  The theory of size effects of the properties of nanocrystalline ferroelectric
ceramic or nanoparticle powder allowing for surface tension and depolarization
field is proposed. Surface tension was included into free energy functional and
surface energy was expressed via surface tension coefficient. The latter was
shown to be dependent on temperature due to its relation to dielectric
permittivity of the nanoparticles. The depolarization field effect was
calculated in the model taking into account the space charge layer on the
surface, this space-charge being able to compensate depolarization field in the
bulk material. Euler-Lagrange Equation for inhomogeneous polarization of
nanomaterial with boundary condition where extrapolation length was shown to be
temperature dependent quantity was solved analytically both in paraelectric and
ferroelectric phase of size driven phase transition. This phase transition
critical temperature dependence on the particle size was calculated.
Temperature and size dependence of nanomaterials polarization and dielectric
susceptibility was obtained. The possibility to calculate these and other
properties by minimization of conventional free energy in the form of different
power polarization series, but with the coefficients which depend on particles
size, temperature, contribution of depolarization field and surface tension
coefficient was demonstrated. These latter effects were shown to influence
essentially the nanomaterial properties. The comparison with available
experimental data is performed.
