Size effects in barium titanate particles and clusters

Clustering has an important effect on the tetragonal-cubic transformation of barium titanate (BaTiO3) particles. Small particles that would be cubic if they were by themselves can be tetragonal if they are in a cluster. The effects of clustering are shown in the behavior of the c/a ratio of the particles and the enthalpy change, Delta H, of transition as a function of particle size. The c/a ratio and the value of Delta H both decrease at a smaller particle size than those which are observed in samples where clustering is minimal. Our results are consistent with the observation that very small grains in polycrystalline samples can remain tetragonal even though the grain size is so small that it would be cubic if it were an individual particle. The transition temperature, T-C, on the other hand, is insensitive to the particle size, which is similar to the observation in polycrystalline BaTiO3 that T-C is insensitive to the grain size. The observed clustering effect is suggested to result from the reduction of depolarization energy of particles in clusters.