1202.5208 (Robert S. Hoy et al.)

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

Robert S. Hoy, Jared Harwayne-Gidansky, Corey S. O'Hern

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.

View original: http://arxiv.org/abs/1202.5208