From Crystals to Disordered Crystals: A Hidden Order-Disorder Transition

We find an order-disorder transition from crystals to disordered crystals for static packings of frictionless spheres. While the geometric indicators are mostly blind to the transition, disordered crystals already exhibit properties apart from crystals. The transition approaches the close packing of hard spheres, giving rise to the singularity of the close packing point. We evidence that both the transition and properties of disordered crystals are jointly determined by the structural orders and density. Near the transition, the elastic moduli and coordination number of disordered crystals show particular pressure dependence distinct from both crystals and jammed solids.