Crystallographic approach to obtain intensive elastic parameters of k33 mode piezoelectric ceramics


The past 100 years have witnessed the technological advancement and application of piezoelectric materials in sensors, transducers and actuators. Such tremendous advancement can be credited to the enhanced computation technology involving finite element analysis, which has become an indispensable tool for the design and optimization of piezoelectric devices. Moreover, accurate intensive parameters are obviously essential when it comes to simulation; especially around the resonance and anti-resonance frequency range. Generally, the elastic properties have been proven to originate from the sound velocity. To be more specific, the sound velocity is usually computed from the resonance frequency of k31 vibration mode and the anti-resonance frequency of k33 vibration mode where the half-wave is generated along the vibration. Unfortunately, by structural constraint, a significant challenge is experienced frequently during the determination of the intensive elastic compliance s33E and the corresponding loss tanϕ’33 in the k33 mode; that is, the mode with elastic vibration along the polarization direction.

Minkyu Choi and Kenji Uchino from International Center for Actuators and Transducers at The Pennsylvania State University in collaboration with Timo Scholehwar and Eberhard Hennig from PI Ceramic GmbH in Germany proposed a study whose main objective was to resolve the aforementioned shortcoming by employing the crystallographic approach. Their goal was to present an advanced piezo-material characterization technique that could, with minimal challenges, obtain intensive elastic parameters of the k33 vibration mode from the k31 geometry. Their work is currently published in Journal of the European Ceramic Society.

Briefly, the research method employed commenced with the preparation of effective k31 samples and conventional k33. The researchers then poled and cut sintered blocks with a precision saw in a predetermined direction so as to have the desired polarization angle. Subsequently, low temperature electroding was done on the cut blocks, after which the various polarization angles were designed. The research team then derived the effective elastic compliance and loss from the measured resonance frequency and corresponding 3 decibels bandwidth on the voltage spectrum.

The authors noted that the relative error of elastic compliance s33E and corresponding intensive loss tanϕ’33 found in the conventional methods were −8.3% and 74% respectively. Additionally, the conventional method on the k33 mode was noted to underestimate the elastic compliance value, while concurrently overestimating the elastic loss.

The Minkyu Choi and colleagues study presented the derivation of the elastic properties of k33 vibration mode of piezoelectric materials from effective k31 mode samples with excellent accuracy, where the obtained elastic parameters are superb with negligible deviation, and no significant sample geometrical error. This work has shown that the reliability of the proposed method is extraordinary, and the implicit relative error in the conventional methods could be avoided. To this end, it is interesting to note that the maximum elastic loss for the effective longitudinal vibration is not incurred where the elastic compliance is maximum.

 intensive elastic parameters of k33 mode piezoelectric ceramics-Advances in Engineering

About the author

Minkyu Choi received the B.S. and M.S. degrees in materials science and engineering from Korea University, Seoul, South Korea in 2007 and 2009, respectively. He contributed in industry developing piezoelectric dispenser systems in Protec, Korea and 6-axis inertial MEMS sensors in Samsung Electro-Mechanics, Korea. He is currently a Ph.D. candidate in International Center for Actuators and Transducers, the Penn State University. His research interests cover the design and analysis of piezoelectric materials, losses, and its applications


Minkyu Choi, Timo Scholehwar, Eberhard Hennig, Kenji Uchino. Crystallographic approach to obtain intensive elastic parameters of k33 mode piezoelectric ceramics. Journal of the European Ceramic Society volume 37 (2017) pages 5109–5112


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