Structural evolution in the packing of uniform spheres.

Structural analysis is very important to understanding the physics of atomic or particle systems of various types. However, properly characterizing the structures at different packing fraction ρ is still a challenge. Here we analyze the local structure, in terms of the so-called common-neighbor-subcluster (CNS), of sphere packings with ρ ∈ (0.2, 0.74). We show that although complicated in structure, there are totally 39 kinds of CNSs of which 12 are dominant. The evolution of these CNSs with the increase of ρ is quantified, and the rules governing the evolution are explored. The results are found to be useful in constructing a comprehensive picture about the critical states and their transition in sphere packing.