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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...

Electric Field of a Non Uniformly Charged Sphere

Electric Field of a Non Uniformly Charged Sphere

Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric...

Electric Field of a Charged Disk

Electric Field of a Charged Disk

The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...

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...

Gauss's Law: Problem-Solving

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...

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Related Experiment Video

Updated: Apr 16, 2026

Preparing a Celadonite Electron Source and Estimating Its Brightness

Preparing a Celadonite Electron Source and Estimating Its Brightness

Published on: November 5, 2019

Density functional theory for field emission from carbon nano-structures.

¹The State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, PR China.

Ultramicroscopy

|March 10, 2015

Summary

Investigating electron field emission in nanomaterials like carbon nanotubes and graphene, this study uses a first-principles approach for deeper insights into quantum mechanical processes and emission characteristics.

Keywords:

Carbon nanotube Density functional theory Electron field emission Graphene

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Last Updated: Apr 16, 2026

Preparing a Celadonite Electron Source and Estimating Its Brightness

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Published on: November 5, 2019

Electrochemical Etching and Characterization of Sharp Field Emission Points for Electron Impact Ionization

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Published on: February 2, 2012

Area of Science:

Quantum Mechanics
Materials Science
Condensed Matter Physics

Background:

Electron field emission is a quantum mechanical process involving quasi-particles transitioning from an emitter to vacuum.
Understanding fundamental concepts like work-function and emission current density is crucial for device applications.

Purpose of the Study:

To investigate fundamental concepts of electron field emission.
To explore the application of these concepts to nanomaterials such as carbon nanotubes and graphene.
To introduce and justify a first-principles approach for analyzing field emission in nanostructures.

Main Methods:

Utilizing a multi-scale algorithm based on density functional theory.
Examining key field emission parameters: field enhancement factor, work-function, edge barrier, and emission current density.
Applying the methodology to carbon nanotubes and graphene as model systems.

Main Results:

The study provides a detailed analysis of electron field emission in carbon nanotubes and graphene.
The first-principles approach offers a more accurate quantitative description of the emission process.
Deeper insights into the physics governing field emission from nanostructures are achieved.

Conclusions:

A first-principles, density functional theory-based approach is necessary for accurate and insightful analysis of field emission from nanostructures.
This methodology enhances the understanding of quantum mechanical many-body effects in electron emission.
The findings are critical for advancing the design and application of field emission devices based on nanomaterials.