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Related Concept Videos

Determination of Crystal Structures01:29

Determination of Crystal Structures

In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
X-ray Crystallography02:18

X-ray Crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
Crystal Field Theory - Octahedral Complexes02:58

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 Complexes02:46

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,...
Ionic Crystal Structures02:42

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...
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

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 requirements are not imposed on the...

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Determining the Ice-binding Planes of Antifreeze Proteins by Fluorescence-based Ice Plane Affinity
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Published on: January 15, 2014

Polarized light scattering by hexagonal ice crystals: theory.

Q Cai1, K N Liou

  • 1University of Utah, Meteorology Department, Salt Lake City, Utah 84112, USA.

Applied Optics
|April 17, 2010
PubMed
Summary
This summary is machine-generated.

A new scattering model for hexagonal ice crystals provides complete polarization information. This model, based on ray tracing, accurately predicts light scattering by ice crystals, crucial for atmospheric studies.

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Area of Science:

  • Atmospheric optics and radiative transfer.
  • Computational physics and electromagnetics.

Background:

  • Accurate modeling of light scattering by atmospheric ice crystals is essential for understanding climate and remote sensing.
  • Previous models often lacked complete polarization information or were limited in their treatment of crystal orientations and shapes.

Purpose of the Study:

  • To develop a comprehensive scattering model for arbitrarily oriented hexagonal ice crystals (columns and plates).
  • To incorporate polarization information, geometric optics (reflection, refraction), and diffraction effects.
  • To provide a traceable and analytic procedure for calculating scattered electric fields and scattering phase matrices.

Main Methods:

  • Developed a ray tracing principle to model light interaction with hexagonal ice crystals.
  • Included contributions from geometric reflection, refraction, and Fraunhofer diffraction.
  • Derived analytic expressions for scattered electric fields and the 16-element scattering phase matrix for randomly oriented crystals.

Main Results:

  • Computed scattering phase matrix elements for large columns and small plates revealed distinct features across scattering angles.
  • The model successfully predicted the scattering phase function, degree of linear polarization, and depolarization ratio.
  • Theoretical results showed good agreement with experimental data, particularly for the depolarization ratio.

Conclusions:

  • The developed geometric optics-based scattering model accurately simulates light polarization by hexagonal ice crystals.
  • The model's agreement with experimental data validates its utility for atmospheric optics research.
  • This provides a robust tool for interpreting remote sensing data and improving climate models.