Effect of Mechanical Boundary Conditions on Phase Diagrams of Epitaxial Ferroelectric Thin Films

A phenomenological thermodynamic theory of ferroelectric thin films epitaxially grown on cubic substrates is developed using a new form of the thermodynamic potential, which corresponds to the actual mechanical boundary conditions of the problem. For single-domain ${\mathrm{BaTiO}}_3$ and ${\mathrm{PbTiO}}_3$ films, the “misfit-temperature” phase diagrams are constructed. It is found that the 2D clamping of the films, apart from a shift of the temperature of the ferroelectric transition, results in a change of its order. A change of the sequence of the phases and the appearance of phases forbidden in the bulk crystals are predicted.