Grain-size effects on the ferroelectric behavior of dense nanocrystallineBaTiO3ceramics

A progressive reduction of tetragonal distortion, heat of transition, Curie temperature, and relative dielectric constant has been observed on dense ${\mathrm{BaTiO}}_{3}$ ceramics with grain size decreasing from 1200 to $50\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The correlations between grain size, extent of tetragonal distortion, and ferroelectric properties strongly support the existence of an intrinsic size effect. From the experimental trends the critical size for disappearance of ferroelectricity has been evaluated to be $10--30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. The strong depression of the relative permittivity observed for the nanocrystalline ceramics can be ascribed to the combination of the intrinsic size effect and of the size-dependent ``dilution'' effect of a grain boundary ``dead'' layer.