Crystal Nucleation in the Hard Sphere System

Abstract

The structure and growth of crystal nuclei that spontaneously form during computer simulations of the simplest nontrivial model of a liquid, the hard sphere system, is described in this work. Compact crystal nuclei are observed to form at densities within the coexistence region of the phase diagram. The nuclei possess a range of morphologies with a predominance of multiply twinned particles possessing in some cases a significant decahedral character. However the multiply twinned particles do not form from an initial decahedral core but appear to nucleate as blocks of a face-centered cubic crystal partially bounded by stacking faults.

Twinning of Polymer Crystals Suppressed by Entropy

“…The cyclic twinned structures that appear in event-driven MD simulations of crystallization of monoatomic hard spheres [16] consist of partially or fully developed cyclic sector twins with a pseudo-fivefold rotation axis, resembling those in [1,22,23]. In our structures, between three and five such sectors can be resolved.…”

“…Systems of individual hard spheres have been used since the very origins of computer simulations of condensed matter. Crystallization of individual hard spheres is observed readily with moderate computational effort and with virtually all simulation techniques [16]. In such simulations, growth twins appear conspicuously with a pentagonal arrangement of sectors ( Figure 1).…”

“…In addition to the experimental evidence, computer studies of the crystallization of assemblies of single (monomeric) hard spheres have shown that twinned morphologies form very easily during crystallization of monomeric (single) hard spheres [16], almost regardless of the details of the simulation methods and protocols. Figure 1 shows an example of a well-developed cyclic twin, formed by five tetrahedral sectors around a common twin axis, marked by the circle in dashed white line.…”

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

“…It is now wellestablished that the face-centered cubic (fee) is marginally thermodynamically more stable than the hexagonal close packed (hep) crystal structure (Bolhuis et al, 1997;Woodcock, 1997). In spite of this, different ordered morphologies can also be observed in experiments and simulations like the random hexagonal close packed (rhep) layered structure or close packed crystallites, randomly oriented with defects being strongly correlated with twinning planes Auer and Frenkel, 2001;Bagley, 1970;Bolhuis et al, 1997;Cheng et al, 2002;Frenkel, 1999;Harland and van Megen, 1997;He et al, 1997;Henderson and van Megen, 1998;Karayiannis et al, 2011Karayiannis et al, , 2012Kawasaki and Tanaka, 2010;Leocmach and Tanaka, 2012;O'Malley and Snook, 2003;Pusey and Vanmegen, 1986;Pusey et al, 1989Pusey et al, , 2009Rintoul and Torquato, 1996;Russo and Tanaka, 2012;Schilling et al, 2010;Zaccarelli et al, 2009). These later crystal structures can be viewed, according to Ostwald's rule (Ostwald, 1897), as intermediate (metastable) thermodynamic stages between the amorphous (random) state and the fee crystal.…”

Microstructure and macroscopic properties of polydisperse systems of hard spheres

“…We also consider the analogous phenomena observed in granular materials, where the hard-sphere approximation is commonly used to successfully model complex rheological behaviours [232]. As the volume fraction is increased, hard-spheres enter an entropy minimization driven phase where glass formation competes with the nucleation and growth of the crystalline phase [235]. Hard-sphere models are known to successfully reproduce the main structural properties of these states for various physical systems, either for crystallization [11,12], or the amorphous solid phase transition [14].…”