Phase-field modeling of the thermo-electro-mechanically coupled behavior of ferroelectric materials
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Ferroelectric materials are widely used in engineering and science applications due to their large nonlinear thermo-electro-mechanical coupling. Of interest recently, has been the study of the giant electrocaloric effect, a large adiabatic temperature change with the application of an electric field, due to its possible application for solid-state cooling. The electrocaloric effect is maximized near phase transitions, where entropy jumps contribute to a large nonlinear effect. This dissertation develops a continuum phase-field model for the thermo-electro-mechanically coupled behavior for ferroelectric materials. The model is derived from thermodynamic considerations and based on a phenomenological free energy function. The finite element method is applied to solve the governing equations for a selected set of boundary value problems. Mechanical displacement, electric potential, polarization and temperature are used as degrees of freedom in the formulation of the finite element implementation of the model. The a geometry for an isothermal stable two-dimensional ferroelectric to paraelectric phase boundary is developed, along with appropriate boundary conditions, and simulated using the nonlinear finite element method for a variety of ferroelectric domain widths. The dependence of the phase coexistence temperature, boundary energy, entropy jump across the boundary and closure domain shape on the ferroelectric laminate domain width is quantified. A simulation of the motion of the phase boundary through the material under entropy/heat input control is demonstrated. Next, a realistic electrocaloric cooling device based on a multilayer ferroelectric capacitor is simulated through a full thermodynamic refrigeration cycle. The model geometry and boundary conditions are chosen to match realistic device configurations. The device is driven through a cycle with two adiabatic and two constant electric field legs, and compared with the analytically computed ideal plane strain electrocaloric cooling cycle. Several inefficiencies arise in the device, including incomplete transformation, entropy loss due to phase boundary motion, and high energy zones with large stresses and closure domains at the electrode tip. Lastly, motivated by potential uses as actuators, the domain structure in three-dimensional ferroelectric nanodots is modeled by cooling from a paraelectric phase. The expected vortex domain structure forms in sufficiently small dots, but distorts upon further cooling to room temperature. The room temperature transfer of dots to a rigid substrate and actuation via an out-of-plane electric field leads to incomplete domain switching, thereby reducing actuator displacements.