Self-assembly of ensembles of supported 2D or 3D nanoclusters (NCs) by surface deposition, and of unsupported 3D NCs by solution-phase synthesis, produces intrinsically nonequilibrium systems. Individual nanoclusters can have far-from-equilibrium shapes and composition profiles. The free energy of the ensemble can be lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening is key for, e.g., avoiding catalyst degradation. In this review, we focus on crystalline metallic NCs. Atomistic-level modeling of equilibration processes typically utilizes stochastic lattice-gas models to access appropriate time-and length-scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution. We also discuss modeling of coarsening including diffusion and decay of individual NCs, and unconventional coarsening processes. We describe high-level modeling integrated with STM studies for 2D epitaxial NCs, and developments in modeling for supported and unsupported 3D NCs motivated by in situ TEM studies.

Using scanning tunneling microscopy, we characterize the size and bias-dependent shape of sulfur atoms on Cu(100) at low coverage (below 0.1 monolayers) and low temperature (quenched from 300 to 5 K). Sulfur atoms populate the Cu(100) terraces more heavily than steps at low coverage, but as coverage approaches 0.1 monolayers, close-packed step edges become fully populated, with sulfur atoms occupying sites on top of the step. Density functional theory (DFT) corroborates the preferential population of terraces at low coverage as well as the step adsorption site. In experiment, small regions with p(2 × 2)-like atomic arrangements emerge on the terraces as sulfur coverage approaches 0.1 monolayer. Using DFT, a lattice gas model has been developed, and Monte Carlo simulations based on this model have been compared with the observed terrace configurations. A model containing eight pairwise interaction energies, all repulsive, gives qualitative agreement. Experiment shows that atomic adsorbed sulfur is the only species on Cu(100) up to a coverage of 0.09 monolayers. There are no Cu-S complexes. In contrast, prior work has shown that a CuS complex forms on Cu(111) under comparable conditions. On the basis of DFT, this difference can be attributed mainly to stronger adsorption of sulfur on Cu(100) as compared with Cu(111).

Sulfur atoms on Ag(100) exhibit bias voltage dependence.