Nucleation and amorphous and crystalline growth: A dynamical model in two dimensions

Publisher Website
Google Scholar
Abstract
A model of nucleation and growth in two dimensions is proposed, which can be applied to covalent or metallic solids. The short- and medium-range correlations are taken into account by finding the energy minimum for a typical local configuration with given coordination number, and by assuming that the energy cost of the local defect is roughly the same for excess or deficiency of neighbors. The growth process is then treated in a probabilistic way, which enables us to derive the system of ordinary differential equations describing the evolution of the probabilities of finding given local configurations. The singular points of this nonlinear differential system correspond to the stable regimes of growth and can give rise to stable or metastable crystalline or amorphous networks. The temperature dependence of the process is discussed. The possibility of obtaining modulated structures via the phenomenon of parametric resonance is suggested.