Dynamic piezoelectric response of relaxor single crystal under electrically driven inter-ferroelectric phase transformations

The continuous development of highly efficient transducers for high-power, low-frequency, and compact-sized sound projectors demands a new class of materials with enhanced properties. High-power underwater acoustic projectors are generally very large and heavy, but recent single crystal transducer development^1,2 promises significant size and weight reductions.^3,4 Specifically, domain-engineered relaxor (1−x)Pb(Mg_1/3Nb_2/3O₃−xPbTiO₃) (PMN–PT) and (1−x)Pb Zn_1/3Nb_2/3O₃−xPbTiO₃ (PZN–PT) systems poled along the equivalent nonpolar (001)_C pseudo-cubic direction are of highest interest. The crystals with compositions close to the morphotropic phase boundary (MPB)^5–9 showed high electromechanical coupling factors of ∼0.9 and large piezoelectric coefficients up to 2000 pm/V.^3–5 It was concluded that this phenomenon of enhanced piezoelectricity can be linked to the presence of intermediate monoclinic (F_M) and orthorhombic (F_O) ferroelectric states in-between the ferroelectric rhombohedral (F_R) and tetragonal (F_T) phases, allowing for enhanced polarization rotation.^3–8 This F_R-to-F_T phase transformation can also be accessed electrically³ with maximum strains on the order of 1% (Ref. 4) in binary compositions of PZN–PT, whereas large an hysteretic strains of up to 0.6% in PMN–PT⁵ have been reported. Electrically induced discontinuities in strain were studied by Okawara and Amin¹¹ and were asserted to be a first-order-like phase transition.

In addition, an elastic instability was reported in both binary and ternary domain engineered single crystals subjected to uniaxial stresses.^9–12 The isothermal elastic response with harmonic stress (∼50 MPa) of domain-engineered (3–3 and 3–2 modes) PZN–PT single crystals with the composition near the MPB was investigated by Amin and Cross.¹³ Okawara and Amin¹¹ observed a reversible and hysteretic stress–strain response of these crystals, which is characterized by a large and sharp strain discontinuity (up to 0.5%) occurring at a critical stress. This strain was attributed to a stress-induced F_R to F_O transition caused by polarization rotation under mechanical compression. The reversible effect is speculated to be due to internal electric fields such as those associated with charged domain walls.¹² Similar observations in domain engineered ternary xPb(In_1/2Nb_1/2)O₃-(1-x-y)Pb(Mg_1/3Nb_2/3)O₃-yPbTiO₃ (x = 0.24, y = 0.32) (PIN–PMN–PT) single crystals were reported by Finkel et al.¹⁴ Recently, using mechanically biased PIN–PMN–PT (110)-poled crystals, we presented a method to deliver strain levels of ∼0.5% at relatively low (∼0.1 kV/mm) drive fields, representing a fourfold increase in strain at only 20% of the drive field as compared to those of other piezoelectric relaxor ferroelectric single crystals (e.g., PMN–PT).^15,16 Despite the critical importance for applications, these phase switching phenomena in PIN–PMN–PT crystals were reported predominately under quasi-static or nearly DC conditions. So far, there has been limited work extending this intrinsic structural phase switching phenomenon into higher frequency ranges required for real sound generating devices. Further progress in exploiting these large enhanced piezoelectric properties, potentially leading to transducers with even greater performance, requires the study of the underlying mechanism of this phase transformation. In this work, we demonstrate the dynamic response based on the large electrostrain generated in the crystalline phase transition found in relaxor ferroelectric [110]-oriented, domain-engineered PIN–PMN–PT single crystals. To achieve this, we have applied a compressive mechanical stress close to the critical compressive stress σ_c needed for phase transformation from F_R to F_O, i.e., mechanical confinement. Compared to the field-induced strain of ∼0.5% at 2 kV/mm in PZN–PT single crystals as reported by Park and Shrout⁷ the present results show similar strains but with over an order of magnitude reduction in the field.

Rectangular bars of PIN–PMN–PT with dimensions of 4 × 4× 12 mm were procured with the longest edge oriented along the pseudo-cubic [001], while the other faces were oriented along ⟨110⟩. These bars were compressed along [001] in several different loading devices for testing the piezoelectric coefficient d₃₂ at different frequencies and compressive stresses.

The first step was to confirm if the prestress was sufficient for reaching the required critical threshold needed for realization of the transition to a phase that had been previously described as orthorhombic.^{8,10,11,13–15} We recorded the stress strain response this time using a custom-built stress rig permitting in situ x-ray diffraction characterization (see the supplementary material). Full 3D reciprocal mapping with a 2D camera revealed that the structural phases are a function of stress and field (more details can be found in Ref. 18). Strain was measured with a strain gauge affixed to the sample on the (⁠$1¯10$⁠) specular face, aligned in the [001] direction. Figure 1 shows the x-ray diffraction lattice parameter change as a function of applied uniaxial compressive stress at zero applied electric field along with simultaneously measured strain, corrected with a Poisson ratio of 0.37 to make the two graphs match. An initial quasi-linear strain softening is identified as the low stress F_R phase. At a critical stress, σ_c > 20 MPa, the elastic properties changed dramatically to a much stiffer response, characteristic of the high-stress phase F_O. The x-ray diffraction data from the (⁠$111$⁠) reflection plotted as x-ray intensity (H–K) contour plots at constant L (L = 1.131) (Fig. 1, insets) for Miller indices H, K, and L show two distinct (hkl) diffracting conditions at low stress transforming to only one (hkl) condition at stresses above σ_c.

Next, the quasi-static (<1 Hz) stress–strain behavior of the crystals was characterized in a load frame (Instron), and from this measurement, the critical stress σ_c for the phase transition was determined to be close to the values evaluated from the in situ x-ray experiment and to the values reported earlier.¹⁷ Strain and polarization hysteresis curves were measured with a ferroelectric test system (Radiant Technologies), while the sample remained mechanically confined under stress along the [001] direction [as shown in the inset of Fig. 1(a)] accompanied by an electric field applied along [110]. Several of the resulting strain vs electric field curves at variable compressive stress ranging from 20 to 26 MPa are shown in Fig. 2. It should be noted that in this range of compressive stresses, an amplitude of the applied electric field <0.2 kV/mm was sufficient to cycle from F_R to F_O and back to F_R. This sharp jump in strain (up to 2000 microstrain) was triggered reversibly with low hysteresis and approximately independent of prestress conditions.

Subsequent to this, a dynamic piezoanalyzer was used to evaluate the direct d₃₂ piezoelectric response under mechanical compressive loads up to 50 MPa, but this time with an AC stress signal (at 1 and 70 Hz) applied superposed on the static preload value for three preloads representing F_R (<20 MPa), F_TRANS (∼23 MPa), and F_O (>26 MPa) phases. The dynamic charge-stress relation was measured with a home-built press. The press contains a quartz reference sensor to measure the force, a lead zirconate titanate, Pb[Zr_xTi_1-x]O₃ (0 ≤ x ≤ 1), (PZT) actuator, two stiff zirconia columns with steel caps for electrical contacts between which the sample is placed, and a stepper motor, all connected mechanically in series and contained within a rigid steel frame. The AC stress is generated by the PZT actuator. The piezoelectric charges produced by the quartz sensor and the sample are measured by two separate charge amplifiers and recorded with an oscilloscope. Both longitudinal and transverse piezoelectric responses can be measured by appropriate orientation of the electroded faces with respect to the crystallographic axes of the sample and direction along which the stress is applied. For charge induced by stress during the phase transition, the compressive force was only applied from 0 to 40 MPa by the stepper motor. The total duration of force application and release for this technique lasts approximately 2 min. More details can be found in Refs. 19 and 20.

The stress-polarization dependence is plotted in Fig. 3(a). It is notable that there is almost no observable hysteresis upon loading and unloading. There are three clearly observable regions with different slopes [as denoted by blue, red, and green symbols in Fig. 3(a)], which correspond to the two phases separated by the sharply increasing polarization region where the transition between them is occurring. As shown by d₃₂ vs stress in the inset of Fig. 3(a), the value is relatively constant in the F_R condition with a large spike at stresses near the phase transition at ∼20 MPa, which corresponds to the optimal loading condition for F_TRANS. At higher stress values, d₃₂ drops off significantly once the crystal is in the orthorhombic regime.

The crystals were also tested in a special spring and mechanical screw loaded fixture and compressively stressed in the ranges as described above. At these loads, bipolar electrical field-strain hysteresis measurements were performed at fields of 0.3 kV/mm at 10 Hz in order to characterize the converse d₃₂^* piezoelectric coefficient (i.e., normalized maximum strain at the maximum applied electric field). The electric field dependence of the strain is plotted in Fig. 3(b), while the crystal is held at a prestress corresponding to either the F_R or F_O phases or at σ_c to achieve the phase transition (F_TRANS). There is a clear difference in the total strain generated for the same electric field swept at 10 Hz.

The d₃₂ and d₃₂^* values as calculated from the slopes of these experiments, as well as the values calculated from the dynamic d₃₂ setup, are summarized in Table I for the three loading conditions of interest corresponding to F_R, F_O, and F_TRANS regions as denoted by blue, red, and green symbols in Fig. 1(a) From the data in Table I, it is clear that the d₃₂ and d₃₂^* values are substantially higher in the transition region although there is a fairly large variation in magnitude depending on the measurement technique. The differences may be due to how the measurements were performed (i.e., changes in the boundary conditions in different load frames) since the dynamic d₃₂ measurement showed only a modest decrease as the frequency changed from 1 to 70 Hz.

After initial characterization of the crystal under low frequency drive conditions, the crystal was installed into a transducer assembly (a Tonpilz-type design) driven over a broader range of frequencies (up to 70 kHz). For this, electrical leads were attached to the electrodes on the surface of the crystal, and the crystal was inserted into the transducer apparatus as shown in the schematic in Fig. 4. A screw on the top was used to apply an adjustable compressive preload to the crystal. The crystal was placed between two ceramic shims, and for optimal boundary conditions, there were several spring washers below the head adapter. Sound was transmitted from the cone on the opposite side, which was submerged in water and directed at the hydrophone. The transducer was not potted with oil or otherwise waterproofed and remained above the surface of water during testing. Initial testing with a square wave pulse was done at the Naval Undersea Warfare Center in Newport, RI. Comparison tests, and then subsequently final characterization discussed herein, were performed at the NRL facility described in detail in the supplementary material.

There are various resonances within the structure, and those resonances shift in frequency and amplitude with applied stress due to the change in sample properties as confirmed by impedance measurements [Fig. 5(a)]; however, the general trend in the sound pressure level (SPL) data is in agreement with the measured piezoelectric coefficients for the three different prestress conditions. The SPL for a 400 V chirp pulse with a broad spectrum waveform [Fig. 5(b)] shows an overall higher result for the crystal under F_TRANS loading conditions in the entire frequency range and particularly above 10 kHz. At a local maximum near 27 kHz, there is an enhancement of 15 dB in the SPL between the F_TRANS (76 dB) and F_R (60 dB) data and a similarly large enhancement as compared to that when the sample is in the F_O regime. This suggests that even at much higher frequencies than shown in Table I, the relationship between the d₃₂^* coefficients still holds and that the corresponding increase in strain generated through the phase transition directly translates to an increase in the acoustic pressure level.

We also monitored the temperature of the crystal inside the transducer using an IR camera (FLIR E95) while driving at 500 V at 1000 Hz through the phase transition for ∼30 min to achieve equilibrium and found that the sample heating is much less than 1 °C under continuous operation. With negligible heat dissipated and the lack of fatigue previously observed for tens of millions cycles in these PIN–PMN–PT systems,^14–16 we believe that these results demonstrate the great potential for using this phase transformational regime for high-power sound-generation transduction. With further chemical and microstructural optimization of single crystal materials—specifically focused on their dynamic piezoelectric properties under stress—we anticipate that such large strains can be generated at even lower fields.

In summary, we investigated and demonstrated a broadband dynamic nonlinear piezoelectric response in [011]-poled ferroelectric 0.24PIN–0.44PMN–0.32PT relaxor single crystals and how to capture this large response for potential application in acoustic transducers. It was shown that compared to linear rhombohedral or orthorhombic modes, the effective nonlinear dynamic d₃₂ or d₃₂^* coefficient is almost a factor of two higher, and this enhancement persists over a wide range of frequencies. Through the use of in situ compressive-stress x-ray diffraction, the optimum mechanical bias was identified as being close to the critical stress for triggering rhombohedral–orthorhombic phase transformations, and we demonstrated the excellent performance of a prototype transducer element and the viability of exploiting this effect. The sound pressure level was enhanced (10–15 dB) throughout a large frequency range when the crystal is driven through the phase transition as compared to that when it was in either of the linear piezoelectric regimes. The advantage of implementing nonlinear phase switching that is permitted in [110]-poled PIN–PMN–PT single crystals leads to opportunities for producing acoustic sources with enhanced performance at lower applied fields for highly efficient sound transduction.

See the supplementary material for a full description of a custom-built stress rig permitting in situ x-ray diffraction characterization and also detailed apparatus and the system for water SPL tests in acoustic sensors.

The authors would like to acknowledge funding from the Office of Naval Research under the U.S. Naval Research Laboratory's Basic Research Program and Office of Naval Research Global, ONRG-NICOP Project No. N62909-18-1-2008 Electrosciences Ltd. Parts of this research work was carried in the framework of the ADVENT project (Grant No. 16ENG06 ADVENT), which was supported by the European Metrology Programme for Innovation and Research (EMPIR). The EMPIR initiative was co-funded by the European's Horizon 2020 research and innovation program and the EMPIR Participating States.