Structural and energetic properties of nickel clusters: 2≤N≤1502 \le N \le 150

The four most stable structures of Ni$_N$ clusters with $N$ from 2 to 150 have been determined using a combination of the embedded-atom method in the version of Daw, Baskes and Foiles, the {\it variable metric/quasi-Newton} method, and our own {\it Aufbau/Abbau} method. A systematic study of energetics, structure, growth, and stability of also larger clusters has been carried through without more or less severe assumptions on the initial geometries in the structure optimization, on the symmetry, or on bond lengths. It is shown that cluster growth is predominantly icosahedral with $islands$ of {\it fcc}, {\it tetrahedral} and {\it decahedral} growth. For the first time in unbiased computations it is found that Ni$_{147}$ is the multilayer (third Mackay) icosahedron. Further, we point to an enhanced ability of {\it fcc} clusters to compete with the icosahedral and decahedral structures in the vicinity of N=79. In addition, it is shown that conversion from the {\it hcp}/anti-Mackay kind of icosahedral growth to the {\it fcc}/Mackay one occurs within a transition layer including several cluster sizes. Moreover, we present and apply different analytical tools in studying structural and energetic properties of such a large class of clusters. These include means for identifying the overall shape, the occurrence of atomic shells, the similarity of the clusters with, e.g., fragments of the {\it fcc} crystal or of a large icosahedral cluster, and a way of analysing whether the $N$-atom cluster can be considered constructed from the $(N-1)$-atom one by adding an extra atom. In addition, we compare in detail with results from chemical-probe experiment. Maybe the most central result is that first for clusters with $N$ above 80 general trends can be identified.Comment: 37 pages, 11 figure

The Kinetic Activation-Relaxation Technique: A Powerful Off-lattice On-the-fly Kinetic Monte Carlo Algorithm

Many materials science phenomena, such as growth and self-organisation, are dominated by activated diffusion processes and occur on timescales that are well beyond the reach of standard-molecular dynamics simulations. Kinetic Monte Carlo (KMC) schemes make it possible to overcome this limitation and achieve experimental timescales. However, most KMC approaches proceed by discretizing the problem in space in order to identify, from the outset, a fixed set of barriers that are used throughout the simulations, limiting the range of problems that can be addressed. Here, we propose a more flexible approach -- the kinetic activation-relaxation technique (k-ART) -- which lifts these constraints. Our method is based on an off-lattice, self-learning, on-the-fly identification and evaluation of activation barriers using ART and a topological description of events. The validity and power of the method are demonstrated through the study of vacancy diffusion in crystalline silicon.Comment: 5 pages, 4 figure

Action-derived molecular dynamics in the study of rare events

We present a practical method to generate classical trajectories with fixed initial and final boundary conditions. Our method is based on the minimization of a suitably defined discretized action. The method finds its most natural application in the study of rare events. Its capabilities are illustrated by non-trivial examples. The algorithm lends itself to straightforward parallelization, and when combined with molecular dynamics (MD) it promises to offer a powerful tool for the study of chemical reactions.Comment: 7 Pages, 4 Figures (3 in color), submitted to Phys. Rev. Let

Melting of aluminium clusters

The melting of Al clusters in the size range 49 <= N <= 62 has been studied using two model interatomic potentials. The results for the two models are significantly different. The glue potential exhibits a smooth relatively featureless heat capacity curve for all sizes except for N = 54 and N = 55, sizes at which icosahedral structures are favoured over the polytetrahedral. Gupta heat capacity curves, instead, show a well-defined peak that is indicative of a first-order-like transition. The differences between the two models reflect the different ground-state structures, and neither potential is able to reproduce or explain the size dependence of the melting transition recently observed in experiments

Accelerated Stochastic Sampling of Discrete Statistical Systems

We propose a method to reduce the relaxation time towards equilibrium in stochastic sampling of complex energy landscapes in statistical systems with discrete degrees of freedom by generalizing the platform previously developed for continuous systems. The method starts from a master equation, in contrast to the Fokker-Planck equation for the continuous case. The master equation is transformed into an imaginary-time Schr\"odinger equation. The Hamiltonian of the Schr\"odinger equation is modified by adding a projector to its known ground state. We show how this transformation decreases the relaxation time and propose a way to use it to accelerate simulated annealing for optimization problems. We implement our method in a simplified kinetic Monte Carlo scheme and show an acceleration by an order of magnitude in simulated annealing of the symmetric traveling salesman problem. Comparisons of simulated annealing are made with the exchange Monte Carlo algorithm for the three-dimensional Ising spin glass. Our implementation can be seen as a step toward accelerating the stochastic sampling of generic systems with complex landscapes and long equilibration times.Comment: 18 pages, 6 figures, to appear in Phys. Rev.

Diffusion-limited reactions on a two-dimensional lattice with binary disorder

Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous desorption of particles. Hopping and desorption are taken to be thermally activated processes. The activation energies are drawn from a binary distribution of well depths, corresponding to `shallow' and `deep' sites. This is the simplest non-trivial distribution, which we use to examine and explain fundamental features of the system. We simulate the system using kinetic Monte Carlo methods and provide a thorough understanding of our findings. We show that the combination of shallow and deep sites broadens the temperature window in which the reaction is efficient, compared to either homogeneous system. We also examine the role of spatial correlations, including systems where one type of site is arranged in a cluster or a sublattice. Finally, we show that a simple rate equation model reproduces simulation results with very good accuracy.Comment: 9 pages, 5 figure

Dimensional Strategies and the Minimization Problem: Barrier-Avoiding Algorithms

In the present paper we examine the role of dimensionality in the minimization problem. Since it has such a powerful influence on the topology of the associated potential energy landscape, we argue that it may prove useful to alter the dimensionality of the space of the original minimization problem. We explore this general idea in the context of finding the minimum energy geometries of Lennard-Jones clusters. We show that it is possible to locate barrier-free, high-dimensional pathways that connect local, three-dimensional cluster minima. The performance of the resulting, “barrier-avoiding minimization” algorithm is examined for clusters containing as many as 55 atoms

A kinetic Monte Carlo approach to study fluid transport in pore networks

The mechanism of fluid migration in porous networks continues to attract great interest. Darcy’s law (phenomenological continuum theory), which is often used to describe macroscopically fluid flow through a porous material, is thought to fail in nano-channels. Transport through heterogeneous and anisotropic systems, characterized by a broad distribution of pores, occurs via a contribution of different transport mechanisms, all of which need to be accounted for. The situation is likely more complicated when immiscible fluid mixtures are present. To generalize the study of fluid transport through a porous network, we developed a stochastic kinetic Monte Carlo (KMC) model. In our lattice model, the pore network is represented as a set of connected finite volumes (voxels), and transport is simulated as a random walk of molecules, which “hop” from voxel to voxel. We simulated fluid transport along an effectively 1D pore and we compared the results to those expected by solving analytically the diffusion equation. The KMC model was then implemented to quantify the transport of methane through hydrated micropores, in which case atomistic molecular dynamic simulation results were reproduced. The model was then used to study flow through pore networks, where it was able to quantify the effect of the pore length and the effect of the network’s connectivity. The results are consistent with experiments but also provide additional physical insights. Extension of the model will be useful to better understand fluid transport in shale rocks

Accelerating the dynamics of infrequent events: Combining hyperdynamics and parallel replica dynamics to treat epitaxial layer growth

During the growth of a surface, morphology-controlling diffusion events occur over time scales that far exceed those accessible to molecular dynamics (MD) simulation. Kinetic Monte Carlo offers a way to reach much longer times, but suffers from the fact that the dynamics are correct only if all possible diffusion events are specified in advance. This is difficult due to the concerted nature of many of the recently discovered surface diffusion mechanisms and the complex configurations that arise during real growth. Here the authors describe two new approaches for this type of problem. The first, hyperdynamics, is an accelerated MD method, in which the trajectory is run on a modified potential energy surface and time is accumulated as a statistical property. Relative to regular MD, hyperdynamics can give computational gains of more than 10{sup 2}. The second method offers a way to parallelize the dynamics efficiently for systems too small for conventional parallel MD algorithms. Both methods exploit the infrequent-event nature of the diffusion process. After an introductory description of these methods, the authors present preliminary results from simulations combining the two approaches to reach near-millisecond time scales on systems relevant to epitaxial metal growth

Stochastic method for accommodation of equilibrating basins in kinetic Monte Carlo simulations

A computationally simple way to accommodate 'basins' of trapping sites in standard kinetic Monte Carlo simulations is presented. By assuming the system is effectively equilibrated in the basin, the residence time (time spent in the basin before escape) and the probabilities for transition to states outside the basin may be calculated. This is demonstrated for point defect diffusion over a periodic grid of sites containing a complex basin.Comment: 4 pages, 1 figur