Influence of Adsorbate-Induced Charge Screening, Depolarization Factor, Mobile Carrier Concentration, and Defect-Induced Microstrain on the Size Effect of a BaTiO3Nanoparticle

Abstract

It has been experimentally reported that the crystal structure of a BaTiO3 single crystal becomes cubic when the crystal size is smaller than a critical one at room temperature, while the crystal structure of the macroscopic BaTiO3 single crystal is tetragonal. The critical size is, however, largely different for different experiments ranging from about 5 to 200 nm. In the present paper, numerical calculations of the free energy have been performed to study the mechanism of the large diversity in the critical size of a BaTiO3 single crystal. The results have indicated that the critical size becomes considerably smaller as the degree of adsorbate-induced charge screening increases because the depolarization energy is reduced. In addition, higher mobile-carrier concentration in a particle as well as smaller depolarization factor and smaller defect-induced microstrain considerably decrease the critical size. Furthermore, it is suggested that above about 30 nm in particle size the domain structure with 90° domain walls or the composite structure, which consists of an inner tetragonal core and a surface cubic layer, is more stable than a single domain below the critical degree of adsorbate-induced charge screening or below a critical mobile-carrier concentration in a particle.