  In the framework of the thermodynamic approach Landau-Ginzburg-Devonshire
(LGD) combined with the equations of electrostatics, we investigated the effect
of polarization surface screening on finite size effects of the phase diagrams,
polar and dielectric properties of ferroelectric nanoparticles of different
shapes. We obtained and analyzed the analytical results for the dependences of
the ferroelectric phase transition temperature, critical size, spontaneous
polarization and thermodynamic coercive field on the shape and size of
nanoparticles. The pronounced size effect of these characteristics on the
scaling parameter, the ratio of the particle characteristic size to the length
of the surface screening, was revealed. Also our modeling predicts a
significant impact of the flexo-chemical effect (that is a joint action of
flexoelectric effect and chemical pressure) on the temperature of phase
transition, polar and dielectric properties of nanoparticles when their
chemical composition deviates from the stoichiometric one. We showed on the
example of the stoichiometric nanosized and fine SrBi2Ta2O9 particles that
except the vicinity of the critical size, where the system splitting into
domains has an important role, results of analytical calculation of the
spontaneous polarization have little difference from the numerical ones. We
revealed a strong impact of the flexo-chemical effect on the phase transition
temperature, polar and dielectric properties of SryBi2+xTa2O9 nanoparticles
when the ratio Sr/Bi deviates from the stoichiometric value of 0.5 from 0.35 to
0.65. From the analysis of experimental data we derived the parameters of the
theory, namely coefficients of expansion of the LGD functional, contribution of
flexo-chemical effect and the length of the surface screening.
