Phase switching at low field and large sustainable strain output in domain engineered ferroic crystals



Fundamental shortcomings of ferroelectrics (FEs) are low induced strain and high electric field often required for practical application in actuation, sensors, and acoustics. Although domain engineered FE single crystals deliver an order of magnitude improvement, fatigue remains another drawback in achieving reliable multiple domain switching crucial for memory storage. We demonstrate that under specially compressive stresses FE relaxors exhibit low field induced reversible and sustainable strain associated with FE–FE phase switching and unusual and unexpected lack of fatigue after several millions cycles is believed due to strain accommodation occurring in ferroics. Polarized light microscopy and X-ray diffraction are in a very good agreement with macroscopic observation and phenomenological model confirming proposed transformational path. The phenomena presented in this work are envisioned to be universal in domain engineered ferroics enabling mechanical stress to be used for strain and polarization control of electromechanical energy conversion.

1 Introduction

The term ferroic 1, 2 is used to describe the many types of mimetically twinned crystals in which the orientation of one or more twin components (domains) may be affected by a suitably chosen driving force. Ferroelectrics (FEs), ferromagnetics, and ferroelastics are examples of primary ferroic crystals in which the active domain walls, that are crystallographic boundaries can be moved by the application of electric, magnetic, and elastic fields, respectively: leading to enhanced piezoelectricity and large induced strain such as demanded by transduction and actuation systems and sensors. Higher order ferroic phenomena in which the domain states may differ in one or more property tensor components are possible 3. The equilibrium domain structure of ferroic crystals is obtained when the conditions of Landau–Ginzburg–Devonshire free energy minima are satisfied 4.

Ferroic crystals can be classified into symmetry species according to their high- and low-temperature symmetries. The symmetry species symbol consists of the high-temperature point group followed by that of the low temperature. Barium titanate (BaTiO3), for example, belongs to the ferroic species m3mF4mm. Here the two groups are separated by the letter F indicating ferroic behavior in the low-temperature phase. The number of FE domains is given by the index of the FE species point group in the high-temperature paraelectric point group. There are six domain states in tetragonal BaTiO3, with both FE 180° and FE–ferroelastic 90° domains being equally probable.

Remarkable progress has been made in the synthesis, and application of relaxor-FE single crystals with high electromechanical coupling. In the early 1980's Kuwate et al. 5 discovered the extraordinary high electromechanical properties in relaxor-FE lead zinc niobate (PZN)–lead titanate (PT) single crystals, for compositions on the rhombohedral side of the morphotropic phase boundary (MPB), with piezoelectric coefficients of d33 >1500 pm V−1, and electromechanical coupling of k33 = 0.92. This discovery was revived by a significant research effort in the mid 1990's in relaxor-FE single crystals 6, particularly in binary systems with the general formula (1 − x)Pb(BI1/3Nb2/3)O3–(x)PbTiO3, where BI can either be Zn or Mg, and more recently, work was focused on ternary lead indium niobate (PIN)–lead magnesium niobate (PMN)–PT 7–11. As a result, sound projectors fabricated from PMN–PT single crystals offer nearly triple the bandwidth, and an order of magnitude higher acoustic power than that of standard PZT projectors because of their significantly higher coupling factor and piezoelectric coefficient 9. Medical ultrasound imagining systems have also benefited from the broadband capabilities of single crystals with vast improvements in axial resolution and contrast.

Large induced strains in FEs can be broadly classified into two types: (i) non180° domain switching, and (ii) phase transformation 12. A combined mechanical stress and electric field are used to induce 90° domain switching in FE tetragonal single crystal BaTiO3 14. A complete switching of polarization direction by 90°, i.e., from a- to c-domains will result in a large lattice strain of approximately 1% (c/a ∼ 1.01) at ∼3 MV m−1. The lattice strain associated with 90° domain switching in PT is even higher at ∼6%. A number of issues were recognized by researchers, amongst which are a quick degradation of the strain due to electrode choice and friction. There are other possible mechanisms of large field induced strain by reversible 90° domain switching in aged FE single crystal BaTiO3 due to a symmetry conforming property of point defects 15. The transduction mechanism strongly depends on the sample prehistory, and the stability of particular stoichiometry and defect configuration.

Park and Shrout 6 have demonstrated an ultrahigh strain of ∼1.2% in domain engineered PZN–PT single crystals driven by very high fields of about 4 MV m−1. This huge strain was attributable to a FE rhombohedral FR to FE tetragonal FT phase transformation and is commensurate with model calculations 7. In spite of extremely attractive electromechanical response of the MPB FEs the transducers fabricated from relaxor-FE single crystals as well as PZT piezoceramics are designed to operate well below any phase transition temperature in order to avoid large swings in load impedance, high electric field drive, and hysteresis losses. Ideally, the material exhibiting anhysteretic response and nearly instant phase transformation induced strain change would be able to overcome these caveats. Therefore, by making the field induced phase transition to occur at significantly lower electric fields and at much faster rates would make it possible to create a material with high effective piezoelectric properties. Recently, it was shown that domain-engineered relaxor-FE crystals with 4 mm and 2 mm macrosymmetries exhibited a large and reversible phase transformation strain under mechanical compression that is tunable by an electric field 7–9, 13. A very sharp hysteretic quasistatic strain curve and polarization jumps accompanied by a dramatic change in stiffness (by a factor of 6–8) at stress less than 15 MPa have been reported first in the PZN–PT crystals 7. However in PMN–PT crystals, the effect was more diffuse and continuous 13. Later this elastic nonlinearity was also reported in different crystals and was shown to be a strong function of temperature and geometry of the crystals 16–18. Recently, we demonstrated a large and reversible strain up to 0.5% at field of ∼0.1 MV m−1 in domain-engineered relaxor-FE PIN–PMN–PT single crystals 16. In all cases this nonlinearity was explained as the stress-induced FE rhombohedral FRFE orthorhombic FO phase transformations. It is the reorientation of the polarization vector Ps aligned along the 〈111〉 direction (see Fig. 1a) under the combined effect of external stress and electric field bias is accountable for this phase transformation switching in the domain engineered systems 10, 16. Surprisingly, the crystal was successfully switched for more than 106 cycles without any signs of fatigue, cracks, or failure.

Figure 1.

(online color at: Stress and field induced phase transformations in relaxor domain-engineered ferroelectrics. (a) Polarization orientations and external stress and electric field geometry for 〈011〉 PIN–PMN–PT single crystal with (32) mode geometry. Combining effect of stress and electric field bias is leading to the spontaneous polarization reorientation inducing FRFO phase transition; (b) elastic response as a function of electric bias (top) and temperature (bottom) with very sharp nonlinearity at critical stress σc. Note that both electric field bias and higher temperature shifts this transition to lower critical stresses; (c) Gibbs's free energy is affected by applied electrical bias and stress.

Even though the phenomenology of the field and stress induced phase transition is salient, very limited information is available about general universal descriptive rules governing the dynamics of this large polarization and strain generated at phase transition in nearly MPB relaxor FE single crystals. If properly understood, one can discover new systems exhibiting extremely high and sharp reversible field- or stress-induced sustainable strain at phase transitions for transduction. In this work we investigated field induced reversible FR → FO phase transitions in near-MPB [011] poled (32)-mode PIN–PMN–0.3PT FE single crystals as a function of applied stress and electrical bias. To gain further insights on domain states and dynamics, we have performed polarized light microscopy (PLM) experiments under applied electric field.

2 Experiment, results and discussion

The elastic temperature dependent quasistatic response was measured under various mechanical and electrical boundary conditions using method described in details elsewhere (see Supporting Information, online at: and Ref. 10. Figure 1b displays the extremely abrupt strain change with prominent relaxation phenomena at the entrance and exit of phase change at the critical stress σc corresponding to the FR → FO transition tunable both by field and temperature (Fig. 1b). This destabilizing bias field effect is in accord to a scenario depicted in Fig. 1a. At zero stress and field conditions there are only two domains states with R3m symmetry corresponding to FR sates with spontaneous polarization Ps along 〈111〉 (Fig. 1a) with the spontaneous polarization reorientation from 〈111〉 to 〈011〉 under cumulative effect of 〈100〉 compressive stress (σ22) and 〈011〉 electric field E (Fig. 1b). It has to be noted that in contrast to the [100] poled (33-mode), the elastic responses of the [011] poled (32-mode) crystals exhibit much sharper nonlinearity and strain change associated with the FR → FO stress-induced phase transition with σc in the range of 12–14 MPa for near-MPB composition. As expected, σc is a function of electric field applied along [011]. In distinction with 33-mode geometry, electrical bias in [011] poled crystals actually destabilizes the FR phase along with the temperature (Fig. 1c) 15. It is important to note the FR → FO phase switching and transition are fully controlled by electric field, either enhanced or completely suppressed by rather low electrical bias 16. In order to explain the driving force governing this transition, we invoke a standard description of the minimization of the Gibbs's free energy as a function of polarization and strain. From first principles, a stability of phases and energy required to stimulate phase transition is determined by minimization of free energy occurred in near critical state (Fig. 1a). The presence of several unresolved minima is strongly affected by applied stress or electric field. For the system with nearly MBP composition with relatively flat energy landscape phases can be readily switched by applying rather small external stress or electric field. As discussed above, here we are interested to predict and tailor special electro-mechanical–thermal boundary conditions satisfying the physical requirements for the system to be within the marginal states that are equally energetically favorable. Meeting these conditions allows for the FR and FO phases to simultaneously coexist. This can be envisioned on the boundary between FR and FO phases at the stability diagram proposed earlier in Refs. 18. Stress–temperature–field stability diagram can be established based on the quasistatic measurements (Fig. 2). The stability diagram clearly defines the plane separating two stable FR and FO states for the 〈011〉 poled (32-mode) crystal as a function of external parameters such as stress, field and temperature. For states poised at a FRFO phase boundary a small perturbation, for example, in 〈011〉 electrical bias, temperature or 〈100〉 stress would be able to trigger polarization reorientation generating large reversible bulk 〈100〉 strain. Consider a crystal that is at room temperature in equilibrium in (FR) macrodomain state now is preloaded to a stress σ ∼ σc near the FRFO transition. In accord to the diagram (Fig. 1a), a sufficient magnitude of the ac electric field drive E3 will induces a strain in the 〈001〉 direction corresponding to the difference between FR and FO equilibrium states. The magnitude of the [001] strain difference was estimated in terms of polarization (P) and electrostriction (Q) assuming polarization continuity in the different phases (R, O, and T). The following analytic expressions can be explicitly written (in reduced tensor notation) for the strain difference ΔS3(R − O) and ΔS3(R − T) associated with the FRFO and FRFT transitions, respectively 7,

equation image((1))
equation image((2))
Figure 2.

(online color at: Stress–field-temperature stability surface for 32-mode geometry for [011] poled PIN–PMN–PT samples. The value of critical compressive stress deduced from the quasistatic elastic isothermal response is plotted as function of applied bias field. States on this surface are poised at FRFOFR boundary. “FO” stable states for any stress, field, and temperature are above surface, while “FR” stable states for any stress, field, and temperature below surface.

For electrostriction coefficients Q11 = 0.0535 m4/C2, Q12 = −0.0267 m4/C2, and polarization P3(R) = 0.25 C m−2 (see Ref. 7) the calculated ΔS3(R − O) from Eq. (1) is ∼0.51%, which is in excellent agreement with experimental results 18. It is interesting to note that according to Eq. (2), the FRFT transition strain is ΔS3(R − T) ∼1% close to that observed in Ref. 6. In this case for FRFO phase transformation maximum theoretical strain of 0.5% that, as shown in our previous work, can be achieved at a significantly lower (<0.1 MV m−1) field as compared to that reported by Park and Shrout 6 and that is more than an order of magnitude smaller than what would be required using the linear piezoelectric mode.

2.1 Harmonic drive measurements

Figure 3a depicts the strain response under harmonic drive of a mechanically clamped PIN–PMN–PT crystal at 14 MPa by electric field of 0.1 MV m−1 applied along [011]. The response shows a reversible hysteretic strain jump with magnitude up to 0.35% at FRFOFR transition (Fig. 3b). The field dependence of the induced strain ε plotted for various loading prehistory (number of switching cycles N) demonstrates lack of fatigue (Fig. 3b). Near the FRFO phase transition the instantaneous piezoelectric coefficient d32 = dε/dE = (3.5 × 10−3/105 V m−1) ∼3.5 × 104 pm V−1 which is more than order of magnitude larger than the linear piezoelectric coefficient (∼2000 pm V−1) of the domain engineered single crystal. Time dependent studies (Fig. 3a) illustrate that this FRFO transition phase switching was sustainable for more than 106 cycles without noticeable degradation. There was no decrease in the magnitude of the strain, nor was there any visible damage to the sample. This was unexpected, as sample fatigue after repeated induced phase transformations of large strains is often pronounced. Undoubtedly, the crystallographic direction along which the field was applied [011] has an important role in this reversibility and fatigue resistance. In FRFO or FRFT transformations, the strain can be elastically accommodated only along the (011) direction. Fields applied along this direction could have a significant advantage in terms of the relaxation of the elastic energy of twin boundary reconstruction or elimination in order establishes the equilibrium boundary condition for the ferroelastic domain to be re-orientated.

Figure 3.

(online color at: Field induced phase transformation strain in mechanically confined crystal. (a) Time dependent strain-field response for PIN–PMN–PT under 16 MPa pre-stress along [100]. Note field induced large 0.35% strain achieved at a significantly lower drive 0.1 MV m−1 field; (b) field dependence of strain for different loading pre-history demonstrating lack of fatigue. Here N is number of switching cycles.

2.2 Polarized light microscopy (PLM) and domain observation

To illustrate the domain configurations and transformations in the vicinity of the field induced transition under zero stress, PLM images were obtained under an electrical bias (Fig. 4). Figure 4a depicts the room temperature polarization and strain hysteresis loops at zero mechanical stress with prominent indication of the field induced phase transformation at electric field ∼1.2 MV m−1 for (011) oriented PIN–PMN–PT crystals. The PLM images were taken under E = 0 and 1.27 MV m−1 (Fig. 4b). Under zero bias, the PLM images reveal the presence of stripe-like domains with a 〈111〉 orientation, which are typical of the FE FR phase of PMN-x%PT crystals 20. Application of electric field resulted in significant domain structure changes and under E = 1.27 MV m−1, the original domain structure disappeared and the crystal became essentially a single domain state; however, some residual contrast remained, indicating that the transformation was not entirely completed. These results support the position that the induced phase transformation is a macrodomain FR → monodomain FO, as illustrated in Fig. 2. Furthermore, the domain transformation was nearly completed at field levels near which the macroinduced transformation strain in the hatched region of Fig. 4a began to become evident. This in conjunction with the observed crystal lattice parameter changes (presented below) indicates that the giant piezoelectricity is due to the abruptness of the induced FRFO transformation. It is noted that these macrosized stripe-like domains in the PLM images are the result of domain rearrangements induced by initial poling, which can more clearly seen by comparisons in the PLM (Fig. 4c) and PFM (Fig. 4d) images for the same sample viewed along the [011] direction. The macrosized stripe-like domains in the PLM image correspond to the large band structures in the PFM image, where sub-micron sized stripe domains oriented along 〈0–11〉 is the matrix of these band structures. This makes manifest the important role of strain accommodation in the configuration of the FE domains. The domain structures along the (100) plane were also investigated in order to provide detailed information about the domain configuration in bulk (011) poled crystals. Along [011], straight domains were observed in the PLM image (Fig. 4e), where as the PFM image (Fig. 4f) revealed chess board-like domains. These chess board structures correspond exactly to the band structures observed along (011) (Fig. 4d). The configuration of the domains along the (011) and (100) planes shows that the R macrodomain state was formed from the sub-macrodomain one under [011] poling.

Figure 4.

(online color at: (a) Room temperature strain and polarization hysteresis loops measured under zero pre-stress; and (b) domain transformations revealed by PLM image viewed along [011] under electric fields of 0 and 1.27 MV m−1, respectively; (c) recovery of the domain configuration after removal of the electric field revealed by PLM; (d) corresponding domain patterns obtained by PFM; (e) configuration of domains viewed along [100] under PLM after electric field load; and (f) corresponding PFM image reveals the existence of chess board-like domain structure.

In order to investigate the microstructural details, stress induced in situ X-ray diffraction analysis was performed on the [011] poled sample (Fig. 5) under zero stress (see Supporting Information). Figure 5b demonstrates reversibility of the lattice parameters change (4.037–4.043 Å, ∼0.175%) associated with the stress induced FRFO phase transition and its magnitude was in a good agreement with the total mechanical strain (∼0.35%) obtained from compression of the bulk samples when corrected by the Poisson's ratio.

Figure 5.

(online color at: X-ray diffraction of PIN–PMN–PT crystals. (a) Diffractogram showing the three principle reflections – (110), (220), and (330). The inset shows a detailed view of the (220) reflections at zero stress, loaded to 26 MPa and then unloaded to 6 MPa. Notice the reproducibility of the peak shift and width. (b) Measured lattice spacing of the two observed 〈110〉 pseudo-cubic X-ray reflections as a function of uniaxial stress along the c-axis. The stress was applied by a home-built fixture that was calibrated by strain gauges.

2.3 Laser spectroscopy measurements

To quantify the dynamic range of the FRFOFR process switching, we performed a laser Doppler (LDV) spectroscopy measurements (see Supporting Information). Figure S1 of Supporting Information shows the magnitude of the strain jump measured by LDV along 〈011〉 direction. From the time dependent displacement plot it can be seen that approximate rise time of the field-induced transition is about ∼50 µs, which is consistent with previous observations 16; however, the value estimated here is an upper bound as the LDV system bandwidth is only 25 kHz. Analyzing relaxation times of the strain ring down during the FRFO stress induced phase transition (red circle Fig. 1b), we noticed that characteristic period of ∼10 ms is in agreement with the value of time of flight of elastic wave propagating through the sample. It has to be mentioned that the only target composition near-MBP systems with very sharp FRFOFR transition would be those with sharp avalanche “first-order-type” abrupt phase transformations and associated strain. This would allow capturing this large strain into a device to avoid unwanted losses and thus is requiring minimum power for switching. Interestingly, one can “recharge” the system mechanically (or even thermally) too, and thus work on the FRFOFR boundary (Fig. 3), making switching essentially anhysteretic. There are two ubiquitous bi-stable states can be realized either mechanically, by stresses at certain electrical bias or electrically, at certain fixed mechanical boundary conditions. It has to be noted that this strain at FRFO transition is practically constant for various bias stress and electric field magnitude and frequency of the Eac drive 16. This implies the displacement amplitude is practically independent of the supplied electrical power 18, 19. Therefore it illustrates relatively broadband capability of the transduction based on reversible FE phase transformation in mechanically confined relaxor single crystals.

Notably, the phase transformation large strain transduction was investigated broadly in ferroelctrics much before discovery of relaxors. The operation near phase transition has proven extremely useful in some applications such as the uncooled infrared imaging technology, developed by Texas Instruments 21. Here, a densely populated two-dimensional imaging array is fabricated from a FE barium strontium titanate (BST) composition whose FE tetragonal FT to paraelectric cubic PC transition temperature is near room temperature. The array is operated under a dc bias voltage to prevent it from depoling, and its temperature is maintained at the FT → PC transition where the pyroelectric coefficient is maximum. The signal-to-noise (S/N) figure of merit is nearly an order of magnitude higher compared to that of detectors operating below TC, using the normal pyroelectric mode. In another example, the field-induced antiferroelectric (AF) to FE phase transformation in lead niobium zirconate stannate titanate (PNZST) is associated with a large ∼0.3% strain 20. Typical fields required for induced AF–FE transitions are in the order of 1–4 MV m−1. In contrast, here we illustrated how for the ferroic crystal placed near a FRFO phase boundary more than order of magnitude lower ac electric field drive would able to trigger a giant sustainable strain of comparable magnitude. Our results show that, by using properly designed mechanical and electrical boundary conditions in specially oriented near MPB relaxor FEs it is possible to achieve low voltage operation and uniform spontaneous polarization switching. These easy switching can be attributed to a low energy barrier between two FE phases and as supported by PFM/PLM images and relatively low hysteresis loop (Fig. 3). These universal properties of near-morphotropic FE relaxor single crystals provide a basis for designing new type of actuators and transducers. In spite of large piezoelectric responses accompanying phase transitions this method has not been demonstrated for practical applications. Although there are also several classes of materials utilizing high strains associated with martensitic phase transition (i.e., shape memory alloys or SMAs), they arguably would be able to provide the dynamic range and switching speed that are achievable in FEs. The high strains in SMAs are thermally activated, and transduction devices based on them have frequency band limitations.

3 Conclusions

To sum up, we showed that the ferroic morphotropic relaxor PIN–PMN–PT crystal exhibited unusual lack of fatigue after one million (0.5%) strain cycles, compared to other ferroic systems degrading after a few cycles. A strain accommodation model has been proposed as a plausible explanation to sustainable phase switching supported by PLM experiments under applied electric field. Although we believe strain accommodation may be a reason for sustainability, there could be other mechanisms but they are not clear at this time. X-ray diffraction experiments on “free” and “clamped” crystals revealed a lattice strain that is in a very good agreement with macroscopic observation and phenomenological model calculation. The results confirmed our proposed hypothesis about macrodomain FE rhombohedral FR → mono-domain FE orthorhombic FO phase transition. A stress–field-temperature phase diagram has been established.

In conclusion, the results reported here open up remarkable alternative method to generate for several million cycles high reversible and sustainable strain at significantly lower field for acoustic source, actuator, or broadband sound generation. The readily switchable bi-stable states presents another opportunity to advance FE memory read and/or write storage devices, sensors, or transformers. Special advantages could be envisioned when this bi-stable system based on the relaxor FE single crystal being a part of a composite multiferroic system exploiting a direct magnetoelectric effect while coupled via strain to the magnetostrictive element 22, 23. In this case stress and/or field triggered sharp and reversible transitions could be further enhanced by magnetoelastic effect to develop magnetic sensors or actuators 24. There are still many unanswered questions. We are not absolutely sure about the validity of our postulate and the subsequent conclusion concerning the sustainability of such a huge ∼0.5% strain. Finally, we hope to stimulate further research in this fascinating area of domain engineered ferroics.


P.F. and A.A. would like to acknowledge full support from the Office of Naval Research. The authors also acknowledge the Naval Undersea Warfare Center staff and facilities and Joseph Stace and Colin Murphy and Wen Dong of UCLA for experiment expertise provided in performing mechanical testing.

Author contributions P.F. and A. A. conceived the idea; P.F. designed the experiment and prepared the manuscript. J.Y. and D.V. implemented PFM/PLS experimental measurements. S.L. and P.F. performed X-ray measurements and analyzed the data.

Supporting Information for this article is available from the Wiley Online Library or from the author.