Three-Dimensional Phase Field Simulations of Hysteresis and Butterfly Loops by the Finite Volume Method

Abstract

Three-dimensional (3D) simulations of ferroelectric hysteresis and butterfly loops have been carried out based on solving the time dependent Ginsburg-Landau equations by using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops has been studied numerically. The 3D ferroelectric domain formation and its evolution have also been presented in the paper. The simulation results successfully reveal the macroscopically nonlinear response to the applied stresses and electric field. 77.80.Dj, 78.20.Bh Ferroelectricity is one of the fastest growing fields during the past several decades. Interest in this field is attributable to the increasing numbers of practical applications in micro-electromechanical systems, microwave devices, and memory PACS:

Modeling of hysteresis loop and its applications in ferroelectric materials

“…Therefore, the reported hysteresis loops measured or predicted under different conditions inevitably presented with diversified patterns. And the diversified patterns obtained experimentally are still beyond on the predictions simulated by using the phenomenological theory of time-dependent Landau Ginzburg Devonshire(TDLGD) [17,18,22].…”