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Related Concept Videos

X-ray Crystallography02:18

X-ray Crystallography

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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.
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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.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
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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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Crystal Field Theory - Octahedral Complexes02:58

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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.
CFT focuses on...
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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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Crystal Field Theory - Tetrahedral and Square Planar Complexes

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Tetrahedral Complexes
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Updated: Jun 18, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Enhancing (quasi-)long-range order in a two-dimensional driven crystal.

R Maire1, A Plati1

  • 1Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, 91405 Orsay, France.

The Journal of Chemical Physics
|August 1, 2024
PubMed
Summary
This summary is machine-generated.

Non-equilibrium driving can maintain crystalline order in 2D systems, overcoming thermal fluctuations. This research explores methods to enhance quasi-long-range order even with a global thermal bath, offering insights for experimental systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics
  • Non-equilibrium Systems

Background:

  • The Hohenberg-Mermin-Wagner (HMW) theorem typically prohibits long-range translational order in 2D equilibrium systems.
  • Athermal driving mechanisms can induce hyperuniformity and violate the HMW theorem, but thermal fluctuations often disrupt this order.
  • Understanding how to maintain order in driven 2D systems with thermal baths is crucial.

Purpose of the Study:

  • To investigate methods for suppressing density fluctuations and preserving long-range order in 2D systems under non-equilibrium conditions.
  • To theoretically model and numerically simulate systems driven by both thermal baths and momentum-conserving noise.
  • To demonstrate the arbitrary enhancement of quasi-long-range order by tuning driving and dissipative parameters.

Main Methods:

  • Development of a theoretical model for a harmonic crystal subjected to a thermal bath and momentum-conserving noise.
  • Analytical derivation of density fluctuations and translational order observables.
  • Numerical simulations of a hard-disk solid driven out-of-equilibrium by active collisions.

Main Results:

  • The model predicts large-wavelength phonons that thermalize at a vanishing effective temperature, explaining HMW theorem violations.
  • Numerical simulations show that tuning driving and dissipative parameters can arbitrarily enhance quasi-long-range order.
  • The degree of order enhancement is independent of the global noise amplitude.

Conclusions:

  • Non-equilibrium driving offers a pathway to achieve and control quasi-long-range order in 2D systems, even in the presence of thermal noise.
  • The findings provide a theoretical framework and practical insights for manipulating order in driven soft matter and granular systems.
  • Experimental realization in granular systems is proposed, bridging theory and practice.