title: Distributional fixed-point equations for island nucleation in one dimension: a retrospective approach for capture-zone scaling.
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.
authors.affiliation: Department of Chemical and Process Engineering, University of Strathclyde, Glasgow. paul.mulheran@strath.ac.uk
authors.forename: P A
authors.initials: PA
authors.lastname: Mulheran
authors.forename: K P
authors.initials: KP
authors.lastname: O'Neill
authors.forename: M
authors.initials: M
authors.lastname: Grinfeld
authors.forename: W
authors.initials: W
authors.lastname: Lamb
mesh_terms: D003198:Computer Simulation; D003460:Crystallization / Q000379:methods*; D004058:Diffusion; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D009010:Monte Carlo Method; D049329:Nanostructures / Q000737:chemistry* / Q000648:ultrastructure*