Order and deterministic chaos in hard-disk arrays

Abstract

Order in computer-generated binary arrays of hard disks grown from a seed cluster is studied. As the composition and ratio of disk diameters are varied, we find both crystalline and amorphous samples, as well as "hexatic" configurations with short-range translational order but extended orientational correlations. A single impurity disk placed at the center of an otherwise homogeneous array traps dislocations and disclinations when its diameter deviates sufficiently from that of the disks packed deterministically around it. For still larger deviations, the impurity disk gives rise to chaotic arrays of stacking faults and grain boundaries. An alternative spiral packing algorithm leads to a particularly simple transition from order to deterministic chaos. The ratio of disk diameters plays the role of a control parameter.