Numerical Characterization of Piezoceramics Using Resonance Curves

Abstract

Piezoelectric materials characterization is a challenging problem involving physical concepts, electrical and mechanical measurements and numerical optimization techniques. Piezoelectric ceramics such as Lead Zirconate Titanate (PZT) belong to the 6 mm symmetry class, which requires five elastic, three piezoelectric and two dielectric constants to fully represent the material properties. If losses are considered, the material properties can be represented by complex numbers. In this case, 20 independent material constants are required to obtain the full model. Several numerical methods have been used to adjust the theoretical models to the experimental results. The continuous improvement of the computer processing ability has allowed the use of a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the piezoelectric constants. This review presents the recent advances in the numerical characterization of 6 mm piezoelectric materials from experimental electrical impedance curves. The basic strategy consists in measuring the electrical impedance curve of a piezoelectric disk, and then combining the Finite Element Method with an iterative algorithm to find a set of material properties that minimizes the difference between the numerical impedance curve and the experimental one. Different methods to validate the results are also discussed. Examples of characterization of some common piezoelectric ceramics are presented to show the practical application of the described methods.

Electromechanical Anisotropy at the Ferroelectric to Relaxor Transition of (Bi0.5Na0.5)0.94Ba0.06TiO3 Ceramics from the Thermal Evolution of Resonance Curves

“…Here the classical local sensitivity analysis is used as proposed by Perez et al [6,7,21]. A global sensitivity analysis [22] is not necessary for the actual purposes.…”

“…After this first condition, the optimization methodology presented in [6,7] was used. Although there may be more efficient solutions, the methodology based in the Nelder-Mead algorithm [20] is generally robust and easy to implement, which are reasons why it was selected here.…”

“…This sample is thermally depolarized, producing changes in the resonance spectrum as a function of temperature. One alternative to do that is using an iterative methodology based in finite-element method (FEM) simulation [6][7][8]. The use of FEM based minimization techniques to obtain the parameters in the piezoelectric models was successfully implemented by several groups in recent years [9][10][11].…”

A systematic analysis of the radial resonance frequency spectra of the PZT-based (Zr/Ti = 52/48) piezoceramic thin disks

“…Moreover, some non-analytical methods are also used for identification of the elastic, dielectric, and piezoelectric constants of piezoceramic disk resonators [15,16]. In recent years, the continuous progress of the computer technology has created a specific numerical method, the Finite Element Method (FEM), to iteratively solve the problem of finding the material constants of piezoceramics [17].…”

Material parameter determination of a piezoelectric disc with triple-ring-electrodes for increased sensitivity

“…Several examples of using piezoelectric discs or plates with electrodes fully covering top and bottom faces (full-faced) that implement these formulations can be found in the literature. 2,6 The recurring problem can be described as a lack of sensitivity for several material parameters, since the simple geometric structures do not allow to fully determine the material properties. Rupitsch et al 8 include surface normal velocities in addition to the impedance measurements using a Laser-Scanning-Vibrometer.…”