Size-dependent piezoelectric coefficient and Curie temperature of nanoparticles

The size-dependent piezoelectric coefficient and Curie temperature of small ferroelectrics are modeled in this paper. It is found that taking account of the size effect is essential in understanding the piezoelectric characteristics of nanoferroelectrics. The model prediction is in good agreement with the experimental results for lead (II) titanate (PbTiO₃) and barium titanate (BaTiO₃) nanoparticles, where the piezoelectric coefficient, d ₃₃(D), increases correspondingly as the particle diameter, D, decreases. In addition, the size effect of the dielectric susceptibility coefficient, η ₃₃(D), is also predicted since η ₃₃(D) ∝ d ₃₃(D) is considered. The estimations of the authors’ model for the η ₃₃(D) function are consistent with other theoretical evidence. Thus, the piezoelectric coefficient, d ₃₃(D), and dielectric susceptibility coefficient, η ₃₃(D), can be predicted well based on the size of the particle. Variations in size will directly affect the piezoelectricity of the materials, and the relevant piezoelectric coefficient reveals strong size-dependency and plays a significant role in the application of nanoferroelectrics.