Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation

Details Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation

2012-02-23

arxiv.org/abs/1202.5208v1

Physics

Condensed Matter

Soft Condensed Matter

15 pages. 16 figures. submitted to Phys. Rev. E

Scientific paper

We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and their diversity of structure and symmetry increases with increasing $N$ and decreases with increasing hyperstaticity $H \equiv N_c - N_{ISO}$, where $N_c$ is the number of pair contacts and $N_{ISO} = 3N-6$. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction $f$ of nuclei with order compatible with the bulk (RHCP) crystal decreases sharply with increasing $N$ due to a high propensity for stacking faults, 5- and near-5-fold symmetric structures, and other motifs that preclude RHCP order. While $f$ increases with increasing $H$, a significant fraction of hyperstatic nuclei for $N$ as small as 11 retain non-RHCP structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of $N\lesssim 10$ particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. These results are applicable systems that interact via hard-core-like repulsive and short-ranged attractive interactions, such as colloids and jammed particulate media.

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