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Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models

O'Neill, Kenneth Peter and Grinfeld, Michael and Lamb, Wilson and Mulheran, Paul (2012) Gap size and capture zone distributions in one-dimensional point island nucleation and growth simulations: asymptotics and models. Physical Review E, 85 (2). ISSN 1539-3755

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Abstract

The nucleation and growth of point islands during submonolayer deposition on a one-dimensional substrate is simulated for critical island size $i=0,1,2,3$. The small and large size asymptotics for the gap size and capture zone distributions (GSD and CZD) are studied. Comparisons to theoretical predictions from fragmentation equation analyses are made, along with those from the recently proposed Generalised Wigner Surmise (GWS). We find that the simulation data can be fully understood in the framework provided by the fragmentation equations, whilst highlighting the theoretical areas that require further development. The GWS works well for the small-size CZD behaviour, but completely fails to describe the large-size CZD asymptotics of the one-dimensional system.

Item type: Article
ID code: 37812
Notes: updated
Keywords: capture zone distributions , point island nucleation , growth simulations , asymptotics, Probabilities. Mathematical statistics, Statistical and Nonlinear Physics, Statistics and Probability, Condensed Matter Physics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Faculty of Engineering > Chemical and Process Engineering
Depositing user: Pure Administrator
Date Deposited: 22 Feb 2012 14:51
Last modified: 27 Mar 2015 07:00
URI: http://strathprints.strath.ac.uk/id/eprint/37812

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