Critical size and anomalous lattice expansion in nanocrystalline BaTiO3 particles

Nanocrystalline barium titanate particles are prepared by the alkoxide meth od. The lattice constants are obtained from the electron diffraction patter ns for various orientations of single particles in the size range of 15-250 nm in diameter. The present result indicates that the structural change fr om a tetragonal (ferroelectric) phase to a cubic (paraelectric) one occurs around 80 nm in diameter, which is in good agreement with a critical diamet er recently reported. Large lattice expansions of more than 2.5% are detect ed 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.