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The full matrix material constants of piezoelectric materials should be characterized first before they have been used to make actuators or sensors. Up to now, they are usually determined by the ultrasonic pulse-echo and electric impedance resonance techniques through using multiple samples with drastically different sizes. However, the constants determined by the aforementioned techniques are probably inconsistent because the sample-to-sample variation cannot be eliminated. The technique of resonant ultrasonic spectroscopy (RUS) only needs one sample to determine the full matrix constants of piezoelectric material. Therefore, the consistency of the constants is guaranteed. During the implementation of the RUS technique, the elastic stiffness cijE and piezoelectric constants cij can be determined from the resonance modes identified from the resonant ultrasonic spectrum. The free and clamped dielectric constants cannot be determined by the RUS technique because they have very weak influence on resonance frequency. However, they can be directly measured from the same sample by using an impedance analyzer. To ensure the reliable inversion of material constants, enough resonance modes should be identified from the measured resonant ultrasonic spectrum. However, there are many missing and overlapped modes in the spectrum, which makes mode identification become a biggest obstacle to the implementation of the RUS technique. The adjacent modes may overlap if the resonance frequencies corresponding to them have a very small difference. In addition, the lower the mechanical quality factor QM, the more likely to overlap the adjacent modes are. During the RUS measurement, the rectangular parallelepiped sample is placed between the transmitting and receiving transducers with contacts only at the opposite corners of the sample. Resonance modes would not be detected if the receiving point, i.e., one corner of the sample, is the node of these modes. Therefore, there are missing modes in the resonant ultrasonic spectrum. To overcome the difficulty in identifying the modes, caused by modes missing and overlapping, the mode identifying method via temperature variation is presented in this study. Note that a change of temperature may change the material properties of a piezoelectric sample. The material properties have a great influence on the resonance frequency of the sample. Moreover, the influences corresponding to resonance modes are different. Therefore, the variation of temperature may make the overlapped modes separated from each other and the missing modes appear, namely, the missing and overlapped modes may be identified by comparing the resonant ultrasonic spectra measured at different temperatures. The experimental results of piezoelectric ceramics (PZT-8) show that this method can effectively improve the accuracy of mode identification and guarantee the reliability of inversion in the RUS technique.
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Keywords:
- piezoelectric materials /
- material constants /
- resonant ultrasonic spectroscopy /
- mode identification via temperature variation
[1] Muralt P 2000 J. Micromech. Microeng. 10 136
[2] Zhou Q F, Lam K H, Zheng H R, Qiu W B, Shung K K 2014 Prog. Mater. Sci. 66 87
[3] Zhang S J, Li F 2012 J. Appl. Phys. 111 031301
[4] Zhang S J, Lee S M, Kim D H, Lee H Y, Shrout T R 2008 J. Am. Ceram. Soc. 91 683
[5] Sun E W, Zhang R, Wu F M, Cao W W 2013 J. Alloys Compd. 553 267
[6] Sun E W 2011 Ph. D. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[孙恩伟2011博士学位论文(哈尔滨:哈尔滨工业大学)]
[7] Topolov V Y 2010 Appl. Phys. Lett. 96 196101
[8] Topolov V Y, Bowen C R 2011 J. Appl. Phys. 109 094107
[9] Tang L G, Cao W W 2015 Appl. Phys. Lett. 106 052902
[10] Ohno I 1990 Phys. Chem. Miner. 17 371
[11] Leisure R G, Willis F A 1997 J. Phys.:Condens. Matter 9 6001
[12] Zadler B J, Rousseau J H L, Scales J A, Smith M L 2004 Geophys. J. Int. 156 154
[13] Migliori A, Maynard J D 2005 Rev. Sci. Instrum. 76 121301
[14] Li S Y, Zheng L M, Jiang W H, Sahul R, Gopalan V, Cao W W 2013 J. Appl. Phys. 114 104505
[15] Frazer D B, LeCraw R C 1964 Rev. Sci. Instrum. 35 1113
[16] Ogi H, Kawasaki Y, Hirao M, Ledbetter H 2002 J. Appl. Phys. 92 2451
[17] Ogi H, Ohmori T, Nakamura N, Hirao M 2006 J. Appl. Phys. 100 053511
[18] Nakamura N, Ogi H, Hirao M 2012 J. Appl. Phys. 111 013509
[19] Tang L G, Tian H, Zhang Y, Cao W W 2016 Appl. Phys. Lett. 108 082901
[20] Mochizuki E 1987 J. Phys. Earth 35 159
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[1] Muralt P 2000 J. Micromech. Microeng. 10 136
[2] Zhou Q F, Lam K H, Zheng H R, Qiu W B, Shung K K 2014 Prog. Mater. Sci. 66 87
[3] Zhang S J, Li F 2012 J. Appl. Phys. 111 031301
[4] Zhang S J, Lee S M, Kim D H, Lee H Y, Shrout T R 2008 J. Am. Ceram. Soc. 91 683
[5] Sun E W, Zhang R, Wu F M, Cao W W 2013 J. Alloys Compd. 553 267
[6] Sun E W 2011 Ph. D. Dissertation (Harbin:Harbin Institute of Technology) (in Chinese)[孙恩伟2011博士学位论文(哈尔滨:哈尔滨工业大学)]
[7] Topolov V Y 2010 Appl. Phys. Lett. 96 196101
[8] Topolov V Y, Bowen C R 2011 J. Appl. Phys. 109 094107
[9] Tang L G, Cao W W 2015 Appl. Phys. Lett. 106 052902
[10] Ohno I 1990 Phys. Chem. Miner. 17 371
[11] Leisure R G, Willis F A 1997 J. Phys.:Condens. Matter 9 6001
[12] Zadler B J, Rousseau J H L, Scales J A, Smith M L 2004 Geophys. J. Int. 156 154
[13] Migliori A, Maynard J D 2005 Rev. Sci. Instrum. 76 121301
[14] Li S Y, Zheng L M, Jiang W H, Sahul R, Gopalan V, Cao W W 2013 J. Appl. Phys. 114 104505
[15] Frazer D B, LeCraw R C 1964 Rev. Sci. Instrum. 35 1113
[16] Ogi H, Kawasaki Y, Hirao M, Ledbetter H 2002 J. Appl. Phys. 92 2451
[17] Ogi H, Ohmori T, Nakamura N, Hirao M 2006 J. Appl. Phys. 100 053511
[18] Nakamura N, Ogi H, Hirao M 2012 J. Appl. Phys. 111 013509
[19] Tang L G, Tian H, Zhang Y, Cao W W 2016 Appl. Phys. Lett. 108 082901
[20] Mochizuki E 1987 J. Phys. Earth 35 159
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