WIAS Preprint No. 1229, (2007)

Ostwald ripening of faceted two-dimensional islands


  • Kaganer, Vladimir
  • Braun, Wolfgang
  • Sabelfeld, Karl

2010 Mathematics Subject Classification

  • 65C05 65C20

2008 Physics and Astronomy Classification Scheme

  • 81.10.Aj,05.10.Ln,68.43.Jk,81.15.-z


  • Ostwald ripening, Lifshitz--Slyozov--Wagner theory, Becker--Döring equations, faceted crystalline droplets, Gibbs--Thomson formula, kinetic Monte Carlo simulations


We study Ostwald ripening of two-dimensional adatom and advacancy islands on a crystal surface by means of kinetic Monte Carlo simulations. At large bond energies the islands are square-shaped, which qualitatively changes the coarsening kinetics. The Gibbs--Thomson chemical potential is violated: the coarsening proceeds through a sequence of `magic' sizes corresponding to square or rectangular islands. The coarsening becomes attachment-limited, but Wagner's asymptotic law is reached only after a very long transient time. The unusual coarsening kinetics obtained in the Monte Carlo simulations are well described by the Becker--Döring equations of nucleation kinetics. These equations can be applied to a wide range of coarsening problems.

Appeared in

  • Phys. Rev. B., 76 (2007) pp. 075415 (11 pages).

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