Alternating current poling (ACP) was performed on Gen III relaxor-PT Mn-doped Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (Mn: PIN-PMN-PT) single crystals with the poling direction of [001]. Experimental results proved that ACP could bring property enhancement to both k31 and k33 mode crystals. Compared to those from traditional direct current poling (DCP), ACP with the optimized conditions (20 kV/cm, 0.1 Hz, and 20 cycles) enhanced the dielectric and piezoelectric properties of k31-mode mode crystals by more than 30%, where the enhanced free dielectric constant and piezoelectric coefficient d33 reached 5300 and 1750 pC/N, respectively. Furthermore, replacing DCP with ACP could increase the advantages of Gen III relaxor-PT. The coupling factors k31 and k33 were enhanced to 0.472 and 0.915, the mechanical quality factor Qm was enhanced by 17%, and the depoling temperature was raised by 17 °C to 123 °C. In the following mechanism study, in situ x-ray diffraction (XRD) combined with the temperature-dependent dielectric constant measurement proved the introduction of the monoclinic phases after ACP, while piezoresponse force microscopy (PFM) observation showed “2R”-like “2M” domain morphologies in ACP single crystals. Both these intrinsic and extrinsic factors are believed to be the keys to the mechanisms of property enhancement behind ACP. This study proved that ACP is an effective property enhancement method suitable for Gen III relaxor-PT single crystals and will promote its applications in high-temperature and high-power devices.

During the rapid development of ferroelectric materials in the past several decades, relaxor-based crystals such as (1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-xPT) exhibit an ultrahigh piezoelectric coefficient (d33 > 1600 pC/N), dielectric constant (εT33/ε0 > 6000), and electromechanical coupling factor (k33 > 0.9) especially with compositions near the morphotropic phase boundary (MPB).1–3 However, there are some drawbacks of these Gen I4 single crystals. For instance, their low coercive field (EC ∼ 2 kV/cm), low rhombohedral-to-tetragonal phase transition temperature (TRT < 90 °C), and low Curie temperature (TC < 140 °C) seriously limit their applications in high-temperature and high-power devices. To overcome these restrictions, the ternary solid solution Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIN-PMN-PT)5–11 was first developed as the Gen II relaxor-PT with higher depoling/Curie temperatures and larger coercive fields. At the same time, the manganese-doped PIN-PMN-PT (Mn: PIN-PMN-PT) was also developed as the Gen III relaxor-PT for high-power applications since the acceptor (Mn) doping could lower the dielectric loss and mechanical loss, which were essential for suppressing heat generation and also for improving the mechanical quality factor (Qm).4 However, the piezoelectric and dielectric properties of the Gen III relaxor-PT were simultaneously impaired.11–13 Thus, finding how to improve the dielectric and piezoelectric properties of Gen III relaxor-PT single crystals after the acceptor doping will become the main task of high-power relaxor-PT application development.

For Gen III relaxor-PT single crystals, it is not suitable to introduce the donor dopant, which can enhance the piezoelectric property but make material “softer.”14 Thus, a domain engineering15 method was used in this study for property enhancement without changing the material compositions. The dependence of the piezoelectric properties on the engineered domain size was first mentioned in the studies on barium titanate crystals by Wada et al.16 It was pointed out that higher domain wall density could lead to higher piezoelectric properties. Most of the domain engineering methods are associated with the poling condition tuning. For example, field cooling17,18 (FC, i.e., cooling a ferroelectric under the application of electric fields from high temperature) is widely used in ferroelectrics poling. Other options include electrode engineering, which, as reported by Yamashita et al.19 and Chang et al.,20 proved that the piezoelectric response of PMN-PT crystals could be enhanced by more than 30% by introducing nanoelectrodes.

In the last few years, alternating current field poling (ACP)21,22 became a popular domain engineering method for property enhancement. The successful applications of ACP on Gen I PMN-PT single crystals23–26 encourage further ACP compatibility studies on ternary Gen II relaxor-PT single crystals.27–31 Ma et al.31 reported that ACP could bring nearly 54% piezoelectric property enhancement on the [001]-poled 0.25PIN-0.43PMN-0.32PT (MPB) single crystal. Other reports by Guo et al.29 and Liu et al.30 proved that the property enhancement from ACP was closely related to the orientations and the phases of relaxor-PT crystals.

Although there are plenty of ACP studies on Gen I & II relaxor-PT single crystals, only Jiang et al.32 reported the effect of ACP on Gen III Mn: PIN-PMN-PT single crystals and the mechanism behind it is still unclear. In this paper, we systematically studied the effects of ACP on the dielectric, piezoelectric, and electromechanical properties of Mn: PIN-PMN-PT single crystals. The domain engineering of ACP was explained by lattice symmetry and domain structure characterization studies, and the mechanisms of property enhancement behind ACP were then discussed based on the structure-property relationship.

The [001]-oriented 1 mol. % Mn: PIN-PMN-0.27PT single crystals (TRS Technologies Inc., PA, USA) were diced into k31 mode (10 × 3 × 1 mm3) and k33 mode (3 × 0.75 × 0.75 mm3) with Ti/Au (10/200 nm) electrodes. The k31-mode samples were used for the main parts of this work including the effect of ACP on dielectric, piezoelectric, and electromechanical properties of the Mn: PINPMNPT single crystals, as well as the single crystal structures, while the k33-mode samples were only used to study the influence of ACP on mechanical quality factor Qm.33 The poling processes were performed under the AC/DC electric field with different parameters in an oil-bathed sample holder. For the ACP samples, a bipolar triangle wave electric field was generated by a function generator (Agilent 33250A, Santa Clara, CA, USA) first and then amplified by a high-voltage amplifier (Trek, 609B, New York, NY, USA) before being applied to the samples. In this work, the AC fields with different frequencies and amplitudes were applied at room temperature, while DCP samples were poled at room temperature with different field amplitudes for 5 min.34–38 

After poling, piezoelectric coefficient d33 was measured using a quasi-static piezo d33 meter (Model ZJ-4B, Chinese Academy of Science, China). Meanwhile, εT33/ε0 was calculated from the electrical capacitance measured using a multi-frequency LCR meter (Agilent 4294A, Santa Clara, CA, USA) at 1 kHz. Electromechanical coupling factors k31 and k33 were calculated at corresponding resonance and antiresonance frequencies.34 The transversely poled length-extensional piezoelectric coefficient (d31) was calculated as per the IEEE standard.34 The mechanical quality factors Qm were calculated by the 3 dB method; and its details are shown in Fig. S1.33 

FIG. 1.

Influences of electric field amplitude and frequency on piezoelectric and dielectric properties of ACP and DCP k31-mode Mn: PIN-PMN-PT single crystals: (a) piezoelectric coefficients d33 and d31, (b) dielectric constant and dielectric loss with different electric field amplitudes, (c) piezoelectric coefficient d33 and d31, and (d) dielectric constant and dielectric loss with different electric field cycle numbers NL at different frequencies.

FIG. 1.

Influences of electric field amplitude and frequency on piezoelectric and dielectric properties of ACP and DCP k31-mode Mn: PIN-PMN-PT single crystals: (a) piezoelectric coefficients d33 and d31, (b) dielectric constant and dielectric loss with different electric field amplitudes, (c) piezoelectric coefficient d33 and d31, and (d) dielectric constant and dielectric loss with different electric field cycle numbers NL at different frequencies.

Close modal

The effect of ACP on the crystal structure was then characterized by in situ x-ray diffraction (XRD) (SmartLab, Rigaku, Tokyo, Japan) and piezoresponse force microscopy (PFM) (Dimension Icon, Bruker, Santa Barbara, CA, USA). XRD and temperature-dependent dielectric constant measurements were used to determine the intrinsic lattice symmetry during the zero field heating (ZFH) or depoling process with the same heating rate of 1 °C/min from 25 °C to 250 °C. The corresponding extrinsic domain morphologies were observed by PFM at room temperature. PFM images were scanned on the freshly cracked (010) surfaces, the same as our previous studies.23,39,40 Three samples for each mode were tested in total to ensure the repeatability of the experiments, where all reported properties are the average values of these samples. Every sample was fully depoled by heating up to 350 °C for 30 min with shorted top and bottom electrodes before every poling process.23,28,40,41

Figure 1 shows the measured dielectric and piezoelectric properties of k31-mode Mn: PIN-PMN-PT samples using both DCP and ACP methods with different poling frequencies and electric field amplitudes. The effect of electric field amplitudes was studied first, and the results are shown in Figs. 1(a) and 1(b). In this case, according to our previous published results,41 the ACP frequency (fACP) and ACP cycle number (NL) were set as 0.1 Hz and 20, respectively. In Figs. 1(a) and 1(b), the piezoelectric coefficients d33 and d31 can reach their highest values when the electric field is higher than a threshold Eth ∼ 20 kV/cm (peak-to-peak). Meanwhile, the hysteresis loop measurement (Fig. S2) at 0.1 Hz shows that the coercive field EC is 5.1 kV/cm, suggesting a relationship of Eth ∼ 4 × EC, which is also reported in Gen I PMN-PT studies.40,41

FIG. 2.

(004) peaks of XRD results of (a) DCP and (b) ACP Mn: PIN-PMN-PT single crystals during the zero field heating process. Lattice symmetries are presented at several temperatures: (c) 30 °C (d) 112 °C, and (e) 150 °C. (f) Unpoled, DCP, and ACP Mn: PIN-PMN-PT single crystals during the zero field heating process.

FIG. 2.

(004) peaks of XRD results of (a) DCP and (b) ACP Mn: PIN-PMN-PT single crystals during the zero field heating process. Lattice symmetries are presented at several temperatures: (c) 30 °C (d) 112 °C, and (e) 150 °C. (f) Unpoled, DCP, and ACP Mn: PIN-PMN-PT single crystals during the zero field heating process.

Close modal

In Figs. 1(a) and 1(b), we selected the fACP value as 0.1 Hz according to our previous result on Gen I PMN-PT.41 Thus, it is still necessary to study the effect of fACP on the ACP process of Mn: PIN-PMN-PT, and the comparison of different fACP is given in Figs. 1(c) and 1(d). With the increase in NL, the piezoelectric coefficients d33 and d31 and free dielectric constant εT33/ε0 gradually became saturated, while dielectric loss decreased quickly first but then slightly increased. Since the ACP saturation processes of 0.1 and 1 Hz were nearly overlapping, the intrinsic bulk polarization switching frequency fi was higher than 1 Hz. Similar to the conclusion on the effect of fACP from our Gen I PMN-PT single crystal report,41 in Figs. 1(c) and 1(d), low-fACP (fACP < fi, 0.1 and 1 Hz) samples needed less NL to get the saturated properties. In contrast, high-fACP (fACP > fi, 10 Hz) needed much higher NL (NL = 100) to achieve the saturated state. For Mn: PIN-PMN-PT, it was expected to have the defect dipoles of [MnTiVO··], which hinder the motion of domain walls.42–44 Such an effect is also revealed in the hysteresis loop measurement (Fig. S2), where the inner biases Ei were 1.10, 1.99, and 2.23 kV/cm for 0.1 Hz, 1 Hz, and 10 Hz, respectively. The difference in Ei showed that the intrinsic defect dipole switching frequency was lower than 0.1 Hz and fi. Compared with low-fACP (0.1 Hz) samples, the d33 value drops by 5.7% from 1750 to 1650 pC/N, and the εT33/ε0 value decreased by nearly 10% from 5300 to 4800 in the case of high-fACP (10 Hz). The disadvantages from the high-fACP are higher in Mn: PIN-PMN-PT than in PMN-PT.41 Compared with PMN-PT, the higher defect dipole concentration in Mn: PIN-PMN-PT caused the severer inner friction during the ACP process, which resulted in the lower property enhancement, especially in the case of high-fACP.

The detailed property comparison between DCP and ACP samples can be found in Table I. Compared with DCP samples, ACP samples had higher piezoelectric coefficients d33 and d31, higher free and clamped dielectric constants, and higher electromechanical coupling factors k31 and k33. The best ACP conditions were found to be 20 kV/cm (peak to peak), 0.1 Hz (fACP), and 20 cycles (NL). It should be noted that ACP can also greatly enhance Qm, which is an essential parameter for high-power applications.1,2,15,45 More discussion about Qm will be mentioned in the latter part of this work.

TABLE I.

Comparison of Unpoled, DCP, and ACP Mn: PIN-PMN-PT single crystals.

d33 (pC/N)d31 (pC/N)Free εT33/ε0Clamed εS33/ε0Dielectric Loss (%)k31k33aQma
Unpoled 1900  0.72    
DCP 1350 −390 3700 590 0.30 0.455 0.908 660 
ACPb 1750 −510 5300 800 0.30 0.472 0.915 770 
d33 (pC/N)d31 (pC/N)Free εT33/ε0Clamed εS33/ε0Dielectric Loss (%)k31k33aQma
Unpoled 1900  0.72    
DCP 1350 −390 3700 590 0.30 0.455 0.908 660 
ACPb 1750 −510 5300 800 0.30 0.472 0.915 770 
a

k33 and Qm are from k33-mode samples, and other properties are all from k31-mode samples. More property values from k33-mode samples are provided in Table SI.

b

The best ACP conditions are 20 kV/cm (peak to peak), 0.1 Hz (fACP), and 20 cycles (NL).

Figure 2 shows the effects of ACP on lattice symmetries as well as the phase transition sequence during the zero field heating (ZFH) or depoling process. First, Figs. 2(a) and 2(b) present the continuous tracking on (004) XRD reflections and show two phase transitions for both DCP and ACP samples. The higher phase transition temperatures were the Curie temperatures, which marked the same tetragonal to cubic phase transitions (TC) for both DCP and ACP samples (TC = 191 °C). Since the lower phase transition temperatures or depoling temperatures (Td-DCP = 106 °C and Td-ACP = 123 °C) were different, three specific XRD measurement temperatures were chosen. The temperatures of 30 °C [Fig. 2(c), T < Td-DCP], 112 °C [Fig. 2(d), Td-DCP< T < Td-ACP], and 150 °C [Fig. 2(e), Td-ACP < T] were used to determine the detailed phase transition sequences. In Fig. 2(c), the unpoled sample was also included, while its symmetric (004) peak shows that it was in the rhombohedral phase (R-phase). Compared with the unpoled sample, the peak of the DCP sample did not shift with the 2θ location but becomes moderately unsymmetric with a slightly narrower full width at half maximum (FWHM), showing that the DCP sample remained in the R-phase. On the other hand, the (004) peak of ACP shifted to a higher 2θ angle and developed a highly unsymmetric peak shape, showing the existence of a field-induced phase transition from rhombohedral to monoclinic (RM).23,46,47 Meanwhile, the FWHM of the (004) peak at room temperature 30 °C [Fig. 2(c)] was narrower in ACP, which indicated a longer range of lattice ordering in the ACP sample compared with the DCP one. With the increasing temperature in Fig. 2(d) (112 °C), the (004) peak of DCP shows a remarkable 2θ angle shift, and the appearance of the peak shoulder on the right proves that the DCP sample was already in the tetragonal phase (T-phase). In contrast, the (004) peak of the ACP sample had an unapparent change from its original 2θ location and peak shape at 30 °C in Fig. 2(c), indicating that the ACP sample remained in the M-phase at 112 °C. In the end, the overlapping of the (004) peaks in Fig. 2(e) (150 °C), as well as the same shape of the T-phase peak for the DCP in Fig. 2(d), marks that both the DCP and ACP samples had entered the T-phase at 150 °C.

Further temperature-dependent dielectric constant measurements are shown in Fig. 2(f), where the temperatures in Figs. 2(c)–2(e) are marked with the phase transition temperatures. Unlike previous PMN-PT studies,23,48,49 the typical double phase transition peaks of the dielectric constant near the depoling temperature (Td) of the ACP sample became one single peak in Fig. 2(f). This indicates that the original phase of the ACP samples at room temperature was the M-phase only. Thus, for Mn: PMN-PIN-PT in this study, the DCP and ACP samples have different phase transition sequences during the ZFH process. The processes were defined as RTC for DCP and MTC for ACP, while Td-DCP is the RT phase transition temperature TRT and Td-ACP is the MT phase transition temperature TMT. According to the reports on Gen I PMN-PT, replacing DCP with ACP either did not change or just slightly decreased the Td.23–26,50,51 In contrast, Fig. 2(f) shows that ACP could increase the Td of Mn: PIN-PMN-PT single crystals by 17 °C, indicating that Gen III relaxor-PT with ACP could broaden its potential in high-temperature device applications.

After determining the intrinsic lattice symmetry difference between DCP and ACP domain engineering, the extrinsic domain morphology differences between DCP and ACP were then characterized by PFM for further ACP mechanism studies. Figure 3 shows the domain patterns at the freshly fractured cross sections of samples after DCP and ACP. As marked, the poling electric field was in the horizontal [001] direction. In Figs. 3(a) and 3(b), small pinnate domains can be observed on DCP samples with long near [100]-orientated 109° domain walls and short near [101]-orientated 71° domain walls. The insets show the magnification of the out-of-plane and in-plane phase images for the area marked by white rectangles in DCP Mn: PIN-PMN-PT single crystals. The blue dashed lines and green dotted lines represent the 109° and 71° domains, respectively. The insets in Figs. 3(a) and 3(b) show how the “4R” configuration is formed and how the 71°/109° domain walls are arranged.

FIG. 3.

Domain structures observed by PFM on the freshly fractured surfaces of (a) and (b) DCP and (c) and (d) ACP Mn: PIN-PMN-PT single crystals. The poling direction is along the horizontal [001] direction. Phase images in (a) and (c) are out-of-plane, while those in (b) and (d) are in-plane. Green dotted lines and blue dashed lines in the insets of (a) and (b) denote 71° and 109° domain walls, respectively.

FIG. 3.

Domain structures observed by PFM on the freshly fractured surfaces of (a) and (b) DCP and (c) and (d) ACP Mn: PIN-PMN-PT single crystals. The poling direction is along the horizontal [001] direction. Phase images in (a) and (c) are out-of-plane, while those in (b) and (d) are in-plane. Green dotted lines and blue dashed lines in the insets of (a) and (b) denote 71° and 109° domain walls, respectively.

Close modal

Since the PFM tip scanning direction and the poling direction are the same, the in-plane phase contrast of domain morphologies should contain 109° domains only, like it was shown in the reported Gen I PMN-PT single crystal study. However, in Fig. 3(b), both the 109° and 71° domain walls can be observed. In addition, the 71°/109° domain widths of DCP PMN-0.3PT single crystals were in the range of 900 nm ± 80/2100 ± 700 nm, respectively.23,40 As a comparison, in this study, the 71°/109° domain width ranges were 110 –310 nm/180–690 nm, indicating the smaller and highly fluctuating domain sizes. The possible origin of this domain morphology difference between PMN-PT and Mn: PIN-PMN-PT was the defect dipoles induced by Mn doping,42–44 which greatly increased the randomness of the domain wall ordering.

As a comparison, the ACP sample showed a typical stripe-like ACP domain configuration,23,40,52 which was not the “2R,” but the “2M” configuration according to Fig. 2. Since the morphology pattern was similar and the polarization at the domain wall center would not change after the RM phase transition,53 here we still used 71° and 109° to distinguish these two domain wall types. Thus, the domain morphology of the ACP sample is in a “2R”-like “2M” configuration. Here, in Figs. 3(c) and 3(d), the average 109°domain width of the ACP sample is about 390 nm, which is 30 nm shorter than the DCP sample (420 nm). Also, the width values of the ACP samples were in a narrower range of 280 nm to 560 nm. The corresponding ‘2M’ domain configurations with higher 109° domain wall density and reduced 71° domain wall density after ACP are the extrinsic reasons for the enhancements of properties of ACP Mn: PIN-PMN-PT single crystals.

In addition to the domain wall density, the 109° domain wall length difference between the DCP and ACP samples was also significant for the Mn: PIN-PMN-PT single crystals. In PMN-PT DCP cases, most of the 109° domain walls of PMN-PT single crystals were longer than 5 μm,23 while in Mn: PIN-PMN-PT single crystals, the average value was less than 2 μm in this study. For the ACP cases, most of the 109° domain walls of both PMN-PT23,40 and Mn: PIN-PMN-PT single crystals in this study were longer than 6 μm. The defects introduced by Mn doping not only clamped the domain wall motions but also caused local heterogeneity, which prevented the merging of domain walls during the poling process. For the DCP samples, the defect was almost uniformly distributed and resulted in short domain wall lengths. In contrast, due to the defect drifting during the ACP process, most defects were trapped by the 109° domain walls after ACP. Such defect redistribution lowered the local heterogeneity and resulted in the relatively longer 109° domain walls and low coercive fields.

Generally, high mechanical quality factors (Qm) can be expected after the introduction of Mn doping. Mn2+/3+ in the perovskite structure results in the formation of acceptor-oxygen vacancy defect dipoles, thus causing a hardening effect.54 Figure S3 and Table SII show the impedance spectra and frequency data of the DCP and ACP samples used for the mechanical quality factor (Qm) calculation. The Qm value of the ACP Mn: PIN-PMN-PT is about 770, which was 17% higher than DCP samples (Qm = 660). ACP and DCP have the same antiresonance frequency fa, but the impedance of the ACP sample at fa is much higher than that of the DCP sample, and the ACP impedance peak is sharper. Several previous studies reported that Qm for the same relaxor-PT crystals changes with the domain patterns.4,8,13,55 The report of Zheng et al. showed that their Mn: PIN-PMN-PT with a “4R” domain pattern had the lowest Qm values.13 Correspondingly, the “2M” configuration from the ACP samples [Fig. 3(c)] also obtained a higher Qm value than the “4R” configuration from the DCP samples [Fig. 3(a)]. Meanwhile, the RM phase transition of the ACP samples might also help to increase the Qm.

In summary, the effects of ACP on the piezoelectric, dielectric, and electromechanical properties of Mn-doped PIN-PMN-PT single crystals and the mechanisms were studied in this study. Experimental results proved that ACP could bring property enhancement to both k31 and k33 mode crystals. Compared to DCP, ACP enhanced the dielectric and piezoelectric properties of k31-mode mode crystals by more than 30%, where the enhanced free dielectric constant εT33/ε0 and piezoelectric coefficient d33 reached 5300 and 1750 pC/N, respectively. The best poling conditions were found to be 0.1 Hz, 20 kV/cm, and 20 cycles. Furthermore, replacing DCP with ACP could increase the advantages of Gen III relaxor-PT, where coupling factors k31 and k33 were enhanced to 0.472 and 0.915, the mechanical quality factor Qm was enhanced by 17%, and the depoling temperature was raised by 17 °C to 12 3 °C. After the intrinsic lattice structure and extrinsic domain structure characterization, the enhanced properties of Mn: PIN-PMN-PT by ACP were attributed to two main factors. The first was the monoclinic phases introduced by ACP, which was concluded from both temperature-dependent dielectric properties and XRD reflection tracking during the zero-field-heating process. The other reason was the domain morphology of the “2M” configurations with higher 109° domain wall density, longer 109° domain wall ordering, and reduced 71° domains observed by PFM after ACP. This work illustrates that ACP is an effective and promising method to promote the applications of Generation III relaxor-PT single crystals in high-temperature and high-power devices.

See the supplementary material for further details of the mechanical quality factor Qm calculation, material properties of DCP and ACP k33-mode Mn: PIN-PMN-PT single crystals, P–E loop results, and impedance spectra of DCP and ACP k33-mode Mn: PIN-PMN-PT single crystals for the Qm calculation.

H.W. and C.L. contributed equally to this work.

This work was primarily supported by ONR under Grant No. N00014–18-1–2538. This work was performed in part at Professor Jacob Jones' lab in the MSE Department and the Analytical Instrumentation Facility (AIF) at North Carolina State University, which was supported by the State of North Carolina and the National Science Foundation (Award No. ECCS-1542015). The AIF is a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), a site in the National Nanotechnology Coordinated Infrastructure (NNCI). We would like to thank Rachel Broughton for her help in the P–E loop tests.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
E.
Sun
and
W.
Cao
,
Prog. Mater. Sci.
65
,
124
(
2014
).
2.
S.
Zhang
,
F.
Li
,
X.
Jiang
,
J.
Kim
,
J.
Luo
, and
X.
Geng
,
Prog. Mater. Sci.
68
,
1
(
2015
).
3.
J.
Luo
and
S.
Zhang
,
Crystals
4
(
3
),
306
(
2014
).
4.
S.
Zhang
,
F.
Li
,
J.
Luo
,
R.
Sahul
, and
T. R.
Shrout
,
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
60
(
8
),
1572
(
2013
).
5.
Y.
Hosono
,
Y.
Yamashita
,
K.
Hirayama
, and
N.
Ichinose
,
Jpn. J. Appl. Phys., Part 1
44
(
9B
),
7037
(
2005
).
6.
S.
Zhang
,
J.
Luo
,
W.
Hackenberger
, and
T. R.
Shrout
,
J. Appl. Phys.
104
(
6
),
064106
(
2008
).
7.
X.
Liu
,
S.
Zhang
,
J.
Luo
,
T. R.
Shrout
, and
W.
Cao
,
J. Appl. Phys.
106
(
7
),
074112
(
2009
).
8.
S.
Zhang
,
J.
Luo
,
W.
Hackenberger
,
N. P.
Sherlock
,
R. J.
Meyer
, Jr.
, and
T. R.
Shrout
,
J. Appl. Phys
105
(
10
),
104506
(
2009
).
9.
S.
Zhang
,
F.
Li
,
J.
Luo
,
R.
Xia
,
W.
Hackenberger
, and
T. R.
Shrout
,
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
58
(
2
),
274
(
2011
).
10.
S.
Zhang
,
G.
Liu
,
W.
Jiang
,
J.
Luo
,
W.
Cao
, and
T. R.
Shrout
,
J. Appl. Phys.
110
(
6
),
064108
(
2011
).
11.
X.
Huo
,
S.
Zhang
,
G.
Liu
,
R.
Zhang
,
J.
Luo
,
R.
Sahul
,
W.
Cao
, and
T. R.
Shrout
,
J. Appl. Phys.
112
(
12
),
124113
(
2012
).
12.
X.
Huo
,
S.
Zhang
,
G.
Liu
,
R.
Zhang
,
J.
Luo
,
R.
Sahul
,
W.
Cao
, and
T. R.
Shrout
,
J. Appl. Phys.
113
(
7
),
074106
(
2013
).
13.
L.
Zheng
,
R.
Sahul
,
S.
Zhang
,
W.
Jiang
,
S.
Li
, and
W.
Cao
,
J. Appl. Phys.
114
(
10
),
104105
(
2013
).
14.
F.
Li
,
M. J.
Cabral
,
B.
Xu
,
Z.
Cheng
,
E. C.
Dickey
,
J. M.
LeBeau
,
J.
Wang
,
J.
Luo
,
S.
Taylor
,
W.
Hackenberger
,
L.
Bellaiche
,
Z.
Xu
,
L.-Q.
Chen
,
T. R.
Shrout
, and
S.
Zhang
,
Science
364
(
6437
),
264
(
2019
).
15.
S.
Zhang
and
F.
Li
,
J. Appl. Phys.
111
(
3
),
031301
(
2012
).
16.
S.
Wada
and
T.
Tsurumi
,
Br. Ceram. Trans.
103
(
2
),
93
(
2004
).
17.
A. B.
Kounga
,
T.
Granzow
,
E.
Aulbach
,
M.
Hinterstein
, and
J.
Rödel
,
J. Appl. Phys.
104
(
2
),
024116
(
2008
).
18.
L.
Luo
,
M.
Dietze
,
C.-H.
Solterbeck
,
H.
Luo
, and
M.
Es-Souni
,
J. Appl. Phys.
114
(
22
),
224112
(
2013
).
19.
Y.
Yamashita
,
N.
Yamamoto
,
K.
Itsumi
, and
Y.
Hosono
,
Jpn. J. Appl. Phys., Part 1
50
(
9S2
),
09NC05
(
2011
).
20.
W.-Y.
Chang
,
C.-C.
Chung
,
Z.
Yuan
,
C.-H.
Chang
,
J.
Tian
,
D.
Viehland
,
J.-F.
Li
,
J. L.
Jones
, and
X.
Jiang
,
Acta Mater.
143
,
166
(
2018
).
21.
N.
Yamamoto
,
Y.
Yamashita
,
Y.
Hosono
,
K.
Itsumi
, and
K.
Higuchi
, “
Ultrasonic probe, piezoelectric transducer, method of manufacturing ultrasonic probe, and method of manufacturing piezoelectric transducer
,”
U.S. patent 2014/0062261 A1
(
2014
).
22.
Y.
Yamashita
,
N.
Yamamoto
,
Y.
Hosono
, and
K.
Itsumi
, “
Piezoelectric transducer, ultrasonic probe, and piezoelectric transducer manufacturing method
,”
U.S. patent 2015/0372219 A1
(
2015
).
23.
W.-Y.
Chang
,
C.-C.
Chung
,
C.
Luo
,
T.
Kim
,
Y.
Yamashita
,
J. L.
Jones
, and
X.
Jiang
,
Mater. Res. Lett.
6
(
10
),
537
(
2018
).
24.
J.
Xu
,
H.
Deng
,
Z.
Zeng
,
Z.
Zhang
,
K.
Zhao
,
J.
Chen
,
N.
Nakamori
,
F.
Wang
,
J.
Ma
,
X.
Li
, and
H.
Luo
,
Appl. Phys. Lett.
112
(
18
),
182901
(
2018
).
25.
Y.
Sun
,
T.
Karaki
,
T.
Fujii
, and
Y.
Yamashita
,
Jpn. J. Appl. Phys., Part 1
58
(
SL
),
SLLC06
(
2019
).
26.
Z.
Zhang
,
J.
Xu
,
L.
Yang
,
S.
Liu
,
J.
Xiao
,
R.
Zhu
,
X.
Li
,
X. a
Wang
, and
H.
Luo
,
J. Appl. Phys.
125
(
3
),
034104
(
2019
).
27.
C.
He
,
T.
Karaki
,
X.
Yang
,
Y. J.
Yamashita
,
Y.
Sun
, and
X.
Long
,
Jpn. J. Appl. Phys., Part 1
58
(
SL
),
SLLD06
(
2019
).
28.
C.
Qiu
,
J.
Liu
,
F.
Li
, and
Z.
Xu
,
J. Appl. Phys.
125
(
1
),
014102
(
2019
).
29.
L.
Guo
,
B.
Su
,
C.
Wang
,
X.
He
,
Z.
Wang
,
X.
Yang
,
X.
Long
, and
C.
He
,
J. Appl. Phys.
127
(
18
),
184104
(
2020
).
30.
J.
Liu
,
C.
Qiu
,
L.
Qiao
,
K.
Song
,
H.
Guo
,
Z.
Xu
, and
F.
Li
,
J. Appl. Phys.
128
(
9
),
094104
(
2020
).
31.
M.
Ma
,
S.
Xia
,
K.
Song
,
H.
Guo
,
S.
Fan
, and
Z.
Li
,
J. Appl. Phys.
127
(
6
),
064106
(
2020
).
32.
Z.
Jiang
and
Z.-G.
Ye
,
Ferroelectrics
557
(
1
),
9
(
2020
).
33.
G.
Liu
,
S.
Zhang
,
W.
Jiang
, and
W.
Cao
,
Mater. Sci. Eng., R
89
,
1
(
2015
).
34.
1859–2017 IEEE Standard for Relaxor-Based Single Crystals for Transducer and Actuator Applications
(
IEEE
,
2017
), pp.
1
25
.
35.
T.
Ogawa
,
M.
Matsushita
, and
K.
Yoshioka
,
Ferroelectrics
339
(
1
),
3
(
2006
).
36.
G.
Shabbir
,
S.
Kojima
, and
C.
Feng
,
J. Appl. Phys.
100
(
6
),
064107
(
2006
).
37.
K. S.
Wong
,
X.
Zhao
,
J. Y.
Dai
,
C. L.
Choy
,
X. Y.
Zhao
, and
H. S.
Luo
,
Appl. Phys. Lett.
89
(
9
),
092906
(
2006
).
38.
S.
Zhang
,
S.-M.
Lee
,
D.-H.
Kim
,
H.-Y.
Lee
, and
T. R.
Shrout
,
J. Am. Ceram. Soc.
91
(
2
),
683
(
2008
).
39.
H.
Takahashi
,
H.
Suzuki
, and
Y.
Namba
,
CIRP Ann. -Manuf. Technol.
65
(
1
),
541
(
2016
).
40.
H.
Wan
,
C.
Luo
,
W.-Y.
Chang
,
Y.
Yamashita
, and
X.
Jiang
,
Appl. Phys. Lett.
114
(
17
),
172901
(
2019
).
41.
C.
Luo
,
H.
Wan
,
W.-Y.
Chang
,
Y.
Yamashita
,
A. R.
Paterson
,
J.
Jones
, and
X.
Jiang
,
Appl. Phys. Lett.
115
(
19
),
192904
(
2019
).
42.
L.
Liu
,
X.
Li
,
X.
Wu
,
Y.
Wang
,
W.
Di
,
D.
Lin
,
X.
Zhao
,
H.
Luo
, and
N.
Neumann
,
Appl. Phys. Lett.
95
(
19
),
192903
(
2009
).
43.
X.
Li
,
X.
Zhao
,
B.
Ren
,
H.
Luo
,
W.
Ge
,
Z.
Jiang
, and
S.
Zhang
,
Scr. Mater.
69
(
5
),
377
(
2013
).
44.
F.
Hu
,
R.
Zhu
,
L.
Lu
,
Z.
Chen
,
R.
Chen
,
W.
Di
,
X.
Wang
, and
H.
Luo
,
J. Mater. Sci.
31
(
15
),
12317
(
2020
).
45.
S.
Zhang
and
T. R.
Shrout
,
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
57
(
10
),
2138
(
2010
).
46.
F.
Bai
,
N.
Wang
,
J.
Li
,
D.
Viehland
,
P. M.
Gehring
,
G.
Xu
, and
G.
Shirane
,
J. Appl. Phys.
96
(
3
),
1620
(
2004
).
47.
H.
Cao
,
J.
Li
,
D.
Viehland
, and
G.
Xu
,
Phys. Rev. B
73
(
18
),
184110
(
2006
).
48.
Z.
Li
,
Z.
Xu
,
X.
Yao
, and
Z.-Y.
Cheng
,
J. Appl. Phys.
104
(
2
),
024112
(
2008
).
49.
D.
Lin
,
Z.
Li
,
S.
Zhang
,
Z.
Xu
, and
X.
Yao
,
J. Appl. Phys.
108
(
3
),
034112
(
2010
).
50.
C.
Luo
,
T.
Karaki
,
Y.
Sun
,
Y.
Yamashita
, and
J.
Xu
,
Jpn. J. Appl. Phys., Part 1
59
(
SP
),
SPPD07
(
2020
).
51.
Y.
Sun
,
T.
Karaki
,
T.
Fujii
, and
Y.
Yamashita
,
Jpn. J. Appl. Phys., Part 1
59
(
SP
),
SPPD08
(
2020
).
52.
C.
Qiu
,
B.
Wang
,
N.
Zhang
,
S.
Zhang
,
J.
Liu
,
D.
Walker
,
Y.
Wang
,
H.
Tian
,
T. R.
Shrout
,
Z.
Xu
,
L.-Q.
Chen
, and
F.
Li
,
Nature
577
(
7790
),
350
(
2020
).
53.
A. J.
Bell
,
P. M.
Shepley
, and
Y.
Li
,
Acta Mater.
195
,
292
(
2020
).
54.
S.
Zhang
,
S.-M.
Lee
,
D.-H.
Kim
,
H.-Y.
Lee
, and
T.
Shrout
,
Appl. Phys. Lett.
93
,
122908
(
2008
).
55.
S.
Zhang
,
N. P.
Sherlock
,
R. J.
Meyer
, Jr.
, and
T. R.
Shrout
,
Appl. Phys. Lett.
94
(
16
),
162906
(
2009
).

Supplementary Material