Intrinsic size effects in a barium titanate glass-ceramic

A series of glass ceramics have been synthesized to produce bulk materials with nanometer-sized barium titanate (Ba-TiO₃) crystals grown in a residue glass matrix. Structure-property relations have been made to determine the size distribution and the dielectric temperature dependence of the ceramics. Through dielectric and density mixing laws, it has been inferred that depolarization fields limit the dielec" tric polarizability of the particles and influence the transi" tion temperature. The transition temperature, dielectric anomaly broadening, and peak dielectric constant all scale systematically with the mean size of the BaTiO₃ crystals, which is consistent with an intrinsic size effect. In addition, scaling the transition temperature with the Ishikawa rela" tion predicts a critical size of 17 nm, for which BaTiO₃ cannot support a ferroelectric transition. These results are discussed in relation to other size studies on ferroelectric materials.