Vogel-Fulcher freezing in relaxor ferroelectrics

TL;DR

This paper proposes a physical mechanism explaining the Vogel-Fulcher freezing behavior in relaxor ferroelectrics by linking PNR reorientation activation energy to cluster volume and applying percolation theory.

Contribution

It introduces a model connecting PNR cluster volume to relaxation time divergence, deriving the Vogel-Fulcher equation from continuum percolation theory.

Findings

Relaxation time diverges at percolation threshold.

Vogel-Fulcher equation derived from percolation theory.

Mechanism explains PNR freezing in relaxors.

Abstract

A physical mechanism for the freezing of polar nanoregions (PNRs) in relaxor ferroelectrics is presented. Assuming that the activation energy for the reorientation of a cluster of PNRs scales with the mean volume of the cluster, the characteristic relaxation time $\tau$ is found to diverge as the cluster volume reaches the percolation limit. Applying the mean field theory of continuum percolation, the familiar Vogel-Fulcher equation for the temperature dependence of $\tau$ is derived.