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Crystal Field Theory - Octahedral Complexes

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 Complexes

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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,...

Crystal Growth: Principles of Crystallization

Crystal Growth: Principles of Crystallization

Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent...

Conformations of Cyclohexane

Conformations of Cyclohexane

Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal...

Polymer Classification: Crystallinity

Polymer Classification: Crystallinity

Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...

Ionic Crystal Structures

Ionic Crystal Structures

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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Updated: Feb 21, 2026

Synthesis and Exfoliation of Discotic Zirconium Phosphates to Obtain Colloidal Liquid Crystals

Synthesis and Exfoliation of Discotic Zirconium Phosphates to Obtain Colloidal Liquid Crystals

Published on: May 25, 2016

Conformal Vortex Crystals.

Raí M Menezes¹, Clécio C de Souza Silva²

¹Departamento de Física, Universidade Federal de Pernambuco, Cidade Universitária, 50670-901, Recife-PE, Brazil.

Scientific Reports

|October 8, 2017

Summary

This summary is machine-generated.

Quantized-flux vortices in superconductors self-organize into conformal crystals at low temperatures. This study proposes methods to engineer these unique, topologically ordered structures for potential experiments.

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Last Updated: Feb 21, 2026

Synthesis and Exfoliation of Discotic Zirconium Phosphates to Obtain Colloidal Liquid Crystals

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Published on: May 25, 2016

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

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Scanning SQUID Study of Vortex Manipulation by Local Contact

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Published on: February 1, 2017

Area of Science:

Condensed matter physics
Superconductivity
Topological matter

Background:

Quantized-flux vortices are fundamental to understanding superconductivity.
Controlling vortex configurations is crucial for technological applications.
Previous research focused on uniform vortex lattices.

Purpose of the Study:

To theoretically investigate nonuniform vortex configurations in superconductors.
To explore the self-organization of vortices into novel structures.
To propose methods for creating and observing these structures.

Main Methods:

Theoretical investigation using numerical simulations.
Analysis of vortex systems under external force fields.
Mathematical mapping of vortex structures.

Main Results:

Vortices self-organize into inhomogeneous conformal crystals below a transition temperature.
These crystals exhibit topological order and can be mapped to triangular lattices.
Above the transition temperature, crystals become unstable, forming polycrystalline structures.

Conclusions:

Conformal vortex crystals represent a new state of matter in superconductors.
A method is proposed to engineer the necessary potential energy profiles.
Potential experimental observations in bulk and thin-film superconductors are suggested.