Finite size effects in submicron barium titanate particles

An experimental and theoretical analysis of finite size effects in submicron barium titanate particles is presented. The dielectric data show that the dielectric constant (∊ = 734) of small particles (d = 20 nm) remains very similar to that of single crystals provided that the particles are grown from an amorphous phase and not mechanically crushed into powder. This shows that what has in the past been mistaken for true size effects (i.e., depolarization fields) is due to lattice strain. The X-ray data show that the Curie temperature (cubic-tetragonal transition temperature) decreases monotonically to zero degree Kelvin as particle size is reduced. However this is shown to be a simple function of lattice constant: The lattice constant expands as the particle diameter d contracts. This is similar to surface relaxation in thin films.