  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.
