Hard Sphere Crystal Nucleation Rates: Reconciliation of Simulation and Experiment

Over the past two decades, a large number of studies addressed the topic of crystal nucleation in suspensions of hard spheres. The shared result of all these efforts is that, at low supersaturations, experimentally observed nucleation rates and numerically computed ones differ by more than 10 orders of magnitude. We present precise simulation results of crystal nucleation rate densities in the metastable hard sphere liquid. To compare these rate densities to experimentally measured ones, we propose an interpretation of the experimental data as a combination of nucleation and crystal growth processes (rather than purely the nucleation process). This interpretation may resolve the long-standing dispute about the differing rates.

Figure 1

Crystal nucleation rates at different volume fractions. Experimental data (open symbols, orange and red) and numerical data (closed symbols, green and blue) from Refs. [3, 17, 20, 21, 22, 23, 24, 25], as well as this Letter (black symbols, see also Tables 1 and 2).

Figure 2

Nucleation time distribution for 219 crystallization events out of 500 trajectories.

Figure 3

Cross section through a snapshot of a crystallite. Particles with face centered cubic environments are marked in green, hexagonally closed packed in red, blue is bcc, and particles marked in orange have an icosahedral surrounding. Particles without a crystalline environment are not shown. The visualization is done by the OVITO-program [33].

Figure 4

Crystalline part of structure factor $S$ as a function of wave number $q$, obtained from simulation snapshots and published experimental data. See main text for details.

Figure 5

Rate of formation of monocrystalline domains Eq. (8) at a characteristic time $t^{*}$. The gap between experiment and simulation is closed.