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 decreasing the volume free energy by polarization and increasing 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.