Critical size and anomalous lattice expansion in nanocrystalline particles

Nanocrystalline barium titanate particles are prepared by the alkoxide method. The lattice constants are obtained from the electron diffraction patterns for various orientations of single particles in the size range of 15-250 nm in diameter. The present result indicates that the structural change from a tetragonal (ferroelectric) phase to a cubic (paraelectric) one occurs around 80 nm in diameter, which is in good agreement with a critical diameter recently reported. Large lattice expansions of more than 2.5% are detected in the particles down to 15 nm in diameter. The origin of the expansion is discussed on the basis of x-ray photoelectron spectroscopic analyses and a computer simulation.