The description of size effects in films of order-disorder ferroelectrics on the basis of the renormalized free energy

Abstract

Films of order–disorder-type ferroelectrics were considered in the mean-field approximation of the Ising model taking into account the depolarization field and four-dipole interactions. It was shown that this system could be described on the basis of the renormalized bulk system free energy with two-dipole interaction constant dependent on the film thickness, surface and depolarization field characteristics. This led to the size-driven phase transition between paraelectric and ferroelectric phases with transition temperature dependent on the film thickness. For small values of the four-dipole interaction constant, the size-driven crossover from the first-order phase transition to the second-order one with film-thickness change was forecasted. An analytical expression for the tricritical point temperature and thickness was obtained. The increase of the four-dipole interaction constant led to the first-order phase-transition existence independently of the film thickness, with the temperature region of the phases' coexistence widening with thickness decrease. The phase diagram in coordinates temperature–film thickness and the order parameter were calculated with the help of the derived free energy. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)