The theory of size effects in nanocrystalline ferroelectric ceramics or nanoparticle powders allowing for surface tension and depolarization field is proposed. Surface tension was included in the free energy functional and extrapolation length was expressed via surface tension coefficient. The latter was shown to be dependent on temperature due to its relation to the dielectric permittivity of the nanoparticles. The depolarization field effect was calculated in the model taking into account the space-charge layer on the surface.The Euler-Lagrange equation for inhomogeneous polarization was solved analytically in both paraelectric and ferroelectric phases. The temperature and size dependence of the spontaneous polarization and dielectric susceptibility of nanomaterials was obtained. The possibility to calculate these and other properties by minimization of the conventional free energy in the form of different power polarization series, but with coefficients that depend on particle size, temperature, contribution of depolarization field and surface tension coefficient, was demonstrated. A comparison with available experimental data is performed.

The theory of the radiospectroscopy (nuclear magnetic resonance [NMR] and electron spin resonance [ESR]) line shape for nanomate¡ is developed. The consideration was performed in the core and shell models which are, respectively, the nanoparticle regions unperturbed and perturbed by the surface influence. The shift of the resonance frequency by the surface tension was taken into account. The homogeneously broadened line shape was supposed to be Gaussian or Lorentzian. Inhomogeneous broadening of lines via the distribution of nanoparticle sizes was calculated for several forms of the size distribution function. The splitting of radiospectroscopy spectra into two lines decreases with particle sizes, which looks like that in the bulk and on the surface. Ir was shown to be the characteristic feamre of nanomaterial spectra. The changing of these lines' intensity and width with the change of the distribution function parameters and the particle size decrease was considered. The comparison of the theory with NMR spectra of ~70 and 25Mg observed recently in nanocrystalline MgO is performed. The calculations fit pretty good the observed size dependence of the line shape, intensity and width.

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