Guided Assembly of Nanostructures via Elastic Interactions

A solid solution can spontaneously separate into phases that self-assemble into patterns. This process can be guided via external fields to form ordered micro- and nanostructures. In this paper, we demonstrate that notions of interaction energies provide powerful insights into the coupling of these fields with the properties of the alloy. A phase-field model is developed that incorporates chemical, interfacial, and elastic energies, including heterogeneous elastic properties, and couples naturally to externally imposed mechanical fields. Aggregation in bulk and in thin films under patterned external load is investigated. The kinetics and morphology of phase separation are shown to depend significantly on elastic properties of the system, which include elastic heterogeneity and the misfit or transformation strain. Eshelby-type asymptotic estimates for interaction energies are shown to be very useful in understanding and predicting the trends observed from the simulations.