Statistical verification of crystallization in hard sphere packings under densification

Lochmann, K.; Аникеенко, А. В.; Elsner, Antje; Medvedev, N. N.; Stoyan, Dietrich

doi:10.1140/epjb/e2006-00348-9

Cited by 45 publications

(54 citation statements)

References 40 publications

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“…9,14,15,25,48 Alternatively, the Delaunay graph of the particle centers 49,50 is used to define NN. 5,20,23,41,51 In this parameterfree method, every sphere which is connected to a sphere a by a Delaunay edge is considered a NN of a. A rarely used definition is to assign a fixed number n f of NN to each particle, n(a) = n f .…”

Section: Ambiguity Of the Neighborhood Definition And Its Effect On Q Lmentioning

confidence: 99%

“…15 For the study of glasses and super-cooled fluids, q 6 and Q 6 have become the most prominent order parameters when searching for glass transitions [16][17][18][19] and crystalline clusters. 4,8,11,[20][21][22] While q l is defined as a local parameter for each particle, other studies have used global averages of bond angles (Q l ) to detect single-crystalline order across the entire sample. [23][24][25] The BOO parameters q l and Q l are defined as structure metrics for ensembles of N spherical particles.…”

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confidence: 99%

“…6 Frequently, histograms of one order parameter only, namely, q 6 , are used to qualitatively compare disorder in particulate matter systems. 5,20,36,37 Our previous work 38 has raised the caution that local configurations can exist that are clearly non-crystalline but have the same values of q 6 as hcp or fcc environments. Several authors have defined bond order functions 39 closely related to the q l for the identification of crystalline clusters.…”

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confidence: 99%

“…11,15,21,40 As a different application from the identification of locally crystalline domains, it has been proposed to use averages q l over all spheres to quantify the degree of order of a configuration. Averages q 6 have been analyzed (as functions of some control parameters such as temperature, pressure, strain, or packing fraction) for random sphere packings, 20 granular packing experiments, 41 model fluids, 42 molecular dynamics simulations of water, 43 or polymer melts. 44 This use of q l to quantify the overall degree of order implies a monotonous relationship between the value of q l and the degree of order.…”

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confidence: 99%

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Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter

Mickel¹,

Kapfer²,

Schröder‐Turk³

et al. 2013

The Journal of Chemical Physics

255

236

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Local structure characterization with the bond-orientational order parameters q 4 , q 6 ,. . . introduced by Steinhardt et al. has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions and cluster formation. Here we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of neighboring spheres NN(p) around a given central particle p; we show that procedure to select the spheres constituting the neighborhood NN(p) can have greater influence on both the numerical values and qualitative trend of q l than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by q l , leads to a lack of robustness of the q l as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics q ′ l . These q ′ l are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [Europhys. Lett. 90, 34001 (2010); Phys. Rev. E. 85, 030301 (2012)].

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Section: Ambiguity Of the Neighborhood Definition And Its Effect On Q Lmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter

Mickel¹,

Kapfer²,

Schröder‐Turk³

et al. 2013

The Journal of Chemical Physics

255

236

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“…To define the local structural properties of the system we use the bond order parameter method [9], which has been widely used in the context of condensed matter physics [9,10], HS systems [11][12][13][14][15][16][17][18][19][20], complex plasmas [21][22][23][24][25], colloidal suspensions [26][27][28][29][30], granular media [31], etc. In this method the rotational invariants of rank l of both second q l (i) and third w l (i) order are calculated for each sphere i in the system from the vectors (bonds) connecting its center with the centers of its N nn (i) nearest neighboring spheres: (2) where…”

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Structural Properties of Dense Hard Sphere Packings

Klumov

Jin²,

Makse³

2014

J. Phys. Chem. B

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The structural properties of dense random packings of identical hard spheres (HS) are investigated. The bond order parameter method is used to obtain detailed information on the local structural properties of the system for different packing fractions φ, in the range between φ = 0.53 and φ = 0.72. A new order parameter, based on the cumulative properties of spheres distribution over the rotational invariant w6, is proposed to characterize crystallization of randomly packed HS systems. It is shown that an increase in the packing fraction of the crystallized HS system first results in the transformation of the individual crystalline clusters into the global three-dimensional crystalline structure, which, upon further densification, transforms into alternating planar layers formed by different lattice types.The model of hard spheres (HS) is of fundamental importance in condensed matter physics and material science since it successfully reproduces the essential structural properties of liquids, crystals, glasses, colloidal suspensions and granular media. Packings of HS have also been used in solving important problems of information and optimization theories [1,2]. In this Letter we focus on the structural properties of dense three dimensional (3D) HS systems at different packing fractions φ = π 6 ρσ 3 , where ρ = N/V is the density of N hard spheres in a system volume V and σ is the diameter of the spheres. In particular, we take a large set of packings composed of N = 10 4 identical spheres with periodic boundary conditions, generated using Jodrey-Tory (JT) [5,6] and Lubashevsky-Stillinger (LS) [7] algorithms as described in detail in Refs. [3,4]. The corresponding packing fractions vary in the ranges φ ≃ 0.53 − 0.71 and φ = 0.58 − 0.68 for JT and LS protocols, respectively. Both ranges include the random close packing state (RCP) at φ c ≃ 0.64 (Bernal limit) [8]. The main purpose is to look into the details on how densification of the disordered solid state affects the local and global order of the HS system.To define the local structural properties of the system we use the bond order parameter method [9], which has been widely used in the context of condensed matter physics [9,10] In this method the rotational invariants of rank l of both second q l (i) and third w l (i) order are calculated for each sphere i in the system from the vectors (bonds) connecting its center with the centers of its N nn (i) nearest neighboring spheres: (2) whereY lm (r ij ), Y lm are the spherical harmonics and r ij = r i −r j are vectors connecting centers of spheres i and j. In Eq. (2) l l l m 1 m 2 m 3 are the Wigner 3j-symbols, and the summation in the latter expression is performed over all the indexes m i = −l, ..., l satisfying the condition m 1 + m 2 + m 3 = 0. In 3D the densest possible packings of identical hard spheres are known to be face centered cubic (fcc) and hexagonal close-packed (hcp) lattices (φ ≃ 0.74). To detect these structures we calculate the rotational invariants q 4 , q 6 , and w 6 for each sphere using the ...

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2013

Stochastic Geometry and Its Applications

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Statistical verification of crystallization in hard sphere packings under densification

Cited by 45 publications

References 40 publications

Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter

Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter

Structural Properties of Dense Hard Sphere Packings

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