Solution of Master and Fokker-Planck equations by propagator methods, applied to Au/NaCl thin film nucleation

James Adams, W. N G Hitchon

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Novel numerical solutions of Master and Fokker-Planck equations are described and compared for equivalent discrete and continuous problems. The two methods involve the calculation of long-time-step propagator matrices, whose single application is equivalent to many iterations of a finite difference scheme. For the discrete method we present two analytic propagators which are exact for growth-only (no decay) processes, and two approximate propagators for growth and decay processes. The continuous method couples a discrete boundary condition for small clusters with an efficient continuous description for large clusters. These two methods are applied to the nucleation and growth of vapor-deposited thin films whose atoms cluster together to form islands (Volmer-Weber growth). Mobility coalescence of islands is included to show how "slow" nonlinear processes may be included in the model.

Original languageEnglish (US)
Pages (from-to)159-175
Number of pages17
JournalJournal of Computational Physics
Volume76
Issue number1
DOIs
StatePublished - 1988
Externally publishedYes

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Fokker Planck equation
Fokker-Planck equation
Nucleation
nucleation
Thin films
propagation
thin films
decay
Coalescence
coalescing
iteration
Vapors
Boundary conditions
vapors
boundary conditions
Atoms
matrices
atoms

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Solution of Master and Fokker-Planck equations by propagator methods, applied to Au/NaCl thin film nucleation. / Adams, James; Hitchon, W. N G.

In: Journal of Computational Physics, Vol. 76, No. 1, 1988, p. 159-175.

Research output: Contribution to journalArticle

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