Jamming criticality of near-crystals

Abstract

Amorphous and crystalline solids have long been considered as two distinct kinds of rigidity at the opposite ends of the order-disorder continuum. Crystals are usually treated in equilibrium with defects arising as perturbations or excitations (Ashcroft N. W. and Mermin N. D., Solid State Physics (Thomson Brooks/Cole) 1976). Amorphous solids are frustrated and out of equilibrium where preparation protocol can be important. Nevertheless the onset of rigidity of athermal amorphous matter (Liu A. J. and Nagel S. R., Nature, 396 (1998) 21) has been established as a critical point with extended universality. The universal scaling behavior that characterizes jamming at high amorphisation has been demonstrated by a wealth of simulations and models, including an infinite-dimensional mean field theory (Charbonneau P. et al., Annu. Rev. Condens. Matter Phys., 8 (2017) 265). At the other end, the crystal of minimal disorder has not been shown to display such universal behavior. Here we provide numerical evidence that slightly polydisperse crystals can become critically jammed at packing fractions extremely close to the maximum close-packed density. At the near-crystal jamming point some of the characteristic scalings are universal and agree with maximally amorphous jamming, others are novel. The set of scaling results we provide establishes jamming criticality of maximum-packing crystals in 2 and 3 dimensions.