Crystal Structure and the Paraelectric-to-Ferroelectric Phase Transition of Nanoscale BaTiO₃

Abstract

We have investigated the paraelectric-to-ferroelectric phase transition of various sizes of nanocrystalline barium titanate (BaTiO3) by using temperature-dependent Raman spectroscopy and powder X-ray diffraction (XRD). Synchrotron X-ray scattering has been used to elucidate the room temperature structures of particles of different sizes by using both Rietveld refinement and pair distribution function (PDF) analysis. We observe the ferroelectric tetragonal phase even for the smallest particles at 26 nm. By using temperature-dependent Raman spectroscopy and XRD, we find that the phase transition is diffuse in temperature for the smaller particles, in contrast to the sharp transition that is found for the bulk sample. However, the actual transition temperature is almost unchanged. Rietveld and PDF analyses suggest increased distortions with decreasing particle size, albeit in conjunction with a tendency to a cubic average structure. These results suggest that although structural distortions are robust to changes in particle size, what is affected is the coherency of the distortions, which is decreased in the smaller particles.