Paraelectric - Ferroelectric Phase Transitions in Particles of the Sphere Shape

TL;DR

This paper investigates phase transitions in spheroidal particles from paraelectric to ferroelectric states, analyzing dielectric properties and resonance frequencies, and compares theoretical predictions with experimental data for specific materials.

Contribution

It provides a detailed theoretical analysis of ferroelectric phase transitions in spheroidal particles, including surface effects and resonance frequencies, with validation against experimental results.

Findings

Transition temperature decreases quadratically with particle diameter.

Existence of a critical diameter below which ferroelectric phase is absent.

Good agreement between theory and experiment when considering a dead layer.

Abstract

A transition in a spheroidal particle from the paraelectric to the ferroelectric phase as well as dynamic susceptibility are studied without approximation in the paraphase. It is assumed that the surface charge is compensated and the boundary condition for the polarisation is P=0, i. e. with zero polarisation at the surface of the particle. There is an infinite number of resonance frequencies in the dynamic dielectric function within the quasistatic approximation. The paraphase properties of the dielectric response of the particle are discussed. The transition temperature decreases with decreasing diameter d of the particles inverse quadratically. There exists such a critical diameter that for the particles with the diameter below the critical one the ferroelectric phase is absent. Comparison of the experiment with theoretical results is carried out. Introduction of a dead layer thickness leads to a very good agreement of theory with the experiment for $PbTiO_{3}$ and to a good agreement with the experimentfor $BaTiO_{3}$.