Diffusion barriers, growth pathways, and scaling relations for small supported metal clusters

Sintering is one of the main causes of degradation of nanocatalysts. With a view to studying the process of sintering, and its relative likelihood across elements, we have used ab initio density functional theory to compute the pathways and energy barriers E_d for the diffusion of small clusters Pt_n on MgO(001), n = 1-4. We compare with the corresponding results for Au_n, Ag_n, and Pd_n. In general, diffusion barriers, but also sintering energies, are highest for Pt, resulting in opposing trends from kinetics and thermodynamics. We find smooth and positive correlations between E_d and E_b, E_b and E_coh, E_coh and T_m, and thus, between E_d and T_m, where E_b is the binding energy of the cluster on MgO, and E_coh and T_m are the cohesive energy and melting temperature, respectively, of the corresponding bulk metal. These trends are present for diffusion of the monomers, trimers, and tetramers, but not the dimers; this can be explained by the topography of the energy landscape separating the global minimum from the transition state. The temperature T₀ at which metal clusters on a given support become mobile is given by α + βT_m, where α and β are constants that depend on the support. We also present similar results for self-diffusion of monomers of the four metals on the (111) surfaces. Such scaling relations could be used to rapidly estimate diffusion barriers, and hence the growth and sintering behavior, of potential catalytic metal clusters.