Phase diagrams and polar properties of ferroelectric nanotubes and nanowires

TL;DR

This study analyzes how size, stress, and depolarization fields influence the phase diagrams and polar properties of ferroelectric nanotubes and nanowires, predicting enhanced ferroelectricity under certain conditions.

Contribution

It provides an analytical model for transition temperatures considering various effects and explains observed ferroelectricity enhancement in specific nanostructures.

Findings

Transition temperature can exceed bulk values under certain conditions.

Polar properties are conserved and enhanced in long nanotubes and nanowires.

Model predictions align well with experimental hysteresis data.

Abstract

In this paper we study the size effects of the ferroelectric nanotube and nanowire phase diagrams and polar properties allowing for radial stress and depolarization field influence. The approximate analytical expression for the paraelectric-ferroelectric transition temperature dependence on the radii of nanotube, polarization gradient coefficient, extrapolation length, radial stress (surface tension) and electrostriction coefficient was derived. It was shown that the transition temperature could be higher than the one of the bulk material for negative electrostriction coefficient and small depolarization field. Therefore we predict conservation and enhancement of polar properties in long cylindrical ferroelectric nanoparticles. Obtained results explain the observed ferroelectricity conservation and enhancement in Pb(Zr,Ti)O_3 and BaTiO_3 nanowires and nanotubes. Moreover, despite made assumptions and approximations our modelling appeared in a surprisingly good agreement with observed ferroelectric and local piezoresponse hysteresis loops.