Sintering of two-dimensional nanoclusters in metal(100) homoepitaxial systems: Deviations from predictions of Mullins continuum theory

Abstract

We present a comparison of the predictions of atomistic and continuum models for the sintering of pairs of near-square two-dimensional nanoclusters adsorbed on the (100) surface in fcc metal homoepitaxial systems. Mass transport underlying these processes is dominated by periphery diffusion (PD) of adatoms along the edge of the clusters. A Mullins-type continuum model for cluster evolution incorporates anisotropy in the step edge stiffness (reflecting the energetics and adsorption site lattice structure in the atomistic model), and can also account for anisotropy in the step edge mobility (reflecting details of the kinetics). In such continuum treatments, the characteristic time τeqfor relaxation of clusters with linear size of order L satisfies τeq∼L4. Deviations may generally be expected for small sizes L or low temperatures T. However, for the relaxation of dumbbell-shaped clusters (formed by corner-to-corner coalescence of square clusters), atomistic simulations for PD with no kink rounding barrier (δ=0) reveal that τeq∼L4 always applies. In contrast, atomistic simulations with a large kink rounding barrier (δ>0) reveal distinct scaling with τeq∼L3, for low T or small L, thus providing an effective way to test for δ>0. For the relaxation of faceted rectangular clusters (formed by side-toside coalescence of square clusters), atomistic simulations for PD with δ=0 reveal that τeq∼L2, for low T or small L. This is consistent with a recent proposal by Combe and Larralde. For large δ>0, τeq has an even weaker dependence on L. We elucidate scaling behavior and the effective activation barrier for relaxation in terms of the individual atomistic PD processes and their barriers. We present a comparison of the predictions of atomistic and continuum models for the sintering of pairs of near-square two-dimensional nanoclusters adsorbed on the ͑100͒ surface in fcc metal homoepitaxial systems. Mass transport underlying these processes is dominated by periphery diffusion ͑PD͒ of adatoms along the edge of the clusters. A Mullins-type continuum model for cluster evolution incorporates anisotropy in the step edge stiffness ͑reflecting the energetics and adsorption site lattice structure in the atomistic model͒, and can also account for anisotropy in the step edge mobility ͑reflecting details of the kinetics͒. In such continuum treatments, the characteristic time eq for relaxation of clusters with linear size of order L satisfies eq ϳL 4 . Deviations may generally be expected for small sizes L or low temperatures T. However, for the relaxation of dumbbell-shaped clusters ͑formed by corner-to-corner coalescence of square clusters͒, atomistic simulations for PD with no kink rounding barrier ͑␦ϭ0͒ reveal that eq ϳL 4 always applies. In contrast, atomistic simulations with a large kink rounding barrier ͑␦Ͼ0͒ reveal distinct scaling with eq ϳL 3 , for low T or small L, thus providing an effective way to test for ␦Ͼ0. For the relaxation of faceted rectangular clusters ͑formed by side-to-side coalescence of square clusters͒, a...

Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling

“…The IVA choice has been used to effectively and elucidate fundamental NC diffusion, reshaping, and sintering processes on (100) surfaces. [153][154][155][156] See Figure 12 and also Sec.5.2, 5.4 and 8.1.…”

“…The lower right frame shows significant variations between different simulation trials particularly in the later stages of evolution. For a more fundamental understanding and analysis of reshaping of convex NCs, it is instructive to utilize the simpler tailored model 153 of Sec.3.3.2 where atoms of a square lattice of adsorption site interact with NN interactions . 153 Periphery diffusion includes NN hops with barrier Ee and rate he for isolated edge atoms on close-packed step edges, and 2NN hops to describe corner or kink rounding of isolated edge atoms with generally higher barrier of Ee + .…”

“…For a more fundamental understanding and analysis of reshaping of convex NCs, it is instructive to utilize the simpler tailored model 153 of Sec.3.3.2 where atoms of a square lattice of adsorption site interact with NN interactions . 153 Periphery diffusion includes NN hops with barrier Ee and rate he for isolated edge atoms on close-packed step edges, and 2NN hops to describe corner or kink rounding of isolated edge atoms with generally higher barrier of Ee + . Barriers for other processes such as escape from kinks to step edges are controlled by detailed-balance as described in Sec.3.3.2.…”

Boundary Conditions for Burton–Cabrera–Frank Type Step-Flow Models: Coarse-Graining of Discrete 2D Deposition-Diffusion Equations

“…More generally, it is known that traditional continuum near-equilibrium treatments may fail when the relevant characteristic length in the system becomes comparable to natural length scales determined by the microscopic parameters of the model. For example, for diffusion and shape-relaxation of 2D islands on surfaces mediated by edge diffusion, this failure occurs when the linear size of the island becomes comparable to the equilibrium kink separation or to another characteristic length associated with inhibited edge diffusion [35,36].…”

Dewetting of a Solid Monolayer

“…The subsequent dynamics combines processes which have been separately studied in the literature: layer-by-layer thickening of the islands [17], coupled to their sintering [18] and Ostwald ripening. We hope to report along these lines in the future.…”