A novel PZT-based high-power piezoelectric vibrator for ultrasonic motors: properties enhanced by Yb institution

Jingjing Shi (Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Ning Qian (Nanjing University of Aeronautics and Astronautics, Nanjing, China) (JITRI Institute of Precision Manufacturing, Nanjing, China)
Honghua Su (Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Ying Yang (Nanjing University of Aeronautics and Astronautics, Nanjing, China)
Yiping Wang (Nanjing University of Aeronautics and Astronautics, Nanjing, China)

Journal of Intelligent Manufacturing and Special Equipment

ISSN: 2633-6596

Article publication date: 31 August 2023

Issue publication date: 22 November 2023

394

Abstract

Purpose

The electrical properties of piezoelectric vibrators have a crucial influence on the operating state of ultrasonic motors. In order to solve the problem that the current piezoelectric vibrator generates a large amount of heat during vibration to degrade its performance, which in turn affects the normal operation of ultrasonic motors, this paper prepares a novel piezoelectric vibrator and tests its maximum vibration velocity under the working condition, which is more than twice as much as that of the current commercial PZT-8.

Design/methodology/approach

The crystal structures of the samples were analyzed by using an X-ray diffractometer. For microstructure observation, samples were observed by scanning electron microscope (SEM). The quasi-static piezoelectric coefficient meter (ZJ-3AN) was used for piezoelectric measurement. Dielectric properties were measured by utilizing an impedance analyzer (Agilent 4294A) with a laboratory heating unit. Ferroelectric hysteresis loops were obtained using a ferroelectric analyzer (Radiant, Multiferroic 100). A Doppler laser vibrometer (Polytec PSV-300F, Germany) and a power amplifier were used for piezoelectric vibration measurements, during which the temperature rise was determined by an infrared radiation thermometer (Victor 303, China).

Findings

The ceramics exhibit enhanced piezoelectric performance at 0.1–0.4 mol% of Yb doping contents. The ceramic of 0.4 mol% Yb reaches the maximal internal bias field and presents a larger mechanical quality factor of 1,692 compared with that of 0.2 mol% Yb-doped ceramic, in spite of a slightly decreased dielectric constant of 439 pC/N, the unit of the piezoelectric constant, which is the ratio of the local charge (pC) to the frontal force (N) and electromechanical coupling coefficient of 0.63. The vibrator with this large mechanical quality factor ceramic displays a vibration velocity of up to 0.81 m/s under the constraint of 20 °C temperature rising, which is much higher than commercial high-power piezoelectric ceramics PZT-8.

Originality/value

The enhanced high-power properties of the piezoelectric vibrator by Yb doping may provide a potential application for the high-performance USM and offer the possibility of long-term stable operation under high power for special equipment like USM. In the subsequent phase of research, the novel PZT-based high-power piezoelectric vibrator can be utilized in the USM, and the motor's performance will be evaluated under aerospace conditions to objectively assess the reliability of the piezoelectric vibrator.

Keywords

Citation

Shi, J., Qian, N., Su, H., Yang, Y. and Wang, Y. (2023), "A novel PZT-based high-power piezoelectric vibrator for ultrasonic motors: properties enhanced by Yb institution", Journal of Intelligent Manufacturing and Special Equipment, Vol. 4 No. 3, pp. 129 -142. https://doi.org/10.1108/JIMSE-05-2023-0003

Publisher

:

Emerald Publishing Limited

Copyright © 2023, Jingjing Shi, Ning Qian, Honghua Su, Ying Yang and Yiping Wang

License

Published in Journal of Intelligent Manufacturing and Special Equipment. Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode


1. Introduction

Spaceflight is a highly demanding and prevalent technology in the world today (Wang et al., 2022; Wang and Cao, 2022). Spacecrafts serve as the carriers of spaceflight applications and are equipped with various high-precision mechanisms to meet diverse needs such as precise control, accurate observation and stable operation. Electric motors act as the driving source for these mechanisms and play a crucial role in the overall performance of spacecraft mechanisms (Bi et al., 2021). In recent years, ultrasonic motor (USM) has attracted much attention to the advantages of light weight, large torque and fast response (Tian et al., 2020). The USM differs from conventional electromagnetic motors in that they generate controlled microscopic vibrations through the inverse piezoelectric effect of the piezoelectric ceramics inside the piezoelectric vibrator (see Figure 1). These vibrations are then transformed into macroscopic rotations through frictional transmission (Zhang et al., 2021). Therefore, the performance of piezoelectric materials plays a crucial role in the mechanical output characteristics and environmental applicability of USM (Dong and Shu, 2012). At present, the most commonly used piezoelectric materials in USM are mainly Pb(Zr, Ti)O3 (PZT) based ceramics, especially, “hard” type PZT-8 commercial piezoelectric ceramics (Li et al., 2014a, b). However, harsher applications such as outer space environments require more advanced USM with larger torque output and longer utilization. Hence, it is urgently necessary to develop piezoelectric ceramics with a large piezoelectric coefficient and electromechanical coupling coefficient, high mechanical quality factor and mechanical strength, as well as low dielectric loss (Guo et al., 2011). Uchino et al. carried out systematic rare earth doping investigations on PZT-Pb(Mn,Sb)O3 (PMS) (Zhu et al., 2005; Gao and Uchino, 2016; Shekhani et al., 1998) and found that certain transition metal substituents show a combination of softening and hardening effects in piezoelectric ceramics. The vibration velocity of the piezoelectric vibrators was significantly increased by these rare earth substituents (from Yb to Cerium (Ce)) under high driving conditions, and Yb has the most significant effect on improving the high-power performance of ternary piezoelectric ceramics such as PZT-PMS. The Pb(In1/3Nb2/3)O3 (PIN) was introduced into PMS-PZT to form a quaternary system, and its mechanical quality factor was higher than that of Pb(Zn,Nb)O3 (PZN)-PMS-PZT (Cheng et al., 2010; Wu et al., 2018), PZN-Pb(Ni,Nb)O3 (PNN)-PZT (Wang et al., 2017; Zhang et al., 2016) and other quaternary high-power piezoelectric ceramics (Li et al., 2019; Feng, 2019). However, to match the requirements of outer space applications, the performance of the piezoelectric ceramics needs to be further improved.

Element substitutions are usually utilized to achieve “soft” and “hard” combination effects in PZT-based piezoelectric ceramics (Xin et al., 2020; Jin et al., 2022). The radius of doping element ions must be between the perovskite structure's A-site ions and B-site ions (Gao and Uchino, 2016). In this paper, 0.92Pb(Zr0.48Ti0.52)O3-0.05Pb(Mn1/3Sb2/3)O3-0.03Pb(In1/2Nb1/2)O3 high-power piezoelectric ceramic was chosen as the base composition, and a novel piezoelectric vibrator was developed, which demonstrated exceptional high-power performance. The incorporation of the element Yb played a crucial role in enhancing the vibrator's functionality `and the effect of Yb3+ doping on the crystal structure, micromorphology and the piezoelectric performance of the ceramic system is studied. And then the vibration velocity and the corresponding high-power characteristics of the vibrators were discussed.

2. Experimental procedures

The ceramics 0.92PZT-0.05PMS-0.03PIN-x mol% Yb (x = 0, 0.1, 0.2, 0.4, 0.6, 0.7) modified by Yb3+ were synthesized by conventional solid-phase reaction method, and the experimental steps are shown in Figure 2. Starting oxides of TiO2 (99.80%), MnO2 (99.95%), ZrO2 (99.90%), PbO (99.90%), In2O3 (99.99%), Nb2O5 (99.99%) and Sb2O3 (99.99%) were weighed stoichiometrically according to the compositional formula 0.92Pb(Zr0.48Ti0.52)O3-0.05Pb(Mn1/3Sb2/3)O3-0.03Pb(In1/2Nb1/2)O3, and 3 wt% excess PbO was added to compensate the possible lead loss during sintering.

InNbO4 precursor was synthesized firstly by calcining In2O3 and Nb2O5 mixture at 850 °C for 4 h. Then the obtained precursor and the other powders were wet-milled for 12 h in an ethanol medium. After drying the mixture was calcined at 850 °C for 2 h, causing the water in the original ingredient oxide to evaporate. Following this, the resulting calcined powder was crushed through ball milling for 16 h. To this milled powder, a 5 wt% polyvinyl alcohol (PVA) binder was added, and the mixture was then pressed into discs under 250 MPa pressure. The ceramics underwent sintering in a sealed alumina crucible at a temperature of 1,150 °C for a duration of 2 h. To minimize the loss of lead, the samples were covered with their original powder. As a result of this process, the volume of the samples decreased while the density increased. To achieve the desired thickness of approximately 500 mm, sandpaper polished the ceramic sheet on both sides. Following this, silver electrodes were brushed onto both sides and the sheet was calcined in a furnace at 700 °C for 30 min to dry and set the electrodes. The sample was poled in silicone oil at a temperature of 120 °C for 20 min while applying an electric field of 4 kV/mm. The electrical properties were measured 24 h after the polling process.

The crystal structures of the sintered samples were analyzed by using an X-ray diffractometer (Panalytical Empyrean, λ = 1.506 nm). For microstructure observation, samples were thermally etched at 1,120 °C for 15 min and observed by scanning electron microscope (SEM, Quanta 200, FEI Company). The quasi-static piezoelectric coefficient meter (ZJ-3AN, Institute of Acoustics, Chinese Academy of Sciences) was used for piezoelectric measurement. Dielectric properties were measured by utilizing an impedance analyzer (Agilent 4294A) with a laboratory heating unit. Ferroelectric hysteresis loops were obtained using a ferroelectric analyzer (Radiant, Multiferroic 100). A Doppler laser vibrometer (Polytec PSV-300F, Germany) and a power amplifier (DPO2014, Tek, America) were used for piezoelectric vibration measurements, during which the temperature rise was determined by an infrared radiation thermometer (Victor 303, China).

3. Result and discussion

  1. Crystal structure and microstructure

Figure 3(a) shows the XRD patterns of PZT-PMS-PIN-x mol% Yb (0 ≤ x ≤ 0.7) ceramics sintered at 1,150 °C. All samples present a pure perovskite structure. The local peaks of (002)T/(200)T and (200)R for tetragonal and rhombohedral symmetry around 43°–46° are presented in Figure 3(b). We analyzed the phase content variations of samples sintered at different Yb3+ concentrations by comparing the ratio of the peak intensities of the tetragonal (t) and rhombohedral (r) phases. The rhombohedral phase content (Χr) was calculated using the formula Χr = I200, t + I200, r + I002, t. (where Χr denotes the content of the rhombohedral phase, I200, r is the peak intensity of the (200)R peak, I200, t is the peak intensity of the (200)T peak and I002, t is the peak intensity of the (002)T peak). The values of I200, t I200, r and I002, t peaks were 21.56%, 23.05%, and 23.42%, 23.74%, 27.16% 62.93%, respectively, for Yb concentrations ranging from 0 to 0.7 mol%. At x = 0, the ceramic of 0.92PZT-0.05PMS-0.03PIN presents mainly tetragonal symmetry. The composition of PZT-PMS-PIN-0.7 mol% Yb shows a rhombohedral symmetry mainly. With the increase of Yb content, the content of rhombohedral overall upward trend, and at Yb additions of x = 0.1 and 0.4, the amount of Χr of this composition is almost unchanged and exhibit coexistence of rhombohedral and tetragonal symmetry.

Figure 4(a) shows the rhombohedral lattice parameters of PZT-PMS-PIN-x mol% Yb ceramics calculated by unit-cell software. The calculation illustrates that the a-axis of the lattice increases and the c-axis decreases with increasing Yb3+ content, hence leading to a decrease in the c/a ratio (Yan et al., 2012). The value of c/a in piezoelectric ceramic lattice determines its tetragonal degree. A c/a value of 1 indicates a tripartite phase, while a value greater than 1 indicates the existence of a tetragonal phase. The decreased c/a ratio indicates the tetragonality of ceramic decreases. According to the element ion radii shown in Table 1 (Liu and Li, 2020), the Yb3+ ion has a radius smaller than the Pb2+ ion, when it locates in A-site to replace the Pb2+ ion, the unit cell parameters will reduce. When Yb3+ replaces B-site ions, the unit cell parameters will enlarge since the radius of Yb3+ is larger than that of B-site ions. According to the change in lattice parameters, it is inferred that Yb3+ trends to dope on B sites, as shown in Figure 4(b).

Figure 5 presents the SEM micrographs of PZT-PMS-PIN-x mol% Yb ceramics, and it can be found that all samples show a dense microstructure. As can be seen from the figure, there are no impurities formed in the ceramic, and as the Yb content increases, the grain size of the ceramics decreases and the size distribution becomes more uniform. At higher doping contents of 0.6 and 0.7 mol%, a few small pores on the grain boundary are observed, which may be due to the component aggregation and volatilization at high doping contents.

  1. Ferroelectric characteristics

Figure 6(a) shows P-E loops of the ceramics under different external electric fields. It can be found that saturated P-E loops can be achieved for all the ceramics under a 4.5 kV/mm electric field. For these ceramics with Yb doping content x ≤ 0.2 mol%, the P-E loops show a pinched shape, indicating the possible existence of oxygen vacancies, defect dipoles alignment pins domain switch during P-E loop measurement (Li et al., 2014b; Eichel, 2010; Shrout and Zhang, 2007; Slabki et al., 2021). With the increase of Yb addition, more rectangular P-E loops are observed. From the asymmetrical P-E loops, the values of the internal electric field (Ei) of the ceramics are obtained. The remnant polarization Pr, coercive field Ec, and the internal electric field Ei of the PZT-PMS-PIN-x mol% Yb ceramics are summarized in Figure 6(b). The Pr increases significantly with the increase of Yb amount, showing that Yb substitution helps to reduce the pinning effects and leads to more complete switch of the domains. The Ec and Ei increase first and then decrease with more amount of Yb addition. At Yb content of 0.4 mol%, the ceramic reaches maxima of Ec and Ei, displaying “hard” characters of Yb doping.

Yb3+ ions tend to preferentially occupy positions with smaller ionic radius differences at a low content. It can be inferred that the Yb3+ ions in this doping range occupy the B-position and combine with oxygen vacancy to form defect dipoles so that the internal electric field of the sample shows an increasing trend with the increase of doping. As the doping amount continues to increase, some of the Yb3+ ions start to occupy the A-site, which results in a reduction of oxygen vacancies inside the sample and a reduction of Ei, and when the doping amount increases to 0.6 mol%, the replacement of the A-site Yb3+ ions increase significantly, the internal electric field decreases and the bundle waist disappears. As reported in PZT-PMS-Yb ceramic, the enhancement of the internal electric field can be explained by an additionally generated oxygen vacancy by Yb doping (Yang et al., 2021), which could increase or stabilize the localized dipole moment. And the enhanced Ei is essential to the piezoelectric ceramic for high-power functions (Yang et al., 2006).

  1. Dielectric and piezoelectric properties

The dependences of room temperature dielectric constant and dielectric loss on the Yb3+ doping contents in PZT-PMS-PIN-x mol% Yb ceramics are illustrated in Figure 7. It shows that the dielectric constant reaches the maximum of 1,496 at 0.1 mol% of Yb content and then decreases monotonously with the increase of Yb addition. Usually, the compositions in the morphological phase boundary (MPB) present a large dielectric constant since the coexistence of rhombohedral and tetragonal phases benefits the transitions between both phases under an external electric field or stress (Zhang et al., 2015). Hence, the ions' motion and polarization are easier, and it results in a larger dielectric response. However, other factors such as grain size, domain structure and electric field bias also exert complicated effects on the dielectric properties of the piezoelectric ceramics (Qi et al., 1999; Li et al., 2005). The enhanced internal electric field in 0.4 mol% Yb-doped ceramic may be responsible for the decreased dielectric constant at room temperature.

The temperature-dependent dielectric constant of PZT-PMS-PIN-x mol% Yb ceramics at 1 kHz frequency is shown in Figure 8. It can be seen that no position shift of the dielectric peak is induced with the addition of the Yb dopant (Liao et al., 2019). The Curie temperature Tc of the ceramics is around 326 °C. The inset shows the maximum εr of the ceramics in terms of Yb contents. With the increase of Yb doping amount, the maximum dielectric constant increases first and then decreases. At 0.2–0.4 mol% of Yb doping contents, the ceramics in the MPB region present a relatively large dielectric maximum.

The piezoelectric properties of PZT-PMS-PIN-x mol% Yb ceramics are presented in Figure 9. For the compositions in the MPB area with Yb from 0.1 to 0.4 mol% enhance piezoelectric coefficient of d33 values are obtained compared to the ceramic without Yb doping. Maximum d33 of 467 pC/N and planar coupling factor kp of 0.67 is achieved in the ceramic of 0.2 mol% Yb addition. However, for x = 0.4 mol% Yb ceramic, the largest mechanical factor Qm of 1,692 is achieved because of the enhanced Ei induced by Yb doping in the ceramic. As can be seen from Figure 6(b) and Figure 9, these curves of Ei and Qm show high consistency concerning Yb doping contents. Despite its slightly decreased d33 and kp values, to a certain degree, large Qm is more beneficial to high-power applications.

  1. High-power properties

Figure 10 shows the measured vibration velocities of PZT-PMS-PIN-x mol% Yb ceramics under different external electric fields. As can be seen, the vibration velocity linearly increases with the driven field. However, the ceramics present different slopes with different Yb contents.

For a round shape sample vibrating in kp mode, the vibration velocity υm is calculated as follows (Li et al., 2005):

(1)vm=ε33T2ρ(1+σ)BkpQmVmT
where εT33 is the relative permittivity at freestream boundary condition, B is a constant with a value of 2.065, kp is the planar coupling coefficient and Qm is the mechanical quality factor, which is a physical quantity that characterizes the energy consumed by piezoelectrics to overcome internal friction during resonance. Vm is the applied AC voltage, ρ is the density of the ceramic sample, σ is the Poisson ratio and T is the thickness of the sample. In this experiment, we used DPO2014 power amplifiers (Tek, America), after sweeping the sample between the resonant frequency and the anti-resonant frequency, the mechanical resonant frequency was determined, which was listed in Table 2, and the vibration mode was axial (thickness direction) vibration, and the vibration rate was recorded for one time period in the fixed frequency vibration mode at this frequency, i.e. the piezoelectric vibrator completes one cycle of movement from positive to negative in the thickness direction.

The vibration velocity of piezoelectric vibrators using PZT-PMS-PIN-x mol% Yb ceramics at a driving voltage of 20V is illustrated in the inset of Figure 10, the black line lists the measured data from Figure 10 and the red line lists the calculated velocities according to Eq. (1). It can be seen that these two curves are highly consistent. With the increase of Yb doping amount, the vibration velocity under the same driving field increases first and then decreases. The sample with 0.4 mol% Yb presents the highest velocity than other ceramics since the sample displays an improved mechanical quality factor.

When piezoelectric vibrators work with high vibration velocity, considerable heat will be generated. To prevent possible performance deterioration from overheating the devices, the vibration velocity of piezoelectric vibrators must be under control during work. Therefore, another parameter to characterize the high-power performance of the piezoelectric ceramic component inside the vibrator is the maximum vibration velocity at the constraint condition of 20 °C temperature rise (Doshida et al., 2019). During the measurement, the piezoelectric vibrator vibrates at different velocities when driven by different electric fields. The corresponding temperature rising is recorded by an IR thermometer. Figure 11 shows temperature rises of PZT-PMS-PIN-x mol% Yb during vibrations. As shown, the temperature of the piezoelectric vibrators rises sharply with the increase in vibration velocity. The inset of Figure 11 displays the reached maximum vibration velocity of the ceramics under 20 °C temperature rise conditions. Among them, the ceramic inside the vibrator with 0.4 mol% Yb content reaches the maximum vibration of 0.81 m/s, which is much higher than that of the conventional PZT ceramics, as we can see the purple lines in Figure 11, where vm is about to 0.4 m/s (Yoon et al., 2010). According to Eq. (1), high Qm benefits high vm. The ceramic PMT-PMS-PZT-0.4 mol% Yb presents the highest mechanical quality factor and thus higher vm under the same driving field or less heat at the same vibration velocity is generated in the vibrator.

4. Conclusion

For the major needs of aerospace development, this paper carried out a study on the modification of piezoelectric vibrators, one of the core components inside the USMs of special equipment for spaceflight. The main conclusions are drawn as follows.

The perovskite structure contains A-site and B-site ions, and the ionic radius of Yb3+ falls between these two ions. When Yb3+ is used as a dopant in ceramics, it replaces the B-site ion due to its smaller size compared to Pb2+. This replacement results in the introduction of oxygen vacancy pinning electric domains. The ceramics exhibit enhanced piezoelectric performance at 0.1–0.4 mol% of Ytterbium (Yb) doping contents since the compositions locate in the MPB region with the coexistence of rhombohedral and tetragonal phase and the addition replaces B-site ions to obtain an enhanced internal bias field. The ceramic of 0.4 mol% Yb reaches the maximal internal bias field and presents a larger mechanical quality factor of 1,692. The vibrator with this large mechanical quality factor ceramic displays a vibration velocity of up to 0.81 m/s under the constraint of 20 °C temperature rising, which is a 103% improvement compared to commercially commercial ceramic PZT-8. This improved high-power characteristic is attributed to the enhanced inner electric-field bias by Yb substitution, and this novel vibrator may provide a potential application for high-performance USMs.

Figures

schematic diagram of ultrasonic motor structure

Figure 1

schematic diagram of ultrasonic motor structure

Experimental flow chart

Figure 2

Experimental flow chart

XRD patterns of PZT-PMS-PIN-x mol% Yb ceramics sintered at 1,150 °C for 2h

Figure 3

XRD patterns of PZT-PMS-PIN-x mol% Yb ceramics sintered at 1,150 °C for 2h

The effect of Yb3+ content on internal lattice changes and (a) lattice constants and c/a ratios (b) schematic diagram of Yb3+ substitution principle

Figure 4

The effect of Yb3+ content on internal lattice changes and (a) lattice constants and c/a ratios (b) schematic diagram of Yb3+ substitution principle

effect of Yb content on SEM micrographs: (a) thermally etched surfaces and (b) cross-section

Figure 5

effect of Yb content on SEM micrographs: (a) thermally etched surfaces and (b) cross-section

The effect of Yb content on Ferroelectric properties: (a) P-E loops of ceramics under different electric field intensities and (b) Pr, Ei, and Ec of the ceramics

Figure 6

The effect of Yb content on Ferroelectric properties: (a) P-E loops of ceramics under different electric field intensities and (b) Pr, Ei, and Ec of the ceramics

The effect of Yb content on dielectric properties

Figure 7

The effect of Yb content on dielectric properties

The effect of Yb content on εr at 1 kHz frequency

Figure 8

The effect of Yb content on εr at 1 kHz frequency

The effect of Yb content on piezoelectric properties

Figure 9

The effect of Yb content on piezoelectric properties

The effect of Yb content on vibration velocity

Figure 10

The effect of Yb content on vibration velocity

The effect of Yb content on temperature rise vs vibration velocity

Figure 11

The effect of Yb content on temperature rise vs vibration velocity

Ion radii of PZT-PMS-PIN-x mol%Yb ceramics

IonsYb3+Pb2+Mn4+Sb3+In3+Nb5+Zr4+Ti4+
Coordination numbers612646666
Radi (Å)0.8681.490.670.760.800.640.720.605

Source(s): Authors’ own work

Frequency of PZT-PMS-PIN-x Yb ceramics

Yb content (mol%)00.10.20.40.60.7
Resonant frequency (kHz)193.15191.08187.98193.50203.85205.68
Anti-resonant frequency (kHz)230.50234.97229.92232.66236.88238.38
Vibration frequency (kHz)195.44194.18189.04196.76211.49212.39

Source(s): Authors' own work

Nomenclature

B

Constant with 2.065

d33

Piezoelectric coefficient

Ec

Coercive field

Ei

Internal electric field

fa

Anti-resonant frequency

fr

Resonant frequency

kp

Electromechanical coupling coefficient

MPB

Morphological phase boundary

Pr

Residual polarization intensity

Qm

Mechanical quality factor

TC

Curie temperature

USM

Ultrasonic motor

vm

Maximum vibration velocity

Vm

Maximum voltage

T

The thickness of the sample

ΔT

Temperature rise

Greek

ε0

Vacuum dielectric constant

εr

Dielectric constant

εT33

Relative permittivity at free stream boundary condition

ρ

Volume density

σ

Poisson ratio

ω

Angular frequency

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Acknowledgements

This work was financially supported by National Natural Science Foundation of China (No. U2037603); the 111 project (No. B12021); Youth Talent Support Project of Jiangsu Provincial Association of Science and Technology (Grant No. TJ-2023-070); and the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Corresponding author

Ning Qian can be contacted at: n.qian@nuaa.edu.cn

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