Kinematic Theory of Ferroelectric Domain Growth

Abstract

Sidewise motion of 180° wall in ferroelectric barium titanate is described, applying the kinematic wave theory developed by Lighthill-Witham. The rather peculiar shapes of the domain in growing and in shrinking processes, observed by Miller and Husimi, can be derived purely kinematically. 180° wall is described as an assembly of steps. Orientation of the wall is described by step density. There is a part of constant orientation that moves with a constant velocity, which is shown to be identical to the kinematic wave velocity. Round squares observed in the growing process and straight domain fronts in the shrinking process are fairly well explained as a result of propagation of kinematic waves, assuming a suitable functional relationship between the velocity and the density of the progressing steps. Discontinuity of wall orientation is interpreted as “kinematic shock wave.”