Finite-size effects in ferroelectric solid solution

We studied the effect of grain size on the ferroelectric phase transitions in ceramics (x = 0.3, 0.5 and 0.7) prepared by a sol-gel method. The samples were observed and analysed by SEM, TEM and x-ray diffraction. The phase transitions were investigated by means of dielectric measurements. With the decrease of grain size, the Curie temperature decreases and the Curie peak becomes lower and broader and eventually disappears. The diffuseness of the dielectric response is understood on the basis of a diffuse phase transition model. The size dependence of can be described by , where is the for bulk , D is the grain size, and C and are two constants. This equation gives three ferroelectric critical sizes of 317 nm, 246 nm and 176 nm for x = 0.3, 0.5 and 0.7 respectively.