A level set approach to domain wall kinetics and domain patterning in elastic ferroelectrics

The level set method is a powerful tool for tracking a moving interface. In ferroelectric materials the boundaries between domains of uniform polarization, referred to as domain walls, are viewed as interfaces. In this work, a variational level set method is used to formulate a model for the behavior of elastic ferroelectrics and more particularly to describe the domain formation and the domain wall kinetics. A regularized version of the sharp-interface theory is introduced by substitution of the singular surfaces with thin transition layers, inserting so inhomogeneities into the energy density function. It is proved that the forces driving domain wall motion are, in fact, inhomogeneity forces. With this description, the level set method becomes an appropriate framework to insert and exploit material forces. The proposed model may interpret typical microstructures in 2-D elastic ferroelectrics with tetragonal crystal symmetry. Comparisons with phase-field models and experiments show good agreement.