Effect of low-frequency alternating current poling on 5-mm-thick 0.7Pb(Mg_1/3Nb_2/3)O₃-0.3PbTiO₃ single crystals

The studies on the solid solution of (1 − x)Pb(Mg_1/3Nb_2/3)O₃-xPbTiO₃ (PMN-xPT) and other ferroelectric relaxors have been the focus for piezoelectric material development over the past few decades due to their outstanding piezoelectric and electromechanical properties.^1–3 Advanced sensors, actuators, and transducers using PMN-xPT as their core components are also extensively investigated.^2,4–8 These growing applications bring rising property requirements for the PMN-xPT single crystals, such as enhanced piezoelectric coefficients and a wide range of working temperatures. To fulfill these demands, a variety of engineering efforts have been conducted for PMN-xPT single crystals. In general, these efforts can be classified into two main types: one is intrinsic or a composition-changing method, including doping or changing the solid solution components^9–11 and the other is extrinsic and represented by domain (wall) engineering methods.² Generally, domain engineering is an essential and time-tested process for property enhancement by utilizing the domain structure-property relationship.^2,12 Nowadays, the domain engineering methods have also developed many different ways to manipulate the domain structure, including applying engineered electrodes^13–17 and tuning the poling conditions.^2,18–21

Recently, alternating current (electric field) poling (ACP), as a type of domain engineering method tuning the poling conditions, has been attracting much attention for its advantages of impressive property enhancement and easy implementation. ACP was introduced in the patents of Yamamoto and Yamashita et al.^22,23 Our previous ACP study¹⁹ on a [001]-oriented PMN-0.3PT single crystal (9.2 × 9.2 × 0.6 mm³) exhibited an enhanced piezoelectric coefficient (d₃₃) of 2000 ± 10 pC/N and a dielectric constant (ε^T₃₃/ε₀) of 8500 ± 100 at room temperature. This 20% enhancement over those of direct current (electric field) poling (DCP) was further improved to 40% in a later ACP temperature optimization study, where the poling temperature was raised from room temperature to about 70 °C.²⁴ At the same time, the effectiveness and reliability of ACP were also proved by many other research groups,^25–27 while the complexity of this method requires more efforts in the enhancement mechanism study. Currently, the domain engineering model is based on the static lattice symmetry from X-ray diffraction (XRD) and domain morphology from piezoresponse force microscopy (PFM).¹⁹ A field-induced phase transition from rhombohedral to monoclinic and higher domain wall density are found in the ACP samples, which are both believed to be the origins of the property enhancement.¹⁹ In comparison to the static model studies above and many domain switching dynamics studies on DCP ferroelectric materials,^28–32 the ACP dynamics during the saturation process has seldom been investigated. For example, the studied ACP frequency (f_ACP), the frequency of the alternating electric field used for poling, was set as 1 Hz^19,26 or higher,²⁵ and the impact of f_ACP has not yet been fully understood.

On the other hand, for relatively low working frequency (50–800 kHz) transducers, high-performance piezoelectric single crystals with thicknesses ranging from several millimeters to a few centimeters are usually the only choice.^2,33 At present, ACP enhanced, thick (more than 1 mm) (001)-oriented PMN-PT has not been reported yet. According to the foregoing domain engineering reports,² the high domain wall density observed in ACP samples^19,24 likely corresponds to the larger number of nuclei for field induced structural phase transitions, which is the key to the property enhancement. Such effect from the domain wall density could be amplified by the sample thickness, and a weak scaling effect was also observed by Qiu et al. for PMN-29PT single crystals from 100 μm to 500 μm, showing the increasing ACP enhancement from the thicker samples.²⁶ Thus, to explore the effective thickness coverage of the scaling effect, the sample thickness is extended to 5 mm in this study.

The purpose of this work was to study the effect of ACP on 5-mm-thick PMN-0.3PT single crystals and the influence of f_ACP. Saturated properties, saturating speed, coercive field, and polarization switching were compared for ACP samples with different f_ACP. The corresponding polarization-vs-electric field hysteresis loops (P-E loops) were analyzed to study the ACP dynamics during the saturation process.

The [001]-oriented PMN-0.3PT single crystals (from CTS Corp., IL, USA) were diced into 5 × 1.25 × 1.25 mm³ bars with Ti/Au (10/100 nm) electrodes on the top and bottom surfaces (1.25 × 1.25 mm²). Four samples were tested in total to ensure the repeatability of experiments. Every sample was heated up to 250 °C for 30 min with shorted top and bottom electrodes to be fully depoled before the poling process. To achieve the ACP, a bipolar voltage was generated by a function generator (Agilent 33250A, Santa Clara, CA, USA), and then amplified by a high-voltage amplifier (Trek Model 2220, Lockport, New York, USA) before application to the samples. According to our previous study,²⁴ the alternating electric field amplitude was set as 10 kV/cm (peak-to-peak field). For the DCP tests, the direct current field of 5 kV/cm was applied for 60 s according to the IEEE standard.³⁴ The overpoling issue³ was not observed in all tests in this study.

To track the ACP process in every ACP cycles, d₃₃ was measured using a quasistatic piezo d₃₃ meter (Model ZJ-4B, Chinese Academy of Science). ε^T₃₃/ε₀ was calculated from the electrical capacitance measured by a precision impedance analyzer (Agilent 4294A, Santa Clara, CA, USA) at 1 kHz. The impedance analyzer also provided the electromechanical coupling factor k₃₃, which was calculated from the measured resonant frequency (f_r) and antiresonant frequency (f_a).

The P-E loops were measured by a Precision Premier II Ferroelectric Tester (Radiant Technologies Inc., Albuquerque, NM, USA). The tested samples were depoled before the measurements. Bipolar triangular voltage with different frequencies was applied to the samples to generate alternating electric fields with a peak amplitude of 10 kV/cm. Here, P-E loop measurements with no preset loop were used to track the ACP saturation dynamics.

Figure 1 illustrates that the piezoelectric properties gradually become saturated with increasing number of ACP cycles, similar to results stated in previous reports.^19,25,26 The saturated properties from Fig. 1 are listed in Table S1 with the exact values. Here, the ACP enhancement on long bar samples is proven to be higher compared with the result on thin plate samples (9.2 × 9.2 × 0.6 mm³ and electrodes on 9.2 × 9.2 mm² surfaces).¹⁹ Using the same f_ACP (1 Hz), the long bar samples can receive 64% and 65% improvement on d₃₃ and ε^T₃₃/ε₀, respectively, while the enhancement on thin plate samples is only 21% (d₃₃) and 38% (ε^T₃₃/ε₀).¹⁹ It proves that the above-mentioned scaling effect is still effective when the sample thickness is increased to 5 mm.

More importantly, Fig. 1 illustrates the influence of f_ACP (from 0.01 Hz to 10 Hz) on ACP saturated properties (replotted in Fig. S1) and the saturation process. In general, ACP samples with lower f_ACP have higher saturated d₃₃, ε^T₃₃/ε₀, and coupling factor k₃₃, as well as lower dielectric loss and faster saturation speed. The highest d₃₃ and ε^T₃₃/ε₀ enhancement from ACP occurs when f_ACP is 0.01 Hz, where d₃₃ and ε^T₃₃/ε₀ are 3200 pC/N and 10 800, respectively. The corresponding percentage increase from 0.01 Hz ACP to DCP on d₃₃ and ε^T₃₃/ε₀ is 67%. Besides, 0.01 Hz ACP samples have the highest k₃₃ (0.94) compared to 0.92 from the DCP samples. Figure S2 provides the detailed frequency response of k₃₃ modes, which also shows 9% of lower frequency constant N₃₃ (703 Hz m) from ACP compared to N₃₃ (768 Hz m) for DCP. The lower N₃₃ is beneficial to lower the cost of single crystal transducers since the same frequency transducer can be manufactured from a smaller dimension.

Compared to the saturated properties, the influence of f_ACP is more significant on the saturation speed (cycle number). As shown in Fig. 1(a), a higher f_ACP corresponds to a lower ACP saturation speed, and a threshold of f_ACP near 1 Hz is observed. More specifically, when f_ACP is lower than 1 Hz, the portion of the property curves associated with the saturation process overlap with each other in Fig. 1. In contrast, the saturation process requires significantly more cycles when f_ACP is higher than 1 Hz. This threshold near 1 Hz was then studied by P-E loop measurements below.

Contrary to the conventional P-E loop measurements, all tested samples in this study were fully depoled, and there was no preset loop before data collection. The electric field used in the P-E loop measurement can be treated as the alternating electric field used for poling. Thus, in Fig. 2, different loops within each panel represent the different ACP cycle numbers during the ACP saturation process, and cycle 1 (the first loop) begins at P = 0.

The influence from f_ACP starts from cycle 1, and a simpler comparison is provided in Fig. S3. The first half cycle of cycle 1 represents a DCP-like monopolar poling process, while the range of the positive remnant polarization (P_r⁺) after the first half cycle is relatively small (25.6–27.8 μC/cm²) for different f_ACP. In contrast, a more significant impact from f_ACP appears in the second half cycle of cycle 1, the first back-switching process. For f_ACP lower than 1 Hz, the polarization can be fully or near-fully back-switched. Relatively, the polarization back-switching process cannot be fully completed for f_ACP higher than 1 Hz, and the positive-negative remnant polarization gap (ΔP_r) values drop dramatically with increasing f_ACP. According to domain switching dynamics, this result is due to the limited speed of domain wall motion^35,36 and back switched domain structure formation (nucleation-growth).^28,30,31 In the case of f_ACP = 10 Hz, the polarization cannot even be back switched after the complete cycle 1. Thus, the f_ACP threshold (1 Hz) in Fig. 1 appears again in the P-E loops (Fig. 2).

To better discuss the origin of the f_ACP influence, the low-frequency and high-frequency ACP processes can be described separately by introducing the intrinsic polarization switching frequency (f_i). Based on the hysteresis loop result shown in Fig. 2, f_i can be defined as: when f_ACP ≤ f_i, the polarization of the ACP sample can be fully back switched after the complete cycle 1. Since the domain growth velocity is thickness-independent,³⁶ the time required for the domain to fully back-switch, as well as f_i, is sample thickness dependent. In this work, f_i is near 1 Hz for 5-mm-thick PMN-PT samples. In the subsequent text, “low-f_ACP” refers to f_ACP, that is, lower than f_i, and “high-f_ACP” refers to f_ACP, that is, higher than f_i.

Except for the first loop (cycle 1), the loops are recentered in each panel of Fig. 2, which results in some polarization discontinuities between the end of one loop and the beginning of the next one. Such polarization discontinuities, as well as the unsaturated back-switching maximum polarization at the same loop, mark that the ACP saturation process contains loops whose polarization is not entirely switched. All the discontinuities disappear with increasing ACP cycle number, while the cycle at which they disappear is frequency dependent. The discontinuities are still evident in high-f_ACP samples [Figs. 2(c) and 2(d)] in cycle 10, while the loops from low-f_ACP [Figs. 2(a) and 2(b)] overlap after 3–5 loops. This difference corresponds to the f_ACP-dependent saturation speed shown in Fig. 1.

Figure 3 shows the coercive fields (E_c) [Fig. 3(a)], positive remnant polarization (P_r⁺) [Fig. 3(b)], and the maximum instantaneous forward-switching current densities (J_max⁺) [Fig. 3(c)] during the ACP saturation process and compares the influence from different f_ACP. The f_ACP-dependent saturation speed can also be observed in Fig. 3. It should be noted first that the saturated E_c is f_ACP-dependent, while the saturated P_r is not. From the view of the energy, the P_r in each loop represents the accumulated static electrical energy from the ACP saturation process, and the E_c represents the switching energy barriers.³⁷ Thus, the f_ACP-independence of saturated P_r shows that the stored static electrical energy has a fixed maximum during the ACP process, while the f_ACP-dependence of the saturated E_c means that the switching energy barrier is f_ACP related. Similar frequency-dependent E_c in ferroelectric materials was previously reported in doped Pb(Zr_0.53Ti_0.47)O₃ ceramics,²⁸ Pb(Zr_0.2Ti_0.8)O₃ thin films,³⁸ Pb(Zn_1/3Nb_2/3)O₃–0.045PbTiO₃ single crystals,³⁷ and PMN-0.29PT single crytals.^32,39 During the polarization reversal, the limit speeds of the opposite domain nucleation and the following domain wall motion are the main reasons for the frequency dependent E_c.^37,38 In addition, the E_c tuning from the f_ACP is also partly affected by the dipolar defects.^28,40 The calculated internal bias fields (E_i) from Fig. 2 (listed in Table S2) show the nonlinear relationship with the f_ACP. In the low-f_ACP cases, the E_i values are close to zero, showing that the dipolar defects are fully switched in every half cycle. In the high-f_ACP cases, the E_i becomes observable, showing that the dipolar defect switching speed is slower than the polarization switching speed.

It should also be noted from Fig. 3(a) that the E_c of ACP samples can be broadly tuned from 1.8 kV/cm to 3.0 kV/cm by changing the f_ACP (0.1–10 Hz). The E_c tunability from ACP is significantly broader compared to the reported 2–2.5 kV/cm in DCP PMN-0.29PT.³² Therefore, ACP can not only be used to considerably enhance the d₃₃ and ε^T₃₃/ε₀, but also the coercive field (67% higher E_c with only 4% degradation in d₃₃ by changing the f_ACP from 0.1 Hz to 10 Hz).

In addition to the P-E loop measurement above, the waveforms of the electric field and current density were recorded synchronously (Fig. S4). Summarized from the waveforms, the relationship between the maximum instantaneous forward-switching current densities (J_max⁺) and f_ACP is then shown in Fig. 3(c). In short, higher J_max⁺ appears with higher f_ACP. In addition, J_max⁺ values are not changing much in the low-f_ACP cases but increase a lot in the high-f_ACP cases during the saturation process. Such a difference is associated with the P_r pattern changes shown in Fig. 3(b).

For the same single crystal size, the higher J_max⁺ also drives the faster domain wall motion and results in the higher internal friction.^41,42 Thus, compared to the low-f_ACP samples, the high-f_ACP ones have even greater energy loss due to the accumulated internal friction within the slower saturation process. As a result, the property degradation increases with the f_ACP, as shown in Fig. 1. Therefore, in practical applications, e.g., low-frequency transducers, it is recommended to use low-f_ACP for better enhancement with lower energy loss. When high-f_ACP is used for higher E_c, the heat generation, mechanical cracks, and other drawbacks from the high switching current during the poling process must also be considered.

In summary, ACP is further studied for 5-mm-thick PMN-0.3PT single crystals, showing a greater property enhancement than we previously achieved on thin plate samples. The impacts from different ACP frequencies (f_ACP) are also compared, and the most significant improvement appears when f_ACP is 0.01 Hz, with d₃₃ and ε^T₃₃/ε₀ increased to 3200 pC/N and 10 500, respectively, which are 67% higher than those from DCP samples. In general, ACP samples with lower f_ACP had higher saturated d₃₃, ε^T₃₃/ε₀, and coupling factor k₃₃, as well as lower dielectric loss and faster saturation speed. In addition, the E_c of ACP samples could be further tuned from 1.8 kV/cm to 3.0 kV/cm by changing the f_ACP (0.1–10 Hz). These findings may be useful for low-frequency transducer (millimeter to centimeter thick single crystal) development.

See the supplementary material for the detailed property enhancement from ACP (Table S1); the effect of different f_ACP on the saturated properties (Fig. S1); the frequency response of k₃₃ mode from both DCP and ACP samples (Fig. S2); the first P-E hysteresis loop (ACP cycle) from every f_ACP extracted from Fig. 3 (Fig. S3); the detailed coercive fields from different f_ACP based on Fig. 2 (Table S2); the waveforms of electric field and current density from P-E hysteresis loops measurement (Fig. S4); the relationship between the maximum instantaneous back-switching current densities and f_ACP (Fig. S5).

This work was primarily supported by ONR under Grant No. N00014-18-1-2538. The author would like to thank Dr. Ching-Chang Chung and Rachel Broughton for their assistance in collecting P-E loop data.