Ostwald ripening of faceted two-dimensional islands

Abstract

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 after a very long transient time. The unusual coarsening kinetics obtained in Monte Carlo simulations are well described by the Becker--D\"oring equations of nucleation kinetics. These equations can be applied to a wide range of coarsening problems

Critical percolation in bidimensional coarsening

“…We later confirmed this observation on a liquid crystal Sicilia-etal08 [40] and recent experiments using phase separating glasses (though in 3d) observe a similar phenomenology Bouttes [41]. A morphological analysis along these lines was later performed on the same 2d model with conserved order parameter modelling phase separation SiSaArBrCu09 [20], see also Kaganer07,Takeuchi15 [42,33]. The effect of weak quenched disorder was consider in SiArBrCu08 [43].…”

Toward a better description of the nucleation rate of crystals and crystalline monolayers

“…It must be answered to this that the principally essential in the processes of crystal growth and dissolution can also be seen even on the simplest model, quite independently of whether the mentally constructed model is realized in nature or not, provided only that it is void of self-inconsistencies." Such simulations as well as simulations on the Ising model continue to be carried out [14][15][16][17][18][19][20][21][22][23][24][25][26] because usually they are considerably less computer-time consuming than the respective molecular dynamics simulations. They referred to the Kossel crystal model which is a concrete case of the latticegas model known to have one-to-one correspondence with the Ising model of ferromagnets.…”

Post-deposition growth kinetics of Ge on Ge(001)

“…The coarsening exponent of n ¼ 1 that was measured in this case implies a strong deviation from classical coarsening theory and from coarsening measured on Si(0 0 1). The explanation for the exotic ''linear'' recovery dynamics measured on GaAs is not yet understood, although kinetic Monte Carlo simulations point to the importance of corner sites of 2D faceted islands for such exotic coarsening behavior [28]. X-ray diffraction studies on GaSb(0 0 1) [22] showed a temperature dependence for the kinetics of sub-ML islands, and at intermediate growth temperatures (385-470 1C) coarsening exponents between 0.27 and 0.40 were measured, suggesting diffusion-limited 2D ripening kinetics.…”