  In recent years, functional oxide-metal based vertically aligned
nanocomposite (VAN) thin films have gained interest due to their intriguing
physical properties and multifunctionalities stemming from the complex
interactions between the two phases in the film and the substrate. In this
work, we develop a model for studying the energetics of these thin film
systems, including the effects of both lattice mismatch and capillary forces
due to interface curvature. Each phase is incorporated into the model using a
phase indicator function, and we introduce the capillary forces as body forces
using a vector density representation of the interface. The model is
implemented using the finite element method to study the deformation of the
thin film which is composed of Au nanopillars embedded in a La0.7Sr0.3MnO3
(LSMO) matrix on an SrTiO3 (STO) substrate. The results suggest that the total
energy is lowest for random configurations of pillars compared to ordered
square and hexagonal lattice configurations, consistent with the random
distribution of pillars found in experiments. Furthermore, we find that the
interfacial energy dominates the total energy of each configuration, suggesting
that interfacial energy in the system is an important design parameter for
nanocomposite growth, along with the lattice mismatch.
