Thermo-electro-mechanical phase-field modeling of paraelectric to ferroelectric transitions

Abstract

Ferroelectric materials are widely used in engineering and science applications due to their large nonlinear thermo-electro-mechanical coupling. This paper develops and studies a phase-field model to describe paraelectric to ferroelectric phase transitions and the giant electrocaloric effect, a large adiabatic temperature change with the application of an electric field. Spatially inhomogeneous temperature distributions, latent heat due to phase changes, and heat conduction are included in the model. The model is derived from fundamental balances of force, charge, micro-force, and energy. The second law of thermodynamics further constrains the constitutive behaviors derived from a phenomenological free energy function for the material. The finite element method is applied to solve the governing equations for a selected set of boundary value problems. First, the motion of a paraelectric/ferroelectric phase boundary controlled by the application and removal of heat is simulated. Then, a model 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 bulk 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.