3.1. Determination of Phase Transformation Curves of Single Crystal Stake Actuators
As mentioned earlier, [011]-poled d32-mode single crystals of both binary PZN-PT and ternary PIN-PMN-PT solid solutions (both with TRO ≈ 110–125 °C) have comparable phase transformation properties and piezoelectric strain coefficients. They also exhibit similar transformation curves. In what follows, only the results obtained with square-pipe stake actuators made of d32-mode PIN-PMN-PT single crystal are reported.
Figure 5 shows the various transformation curves of stake actuators made of d
32-mode PIN-PMN-PT single crystals (T
RO ≈ 110–125 °C). In this plot, the added load was converted to axial compressive stress experienced by the component crystals and the applied voltage to an applied electric field using known total load bearing area of the crystals and crystal thickness, respectively, so that the results obtained are applicable to stakes made of crystals of different dimensions. This figure shows that the transformation stress increases with decreasing applied electric field and vice versa. Also, at higher temperature, both the transformation stress and electric field decrease accordingly.
In this figure, each curve represents the transformation electric field and transformation compressive stress at a given use temperature. For operating conditions (combinations of applied electric field and axial compressive load) that lie above the transformation curve, the R–O phase transformation will take place in the component crystals. The stake actuator will no longer be linear and would display large strain jump and hysteresis. In contrast, the strain response of the stake actuator remains linear with minimum hysteresis when the stake actuator is operated under conditions below the transformation curve.
The various transformation curves in
Figure 5 show that at a given applied electric field, the maximum operating stress allowed decreases with increasing temperature. Furthermore, at too high applied voltage, the operating temperature and load allowed may be limited. The information contained in this figure is thus very useful for defining the operating conditions of a linear, hysteresis-free stake actuator.
Based on the information provided in
Figure 5, the maximum applied voltage of the stake was fixed at 240 V, to enable the various stake actuators fabricated to be used over practical operating conditions, i.e., of up 40 °C and under a load of up to 10 kg, while maintaining higher strain linearity with negligible hysteresis. This applies to stake actuators driven by d
32-mode single crystals of both PZN-PT and PIN-PMN-PT single crystals (both with T
RO ≈ 110–125 °C) fabricated in the present work.
3.2. Displacement Responses of Hi-Fi Stake Actuators
With the maximum applied voltage fixed at 240 V, the linear operating ranges of the various stake actuators made in this work are provided in
Table 1. The maximum displacement attainable and the calculated stiffness are also listed.
Figure 6,
Figure 7 and
Figure 8 show, respectively, the displacement responses of the set of four 7.5 × 7.5 mm
2 stake actuators under different loads at ambient (22 °C), 32 °C and 40 °C, when driven up to +240 V. The result shows that there is no phase transformation for all the stake actuators studied under the various operating conditions. The registered stroke (at 240 V) varies from −14 to −58 µm for the four different lengths of stake fabricated.
These 3 figures show that the displacements of all the stakes increase slightly with increasing added load. Despite this, the displacement responses remain largely linear with negligible strain hysteresis. That is, they display high fidelity in their displacement (or strain) response over the operating conditions listed in
Table 1.
While the stroke is relatively insensitive to the applied load, at a given voltage, the displacement increases with temperature. This is because of the temperature dependence of piezoelectric strain coefficients of lead-based relaxor-PT solid solution single crystals. The present study shows that all the curves in
Figure 6,
Figure 7 and
Figure 8 can be fitted to the expression:
where ΔL is the displacement in μm, T the temperature in °C, V the applied voltage in volt, L
ac the active length of the actuator in mm; and a = 4.8 × 10
−3 and b = 7 × 10
−5 in Equation (1). For the three sets of stake actuators shown in
Table 1, L
ac = (L − 3) for L ≤ 28 mm and L
ac = (L − 4) for L ≥ 41 mm, corresponding to single-level and 2-level stake constructions, respectively, where the length differential (L − L
ac) gives the total length of the inactive components in the various stakes. This equation can be used as a guide to estimate the displacement of the actuator under various temperatures and applied voltages.
As mentioned previously, [011]-poled d32-mode single crystals of both binary PZN-PT and ternary PIN-PMN-PT solid solutions having TRO ≈ 110–125 °C have comparable phase transformation and piezoelectric strain coefficients. The present work further shows that stake actuators of identical construction made of d32-mode single crystals of PZN-PT and PIN-PMN-PT exhibit very similar transformation curves and performance characteristics.
3.4. Comparison with Commercial Piezoceramic Stacks
Table 2 compares the performance of the Hi-Fi stake actuator studied in the present work with three state-of-the-art commercial piezoceramic stacks of comparable overall length of L = 36–41 mm. The three commercial stacks chosen are: P.I. (P-885.91; Lederhose, Germany) [
12], NEC-Tokin (AE0505D44H40DF; Shiroishi, Japan) [
13] and Thorlabs (PK4FYP2; Newton, NJ, USA) [
14].
This table shows that the Hi-Fi stake actuator not only has comparable stroke but also its displacement response is linear with negligible hysteresis. In contrast, while state-of-the-art PZT multilayer stack actuators are of comparable or larger stroke, their displacement responses are non-linear and of large hysteresis (of ≥12% typically).
Commercial stack actuators are of multilayer construction, in which each PZT ceramic layer could be 0.15 mm or smaller in thickness, and up to hundreds of layers are possible. As such, they are driven at comparatively high electric fields. Domain switching and domain wall movements are the key mechanisms responsible for the induced strain and hence displacement in piezoceramics. These mechanisms dissipate energy, resulting in large hysteresis in the resultant device [
3,
4,
5].
Also provided in
Table 2 (last column) is a multilayer stack actuator made of [001]-poled PMN-PT single crystal reported by Jiang et al. [
15]. It is interesting to note that despite having a higher equivalent maximum strain, the PMN-PT single crystal stack also displays considerable strain hysteresis of >10%. Similar observations were also made by other researchers [
16,
17]. We shall discuss the plausible reasons below.
3.5. Large Stroke, Hysteresis-Free Response of Single Crystal Stake Actuators
The reasons for the large stroke yet linear and hysteresis-free displacement response of the Hi-Fi stake single crystal actuators studied have been discussed at length in Ref. [
10]. That is, they are the result of the highly stable engineered domains in piezoelectric single crystals and the simple pipe-like construction of the device.
The extremely large piezoelectric coefficients and the extremely low S–E hysteresis of lead-based relaxor-PT solid solution single crystals have been the subject of several investigations [
18,
19]. Unlike piezoceramics, when the single crystal is poled along certain low-index non-polarization crystal directions, say, along either [001] or [011] crystal directions, very few stable polarization states remain and a high macroscopic symmetry multi-domain structure is formed, i.e., of 4R or 2R domain state in [001] and [011]-poled single crystals, respectively, R denoting the room temperature rhombohedral phase. The polarization vectors of the resultant domains in both cases lie at large angles to the applied electric field direction, which is typically the same low-index crystal poling direction. For lead-based relaxor-PT solid solution single crystals of compositions close to the morphotropic phase boundary (MPB), the energy profiles of the various phases are relatively flat, which facilitates polarization rotation in the crystal from the R phase via metastable phases of comparable energy [
20,
21,
22]. This results in extremely large shear piezoelectric coefficients and, correspondingly, large longitudinal and transverse piezoelectric coefficients and hence axial strains of [001] and [011]-poled single crystals [
23].
In a recent work, Li et al. [
24] reported the results of a phase field study, which shows that this phenomenon is closely linked to the existence of polar nano-regions in lead-based relaxor single crystals. At temperatures above about 120 K, these polar nano-regions would line up to lower the strain gradient and elastic energy in the crystal with their polarization vectors lying at large angles to the applied electric field. The said colinear configuration of polar nano-regions, together with the relatively flat energy profiles of the various phases in both the polar nano-regions and the ferroelectric matrix phase of near MPB composition, gives rise to an abrupt increase in the transverse dielectric permittivity and piezoelectric shear coefficients of the crystal. For [001] and [011] poled domain-engineered relaxor-PT single crystals, this not only leads to large longitudinal and transverse strains via easy polarization rotation but also the induced piezoelectric effect is nonhysteretic [
24]. Their experimental results further showed that the said phenomenon accounts for close to 50–80% of the piezoelectric coefficients at room temperature.
It should be stressed that the large angular difference of the polarization vectors between adjacent domains and their high symmetry deposition make the engineered domain structure highly stable against domain switching and domain wall movement even at an applied electric field close to the transformation field of the crystal. All these account concertedly for the large but nonhysteretic longitudinal and transverse strains in [001] and [011]-poled lead-based relaxor-PT solid solution single crystals [
18,
19,
24].
Another important reason of the hysteresis-free strain behaviors of the stake single crystal actuator is its very simple construction. As described above, attempts had also been made by contemporary researchers to fabricate multilayer stack actuators from domain-engineered single crystals [
15,
16,
17]. However, strain hysteresis was again noted in the fabricated single crystal stacks, as evident in
Table 2.
Two reasons may account for the unexpectedly large strain hysteresis displayed by the single crystal stacks. First, thin [001]-poled PMN-PT single crystals were used in the quoted studies [
15,
16,
17]. This crystal has lower transformation properties compared with PZN-PT and PIN-PMN-PT single crystals used in the present work. Even at 150 V, the applied electric field could be quite close to the phase transformation field of the PMN-PT crystals used. It is thus possible that local phase transformation could have occurred in the component crystals. Second, since strain hysteresis persists even at lower applied voltages [
15], the complex structure of the single crystal stack actuator with many intermittent piezoelectric and nonpiezoelectric layers may also play a role. Structurally, the nonpiezoelectric component in the stack will produce a constraint effect on the responding piezoelectric components. For instance, Feng et al. [
16] noted that the electrodes in between the crystals produce a clamping effect on the piezoelectric material, reducing its piezoelectric response. The said constraint effects introduce internal stresses and strains in the device during operation which is a source of mechanical strain hysteresis. As similar mechanical constraints also present in multilayer piezoceramic stacks, this may partly account for the high S–E hysteresis displayed by the various commercial stacks in
Table 2.
The Hi-Fi stake actuators studied in the present work are constructed by bonding 4 rectangular [011]-poled PZN-PT or PIN-PMN-PT single crystals into a square-pipe construction with soft and compliant polycarbonate edge guides, which help to simplify the fabrication process. Such a construction minimizes the number of epoxy joints in the device. This, together with the relatively soft edge guides, enables the crystals to deform freely under the influence of the external field, thus minimizing mechanical hysteresis arising from differential strains in the resultant actuator. In addition, the hollow square-pipe construction also serves two other important functions. Firstly, it helps to limit the volume of the single crystal needed for cost effectiveness. Secondly, despite the edge guides being made of soft PC strips, their use enables the bonded crystals to reinforce and strengthen one another to various degrees which, in turn, greatly increases the bending and twisting strength of the resultant stake actuator.
Lastly, to obtain near-hysteresis-free linear S-E behavior, the operating conditions of the stake actuators must be kept below the transformation field of the active material, taking into consideration the temperature and stress experienced by the component crystals. The use of [011]-poled PZN-PT and PIN-PMN-PT single crystals of relatively high transformation temperatures are critical in this regard.
While the focus of the present work is on cost-effective Hi-Fi Stake piezo single crystal actuators for practical purposes, it should be noted that the performance of the stake actuators depends strongly on the actual operating condition and the volume of the crystal used provided that the occurrence of phase transformation in the crystals during use could be avoided. For instance, at low operating loads (say, ≤2 kg), the stroke of a similar stake actuator of 28 mm in length made of PZN-5.5%PT single crystal can be effectively increased to 37 μm when the maximum applied voltage is increased to 300 V [
10]. This gives an equivalent maximum strain of 0.13%, which is 15–30% larger than that available with state-of-the-art commercial PZT stacks of the same length. When needed, the stroke, operating loads and use temperature of the stake actuator can be increased accordingly by using a larger crystal volume. Furthermore, by using a high-bending-stiffness 2-level (2×-) connector currently being experimented with by us, the stroke and blocking force of the resultant device can be easily doubled (or tripled) [
25].
Also being studied is the fatigue property of Hi-Fi Stake piezo single crystal actuators developed in the present work. It should be noted that in addition to the linear and extremely low strain hysteresis characteristics, PZN-PT and PIN-PMN-PT single crystals of d
32 mode have extremely low dielectric loss, being ≤0.2% compared with 0.4–0.8% for hard PZT ceramics and 2–5% for typical soft PZT ceramics. All these are expected to give rise to improved fatigue properties of the Hi-Fi stake actuator and resultant devices. For instance, d
32 mode PZN-5.5%PT single crystals have been successfully utilized by us to make compact, low frequency (of 15 kHz central frequency) broad band underwater projectors. When operating at full source level at 10% duty cycle (at 100 V
rms, corresponding to a source level of 180 dB re 1 µPa at 1 m), the temperature increase is only a few degrees (i.e., <5 °C) as judged from the capacitance increase of the single crystal [
26]. This compares favorably with the severe heat generation for underwater projectors made of PZT ceramics, of which a 50 °C–100 °C temperature increase is common. The results of the various studies described above on Hi-Fi stake piezo single crystal actuators will be published when available.