Self-diffusion of small Ni clusters on the Ni(111) surface: A self-learning kinetic Monte Carlo study

Abstract

We have examined the self-diffusion of small 2D Ni islands (consisting of up to 10 atoms) on the Ni(111) surface using a self-learning kinetic Monte Carlo (SLKMC-II) method with an improved pattern-recognition scheme that allows inclusion of both fcc and hcp sites in the simulations. Activation energy barriers for the identified diffusion processes were calculated on the fly using a semiempirical interaction potential based on the embedded-atom method. Although a variety of concerted, multiatom, and single-atom processes were automatically revealed in our simulations, we found that, in the temperature range of 300 K-700 K, these small islands diffuse primarily via concerted motion. Single-atom processes play an important role in ensuring that diffusion is random for islands containing 5 or more atoms, while multiatom processes (shearing and reptation) come into play for noncompact islands. The effective activation energy barriers obtained from the Arrhenius plot of the diffusion coefficients showed an increase with the size of the island, although there were interesting deviations from linear dependence. Several other processes also contributing to diffusion of islands were identified.

Atomic mechanisms and diffusion anisotropy of Cu tetramers on Cu(111)

“…For the short-diagonal jumps, we obtain a prefactor of 2.0(×2.0 ±1 ) × 10 12 Hz. This value also coincides within the error bars with those deduced from the analysis of the mean-square displacements of similar clusters in kinetic Monte Carlo simulations: 1.57 × 10 12 Hz for Ni tetramers diffusing on Ni(111) [42] and 1.07 × 10 12 Hz for Cu tetramers on Cu(111) [40]. Such a coincidence is not surprising because most of the distance covered by the tetramers, at least below 500 K, is due precisely to the short-diagonal glide jumps: the different types of rotations produce a much shorter motion of the cluster's center of mass, and the long-diagonal jumps are scarce.…”

“…It is remarkable that from the three possible bridge crossings existing at each adsorption site, the one situated along the tetramer's long diagonal is systematically avoided in these displacements. This latter jump, which has also shown up in various other studies of jump energetics [17,40,42,45,53], only appears at the highest temperatures explored in our study. In fact, it is the least abundant event in our simulations and, most significantly, it does not involve any dislocation or shearing of the tetramer, but rather takes place as a concerted motion of the cluster as a whole.…”

“…The whole process takes in general more than 1 ps in our simulations (about 3 ps in this particular example), thus supporting our choice of 0.8 ps for the threshold to discriminate stable jumps. This mechanism was first proposed by Wang and Ehrlich based on their groundbreaking FIM experiments on Ir 4 /Ir(111) [24], who even succeeded in imaging one tetramer frozen at the transition stage, and confirmed later by numerous reports [17,33,40,42,45,53,65,66]. It is remarkable that from the three possible bridge crossings existing at each adsorption site, the one situated along the tetramer's long diagonal is systematically avoided in these displacements.…”

“…It seems well established now that there exist two regimes for the diffusion of 2D islands as a function of their size: while the large ones move by displacements of atoms around their periphery with a roughly constant effective activation energy [31,37,38], for small islands this energy typically shows an increasing trend with island size [5,32,39,40] that reflects the growing difficulty in achieving the concerted motion of all the atoms in the cluster. Some oscillations that are related to the existence of magic island sizes of particular stability [3,5,17,[41][42][43][44] are frequently observed superimposed on this general increasing trend; for instance, compact tetramers are usually more mobile on fcc-(111) surfaces than trimers [17,22,24,42,45]. The crossover between those two regimes appears when the limiting process for edge diffusion, namely the detachment of an adatom from a kink or corner site, becomes energetically favorable with respect to the energy required to move the island by any of the collective mechanisms [38].…”

“…Diffusion anisotropy has a strong influence in nucleation, growth, and the formation and morphology of nanostructures [3,34,49]. The tetramer is still a reasonably simple object yet complex enough to have already shown a variety of diffusion mechanisms in previous studies [17,33,40,42,45,[50][51][52][53]. Furthermore, the tetramer is also one of the magic sizes that show an anomalously low activation energy, being one atom larger than the more morphologically stable trimer [22,54].…”