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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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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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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...
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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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Dimensional Analysis03:40

Dimensional Analysis

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Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
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Dimensional Analysis01:27

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Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
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Related Experiment Video

Updated: Jan 25, 2026

Fabrication of 1-D Photonic Crystal Cavity on a Nanofiber Using Femtosecond Laser-induced Ablation
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Hyper collimation ability of two-dimensional photonic crystals.

Guangzhe Ru, Yaoxian Zheng, Jiaxi Liu

    Optics Express
    |May 5, 2019
    PubMed
    Summary

    Researchers explored photonic crystals (PhCs) for beam collimation, discovering a rectangular lattice design with "hyper collimation ability." This breakthrough offers potential for advanced photonic circuits.

    Area of Science:

    • Optics and Photonics
    • Materials Science

    Background:

    • Photonic crystals (PhCs) offer unique light manipulation properties.
    • Evaluating the collimation ability of PhC structures is crucial for device design.

    Purpose of the Study:

    • To theoretically investigate and design PhC structures with enhanced beam collimation.
    • To introduce a new metric for quantifying collimation ability.

    Main Methods:

    • Theoretical investigation of photonic crystal equi-frequency contours (EFCs).
    • Design and analysis of a rectangular lattice PhC structure.
    • Introduction of the normalized collimation length (NCL) as an evaluation parameter.

    Main Results:

    • A rectangular lattice PhC design exhibiting ultra-high, or

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  • hyper collimation ability
  • was identified.
  • The study revealed a critical trade-off between the range and flatness of EFC "flat segments" for optimal collimation.
  • The normalized collimation length (NCL) effectively quantifies PhC collimation performance.

    • Conclusions:

    • Tuning the aspect ratio of rectangular lattice PhCs enables hyper collimation.
    • Theoretical predictions align well with numerical simulations of beam propagation.
    • PhCs with hyper collimation ability hold significant promise for photonic integrated circuits and devices.