Microscopic simulations of the behavior of ferroelectrics and ferromagnetics

Ferroelectric and ferromagnetic materials have wide engineering applications. The defects and size effects are important reliability and sensitivity issues in the application of such materials. In this paper, phase field simulations were carried out to study the effects of cracks in ferroelectrics and size effects on ferromagnetics. In the former simulation, the crack tip domain switching regions and stress fields were plotted. The results obtained showed that a negative electric field tends to open the crack, whereas a positive field tends to close it. In the latter simulation, it was found that both the hysteresis and coercivity were greatly affected by the ratio of the characteristic length to domain wall width