Low frequency modelling of hysteresis behaviour and dielectric permittivity in ferroelectric ceramics under electric field

The properties of ferroelectric ceramics strongly depend on the electromechanical loading and their measurement conditions. In this paper, a nonlinear phenomenological one-dimensional model based on the dry friction concept is presented to describe the hysteretic polarization behaviour. Dielectric permittivities versus dc electric field ( or capacitance C versus voltage V) loops are determined for the characterization of ferroelectric material. The epsilon(33) coefficient is used for the ceramic characterization because it is strongly correlated with the ceramic quality. The purpose of this paper is to develop a model of reversal polarization behaviour close to physical realities, able to provide good performances on the simulation of dielectric permittivity loop epsilon(33)( E-dc). Simulated behaviours are finally compared with experimental results on a typically soft PZT ferroelectric ceramic.