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Metallic Solids

Metallic Solids

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.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...

The Seven Crystal Systems: Overview

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Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...

Ionic Crystal Structures

Ionic Crystal Structures

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.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...

Structures of Solids

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...

Crystallographic Point Groups

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...

VSEPR Theory and the Basic Shapes

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Construction and Systematical Symmetric Studies of a Series of Supramolecular Clusters with Binary or Ternary Ammonium Triphenylacetates

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Maximum and minimum stable random packings of Platonic solids.

Jessica Baker¹, Arshad Kudrolli

¹Department of Physics, Clark University, Worcester, Massachusetts 01610, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2011

Summary

Particle shape significantly impacts how objects pack. The cube, capable of tessellating space, achieved the highest packing density among Platonic solids, with density decreasing as the number of sides increased.

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Area of Science:

Materials Science
Physics
Statistical Mechanics

Background:

The relationship between particle geometry and packing efficiency is a fundamental concept in materials science and physics.
Platonic solids, a specific class of convex polyhedra, offer a geometrically defined set of shapes for studying packing phenomena.

Purpose of the Study:

To experimentally measure the volume fraction (packing density) of Platonic solids in both random loose packing (rlp) and densest packing (rcp) configurations.
To investigate the influence of particle shape, specifically the number of sides and surface friction, on packing efficiency.

Main Methods:

Utilized plastic dice shaped as Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron).
Employed fluidization and mechanical vibration techniques to achieve stable random loose and densest packing states.
Conducted additional experiments with ceramic tetrahedrons to assess the effect of friction.

Main Results:

Packing densities (ϕ) were measured: ϕ(rlp) ranged from 0.50 to 0.54, and ϕ(rcp) ranged from 0.59 to 0.67, with a standard deviation of approximately ±0.01.
The cube, the only Platonic solid that can tessellate space, exhibited the highest packing density across all protocols.
A trend of decreasing packing density with an increasing number of sides was observed for Platonic solids. Higher friction, as seen with ceramic tetrahedrons, resulted in lower packing densities.

Conclusions:

Particle shape, particularly the ability to tessellate and the number of sides, critically influences packing efficiency.
The packing densities achieved are systematically lower than theoretical maximums for frictionless solids and for spheres in loose packing.
Surface friction plays a significant role, reducing packing density, as demonstrated by the ceramic tetrahedron experiments.