Probable Nature of the Internal Symmetry of Crystals

Barlow, William

doi:10.1038/029186a0

Cited by 98 publications

(48 citation statements)

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“…For each δ, Q 6 (R) is sigmoidal with a midpoint that defines the critical cooling rate R c . As R decreases toward R c , systems with z = 12 form ordered Barlow packings [27] and Q 6 begins to increase as shown in Figure 1. In the δ → 0 limit, R c converges to that for the Weeks-Chandler-Andersen (WCA) purely repulsive potential [28].…”

Section: Resultsmentioning

confidence: 99%

The glass-forming ability of model metal-metalloid alloys

Zhang

Liu

Schroers

et al. 2015

The Journal of Chemical Physics

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Bulk metallic glasses (BMGs) are amorphous alloys with desirable mechanical properties and processing capabilities. To date, the design of new BMGs has largely employed empirical rules and trial-and-error experimental approaches. Ab initio computational methods are currently prohibitively slow to be practically used in searching the vast space of possible atomic combinations for bulk glass formers. Here, we perform molecular dynamics simulations of a coarse-grained, anisotropic potential, which mimics interatomic covalent bonding, to measure the critical cooling rates for metalmetalloid alloys as a function of the atomic size ratio σS/σL and number fraction xS of the metalloid species. We show that the regime in the space of σS/σL and xS where well-mixed, optimal glass formers occur for patchy and LJ particle mixtures coincides with that for experimentally observed metal-metalloid glass formers. Our simple computational model provides the capability to perform combinatorial searches to identify novel glass-forming alloys.

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Section: Resultsmentioning

confidence: 99%

The glass-forming ability of model metal-metalloid alloys

Zhang

Liu

Schroers

et al. 2015

The Journal of Chemical Physics

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“…Barlow packings [9,10] are hard-sphere packings composed of layered hexagonal-close-packed planes; their three-dimensional order may be FCC, HCP, or mixed FCC/HCP, but they possess no defects (e.g. stack faults.)…”

Section: F Structural Analysesmentioning

confidence: 99%

“…However, this approach should work if and only if these packings possess the same structural order as the bulk crystalline phase. A recent study by Hopkins et al [8] showed that this condition fails; the densest packings did not in general have FCC, HCP, or Barlow [9,10] order. Instead, their surface order was dominated by the spherical boundary conditions, and so they may not correspond to the stable nuclei that form in unconfined geometries, i.e.…”

Section: Introductionmentioning

confidence: 99%

Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation

2012

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We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres N , and their diversity of structure and symmetry increases with increasing N and decreases with increasing hyperstaticity H ≡ Nc − NISO, where Nc is the number of pair contacts and NISO = 3N − 6. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction f of nuclei with order compatible with the bulk (RHCP) crystal decreases sharply with increasing N due to a high propensity for stacking faults, 5-and near-5-fold symmetric structures, and other motifs that preclude RHCP order. While f increases with increasing H, a significant fraction of hyperstatic nuclei for N as small as 11 retain non-RHCP structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of N < ∼ 10 particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. Our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard-core-like repulsive and short-ranged attractive interactions.

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“…Local ordering within these states may be FCC, HCP, or mixed FCC/HCP. Barlow packings [29] are finite-N "grains" (subsets) of any member of S. Since they correspond to "on-pathway" nuclei that can grow into defect-free members of S, they are expected [8] to be be critical to understanding crystal nucleation and growth in systems with hard-core-like repulsions and short-range attractions. It is important to find all such nuclei that can form (as opposed to those that do form under specific conditions); this is most conveniently achieved via exact enumeration of sticky-hardsphere packings.…”

Section: Resultsmentioning

confidence: 99%

Structure and dynamics of model colloidal clusters with short-range attractions

Hoy

2015

Phys. Rev. E

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We examine the structure and dynamics of small isolated N -particle clusters interacting via shortranged Morse potentials. "Ideally preprared ensembles" obtained via exact enumeration studies of sticky hard sphere packings serve as reference states allowing us to identify key statistical-geometrical properties and to quantitatively characterize how nonequilibrium ensembles prepared by thermal quenches at different ratesṪ differ from their equilibrium counterparts. Studies of equilibrium dynamics show nontrival temperature dependence: nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures. Our results should be useful for extending recent experimental studies of small colloidal clusters to examine both equilibrium relaxation dynamics at fixed T and a variety of nonequilibrium phenomena.

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Probable Nature of the Internal Symmetry of Crystals

Abstract: SOME studies pursued by the writer as to the nature of molecules have led him to believe that in the atom-groupings which modern chemistry reveals to us the several atoms occupy distinct portions of space and do not lose their individuality.

Cited by 98 publications

References 0 publications

The glass-forming ability of model metal-metalloid alloys

The glass-forming ability of model metal-metalloid alloys

Structure of finite sphere packings via exact enumeration: Implications for colloidal crystal nucleation

Structure and dynamics of model colloidal clusters with short-range attractions

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