Size effect on the crystal structure of barium titanate nanoparticles Available to Purchase

A size effect on crystal structure has been investigated for barium titanate $(BaTiO3)$ nanoparticles of 40-, 140-, and 430-nm sizes, by means of neutron and high-resolution synchrotron x-ray powder-diffraction and Raman-scattering techniques. These samples were prepared by a modified two-step thermal decomposition method from barium titanyl oxalate, resulting in very few lattice impurities. Rietveld analysis of the neutron-diffraction data for the 430-nm- and 140-nm-sized $BaTiO3$ particles was performed assuming a single phase of tetragonal $(P4mm)$ structure. The axial ratio $c∕a$ of tetragonal $BaTiO3$ decreases with a decrease in particle size from 430 to 140 nm. Barium titanate particles with a size of 40 nm consist of (1) tetragonal crystals (83 wt %) with a large cell volume and an axial ratio of unity $c∕a=1.000(5)$ and of (2) a hexagonal phase (⁠$P63mmc$⁠, 17 wt %) with a large unit-cell volume. Rietveld and maximum-entropy method analyses suggest that there exist atomic displacements from the ideal site of a cubic structure and a spontaneous polarization of the tetragonal phase even in the 40-nm-sized $BaTiO3$ particles. The nuclear-density distribution of the 140-nm-sized particles with a high dielectric constant does not exhibit a large positional disorder, while the Ba atom of tetragonal $BaTiO3$ in the 40-nm-sized particles has a smaller atomic displacement parameter.