Surface diffusion capture in nucleation theory

B. Lewis, V. Halpern

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


The diffusion of adatoms over a substrate, their capture by isolated clusters of atoms and their release from such clusters is examined, in order to calculate nucleation rates. Two approaches are used: the first considers the fluxes of distinct atoms between the clusters and the vapour, while the second considers the total transfer rates between the clusters and adsorbed monomer. While the two approaches lead to similar results, the first is simpler to apply. It is shown that the monomer density in the neighbourhood of clusters is uniform only when captured atoms are replenished by cluster decay, i.e. when the net growth rate is zero, and is depleted below the mean value near growing clusters, including those growing through the critical size. It is further shown that the net capture rate of monomer by critical nuclei, i.e. the net rate at which they become supercritical, cannot exceed the steady-state surface diffusion limited flux of distinct atoms, and that nucleation rate relations derived with the assumption of a uniform monomer density are wrong. The correct relations are given.

Original languageEnglish
Pages (from-to)39-52
Number of pages14
JournalJournal of Crystal Growth
Issue number1
StatePublished - Apr 1976
Externally publishedYes

Bibliographical note

Funding Information:
The authors thank Professor S.J. Hruska for general comments and the elucidation of his views on nucleation rates. One of us (B.L.) thanks the Plessey Company Limited for support and permission to publish, and the other (V.11.) thanks the Israel Academy of Sciences and Humanities and the Royal Society, London for a travel grant to enable him to work at Chelsea College, and Professor A.K. Jonscher for his hospitality there.


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