A Theory of D-E Hysteresis Loop Based on the Avrami Model

The D - E hysteresis loop of ferroelectrics is theoretically studied on the basis of the extended Avrami theory. If the sideway velocity depends only on the instant value of the applied field, the volume fraction of the reversed area is expressed as q ( E )=1-exp (- f - d Φ( E )), where f and d are, respectively, the frequency of the applied field and the growth dimension of domains, and Φ is a function of E . This result is obtained irrespective of the waveform of the applied field and the field dependence of the sideway velocity, if the nucleation event is deterministic. For the stochastic nucleation due to thermal fluctuation, on the other hand, the above result is modified as q ( E )=1-exp (- f -( d +1) Φ( E )). The effect of the delay of wall motion is also discussed.