to the dipole moment in the tetragonal unit cell, the spontaneous polarization can be calculated from the antiparallel 21

24 cation displacements. As shown in Fig. 9, the calculated spontaneous polarization is surprisingly high in the P4bm phase. The presence of spontaneous polarization in the tetragonal phase has been supported by second harmonic generation experiments. 144 It has been observed that the temperatures of dielectric phase transitions do not correlate with that of the structural phase transitions in (Bi1/2Na1/2)TiO3. 145,146 This discrepancy seems to be solved recently by a detailed TEM in situ heating study. 145,146 The ferroelectric/ferroelastic domains in the rhombohedral phase disappear at ~200 C and a modulated phase corresponding to an intergrowth of orthorhombic Pnma thin sheets in rhombohedral perovskite blocks is formed from 230 to 300 C. The orthorhombic phase then turns into the tetragonal phase near 320 C. Therefore, the ferroelectric-antiferroelectric phase transition at ~200 C corresponds to the rhombohedral-orthorhombic structural change while the antiferroelectric-paraelectric transition at ~320 C corresponds to the orthorhombic-tetragonal phase transition. 145,146 The orthorhombic Pnma thin sheets are actually 180 domain walls. Following the same argument for modulated PbZrO3-based antiferroelectric ceramics (Fig. 1), 60 the double P~E hysteresis loops observed between 200 and 320 C in (Bi1/2Na1/2)TiO3 are due to 180 polarization reversal of the high density Pnma thin sheets. 145 It is interesting to notice that previous X-ray or neutron diffraction experiments did not detect the nanostructured orthorhombic phase. Electron diffraction in TEM has shown unique capabilities in establishing the structure-property relationship in (Bi1/2Na1/2)TiO3. The scenario revealed by TEM observations is complemented by a combined piezoresponse force microscopy and polarized light microscopy investigation. 79 During cooling of a (Bi1/2Na1/2)TiO3 single crystal, it is found that the high temperature tetragonal ferroelastic domains are inherited by the ferroelectric rhombohedral phase. Polar microdomains form within the geometrical restrictions imposed by the ferroelastic domains. 79 Another puzzling experimental observation in (Bi1/2Na1/2)TiO3 is the frequency dispersion in dielectric constant. Diffused antiferroelectric phase transition 143,147 has been used previously to describe the associated transition. It is known that in Pb(Mg1/3Nb2/3)O3-based relaxor ferroelectrics, the presence of nanoscale cation order and its associated polar nanoregions are responsible for the strong frequency dispersion in the dielectric constant. 138,148,149 The diffuse scattering of neutrons suggested that polar regions of ~7 nm start to form at 280 C in 22

25 (Bi1/2Na1/2)TiO3 during cooling. 143 A recent TEM study 150 imaged (001) tetragonal platelets a few cells thick within the R3c matrix in (Bi1/2Na1/2)TiO3 at room temperature and suggested these platelets play the same role as the polar nanoregions in Pb(Mg1/3Nb2/3)O3. The presence of these nanoscale features in (Bi1/2Na1/2)TiO3 was proposed to be associated with the Bi 3+ /Na + cation order. 141,151 However, cation order in (Bi1/2Na1/2)TiO3 is only supported by infrared reflectivity and Raman spectroscopy data 151 and has never been detected by either X-ray or neutron diffraction experiments ,152 This might be due to the facts that only short range 1 2 Bi/Na order takes place and the ooo c superlattice peak characterizing the cation order coincides with the superlattice peaks from the (a - a - a - ) antiphase oxygen octahedron tilts in the R3c phase. Electron diffraction of the tetragonal and cubic phases at high temperature seems to overcome these difficulties and has confirmed the nanometer scale Bi 3+ /Na + cation order. 146 (2) The Antiferroelectric ferroelectric transition in the (Bi1/2Na1/2)TiO3 BaTiO3 solid solution The (Bi1/2Na1/2)TiO3 BaTiO3 solid solution The antiferroelectric phase in (Bi1/2Na1/2)TiO3 can be stabilized to lower temperatures by forming solid solution with SrTiO3. 9 A similar phenomenon was observed in the solid solution (1-x)(Bi1/2Na1/2)TiO3 xbatio3, which has been one of the most investigated lead-free piezoelectric compositions. 37,39 Takenaka et al. 37 discovered a morphotropic phase boundary (MPB) separating the ferroelectric R3c and P4mm phases in poled (1-x)(Bi1/2Na1/2)TiO3 xbatio3 ceramics at x = 0.06 [Fig. 10(a)]. Following the same trend in (1-x)PbZrO3 xpbtio3, 36 the piezoelectric properties of poled (Bi1/2Na1/2)TiO3 BaTiO3 ceramics peak at the MPB composition. Consequently, compositions in the vicinity of the MPB in (1-x)(Bi1/2Na1/2)TiO3 xbatio3 have been a focal point in the search for lead-free piezoelectric ceramics. 37,39-43,136,137 The significance of antiferroelectricity in the (1-x)(Bi1/2Na1/2)TiO3 xbatio3 solid solution was revealed by recent TEM studies on unpoled ceramics Exactly in the vicinity of the MPB composition, a P4bm phase with uncompensated antiferroelectric order (ferrielectric) was discovered in as-sintered ceramics, as shown in Fig. 10 (b). 23

26 The uncompensated antiferroelectric phase with P4bm symmetry in (1- x)(bi1/2na1/2)tio3 xbatio3 is obviously inherited from the same phase in pure (Bi1/2Na1/2)TiO3. Both X-ray diffraction 156 and anelastic measurements 157 indicate that the rhombohedraltetragonal phase transition temperature drops significantly with increasing x. Considering the fact that nanoscale P4bm platelets are already present at room temperature in undoped (Bi1/2Na1/2)TiO3, 150 the development of a pure P4bm phase in the composition range of 0.07 x 0.09 is not a surprise. The dielectric constant vs. temperature curves of unpoled ceramics with the pure P4bm phase show a strong frequency dependence from at least -140 C up to TRE, a critical temperature where the relaxor behavior vanishes. Typically TRE is ~30 C below Tm. In addition, these compositions with pure P4bm phase do not display any dielectric anomaly indicating the presence of Td. 154 An in situ TEM study indicates that a pure P4bm phase is also developed during heating above Td in other compositions. 155 The frequency dependent dielectric behavior of the uncompensated antiferroelectric P4bm phase traces its origin to the nanometer scale domain morphology (Fig. 11) The contrast of individual nanodomains was observed in the centered-dark-field image formed with 1 the (310) 2 superlattice diffraction spot in the [130]c-zone axis. 155 These nanodomains are thin 1 platelets parallel to the (001) plane, which cause streaking of {ooe} diffraction spots along the 2 [001] direction. Following the superparaelectric model for the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3, 138 the P4bm nanodomains in (1-x)(Bi1/2Na1/2)TiO3 xbatio3 are probably embedded in a cubic matrix. Within each nanodomain, the displacements of A-site cations (Bi 3+, Na +, and Ba 2+ ) are antiparallel to those of B-site cations (Ti 4+ ) along one of the six equivalent <001>c directions. As seen from Fig. 9, a net polarization can be resulted from the incomplete cancellation of dipole moments within a unit cell in (Bi1/2Na1/2)TiO3. Presumably adding Ba 2+ to the A-site decreases the net polarization but still a non-zero value should be anticipated. Therefore, these nanodomains are weakly polar ferrielectric domains and their dynamic fluctuation among the six equivalent directions leads to the relaxor behavior. We suggested the term relaxor antiferroelectric for the P4bm phase with nanodomains in (1-x)(Bi1/2Na1/2)TiO3 xbatio3, 154 in parallel to relaxor ferroelectric for Pb(Mg1/3Nb2/3)O3. Rigorously speaking, the 24

27 P4bm phase with nanodomains should be described as relaxor ferrielectric. Figure 11(b) schematically explains the P4bm nanodomains with the uncompensated antiferroelectric, or ferrielectric order. The formation of nanodomains by introducing Ba 2+ to the A-site of the lattice in (Bi1/2Na1/2)TiO3 is also confirmed by a recent study in single crystals of (1-x)(Bi1/2Na1/2)TiO3 xbatio3 with x = 0.0, 0.045, and The addition of BaTiO3 was found to refine the size of polar domains and to suppress the formation of ferroelastic domains at high temperatures. Comparison between the phase diagrams shown in Fig. 10 suggests that there are electric field-induced phase transitions during the poling process, which has been verified by structural analysis with X-ray 40,42 and neutron 159 diffraction experiments. After poling, a ferroelectric phase with P4mm symmetry was observed in the composition of 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3 and a ferroelectric R3c phase was formed in 0.94(Bi1/2Na1/2)TiO3 0.06BaTiO3. 40,159 The induced ferroelectric phases are metastable at room temperature and do not return to the original P4bm phase after the removal of the applied field. As a result, typical double P~E hysteresis loops are not seen in these compositions at room temperature. Double hysteresis loops are recorded when the measurement is conducted around 100 C. 136,160 The situation is quite similar to that of the PNZST43/7.1/2 antiferroelectric ceramic. 92 Obviously the electric field-induced antiferroelectric (ferrielectric)-to-ferroelectric phase transition dictates the effectiveness of the electric poling process in (1-x)(Bi1/2Na1/2)TiO3 xbatio3 lead-free piezoelectric ceramics. Strong piezoelectricity through phase transition With the unique electric field in-situ TEM technique we have developed over the years, the electric-field-induced P4bm-to-P4mm phase transition was revealed with nanometer resolution in real time. The results are presented in Fig. 12 for the composition 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3. It should be pointed out that the values of the applied field in Fig. 12 are nominal. As explained previously, 165 the actual field is at least two times of the nominal field due to the presence of the perforation in TEM specimens. The grain shown in Fig. 12(a) originally displays only P4bm nanodomains with apparent 1 {ooe} superlattice diffraction spots. Brief exposure to the electron beam in TEM leads to the 2 formation of the lamellar domains in the upper right region. When an electric field at the nominal 25

28 value of 5kV/cm is applied along the direction indicated by the arrow in Fig. 12(c), lamellar domains are formed starting from the upper left grain boundary. At 7.5kV/cm, the volume occupied by the lamellar domains increases [Fig. 12(d)]. Electron diffraction from this volume, 1 as seen in Fig. 12(e), reveals the absence of the {ooe} superlattice spots, indicating that the 2 formation of lamellar domains is the manifestation of the ferrielectric P4bm-to-ferroelectric P4mm phase transition. Therefore, the electric field induced phase transition during poling observed by X-ray diffraction 40 is confirmed for the first time by in situ TEM observation in 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3. The two sets of tetragonal 90 ferroelectric domains in the P4mm phase have their domain walls on {110}c planes. At 10 kv/cm, the electric field-induced phase transition continues and the volume for the P4mm phase grows further at the expense of the P4bm phase. A third set of {110}c ferroelectric domains form in the right-hand part of the grain. What is more interesting in Fig. 12(g) is the revealing of the domain switching process, i.e. the real electric poling process. In the middle part of the lamellar domain colony, many domain walls disappear and a large ferroelectric domain is formed. At 12.5 kv/cm, the P4bm-to-P4mm transition is complete in this grain and the large ferroelectric domain grows significantly [Fig. 12(h)]. At 25 kv/cm, the whole grain becomes almost a single domain grain and 90 lamellar domains are only observed in regions very close to grain boundaries [Fig. 12(i)]. Upon removal of the applied electric field, only very slight changes in the configuration of the domains close to grain boundaries are observed. The induced ferroelectric P4mm phase remains and the original P4bm phase is not resumed. This in situ TEM observation is significant because it reveals the domain mechanism for the electric field-induced antiferroelectric (ferrielectric)-to-ferroelectric phase transition in (1- x)(bi1/2na1/2)tio3 xbatio3 lead-free piezoelectric ceramics for the first time. The phase transition manifests itself as the change of nanodomains with P4bm symmetry to P4mm lamellar domains in 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3. It starts from the grain boundary and proceeds as the applied field increases. During this process there is also domain switching in the induced P4mm ferroelectric phase which accounts for the electric poling. The key reason that these compositions are piezoelectric lies in the fact that the induced P4mm ferroelectric phase remains poled and the original ferrielectric P4bm phase does not return when the poling field is removed. 26

29 A recent measurement of longitudinal and transverse strains developed under the very first cycle of bipolar electric field on (1-x)(Bi1/2Na1/2)TiO3 xbatio3 seems to suggest that the electric field-induced P4bm-to-P4mm transition occurs in all compositions with 0.07 x The transverse strain x11 is negligibly small and the volume strain (x33 + 2x11) largely follows the change of the longitudinal strain x33 under applied electric field. An almost constant volume expansion of ~0.15% is seen at the phase transition in all these compositions. 168 Ultrahigh strain through phase transition The original uncompensated antiferroelectric P4bm phase gets more stable against the induced ferroelectric phase in (1-x)(Bi1/2Na1/2)TiO3 xbatio3 as temperature rises moderately. 136,160 As a result, the P4bm phase re-appears after the removal of the applied field and typical double P~E loops are seen. A minor amount (1~3 mol.%) of (K0.5Na0.5)NbO3 doping was observed to show similar effects of restoring the P4bm phase. 41,43, A reversible electric field-induced phase transition is seen at room temperature in these (K0.5Na0.5)NbO3-doped compositions. The significance of such a reversible phase transition is the generation of ultrahigh strains (x33 up to ~0.45%) repeatedly. 169 The key for realizing such a high strain is the stable P4bm ferrielectric phase which destroys the poled ferroelectric phase after the field is removed. 41 It should be noted that the P4bm ferrielectric phase is polar. A weak, but non-zero, piezoelectric d33 coefficient has been experimentally measured. 170 So another key factor for the high strain is the nanodomain morphology of the P4bm phase and its small lattice distortion. This makes the poling of the P4bm ferrielectric phase nearly impossible and generates near-zero remanent strain. A relevant effect associated with the nanodomain morphology of the P4bm phase is the almost linear elastic behavior under mechanical compressive stresses, 172 similar to that in a Pb(Mg1/3Nb2/3)O3-based relaxor ferroelectric ceramic. 78 The longitudinal strain observed in (K0.5Na0.5)NbO3-doped (1-x)(Bi1/2Na1/2)TiO3 xbatio3 compositions with a reversible phase transition is comparable to that measured in PbZrO3-based antiferroelectric ceramics. 26,65 However, the transverse strain x11 is always negative, 41,172 opposite to the x11 in PbZrO3-based ceramics. 65,70,82,92 As a consequence, no auxetic behavior is observed, and the volume strain (x33 + 2x11) is minimal (~0.1%) in these leadfree compositions. 41 It is suggested that the ultrahigh longitudinal strain x33 in (K0.5Na0.5)NbO3-27

30 doped (1-x)(Bi1/2Na1/2)TiO3 xbatio3 ceramics has contributions primarily from the first order and the second order piezoelectric effect (second order piezoelectric effect is electrostriction) of the P4bm phase, 174 the phase transition to a ferroelectric phase, and the piezoelectric effect (domain switching and lattice distortion) of the induced ferroelectric phase. Different from that in 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3, the electric field-induced ferroelectric phase in (K0.5Na0.5)NbO3-doped (1-x)(Bi1/2Na1/2)TiO3 xbatio3 ceramics seems to be rhombohedral with the R3c space group, as suggested by electric field in situ TEM study 43 and later confirmed by in situ X-ray and neutron diffraction experiments. 173 In the ceramic of 0.91(Bi1/2Na1/2)TiO3 0.06BaTiO3 0.03(K0.5Na0.5)NbO3, nanodomains are the dominant feature of the P4bm phase at zero field. At the nominal field of 25 kv/cm applied roughly along the <001>c direction, large lamellar domains are formed and clearly visible when imaged along the [110]c-zone axis Electron diffraction reveals the presence of the {ooo} superlattice 2 diffraction spots from the induced lamellar domains. On removal of the field, the domain contrast completely disappears, indicating a reversible phase transition. The in situ highresolution X-ray and neutron diffraction study on a similar composition 0.92(Bi1/2Na1/2)TiO3 0.06BaTiO3 0.02(K0.5Na0.5)NbO3 directly confirmed that the initial P4bm phase underwent a reversible phase transition to a significantly distorted R3c phase under electric fields. 173 The combined Rietveld refinement with neutron and X-ray data yields a weak tetragonal distortion of only 0.026% of the P4bm phase at room temperature. Again, it was observed that the P4bm phase was completely recovered immediately after the removal of the applied electric field. IV. Summary In PbZrO3-based antiferroelectric perovskite ceramics, the incommensurate modulation is actually an average effect of a mixture of commensurate modulations, which are essentially thin 180 domains resulted from competing interactions between antiferroelectric and ferroelectric orders. Antiferroelectric order favors thinner 180 domain slabs and ferroelectric order favors thicker slabs. The abrupt volume expansion at the antiferroelectric-to-ferroelectric phase transition leads to the strong impact of mechanical confinement on the transition and can provoke a phase transition toughening effect in these compositions. In the electric field-induced 28

31 ferroelectric R3c phase, a further transition to R3m phase can produce an auxetic behavior. Composition engineering has led to ceramics with a metastable induced ferroelectric phase at ambient conditions. When the applied field is reversed in polarity, the volume contraction from the converse piezoelectric effect in the induced ferroelectric phase triggers a ferroelectric-toantiferroelectric phase transition. The previously thought antiferroelectric phase in (Bi1/2Na1/2)TiO3-based compositions is actually polar ferrielectric with the P4bm space group. Application of electric fields to these compositions leads to the ferrielectric-to-ferroelectric phase transition. The in situ TEM observation reveals the competing phase transition and domain switching processes in 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3 at room temperature. The induced ferroelectric phase of MPB compositions in the (Bi1/2Na1/2)TiO3 BaTiO3 solid solution is metastable and the irreversible electric field-induced ferrielectric-to-ferroelectric phase transition is crucial to the poling process for piezoelectricity. Doping minor amounts of (K0.5Na0.5)NbO3 to this binary system makes the P4bm phase more stable, and the ferrielectric phase with nanodomains returns once the applied field is removed. The elimination of the remanent strain in these compositions with a reversible electric field-induced phase transition leads to recurring ultrahigh strains. The success of generating large strains with electric field through phase transition in PbZrO3-based and (Bi1/2Na1/2)TiO3 BaTiO3-based compositions can be duplicated in NaNbO3- based and AgNbO3-based antiferroelectric solid solutions. However, systematic investigations are needed to identify the best compositions. 29

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48 Table I Summary of the temperature-induced phase transitions of NaNbO3 characterized by X- ray diffraction (XRD), Raman spectroscopy, 102 dielectric analysis, 102 and neutron powder diffraction (NPD) 107. Phase Symmetry XRD NPD XRD/Raman/Dielectric Temp. (ºC) Symmetry Temp. (ºC) Symmetry Temp. (ºC) N Rhombohedral (R3c) < -100 Rhombohedral (R3c) < 7 Rhombohedral (R3c) < -23 P m: Monoclinic -23 ~ 137 P Orthorhombic (Pbcm) -100 ~ 360 Orthorhombic (Pbcm) -258 ~ 407 INC: Incommensurate 137 ~ 187 P O: Orthorhombic 187 ~ 360 R Orthorhombic (Pmnm) 360 ~ 480 Orthorhombic (Pbnm) 360 ~ 482 Orthorhombic (Pmnm) 360 ~ 480 S T 1 T 2 Orthorhombic (Pnmm) Orthorhombic (Ccmm) Tetragonal (P4/mbm) 480 ~ ~ ~ 640 Orthorhombic (Pbnm) Orthorhombic (Ccmm) Tetragonal (P4/mbm) 482 ~ 537 Orthorhombic (Pnmm) 537 ~ 592 Orthorhombic (Ccmm) 592 ~ 677 Tetragonal (P4/mbm) 480 ~ ~ ~ 640 U Cubic (Pm3m) > 640 Cubic (Pm3m) > 677 Cubic (Pm3m) >

49 Table II Summary of the temperature-induced phase transitions of AgNbO PE and AFE stands for paraelectric and antiferroelectric, respectively. Phase Temp. (ºC) Symmetry Tilting system Physical nature M 1 < 67 Pmc2 1 (a - b - c + )/(a - b - c - ) Uncompensated AFE (ferrielectric) M 2 67 ~ 267 Pbcm (a - b - c + )/(a - b - c - ) AFE M ~ 353 Pbcm (a - b - c + )/(a - b - c - ) AFE O ~361 Orthorhombic Undetermined PE O ~ 387 Cmcm a 0 b - c + PE T 387 ~ 579 P4/mbm a 0 b 0 c + PE C > 579 Pm 3 m a 0 a 0 a 0 PE 47

50 Figure Captions: Fig. 1. Structure models for PbZrO3-based antiferroelectrics. (a) The structure for PbZrO3, redrawn from Ref. [2]. The orthorhombic unit cell is indicated by the red box. (b) The structure for PbZrO3-based solid solutions with incommensurate modulations. The incommensurate modulation is suggested to be a mixture of commensurate modulations. 60 Fig. 2. Evolution of the satellite reflections surrounding the (120)c and (210)c fundamental diffraction spots in the <001>c-zone axis in Pb0.99Nb0.02[(Zr0.58Sn0.42)0.955Ti0.045]0.98O3. 60 (a) E = 0 kv/cm, (b) E = 8 kv/cm, (c) E = 20 kv/cm, (d) E = 30 kv/cm, (e) E = 40 kv/cm, and (f) E = 60 kv/cm. Fig. 3. Evolution of the <112>c-zone axis selected area diffraction pattern under applied electric fields in Pb0.99Nb0.02[(Zr0.55Sn0.45)0.94Ti0.06]0.98O3. 58 (a) E = 0 kv/cm, (b) E = 48 kv/cm, (c) E = 56 kv/cm. Fig. 4. The response of Pb0.99Nb0.02[(Zr0.57Sn0.43)0.94Ti0.06]0.98O3 (PNZST43/6.0/2) ceramics under unipolar electric fields up to 140kV/cm. 70 (a) The profile of the applied electric field. Point Z denotes the condition where the electric field-induced strains x33 and x11 are set to zero. (b) The strains x33 and x11 developed under electric fields in segments A, B, C, and D, each with a different color which corresponds to that in (a). Fig. 5. The electric field-induced transverse strain x11 in PNZST43/6.0/2, 43/6.3/2, 43/6.7/2 ceramics. The point where x11 starts to decrease in the induced ferroelectric phase with increasing field is marked. Fig. 6. The compressive stress-strain curves of the PNZST43/6.0/2 ceramic in its antiferroelectric (25 C), multiple cell cubic (175 C), and single cell cubic (250 C) states. Fig. 7. The polarization vs. electric field hysteresis loops with a peak field of 60 kv/cm in the PNZST43/6.0/2 ceramic under (a) uniaxial compressive pre-stresses, and (b) radial compressive pre-stresses

51 Fig. 8. The X-ray diffraction results from annealed ceramic specimens under electric fields at 25 C. 92 (a) The pseudo-cubic {200}c peak, and (b) the pseudo-cubic {222}c peak of PNZST43/6.0/2. (c) The {200}c peak, and (d) the {222}c peak of PNZST43/7.1/2. The evolution of the T(002) peak under different conditions is highlighted by the dashed boxes in (a) and (c). Fig. 9. Calculated spontaneous polarization PS as a function temperature using the data of Bi 3+ /Na +, Ti 4+ displacements and unit cell volume from Ref. [144]. Fig. 10. The phase diagram for the (1-x)(Bi1/2Na1/2)TiO3 xbatio3 binary system under (a) poled, 37 and (b) unpoled conditions. 154 The crystal structure and domain morphology at room temperature are highlighted as shaded boxes. Symbols of solid squares, open circles, and solid triangles represent Tm, TRE, and Td, respectively, determined from dielectric measurements. PE, AFE, and FE stand for paraelectric, antiferroelectric, and ferroelectric, respectively. Fig. 11. The P4bm uncompensated antiferroelectric (ferrielectric) phase with a nanodomain morphology. (a) The TEM bright field micrograph from an unpoled 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3 ceramic at room temperature. The bright arrow in the electron diffraction pattern 1 indicates the {ooe} superlattice spots. (b) A schematic diagram of the polar ferrielectric 2 nanodomains in (1-x)(Bi1/2Na1/2)TiO3 xbatio3, refined from Ref. [154]. The ferrielectric nanodomains (the grey islands in the diagram) with the P4bm symmetry are embedded in the undistorted cubic matrix (the white background in the diagram). The antiparallel arrow pairs with unequal amplitudes denote the cation displacements which fluctuate among the six equivalent <001>c directions. Fig. 12. The electric field in situ TEM study on the P4bm-to-P4mm phase transition and the domain switching in the P4mm phase in the 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3 ceramic at room temperature viewed with the <112>c-zone axis. (a) The bright field micrograph from 0.93(Bi1/2Na1/2)TiO3 0.07BaTiO3 ceramic at E = 0 kv/cm. (b) The electron diffraction 1 pattern reveals the presence of the {ooe} superlattice spots, indicating the P4bm 2 49

52 symmetry. (c) E = 5 kv/cm. The direction of the applied field is roughly along the bright arrow. (d) E = 7.5 kv/cm. (e) Selected area electron diffraction pattern from the lamellar domain area in the upper left portion of the grain shown in (d). (f) Diffraction pattern from the nanodomain area in the central portion of the grain. (g) E = 10 kv/cm. (h) E = 12.5 kv/cm. (i) E = 25 kv/cm. 50

53 (a) 4 4 (b) Fig. 1 51

54 Fig. 2 52

55 Fig. 3 53

56 150 (a) E (kv/cm) Seg. A Z Seg. B Seg. C Seg. D (b) x 33 (%) Seg. B Seg. D Seg. C x 11 (%) 0.02 Seg. A Time (second) Fig. 4 54

57 x 11 (%) PNZST43/6.3/2 PNZST43/6.0/2 PNZST43/6.7/ E (kv/cm) Fig. 5 55

58 0-50 PNZST43/6.0/2 Stress (MPa) C 175 C 250 C Strain (%) Fig. 6 56

59 P (μc/cm 2 ) (a) Axial (b) 0 MPa 75 MPa 100 MPa 250 MPa P (μc/cm 2 ) Radial 0 MPa 90 MPa 135 MPa 180 MPa 360 MPa E (kv/cm) Fig. 7 57

60 (a) T(200) 43/6.0/2 (b) T(222) R(200) Kα 2 Kα 2 0kV/cm Counts (a.u.) 0kV/cm T(002) Kα 2 Sequence R(222) R(222)+ Kα 2-40kV/cm -40kV/cm (c) Virgin T(200) 43/7.1/2 (d) Virgin R(222) Counts (a.u.) R(200) +5kV/cm 0kV/cm Kα 2 T(002) Kα 2 Sequence R(222)+ Kα 2 Kα T(222) 2-25kV/cm Kα 2-25kV/cm Virgin Virgin θ θ Fig. 8 58

61 16 Calculated P S (μc/cm 2 ) T ( o C) Fig. 9 59

62 (a) PE AFE FE FE (b) T ( o C) FE PE AFE relaxor AFE FE R3c complex domain P4bm nanodomain P4mm lamellar domain BNT x BT Fig

63 (b) <010> <100> Fig