390 research outputs found
Structural and energetic properties of nickel clusters:
The four most stable structures of Ni clusters with 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 of
{\it fcc}, {\it tetrahedral} and {\it decahedral} growth. For the first time in
unbiased computations it is found that Ni 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 -atom cluster can be
considered constructed from the -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 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, âbarrier-avoiding minimizationâ 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. Darcyâs 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 âhopâ 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 networkâs 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
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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
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