Ferroelectric phase transition in barium titanate nanoparticles

Size-dependent changes were found in the Ba-137 NMR spectra of ensembles of very small BaTiO3 particles. The NMR line shapes were studied at different Larmor frequencies over a broad temperature range. In the tetragonal phase, the NMR lines may be decomposed into a contribution typical for the line shape of bulk samples ("ordered" part) and a part in which the tetragonal symmetry is no longer visible ("disordered" part). Both contributions reveal typical changes when the temperature is varied in the range of the tetragonal phase, i.e., between approximately 400 and 300 K. The "ordered" part reveals a first-order phase transition at temperature T-f which decreases when the particle size becomes smaller. As is known, in the case of bulk material the quadrupole coupling constant C-Q may be related to the order parameter (spontaneous polarization P-S). Therefore, for all samples the temperature dependence of the C-Q in the "ordered" part was studied in the whole tetragonal phase. Its temperature dependence below T-f, with a jump at the first-order phase transition, can be described by an exponential law C-Q proportional to(T-f-T)(beta)+const for T < T-f, in analogy to the Landau theory, but the parameter beta is less than 1/2. The "disordered" part shows no jump at T-f where its quadrupole coupling constant is approximately zero. The data are used to discuss a structural model for the fine particles.