Modeling and characterization of electrostrictive ceramics

We present a non-linear theory for electromechanical materials based on a Taylor's series expansion of the thermodynamic potentials to 3rd and higher order terms in field and stress, and we show that this general theory is applicable to both piezoelectric and ideal electrostrictive materials depending with an appropriate choice of material coefficients. The model allows for the non-zero piezoelectric behavior found in some nominally electrostrictive materials. The quasistatic non-linear equations used to describe low frequency electromechanical devices are shown to account for saturation in both strain and polarization as well as the stress dependence. The `reversible' electrostrictive ceramic PMN/PT/La (0.9/0.1/1%) operating above T max is used to illustrate the suitability of the model. Under a DC bias field, these materials behave as a piezoelectric ceramic material with C ∞ ) symmetry. The effective piezoelectric is found to be linear as a function of the DC bias field up to about 0.5MV/m. Above 0.5 MV/m, the piezoelectric and the electromechanical coupling constants begin to saturate due to higher 4th order electrostriction (S ∝ kE 4 with k negative), which is shown to be the result of the saturation in the dielectric response. A switchable, low field, linear component of the piezoelectric voltage coefficient, g, is found in the S vs D response. The g coefficient is found to change sign depending on the sign of the measurement field. These materials behave as a tunable piezoelectric with the piezoelectric coefficient being directly proportional to the electrostrictive coefficient and the DC bias field, up to saturation.