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Related Concept Videos

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
Imagine taking a large number of identical...
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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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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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X-ray Crystallography02:18

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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
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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.
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Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
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Updated: Aug 22, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Localization in Two-Dimensional Quasicrystalline Lattices.

Luis Antonio González-García1, Héctor Alva-Sánchez1, Rosario Paredes1

  • 1Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, México D. F. 01000, Mexico.

Entropy (Basel, Switzerland)
|November 11, 2022
PubMed
Summary

Localization in Bose gases within quasicrystalline lattices was studied. Findings reveal specific potential depths trigger localization, with five-fold symmetry localizing earlier than eight-fold and twelve-fold symmetries.

Keywords:
Bose–Einstein condensatesGross–Pitaevskii equationlocalization in quasicrystals

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Bose gases exhibit unique quantum phenomena when confined.
  • Quasicrystalline lattices offer novel potential landscapes for atomic systems.
  • Understanding localization is key to controlling quantum states.

Purpose of the Study:

  • To investigate the emergence of localization in a Bose gas.
  • To analyze localization in quasicrystalline lattices with 5, 8, and 12-fold rotational symmetry.
  • To determine the influence of potential depth on localization phenomena.

Main Methods:

  • Mean-field analysis of a weakly interacting Bose gas.
  • Calculation of inverse participation ratio (IPR) and Shannon entropy.
  • Statistical study of stationary density profiles.

Main Results:

  • Localization was identified as a function of potential depth for each lattice symmetry.
  • Condensate density localized from partial to full site occupancy.
  • Localization occurred at (6ER,9ER) for five-fold symmetry and (12ER,15ER) for octagonal and dodecagonal symmetries.

Conclusions:

  • Potential depth is a critical parameter controlling Bose gas localization in quasicrystals.
  • The degree of localization depends on the specific quasicrystalline symmetry.
  • This research provides insights into quantum state control in complex potentials.