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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.
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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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Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
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Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
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Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Correlations in randomly stacked solids.

Amna Khairi Nasr1,2, R Ganesh2

  • 1Sir Winston Churchill Secondary School, St Catharines, Ontario, Canada, L2T 2N1.

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|October 18, 2023
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Summary
This summary is machine-generated.

Sphere packing structures like Barlow stackings and Torquato-Stillinger stackings exhibit exponential decay in layer correlations, even with biases favoring specific arrangements. This finding impacts understanding of solid ordering and synthesis methods.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Sphere packing is a fundamental problem with historical roots, leading to dense structures like face-centered-cubic (FCC) and hexagonal-close-packed (HCP).
  • Barlow stackings represent maximal-density structures, while Torquato-Stillinger stackings are proposed for minimal density while maintaining stability.
  • Understanding layer correlations is crucial for predicting the properties and formation of stacked solids.

Purpose of the Study:

  • To characterize layer correlations in random Barlow and Torquato-Stillinger stacking families.
  • To investigate the effect of chirality bias on layer correlations in Barlow stackings.
  • To relate stacking structures to models in statistical mechanics for analytical insights.

Main Methods:

  • Utilizing the Hägg code to map Barlow stackings to a one-dimensional Ising magnet model.
  • Relating layer correlation functions to moment-generating functions of the Ising model.
  • Analyzing Torquato-Stillinger stackings by mapping them to a combined Ising and three-state Potts model.

Main Results:

  • Random Barlow stackings exhibit exponentially decaying layer correlations.
  • Introducing a chirality bias, favoring FCC ordering, still results in exponential decay, indicating no long-ranged order.
  • Random Torquato-Stillinger stackings also show exponentially decaying correlations, similar in form to Barlow stackings.

Conclusions:

  • Layer correlations in both maximal (Barlow) and minimal (Torquato-Stillinger) density stacking families decay exponentially under random conditions.
  • Even with a bias towards specific structures like FCC, long-range order is not achieved in these stacking models.
  • The findings have implications for the ordering of clusters in stacked solids and for layer-deposition synthesis techniques.