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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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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

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Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
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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
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Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
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Molecular crystalline solids, such as ice, sucrose (table sugar), and iodine, are solids that are composed of neutral molecules as their constituent units. These molecules are held together by weak intermolecular forces such as London dispersion forces, dipole-dipole interactions, or hydrogen bonds, which...
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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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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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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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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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λ-Jellium Model for the Anomalous Hall Crystal.

Tomohiro Soejima1, Junkai Dong1,2, Ashvin Vishwanath1

  • 1Harvard University, Department of Physics, Cambridge, Massachusetts 02138, USA.

Physical Review Letters
|November 17, 2025
PubMed
Summary
This summary is machine-generated.

We introduce λ-jellium, a model exploring Berry curvature

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Area of Science:

  • Condensed Matter Physics
  • Quantum Geometry
  • Topological Matter

Background:

  • The standard jellium model exhibits metallic and Wigner crystal phases.
  • Its vanishing Berry curvature limits studies of systems with strong interactions and quantum geometry.
  • The anomalous Hall crystal (AHC) is a topological Wigner crystal variant with nonzero Chern number.

Purpose of the Study:

  • Introduce λ-jellium, a tunable extension of the jellium model.
  • Systematically explore Berry curvature's effect on electron crystallization.
  • Investigate the phase diagram of interacting electrons with nontrivial quantum geometry.

Main Methods:

  • Self-consistent Hartree-Fock calculations.
  • Phase diagram analysis of the λ-jellium model.
  • Exploration of electron crystallization driven by Berry curvature.

Main Results:

  • The AHC phase is extensive in the phase diagram.
  • Identified two distinct Wigner crystal phases and two Fermi liquid phases.
  • Observed a continuous phase transition between AHC and a Wigner crystal phase.
  • Discovered nontriangular lattice geometries in parts of the AHC phase.

Conclusions:

  • The λ-jellium model provides a tunable platform for studying electron systems with Berry curvature.
  • Quantum geometry significantly influences electron crystallization and phase transitions.
  • The model serves as a foundation for advanced numerical studies in topological condensed matter.