  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.
