Formation and rapid evolution of domain structure at phase transitions in slightly inhomogeneous ferroelectrics and ferroelastics

TL;DR

This paper analytically investigates how tiny inhomogeneities in ferroelectric and ferroelastic materials lead to the formation and rapid evolution of domain structures during phase transitions, highlighting the sensitivity of domain patterns to small temperature differences.

Contribution

It provides an exactly solvable model demonstrating that minimal inhomogeneities cause domain formation and describes how domain width evolves with temperature in such systems.

Findings

Tiny inhomogeneities trigger domain formation below phase transition.

Domain width increases rapidly as temperature decreases.

Even microkelvin-level differences significantly affect domain structures.

Abstract

We present the analytical study of stability loss and evolution of domain structure in inhomogeneous ferroelectric and ferroelastic samples for exactly solvable models. The model assumes a short-circuited ferroelectric capacitor (free ferroelastic) with two regions with slightly different critical temperatures Tc1 Tc2, where Tc1-Tc2 << Tc1, Tc2. We show that even a tiny inhomogeneity like 10-5 K results in splitting the system into domains below the phase transition temperature. At T < Tc2 the domain width a is proportional to (Tc1-T)/(Tc1-Tc2) and quickly increases with lowering temperature. The minute inhomogeneities in Tc may result from structural (growth) inhomogeneities, which are always present in real samples, and a similar role can be played by inevitable temperature gradients.