Distributional fixed-point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling

Paul Mulheran, Kenneth Peter O'Neill, Michael Grinfeld, Wilson Lamb

Research output: Contribution to journalArticle

  • 7 Citations

Abstract

The distributions of inter-island gaps and captures zones for islands nucleated on a one-dimensional substrate during submonolayer deposition are considered using a novel retrospective view. This provides an alternative perspective on why scaling occurs in this continuously evolving system. Distributional fixed point equations for the gaps are derived both with and without a mean field approximation for nearest neighbour gap size correlation. Solutions to the equations show that correct consideration of fragmentation bias justifies the
mean field approach which can be extended to provide closed-from equations for the capture zones. Our results compare favourably to Monte Carlo data for both point and extended islands using a range of critical island size i = 0, 1, 2, 3. We also find satisfactory agreement with theoretical models based on more traditional fragmentation theory approaches
LanguageEnglish
Article number051606
Number of pages8
JournalPhysical Review E
Volume86
Issue number5
DOIs
StatePublished - 15 Nov 2012

Fingerprint

Fixed-point Equation
Fragmentation
Nucleation
One Dimension
nucleation
Scaling
scaling
Mean-field Approximation
Justify
Mean Field
Theoretical Model
Nearest Neighbor
fragmentation
Substrate
Model-based
Closed
Alternatives
Range of data
approximation

Keywords

  • gap size distribution
  • capture zone distribution
  • distributional
  • fixed-point equations
  • island nucleation
  • one dimension
  • retrospective approach
  • capture-zone scaling

Cite this

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abstract = "The distributions of inter-island gaps and captures zones for islands nucleated on a one-dimensional substrate during submonolayer deposition are considered using a novel retrospective view. This provides an alternative perspective on why scaling occurs in this continuously evolving system. Distributional fixed point equations for the gaps are derived both with and without a mean field approximation for nearest neighbour gap size correlation. Solutions to the equations show that correct consideration of fragmentation bias justifies themean field approach which can be extended to provide closed-from equations for the capture zones. Our results compare favourably to Monte Carlo data for both point and extended islands using a range of critical island size i = 0, 1, 2, 3. We also find satisfactory agreement with theoretical models based on more traditional fragmentation theory approaches",
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Distributional fixed-point equations for island nucleation in one dimension : a retrospective approach for capture zone scaling. / Mulheran, Paul; O'Neill, Kenneth Peter; Grinfeld, Michael; Lamb, Wilson.

In: Physical Review E, Vol. 86, No. 5, 051606, 15.11.2012.

Research output: Contribution to journalArticle

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