Patterns of broken symmetry in the impurity-perturbed rigid-disk crystal

Abstract

As a new example of spontaneous pattern formation in many-body systems, we examine the collective means by which a close-packed disk crystal reacts to the presence of a single oversized impurity disk. Computer simulation has been used for this purpose; it creates the jammed impurity-containing packings by a kinetic particle-growth algorithm. Hexagonal primitive cells with periodic boundary conditions were employed, and the “natural” number 3n ² of disks (including the impurity) ranged upt to 10,800. For impurity diameter 1.2 times that of the other disks, the patterns of observed crystal perturbation displayed several remarkable features. Particle displacements relative to the unperturbed triangular crystal possess local irregularity but long-range coherence. The symmetry of the coherent patterns preserved that of the hexagonal cell for rapid growth, but was lower for slower growth. The final jammed packings contain “rattler” disks of the sort known to apper in random disk packings. Finally, the area increase induced by the presence of a fixed-size impurity appears to grow without bound as the system size (i.e., 3n ²) itself increases.