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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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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Imagine taking a large number of identical...
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Crystal Field Theory - Octahedral Complexes

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.
CFT focuses on...
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Structures of Solids

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...
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
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Metallic Solids

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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Unit Cells

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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Crystallizing Electrons with Artificially Patterned Lattices.

Trevor G Stanfill1, Daniel N Shanks1, Michael R Koehler2

  • 1Department of Physics, The University of Arizona, Tucson, Arizona 85721, United States.

Nano Letters
|July 9, 2026
PubMed
Summary

Researchers created stable Wigner crystals at higher temperatures using nanofabrication. This engineered potential landscape allows for real-time control over crystalline states, transforming Wigner crystals into reconfigurable quantum matter.

Keywords:
MoSe2Wigner crystalsexcitonsgeneralized Wigner crystalstelegraph noisetransition metal dichalcogenides

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Nanotechnology

Background:

  • Wigner crystals traditionally require ultralow temperatures for stability.
  • Moiré superlattices offer higher temperature stability but lack tunability.
  • Existing methods for Wigner crystal formation are limited by fixed lattice geometries.

Purpose of the Study:

  • To develop a novel method for creating stable Wigner crystals at higher temperatures.
  • To overcome the limitations of delicate stacking and fixed geometry in existing Wigner crystal platforms.
  • To achieve real-time tunability and control over Wigner crystal states.

Main Methods:

  • Utilizing high-resolution nanofabrication to pattern a nanoscale triangular lattice.
  • Integrating a patterned graphene gate with a monolayer MoSe2 semiconductor.
  • Engineering a potential landscape to localize electrons into Wigner crystal states.

Main Results:

  • Achieved stable Wigner crystal states persisting up to 15 K and densities of 2 × 1012 cm-2.
  • Demonstrated an order of magnitude improvement in stability compared to pristine monolayer MoSe2.
  • Enabled real-time switching between stable and unstable crystalline states via gate-voltage control.

Conclusions:

  • The lithographic approach bypasses constraints of traditional Wigner crystal formation.
  • Engineered potential landscapes offer a new platform for reconfigurable quantum matter.
  • This method transforms Wigner crystals from fragile, static phases into tunable systems.