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Related Concept Videos

The Seven Crystal Systems: Overview01:24

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...
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Crystallographic Point Groups01:29

Crystallographic Point Groups

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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...
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Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

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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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Imperfections in Crystal Structure: Point, Line and Plane Defects01:25

Imperfections in Crystal Structure: Point, Line and Plane Defects

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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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Imperfections in Crystal Structure: Non-Stoichiometric Defects01:29

Imperfections in Crystal Structure: Non-Stoichiometric Defects

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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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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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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Hyperuniformity variation with quasicrystal local isomorphism class.

C Lin1, P J Steinhardt1,2, S Torquato1,2,3,4,5

  • 1Department of Physics, Princeton University, Princeton, NJ 08544, United States of America.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 28, 2017
PubMed
Summary
This summary is machine-generated.

This study reveals that the degree of hyperuniformity in quasicrystals is primarily linked to local atomic arrangements, with the Penrose tiling exhibiting the highest level. This finding impacts understanding of their physical properties.

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Area of Science:

  • Condensed matter physics
  • Materials science
  • Crystallography

Background:

  • Hyperuniformity describes systems with suppressed long-wavelength density fluctuations.
  • Quasicrystals possess unique long-range order without translational periodicity.
  • Understanding hyperuniformity in quasicrystals is key to predicting their physical behavior.

Purpose of the Study:

  • To investigate the relationship between hyperuniformity and local isomorphism classes in quasicrystals.
  • To determine the factors influencing the degree of hyperuniformity in these materials.
  • To identify quasicrystal structures with optimal hyperuniform properties.

Main Methods:

  • Analysis of pentagonal quasicrystal tilings generated via projection from a 5D hypercubic lattice.
  • Quantification of hyperuniformity using the parameter [[Formula: see text]].
  • Examination of local vertex environments and restorability of quasicrystal structures.

Main Results:

  • Hyperuniformity [[Formula: see text]] is mainly determined by the distribution of local vertex environments.
  • Restorability also plays a role in the degree of hyperuniformity.
  • The Penrose local isomorphism class exhibits the highest degree of hyperuniformity (smallest [[Formula: see text]]).

Conclusions:

  • Local structure, particularly vertex environments, is the dominant factor controlling hyperuniformity in quasicrystals.
  • The distinct hyperuniformity levels across different isomorphism classes are expected to influence physical properties like transport.
  • This research provides a framework for designing quasicrystals with tailored physical characteristics.