Finite-size effects in ferroelectric solid solution BaxSr1-xTiO3

We studied the effect of grain size on the ferroelectric phase transitions in BaxSr1-xTiO3 ceramics (x = 0.3, 0.5 and 0.7) prepared by a sol-gel metho d. The samples were observed and analysed by SEM, TEM and x-ray diffraction . The phase transitions were investigated by means of dielectric measuremen ts. With the decrease of grain size, the Curie temperature decreases and th e Curie peak becomes lower and broader and eventually disappears. The diffu seness of the dielectric response is understood on the basis of a diffuse p hase transition model. The size dependence of T-c can be described by T-c(D ) = T-c(infinity) - C/(D - D-s), where T-c(infinity) is the T-c for bulk Ba xSr1-xTiO3, D is the grain size, and C and D, are two constants. This equat ion gives three ferroelectric critical sizes of 317 nm, 246 nm and 176 nm f or x = 0.3, 0.5 and 0.7 respectively.