Self-learning Kinetic Monte Carlo Research Articles

Self-learning kinetic Monte Carlo simulations of Al diffusion in Mg

Vacancy-mediated diffusion of an Al atom in the pure Mg matrix is studied using the atomistic, on-lattice self-learning kinetic Monte Carlo (SLKMC) method. Activation barriers for vacancy-Mg and vacancy-Al atom exchange processes are calculated on the fly using the climbing image nudged-elastic-band method and binary Mg–Al modified embedded-atom method interatomic potential. Diffusivities of an Al atom obtained from SLKMC simulations show the same behavior as observed in experimental and theoretical studies available in the literature; that is, an Al atom diffuses faster within the basal plane than along the c-axis. Although the effective activation barriers for an Al atom diffusion from SLKMC simulations are close to experimental and theoretical values, the effective prefactors are lower than those obtained from experiments. We present all the possible vacancy-Mg and vacancy-Al atom exchange processes and their activation barriers identified in SLKMC simulations. A simple mapping scheme to map an HCP lattice onto a simple cubic lattice is described, which enables simulation of the HCP lattice using the on-lattice framework. We also present the pattern recognition scheme which is used in SLKMC simulations to identify the local Al atom configuration around a vacancy.

Self-learning kinetic Monte Carlo simulations of self-diffusion of small Ag islands on the Ag(111) surface

We studied self-diffusion of small two-dimensional Ag islands, containing up to ten atoms, on the Ag(111) surface using self-learning kinetic Monte Carlo (SLKMC) simulations. Activation barriers are calculated using the semi-empirical embedded atom method (EAM) potential. We find that two- to seven-atom islands primarily diffuse via concerted translation processes with small contributions from multi-atom and single-atom processes, while eight- to ten-atom islands diffuse via single-atom processes, especially edge diffusion, corner rounding and kink detachment, along with a minimal contribution from concerted processes. For each island size, we give a detailed description of the important processes, and their activation barriers, responsible for its diffusion.

THERMAL DIFFUSION DYNAMIC BEHAVIOR OF TWO-DIMENSIONAL Ag-SMALL CLUSTERS ON Ag(1 1 1) SURFACE

In this paper, the thermal diffusion behavior of small two-dimensional Ag -islands on Ag (1 1 1) surface has been explored using molecular dynamics (MD) simulations. The approach is based on semi-empirical potentials. The key microscopic processes responsible for the diffusion of Ag 1−5 adislands on Ag (1 1 1) surface are identified. The hopping and zigzag concerted motion along with rotation are observed for Ag one-atom to three-atom islands while single-atom and multi-atom processes are revealed for Ag four-atom and five-atom islands, during the diffusion on Ag (1 1 1) surface. The same increasing/decreasing trend in the diffusion coefficient and effective energy barrier is observed in both the self learning kinetic Monte Carlo (SLKMC) and MD calculations, for the temperature range of 300–700 K. An increase in the value of effective energy barrier is noticed with corresponding increase in the number of atoms in Ag -adislands. A reasonable linear fit is observed for the diffusion coefficient for studied temperatures (300, 500 and 700 K). For the observed diffusion mechanisms, our findings are in good agreement with ab initio density-functional theory (DFT) calculations for Al / Al (1 1 1) while the energy barrier values are in same range as the experimental values for Cu / Ag (1 1 1) and the theoretical values using ab initio DFT supplemented with embedded-atom method for Ag / Ag (1 1 1).

Kinetically driven shape changes in early stages of two-dimensional island coarsening: Ag/Ag(111)

We present here a detailed analysis of the shapes of two-dimensional Ag islands of various sizes observed during the early stages of coarsening on the Ag(111) surface, using kinetic Monte Carlo (KMC) simulations, and show that selectivity is due to the formation of kinetically stable island shapes that survive longer than nonselected sizes, which decay into nearby selected sizes. The stable shapes have a closed-shell structure---one in which every atom on the periphery has at least three nearest neighbors. These findings further explain our earlier study in which we found that in the early stages coarsening proceeds as a sequence of selected island sizes resulting in peaks and valleys in the island size distribution [G. Nandipati, A. Kara, S. I. Shah, and T. S. Rahman, J. Phys.: Condens. Matter 23, 262001 (2011)]. This selectivity is dictated by the relative energetics of edge-atom diffusion and detachment and attachment processes and by the large activation barrier for kink detachment. Our simulations were carried out using a very large database of processes identified by each atom's unique local environment using the self-learning KMC scheme. The activation barriers were calculated using semiempirical interaction potentials based on the embedded-atom method.

Self-learning kinetic Monte Carlo model for arbitrary surface orientations

ABSTRACTWhile the self-learning kinetic Monte Carlo (SLKMC) method enables the calculation of transition rates from a realistic potential, implementations of it were usually limited to one specific surface orientation. An example is the fcc (111) surface in Latz et al. 2012, J. Phys.: Condens. Matter 24, 485005. This work provides an extension by means of detecting the local orientation, and thus allows for the accurate simulation of arbitrarily shaped surfaces. We applied the model to the diffusion of Ag monolayer islands and voids on a Ag(111) and Ag(001) surface, as well as the relaxation of a three-dimensional spherical particle.

A three-dimensional self-learning kinetic Monte Carlo model: application to Ag(111)

The reliability of kinetic Monte Carlo (KMC) simulations depends on accurate transition rates. The self-learning KMC method (Trushin et al 2005 Phys. Rev. B 72 115401) combines the accuracy of rates calculated from a realistic potential with the efficiency of a rate catalog, using a pattern recognition scheme. This work expands the original two-dimensional method to three dimensions. The concomitant huge increase in the number of rate calculations on the fly needed can be avoided by setting up an initial database, containing exact activation energies calculated for processes gathered from a simpler KMC model. To provide two representative examples, the model is applied to the diffusion of Ag monolayer islands on Ag(111), and the homoepitaxial growth of Ag on Ag(111) at low temperatures.

Diffusion of small two-dimensional Cu islands on Cu(111) studied with a kinetic Monte Carlo method

Diffusion of small two-dimensional Cu islands (containing up to 10 atoms) on Cu(111) has been studied using the newly developed self-learning Kinetic Monte Carlo (SLKMC) method which is based on a database of diffusion processes and their energetics accumulated automatically during the implementation of the SLKMC code. Results obtained from simulations in which atoms hop from one fcc hollow site to another are compared with those obtained from a parallel set of simulations in which the database is supplemented by processes revealed in complementary molecular dynamics simulations at $500\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. They include processes involving the hcp (stacking-fault) sites, which facilitate concerted motion of the islands (simultaneous motion of all atoms in the island). A significant difference in the scaling of the effective diffusion barriers with island size is observed in the two cases. In particular, the presence of concerted island motion leads to an almost linear increase in the effective diffusion barrier with size, while its absence accounts for strong size-dependent oscillations and anomalous behavior for trimers and heptamers. We also identify and discuss in detail the key microscopic processes responsible for the diffusion and examine the frequencies of their occurrence, as a function of island size and substrate temperature.