Precursor-Mediated Crystallization Process in Suspensions of Hard Spheres

We report on a large scale computer simulation study of crystal nucleation in hard spheres. Through a combined analysis of real- and reciprocal-space data, a picture of a two-step crystallization process is supported: First, dense, amorphous clusters form which then act as precursors for the nucleation of well-ordered crystallites. This kind of crystallization process has been previously observed in systems that interact via potentials that have an attractive as well as a repulsive part, most prominently in protein solutions. In this context the effect has been attributed to the presence of metastable fluid-fluid demixing. Our simulations, however, show that a purely repulsive system (that has no metastable fluid-fluid coexistence) crystallizes via the same mechanism.

Figure 1

System snapshots at (a) 350 000 sweeps and (b) 450 000 sweeps. Particles with $n_b>5$ (light brown) and $n_b>10$ (green). Particles with fewer bonds are not shown. (c) Time series of cluster evolution.

Figure 2

Evolution of crystallinity. (a) Fraction $X$ of particles in clusters for various values of $n_b$ [number of crystalline bonds according to Eq. (1) and text thereafter]. (b) Number of particles in crystallites (clusters with $n_b>10$, open green diamonds) and in clusters with $n_b>5$ either containing crystallites (black squares) or not containing crystallites (red circles). (c),(d) Cluster size distribution at $t=300000$ and 600 000 sweeps. $⟨N_c⟩$ denotes the average number of clusters per 5000 sweeps with an averaging time window of 100 000 sweeps. The meaning of the symbols is as in (b).

Figure 3

Evolution of crystal structure factor. Different colors correspond to different times given in ${10}^3$ MC sweeps as indicated. For further details see text.

Figure 4

Evolution of parameters extracted from analysis of the crystal structure factor. (a) Crystallinity, red line: data from Fig. 2a ($n_b=12$) for comparison. (b) Average domain size. (c) Volume fraction and (d) number of clusters or crystals. Black squares fcc, (111) peak; open circles, fcc (220) peak.