Phase field modeling of self-assembling nanostructures in constrained films

We present a thermodynamic analysis and phase field modeling of self-assembled multiphase nanostructures produced by phase transformations in constrained layers. Due to coherency between the phases, the elastic interactions between them and between each phase and the substrate layer play an important role in the formation of the nanostructures. It has been shown that a variety of morphologies of heterophase nanostructures can be obtained depending on the crystallographic characteristics of transformations, elastic properties of the phases, relative fractions of the phases, and the thickness of the film. The results obtained by phase-field modeling agree well with predictions of an analytical thermodynamic model. The final equilibrium structures are determined by thermodynamic parameters and do not depend on the transformation path and, therefore, the phase-field approach developed in this paper can be expanded to finding equilibrium multiphase coherent nanostructures created as a result of solid–solid or solid–liquid transformations as well as during co-deposition on a substrate.