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

Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051606. doi: 10.1103/PhysRevE.86.051606. Epub 2012 Nov 15.

Abstract

The distributions of interisland 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 neighbor 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 favorably 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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Computer Simulation
  • Crystallization / methods*
  • Diffusion
  • Models, Chemical*
  • Models, Molecular*
  • Models, Statistical*
  • Monte Carlo Method
  • Nanostructures / chemistry*
  • Nanostructures / ultrastructure*