We report a size effect on the ferroelectric phase transition in ${\mathrm{PbTiO}}_3$ ultrafine particles. The samples were synthesized by an alkoxide method. The size was determined by x-ray analysis with the aid of Scherrer’s equation. When the particle size is less than 50 nm, the transition temperature $T_c$, determined by Raman scattering, decreases from its bulk value (500 °C) as the size decreases. The temperature $T_c$ is described by an empirical expression, $T_c$=500-588.5/(D-12.6) (°C), where D is the average particle size (nm).

• Received 27 July 1987

DOI:https://doi.org/10.1103/PhysRevB.37.5852