Crystallization of Dense Binary Hard-Sphere Mixtures with Marginal Size Ratio

Molecular dynamics simulations are performed for binary hard-sphere mixtures with a size ratio of $\gamma =0.9$ and a volume fraction of $\varphi =0.58$ over a range of compositions. We show how, at this high volume fraction, crystallization depends sensitively on the composition. Evidence is presented that crystallization in these mixtures does not proceed by the standard nucleation and growth paradigm. Rather, some crystallite forms almost immediately and then an interplay between compositional fluctuations and crystal growth is able to dramatically extend the time scale on which further crystallization occurs. This can be seen as a form of geometric frustration.

Figure 1

Results from simulations, each repeated 10 times (except for $X=0.7$ and 0.78 which were repeated 100 times), at various compositions $X=N_s/N=N_s/(N_s+N_l)$. (a) The average percentage of particles by number identified as being crystallite $⟨p_c⟩$, plotted against time $t$ for the compositions given in the legend (integer values for $N_S$ which gave values of $X$ closest to those in the legend were used). Note: the data for the composition of $X=0.5$ and $X=0.7$ are not distinguishably different. (b) The relative portion of large particles $(1-X_c)/(1-X)$ which are crystallite, where $X_c$ is the composition of the crystallite particles and $X$ is the composition of the total system, for compositions given in the legend (with the exception of $X=1$).

Figure 2

A typical largest connected region of crystallite particles, taken from a simulation with $X=0.7$ at time $t=3000$. This accounts for 43% of the crystallite particles, but only 3% of the total particles.

Figure 3

Main graph: The composition of the noncrystallite particles $X_f(r)$, divided by the total composition $X=0.7$, as a function of the distance from the center of mass of the largest connected region of crystallite particles $r$, at the time of $t=3000$ after the quench. Data from 100 independent simulations. Inset: The percentage of crystallite particles, $\%C_{\tau }$, present at time $t=2000$ that remained crystallite at time $t=2000+\tau$.

Figure 4

The probability density of finding a simulation with percentage $p_c$ of crystallite particles at times of $t=3000$, 5000, and 6500, for the simulations with a total composition of $X=0.7$. The results from 100 independent simulations are shown.