A PHYSICAL MODEL FOR HYSTERESIS CURVES OF FERROELECTRIC CERAMICS

A general model for the simulation and for the interpretation of hysteresis curves is presented. The model opens the possibility to calculate hysteresis curves if the electrostatic interaction of grains in a critical volume can be treated quantitatively. The hysteresis curve is described by a progress parameter delta. The effective polarization P(off)(delta) in the process of inversion is approximated by a switching procedure. The average polarization of most grains is inverted by 180 degrees. The hysteresis function of the electric switching field E(delta) which is dependent on the same progress parameter delta is derived from an electrostatic equation which allows to calculate the electric field in a polar inclusion in a homogeneous ferroelectric matrix. In the model the ferroelectric matrix is replaced by the quasi-homogeneous ceramic and the inclusions are replaced by spherical regions with interacting grains. The average polarization in the regions lags more or less behind the effective polarization or is ahead of it. Interaction is caused by strong local electric field fluctuations which are due to the discontinuities of the polarization from grain to grain. Making simple assumptions about the electric field in the critical regions. hysteresis curves can be simulated. The method of calculation employed gives an insight into the various field components involved in switching, including the collective effects of the grains.