# Characterization of 1-3 Piezoelectric Composite with a 3-Tier Polymer Structure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Structure of the 1-3 Piezoelectric Composite with 3-Tier Polymer Structure

_{s}. So the thickness of epoxy resin is t-2t

_{s}. The volume fraction of piezoelectric ceramic in composite v

_{c}can be expressed as a

^{2}/(a + b)

^{2}, and the volume fraction of the silicone rubber in the polymer phase v

_{s}is defined as 2t

_{s}/t.

## 3. Finite Element Analysis of the Novel Composite

_{s}on the properties of the composite, harmonic response analysis was used to obtain the admittance curve of the composite, while the volume fraction of the piezoelectric ceramics v

_{c}was set to 0.4. As shown in Figure 3, the resonant frequency f

_{s}is the frequency at the maximum modulus point of the admittance curve and the anti-resonant frequency f

_{p}appears at the minimum point.

_{eff}and sound velocity c can be calculated using (1) and (2), respectively. In addition, the equivalent density ρ and characteristic impedance z of the composite is given by (3) and (4).

_{eff}= ((f

_{p}

^{2}− f

_{s}

^{2})/f

_{p}

^{2})

^{1/2}

_{p}t

_{c}ρ

_{c}+ (1 − v

_{c})(v

_{s}ρ

_{s}+ (1 − v

_{s})ρ

_{e})

_{c}is the density of the piezoelectric phase material, ρ

_{e}is the density of epoxy resin, and ρ

_{s}is the density of silicone rubber.

_{s}are shown in Table 3. Accordingly, the f

_{s}and f

_{p}~ v

_{s}, k

_{eff}~ v

_{s}, c ~ v

_{s}and z ~ v

_{s}curves are displayed in Figure 4a–d.

_{s}and the anti-resonant frequency f

_{p}change slightly with the increase of v

_{s}. The resonant frequency f

_{s}is mainly determined by the thickness of the composite, which does not change in the simulation, so this is the reason for that phenomenon [28]. Furthermore, the changing trend of f

_{s}and f

_{p}is almost the same. When the equivalent performance parameters of the composite material are fixed, the ratio between f

_{s}and f

_{p}is a constant [28]. The equivalent performance parameters of the composite material do not change much in the simulation. Hence, the resonant frequency f

_{s}and the anti-resonant frequency f

_{p}share a similar variation tendency.

_{eff}of the composite increases with the variation of v

_{s}, generally. Yet, when v

_{s}increases from 0.2 to 0.3, the electromechanical coupling factor k

_{eff}decreases correspondingly. In this section, the increase rate of anti-resonant frequency is lower compared to that of resonant frequency, which is the reason for the decrease in k

_{eff}.

_{s}is shown in Figure 4c. As can be seen from equation (2), the sound velocity c is determined by the anti-resonant frequency and the thickness of the composite. In the simulation, the changing curve of the sound velocity c is basically consistent with the anti-resonant frequency.

_{s}. The characteristic impedance z is the product of equivalent density ρ and sound velocity c. The changing trend of sound velocity c is in accordance with the anti-resonant frequency f

_{p}and the equivalent density ρ of the composite varies slightly with the increase of v

_{s}. Therefore, the curves of the characteristic impedance z and anti-resonant frequency f

_{p}are alike.

_{s}has a great influence on the electromechanical coupling factor k

_{eff}of the composite. When v

_{s}is 0.6, the electromechanical coupling factor k

_{eff}is 0.692, and the composite is not easily deformed under this condition. Therefore, the influence of the volume fraction of piezoelectric ceramic v

_{c}on the properties of the composite was studied, when the volume fraction of silicone rubber v

_{s}was 0.6.

_{c}are shown in Table 4. Accordingly, the f

_{s}and f

_{p}~ v

_{c}, k

_{eff}~ v

_{c}, c ~ v

_{c}and z ~ v

_{c}curves are displayed in Figure 5a–d.

_{eff}showed a downward trend in general, which becomes faster and faster as v

_{c}varies. When v

_{c}increases, the resonant frequency f

_{s}and the anti-resonant frequency f

_{p}will increase simultaneously, and the growth rate of f

_{s}will be slightly larger than that of f

_{p}. Thus, the electromechanical coupling factor k

_{eff}will decrease as a whole. When v

_{c}alters from 0.8 to 0.9, the rising pace of f

_{s}is much larger than that of f

_{p}, so that k

_{eff}has the largest rate of decline in this section.

_{c}. When v

_{c}rises, the equivalent density ρ increases linearly, as can be seen from Table 4, and the fluctuation of sound velocity c is not significant. Therefore, the equivalent density ρ determines the changing trend of characteristic impedance z, which also shows a linear rise state.

## 4. Fabrication and Test

_{c}is 0.4, and the volume fraction of silicone rubber v

_{s}increases from 0 to 1 with an increment of 0.2. In Figure 7b, the volume fraction of silicone rubber v

_{s}is 0.6 and the volume fraction of piezoelectric ceramic v

_{c}increases from 0.1 to 0.7 by 0.2. Two pieces of each type of sample are made and one of them is selected for display. The samples are measured by Impedance Analyzer (4294A, Agilent Technologies, Inc., Santa Clara, CA, USA), and the experimental data of the samples are summarized in Table 5 and Table 6.

_{eff}of the majority of 1-3 piezoelectric composites with 3-tier polymer structure (except the composite of v

_{s}= 0 and v

_{s}= 1) is greater than 0.64, which indicates that the 3-tier polymer structure is beneficial in improving the electromechanical coupling factor of piezoelectric composites. In the meantime, the composite with lower characteristic impedance can be acquired, when v

_{c}is less than 0.3.

_{s}varies, the comparison between experiment and simulation are shown in Figure 8, in which the experimental data agree well with the simulation results. There are some errors between the experimental results and the simulation data, because of the difference of material parameters between experiment and simulation.

_{s}increases, the electromechanical coupling factor of the new composite will also increase accordingly. When v

_{s}is 0.6, the electromechanical coupling factor of the advanced composite is 0.656, enhanced by 6.4%, compared with traditional 1-3 ceramic/epoxy composite (0.616). When v

_{s}> 0.6, the electromechanical coupling factor k

_{eff}of the composite will more than 0.67, enhancing by 8.7%. These data are calculated from Equation (5).

_{1}− X

_{2}|/X

_{1}

_{1}represents the parameters of traditional 1-3 piezoelectric composite, and X

_{2}represents. The parameters of the 1-3 piezoelectric composite with 3-tier polymer structure.

_{c}varies, the comparisons between experiment and simulation are shown in Figure 9, in which the experiment data also fit well with the simulation results. In Figure 9b, although the electromechanical coupling factor k

_{eff}decreases with the increase of the volume fraction of piezoelectric ceramics v

_{c}, the k

_{eff}of the composites remain at a high level, greater than 0.64, because the volume fraction of silicone rubber v

_{s}in the composite remains unchanged. In Figure 9d, when v

_{c}increases, both the test values of the characteristic impedance z and the simulation data show a linear upward trend. Moreover, the experiment–simulation error does not exceed 1%. When the volume fraction of ceramic v

_{c}is less than 0.5, the characteristic impedance z of the composite can be kept at a comparatively low level. When v

_{c}= 0.1 and v

_{s}= 0.6, the characteristic impedance of the advanced composite is 6.53 MRayl declining by 52.8%, and the electromechanical coupling factor is 0.668 enhanced by 8.4%, compared with the traditional 1-3 ceramic/epoxy composite (13.84 MRayl, 0.616), which are also calculated by Equation (5).

## 5. Discussion

## 6. Conclusions

_{c}is 0.1 and v

_{s}is 0.6, the electromechanical coupling factor of the composite is enhanced by 8.4% and the characteristic impedance is decreased by 52.8%, compared with traditional 1-3 ceramic/epoxy composite.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Uchino, K.; Ando, A.; Kimura, M. Advanced Piezoelectric Material: Science and Technology, 2nd ed.; Uchino, K., Ed.; Woodhead Publishing: Duxford, UK, 2017; pp. 2–7, 319–320. [Google Scholar]
- Teng, D.; Yang, H.; Li, D.J. The Foundation of Underwater Acoustic Transducer; Northwestern Polytechnic University Press: Xian, China, 2016; pp. 2–4. [Google Scholar]
- D’Amico, A.; Pittenger, R. A Brief History of Active Sonar. Aquat. Mamm.
**2009**, 35, 426–434. [Google Scholar] [CrossRef] [Green Version] - Fujishima, S. The History of Ceramic Filters. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2000**, 47, 1–7. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Jaffe, B.; Cook, W.R., Jr.; Jaffe, H. Piezoelectric Ceramics; Academic Press: London, UK, 1971; pp. 1–5. [Google Scholar]
- Newnham, R.E.; Skinner, D.P.; Cross, L.E. Connectivity and Piezoelectric-pyroelectric Composites. Mater. Res. Bull.
**1978**, 13, 525–536. [Google Scholar] [CrossRef] - Cross, L.E. Ferroelectric Materials for Electromechanical Transducer Applications. Mater. Chem. Phys.
**1996**, 43, 108–115. [Google Scholar] [CrossRef] - Lee, H.; Zhang, S.; Bar-Cohen, Y.; Sherrit, S. High Temperature, High Power Piezoelectric Composite Transducers. Sensors
**2014**, 14, 14526–14552. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Savakus, H.P.; Klicker, K.A.; Newnham, R.E. PZT-epoxy piezoelectric transducers: A Simplified Fabrication Procedure. Mater. Res. Bull.
**1981**, 16, 677–680. [Google Scholar] [CrossRef] - Zhang, Y.; Wang, L.; Qin, L.; Liao, Q.; Zhong, C. A Doubly-Curved Piezoelectric Composite with 1-3 Connectivity for Underwater Transducer Applications. In IOP Conference Series: Materials Science and Engineering; IOP Publishing: Bristol, UK, 2018; Volume 317. [Google Scholar]
- Zhang, H.; Chen, H.J. The Research on 1-3 Type Piezoelectric Composite Material Application in Vector Hydrophone. In IEEE/OES China Ocean Acoustics (COA); IEEE: San Juan, PR, USA, 2016. [Google Scholar]
- Zhou, D.; Lam, K.H.; Chen, Y.; Zhang, Q.; Chiu, Y.C.; Luo, H.; Dai, J.; Chan, H.L.W. Lead-free Piezoelectric Single Crystal Based 1-3 Composites for Ultrasonic Transducer Applications. Sens. Actuators A Phys.
**2012**, 182, 95–100. [Google Scholar] [CrossRef] - Benjamin, K.C. Recent Advances in 1-3 Piezoelectric Polymer Composite Transducer Technology for AUV/UUV Acoustic Imaging Applications. J. Electroceram
**2002**, 8, 145–154. [Google Scholar] [CrossRef] - Felix, N.; Tran-Huu-Hue, L.P.; Walker, L.; Millar, C.; Lethiecq, M. The Application of High Permittivity Piezoelectric Ceramics to 2D Array Transducers for Medical Imaging. Ultrasonics
**2000**, 38, 127–130. [Google Scholar] [CrossRef] - Sun, P.; Wang, G.; Wu, D.; Zhu, B.; Hu, C.; Liu, C.; Shung, K.K. High Frequency PMN-PT 1-3 Composite Transducer for Ultrasonic Imaging Application. Ferroelectrics
**2010**, 408, 120–128. [Google Scholar] [CrossRef] [PubMed] - Zhang, Y.; Zhao, X.; Wang, W.; Ren, B.; Liu, D.A.; Luo, H. Fabrication of PIMNT/Epoxy 1-3 Composites and Ultrasonic Transducer for Nondestructive Evaluation. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2011**, 58, 1774–1781. [Google Scholar] [CrossRef] [PubMed] - Jiang, X.; Snook, K.; Hackenberger, W.S.; Geng, X. Single Crystal Piezoelectric Composites for Advanced NDT Ultrasound. In Nondestructive Characterization for Composite Materials, Aerospace Engineering, Civil Infrastructure, and Homeland Security; International Society for Optics and Photonics: Pittsburgh, PA, USA, 2007; Volume 6531. [Google Scholar]
- Kobayashi, M.; Jen, C.K.; Bussiere, J.F.; Wu, K.T. High-temperature Integrated and Flexible Ultrasonic Transducers for Nondestructive Testing. NDT E Int.
**2009**, 42, 157–161. [Google Scholar] [CrossRef] [Green Version] - Li, D.H.; Ju, J.W.; Jia, M.J. Novel Piezoelectric Composite Transducer and Application; The Science Publishing Company: Beijing, China, 2007; pp. 6–7. [Google Scholar]
- Zhong, C.; Wang, L.; Qin, L.; Zhang, Y. Characterization of an Improved 1-3 Piezoelectric Composite by Simulation and Experiment. J. Appl. Biomater.
**2017**, 15, S38–S44. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Qin, L.; Wang, L.K.; Long, D.; Zhong, C.; Zhang, B.; Liu, J.J. The Study of 1-1-3 Piezoelectric Composite Based on Relaxor Ferroelectric Single Crystal; IEEE (ISAF/IWATMD/PFM): San Juan, PR, USA, 2014. [Google Scholar]
- Lee, H.J.; Zhang, S. Design of Low-loss 1-3 Piezoelectric Composites for High-power Transducer Applications. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2012**, 59, 1969–1975. [Google Scholar] [PubMed] - Jae Lee, H.; Zhang, S.; Meyer, R.J., Jr.; Sherlock, N.P.; Shrout, T.R. Characterization of Piezoelectric Ceramics and 1-3 Composites for High Power Transducers. Appl. Phys. Lett.
**2012**, 101, 32902. [Google Scholar] [CrossRef] [PubMed] - Ivanov, V. Direct electro-optic effect in langasites and α-quartz. Opt. Mater.
**2018**, 79, 1–7. [Google Scholar] [CrossRef] - Matko, V.; Šafarič, R. Major improvements of quartz crystal pulling sensitivity and linearity using series reactance. Sensors
**2009**, 9, 8263–8270. [Google Scholar] [CrossRef] [PubMed] - Huang, X.; Yang, M.; Liu, T.; Su, H.; Cui, X. An approach on a new variable amplitude waveform sensor. Optik
**2017**, 132, 52–66. [Google Scholar] [CrossRef] - Matko, V.; Milanovic, M. Temperature-compensated capacitance-frequency converter with high resolution. Sens. Actuators A Phys.
**2014**, 220, 262–269. [Google Scholar] [CrossRef] [Green Version] - Chao, Z. Research on Three-Phase Piezocomposite and Curved Surface Transducer. Ph.D. Thesis, Beijing University of Posts and Telecommunications, Beijing, China, 2019. [Google Scholar]

Density (kg/m ^{3}) | Piezoelectric Stress Constant (C/m^{2}) | Dielectric Constant | Elastic Stiffness Coefficient (10 ^{10} N/m^{2}) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

ρ_{c} | e_{31} | e_{33} | e_{15} | ε^{S}_{11}/ε_{0} | ε^{S}_{33}/ε_{0} | c_{11} | c_{12} | c_{13} | c_{33} | c_{44} | c_{66} |

7500 | −6.5 | 23.3 | 17 | 1700 | 1470 | 12.6 | 7.95 | 8.41 | 11.7 | 2.3 | 2.35 |

Polymer | Density (kg/m^{3}) | Young’s Modulus (N/m^{2}) | Poisson’s Ratio |
---|---|---|---|

618 epoxy resin | 1200 | 6.3 × 10^{9} | 0.3 |

704 silicon rubber | 1070 | 2.55 × 10^{9} | 0.49 |

Silicone Rubber Fraction v_{s} | Resonant Frequency f_{s} (kHz) | Anti-Resonant Frequency f_{p} (kHz) | Electromechanical Coupling Factor k_{eff} | Sound Velocity c (m/s) | Density ρ (kg/m ^{3}) | Characteristic Impedance z (MRayl) |
---|---|---|---|---|---|---|

0 | 287 | 372 | 0.636 | 3720 | 3720 | 13.84 |

0.1 | 287 | 380 | 0.655 | 3800 | 3712.2 | 14.11 |

0.2 | 287 | 386 | 0.669 | 3860 | 3704.4 | 14.3 |

0.3 | 293 | 389 | 0.658 | 3890 | 3696.6 | 14.38 |

0.4 | 291 | 392 | 0.67 | 3920 | 3688.8 | 14.46 |

0.5 | 288 | 392 | 0.678 | 3920 | 3681 | 14.43 |

0.6 | 281 | 389 | 0.692 | 3890 | 3673.2 | 14.29 |

0.7 | 275 | 386 | 0.702 | 3860 | 3665.4 | 14.15 |

0.8 | 269 | 381 | 0.708 | 3810 | 3657.6 | 13.94 |

0.9 | 264 | 377 | 0.714 | 3770 | 3649.8 | 13.76 |

1 | 261 | 375 | 0.718 | 3750 | 3642 | 13.66 |

Piezoceramic Fraction v_{c} | Resonant Frequency f_{s} (kHz) | Anti-Resonant Frequency f_{p} (kHz) | Electromechanical Coupling Factor k_{eff} | Sound Velocity c (m/s) | Density ρ (kg/m ^{3}) | Characteristic Impedance z (MRayl) |
---|---|---|---|---|---|---|

0.1 | 275 | 383 | 0.696 | 3830 | 1759.8 | 6.74 |

0.2 | 278 | 386 | 0.694 | 3860 | 2397.6 | 9.25 |

0.3 | 281 | 389 | 0.692 | 3890 | 3035.4 | 11.81 |

0.4 | 281 | 389 | 0.692 | 3890 | 3673.2 | 14.29 |

0.5 | 284 | 392 | 0.689 | 3920 | 4311 | 16.9 |

0.6 | 285 | 392 | 0.687 | 3920 | 4948.8 | 19.4 |

0.7 | 290 | 395 | 0.679 | 3950 | 5586.6 | 22.07 |

0.8 | 296 | 399 | 0.671 | 3990 | 6224.4 | 24.84 |

0.9 | 312 | 410 | 0.649 | 4100 | 6862.2 | 28.14 |

Silicone Rubber Fraction v_{s} | Resonant Frequency f_{s} (kHz) | Anti-Resonant Frequency f _{p} (kHz) | Electromechanical Coupling Factor k_{eff} | Sound Velocity c (m/s) | Characteristic Impedance z (MRayl) |
---|---|---|---|---|---|

0 | 293 | 372 | 0.616 | 3720 | 13.84 |

0.2 | 297 | 379 | 0.621 | 3790 | 14.04 |

0.4 | 302 | 388 | 0.627 | 3880 | 14.31 |

0.6 | 292 | 387 | 0.656 | 3870 | 14.22 |

0.8 | 283 | 383 | 0.673 | 3830 | 14.01 |

1 | 271 | 368 | 0.676 | 3680 | 13.4 |

Piezoceramic Fraction v_{c} | Resonant Frequency f_{s} (kHz) | Anti-Resonant Frequency f_{p}(kHz) | Electromechanical Coupling Factor k_{eff} | Sound Velocity c (m/s) | Characteristic Impedance z (MRayl) |
---|---|---|---|---|---|

0.1 | 276 | 371 | 0.668 | 3710 | 6.53 |

0.3 | 294 | 389 | 0.654 | 3890 | 11.81 |

0.5 | 298 | 395 | 0.656 | 3950 | 17.03 |

0.7 | 306 | 400 | 0.644 | 4000 | 22.35 |

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**MDPI and ACS Style**

Sun, R.; Wang, L.; Zhang, Y.; Zhong, C.
Characterization of 1-3 Piezoelectric Composite with a 3-Tier Polymer Structure. *Materials* **2020**, *13*, 397.
https://doi.org/10.3390/ma13020397

**AMA Style**

Sun R, Wang L, Zhang Y, Zhong C.
Characterization of 1-3 Piezoelectric Composite with a 3-Tier Polymer Structure. *Materials*. 2020; 13(2):397.
https://doi.org/10.3390/ma13020397

**Chicago/Turabian Style**

Sun, Ruiqing, Likun Wang, Yanjun Zhang, and Chao Zhong.
2020. "Characterization of 1-3 Piezoelectric Composite with a 3-Tier Polymer Structure" *Materials* 13, no. 2: 397.
https://doi.org/10.3390/ma13020397