Theory of Size-Driven Transitions in Displacive and Order-Disorder Ferroelectrics

TL;DR

This paper develops a simple theoretical framework explaining size-driven phase transitions in displacive ferroelectrics, highlighting how system size influences transition temperature, with contrasting behavior in order-disorder ferroelectrics supported by experimental evidence.

Contribution

It introduces a unified theory for size-dependent ferroelectric transitions, distinguishing between displacive and order-disorder types and explaining their different size effects.

Findings

Transition temperature decreases with system size in displacive ferroelectrics.

Order-disorder ferroelectrics show negligible size effect on transition temperature.

Theory aligns with experimental observations for both ferroelectric types.

Abstract

We present a simple theory for structural transitions in displacive ferroelectrics of the perovskite type. In our theory, the competition between the elastic energy cost for the displacement of the homopolar ion from the centrosymmetric position, and the energy gain due to a ferroelectric ordering of the dipoles formed by the ionic displacements, leads naturally to a first-order transition from a paraelectric to a ferroelectric phase. This transition takes place at a certain temperature $T_c(L)$ as the temperature is decreased and, at a certain size $L_c (T)$ as the size of the system is increased. The transition temperature $T_c (L)$ is suppressed as the sample size is reduced, and vanishes for samples below a certain size. For order-disorder ferroelectrics, our theory shows that the suppression of $T_c$ by a reduction in system size is not appreciable, a result that is borne out by experiments.