Full Analysis of the Ferroelectric Phase Transition in a Thin Film with Various Boundary Conditions

Abstract

Second order ferroelectric phase transition for a thin film with arbitrary boundary conditions is considered within the framework of the Landau theory. General phase-plane portraits for the relevant Euler-Lagrange equation are constructed and different types of trajectories are analyzed. Full set of order parameter profiles is found. The method of reconstructing the admissible order parameter profiles for particular film thickness and extrapolation lengths is discussed.

Keywords:

• Phase transition
• thin film
• Landau theory
• arbitrary boundary conditions
• phase portrait
• order parameter profile