Packing Spheres Tightly: Influence of Mechanical Stability on Close-Packed Sphere Structures

Abstract

Many experiments and simulations of packings of monodisperse hard spheres report a dominance of the face-centered cubic structure in the hexagonally close-packed limit, even though it has no significant energetic or entropic gain over other close-packed configurations. Combining simulations and experiments, we demonstrate that a simple mechanical instability which occurs during the packing process may play an important role in selecting the face-centered cubic structure over other close-packed alternatives. Our argument is supported by detailed quantitative analyses of key configurations in sphere packings and highlights the importance of the packing dynamics. The proposed mechanism is elementary and should therefore play a role in a wide range of sphere systems.

Direct Numerical Simulations of spherical bubbles in vertical turbulent channel flow

“…Bubble-bubble and bubble-wall collisions are accounted for by a repulsive potential force depending on the distance vector between the respective surfaces, as proposed by Heitkam et al (2012). The force induced on bubble i by bubble j reads…”

The potential energy landscape for crystallisation of a Lennard-Jones fluid

“…It has been shown that close-packed structures form with equal probability. However, the FCC structure is mechanically more stable and less often destroyed in the continuing dynamical growth process, as newly arrived atoms impact upon the structure [53].…”

Structure and energy of liquid foams

“…This has been attributed to a reduced mechanical stability of non-FCC structures: forces between neighbouring spheres are not transmitted in the same way in FCC and HCP packings, making HCP packings noticeably less stable [26].…”

“…This is particularly so for disordered samples, which require manually dealing with individual topological changes as liquid fraction is varied. Investigations close to the jamming transition commonly simulate the foam as a dense packing of spheres which interact via a pairwise potential [26,[51][52][53]71].…”