The nature of ferroelectric order in finite systems

The ferroelectric phase transition in the technologically important perovskite-type (ABO(3)) systems is strongly affected by a reduction in the particle size below approximate to 100 nm. With decreasing size, there is a monotonic reduction in the T-C, and in the off-center displacement of the B-ion. Thus there is a size-induced structural distortion that reverts the crystal to ifs high-symmetry paraelectric phase (which is normally stable only above T-C) even at room temperature. We briefly review our data on nanocrystalline ferroelectric PbTiO3 and antiferroelectric PbZrO3, and present a simple microscopic model for structural transitions in displacive ferroelectrics. We show that a competition between the elastic energy spent in displacing the central (B) ion and energy gain due to dipolar ordering, leads naturally to a first order transition front the paraelectric to the ferroelectric phase. The transition may occur either with decreasing temperature (for a fixed size) or with decreasing size (at a fixed temperature): The model is in good agreement with our data on nanocrystalline PbTiO3. (C)1999 Acta Metallurgica Inc.