Toward Controlling the Morphology in Nanocrystal Growth—Thermodynamic vs. Kinetic Shapes

Metal nanocrystals have the capability to revolutionize established technologies, such as catalysis, plasmonic, and electronic devices, sensing, and photovoltaics. Additionally, metal nanocrystals will figure prominently in upcoming technologies, such as photothermal desalination,triboelectric nanogenerators,electromagnetic interference shielding, and "smart" technologies, such as electrochromic and photochromic devices, fabrics and wearable devices, and e-skin. For most established applications, there is ample evidence that the efficacy of a nanocrystal is sensitive to its shape and fine details of its structure. Thus, there is significant impetus to be able to predict and characterize fine details of nanocrystal structure. Crystal growth begins with the nucleation of metal atoms from a (partially) reduced metal salt. It is often stated that the nuclei grow to seeds that determine the final nanocrystal shape, which presents a compelling case for understanding how seeds acquire their shape. How seeds grow to final, kinetic shapes is an enigma and the subject of this study.<br/><br/>We use parallel tempering molecular dynamics (MD) simulations, accelerated MD, and machine learning (ML) to quantify equilibrium and kinetic shapes of Ag and Cu nanocrystals as they grow and transition from equilibrium to kinetic shapes. 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. We find that small (sub-nanometer to single nanometer) nanocrystals assume an equilibrium distribution of shapes for experimental temperatures and deposition rates. As the nanocrystals grow beyond this size range, the rate to transform between shapes decreases and becomes slower than the rate at which species add to the nanocrystals and growth becomes a kinetic phenomenon. We probe the growth of nanocrystals that evolve via both monomer addition and aggregation with other nanocrystals and find interesting differences between the two growth modes.<br/><br/>The shapes of fcc metal nanoparticles are typically quantified in terms of perfect morphologies: octahedron, icosahedron (Ih), decahedron (Dh), etc., but such shapes only arise for certain “magic numbers” of atoms that give the crystal a perfect shape. Here, we analyze and quantify the generated nanoparticle morphologies using ML. We find a hierarchy of shape classes for these nanocrystals: two broad classes (amorphous and crystalline), five broad sub-classes, and 14-15 different fine-structured sub-sub-classes. Overall, these studies provide a promising framework for understanding how nanocrystals grow and how shapes might be classified for applications.