Phase transition in PbTiO3ultrafine particles of different sizes

Abstract

The size effect on the ferroelectric phase transition in PbTiO₃ ultra-fine particles is reported. Samples with particle sizes from 20 to 200 nm were prepared by a sol-gel process followed by calcining at different temperatures. The particle size was determined by X-ray diffraction from the integrated width of diffractions. The soft-mode frequency at room temperature was measured by Raman scattering. It decreases with decreasing particle size. The ferroelectric phase transition was traced by specific-heat measurement. The transition temperature decreases and the transition becomes diffused as the particle size decreases. The size dependence of T_C can be described by T_C(D)=766-256/(D-8.8) (K), where 766 K is the T_C for bulk PbTiO₃ and D (nm) is the particle size. This equation gives a critical size of 9.1 nm below which ferroelectricity disappears.