Constructing Ideal Amorphous Packings in Two Dimensions

We propose that an ideal amorphous packing is one that is free of any crystalline order, stable, fully coordinated, and as densely packed as possible for a given pressure. We initially produce nearly ideal, polydisperse, amorphous packings of soft spheres by performing an energy minimization with respect to both particle radii and positions as degrees of freedom, while fixing several of the moments of the radius distribution. Radii are chosen from a log normal distribution, with a packing fraction selected to ensure overjamming. Such a method produces systems that are nearly triangulated. The fully triangulated network of contacts and nearest neighbors is fed into the CirclePack[1] circle packing algorithm, which produces packings that are stable and defect free at critical jamming while nearly preserving the distribution of radii. Surprisingly, shear and bulk moduli are of the same order, even at vanishing pressure, and the jamming density is greater than that of size-segregated crystals, independent of system size and initial conditions. We argue that these constitute ideal amorphous packings, and that given their mechanical properties ‘amorphous crystal’ is an appropriate appellation.

[1] K. Stephenson, CirclePack Software, 1992, http://www.circlepack.com/software.html.