A phase-field model for ferroelectrics with general kinetics. Part I: Model formulation

Abstract

When subjected to electro-mechanical loading, ferroelectrics see their polarization evolve through the nucleation and evolution of domains. Existing mesoscale phase-field models for ferroelectrics are typically based on a gradient-descent law for the evolution of the order parameter. While this implicitly assumes that domain walls evolve with linear kinetics, experiments instead indicate that domain wall kinetics is nonlinear. This, in turn, is an important feature for the modeling of rate-dependent effects in polarization switching. We propose a new multiple-phase-field model for ferroelectrics, which permits domain wall motion with nonlinear kinetics, with applications in other solid-solid phase transformation problems. By means of analytical traveling-wave solutions, we characterize the interfacial properties (energy and width) and the interface kinetics of straight domain walls, as furnished by the general kinetics model, and compare them to those of the classical Allen-Cahn model. We show that the proposed model propagates domain walls with arbitrarily chosen nonlinear kinetic relations, which can be tuned to differ for the different types of domain walls in accordance with experimental evidence. In a companion paper, we implement numerically the general kinetics model and characterize the evolution of curved walls and junction points for multiple phases.

Model-based investigations of ferroelectric energy harvesting with regard to an improvement of life span and operability

“…However, G (n) , as given by equation (35), cannot be used explicitly for a switching criterion, since no process direction is indicated in its formulation. Instead, the thermodynamic driving force f (n→k) is introduced as follows, see [22,26,27]:…”