Diffusion of Monolayer Adatom and Vacancy Clusters: Langevin Analysis and Monte Carlo Simulations of their Brownian Motion

Khare, S. V.; Bartelt, N. C.; Einstein, T. L.

doi:10.1103/physrevlett.75.2148

Cited by 174 publications

(170 citation statements)

References 22 publications

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“…From simulations performed at T = 300 K, 500 K, and 700 K, the effective diffusion barriers are found to increase almost monotonically with size, while the diffusion coefficient takes the form shown in is mildly temperature dependent [28]. This is consistent with the theoretical value of 3/2 for large island motion dominated by atom diffusion along island perimeter [17]. …”

Section: Diffusion Coefficientssupporting

confidence: 76%

“…One of the most important questions that still remains open is the role of island diffusion, since for mobile islands the aggregation rates in the RE approach depend explicitly on the diffusion coefficients D s of islands of different sizes s. Island diffusion on surfaces has been studied both theoretically [7,8,9] and experimentally [10,11,12,13,14,15,16]. While in the large island limit the size dependence of the island diffusion coefficients can be classified based on simple basic processes [17], for smaller islands D s depends on the geometric and energetic details of the underlying surface, and can be a complicated, non-monotonic function of s [18,19].…”

Section: Introductionmentioning

confidence: 99%

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Diffusion and submonolayer island growth during hyperthermal deposition on Cu(100) and Cu(111)

et al. 2005

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We consider the influence of realistic island diffusion rates to homoepitaxial growth on metallic surfaces using a recently developed rate equation model which describes growth in the submonolayer regime with hyperthermal deposition. To this end, we incorporate realistic size and temperature-dependent island diffusion coefficients for the case of homoepitaxial growth on Cu(100) and Cu(111) surfaces. We demonstrate that the generic features of growth remain unaffected by the details of island diffusion, thus validating the generic scenario of high density of small islands found experimentally and theoretically for large detachment rates. However, the details of the morphological transition and scaling of the mean island size are Preprint submitted to Surface Science 7 March 2018 strongly influenced by the size dependence of island diffusion. This is reflected in the scaling exponent of the mean island size, which depends on both temperature and the surface geometry.

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Section: Diffusion Coefficientssupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Diffusion and submonolayer island growth during hyperthermal deposition on Cu(100) and Cu(111)

et al. 2005

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“…Traditional simplistic mean-field-type analyses of the dependence of cluster diffusion coefficient D on size N ͑for large N͒ suggest different behavior for the TD and PD classes. 8,11 However, it is clear that the actual behavior will depend strongly on the magnitude of the rate controlling bulk vacancy transport ͑relative to other rates͒ and on the size of the cluster. In our current studies, the clusters are sufficiently small that bulk vacancies cannot form, so cluster diffusion is unambiguously associated with the PD class.…”

Section: Lattice-gas Models For Cluster Diffusionmentioning

confidence: 99%

“…[8][9][10][11] If they do, we are implicitly regarding the four atoms adjacent to the interior vacancy as ''perimeter'' atoms and the kinetic rules would allow one of them to exchange with the vacancy, thus facilitating its diffusion. Such models are traditionally placed in the so-called terrace diffusion ͑TD͒ class.…”

Section: Lattice-gas Models For Cluster Diffusionmentioning

confidence: 99%

“…The dependence of D on cluster size N ͑i.e., the number of atoms͒ was assessed and cluster diffusion and coalescence was shown to dominate adlayer coarsening in metal ͑100͒ homoepitaxial systems under certain conditions. 8,9 Kinetic Monte Carlo simulations of large cluster diffusion have also been utilized to examine the dependence of D on N for various mass transport pathways 6,11 and to examine correlations in the cluster's walk. 12 However, a comprehensive understanding of large cluster diffusion is still lacking.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion of small clusters on metal (100) surfaces: Exact master-equation analysis for lattice-gas models

Sánchez

Evans

1999

Phys. Rev. B

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Exact results are presented for the surface diffusion of small two-dimensional clusters, the constituent atoms of which are commensurate with a square lattice of adsorption sites. Cluster motion is due to the hopping of atoms along the cluster perimeter with various rates. We apply the formalism of Titulaer and Deutch [ J. Chem. Phys. 77, 472 (1982)], which describes evolution in reciprocal space via a linear master equation with dimension equal to the number of cluster configurations. We focus on the regime of rapid hopping of atoms along straight close-packed edges, where certain subsets of configurations cycle rapidly between each other. Each such subset is treated as a single quasiconfiguration, thereby reducing the dimension of the evolution equation, simplifying the analysis, and elucidating limiting behavior. We also discuss the influence of concerted atom motions on the diffusion of tetramers and larger clusters. Exact results are presented for the surface diffusion of small two-dimensional clusters, the constituent atoms of which are commensurate with a square lattice of adsorption sites. Cluster motion is due to the hopping of atoms along the cluster perimeter with various rates. We apply the formalism of Titulaer and Deutch ͓J. Chem. Phys. 77, 472 ͑1982͔͒, which describes evolution in reciprocal space via a linear master equation with dimension equal to the number of cluster configurations. We focus on the regime of rapid hopping of atoms along straight close-packed edges, where certain subsets of configurations cycle rapidly between each other. Each such subset is treated as a single quasiconfiguration, thereby reducing the dimension of the evolution equation, simplifying the analysis, and elucidating limiting behavior. We also discuss the influence of concerted atom motions on the diffusion of tetramers and larger clusters. ͓S0163-1829͑99͒05704-5͔ Disciplines Condensed Matter Physics | Mathematics

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Effect of Channel Confinement on the Coarsening Kinetics of Nanoparticles Deposited on Semicrystalline Polymer Templates

Pavan

Shenhar

2013

ChemPlusChem

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Dodecanethiol‐capped gold nanoparticles (NPs) deposited onto a poly(ethylene glycol) substrate quickly coarsen over a timescale of days when stored under ambient conditions. The NP coarsening was studied at different surface coverages and temperatures. The coarsening of NPs depended on their location on the film; NPs located inside the channels coarsened in a different fashion than NPs deposited on the plateaus. Size distributions studied by image analysis and comparison to theoretical distribution functions shed light on the coarsening mechanism in each case, revealing the role of dimensionality.

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Diffusion of Monolayer Adatom and Vacancy Clusters: Langevin Analysis and Monte Carlo Simulations of their Brownian Motion

Cited by 174 publications

References 22 publications

Diffusion and submonolayer island growth during hyperthermal deposition on Cu(100) and Cu(111)

Diffusion and submonolayer island growth during hyperthermal deposition on Cu(100) and Cu(111)

Diffusion of small clusters on metal (100) surfaces: Exact master-equation analysis for lattice-gas models

Effect of Channel Confinement on the Coarsening Kinetics of Nanoparticles Deposited on Semicrystalline Polymer Templates

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