Bimodal self-assembly of granular spheres under vertical vibration

As granular particles in a packing are athermal, their self-assembly has to be realized with the input of energy via walls. But different manners of energy input, e.g., through tapping or shearing walls, have not been discriminated previously. We address this problem in the self-assembly of identical granular spheres in prism-like containers subjected to one-dimensional (1D) vertical vibration by numerical simulations. The edge lengths or diameter of the containers are the integer multiples of the particle diameter. When energy is input with the vibration, the particles can self-assemble into mainly mixed FCC (face-centred-cubic) and HCP (hexagonal-close-packed) structures from the bottom wall and/or the side walls. According to different movements of the walls, the shear-induced and tap-induced self-assemblies are distinguished. These two self-assembly modes can emerge solely or simultaneously, with different but overlapping regions in the vibration amplitude and frequency phase diagram. The structures of the self-assembly from the two modes also present different features, suggesting different formation mechanisms. Moreover, it is found that the close-packed planes of the ordered clusters formed from different walls are often misaligned, leading to conflicts in the self-assembly of the whole system. These findings are helpful for both the understanding and controlling of the self-assembly of granular particles and other similar athermal and low-thermal systems.