Monte Carlo studies of equilibrium and growth shapes of a crystal

The equilibrium and growth morphology of a crystal in a diffusion field are studied by means of a lattice-gas model in a unified way. In a closed system the crystal takes an equilibrium form, and its shape and size in two dimensions agree with those expected from the exact solutions of the corresponding Ising model. In an open system where a crystal is in contact with a gas reservoir, the crystal grows steadily. For a small crystal or at a small chemical potential difference {Δ}{μ} between the gas and the crystal, the growth form is polygonal. Its growth rate and the size are interpreted by a single nucleation and growth mechanism. On increasing {Δ}{μ} or for a large crystal, it becomes dendritic. Further increase of {Δ}{μ} results in a fractal aggregate, which is, however, ``compact'' in a large scale due to the finiteness of the gas density.