| A phase-field approach describing the formation and evolution of an hexagonally patterned surface is presented. We studied a free-energy and a time-dependent Ginzburg-Landau equation for which the order parameter is non-conserved. We give a review of the scaling phenomena in general and of hexagonal systems in particular, both from theoretical and experimental points of views. A squared shaped grid of varied sizes, with periodical boundary conditions, was used for the simulations. First, we studied the evolution of surfaces themselves. Then, we considered the evolution of the structure factor's maximum amplitude, and full width at half maximum. Scaling laws as a function of system size were found for these variables. We also made a study of surface energies. We monitored the evolution of the surface energies with time, and propose a scaling law for the energies. Finally, we studied the evolution of temporal correlation functions. We propose a further scaling law for the temporal correlation functions. |
