Finite size effects in ferroelectric nanocrystals: Myths & facts

A phenomenological intrinsic finite size effect model for a single domain, mechanically free, and surface charge compensated ABO3 (PbTiO3 or BaTiO3) nanocrystals undergoing a first order tetragonal¿cubic phase transition is propsoed. By using experimental particle size-dependent spontaneous polarization data for PbTiO3 and BaTiO3, free energy expansion coefficients coefficients up to the sixth order as a function of ¿ is computed in the range <150 nm. It will be shown that the thermodynamic potential is able to predict the size-induced phase transition as well as the metastable tetragonal phase in the cubic phase field rigorously. The free energy surface is then contructed, which describes the decrease in tetragonal phase stability with decreasing ¿ rigorously. The intrinsic dielectric and piezoelectric properties of single domain, mechanically free, and surface charge compensated PbTiO3 nanocrystals are then evaluated. It will be shown that a decrease in dielectric susceptibility at the transition temperature with decreasing particle size is commensurate with predictions of lattice dynamics considerations. It will also be shown that an anomalous increase in piezocharge coefficients near ~15 nm is predicted. Finite size effects will then be discusssed in terms of depolarization fields, surface effects, role of defects, among others and salient aspects of myths & facts in the published literature will be analyzed.