Tri-Duality Theory in Phase Transformations of Ferroelectric Crystals with Random Defects

Abstract

This paper presents a general solution theory to the Landau-Ginzburg (LG) equation in the presence of a high concentration of point defects of which a small concentration is charged, and subsequently applied to disordered ferroelectric crystals. Beginning with a canonical dual transformation method, a triality theorem is developed for solving the non-convex variational problem associated with LG equation. The approach allows for an exact solution of the LG equation in the case of strong Ginzburg contributions to the total energy, avoiding conventional linearization of the order parameter into Fourier components. It is demonstrated that the Ginzburg and random-field terms have similar effects, both acting as a driving force. The imperfect contribution from high concentrations of uncharged point defects acts to decrease the stability of the double potential well, favoring a single well. It is shown that the order parameter is unstable with increasing magnitude of the Ginzburg/random-field and imperfect contributions. Both theoretical and experimental results demonstrate with increasing polarization nonuniformity, that ferroelectric domains breakup into subdomains, resulting in pseudo-cubic symmetry.