Vogel-Fulcher freezing in relaxor ferroelectrics

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 $\ensuremath{\tau}$ 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 $\ensuremath{\tau}$ is derived.