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A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
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Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
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Non-stoichiometric defects refer to a type of defect in the crystal structure of a compound where the ratio of its constituent elements deviates from the ideal stoichiometric ratio. There are two main types of non-stoichiometric defects: metal excess defects and metal deficiency defects.Metal excess defects occur when there is a slight surplus of metal ions than what is required by the stoichiometric ratio of the compound. For example, heating a sodium chloride crystal in sodium vapor results...
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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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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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Lumber defects, which can affect both the appearance and structural integrity of wood, include a variety of growth and manufacturing flaws. Growth defects such as knots and knotholes occur where branches were once attached to the tree trunk, with knotholes forming when these knots fall out. Other natural defects include decay and insect damage, which compromise the wood's strength and durability.
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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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Honeycomb lattices with defects.

Meryl A Spencer1, Robert M Ziff2

  • 1Department of Physics, University of Michigan, Ann Arbor, Michigan 48104, USA.

Physical Review. E
|May 14, 2016
PubMed
Summary
This summary is machine-generated.

Researchers created a new random honeycomb lattice by swapping bonds, useful for studying percolation. This model allows for a range of random network properties, aiding in the analysis of disordered systems.

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Area of Science:

  • Materials Science
  • Statistical Physics
  • Network Science

Background:

  • Honeycomb lattices are fundamental structures in various scientific fields.
  • Understanding disordered systems is crucial for modeling real-world phenomena.

Purpose of the Study:

  • To introduce and analyze a novel variant of the honeycomb lattice with engineered defects.
  • To investigate the percolation properties of these randomly tiled lattices.

Main Methods:

  • A computational approach was employed to study lattices with randomly exchanged bonds.
  • The distribution of polygon edges in the random tiling was analyzed.

Main Results:

  • Percolation thresholds were calculated as a function of defect density.
  • The findings align with theoretical predictions for three-coordinated lattices with controlled degree distribution variance.

Conclusions:

  • The introduced lattice variant provides a tunable platform for studying percolation.
  • These random lattices are valuable for modeling diverse disordered systems and their properties.