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 s₃₃^E 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 s₃₃^E 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.