Size Effects in Radiospectroscopy Spectra of Ferroelectric Nanopowders

The theoretical and experimental investigation of ferroelectric nanopowders is performed. The manifestation in radiospectroscopy spectra of size driven ferroelectric-paraelectric phase transition at some critical particle average size R = R$\text{}_{c}$ was the main goal of the consideration. In theoretical part the size effect for the materials with ferroelectric tetragonal phase at room temperature and cubic paraelectric phase was considered allowing for the spontaneous polarization inhomogeneity inside a particle and distribution of particle sizes. In ESR the transformation of the spectra from tetragonal symmetry to cubic symmetry lines with decrease in nanoparticle sizes was calculated. The method of R$\text{}_{c}$ value extraction from the ratio of the different symmetry lines intensities in the absorption spectra was proposed. Measurements of Fe$\text{}^{3+}$ ESR spectra in nanopowder of BaTiO$\text{}_{3}$ were carried out at room temperature. The samples were prepared by rate-controlled method with different particle sizes, which depend on annealing temperature. The decrease in intensity of tetragonal symmetry ESR lines of Fe$\text{}^{3+}$ and appearance of cubic symmetry line with asymmetry of the shoulders was observed with the average sizes decrease with complete disappearance of tetragonal spectrum at R ≤ 40 nm. The comparison of the theory with experiment was carried out. The theory fits experimental data pretty good. The value of critical size R$\text{}_{c}$ ≈ 40 nm was extracted from ESR data. The asymmetry and broadening of right hand side shoulder of ESR cubic symmetry line was shown to be related to contribution of paramagnetic centers in the vicinity of the particles surface with lower than cubic symmetry. The deconvolution of the cubic line allowed to show that this region size is about 3 nm.