Complex oscillatory decrease with size in the diffusivity of epitaxially-supported 3D metal nanoclusters

Diffusion of 3D fcc metal nanoclusters
Diffusion of 3D fcc metal nanoclusters epitaxially supported on a {100} facet to a substrate with moderate adhesion. An example of this class of systems is Ag on MgO(001). Diffusion involves dissolution and re-formation of outer layers of facets.  Clusters with sizes corresponding to “closed shell” ground states are usually slow.

Catalytically active 3D metal nanoclusters weakly adhered to oxide or other supports play a central role in heterogeneous catalysis. It is well recognized that diffusion of such nanoclusters, and subsequent coalescence or sintering, is a possible pathway for catalyst degradation. Classic studies (Ruckenstein and Pulvermacher, Wynblatt and Gjostein) have related coarsening kinetics to the size-dependence of cluster diffusivity. However, these studies assume that the cluster diffusion coefficient, D_N, decreases monotonically with size N like D_N ~ N^{-beta}, where beta = 4/3 in a simple mean-field treatment.

We develop a stochastic atomistic level model for surface-diffusion mediated nanocluster diffusion. Significantly, rather than the standard generic description of diffusion rates in different local environments (which fails to capture behavior for fcc metal surfaces), we incorporate a realistic prescription as is needed for predictive modeling. Kinetic Monte Carlo simulation of this model reveals a complex oscillatory decrease of diffusivity with size. This behavior is elucidated by first identifying the diffusion pathway (dissolution of outer facet layers on one side of the NC, and their re-formation on another), and then providing an analytic determination of the variation of system energy along this pathway.

The same stochastic model can describe the sintering of pairs of nanoclusters. It has successfully predicted the time scale, t_s, of this process for conditions where t_s ~ 100 sec, a regime not accessible by MD simulation. See Lai et al. Chem. Rev. 2019, 119, 6670.

: King C. Lai and James W. Evans,  Complex oscillatory decrease with size in diffusivity of {100}-epitaxially supported 3D fcc metal nanoclusters, Nanoscale, 2019, 11, 17506-17516