DEM construction of binary hard sphere crystals and radical tessellation

Wang, Defeng; An, Xizhong; Gou, Dazhao; Zhao, Hongwei; Wang, Lin; Huang, Fei

doi:10.1063/1.5052478

Cited by 8 publications

(8 citation statements)

References 60 publications

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“…It was proved only in the 2000s that the densest unary sphere packing (DUSPs) is the Barlow packings [1]. The densest binary sphere packings (DBSPs) for given compositions are not determined in a mathematically rigorous way, however, there have been several studies that estimate the DBSPs by numerical calculations [2][3][4][5][6][7][8]. In 2012, Hopkins et al explored the DBSPs under the restriction that the number of spheres in the unit cell with periodic boundary condition is less than or equal to 12 and constructed the phase diagram for the first time [9,10].…”

Section: Introductionmentioning

confidence: 99%

Densest ternary sphere packings

Koshoji

Ozaki²

2021

Phys. Rev. E

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We present our exhaustive exploration of the densest ternary sphere packings (DTSPs) for 45 radius ratios and 237 kinds of compositions, which is a packing problem of three kinds of hard spheres with different radii, under periodic boundary conditions by a random structure searching method. To efficiently explore DTSPs we further develop the searching method based on the pilingup and iterative balance methods [Koshoji et al., Phys. Rev. E 103, 023307 (2021)]. The unbiased exploration identifies diverse 38 putative DTSPs appearing on phase diagrams in which 37 DTSPs of them are discovered in the study. The structural trend of DTSPs changes depending especially on the radius of small spheres. In case that the radius of small spheres is relatively small, structures of many DTSPs can be understood as derivatives of densest binary sphere packings (DBSPs), while characteristic structures specific to the ternary system emerge as the radius of small spheres becomes larger. In addition to DTSPs, we reveal a lot of semi-DTSPs (SDTSPs) which are obtained by excluding DBSPs in the calculation of phase diagram, and investigate the correspondence of DTSPs and SDTSPs with real crystals based on the space group, showing a considerable correspondence of SDTSPs having high symmetries with real crystals including Cu2GaSr and ThCr2Si2 structures. Our study suggests that the diverse structures of DBSPs, DTSPs, and SDTSPs can be effectively used as structural prototypes for searching complex crystal structures.

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Section: Introductionmentioning

confidence: 99%

Densest ternary sphere packings

Koshoji

Ozaki²

2021

Phys. Rev. E

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“…The largest pore radius is observed for a configuration that is close to mono-modal simple cubic (SC) packing. It is well known that the pore size of an SC lattice is a factor 0.55/0.41 ≈ 1.34 larger than that of the initial body-centered (BCC) cubic lattice [74]. This ratio equals the ratio 7.4/5.5 ≈ 1.34 observed for the largest strain rate in Figure 11a.…”

Section: Pore Size Analysismentioning

confidence: 69%

Ionic Polymer Nanocomposites Subjected to Uniaxial Extension: A Nonequilibrium Molecular Dynamics Study

2021

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We explore the behavior of coarse-grained ionic polymer nanocomposites (IPNCs) under uniaxial extension up to 800% strain by means of nonequilibrium molecular dynamics simulations. We observe a simultaneous increase of stiffness and toughness of the IPNCs upon increasing the engineering strain rate, in agreement with experimental observations. We reveal that the excellent toughness of the IPNCs originates from the electrostatic interaction between polymers and nanoparticles, and that it is not due to the mobility of the nanoparticles or the presence of polymer–polymer entanglements. During the extension, and depending on the nanoparticle volume fraction, polymer–nanoparticle ionic crosslinks are suppressed with the increase of strain rate and electrostatic strength, while the mean pore radius increases with strain rate and is altered by the nanoparticle volume fraction and electrostatic strength. At relatively low strain rates, IPNCs containing an entangled matrix exhibit self-strengthening behavior. We provide microscopic insight into the structural, conformational properties and crosslinks of IPNCs, also referred to as polymer nanocomposite electrolytes, accompanying their unusual mechanical behavior.

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“…The longstanding effort to the analytic identification of the densest unary sphere packing (DUSP) has been fulfilled in the 2000s despite the simpleness of the problem [1]. Likewise, analytic identification of the densest binary sphere packings (DBSPs) is also too difficult to prove, however, the development of computers has been enabling us to explore the DBSPs by computer simulations [2][3][4][5][6][7][8][9][10]. As a result, a total of 28 putative DBSPs are known at the present time [11].…”

Section: Introductionmentioning

confidence: 99%

Diverse densest ternary sphere packings

Koshoji

Ozaki

2022

J. Phys. Commun.

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The exploration of the densest spheres packings is a fundamental problem in mathematics and a wide variety of sciences including materials science. We present our exhaustive computational exploration of the densest ternary sphere packings (DTSPs) for 451 radius ratios and 436 compositions on top of our previous study [Koshoji and Ozaki, Phys. Rev. E 104, 024101 (2021)]. The unbiased exploration by a random structure searching method discovers diverse 22 putative DTSPs, and thereby 60 putative DTSPs are identified in total including the 38 DTSPs discussed by the previous study. Some of the discovered DTSPs are well-ordered, for example, the medium spheres in the (9-7-3) structure are placed in a straight line with comprising the unit cell, and the DTSP has the Pm-3m symmetry if the structural distortion is corrected. At a considerable number of radius ratios, the highest packing fractions are achieved by the phase separations consisting of only the FCC and/or the putative densest binary sphere packings (DBSPs) for all compositions. The trend is becoming more evident as the small and medium spheres are getting larger, which suggests either the binary packings are actually the densest packings or that the dense ternary packings have unit cells larger than those in this study. On the other hand, the number of the DTSPs increase as the particle size of small spheres gets small. The structural diversity indicates that many unknown DTSPs may hide in a very narrow range of radius ratio where the size of small spheres is smaller due to the competition with respect to the packing fractions of many structural candidates. Finally, we discuss the correspondence of the DTSPs with real crystals based on the space group. Our study suggests that the diverse structures of DTSPs can be effectively used as structural prototypes for searching multinary crystal structures.

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DEM construction of binary hard sphere crystals and radical tessellation

Cited by 8 publications

References 60 publications

Densest ternary sphere packings

Densest ternary sphere packings

Ionic Polymer Nanocomposites Subjected to Uniaxial Extension: A Nonequilibrium Molecular Dynamics Study

Diverse densest ternary sphere packings

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