Ferroic Domain Structures using Ginzburg-Landau Methods

Abstract

We present a strain-based formalism of domain wall formation and microstructure in ferroic materials within a Ginzburg-Landau framework. Certain omponents of the strain tensor serve as the order parameter for the transition. Elastic compatibility is explicitly included as an anisotropic, long-range interaction between the order parameter strain components. Our method is compared with the phase-field method and that used by the applied mathematics community. We consider representative free energies for a twodimensional triangle to rectangle transition and a three-dimensional cubic to tetragonal transition. We also provide illustrative simulation results for the two-dimensional case and compare the constitutive response of a polycrystal with that of a single crystal.