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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...

Lattice Centering and Coordination Number

Lattice Centering and Coordination Number

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
Imagine taking a large number of identical...

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,...

Trends in Lattice Energy: Ion Size and Charge

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:

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...

Metallic Solids

Metallic Solids

Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Published on: August 2, 2019

High topological charge lasing in quasicrystals.

Kristian Arjas¹, Jani Matti Taskinen¹, Rebecca Heilmann¹

¹Department of Applied Physics, Aalto University School of Science, Espoo, Finland.

Nature Communications

|November 5, 2024

Summary

Researchers achieved high-order topological charge lasing in quasicrystals, overcoming limitations of periodic lattices. This opens new avenues for advanced photonic devices and fundamental physics research.

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Area of Science:

Photonics and Optics
Condensed Matter Physics
Materials Science

Background:

Photonic modes with polarization vortices possess topological charge.
Lasing with high topological charges is limited in periodic lattices due to symmetry constraints.

Purpose of the Study:

To experimentally demonstrate lasing with higher-order topological charges.
To explore the potential of quasicrystals for advanced photonic applications.

Main Methods:

Utilized quasicrystals with specific symmetries to support higher-order topological charges.
Employed group theory to identify electromagnetic field nodes.
Integrated lossy plasmonic nanoparticles at strategic positions to maximize optical gain.

Main Results:

Successfully demonstrated lasing with topological charges up to +/-19 in quasicrystals.
Observed intricate ordered structures in reciprocal space corresponding to increasing topological charges.
Quasicrystal design enabled overcoming symmetry limitations of periodic lattices.

Conclusions:

Quasicrystals provide a novel platform for achieving high-order topological charge lasing.
This research paves the way for fundamental studies of topological defects and coherent light beams.
Potential applications include omni-directional and flat-band-like lasing devices.