  In this paper we study the size effects of the ferroelectric nanotube phase
diagrams and polar properties allowing for effective surface tension 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, 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. Therefore we predict conservation and
enhancement of polarization in long ferroelectric nanotubes. Obtained results
explain the observed ferroelectricity conservation and enhancement in
Pb(Zr,Ti)O_3 and BaTiO_3 nanotubes.
