Synthesis and applications of metallic nanocrystals (NCs) has been a focus of the science and engineering communities for the last twenty years. This is due to the potential impact in a wide area in applications (e.g. plasmonics, catalysis, drug delivery) and the high flexibility in design of NC shape and structure. Advances in nanoscience rely on fundamental understanding of physical properties of nanoparticles and nanostructures. Our focus is on the post-synthesis dynamics or evolution of NCs which is mediated by diffusion of atoms around their periphery.

Long-range diffusion and coalescence of NCs synthesized by deposition on crystalline surfaces is observed experimentally. The process is referred as Smoluchowski Ripening (SR). Although a coarse-grained mean-field theory of the long-range diffusion provides a macroscopic understanding, features deriving from the discreteness of small size islands ($O(10)-O(10^2)$ atoms) are not captured. We performed kinetic Monte Carlo (kMC) simulations of a suitably crafted stochastic atomistic model for epitaxial 2D metal (M) NCs at various temperatures on a M$(100)$ substrate and discovered a complex oscillatory decrease with size in diffusivity. Behavior was explained by analysis of energetic and entropic factors (the latter involving combinatorial analysis of NC configurations). For diffusion of epitaxial 3D NCs of relevance to catalysts degradation, we developed an atomistic model incorporating the first realistic description of periphery (surface) diffusion kinetics. Similar oscillatory nature in diffusivity was observed in simulation of $\left\lbrace100\right\rbrace$-epitaxially supported 3D NCs, and explained identifying the diffusion pathway and characterizing its energetics.

The same atomistic model was applied to study: reshaping of individual NCs synthesized with non-equilibrium cubic, octahedral, etc. forms; sintering of pairs of NCs; and pinch-off of elongated nanorods. The time scale of sintering for two $\sim4$ nm gold nanocrystals observed in experiment is recovered in our simulation model.