Off-lattice self-learning kinetic Monte Carlo: application to 2D cluster diffusion on the fcc(111) surface.

We report developments of the kinetic Monte Carlo (KMC) method with improved accuracy and increased versatility for the description of atomic diffusivity on metal surfaces. The on-lattice constraint built into our recently proposed self-learning KMC (SLKMC) (Trushin et al 2005 Phys. Rev. B 72 115401) is released, leaving atoms free to occupy 'off-lattice' positions to accommodate several processes responsible for small-cluster diffusion, periphery atom motion and heteroepitaxial growth. This technique combines the ideas embedded in the SLKMC method with a new pattern-recognition scheme fitted to an off-lattice model in which relative atomic positions are used to characterize and store configurations. Application of a combination of the 'drag' and the repulsive bias potential (RBP) methods for saddle point searches allows the treatment of concerted cluster, and multiple- and single-atom, motions on an equal footing. This tandem approach has helped reveal several new atomic mechanisms which contribute to cluster migration. We present applications of this off-lattice SLKMC to the diffusion of 2D islands of Cu (containing 2-30 atoms) on Cu and Ag(111), using the interatomic potential from the embedded-atom method. For the hetero-system Cu/Ag(111), this technique has uncovered mechanisms involving concerted motions such as shear, breathing and commensurate-incommensurate occupancies. Although the technique introduces complexities in storage and retrieval, it does not introduce noticeable extra computational cost.

Parallel kinetic Monte Carlo simulations of Ag(111) island coarsening using a large database.

The results of parallel kinetic Monte Carlo (KMC) simulations of the room-temperature coarsening of Ag(111) islands carried out using a very large database obtained via self-learning KMC simulations are presented. Our results indicate that, while cluster diffusion and coalescence play an important role for small clusters and at very early times, at late time the coarsening proceeds via Ostwald ripening, i.e. large clusters grow while small clusters evaporate. In addition, an asymptotic analysis of our results for the average island size S(t) as a function of time t leads to a coarsening exponent n = 1/3 (where S(t)∼t(2n)), in good agreement with theoretical predictions. However, by comparing with simulations without concerted (multi-atom) moves, we also find that the inclusion of such moves significantly increases the average island size. Somewhat surprisingly we also find that, while the average island size increases during coarsening, the scaled island-size distribution does not change significantly. Our simulations were carried out both as a test of, and as an application of, a variety of different algorithms for parallel kinetic Monte Carlo including the recently developed optimistic synchronous relaxation (OSR) algorithm as well as the semi-rigorous synchronous sublattice (SL) algorithm. A variation of the OSR algorithm corresponding to optimistic synchronous relaxation with pseudo-rollback (OSRPR) is also proposed along with a method for improving the parallel efficiency and reducing the number of boundary events via dynamic boundary allocation (DBA). A variety of other methods for enhancing the efficiency of our simulations are also discussed. We note that, because of the relatively high temperature of our simulations, as well as the large range of energy barriers (ranging from 0.05 to 0.8 eV), developing an efficient algorithm for parallel KMC and/or SLKMC simulations is particularly challenging. However, by using DBA to minimize the number of boundary events, we have achieved significantly improved parallel efficiencies for the OSRPR and SL algorithms. Finally, we note that, among the three parallel algorithms which we have tested here, the semi-rigorous SL algorithm with DBA led to the highest parallel efficiencies. As a result, we have obtained reasonable parallel efficiencies in our simulations of room-temperature Ag(111) island coarsening for a small number of processors (e.g. N(p) = 2 and 4). Since the SL algorithm scales with system size for fixed processor size, we expect that comparable and/or even larger parallel efficiencies should be possible for parallel KMC and/or SLKMC simulations of larger systems with larger numbers of processors.

The crossover from collective motion to periphery diffusion for two-dimensional adatom-islands on Cu(111).

The diffusion of two-dimensional adatom-islands (up to 100 atoms) on Cu(111) has been studied, using the self-learning kinetic Monte Carlo method (Trushin et al 2005 Phys. Rev. B 72 115401). A variety of multiple- and single-atom processes are revealed in the simulations, and the size dependences of the diffusion coefficients and effective diffusion barriers are calculated for each. From the tabulated frequencies of events found in the simulation, we show a crossover from diffusion due to the collective motion of the island to a regime in which the island diffuses through periphery-dominated mass transport. This crossover occurs for island sizes between 13 and 19 atoms. For islands containing 19-100 atoms the scaling exponent is 1.5, which is in good agreement with previous work. The diffusion of islands containing 2-13 atoms can be explained primarily on the basis of a linear increase of the barrier for the collective motion with the size of the island.

Dispersed forces from measured shape anisotropy of adatom islands: revelations from an accelerated simulation scheme.

High resolution diffraction measurements reveal the emergence of anisotropic adatom islands during submonolayer homoepitaxial growth of Cu(001) at grazing incidence. This anisotropy is mimicked well in simulations only after the incorporation of attractive dipolar interactions between the surface and the atoms in the gas phase. The anisotropy of the islands depends markedly on the range of the attractive potential, which allows quantitative insight into the shape of the potential. The role of long- and short-ranged interactions is delineated.