Size effects and depolarization field influence on the phase diagrams of cylindrical ferroelectric nanoparticles

TL;DR

This paper investigates how size, surface tension, and depolarization fields affect the phase diagrams of cylindrical ferroelectric nanoparticles, revealing conditions for enhanced ferroelectricity in nanorods and nanowires.

Contribution

It provides an analytical model for phase transition temperatures considering surface and depolarization effects in cylindrical nanoparticles, highlighting shape-dependent size effects.

Findings

Transition temperature can be higher than bulk in nanorods and nanowires.

Critical sizes for phase transition are calculated, with nanobars having minimal critical volume.

Enhanced ferroelectric properties are predicted in nanorods and nanowires.

Abstract

Ferroelectric nanoparticles of different shape and their nanocomposites are actively studied in modern physics. Because of their applications in many fields of nanotechnology, the size effects and the possible disappearance of ferroelectricity at a critical particle volume attract a growing scientific interest. In this paper we study the size effects of the cylindrical nanoparticle phase diagrams allowing for effective surface tension and depolarization field influence. The Euler-Lagrange equations were solved by direct variational method. The approximate analytical expression for the paraelectric-ferroelectric transition temperature dependence on nanoparticle sizes, polarization gradient coefficient, extrapolation length, effective 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 nanorods and nanowires in contrast to nanodisks, where the decrease takes place. The critical sizes and volume of ferroelectric-paraelectric phase transition are calculated. We proved that among all cylindrical shapes a nanobar reveals the minimal critical volume. We predicted the enhancement of ferroelectric properties in nanorods and nanowires. Obtained results explain the observed ferroelectricity enhancement in nanorods and could be very useful for elaboration of modern nanocomposites with perfect polar properties.