Statistics modification under monomer diffusion

TL;DR

This paper develops analytical formulas to predict the final cluster size distribution on nanostructured surfaces based on atom diffusion and nucleation processes, providing insights into cluster formation under specific conditions.

Contribution

It introduces a new statistical approach and formulas for predicting cluster size distributions during atom diffusion and nucleation on surfaces, especially for homogeneous nucleation with critical germ size 2.

Findings

Formulas enable prediction of final cluster size distribution from initial states.

Statistical law derived for size histogram during homogeneous nucleation.

Applicable when nucleation occurs after atom deposition is complete.

Abstract

The diffusion and coalescence of individual atoms on a nanostructured surface are treated in a purely statistical way. From this, analytical formulas are derived which, from a known initial state, give the final cluster size distribution on a surface after the diffusion of all the individual atoms. Unexpectedly, it turns out that these formulas allow obtaining a statistical law giving the size histogram of the clusters when only homogeneous nucleation occurs with a critical germ equal to 2, and in the situation where nucleation starts once the deposition of the atoms is completed.