Theory of size-driven transitions in displacive and order-disorder ferroelectrics

We present a simple theory for structural transitions in displacive ferroel ectrics of the perovskite (ABO(3)) type. As in earlier approaches, our mode l is based on the competition between the elastic energy cost for the displ acement of the B-ion from the centrosymmetric position, and the energy gain due to ferroelectric ordering of the dipoles. We use an effective single-s ite approximation which leads naturally to a first-order transition. This t ransition takes place at a certain temperature T-c(L) as the temperature is varied, and at a certain size L-c(T) as the size of the system is varied. The transition temperature T-c(L) is suppressed as the sample size is reduc ed, and vanishes for samples below a certain size. This is in accordance wi th recent observations on nanocrystalline perovskites. For systems with a c ontinuous bulk transition, which can also be treated within our theory, we show that size effects are highly suppressed, a result that is also borne o ut by experiments on order-disorder ferroelectrics with a continuous transi tion.