Computer Simulated Growth of Icosahedral Glass

Abstract

One possible model for materials displaying classically forbidden symmetry properties (apart from perfect quasicrystals) is the icosahedral glass model. We simulate the random growth of two types of two-dimensional icosahedral glasses consisting of the Penrose tiles, First we restrict the growth with the arrow rules, then we let the structure develop totally freely. The diffraction patterns have a clear five-fold symmetry in both cases. The diffraction peak intensities do not differ, but shapes of the central peaks vary depending on whether the arrow rules are imposed or not. Finally, we show that the half-width of the central peak decreases when the size of the simulation increases until a finite disorder-limited value is achieved. This phenomenon is in agreement with the behaviour of physical quasicrystallites and in contradiction with perfect mathematical quasicrystals which have Bragg peaks of zero width.