Size effects on the second order ferroelectric phase transition in a thin film with non-symmetric boundary conditions

TL;DR

This paper provides an analytical study of how size and boundary conditions influence the second order ferroelectric phase transition in thin films, revealing that certain boundary conditions significantly weaken size effects.

Contribution

It offers an analytical solution and phase-plane analysis for ferroelectric phase transitions in thin films with arbitrary boundary conditions, including numerical considerations for opposite sign extrapolation lengths.

Findings

Size effects on the order parameter are weakened with opposite sign extrapolation lengths.

Transition temperature's size dependence is affected by boundary conditions.

Analytical and numerical methods are used to analyze boundary condition impacts.

Abstract

The analytical solution is considered for the phenomenological theory of the second order ferroelectric or ferroelastic phase transition in a thin film with arbitrary boundary conditions. The general phase-plane portrait for the relevant Euler-Lagrange equation was analyzed. The order parameter distribution in the film was found for some particular sets of extrapolation lengths. The case of extrapolation lengths with opposite signs was also considered numerically. It was shown that the size effect on the order parameter and transition temperature is remarkably weakened when the extrapolation lengths have similar absolute values and opposite signs.