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Related Concept Videos

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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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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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...
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The number of independent ways a gas molecule can move along straight line, rotate, and vibrate is called its degrees of freedom. Supposing d represents the number of degrees of freedom of an ideal gas, the molar heat capacity at constant volume of an ideal gas in terms of d is
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Theory of Metallic Conduction01:17

Theory of Metallic Conduction

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The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the results of quantum mechanics. It is called the theory of metallic conduction.
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...
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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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Related Experiment Video

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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Heat conduction in a three dimensional anharmonic crystal.

Keiji Saito1, Abhishek Dhar

  • 1Graduate School of Science, University of Tokyo, Tokyo, 113-0033, Japan. saitoh@spin.phys.s.u-tokyo.ac.jp

Physical Review Letters
|April 7, 2010
PubMed
Summary

This study simulates heat conduction in a 3D lattice, finding thermal conductivity kappa is finite. This provides the first verification of Fourier

Area of Science:

  • Condensed Matter Physics
  • Computational Physics
  • Statistical Mechanics

Background:

  • Heat conduction is fundamental to understanding energy transport in materials.
  • Fourier's Law describes heat conduction but requires verification in complex systems.
  • Anharmonic lattices present challenges for theoretical modeling of thermal properties.

Purpose of the Study:

  • To investigate the crossover from 1D to 3D behavior in thermal conductivity.
  • To determine if thermal conductivity (kappa) diverges in a 3D anharmonic lattice.
  • To verify Fourier's Law in a system lacking pinning effects.

Main Methods:

  • Nonequilibrium simulations were employed to model heat conduction.
  • Studies focused on three-dimensional anharmonic lattice slabs of varying dimensions (N and W).

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  • Analysis examined the aspect ratio (W/N) to understand dimensional crossover.

    • Main Results:

    • A crossover from 1D to 3D thermal conductivity behavior was observed.
    • This crossover occurred at a small aspect ratio (W/N) for large lattice lengths (N).
    • The three-dimensional system exhibited a finite, nondiverging thermal conductivity (kappa).

    Conclusions:

    • The findings confirm a finite thermal conductivity in the simulated 3D anharmonic lattice.
    • This study offers the first numerical verification of Fourier's Law in a system without pinning.
    • Results contribute to understanding heat transport mechanisms in complex materials.