It is shown that by properly controlling vibrational and charging conditions, the transition from disordered to ordered, densest packing of particles can be obtained consistently. The method applies to both spherical and nonspherical particles. For spheres, face centered cubic packing with different orientations can be achieved by monitoring the vibration amplitude and frequency, and the structure of the bottom layer, in particular. The resultant force structures are ordered but do not necessarily correspond to the packing structures fully. The implications of the findings are also discussed.

Micro structures of equal sphere packing (ranging from loose to dense packing) generated numerically by discrete element method under different vibration conditions are characterized using Voronoi/Delaunay tessellation, which is applied on a wide range of packing densities. The analysis on micro properties such as the total perimeter, surface area, and the face number distribution of each Voronoi polyhedron, and the pore size distribution in each Voronoi/Delaunay subunit is systematically carried out. The results show that with the increasing density of sphere packing, the Voronoi/Delaunay pore size distribution is narrowed. That indicates large pores to be gradually substituted by small uniformed ones during densification. Meanwhile, the distributions of face number, total perimeter, and surface area of Voronoi polyhedra at high packing densities tend to be narrower and higher, which is in good agreement with those in random loose packing.

This paper presents a study of the structural transition of the packing of uniform spheres with a wide range of packing fractions. Several critical states are identified including the onset of local jamming, onset of global jamming and maximally random jammed (MRJ) states. With the increase of packing fraction , the packing structure transforms from one-dimensional chains to two-dimensional triangles and finally three-dimensional tetrahedra, correspondingly undergoing phase changes from non-jamming to local jamming, global jamming, MRJ and finally crystal structure. There is a competition between FCC (face-centred cubic) and HCP (hexagonal closed packed) in the transition from disordered to ordered structure with the increase of . HCP can transform to FCC after reaching its maximum at =0.7

The crystallization, corresponding to the fcc structure (with packing density p≈ 0.74), of smooth equal hard spheres under batch-wised feeding and three-dimensional interval vibration is numerically obtained by using the discrete element method. The numerical experiment shows that the ordered packing can be realized by proper control of the dynamic parameters such as batch of each feeding ξ and vibration amplitude A. The radial distribution function and force network are used to characterize the ordered structure. The defect formed during vibrated packing is characterized as well. The results in our work fill the gap of getting packing density between random close packing and fcc packing in phase diagram which provides an effective way of theoretically investigating the complex process and mechanism of hard sphere crystallization and its dynamics.