Evolution of fivefold local symmetry during crystal nucleation and growth in dense hard-sphere packings

Abstract

Crystal nucleation and growth of monodisperse hard-spheres as a function of packing density is studied by collision-driven molecular dynamics simulations. Short-range order in the form of fivefold local symmetry is identified and its dynamical and structural evolution is tracked as the originally amorphous assembly transits to the stable ordered phase. A cluster-based approach shows that hardsphere configurations having initially a similar average fraction of fivefold and ordered sites can crystallize in completely different patterns both in terms of dynamics and morphology. It is found that at high volume fractions crystallization is significantly delayed in assemblies where sites with fivefold symmetry are abundant. Eventually, once the crystal phase is reached, fivefold symmetry either diminishes or arranges in specific geometric patterns. Such defects are spatially strongly correlated with twinning planes at crystalline boundaries. A detailed analysis is provided on the structural characteristics of the established crystal morphologies.

Twinning of Polymer Crystals Suppressed by Entropy

“…In the morphologies typically encountered in event-driven MD, a quantitative analysis of the twin elements [27] confirms that morphologies such as that in Figure 1 are indeed multiple, cyclic twins with twin rotation 70.7° ± 0.4° (one standard deviation in the mean), in very good agreement with the expected tetrahedral value of 70.53°. A rational lattice row [110] is found to coincide for both adjacent sectors, and twinning axes and planes are identified in all cases as [110] and (111) respectively.…”

“…Less frequently, a fifth sector develops beyond a vestigial stage. A full description of the twinned structures can be found elsewhere [27,28]. In the most completely developed twinned structures, all coherent primary twins were Σ = 3 boundaries.…”

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.…”

“…Consequently, the proposed metric is highly discriminating between different crystal structures. This feature renders the CCE norm a robust descriptor to accurately identify crystal nucleation and growth in general atomic and particulate systems (Hoy and Karayiannis, 2013;Karayiannis et al, 2009bKarayiannis et al, , 2009cKarayiannis et al, ,2011Karayiannis et al, , 2012Karayiannis et al, , 2013aKarayiannis et al, , 2013bWu et al, 2014). The mathematical formulation of the CCE descriptor along with details on the algorithmic implementation can be found elsewhere (Karayiannis et al, 2010;Karayiannis et al, 2009bKarayiannis et al, , 2013b.…”

“…As reported in Section 1, for dense hard-sphere packings the emerging and prevailing crystal morphologies consist of close packed sites. Thus, for athermal polymers local structure is identified through the calculation of the fee, hep and fivefold CCE norms (Karayiannis et al, 2011(Karayiannis et al, , 2012.…”