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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.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability....
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Structures of Solids02:22

Structures of Solids

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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...
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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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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.
Types of Unit Cells
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Unit Cells01:18

Unit Cells

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A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...
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Ionic Crystal Structures02:42

Ionic Crystal Structures

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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.
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...
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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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Packing of nonoverlapping cubic particles: Computational algorithms and microstructural characteristics.

Hessam Malmir1, Muhammad Sahimi1, M Reza Rahimi Tabar2

  • 1Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA.

Physical Review. E
|January 14, 2017
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Summary

This study characterizes cubic particle packings using a modified random sequential addition algorithm. Results reveal long-range order in dense packings, with a maximum packing fraction of approximately 0.57.

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Area of Science:

  • Materials Science
  • Statistical Mechanics
  • Computational Physics

Background:

  • Packing of cubic particles is relevant to diverse fields including materials science, colloid physics, and geological processes like CO2 sequestration.
  • Understanding the microstructure and statistical properties of these packings is crucial but not well-established.

Purpose of the Study:

  • To present a detailed simulation and microstructural characterization of nonoverlapping monodisperse cubic particle packings.
  • To investigate the structural order and statistical descriptors as a function of packing density.

Main Methods:

  • A modified random sequential addition (RSA) algorithm was developed to generate cubic particle packings.
  • Various microstructural descriptors were computed, including radial distribution, correlation, probability, cluster, lineal-path, and pore-size distribution functions.

Main Results:

  • The study identified the existence of both spatial and orientational long-range order with increasing packing density.
  • The maximum packing fraction achieved using the RSA method was found to be approximately 0.57.
  • Computed descriptors included specific surface and mean chord length.

Conclusions:

  • The developed RSA method enables the generation and characterization of cubic particle packings.
  • The findings provide insights into the ordered structures formed by cubic particles at high densities, relevant to liquid crystal-like states.