Crystallisation in a granular material

Abstract

The athermal and dissipative nature of packings of grains is still challenging our understanding of their compaction as well as their crystallisation. For instance, some beads poured in a container get jammed in random disordered con gurations, which cannot be denser than 64%, the random closed packing (RCP) limit. Remarkably it has been suggested that the RCP bound is saturated with dense patterns of beads aggregated into polytetrahedral structures. Yet when a suitable vibration is applied, a packing of beads might start to order and some regular patterns appear. We present new experiments on the crystallisation of the packing of beads. By extending tapping techniques, we have obtained packings with volume fractions φ ranging from the RCP to the crystal (φ = 0.74). Computing tomography has been used to scan the internal structure of large packings (≈200,000 beads). Voronoi and Delaunay space partitions on the grain centres were performed to characterise the structural rearrangements during the crystallisation. This allows us to describe statistical properties of the local volume uctuations and the evolution of the densest patterns of beads. In terms of statistical description, a parameter based on the volume uctuations discloses different regimes during the transition. In terms of geometry, we con rm that polytetrahedral dense clusters are ubiquitous at the RCP. We describe some intrinsic features of these clusters such as rings of tetrahedra and show how they disappear as the crystal grows. This experiment enlightens how an athermal system jammed in a complex frustrated con guration is gradually converted into a periodic crystal.