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

Sánchez, J. R.; Evans, James W.

doi:10.1103/physrevb.59.3224

Cited by 29 publications

(26 citation statements)

References 22 publications

(27 reference statements)

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“…13 However, it has been noted that the relative dominance of PD versus vacancy TD will be strongly sensitive to the magnitude of rate for vacancy diffusion relative to the various PD rates, as well as to the cluster size. 21,22 From this perspective, the study in Ref. 13 might be somewhat biased towards vacancy TD, as it incorporates a very low choice of activation barrier for vacancy diffusion.…”

Section: Introductionmentioning

confidence: 99%

Smoluchowski ripening of Ag islands on Ag(100)

Stoldt

Jenks

Thiel

et al. 1999

The Journal of Chemical Physics

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Using scanning tunneling microscopy, we study the post-deposition coarsening of distributions of large, twodimensional Ag islands on a perfect Ag(100) surface at 295 K. The coarsening process is dominated by diffusion, and subsequent collision and coalescence of these islands. To obtain a comprehensive characterization of the coarsening kinetics, we perform tailored families of experiments, systematically varying the initial value of the average island size by adjusting the amount of Ag deposited (up to 0.25 ML). Results unambiguously indicate a strong decrease in island diffusivity with increasing island size. An estimate of the size scaling exponent follows from a mean-field Smoluchowski rate equation analysis of experimental data. These rate equations also predict a rapid depletion in the initial population of smaller islands. This leads to narrowing of the size distribution scaling function from its initial form, which is determined by the process of island nucleation and growth during deposition. However, for later times, a steady increase in the width of this scaling function is predicted, consistent with observed behavior. Finally, we examine the evolution of Ag adlayers on a strained Ag(100) surface, and find significantly enhanced rates for island diffusion and coarsening. KeywordsInstitute of Physical Research and Technology, scanning tunnelling microsopy, nucleation, adsorbed layers, silver, deposition, surface properties, islands, roughness, adsorbents, diffusion, scanning electron microscopy, thin films Disciplines Mathematics | Physical Chemistry CommentsThe following article appeared in The Journal of Chemical Physics 111, no. 11 (1999) Using scanning tunneling microscopy, we study the post-deposition coarsening of distributions of large, two-dimensional Ag islands on a perfect Ag͑100͒ surface at 295 K. The coarsening process is dominated by diffusion, and subsequent collision and coalescence of these islands. To obtain a comprehensive characterization of the coarsening kinetics, we perform tailored families of experiments, systematically varying the initial value of the average island size by adjusting the amount of Ag deposited ͑up to 0.25 ML͒. Results unambiguously indicate a strong decrease in island diffusivity with increasing island size. An estimate of the size scaling exponent follows from a mean-field Smoluchowski rate equation analysis of experimental data. These rate equations also predict a rapid depletion in the initial population of smaller islands. This leads to narrowing of the size distribution scaling function from its initial form, which is determined by the process of island nucleation and growth during deposition. However, for later times, a steady increase in the width of this scaling function is predicted, consistent with observed behavior. Finally, we examine the evolution of Ag adlayers on a strained Ag͑100͒ surface, and find significantly enhanced rates for island diffusion and coarsening.

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Section: Introductionmentioning

confidence: 99%

Smoluchowski ripening of Ag islands on Ag(100)

Stoldt

Jenks

Thiel

et al. 1999

The Journal of Chemical Physics

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“…This matrix is extracted by Fourier transformation of the linear master equations. 30,31 However, this analysis is only viable for small N, as Ω N grows rapidly with N. Thus, we instead apply alternative combinatorial analyses. Prior to presenting KMC results, we characterize nucleation-mediated versus "facile" cluster diffusion for moderate sizes with N ≥ 9.…”

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Communication: Diverse nanoscale cluster dynamics: Diffusion of 2D epitaxial clusters

Lai

Evans

Liu

2017

The Journal of Chemical Physics

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The dynamics of nanoscale clusters can be distinct from macroscale behavior described by continuum formalisms. For diffusion of 2D clusters of N atoms in homoepitaxial systems mediated by edge atom hopping, macroscale theory predicts simple monotonic size scaling of the diffusion coefficient, DN ∼ N−β, with β = 3/2. However, modeling for nanoclusters on metal(100) surfaces reveals that slow nucleation-mediated diffusion displaying weak size scaling β < 1 occurs for “perfect” sizes Np = L2 and L(L+1) for integer L = 3,4,… (with unique square or near-square ground state shapes), and also for Np+3, Np+4,…. In contrast, fast facile nucleation-free diffusion displaying strong size scaling β ≈ 2.5 occurs for sizes Np+1 and Np+2. DN versus N oscillates strongly between the slowest branch (for Np+3) and the fastest branch (for Np+1). All branches merge for N = O(102), but macroscale behavior is only achieved for much larger N = O(103). This analysis reveals the unprecedented diversity of behavior on the nanoscale.

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“…To this end, we calculate D s for small islands using the analytic master equation ͑ME͒ formalism by Titulaer and Deutsch, 16 as modified by Sanchez and Evans ͑SE͒. 17 This method is based on the Markovian approximation of independent transitions between different configurations. With all the relevant transition rates known, D s can be obtained explicitly at all temperatures where the Markovian approximation holds.…”

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confidence: 99%