Phase-field Simulation Of Bi₄Ti₃O₁₂ Ferroelectrics And Expansion Of The Landau Free Energy Of BaTiO₃

In this dissertation,two aspects related to the ferroelectric materials have been discussed systematically:（1）The Ginzburg-Landau equation has been numerically solved by finite volume method for the Bi₄Ti₃O₁₂ ferroelectric materials.The effects of the applied tensile strain and compressive strain under external electric field on the hysteresis and the butterfly loops of Bi₄Ti₃O₁₂ ferroelectric materials have been simulated in three-dimensional space.The results are in line with the reported data in the literature.This indicates that the finite volume method is one of the main computational methods for the phase field simulation.The results are beneficial to investigate the macroscopic response in external electric field and mechanical loading and to understand the macroscopic properties through the domain structures of the ferroelectric materials.（2）In order to develop the Landau-Ginzburg-Devonshire（LGD）potential of the pervoskites BaTiO₃,the Gibbs free energy of BaTiO₃ single crystal has been expanded up to the 10th-order terms.The coefficients of the LGD formulation have been phenomenologically derived based on the proposed LGD model.The dependences of the spontaneous polarization,the dielectric property,and the ferroelectric hysteresis loop on temperature have been investigated systematically by using the developed 10th-order LGD model.The phenomenological thermodynamic potential near the Curie point,and the three dimensional non-convex free energy landscapes corresponding to the 4th,6th,8th,and 10th order model have been analyzed numerically.The predicted results based on our proposed potential and coefficients in this paper have also been compared with experimental results as well as theoretically results reported by other researchers.