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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

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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

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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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 Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

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Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific...
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Crystallographic Point Groups01:29

Crystallographic Point Groups

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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...
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Unit Cells01:18

Unit Cells

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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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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.
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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Three-Dimensional Icosahedral Phase Field Quasicrystal.

P Subramanian1, A J Archer2, E Knobloch3

  • 1Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom.

Physical Review Letters
|August 27, 2016
PubMed
Summary
This summary is machine-generated.

We explored 3D quasicrystal formation using a phase field crystal model. Nonlinear density wave interactions stabilize these complex structures, revealing key parameters for their stable formation in soft matter.

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Area of Science:

  • Materials Science
  • Condensed Matter Physics
  • Crystallography

Background:

  • Quasicrystalline structures exhibit unique atomic arrangements not found in traditional crystals.
  • Understanding the formation mechanisms of three-dimensional (3D) quasicrystals is crucial for materials design.

Purpose of the Study:

  • To investigate the formation and stability of 3D icosahedral quasicrystalline structures.
  • To identify the critical parameters and conditions for stable 3D quasicrystal formation.

Main Methods:

  • Utilized a dynamic phase field crystal (PFC) model.
  • Analyzed nonlinear interactions between density waves at multiple length scales.
  • Determined the phase diagram and free energy landscape.

Main Results:

  • Nonlinear interactions between density waves stabilize 3D quasicrystals.
  • Identified specific parameter values for the quasicrystal to be the global minimum free energy state.
  • Demonstrated that 2D quasicrystal formation traits are present in 3D systems.

Conclusions:

  • 3D soft matter quasicrystal formation is achievable under specific conditions.
  • The study highlights essential characteristics for designing and synthesizing 3D quasicrystals.
  • Phase field crystal modeling provides a robust framework for studying complex ordered matter.