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Crystal Field Theory - Octahedral Complexes02:58

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...
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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Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
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Imperfections in Crystal Structure: Point, Line and Plane Defects

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

Imperfections in Crystal Structure: Stoichiometric Point Defects

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...
Crystallographic Point Groups01:29

Crystallographic Point Groups

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 and...

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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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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Phase-field-crystal methodology for modeling of structural transformations.

Michael Greenwood1, Jörg Rottler, Nikolas Provatas

  • 1Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T1Z1, Canada.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 27, 2011
PubMed
Summary

We developed new free-energy functionals for modeling solids with various crystal structures using the phase-field-crystal method. This approach efficiently simulates phase transformations and elastic properties across different lattice symmetries.

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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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Area of Science:

  • Materials Science
  • Computational Physics
  • Condensed Matter Physics

Background:

  • Phase-field-crystal (PFC) methodology is a powerful tool for simulating materials at atomic scales.
  • Modeling diverse crystallographic symmetries within PFC requires accurate free-energy functionals.
  • Existing models may lack computational efficiency or the flexibility to capture various crystal structures.

Purpose of the Study:

  • To introduce and characterize novel free-energy functionals for the PFC method.
  • To enable the modeling of solids with various crystallographic symmetries, including body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and simple-cubic (sc) lattices.
  • To provide a computationally efficient yet versatile framework for studying phase transformations and elastic properties.

Main Methods:

  • Development of free-energy functionals inspired by classical density-functional theory.
  • Minimal description of direct correlation function modes for computational efficiency.
  • Introduction of parameters to control crystal structure, temperature, and surface energies.
  • Dynamic simulation of phase transformations and coexistence phenomena.

Main Results:

  • Successful characterization of free-energy functionals for multiple crystallographic symmetries.
  • Computation of the fcc-bcc-liquid coexistence phase diagram in the temperature-density plane.
  • Demonstration of hcp-liquid coexistence simulation from a seeded nucleus.
  • Quantification of elastic constant dependence on model parameters and tuning of elastic anisotropy.

Conclusions:

  • The developed free-energy functionals offer a versatile and computationally efficient approach for modeling diverse solid structures within the PFC framework.
  • The model allows for the study of phase transformations and the prediction of elastic properties across different lattice symmetries.
  • This work provides a valuable tool for exploring materials behavior with varying crystallographic characteristics.