Real Space Phase Field Simulations of Ferroelectric Materials

Ferroelectric perovskites are used in various transducer, memory and optical applications due to their attractive electromechanical and optical properties. In these applications, ferroelectrics often have complex geometries and function under complex electro-mechanical loadings. Phase-field models are typically used to predict the formation of microstructural patterns and subsequent evolution for ferroelectrics under these applied loads. In addition, boundary element method can be integrated into the phase-field model to resolves the electrical fields generated from these devices over all space, not just confined inside the specimen. In this research, we develop a simple method to construct an energy density function for phase-field modeling to predict the microstructure of multifunction materials. This formulation can handle complex equilibrium structures and crystallographic symmetry with ease. We validate this method on a NiTi shape-memory thin film with cubic to monoclinic transformation with 12 variants that are symmetry related. Next, we present an iterative boundary element method for the solution of the exterior all-space electrostatic problem for nonlinear dielectric media. In contrast to direct solution of the electrostatic problems, this method avoids the construction, storage and solution of dense and large linear systems. This provides important advantages for multiphysics problems, such as ferroelectrics modeling, that couple the linear electrostatic Poisson problem to nonlinear physics. We integrate this iterative approach into the conventional phase field model. After that, We implement this method to simulate the ferroelectric materials in various examples. First, we studied the effect of lattice orientation, surface modulation, and applied fields on free-surface domain microstructure in ferroelectrics. Second, we consider the free-surface domain microstructure in ferroelectrics with a stationary crack. Next, we investigate the ferroelectric domain nucleation under a charged tip. After that, we simulate the Piezoresponse Force Microscopy on scanning the ferroelectric surfaces. At last, we examine the domain microstructure and space charge distribution of ferroelectrics under the effect of semiconductor doping.