Size Driven Ferroelectric-Paraelectric Phase Transition from the Surface Energy Viewpoint

The size driven ferroelectric-paraelectric phase transition in a ferroelectric of small size is studied within the framework of Landau phase transition theory. The transition is a consequence of the competition between the decrease of the volume free energy by polarization and the increase of the surface energy of the ferroelectric phase, which has a surface energy density higher than that in the paraelectric phase. A simple expression for the ferroelectric critical size as a function of the Landau free energy coefficients and the surface energy density is derived.