The equivalence of thermodynamic potentials for ferroelectric thin films

A ferroelectric thin film epitaxially deposited on a substrate is usually subjected to the mixed mechanical boundary conditions that can neither be treated as purely fixed-strain boundaries nor purely fixed-stress ones, thus causing the inconsistency or inaccuracy for choice of the Helmholtz or Gibbs thermodynamic potential. It would be of interest to clarify this inconsistency and set up some rules for such a choice. In this work, we discuss various roadmaps to construct two types of modified thermodynamic potentials under the epitaxial thin film boundary conditions. The equivalence of these thermodynamic potentials is then established. Subsequently, a set of misfit strain–strain phase diagrams by choosing K0.5Na0.5NbO3 thin films as an example of realistic calculations are constructed to check this equivalence. Finally, some scenarios on choosing various thermodynamic potentials for ferroelectric thin films are discussed.