We use parallel tempering molecular dynamics (MD) simulations, accelerated MD, and machine learning (ML) to quantify equilibrium shapes of Ag, Cu, Ag-Cu, Pt, Pd and Pt-Pd nanocrystals. In our approach, we describe the nanoparticles with Machine Learning Force Fields (MLFF) with high fidelity to first-principles density functional theory. We find equilibrium nanocrystal shapes can change significantly with temperature, indicating that the nanocrystal shape with the minimum potential energy (at zero K) is not necessarily the shape seen at a higher temperature in an experiment. Moreover, the preferred nanocrystal shapes at low temperatures change drastically with size. These qualitative features have significant ramifications for experiments: It can be vastly more important to understand the free energies of nanocrystals than potential energies.
The shapes of fcc metal nanoparticles are typically quantified in terms of perfect morphologies: octahedron, icosahedron, decahedron, etc., but such shapes only arise for certain “magic numbers” of atoms that give the crystal a perfect shape. Here, we analyze and quantify both ideal and non-ideal nanoparticle morphologies using ML. We classify distinct shape classes with seemingly little order to the eye and these can have the minimum energy. Our work uncovers catalytically significant morphologies for bimetallics, which include single-atom alloys, core@shell, and patchy particles. Our approach has much promise for understanding and categorizing nanocrystal shapes and designing synthesis and processing routes for achieving these shapes.