Phase-field Simulation Of Domain Switching And Phase Transition In Ferroelectric Materials Induced By Inhomogeneous Forces

Ferroelectric materials are a kind of the functional materials which have been widely used as core componet in high-tech electromechanical equipments,such as microelectronic devices,high precision sensors,transducers,energy storage devices.Recently,there are many studies on the macroscopic mechanical-electrical behavior,the microstructure characteristics and the domain switching of ferroelectric materials under a single external field.Given that more smart devices based on ferroelectric material serve in extreme multi-field environments,the microstructure evolution of ferroelectric material induced by complex external fields,like domain switching and phase transitions,directly affects the electrical and mechanical properties and the electromechanical coupling behavior of this functional materials.However,there is still a lack of in-depth research on the evolution of the domain structure,and the phase transition mechanism between different ferroelectric phases induced by non-uniform forces.In this thesis,we systematicly studied the domain evolution and electromechanical coupling response in conventional ferroelectric thin film materials under local loading or with crack defect,as well as the phase transition characteristics and domain evolution of relaxor ferroelectric single crystal under non-uniform field based on phase-field method.Firstly,the phase-field model incorporating the surface effects and flexoelectric effect was established to explore the domain switching and mechanical-electric coupling behavior of Pb Ti O₃ferroelectric thin films subjected to a local mechanical load.And the finite element method was used to numerically solve the partical differential equations of the phase-field model.In this process,we analyzed the effects of surface elasticity and residual stress on domain switching of ferroelectric thin film,reveling the physical mechanism of the size dependence of domain switching caused by surface effects.The results show that the 180^o domain switching in the ferroelectric film occurs and the discretely distributed of 180^o submicrostructure domains are induced on the surface of the loading region.These submicrostructures are closely related to the non-uniform deformation on the surface of the loading area.Besides,the mechanical-induced 180^o domain switching in the ferroelectric thin film exhibits significant size dependence:when the thickness of the film or the width of the local load is below a certain critical value,the 180^o domain switching cannot be achieved.Secondly,there are various defects in the ferroelectric materials,like tiny cracks generated during the material preparation and application,which will significantly impact the mechanical properties and mechanical-electric coupling properties.To study this problem,a mechanical-electric coupling fracture phase field model including the flexoelectric effect was established.We numerically studied the domain switching and the polarization characteristics near the crack tip,as well as the crack propagation of Ba Ti O₃ single crystal.It is found that the 90^o domain switching occurs near the crack tip,forming the airfoil twin domains.The stronger the flexoelectric effect,the smaller the area of domain switching.In the meantime,flexoelectric effect obviously influences the process of crack propagation:when the directions of the initial polarization and the crack propagation are same,the crack length decreases with the increasing of the flexoelectric coefficients,implying the effect of inhibiting the crack propagation;contrarily,when the two directions are opposite,it demenstates a tendency to promote the crack propagation.Moreover,we analyzed the stress distribution,stress concentration along the crack propagation direction,and explained the influence of the flexoelectric effect on crack propagation.Experimental observations show that the external fields can not only cause the domain switching of ferroelectric materials in the same ferroelectric phase,but also trigger the phase transitions between different ferroelectric phases.To study the phase transition of relaxor ferroelectric single crystal,especially the path and mechanism of phase transition during mechanical loading/unloading process,a mechanical-electric coupling phase-field model in a 2D rhombohedral coordinate system was established in this thesis.Furthermore,a finite element model is developed to numerically study the domain evolution and phase transition of PMN-0.3PT single crystal during mechanical loading/unloading process.It is turned out that the phase transition of the material exhibits anisotropic characteristics during mechanical loading:the irreversible phase transition from rhombohedral phase（R）to tetragonal phase（T）is induced along the crystal[110]direction during the loading/unloading process;the reversible phase transition from rhombohedral phase（R）to orthorhombic phase（O）is triggered along the crystal[001]direction.Moreover,we quantitatively get the characterisitics of stress-strain curves,electric field-polarization hysteresis curves,and electric field-strain curves under the mechanical-electric coupling fields,which reveal that the energy barrier in different crystal directions determines its mechanical-electric response characteristics and that the difference of the energy barrier in different directions is responsible for the reversible/irreversible phase transition.Finally,a phase field model is established to characterize the evolution of mechanical-induced domain switching and phase transition for the relaxor ferroelectric materials under nano-indenter.Based on this model,we systematically studied the mechanical features and phase transition behavior of PMN-0.3PT single crystal under the indenter load,getting the load-displacement curves.These results suggest that the local phase transition from R phase to T phase is responsible for the pop-in phenomenon in the load-displacement curve,explaining the pop-in phenomenon in the mechanical indentation experiments of this ferroelectric materials.In fact,it is the first time to demonstrate the correlation between the pop-in phenomenon and the ferroelectric phase transition.In addition,we also find that different indenters（cone,sphere,and cylinder）can induce phase transition and that the geometry of indenter has a profound influence on the phase transition of this material,that is,the increasing of geometric size decreases the stress concentration below the indenter,thus increasing the critical load of phase transition.Plus,the external electric field also has an impact on the characteristics of the phase transition and mechanical response induced by the indenter.In this case,different directions of electric field promote or inhibit the phase transition induced by the indenter:the combination of different fields can manipulate the phase transition to a certain degree.To sum up,this thesis explores ferroelectric domain switching and phase transition triggered by non-uniform force field to provide more theoretical guidance for the revelation of the mechanism of mechanical-electric coupling,the manipulation of macroscopic mechanical-electric response and the prediction of the behavior of ferroelectric materials driven by complex external fields.