Growth of Hard-Sphere Models with Two Different Sizes: Can a Quasicrystal Result?

Abstract

We define a growth model analogous to the Eden model, but with two types of atoms interacting through hard-sphere potentials. In some two-dimensional cases, these models generate structures which are neither periodic nor quasiperiodic, but have a characteristic topology that distinguishes them from glasses. This topology is analogous to that of Penrose lattices. Locally, the structure is of the Hendricks-Teller type: alternation of strips of fat and skinny Penrose rhombi.