Diverse densest binary sphere packings and phase diagram

Koshoji, Ryotaro; Kawamura, Masaya; Fukuda, Masahiro; Ozaki, Taisuke

doi:10.1103/physreve.103.023307

Cited by 18 publications

(83 citation statements)

References 34 publications

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“…Despite the long-standing study, even the densest unary sphere packing (DUSPs), which is the simplest case, has been mathematically proven to be Barrow packings in the 2000s. On the other hand, along with the development of computers, the densest binary sphere packings (DBSPs) have been explored by computer simulations [1][2][3][4][5][6][7][8][9], and as a result a total of 28 putative DBSPs are known at the present time [10].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The discovery of 37 putative DTSPs has been realized by an algorithm we have developed [10,16]. The algorithm is based on two methods: The piling-up method and the iterative balance method [10,16]. The pilingup method randomly generates multilayered initial struc-tures, which can be smoothly optimized to packing structures, by randomly choosing the number of spheres on each layer while avoiding a large overlap between spheres.…”

Section: Introductionmentioning

confidence: 99%

“…The iterative balance method optimizes initial structures to packing structures by minimizing the volume of unit cells and the overlaps between spheres simultaneously by the steepest descent method under pressure with the hard sphere potential. The combination of the two methods enables us to explore a vast configuration space and to accurately determine the packing fraction, resulting in the discovery of the 12 putative DBSPs [10] and 37 putative DTSPs [16]. The success indicates that this methodology can be applied to explore unknown DSPs for multi-sized sphere and/or higher dimensional packings.…”

Section: Introductionmentioning

confidence: 99%

“…The correspondence of the DBSPs and crystals was discussed in Ref. [10], and the result showed that many crystals can be understood as DBSPs. For example, the crystal of the LaH 10 , which is one of the superhydrides synthesized under high pressure, corresponds to the XY 10 structure that is one of the DBSPs.…”

Section: Introductionmentioning

confidence: 99%

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Diverse densest ternary sphere packings

Koshoji¹,

Ozaki²

2021

Preprint

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The exploration of the densest structures of multi-sized hard spheres under periodic boundary conditions 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. We classify the 60 DTSPs into seven groups based on how the structural framework is comprised of small, medium, and large spheres. Since the radius ratio of small spheres is not so small relatively, the discovered DTSPs are well-ordered; for example, the (9-7-3) structure is comprised of the cubic unit cell constituted by medium spheres, and the DTSP has the P m 3m symmetry if the structural distortion is corrected. The correspondence of DTSPs with real crystals is found based on the space group, and similarities of structural features in DTSPs are discussed for crystals synthesized experimentally or predicted computationally under high pressure. Our study suggests that the diverse structures of DTSPs can be effectively used as structural prototypes for searching complex crystal structures.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Diverse densest ternary sphere packings

Koshoji¹,

Ozaki²

2021

Preprint

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Rational Design of Superconducting Metal Hydrides via Chemical Pressure Tuning**

Hilleke

Zurek

2022

Angewandte Chemie

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The high critical superconducting temperatures (T c s) of metal hydride phases with clathrate-like hydrogen networks have generated great interest. Herein, we employ the Density Functional Theory-Chemical Pressure (DFT-CP) method to explain why certain electropositive elements adopt these structure types, whereas others distort the hydrogenic lattice, thereby decreasing the T c . The progressive opening of the H 24 polyhedra in MH 6 phases is shown to arise from internal pressures exerted by large metal atoms, some of which may favor an even higher hydrogen content that loosens the metal atom coordination environments. The stability of the LaH 10 and LaBH 8 phases is tied to stuffing of their shared hydrogen network with either additional hydrogen or boron atoms. The predictive capabilities of DFT-CP are finally applied to the YÀ XÀ H system to identify possible ternary additions yielding a superconducting phase stable to low pressures.

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Rational Design of Superconducting Metal Hydrides via Chemical Pressure Tuning**

Hilleke

Zurek

2022

Angew Chem Int Ed

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The high critical superconducting temperatures (Tcs) of metal hydride phases with clathrate‐like hydrogen networks have generated great interest. Herein, we employ the Density Functional Theory‐Chemical Pressure (DFT‐CP) method to explain why certain electropositive elements adopt these structure types, whereas others distort the hydrogenic lattice, thereby decreasing the Tc. The progressive opening of the H24 polyhedra in MH6 phases is shown to arise from internal pressures exerted by large metal atoms, some of which may favor an even higher hydrogen content that loosens the metal atom coordination environments. The stability of the LaH10 and LaBH8 phases is tied to stuffing of their shared hydrogen network with either additional hydrogen or boron atoms. The predictive capabilities of DFT‐CP are finally applied to the Y−X−H system to identify possible ternary additions yielding a superconducting phase stable to low pressures.

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Diverse densest binary sphere packings and phase diagram

Cited by 18 publications

References 34 publications

Diverse densest ternary sphere packings

Diverse densest ternary sphere packings

Rational Design of Superconducting Metal Hydrides via Chemical Pressure Tuning**

Rational Design of Superconducting Metal Hydrides via Chemical Pressure Tuning**

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