Characterizing elastic and piezoelectric constants of piezoelectric materials from one sample using resonant ultrasound spectroscopy

The full matrix material constants of a piezoelectric sample obtained by ultrasonic pulse-echo and IEEE resonance methods probably are inconsistent because they are obtained from multiple samples. To guarantee the self-consistency of the characterization, all material constants should be derived from the same sample. Resonant ultrasound spectroscopy (RUS) can characterize all elastic and piezoelectric constants of piezoelectric materials using only one sample. The most challenging barrier in RUS is the identification of sufficient resonance modes from the ultrasound resonant spectrum. To reduce the difficulty of mode identification and improve its reliability, the ultrasound resonant spectra of a rectangular parallelepiped piezoelectric sample are suggested to be measured under two different boundary conditions in this study. One boundary condition is that all surfaces of the sample are free. Another is that one surface of the sample is equipotential, i.e., this surface is attached with an electrode, and the other surfaces are free. Subsequently, resonance frequencies are identified from the aforementioned ultrasound resonant spectra and used in the RUS inversion. If 2n modes are required in the inversion, only n modes are to be identified from each spectrum. It is noteworthy that the higher the frequency, the more difficult is the mode identification. Therefore, identifying n modes from the spectrum is far easier than identifying 2n modes from it. The characterization of a PZT-8 sample is used as an example to verify the validity of the method presented herein.