Characterization of the high power properties of piezoelectric ceramics using the burst method: Methodology, analysis, and experimental approach

摘要

Piezoelectric materials are used in a variety of high power applications such as ultrasonic motors and underwater sonar transducers. The properties of these materials are subject to the conditions in which they are applied. Therefore, the properties must be measured in comparable high power testing environments in order to achieve relevant measurements. This dissertation addresses many topics related to the burst or transient method for measuring the properties of piezoelectric materials in high power conditions using a comprehensive approach. The burst method offers several advantages over other high power measurement methods, namely, appropriate application of linear theory, short measurement time, data collection over large range of vibration levels in single measurement, simplicity in experimental application, and no heat generation/temperature rise during measurement.;This dissertation provides the derivations for measurement of the fundamental material constants from resonance and antiresonance characterization, via the force factor A and the newly termed voltage factor B. The force factor is defined as the ratio between short circuit current and edge vibration velocity during natural vibration in short circuit conditions, corresponding to the electrical resonance condition. The voltage factor is defined as the ratio between open circuit voltage and edge displacement during natural vibration in open circuit conditions, corresponding to the electrical antiresonance condition. The derivations of the force factor and the voltage factor are provided for the k31, kp, and k33 extensional modes, beginning from the appropriate constitutive equations. The force factor was found to be related to the piezoelectric stress coefficient e, and the voltage factor was found to be related to the converse piezoelectric coefficient h..;A complete methodology for calculating these material constants is explained, measuring the e, d, and s E at resonance and k and h at antiresonance. The experimental method for achieving an open circuit condition with minimal circuitry is explained via an electromechanical relay. Extensive characterization of k31 samples of commercially available hard and soft PZT compositions was presented to demonstrate the impact of the technique. e, d, k and sE was found to increase with vibration velocity, but h decreased with vibration velocity. Hard PZT demonstrated more stable properties than soft PZT. Notably, the method to determine the dielectric permittivity in high power conditions directly was considered and applied toward the experimental results.;The relationship between the elastic behavior under alternating stress of a PZT resonator and domain wall motion was analyzed using the Rayleigh law. Firstly, because existing Rayleigh law formulations in the literature apply only to a constant energy distribution, a new derivation describing the application of the law for a resonating sample, a sample with energy distribution, is performed. The change in elastic compliance sE 11 with applied stress and the change in the elastic loss tangent tan &phis; '11 with applied stress were related using the Rayleigh parameter alphaX. Utilizing the traditional Rayleigh law, the elastic response for soft and hard PZT was analyzed. Soft PZT was found to have Rayleigh type behavior; however, hard PZT exhibited higher order nonlinearity until large stress levels. Also, the Rayleigh parameter determined from the elastic loss behavior matched that of elastic compliance. This can verify the applicability of the Rayleigh law to the domain wall dynamics of the material. In order to address the discrepancy in hard PZT, the hyperbolic Rayleigh law was implemented. It accounts for reversible domain wall motion explicitly. It allows for the precise determination of the threshold stress as the ratio between the reversible domain wall contribution to the elastic compliance and the Rayleigh coefficient. It was found that the threshold stress of hard PZT is 9 times larger than that of the soft PZT measured.;A new approach to determine the high power figure of merit, Q versus vibration velocity, was discussed using calculated vibration. The method draws off of the technique of using charge measurement to estimate the displacement of an off-resonance transducer. If the force factor or voltage factor measured from low power measurements is assumed to apply to high power conditions, the vibration velocity can be calculated by measuring current in resonance or voltage in antiresonance. Because the quality factor can change by a factor of 3 and the force factor and voltage factor changes less than 7% for large vibration velocities, the error caused by using calculated vibration is expected to be small. Using samples of hard and soft PZT, it was verified that the trend of Q vs. measured vibration velocity and calculated vibration velocity are nearly identical. Therefore, vibration does not need to be measured to determine the figure of merit: this reduces the experimental complexity, which makes the method more accessible to research and production environments. Because the resonance vibration distribution for k 31 and kp resonators are fundamentally different, the stored energy density in each resonator differs for a given edge vibration condition. Therefore, the method of comparing the k 31 and kp piezoelectric resonators using energy density was shown to equate quality factor measurements for hard and soft PZT.;The practical implications of this dissertation is that it furthers the utility of the burst mode measurement to analyze the high power properties of piezoelectric materials. The force factor and voltage factor analysis create a simple framework in which to calculate material properties from experimental measurements. The complete characterization of k31 mode piezoelectric resonators was shown to demonstrate the practical capability of the burst mode to provide comprehensive characterization of the electromechanical properties. The burst mode generates no temperature variation in the sample, therefore, scientific analysis of the properties from high power measurements can be correlated to internal stress levels. The Rayleigh law was specifically adapted to provide the method of analysis regarding reversible and irreversible domain wall motion. Finally, a simplified measurement approach to determine perhaps the most crucial high power figure of merit, quality factor versus vibration velocity, was presented using calculated vibration.