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Related Concept Videos

Metallic Solids02:37

Metallic Solids

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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
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Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
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Three-Dimensional Particle Shape Analysis Using X-ray Computed Tomography: Experimental Procedure and Analysis Algorithms for Metal Powders
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Densest ternary sphere packings.

Ryotaro Koshoji1, Taisuke Ozaki1

  • 1Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan.

Physical Review. E
|September 16, 2021
PubMed
Summary
This summary is machine-generated.

We discovered 38 new densest ternary sphere packings (DTSPs) by exploring 237 compositions. These structures, including semi-DTSPs, offer prototypes for complex crystal structures, especially those with high symmetries.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Crystallography

Background:

  • Sphere packing problems are fundamental in materials science and physics.
  • Understanding ternary sphere packings (DTSPs) is crucial for designing new materials.
  • Existing methods for exploring sphere packings require enhancement for complex systems.

Purpose of the Study:

  • To exhaustively explore densest ternary sphere packings (DTSPs) for various radius ratios and compositions.
  • To develop an efficient random structure searching method for DTSPs.
  • To investigate the relationship between DTSPs, semi-DTSPs (SDTSPs), and real crystal structures.

Main Methods:

  • Utilized a random structure searching method enhanced by piling-up and iterative balance techniques.
  • Explored 45 radius ratios and 237 compositions under periodic boundary conditions.
  • Analyzed phase diagrams to identify DTSPs and SDTSPs, comparing them with known crystal structures via space group analysis.

Main Results:

  • Identified 38 putative DTSPs, with 37 being novel discoveries.
  • Observed that DTSP structural trends are highly dependent on the radius of smaller spheres.
  • Revealed numerous SDTSPs with high symmetries, showing considerable correspondence with real crystals like Cu2GaSr and ThCr2Si2 structures.

Conclusions:

  • The developed searching method efficiently identifies diverse DTSPs and SDTSPs.
  • Ternary sphere packing structures provide valuable prototypes for discovering complex crystal structures.
  • The findings offer a pathway for designing novel materials with specific properties based on packing structures.