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actuators Review Antiferroelectric Shape Memory Ceramics Kenji Uchino International Center for Actuators and Transducers, The Pennsylvania State University, University Park, PA 16801, USA; [email protected]; Tel.: +1-814-863-8035 Academic Editor: Delbert Tesar Received: 21 March 2016; Accepted: 11 May 2016; Published: 18 May 2016 Abstract: Antiferroelectrics (AFE) can exhibit a “shape memory function controllable by electric field”, with huge isotropic volumetric expansion (0.26%) associated with the AFE to Ferroelectric (FE) phase transformation. Small inverse electric field application can realize the original AFE phase. The response speed is quick (2.5 ms). In the Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 (PNZST) system, the shape memory function is observed in the intermediate range between high temperature AFE and low temperature FE, or low Ti-concentration AFE and high Ti-concentration FE in the composition. In the AFE multilayer actuators (MLAs), the crack is initiated in the center of a pair of internal electrodes under cyclic electric field, rather than the edge area of the internal electrodes in normal piezoelectric MLAs. The two-sublattice polarization coupling model is proposed to explain: (1) isotropic volume expansion during the AFE-FE transformation; and (2) piezoelectric anisotropy. We introduce latching relays and mechanical clampers as possible unique applications of shape memory ceramics. Keywords: antiferroelectrics; PNZST; shape memory ceramics; phase transformation; two-sublattice polarization coupling model; electrostriction 1. Development Trend of Solid State Actuators Development of solid state actuators aimed at replacing conventional electromagnetic motors has been remarkable in the following three areas: precision positioning, vibration suppression and miniature motors. Particular attention has been given to piezoelectric/electrostrictive ceramic actuators, shape memory devices of alloys such as Ni-Ti and Cu-Zn-Al, and magnetostrictive actuators using Terfenol D (Tb-Fe-Dy) alloys. Rigid strains induced in a piezoelectric ceramic by an external electric field have been used as ultraprecision cutting machines, in the Hubble telescope on the space shuttle and in dot-matrix printer heads [1–5]. There has also been proposed a parabolic antenna made of shape memory alloy, which is in a compactly folded shape when first launched on an artificial satellite, and subsequently recovers its original shape in space when exposed to the heat of the sun. Smart skins on submarines or military tanks were targets for solid state actuators [6]. In general, thermally-driven actuators such as shape memory alloys can show very large strains, but require large drive energy and exhibit slow response. Magnetic field-driven magnetostrictive devices have serious problems with size because of the necessity for the magnetic coil and shield. The subsequent Joule heat causes thermal dilatation in the system, and leakage magnetic field sometimes interferes with the operating hybrid electronic circuitry. On the contrary, electric field-driven piezoelectric and electrostrictive actuators have been most developed because of their high efficiency, quick response, compact size, no generation of heat or magnetic field, in spite of relatively small induced strains. This article reviews shape memory properties of ceramics, focusing on antiferroelectric lead zirconate titanate (Pb(Zr,Ti)O3 , PZT) based ceramics. The shape memory effect can be observed, not only in special alloys and polymers, but also in ceramics such as partially stabilized zirconia Actuators 2016, 5, 11; doi:10.3390/act5020011 www.mdpi.com/journal/actuators Actuators 2016, 5, 11 2 of 23 and ferroelectric lead zirconate titanate. A new concept of “shape memory” is proposed in this article: the elastic strain change associated with the electric field-induced phase transition is utilized instead of stress-induced or thermally-induced phase transitions, which enables many smarter actuator applications than the normal piezoelectrics or electrostrictors. The principle of the ceramic shape memory effect is described firstly in comparison with the case of alloys. Phase diagrams, domain reversal mechanisms and fundamental actuator characteristics are then discussed, followed by the practical distinctions between these new ceramics and shape memory alloys. Phenomenological explanations are described on the field-induced strain jump associated Actuators 2016, 5, 11 3 of 22 with the phase transformation, and on the piezoelectric anisotropy in a two-sublattice polarization coupling model. Finally, possible unique applications are proposed including a latching relay and a When the free energy of the antipolar state is close to the energy of the polar state, the dipole mechanical clamp. configuration is rearranged by the external electric field or stress. Figure 4 shows the applied electric This review paper is to provide author’s comprehensive idea on the AFE-FE phase transition by field versus induced polarization curves in PE, FE and AFE materials. A linear relation and a coupling experimental results [7] and theoretical approach [8]. hysteresis due to the spontaneous polarization reversal between positive and negative directions are observed in a PE and in a FE, respectively. On the contrary, an AFE exhibits an electric field-induced 2. Shape Memory Ceramics phase transition to a FE state above a critical field Et, accompanied by a hysteresis above Et. Reducing Shape memory effect observed not only in special or polymers, also in ceramics. the field down to zero, theis remanent polarization is not alloys observed, providingbut a so-called “double The shape memory effect in alloys (such as NiTiNOL) originates from a thermally-induced or hysteresis” curve in total. A large strain jump is theoretically associated with this phase transition, stress-induced “martensitic” phase transformation. After the alloy is deformed largely in the which also appears as a double hysteresis. In a certain case, once the FE state is induced, this FE state martensitic apparently permanent strainto is zero; recovered to its originaltoshape when heated to is sustainedstate, eventhis if the electric field is decreased this corresponds the “shape memory” cause the reverse Then,memory upon cooling, thethe shape to its state phenomenon. Themartensitic mechanismtransition. for the shape effect in AFEreturns ceramics is original schematically (Figure 1a). illustrated in Figure 1b. Figure 1. Comparison of the mechanisms for the shape memory effect in alloys (a) and in Figure 1. Comparison of the mechanisms for the shape memory effect in alloys (a) and in antiferroelectric ceramics (b). antiferroelectric ceramics (b). A similar effect is anticipated in ceramics with a certain phase transition, i.e., a “ferroelastic” phase transition. Reyes-Morel et al. demonstrated the shape memory effect, as well as superelasticity in a CeO2 -stabilized tetragonal zirconia (ZrO2 ) polycrystal [9]. Under uniaxial compression, the specimen Ti 4+ deforms plastically owing to a stress-induced tetragonal to monoclinic transition in Ce-doped zirconia. Ba 2+ O 2- T>T C T<T C T C : Curie temperature field versus induced polarization curves in PE, FE and AFE materials. A linear relation and a hysteresis due to the spontaneous polarization reversal between positive and negative directions are observed in a PE and in a FE, respectively. On the contrary, an AFE exhibits an electric field-induced phase transition to a FE state above a critical field Et, accompanied by a hysteresis above Et. Reducing the field down to zero, the remanent polarization is not observed, providing a so-called “double Actuators 2016, 5, 11 3 of 23 hysteresis” curve in total. A large strain jump is theoretically associated with this phase transition, which also appears as a double hysteresis. In a certain case, once the FE state is induced, this FE state is sustained deformation even if the electric field is decreased to load zero;drops, this corresponds the “shape memory” Continuous is interrupted by repeated providing atonearly constant upper phenomenon. TheGPa. mechanism forunloading, the shape large memory effectplastic in theaxial AFEstrain ceramics is schematically yield stress of 0.7 Even after residual («0.7%) is observed. illustrated inheating Figure 1b. Subsequent produces a gradual recovery of the residual strain due to the reverse phase transition starting at 60 ˝ C and a burst of strain recovery at 186 ˝ C. The burst is very sharp, above which approximately 95% of the prior axial strain is recovered. Though recent conventional shape memory studies based on Martensitic phase transformation in structural ceramics can be found [10], we do not discuss them because they are out of our objective; that is, electric-field controllable shape memory. Ceramics “shape memory” has also been reported for certain ferroelectricity-related transitions, namely paraelectric–ferroelectric [11] and antiferroelectric (AFE)–ferroelectric (FE) transitions [12,13]. The former thermally-induced transition revealed a shape-recovery phenomenon similar to zirconia ceramics. On the contrary, the latter is related to an electric field-induced transition, and exhibits large displacement (0.4%) with a “digital” characteristic or a shape memory function, which is in contrast to the essentially “analogue” nature of conventional piezoelectric and electrostrictive strains with 0.1% in magnitude (Figure 1b). Note that the “memory” terminology is different in the AFE shape memory; that is, field-induced FE expanded shape is “memorized” even after removing the field, and to recover the original AFE small shape, we apply a small reverse electric field. Let us review ferroelectricity and antiferroelectricity here for further understanding [14]. Figure 2 shows the crystal structure changes in a typical ferroelectric, barium titanate (BaTiO3 , BT). At an elevated temperature above the transition point of 130 ˝ C (Curie temperature, denoted as TC ), BT shows a cubic “perovskite” structure (paraelectric (PE) phase), as illustrated in Figure 2a. With decreasing temperature below TC , the cations (Ba2+ and Ti4+ ) shift against the anions (O2´ ) as illustrated in Figure 2b, exhibiting spontaneous polarization as well as spontaneous strain (ferroelectric (FE) phase). Notice that the electric dipole moments in each crystal unit cell are arranged in parallel in a ferroelectric. On the other hand, there exists an antiferroelectric where the dipoles are arranged antiparallel to each 1. Comparison of polarization. the mechanisms for the shapethe memory effect in alloys (a) and models in otherFigure so as not to produce net Figure 3 shows antipolar dipole arrangement antiferroelectric ceramics (b). in contrast to nonpolar and polar models. Ti 4+ Ba 2+ O 2- T>T C T<T C T C : Curie temperature (a) (b) Figure 2. 2. Crystal paraelectric state and in in the the ferroelectric ferroelectric Figure Crystal structures structures of of barium barium titanate titanate in in the the paraelectric state (a) (a) and 4 of 22 state (b). state (b). Actuators 2016, 5, 11 Figure 3. Two antipolar dipole arrangement models (c) in contrast to nonpolar (a) and polar (b) models. Figure 3. Two antipolar dipole arrangement models (c) in contrast to nonpolar (a) and polar (b) models. Actuators 2016, 5, 11 Actuators 2016, 5, 11 4 of 23 4 of 22 When the free energy of the antipolar state is close to the energy of the polar state, the dipole configuration is rearranged by the external electric field or stress. Figure 4 shows the applied electric field versus induced polarization curves in PE, FE and AFE materials. A linear relation and a hysteresis due to the spontaneous polarization reversal between positive and negative directions are observed in a PE and in a FE, respectively. On the contrary, an AFE exhibits an electric field-induced phase transition to a FE state above a critical field Et , accompanied by a hysteresis above Et . Reducing the field down to zero, the remanent polarization is not observed, providing a so-called “double hysteresis” curve in total. A large strain jump is theoretically associated with this phase transition, which also appears as a double hysteresis. In a certain case, once the FE state is induced, this FE state is sustained even if the electric field is decreased to zero; this corresponds phenomenon. Figure 3. Two antipolar dipole arrangement models to (c)the in “shape contrast memory” to nonpolar (a) and polarThe (b) models. mechanism for the shape memory effect in the AFE ceramics is schematically illustrated in Figure 1b. Figure4. 4.Electric Electricfield fieldvs.vs.induced inducedpolarization polarizationcurves curvesin:in:paraelectric paraelectric(a); (a);ferroelectric ferroelectric(b); (b);and and Figure antiferroelectric materials. antiferroelectric (c)(c) materials. SamplePreparation Preparationand andExperiments Experiments 3.3.Sample Thissection sectionintroduces introducessample samplepreparation preparationand andexperimental experimentalprocedures proceduresofofshape shapememory memory This 3 rich compositions) have ceramics. Antiferroelectric perovskite ceramics from the PZT system (PbZrO ceramics. Antiferroelectric perovskite ceramics from the PZT system (PbZrO3 rich compositions) have been investigated, in which successive phase transitions a PE, through to a appear FE state been investigated, in which successive phase transitions from from a PE, through an AFE,antoAFE, a FE state appear with decreasing temperature [15]. PZTPb ceramics Pb 0.99NbSn 0.02[(Zr 0.6Ti Sn 0.4)1-yO Ti y(0.05 ] 0.98O3<(0.05 <y< with decreasing temperature [15]. PZT ceramics Nb [(Zr ) ] y < 0.09) 0.99 0.02 0.6 0.4 1-y y 0.98 3 0.09) (abbreviated hereafter as PNZST) were prepared from reagent grade oxide raw materials, (abbreviated hereafter as PNZST) were prepared from reagent grade oxide raw materials, PbO, Nb2PbO, O5 , Nb22,OSnO 5, ZrO 2, SnO 2 and TiO 2. We introduced “Sn” to stabilize the antiferroelectric phase, and “Nb” to ZrO and TiO . We introduced “Sn” to stabilize the antiferroelectric phase, and “Nb” to increase 2 2 ˝ increase the sinterability basically. Bulk samples were prepared by hot-press sintering at 1200 °C. the sinterability basically. Bulk samples were prepared by hot-press sintering at 1200 C. Unimorphs Unimorphs were with two thin rectangular mmmm × thick) 7 mmbonded × 0.2 mm thick) were fabricated withfabricated two thin rectangular plates (22 mm ˆplates 7 mm(22 ˆ 0.2 together. bonded together. mmmm × 4.3 mmwith × 4.3 mmlayer thick) with layer 140 were μm in Multilayer samplesMultilayer (12 mm ˆsamples 4.3 mm(12 ˆ 4.3 thick) each 140 µmeach in thickness thickness were also fabricated using the tape casting technique: Those with platinum electrodes were also fabricated using the tape casting technique: Those with platinum electrodes were sintered at a ˝ sintered at aoftemperature temperature about 1250 of C.about 1250 °C. Thefield-induced field-inducedlattice latticechange changewas wasdetermined determinedbybyX-ray X-raydiffraction. diffraction.The Thesurfaces surfacesofofthe thethin thin The ceramic plate (t = 0.2 mm) were coated with carbon evaporated electrode. X-ray diffraction patterns ceramic plate (t = 0.2 mm) were coated with carbon evaporated electrode. X-ray diffraction patterns wererecorded recordedatatthe theelectrode electrodesurface surfacefor forseveral severaldifferent differentbias biasvoltages. voltages.The Thedisplacement displacementororstrain strain were induced by an alternating electric field (0.05 Hz) was detected with a strain gauge (Kyowa Dengyo, induced by an alternating electric field (0.05 Hz) was detected with a strain gauge (Kyowa Dengyo, Tokyo, Japan, KFR-02-C1-11), a magneto-resistive potentiometer (Midori Precisions, Tokyo, Japan, KFR-02-C1-11), a magneto-resistive potentiometer (Midori Precisions, Tokyo,Tokyo, Japan, Japan, LP-1 or a differential transformer-type Tokyo, Japan,For No. Fordisplacement the dynamic U)LP-1 or a U) differential transformer-type (Millitron, (Millitron, Tokyo, Japan, No. 1202). the1202). dynamic unimorphs, aeddy noncontact-type eddy current displacement sensor (Kaman, indisplacement unimorphs, a in noncontact-type current displacement sensor (Kaman, Colorado Springs, CO, Colorado Springs, CO, USA, KD-2300) was used. The electric polarization and the permittivity were measured with a Sawyer–Tower circuit and an impedance analyzer (Hewlett-Packard, now Agilent, Santa Clara, CA, USA, 4192A), respectively. To observe the domain structures, a CCD microscope Actuators 2016, 5, 11 5 of 23 USA, KD-2300) was used. The electric polarization and the permittivity were measured with a Sawyer–Tower Actuators 2016, 5, 11circuit and an impedance analyzer (Hewlett-Packard, now Agilent, Santa Clara,5 CA, of 22 USA, 4192A), respectively. To observe the domain structures, a CCD microscope with a magnification of ˆ1300 applied to aofthinly-sliced sample of grain (>50sample µm) PNZST ceramics withμm) interdigital with awas magnification ×1300 was applied tolarge a thinly-sliced of large grain (>50 PNZST electrodes on the surface. electrodes on the surface. ceramics with interdigital Figure Figure5a 5ashows showsaaPZT PZTphase phasediagram diagramwith withaaparticular particularinterest interestin inPbZrO PbZrO33 (PZ) (PZ) rich rich region, region, and and 2+ ionic shift in a PZ unit cell to visualize the antipolar structure Figure5b 5billustrates illustratesthe thePb Pb2+ structure [16]. [16]. Figure (a) (b) Figure5.5. (a) (a)PZT PZTsystem systemphase phasediagram diagramwith withaaparticular particularinterest interestin inthe thePZ PZrich richregion; region;and and(b) (b)Pb Pb2+2+ Figure ionicshift shiftin inaaPZ PZunit unitcell cellto tovisualize visualizethe theantipolar antipolarstructure structure[16]. [16]. ionic 4. Fundamental Properties of the Electric Field-Induced Phase Transition 4. Fundamental Properties of the Electric Field-Induced Phase Transition The antiparallel arrangement of electric dipoles in the sublattices of AFE is rearranged in parallel The antiparallel arrangement of electric dipoles in the sublattices of AFE is rearranged in parallel by an applied electric field, and the dielectric and electromechanical properties are changed by an applied electric field, and the dielectric and electromechanical properties are changed remarkably remarkably at this phase change. at this phase change. 4.1. Electric Electric Field Field Dependence Dependence of of Lattice Lattice Parameters Parameters 4.1. The field-induced field-induced change change in in lattice lattice parameters parameters for for aa sample Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 with The sample Pb Pb0.99 0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 y = 0.06 plotted in Figure 6a [7].6aThe transition from from the AFE theto FEthe phase gives gives rise torise the with y = is 0.06 is plotted in Figure [7].forced The forced transition theto AFE FE phase simultaneous increase of a and c in the perovskite unit cell, thereby keeping the tetragonality, c/a, to the simultaneous increase of a and c in the perovskite unit cell, thereby keeping the tetragonality, nearly constant. Since the the angle γ makes onlyonly a negligible contribution to the volume change, the c/a, nearly constant. Since angle γ makes a negligible contribution to the volume change, −4 strain change at the transition is nearly isotropic with with a magnitude of ΔL/L 8.5 ×=108.5. Though the strain change at phase the phase transition is nearly isotropic a magnitude of =∆L/L ˆ 10´4 . we observe minor changes in the parameters c, c/a and γ between AFE-FE On-set and FE-AFE OffThough we observe minor changes in the parameters c, c/a and γ between AFE-FE On-set and FE-AFE set electric fields, wewe cannot discuss further on aa Off-set electric fields, cannot discuss furtherononthis, this,because becausethe the measurement measurement was was made made on polycrystalline sample and the effective electric field on a certain crystal orientation in each grain was polycrystalline sample and the effective electric field on a certain crystal orientation in each grain distributing. was distributing. The intensity change of the X-ray reflections with the application of an electric field suggests that the spontaneous polarization in the FE state lies in the c-plane, parallel with the perovskite [1 1 0] axis, and that the sublattice polarization configuration in the AFE state is very similar to that of PbZr03 (see Figure 5b) [16]. Figure 6b illustrates the simplest two-sublattice model. Actuators 2016, 5, 11 6 of 23 Actuators 2016, 5, 11 6 of 22 (a) (b) Figure 6. (a) Variation of lattice parameters with bias electric field at room temperature (y = 0.06); and Figure 6. (a) Variation of lattice parameters with bias electric field at room temperature (y = 0.06); and (b) two-sublattice model of the polarization configuration for the AFE and FE states. (After Uchino (b) two-sublattice model of the polarization configuration for the AFE and FE states. (After Uchino and and Nomura Nomura [7]). [7]). 4.2. Temperature Dependence of the Permittivity The intensity change of the X-ray reflections with the application of an electric field suggests that Figure 7 shows change in of the permittivity with temperature under with various electric[1field in a the spontaneous polarization FE state lies in the c-plane, parallel the bias perovskite 1 0] axis, composition y = 0.06, Pb 0.99 Nb 0.02 [(Zr 0.6 Sn 0.4 ) 0.94 Ti 0.06 ] 0.98 O 3 [7]. With an increase in temperature the ferroand that the sublattice polarization configuration in the AFE state is very similar to that of PbZr03 to antiferroelectric is clearly observed in a poled specimen (see Figure 5b) [16].phase Figuretransition 6b illustrates the simplest two-sublattice model. as a permittivity hump. Note that the reverse antiferro- to ferroelectric transition occurs with a considerably large hysteresis 4.2. Dependence of theThough Permittivity withTemperature temperature decreasing. we observe another narrow pseudo-cubic antiferroelectric phase (which may correspond Aβ Phase inwith Figure 5a) just below the various Neel temperature under Figure 7 shows change oftopermittivity temperature under bias electric fieldsmall in a bias electric field, we will not discuss its details in this paper. composition y = 0.06, Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 [7]. With an increase in temperature the 8a shows the relation between is theclearly electric field andinpolarization. The typical double and ferro-Figure to antiferroelectric phase transition observed a poled specimen as a permittivity ferroelectric hysteresis areantiferroobserved to at room temperature and −76 °C, with respectively, while a hump. Note that the loops reverse ferroelectric transition occurs a considerably transitive shape with humps is observed at intermediate temperatures. large hysteresis with temperature decreasing. Though we observe another narrow pseudo-cubic The transitive process can may be observed moretoclearly in theinstrain curve. Figure 8b shows the antiferroelectric phase (which correspond Aβ Phase Figure 5a) just below the Neel transversely under induced strains. The forced transition from AFE to FEin at temperature small bias electric field, we will not discuss its details thisroom paper.temperature is characterized by a huge strain discontinuity. On the other hand, a typical ferroelectric butterfly-type Figure 8a shows the relation between the electric field and polarization. The typical double and hysteresis is observed at −76 °C, corresponding to polarization reversal. It is important to note that ferroelectric hysteresis loops are observed at room temperature and ´76 ˝ C, respectively, while a the strain discontinuities associated with the phase transition have the same positive expansion in transitive shape with humps is observed at intermediate temperatures. both longitudinal and transverse directions with respect to the electric field (i.e., the apparent The transitive process can be observed more clearly in the strain curve. Figure 8b shows Poisson’s ratio is negative!), while the piezo-striction is negative and positive in the transverse and the transversely induced strains. The forced transition from AFE to FE at room temperature is longitudinal directions, respectively, which will further be discussed in Section 4.4. characterized by a huge strain discontinuity. On the other hand, a typical ferroelectric butterfly-type The shape memory effect is observed on this loop at −4 °C. When a large electric field is applied hysteresis is observed at ´76 ˝ C, corresponding to polarization reversal. It is important to note that the to the annealed AFE sample, a massive strain ΔL/L of about 7 × 10−4 is produced and maintained strain discontinuities associated with the phase transition have the same positive expansion in both metastably even after the field is removed. After applying a small reverse field or thermal annealing, longitudinal and transverse directions with respect to the electric field (i.e., the apparent Poisson’s the original AFE shape is observed. ratio is negative!), while the piezo-striction is negative and positive in the transverse and longitudinal The reverse critical field related to the FE-AFE transition is plotted with solid lines in the phase directions, respectively, which will further be discussed in Section 4.4. diagram for the sample with y = 0.06 in Figure 9, in which the temperature-field points are based on The shape memory effect is observed on this loop at ´4 ˝ C. When a large electric field is applied the measurements in permittivity, polarization and strain. In the temperature range from −30 °C to to the annealed AFE sample, a massive strain ∆L/L of about 7 ˆ 10´4 is produced and maintained 10 °C, a hump-type hysteresis in the field versus polarization curve and an inverse hysteresis in the metastably even after the field is removed. After applying a small reverse field or thermal annealing, field-induced strain are observed: this has previously often been misinterpreted as another AFE the original AFE shape is observed. phase different from the phase above 10 °C. The annealed state below −30 °C down to −200 °C is AFE. However, once the FE state is induced, the AFE phase is never observed during a cycle of rising and falling electric field. The critical field line for the FE to AFE transition (the solid line) in the Actuators 2016, 5, 11 Actuators 2016, 5, 11 7 of 22 7 of 22 temperature range −30 °C to 10 °C intersects the coercive field line for the + FE to − FE reversal (the 7 of 23 temperature range −30 dashed line) below −30 °C °C.to 10 °C intersects the coercive field line for the + FE to − FE reversal (the dashed line) below −30 °C. Actuators 2016, 5, 11 Figure Change of of permittivity permittivity with with temperature temperature under under various various bias bias electric Figure 7. 7. Change electric field field in in PNZST PNZST (y = 0.06) [7]. Figure 7. Change of permittivity with temperature under various bias electric field in PNZST (y = 0.06) [7]. (y = 0.06) [7]. (a) (a) (b) (b) Figure 8. Polarization (a) and transverse elastic strain (b) induced by electric field for several Figure 8. Polarization transverse electric field field for for several several temperatures in PNZST(a) (y 0.06). Figure 8. Polarization (a)=and and transverse elastic elastic strain strain (b) (b) induced induced by by electric temperatures in in PNZST PNZST (y (y == 0.06). 0.06). temperatures The reverse critical field related to the FE-AFE transition is plotted with solid lines in the phase diagram for the sample with y = 0.06 in Figure 9, in which the temperature-field points are based on the measurements in permittivity, polarization and strain. In the temperature range from ´30 ˝ C to 10 ˝ C, a hump-type hysteresis in the field versus polarization curve and an inverse hysteresis in Actuators 2016, 5, 11 8 of 23 the field-induced strain are observed: this has previously often been misinterpreted as another AFE phase different from the phase above 10 ˝ C. The annealed state below ´30 ˝ C down to ´200 ˝ C is AFE. However, once the FE state is induced, the AFE phase is never observed during a cycle of rising and falling electric field. The critical field line for the FE to AFE transition (the solid line) in the temperature range ´30 ˝ C to 10 ˝ C intersects the coercive field line for the + FE to ´ FE reversal (the dashed line) Actuators 2016, 5, 11 8 of 22 below ´30 ˝ C. (a) Figure 9. (a) Phase diagram (b) on the temperature-bias electric field plane for Figure 9. (a) Phase on the temperature-bias electric field plane for Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Pb0.99Nbdiagram 0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3). (b) Schematic 3D view for improved understanding of the Antiferroelectric – Ferroelectric (AFE-FE) transformation hysteresis. Ti0.06 ]0.98 O3 ). (b) Schematic 3D view for improved understanding of the Antiferroelectric – Ferroelectric (AFE-FE) transformation hysteresis. 4.3. Composition Dependence of the Induced Strain Figure 10 shows the strain curves induced transversely by the external field at room temperature 4.3. Composition Dependence of the Induced Strain [8]. The molar fraction of Ti, y, is increased from 0.06 for samples of several different compositions (Figure 10a) to 0.065 (Figure 10c). The initial state was obtained by annealing at 150 °C, which is above Figure 10theshows the strain curves induced transversely by the external field at room temperature Curie (or Neel) temperature for all the samples. A typical double hysteresis curve (Type I) is for samples of several different compositions [8].jumps The in molar fraction of Ti, y, is increased from 0.06 observed in the sample containing y = 0.06. Large the strain are observed at the forced phase In comparison, the strain change with˝ C, which is the AFE to the FE initial phase (ΔL/L = 8was × 10−4). (Figure 10a) transitions to 0.065 from (Figure 10c). The state obtained by annealing at 150 electric field in either the AFE or FE state is rather small: this suggests a possible application for the above the Curie (or Neel) temperature fortransducer, all the samples. A typical double hysteresis curve (Type I) is material as a “digital” displacement having OFF/ON displacement states. The difference observed in the sample containing y = 0.06.in Large jumps in the areinobserved at theatforced phase in the strain between that occurring the initial state and thatstrain appearing a cyclic process 4 ). In comparison, E = 0 kV/cm is also and will(∆L/L be explained the´following section. transitions from the AFE tonoteworthy the FE phase = 8 ˆin10 the strain change with In the sample with y = 0.063, a Ti concentration slightly higher than that just described, the fieldelectric field induced in either AFE or FE state is AFE rather this suggests possible application for the FE the phase will not return to the statesmall: even after decreasing the afield to zero (Type II, 10b): this is called “memorizing” the FEhaving strain state. In order todisplacement obtain the initial AFE state,The a material as a Figure “digital” displacement transducer, OFF/ON states. difference reverse that bias field is required.inFigure showsstate the strain the sample with 0.065, process at in the strain small between occurring the 10c initial andcurve thatforappearing in ya= cyclic which exhibits irreversible characteristics during an electric field cycle (Type III). The initial strain E = 0 kV/cm state is also noteworthy will be explained in°C. the following section. can only be recoveredand by thermal annealing up to 50 Datawith derived these strain may be utilizedslightly to construct a phase than diagram of thejust system In the sample yfrom = 0.063, a Ticurves concentration higher that described, the Pb0.99Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature with respect to the composition y and the field-induced FE phase will not return to the AFE state even after decreasing the field to zero (Type II, applied electric field E (Figure 11). If the Ti concentration of the horizontal axis is redefined in terms Figure 10b): of this is calledand “memorizing” the FEdirection, strain this state. Indiagram orderisto obtain the temperature evaluated in the opposite phase topologically the initial same AFE state, as the phase diagram of Figure 9. The key10c feature of thisthe phase diagram is thefor existence of the three a small reverse bias field is required. Figure shows strain curve the sample with y = 0.065, phases, namely the AFE, the positively poled FE (+ FE), and the negatively poled FE (− FE) phases, which exhibits irreversible characteristics during an electric field cycle (Type III). The initial strain state the boundaries of which are characterized by the two transition lines corresponding to rising and can only be recovered byfields. thermal annealing up to 50 ˝ C. falling electric The composition regions curves I and IV exhibit the utilized typical double hysteresis and ferroelectric domainof the system Data derived from these strain may be to construct a phase diagram reversal, respectively. The shape memory effect is observed in regions II and III. It is important to Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 at room temperature with respect to the composition y and the consider the magnitude of the electric field associated with the + FE → AFE transition (notice the applied electric fieldofEthe (Figure If consider the Ti concentration of the horizontal axis is after redefined in terms direction arrow!).11). Let us the transition process under an inverse bias field the + FE is induced by the positive electric field. If the magnitude of the field for the + FE → AFE transition of temperature and evaluated in the opposite direction, this phase diagram is topologically the same smaller than the coercive field for + FE → − FE (Region II, 0.0625 < y < 0.065), the AFE phase appears as the phase is diagram of Figure 9. The key feature of this phase diagram is the existence of the three once under a small inverse field, then the − FE phase is induced at the AFE → − FE transition field. In phases, namely the AFE, the positively poled FE (+ FE), and the negatively poled FE (´ FE) phases, the boundaries of which are characterized by the two transition lines corresponding to rising and falling electric fields. Actuators 2016, 5, 11 9 of 22 Actuators 2016, 5, 11 9 of 22 this case, the shape memory is reversible to the initial state only with the application of a reverse this case, the(Type shapeII): memory is reversible theother initial stateif the only+ FE with of is a reverse electric field this is very useful! Ontothe hand, → the − FEapplication coercive field smaller electric II):field this (Region is very useful! On the hand, the + FEreversal → − FE to coercive field iswithout smaller than thefield + FE(Type → AFE III, 0.0625 < Y other < 0.085), theifdomain − FE appears Actuators 2016, 5, 11 9 of 23 than the +through FE → AFE < 0.085), domain reversal to − FE annealing appears without passing thefield AFE(Region phase. III, The0.0625 initial< Ystate can the be obtained by thermally up to passing the AFE phase. The initial state can be obtained by thermally annealing up to 50–70 °Cthrough (Type III). 50–70 °C (Type III). Figure 10. 10. Transverse Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature: (a) for Figure Transverse induced induced strains strainsin inPb Pb0.99 0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 at room temperature: y =for 0.06; for (b) y =for 0.063; (c) for y = for 0.065. Figure Transverse induced strains Pby0.99=Nb 0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature: (a) for (a) y10. =(b) 0.06; y = and 0.063; and (c)in 0.065. y = 0.06; (b) for y = 0.063; and (c) for y = 0.065. Figure 11. Phase diagram of Pb0.99Nb0.02[(Zr0.6Sn0.4)1-yTiy]0.98O3 at room temperature with respect to the Figure 11. diagram of Nb0.02 [(Zr0.6E. Oroom temperature respect to y ]O composition y and the applied electric field 0.02 0.6 1-yy]Ti 0.98 3 at room Figure 11. Phase Phase diagram of Pb Pb0.99 0.99 Nb [(Zr SnSn 0.40.4 )1-y)Ti 0.98 3 at temperature withwith respect to the the composition y and applied electric field composition y and the the applied electric field E. E. 4.4. Domain Reorientation Mechanism in Antiferroelectrics 4.4. Domain Reorientation Mechanism IV in Antiferroelectrics The composition regions exhibit the typical double hysteresis andthey ferroelectric domain Antiferroelectrics cannotI and be poled macroscopically. However, since have sublattice reversal, respectively. The shape memory effect is observed in regions II and III. It is important to Antiferroelectrics cannotwith be the poled macroscopically. However, since they have sublattice polarizations closely coupled lattice distortion, it is possible to consider ferroelastic domain consider the in magnitude of thewith electric field associated with the + FEtoÑconsider AFE transition (notice polarizations closely coupled the is lattice distortion, it is possible ferroelastic domain orientations antiferroelectrics. This a possible approach to understanding the difference in the the direction of the arrow!). Let us consider the transition process under an inverse bias field after the FE orientations in antiferroelectrics. This is a possible approach to understanding the difference in+ the is induced by the positive electric field. If the magnitude of the field for the + FE Ñ AFE transition is smaller than the coercive field for + FE Ñ ´ FE (Region II, 0.0625 < y < 0.065), the AFE phase appears once under a small inverse field, then the ´ FE phase is induced at the AFE Ñ ´ FE transition field. In this case, the shape memory is reversible to the initial state only with the application of a reverse Actuators 2016, 5, 11 10 of 23 electric field (Type II): this is very useful! On the other hand, if the + FE Ñ ´ FE coercive field is smaller than the + FE Ñ AFE field (Region III, 0.0625 < Y < 0.085), the domain reversal to ´ FE appears Actuators 2016, 5, 11 10 of 22 without passing through the AFE phase. The initial state can be obtained by thermally annealing up to ˝ C (Type III). 50–70 strain between that occurring in the initial state and that arising in a cyclic process, as shown in Figure 12b (retraced from Figure 10a). 4.4. Domain Reorientation Mechanism in Antiferroelectrics Figure 12a shows the longitudinal and transverse strains induced in the sample y = 0.075 in Antiferroelectrics cannot be poled macroscopically. have sublattice Region III [8]. The strain induction process can be consideredHowever, to consistsince of twothey stages: first, there is −4 polarizations closely coupled with the lattice distortion, it is possible to consider ferroelastic domain an isotropic volume expansion (0 → A, A’: ΔL/L = 8 × 10 ) due to the AFE to FE phase transition orientations in antiferroelectrics. This is a possible approach to understanding difference the (remember Figure 6a, where the perovskite cell expands almost isotropically bythe ΔL/L = 8 × 10−4in ); and strain between the initial state and in a cyclic process, in second, there isthat an occurring anisotropicinstrain associated withthat the arising FE domain rotation (A → as B, shown A’ → B’: −4 −4 Figure 12b (retraced from Figure 10a). x3 = 9×10 , x1 = −3 × 10 ). (a) (b) Figure 12. (a) Longitudinal and transverse induced strains in the sample Figure 12. (a) Longitudinal and transverse induced strains in the sample Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.925 Pb0.99Nb0.02[(Zr0.6Sn0.4)0.925Ti0.075]0.98O3; and (b) transverse strains in Pb0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3. Ti0.075 ]0.98 O3 ; and (b) transverse strains in Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 . This process is shown schematically as the antiferroelectric domain reorientation in Figure 13, Figure 12a shows the and transverse strains the is sample y = 0.075 in where a probable model forlongitudinal the double-hysteresis sample (Typeinduced I, Figurein12b) also illustrated. In Region III [8]. The strain induction process can be considered to consist of two stages: first, the Type I PNZST, in comparison with the original annealed AFE state, once the ferroelectricthere state is is ´4 ) due to the AFE to FE phase transition an isotropic volume expansion (0 Ñ A, A’: ∆L/L = 8 ˆ 10 electrically induced, the same AFE state exhibits lower strain status along the transversal direction 4 ); (remember Figurestatus 6a, where thethe perovskite cell expands isotropically 10´ (or higher strain along electric field). Taking almost into account Figureby 6a,∆L/L a/c = > 81,ˆwe can and second, the there is anreduction anisotropic strain associated withphase the FEatdomain rotation (Athe Ñ B, A’ Ñthat B’: understand strain in Figure 12b in the AFE E = 0 kV/cm from model ´ 4 ´ 4 xthe 9ˆ10 , xorientation ). 3 =antipolar 1 = ´3 ˆ 10is re-arranged along the electric field direction. As previously pointed out, This process is shown schematically as the through antiferroelectric domain in Figure 13, even for AFEs, domain reorientation is possible the forced phase reorientation transition to FEs. where a probable model forinthe double-hysteresis sample I, Figure 12b) is also illustrated. Domain configuration PNZST y = 0.063 (Type II) was(Type observed as a function of electric field In the Type I PNZST, in comparison with the original annealed AFE state, once the ferroelectric at room temperature [17]. No clear domains were observed in the initial state obtained by annealing state is electrically induced, the same AFE state exhibits lower strain alongabove the transversal the sample at 70 °C. As the electric field increased, clear domain wallsstatus appeared 20 kV/cm, direction (or higher strain status along the electric field). Taking into account Figure 6a, a/c > 1, we can arranged almost perpendicularly to the electric field direction. This value of electric field is coincident understand the strain reduction in Figure 12b in the AFE phase at E = 0 kV/cm from the model that with the critical field that can cause the transition from AFE to FE. Therefore, these domain walls the antipolar orientation is re-arranged along the electric field direction. As previously pointed were caused by the induced ferroelectricity. The domain walls did not diminish whilst removingout, the even forfield, AFEs,because domainthe reorientation possible through the forced to FEs. electric sample hasisthe shape memory effect. Thephase walls transition disappeared when slightly Domain inexpected PNZST yin= the 0.063 (Type II) was observed as a function of electric field negative bias configuration was applied, as Type II specimen. at room [17]. No response clear domains were observed the initial state obtained by annealing Let temperature us discuss the strain time relating with theindomain reorientation. As we discussed ˝ C. As the electric field increased, clear domain walls appeared above 20 kV/cm, the sample at 70 above, there are two stages for the strain generation in the shape memory ceramics: (1) phase arranged almost from perpendicularly the and electric direction. Thisinduced value of ferroelectric electric field is coincident transformation the AFE totoFE; (2) field alignment of the domains. In with the critical field that can cause the transition from AFE to FE. Therefore, these domain walls were particular, since the phase transformation requires a “latent” heat, a longer response time is expected. caused the induced ferroelectricity. Thestrain domain walls did diminish whilstfrequency removing measure the electric Figure by 14 shows the transverse induced response as anot function of drive in field, because the sample has the shape memory effect. The walls disappeared when slightly negative the Type I sample, Pb0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3. The phase transformation seems to follow up bias wasHz. applied, as expected inHz, the the Type II specimen. to 5–10 However, above 50 induced FE phase may not return to the AFE phase anymore during the short interval, exhibiting a piezoelectric butterfly-like transverse strain curve. This time delay due to the latent heat will be discussed again in Section 7. Actuators 2016, 5, 11 Actuators 2016, 5, 11 11 of 23 11 of 22 Actuators 2016, 5, 11 11 of 22 Figure13. 13.Schematic Schematicillustration illustration of the antiferroelectric domain reorientation associated with the Figure of the antiferroelectric domain reorientation associated with the forced forcedtransition. phase transition. phase Let us discuss the strain response time relating with the domain reorientation. As we discussed above, there are two stages for the strain generation in the shape memory ceramics: (1) phase transformation from the AFE to FE; and (2) alignment of the induced ferroelectric domains. In particular, since the phase transformation requires a “latent” heat, a longer response time is expected. Figure 14 shows the transverse induced strain response as a function of drive frequency measure in the Type I sample, Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 . The phase transformation seems to follow up to 5–10 Hz. However, above 50 Hz, the induced FE phase may not return to the AFE phase anymore Figure 13. Schematic illustration of the antiferroelectric domain reorientation associated with the during the short interval, exhibiting a piezoelectric butterfly-like transverse strain curve. This time forced phase transition. delay due to the latent heat will be discussed again in Section 7. Figure 14. Transverse induced strain response as a function of drive frequency measure in Pb0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3. 4.5. Pressure Dependence of the Field-Induced Strain One of the most important criteria for an actuator is reliable and stable driving under a large applied stress, as required for its application as a positioner in precision cutting machinery. Figure 15 shows the longitudinally induced strains in a shape memory sample of PNZST y = 0.0707 in both the AFE and FE states at room temperature plotted as a function of uniaxial compressive stress for several electric fields [13]. For comparison, a similar plot for a lead magnesium niobate Figure 14.ceramic Transverse induced response as a function of drive frequency measure in (PMN) based (Pb(Mg 1/3Nb2/3strain )0.65Ti0.35 O3, a well-known electrostrictive material) is also shown. Figure 14. Transverse induced strain response as a function of drive frequency measure in Pb Nb [(Zr Sn ) Ti ] O . Roughly speaking, the strain versus stress curve for the AFE PNZST ceramic is shifted along the 0.02 0.6 0.4 0.94 0.06 0.98 3 0.99Nb0.02[(Zr0.6Sn0.4)0.94Ti0.06]0.98O3. Pb0.99 strain axis with respect to that for PMN due to the difference between the spontaneous strains in the AFEPressure and theDependence FE states. Consequently, the Strain maximum generative force obtained when the ceramic is 4.5. of the Field-Induced mechanically clamped so as not to generate a displacement is raised to 80 MPa, in comparison with One of the most important criteria for an actuator is reliable and stable driving under a large the normal value for the ferroelectric, 35 MPa in the PMN. applied stress, as required for its application as a positioner in precision cutting machinery. Figure 15 shows the longitudinally induced strains in a shape memory sample of PNZST y = 0.0707 in both the AFE and FE states at room temperature plotted as a function of uniaxial compressive Actuators 2016, 5, 11 12 of 22 Crack Actuators 2016, 5, 11generation and propagation process is very unique in 12 of 23a Pb0.99Nb0.02[(Zr0.6Sn0.4)0.955Ti0.045]0.98O3 multilayer (ML) sample, as pictured in Figure 16 [18]. As is wellknown, the crack is usually initiated around the edge of the internal electrode, then propagates to the 4.5. Dependence of the Field-Induced MLPressure side-wall in a regular piezoelectric MLStrain sample. However, in the PNZSM ML, the crack is initiated between two layers slightly electrode edge area, propagates in under parallela to the One of theelectrode most important criteriainside for anthe actuator is reliable and stable driving large electrode layer, then branches into a Y-shape around the electrode edge area. This unique crack applied stress, as required for its application as a positioner in precision cutting machinery. Figure 15 propagation mechanism induced may be originated the negative Poisson’s ratio or volumetric shows the longitudinally strains in afrom shape memory sample of PNZST y isotropic = 0.0707 in both the expansion associated with the AFE to FE phase transformation. Supposing that theseveral phase AFE and FE states at room temperature plotted as a function of uniaxial compressive stress for transformation starts from the electrode and the phase boundary moves to the center between a pair electric fields [13]. For comparison, a similar plot for a lead magnesium niobate (PMN) based ceramic of the electrodes, is induced around thematerial) center area, leading to the crack initiation. (Pb(Mg Nb ) large Ti tensile O , a stress well-known electrostrictive is also shown. 1/3 2/3 0.65 0.35 3 Figure Longitudinalinduced induced strains a shape memory sample Pb0.02 Nb0.6 Sn0.07 )0.93 0.99[(Zr 0.02 0.6Ti 0.4]0.98 Figure 15. 15. Longitudinal strains in ainshape memory sample Pb0.99Nb Sn[(Zr 0.4)0.93 O3 Tiat0.07 ] O at room temperature plotted as a function of uniaxial compressive stress [13]. 0.98 3 room temperature plotted as a function of uniaxial compressive stress [13]. Roughly speaking, the strain versus stress curve for the AFE PNZST ceramic is shifted along the strain axis with respect to that for PMN due to the difference between the spontaneous strains in the AFE and the FE states. Consequently, the maximum generative force obtained when the ceramic is mechanically clamped so as not to generate a displacement is raised to 80 MPa, in comparison with the normal value for the ferroelectric, 35 MPa in the PMN. Crack generation and propagation process is very unique in a Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.955 Ti0.045 ]0.98 O3 multilayer (ML) sample, as pictured in Figure 16 [18]. As is well-known, the crack is usually initiated around the edge of the internal electrode, then propagates to the ML side-wall in a regular piezoelectric ML sample. However, in the PNZSM ML, the crack is initiated between two electrode layers slightly inside the electrode edge area, propagates in parallel to the electrode layer, then branches into a Y-shape around the electrode edge area. This unique crack propagation mechanism may be originated from the negative Poisson’s ratio or isotropic volumetric expansion associated with the AFE to FE phase transformation. Supposing that the phase transformation starts from the electrode and the phase boundary moves to the center between a pair of the electrodes, large tensile stress is induced around the center area, leading to the crack initiation. Figure 16. Crack generation and propagation process in a Pb0.99Nb0.02[(Zr0.6Sn0.4)0.955Ti0.045]0.98O3 multilayer sample under cyclic electric field application [18]. (Top)during first field cycle, (middle) during the 30th cycle, (bottom) during the 70th cycle. Figure induced strains in a shape memory sample Pb0.99Nb0.02[(Zr0.6Sn0.4)0.93Ti0.07]0.98O13 3 of 23 Actuators 2016,15. 5, Longitudinal 11 at room temperature plotted as a function of uniaxial compressive stress [13]. Figure 16. 16.Crack Crackgeneration generation and propagation process in a Nb Pb0.99Nb 0.02[(Zr0.6Sn0.4)0.955Ti0.045]0.98O3 Figure and propagation process in a Pb 0.99 0.02 [(Zr0.6 Sn0.4 )0.955 Ti0.045 ]0.98 O3 multilayer sample under cyclic electric field application [18]. (Top)during fieldfirst cycle, (middle) multilayer sample under cyclic electric field application [18]. (Top) first during field cycle, th cycle, (bottom) during the 70th cycle. during the 30 (middle) during the 30th cycle, (bottom) during the 70th cycle. 5. Phenomenological Approach 5.1. Electrostrictive Coupling in Antiferroelectrics We will discuss here the introduction of electrostrictive coupling in Kittel’s free energy expression for antiferroelectrics [19,20]. The simplest model for antiferroelectrics is the “one-dimensional two-sublattice model”. It treats the coordinates as one-dimensional, and a superlattice (twice the unit lattice) is formed from two neighboring sublattices each having a sublattice polarization Pa and Pb . The state Pa = Pb represents the ferroelectric phase, while Pa = ´Pb , the antiferroelectric phase. For the electrostrictive effect, ignoring the coupling between the two sublattices, the strains from the two sublattices are QPa 2 and QPb 2 , respectively (assuming equal electrostrictive constants Q for both sublattices). The total strain of the crystal becomes x “ Q¨pPa 2 ` Pb 2 q{2 (1) However, since antiferroelectricity originates from the coupling between the sublattices, it is appropriate to consider the sublattice coupling also for the electrostrictive effect. The coupling term for the electrostriction Ω was introduced by Uchino et al. first in the following form [8,21]: G1 “ p1{4q¨α¨pPa 2 ` Pb 2 q ` p1{8q¨β¨pPa 4 ` Pb 4 q ` p1{12q¨γ¨pPa 6 ` Pb 6 q ` p1{2q¨η¨Pa Pb ´ p1{2q¨χT ¨p2 ` p1{2q¨Qh ¨pPa 2 ` Pb 2 ` 2Ω¨Pa Pb q p (2) in which hydrostatic pressure p was employed, and χT is the isothermal compressibility, Qh (= Q11 + 2Q12 ) and Ω are the electrostrictive constants. Introducing the L. E. Cross’ transformations PF = (Pa + Pb )/2 and PA = (Pa ´ Pb )/2 leads to the following expression: G1 “ p1{2q¨α¨pPF 2 ` PA 2 q ` p1{4q¨β¨pPF 4 ` PA 4 ` 6¨PF 2 PA 2 q ` p1{6q¨γ¨pPF 6 ` PA 6 ` 15¨PF 4 PA 2 ` 15¨PF 2 PA 4 q ` p1{2q¨η¨pPF 2 ´ PA 2 q ´ p1{2q¨χT ¨p2 ` Qh ¨rPF 2 ` PA 2 ` Ω¨ pPF 2 ´ PA 2 qs¨p (3) Actuators 2016, 5, 11 14 of 23 The dielectric and elastic equations of state follow as BG1 {BPF “ E “ PF rα ` η ` 2Qh p1 ` Ωqp ` β¨PF 2 ` 3β¨PA 2 ` γ¨PF 4 ` 10γ¨PF 2 PA 2 ` 5γ¨PA 4 s (4) BG1 {BPA “ 0 “ PA rα ´ η ` 2Qh ¨p1 ´ Ωqp ` β¨PA 2 ` 3β¨PF 2 ` γ¨PA 4 ` 10γ¨PF 2 PA 2 ` 5γ¨PF 4 s (5) BG1 {Bp “ ∆V{V “ ´ χT ¨p ` Qh ¨p1 ` Ωq¨PF 2 ` Qh ¨p1 ´ Ωq¨PA 2 (6) Hence, the induced volume change in the paraelectric phase can be related to the induced ferroelectric polarization by the following formula: p∆V{Vqind “ Qh ¨p1 ` ΩqPF,ind 2 (7) Below the phase transition temperature (this temperature for antiferroelectrics is called Neel temperature) the spontaneous volume strain and the spontaneous antiferroelectric polarization are related as p∆ V{VqS “ Qh ¨p1 ´ ΩqPA,S 2 (8) Even if the perovskite crystal shows Qh > 0, the spontaneous volume strain can be positive or negative depending on the value of Ω (Ω < 1 or Ω > 1), that is, if the inter-sublattice coupling is stronger than the intra-sublattice coupling (i.e., Ω > 1), a volume contraction is observed at the Neel point. This is quite different from ferroelectrics, which always show a volume expansion at the Curie point, such as in BaTiO3 and PbTiO3 . The large change in the strain associated with the field-induced transition from the antiferroelectric to ferroelectric phase can be estimated to be p∆V{Vq “ Qh ¨p1 ` ΩqPF,S 2 ` Qh ¨p1 ´ ΩqPA,S 2 “ 2¨Qh ¨Ω¨PF,S 2 (9) Here, we assume that the magnitudes of Pa and Pb do not change drastically through the phase transition; that is, PF,S « PA,S . Figure 17 illustrates the spontaneous strains in a crystal schematically for Ω > 0 (you may interpret Ω = q33 /Q33 in the figure). When Pa and Pb are in the parallel configuration (ferroelectric phase), the Ω-term acts to increase the strain xS , when they are in the anti-parallel configuration (antiferroelctric Actuatorsthe 2016,Ω-term 5, 11 16 of 22 phase), acts to decrease the strain. Figure 17. 17. Spontaneous Spontaneous strain strain changes changes associated associated with with sublattice sublattice interactions interactions in in the the electrostrictive electrostrictive Figure effect. >0.0. effect. Illustration Illustration is is drawn drawn in inthe thecase caseof ofqq33 33 and q33 33 > Using the above physical parameters in Section 5.2 and ε3 = 600 in Figure 7, we can evaluate d31 = 2(Q31 + q31)∙ε0∙ε3∙PF3,S = −8 × 10−12 m/V. This value is close to the experimentally obtained d31 = −7 × 10−12 m/V, as shown in Figure 18, though we use a rough cubic-symmetry approximation such as s33E = s11E, s31E = s12E, etc. The “piezoelectric Poisson’s” ratio d31/d33 is given by Actuators 2016, 5, 11 15 of 23 We expand the phenomenology to a three-dimensional formulation [22]. Considering the simplest case of a tetragonal spontaneous distortion of the primitive perovskite cell, let us start by reducing the 3D polarization (P1 P2 P3 ) to a simple form (0 0 P3 ). The Gibbs elastic free energy is represented by using two-sublattice polarization Pa and Pb , and stress X under a cubical supposition that s33 E = s11 E , s31 E = s12 E , etc.: G “ p1{4q α¨pPa3 2 ` Pb3 2 q ` p1{8q β¨pPa3 4 ` Pb3 4 q ` p1{12q γ¨pPa3 6 ` Pb3 6 q ` p1{2q η¨Pa3 ¨Pb3 ´ p1{2q s33 E ¨pX1 2 ` X2 2 ` X3 2 q ´ s31 E ¨pX1 X2 ` X2 X3 ` X3 X1 q ´ p1{2q s44 E ¨pX4 2 ` X5 2 ` X6 2 q ´ p1{2q Q33 ¨pPa3 2 ` Pb3 2 qX3 ´ p1{2q Q31 ¨pPa3 2 ` Pb3 2 qpX1 ` X2 q ´ q33 Pa3 Pb3 X3 ´ q31 Pa3 Pb3 ¨pX1 ` X2 q (10) Here, Q33 and Q31 denote the conventional longitudinal and transverse electrostrictive coefficients (intrasublattice coupling), and q33 and q31 are the corresponding intersublattice coupling parameters (the ratio q/Q was denoted as Ω in the above). Introducing the transformations PF3 “ pPa3 ` Pb3 q{2, PA3 “ pPa3 ´ Pb3 q{2 (11) leads to four types of stable states under zero applied electric field: nonpolar (PF3 = PA3 = 0), polar (PF3 ‰ 0, PA3 = 0), antipolar (PF3 = 0, PA3 ‰ 0), and semipolar (PF3 ‰ 0, PA3 ‰ 0) states. The spontaneous polarization and strains derived from the free-energy function are summarized as follows for the ferroelectric and antiferroelectric and antiferroelectric states: Ferroelectric: PF3 2 PA3 “ 0 “ r´β ` tp1{4q β2 ´ 4γpT ´ TC pXqq{ε0 Cu1/2 s{2γ (12) TC pXq “ TC ` 2ε0 CtpQ33 ` q33 qX3 ` pQ31 ` q31 qpX1 ` X2 qu (13) x3 “ s33 E X3 ` s31 E pX1 ` X2 q ` pQ33 ` q33 q¨PF3 2 (14) x1 “ s33 E X1 ` s31 E pX2 ` X3 q ` pQ31 ` q31 q¨PF3 2 (15) p∆ V{Vq “ ps33 E ` 2s31 E qpX1 ` X2 ` X3 q ` pQ33 ` 2Q31 ` q33 ` 2q31 q¨PF3 2 (16) Antiferroelectric: PA3 2 PF3 “ 0 “ r´β ` tp1{4q β2 ´ 4γpT ´ TN pXqq{ε0 Cu1/2 s{2γ (17) TN pXq “ TN ` 2ε0 CtpQ33 ´ q33 qX3 ` pQ31 ´ q31 qpX1 ` X2 qu (18) x3 “ s33 E X3 ` s31 E pX1 ` X2 q ` pQ33 ´ q33 q¨PA3 2 (19) x1 “ s33 E X1 ` s31 E pX2 ` X3 q ` pQ31 ´ q31 q¨PA3 2 (20) p∆V{Vq “ ps33 E ` 2s31 E qpX1 ` X2 ` X3 q ` pQ33 ` 2Q31 ´ q33 ´ 2q31 q¨PA3 2 (21) Here, TC and TN are the Curie and Neel temperatures, respectively, and C is the Curie–Weiss constant. Note again that we presume the cubical symmetry physical parameter components. 5.2. Estimation of q33 and q31 The values of q33 and q31 can be obtained from the strain changes associated with the electric-field-induced and thermally induced phase transitions. The spontaneous strains generated at the phase transition from paraelectric to antiferroelectric are described as x3 “ pQ33 ´ q33 q¨PA3 2 (22) x1 “ pQ31 ´ q31 q¨PA3 2 (23) Actuators 2016, 5, 11 16 of 23 The strain changes associated with the field-induced transition from antiferroelectric to ferroelectric are given by ∆x3 “ pQ33 ` q33 q¨PF3 2 ´ pQ33 ´ q33 q¨PA3 2 “ 2q33 ¨PF3 2 (24) ∆x1 “ pQ31 ` q31 q¨PF3 2 ´ pQ31 ´ q31 q¨PA3 2 “ 2q31 ¨PF3 2 (25) Here we have assumed that PF3 = PA3 because only the flipping of polarizations Pa and Pb would occur at the transition. Let us estimate the q33 and q31 values using experimental strains and polarization data for Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.94 Ti0.06 ]0.98 O3 (Figures 6 and 8a) [7] and δTN /δp of the PbZrO3 -based sample [21]: PF3 “ PA3 “ 0.4 pC¨ m-2 q ∆x3 “ ∆x1 “ 8 ˆ 10-4 Qh “ Q33 ` 2Q31 “ 0.5 ˆ 10-2 pm4 ¨ C-2 q qh “ q33 ` 2q31 “ 0.9 ˆ 10-2 pm4 ¨ C-2 q Then we derive the followings: Q33 “ 1.5 ˆ 10-2 pm4 ¨ C-2 q, Q31 “ ´ 0.5 ˆ 10-2 pm4 ¨ C-2 q, q33 “ 0.3 ˆ 10-2 pm4 ¨ C-2 q, q31 “ 0.3 ˆ 10-2 pm4 ¨ C-2 q It is noteworthy that q33 and q31 have the same positive sign (accidentally almost the same value), while Q33 and Q31 have the opposite sign with a “piezoelectric Poisson’s” ratio of 1/3. 5.3. Piezoelectric Anisotropy in Antiferroelectrics Let us derive the piezoelectric coefficients for the ferroelectric state with the sublattice polarization coupling. Under a small external field E applied, the polarization is given by PF3 “ PF3,S ` ε0 ε3 E3 (26) where ε3 is the relative permittivity. Using Equations (14) and (15), longitudinal and transversal strains are represented as x3 “ pQ33 ` q33 q¨PF3,S 2 ` 2pQ33 ` q33 q¨ε0 ¨ε3 ¨PF3,S ¨E3 ` pQ33 ` q33 q¨ε0 2 ¨ε3 2 ¨E3 2 (27) x1 “ pQ31 ` q31 q PF3,S 2 ` 2pQ31 ` q31 q ε0 ε3 PF3,S ¨E3 ` pQ31 ` q31 q ε0 2 ε3 2 E3 2 (28) The first term describes the spontaneous strains, and Figure 17 illustrates the spontaneous strain changes due to the sublattice interactions in the case of q33 , q31 > 0. When the spontaneous polarization PF3,S exists, the third term (pure electrostriction) is negligibly small in comparison with the second term (piezostriction), and the piezoelectric d coefficients are denoted as d33 “ 2pQ33 ` q33 q¨ε0 ¨ε3 ¨PF3,S (29) d31 “ 2pQ31 ` q31 q¨ε0 ¨ε3 ¨PF3,S (30) Using the above physical parameters in Section 5.2 and ε3 = 600 in Figure 7, we can evaluate d31 = 2(Q31 + q31 )¨ε0 ¨ε3 ¨PF3,S = ´8 ˆ 10´12 m/V. This value is close to the experimentally obtained d31 = ´7 ˆ 10´12 m/V, as shown in Figure 18, though we use a rough cubic-symmetry approximation such as s33 E = s11 E , s31 E = s12 E , etc. The “piezoelectric Poisson’s” ratio d31 /d33 is given by (Q31 + q31 )/(Q33 + q33 ) and it can differ from the usual value Q31 /Q33 (« ´1/3) of the normal Figure 17. Spontaneous strain changes associated with sublattice interactions in the electrostrictive effect. Illustration is drawn in the case of q33 and q33 > 0. Using the above physical parameters in Section 5.2 and ε3 = 600 in Figure 7, we can evaluate d31 = 2(Q31 + q31)∙ε0∙ε3∙PF3,S = −8 × 10−12 m/V. This value is close to the experimentally obtained Actuators 2016, 5, 11 17 of 23 d31 = −7 × 10−12 m/V, as shown in Figure 18, though we use a rough cubic-symmetry approximation such as s33E = s11E, s31E = s12E, etc. The “piezoelectric Poisson’s” ratio d31/d33 is given by ferroelectrics, to the values q33 the andusual q31 . value UsingQthe values again, weferroelectrics, can estimate (Q31 + q31)/(Q33 owing + q33) and it can differof from 31/Qabove 33 (≈ −1/3) of the normal d /d = ´(1/9). owing to the values of q 33 and q 31 . Using the above values again, we can estimate d 31 /d 33 = −(1/9). 31 33 Figure 18.18.Piezoelectric Piezoelectric d31 measurement in the induced phase ferroelectric phase in Figure d31 measurement in the induced ferroelectric in Pb0.99 Nb 0.02 [(Zr0.6 Pb 0.99 Nb 0.02 [(Zr 0.6 Sn 0.4 ) 0.94 Ti 0.06 ] 0.98 O 3 . Sn0.4 )0.94 Ti0.06 ]0.98 O3 . The electromechanical coupling factors kt and kp are represented as The electromechanical coupling factors kt and kp are represented as Supposing again that ≈ E « sE , Supposing again that s33 11 , c d kt = ε x33 d33 kt “ b D c33 E εX s33 33 kp = c ‒ d31 2 kp “ b 1´σ E εX s11 ≈ 0.75, and 33 σ ≈ 1/3, we obtain ε x33 D c33 (31) (31) (32) (32) « 0.75, and σ « 1/3, we obtain kt {kp « 0.5 d33 {d31 (33) For the antiferroelectric-based piezoelectrics, taking into account the above discussion, kt /kp will be equal to 4.5, much larger than the normal PZT value around 2.0. Table 1 lists several anisotropic piezoelectric data for field-biased PNZST’s, PbZrO3 - and PbTiO3 -based ceramics [23]. The electromechanical coupling factors kt (thickness mode) and kp (planar mode) range from 0.5 to 0.6 and 0.05 to 0.15, respectively, and the anisotropy kt /kp reaches more than 4.0. In contrast, the ratio kt /kp for the intermediate composition of the solid solution Pb(Zr,Ti)O3 will not exceed 2.5, which is also listed in Table 1 [23]. Actuators 2016, 5, 11 18 of 23 Table 1. Anisotropic PbTiO3 -based ceramics. piezoelectric constants in field-biased PNZST, PbZrO3 - and Electromechanical Coupling Factor Composition Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.937 Ti0.063 ]0.98 O3 Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.936 Ti0.064 ]0.98 O3 Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.934 Ti0.066 ]0.98 O3 Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.920 Ti0.080 ]0.98 O3 Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )0.910 Ti0.090 ]0.98 O3 Pb(Zr0.9 Ti0.1 )O3 [24] (Pb0.8 Ca0.2 )TiO3 [25] Pb(Zr0.5 Ti0.5 )O3 [26] under 22.5 kV/cm under 22.5 kV/cm under 22.5 kV/cm under 22.5 kV/cm under 22.5 kV/cm kt kp kt /kp 0.456 0.501 0.622 0.575 0.564 0.325 0.530 0.752 0.114 0.123 0.137 0.145 0.136 0.072 0.050 0.388 4.00 4.15 4.56 4.02 4.15 4.52 10.60 1.938 It is important to note that most of the samples exhibiting piezoelectric anisotropy are closely related to antiferroelectricity or sublattice structure. Some of them based on PbZrO3 are originally antiferroelectric at a low temperature or even at room temperature, and the ferroelectricity is induced after a very high electric field is applied (i.e., poling process). In Ca-modified PbTiO3 ceramics [25], a crystallographic superlattice structure has been observed in the annealed state, which suggests an antiferroelectric sublattice structure. In conclusion, we would remark that even if the sample is not originally antiferroelectric, it seems to possess rather large sublattice dipole coupling. 6. Comparison with Shape Memory Alloys The phenomenon associated with shape memory alloys is attributed to the stress-induced (as well as thermally-induced) phase transition referred to as “martensitic”. The new strain phenomena in AFE ceramics described here are very easily understandable, if we use the terminology conventionally used for these alloys, replacing electric field E for stress X. The “digital displacement” and the ferroelectric-state memorization discussed here correspond to the “superelasticity” and the shape memory effect in the alloys, respectively. Outstanding merits of the ceramics over the alloys are: 1. 2. 3. 4. quick response in ms; good controllability by electric field to memorize and recover the shape without generating heat; low energy consumption as low as 1/100 of the alloy; and wide space is not required to obtain the initial shape deformation. Numerical comparison among the shape memory alloys and antiferroelectric ceramics is summarized in Table 2. Table 2. Comparison of the shape memory characteristics between alloys and antiferroelectric ceramics. Properties Antiferroelectrics Shape Memory Alloy Driving power Strain (∆L/L) Generative force Response speed Durability Voltage (mW~W) 10´3 ~ 10´2 100 MPa 1 ~ 10 ms >106 cycles Heat (W~kW) 10´2 ~ 10´1 1000 MPa s ~ min 104 cycles 7. Applications of Shape Memory Ceramics The conventional piezoelectric/electrostrictive actuators have been developed with the aim of realizing “analogue displacement transducers”, in which a certain magnitude of electric field corresponds to only one strain state without any hysteresis during rising and falling electric field. Durability >106 cycles 104 cycles 7. Applications of Shape Memory Ceramics The conventional piezoelectric/electrostrictive actuators have been developed with the aim of 19 of 23 realizing “analogue displacement transducers”, in which a certain magnitude of electric field corresponds to only one strain state without any hysteresis during rising and falling electric field. This is exemplified by the electrostrictive PMN based ceramics. On the the contrary, contrary, the antiferroelectrics introduced in this article may be utilized in a device based on a new concept, “a digital displacement transducer”, in in which whichbistable bistableON ONand andOFF OFF strain states exist a certain electric field. idea strain states exist forfor a certain electric field. This This idea may may be interpreted as a stepping motor the conventional terminology of electromagnetic motors. be interpreted as a stepping motor in theinconventional terminology of electromagnetic motors. The The discrete movement through a constant distance achieved by the new actuator is well suited discrete movement through a constant distance achieved by the new actuator is well suited for applications such as an optical-grid manufacturing apparatus or aa swing-type swing-type charge charge coupled coupled device. device. The shape memory ceramics were applied to devices such as latching relays and mechanical mechanical clampers, where the ceramic is capable of maintaining the excited ON state even when electricity is not applied continuously to it. Actuators 2016, 5, 11 7.1. Latching Relay Relay 7.1. Latching Figure relay, which Figure 19 19 shows shows the the structure structure of of aa fabricated fabricated latching latching relay, which is is composed composed essentially essentially of of aa mechanical snap-action switch and a shape memory unimorph driving part [27]. The snap-action mechanical snap-action switch and a shape memory unimorph driving part [28]. The snap-action switch bistable states. The unimorph is switch is is easily easily driven drivenby byaa50-µm 50-μmdisplacement, displacement,having havingmechanically mechanically bistable states. The unimorph fabricated with two y= is fabricated with two y =0.063 0.063ceramic ceramicplates platesofof2222mm mmˆ×77mm mmarea areaand and 0.2 0.2 mm mm thickness, thickness, bonded bonded together with adhesive. together with adhesive. Figure 19. Structure of the latching relay using shape memory ceramic. Figure 19. Structure of the latching relay using shape memory ceramic. Figure 20 shows the It is noteworthy that the phase the dynamical dynamical response response of of the the unimorph. unimorph. It transition arises quickly enough to generate generate the the following following mechanical mechanical resonant resonant vibration vibration (Figure (Figure 20a). 20a). When the rise time of the electric field is adjusted to 4.7 ms (Figure 20b), which is the sum of the mechanical resonance period (2.2 ms) and the lag time to cause the phase transition (2.5 ms), the ringing can be suppressed completely. As shown in Figure 20c, too slow pulse exhibits again the vibration ringing, which may may induce induce the the “chattering” “chattering” problem problem in in the the relay. relay. Figure 21 shows the unimorph tip displacement degradation under an external load, which guarantees the 50 µm, minimum displacement to ensure the snap-action, under a couple of tens of gram force, which needs to operate the snap-action switch. The new relay is very compact in size (20 ˆ 10 ˆ 10 mm3 ), 1/10 of a conventional electromagnetic type (20 ˆ 26 ˆ 34 mm3 ), and is operated by a pulse voltage, which provides a significant energy saving. The relay is turned ON at 350 V with 4 ms rise time, and turned OFF at ´50 V, as depicted in Figure 22. Figure 23 demonstrates dynamical response of the latching relays of shape memory ceramic type (Figure 23a), and a conventional electromagnetic coil type (Figure 23b). The required duration of the drive voltage 600 V is only 3.4 ms (maximum 10 mA) for the ceramic, while it is 16 ms for the electromagnetic type (i.e., 1/5 energy saving, compared with the electromagnetic type!). Note also the response time (to realize ON) difference of only 1.8 ms in the ceramic from 8.0 ms in the electromagnetic coil type, which is originated from the actuator response speed (i.e., electromagnetic actuators are slow!). The existing chattering problem in the antiferroelectric ceramic for 11 ms will be solved technically in the snap-action switch design improvement. Actuators 2016, 5, 11 Actuators 2016, 5, 11 20 of 23 19 of 22 Figure 20. 20. Dynamical Dynamical response response of of the the tip tip displacement displacement of the shape shape memory memory unimorph 0.063 Figure of the unimorph with with yy = = 0.063 under various drive pulse conditions for the rise time of (a) 3 ms, (b) 4.7 ms, (c) 6 ms. under various drive pulse conditions for the rise time of (a) 3 ms, (b) 4.7 ms, (c) 6 ms. Figure 21 shows the unimorph tip displacement degradation under an external load, which guarantees the 50 μm, minimum displacement to ensure the snap-action, under a couple of tens of gram force, which needs to operate the snap-action switch. The new relay is very compact in size (20 × 10 × 10 mm3), 1/10 of a conventional electromagnetic type (20 × 26 × 34 mm3), and is operated by a pulse voltage, which provides a significant energy saving. The relay is turned ON at 350 V with 4 ms rise time, and turned OFF at −50 V, as depicted in Figure 22. Figure 23 demonstrates dynamical response of the latching relays of shape memory ceramic type (Figure 23a), and a conventional electromagnetic coil type (Figure 23b). The required duration of the drive voltage 600 V is only 3.4 ms (maximum 10 mA) for the ceramic, while it is 16 ms for the electromagnetic type (i.e., 1/5 energy saving, compared with the electromagnetic type!). Note also the response time (to realize ON) difference of only 1.8 ms in the ceramic from 8.0 ms in the electromagnetic coil type, which is originated from the actuator response speed (i.e., electromagnetic actuators are slow!). Theshape existing chattering problem the antiferroelectric Figure 21. Tip displacement of the memory unimorph (y = in 0.063) as a function of ceramic the for 11 ms will be solved technically in the snap-action switch design improvement. external load. Actuators 2016, 5, 11 20 of 22 Figure 21. Tip displacement of the shape memory unimorph (y = 0.063) as a function of the external load. Figure 22. Basic ON/OFF function of the latching relay using the shape memory ceramic. Figure 22. Basic ON/OFF function of the latching relay using the shape memory ceramic. Actuators 2016, 5, 11 Figure 22. Basic ON/OFF function of the latching relay using the shape memory ceramic. (a) 21 of 23 (b) Figure 23. Dynamical type; and Figure 23. Dynamical response response of of the the latching latching relay: relay: (a) (a) shape shape memory memory ceramic ceramic type; and (b) electromagnetic coil type. (b) electromagnetic coil type. 7.2. Mechanical Clamper 7.2. Mechanical Clamper A mechanical damper suitable for microscope sample holders has been constructed by A mechanical damper suitable for microscope sample holders has been constructed by combining combining a 20-layer shape memory stacked device (y = 0.0635) and a hinge-lever mechanism as a 20-layer shape memory stacked device (y = 0.0635) and a hinge-lever mechanism as shown in shown in Figure 24 [29]. Application of a 1 ms pulse voltage of 200 V can generate the longitudinal Figure 24 [28]. Application of a 1 ms pulse voltage of 200 V can generate the longitudinal displacement displacement of 4 μm in the 4 mm-thick multilayer device, leading to 30 μm tip movement of the of 4 µm in the 4 mm-thick multilayer device, leading to 30 µm tip movement of the hinge lever after hinge lever after the displacement amplification. Stable grip was verified for more than several hours. the displacement amplification. Stable grip was verified for more than several hours. This gripper is This gripper is useful for optical and/or electron microscope sample stages, because no continuous useful for optical and/or electron microscope sample stages, because no continuous electric voltage electric voltage application is required during the experiment. To release the sample, small reverse application is required during the experiment. To release the sample, small reverse pulse voltage is pulse voltage is applied on the multilayer actuator. applied on the multilayer actuator. Figure 24. 24. Construction Construction of of the the mechanical mechanical damper damper using using aa shape shape memory memory multilayer multilayer device. device. Figure 8. Summary Antiferroelectrics (AFE) can exhibit a shape memory function controllable by electric field, with huge isotropic volumetric expansion (0.26%) associated with the AFE to Ferroelectric (FE) phase transformation. Small inverse electric field application can realize the original AFE phase. The response speed is quick (2.5 ms). In the Pb0.99 Nb0.02 [(Zr0.6 Sn0.4 )1-y Tiy ]0.98 O3 (PNZST) system, the shape memory function is observed in the intermediate range between high temperature AFE and low temperature FE, or low Ti-concentration AFE and high Ti-concentration FE. In the AFE multilayer actuators (MLAs), the crack is initiated in the center of a pair of internal electrodes under cyclic electric field, rather than the edge area of the internal electrodes in normal piezoelectric MLAs. The two-sublattice polarization coupling model was proposed to explain: (1) isotropic volume expansion during the AFE-FE transformation; and (2) piezoelectric anisotropy. We introduced latching relays and mechanical clampers as possible unique applications of shape memory ceramics. Actuators 2016, 5, 11 22 of 23 The study of shape memory antiferroelectric materials was initiated by our group in the 1980s–1990s. Further investigations on the improvement of the induced strain magnitude, the stability of the strain characteristics with respect to temperature change, mechanical strength and durability after repeated driving are required to produce practical and reliable devices. 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