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

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 paraelectricferroelectric 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.

Hyper-sensitive piezophotovoltaic effects in ferroelectric nanocylinders

“…In absence of an external electric field, the internal electric field comes from the depolarization field produced by polarization screening charges in the metal electrodes and the inhomogeneous polarization distribution near interfaces. Here the homogeneous polarization distribution is affected by complex factors, 1,8,[28][29][30][31][32][33][34][35] such as surface discontinuity of the ferroelectric layer, 8,27,31,32 and Schottky barriers at interface, etc. 10,14,27,29 Theories and experiments on FNCs taking various forms such as nanodisks ͑ND͒, nanorods ͑NR͒, nanowires ͑NW͒, and nanotubes ͑NT͒ have indicated that their phase-transition or near-phase-transition properties are very sensitive to the applied stress.…”

“…10,14,27,29 Theories and experiments on FNCs taking various forms such as nanodisks ͑ND͒, nanorods ͑NR͒, nanowires ͑NW͒, and nanotubes ͑NT͒ have indicated that their phase-transition or near-phase-transition properties are very sensitive to the applied stress. [33][34][35][36][37][38][39][40][41][42] In these investigations, stresses produced by surface tension and external mechanical loads have been found to significantly affect the Curie temperature, polarization, susceptibility and other related properties near the ferro/ paraelectric phase transition, resulting in remnant polarization and coercive fields that may exceed the bulk values. Indeed, under an uniaxial load of suitable magnitude and frequency, an appropriately dimensioned ferroelectric NW may produce a sizeable ac voltage, sufficient as a nanopower source for energy harvesting, or as an effective nanomechanical sensor.…”

“…8,[27][28][29][30][31][32]46,[57][58][59][60][61] The effects of the surface and interface on the profile of the depolarization field in the FNC and FTF have been discussed in previous works. 34,35,42,53 In general, the profile of the depolarization field is nonuniform near the interfaces, and can be opposite to those at the center of the FNC and FTF.…”

Theoretical study of ferroelectric nanoparticles using phase reconstructed electron microscopy

“…A lot of progress has been made toward understanding nanoscale effects on ferromagnetic properties, however the formalism for describing finite size and shape effects on ferroelectric properties is less developed. There are various reports in the literature describing complete suppression of ferroelectric behavior at nanoscale sizes as well as unusual phase transitions in nanodisks [3][4][5]. An in-depth understanding can be obtained by observing simultaneously the polarization, shape, and size of the nanostructures.…”

Additive-Assisted Aqueous Synthesis of BaTiO3 Nanopowders

“…These observations have stimulated an exponential growth on research aiming to understand the effect of scaling on the ferroelectric properties. Recently, some theoretical studies predicted an enhancement of ferroelectricity in anisotropic "cylindrical" shaped particles 7 and a new kind of ferroelectric order for ferroelectric nanoparticles with one-dimension (1D) structure as nanotubes, nanowires, nanorods, nanobelts, nanofibres. 8 Morphology control and fabrication of ferroelectric nanoparticles with different shapes are then important.…”