The characterisation and modelling of electrostrictive ceramics for transducers

Abstract

We have measured the electromechanical properties of the “reversible” electrostrictive ceramic (TRS Ceramics Inc) PMN/PT/La (0.9/0.1/1%) at room temperature, which is slightly above Tmax, the temperature at which the real part of the material's low frequency permittivity has a maximum. Under DC bias fields up to about 0.5 MV/m, the material behaves as a piezoelectric ceramic material with C\\infty symmetry. The effective piezoelectric and electromechanical coupling coefficients having a linear dependence on the bias field while the dielectric constant (at constant stress) and elastic constant (at constant field) are found to have a quadratic dependence on the bias field. Under higher bias fields, the piezoelectric and electromechanical coupling coefficients begin to saturate. In order to understand our measurements, we have used Mason's model for electrostriction and we have developed a nonlinear macroscopic model for electromechanical materials based on a Taylor's series expansion of the thermodynamic potentials to third and higher order terms in field and stress. The resonance equations for the DC biased length extensional resonator have been obtained and DC biased resonance techniques are shown to be useful in determining the electrostrictive and other higher order coefficients. The saturation at higher bias fields arises from higher fourth order terms (S∞kE4, with k negative) that result from saturation in the dielectric response.