A graph theoretical representation of multidomain nanoparticle morphologies

Multiphase nanoparticles are currently being synthesized and explored in massive high-throughput combinatorial libraries. The design of materials with targeted properties is complicated by the astronomical number of possible compositions, phases, and internal morphologies.

Here, we demonstrate a graph theoretical approach to predict and enumerate the internal nanoscale morphology of the phases formed in multiphase nanoparticles. The approach is based on the minimization of the surface and interfacial energies between all combinations of phases within the particle. DFT-calculated surface and interfacial energies have been used to predict NP morphologies. Our proposed graph theoretical approach recovers previously reported and predicted NP morphologies and provides the tools to ensure all possible internal NP morphologies are explored. The morphologies formed can be complex, thus a graph theoretical approach is proposed to predict all possible internal nanoparticle morphologies in an n-phase nanoparticle.

We use this approach to enumerate representations for n-phase nanoparticles between n=1 and n=10. We subsequently present constructed predicted interface morphologies and show how a subset of these morphologies corresponds to experimentally reported morphologies. Finally, we demonstrate how this approach enables the counting of all possible interface morphologies and informs bounds on morphology properties.