First order ferroelectric-paraelectric phase transition in thin films: Imperfection influence

A general numerical scheme based on Landau-Devonshire free energy is applied for ferroelectric thin films undergoing a first order phase transition to describe the influence of imperfect surface layers and depolarization field on profile of polarization P(z) and phase transition temperature. It is known that the physical properties of thin films are significantly different from those of bulk ferroelectrics. The surface effect is one of this important proprieties observed in ferroelectric thin films; at the surface of the film the coordination of atoms is different from that inside the film. As a consequence, surface atoms would have an equilibrium interatomic spacing dissimilar from that of the interior atoms if the film were free standing. In this work, ferroelectric-paraelectric phase transition is discussed from the LD phenomenological theory, the profile distribution P(z) of the order parameter is described by an Euler-Lagrange equation with apply a corresponding boundary condition on P.