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Determination of Crystal Structures

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...

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...

X-ray Crystallography

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 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...

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.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...

Phase Transitions: Sublimation and Deposition

Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...

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Updated: Jun 6, 2026

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Light scattering by absorbing hexagonal ice crystals in cirrus clouds.

|November 10, 2010

Summary

This study presents an improved ray-optics model for light scattering by ice crystals. The new model accurately simulates single scattering and polarization, enhancing atmospheric optics research.

Area of Science:

Atmospheric Optics
Radiative Transfer Theory

Background:

Accurate simulation of light scattering by atmospheric ice crystals is crucial for understanding Earth's radiative balance.
Existing models often simplify the complex optical properties of hexagonal ice crystals, particularly concerning absorption and polarization.

Purpose of the Study:

To develop an improved ray-optics theory for single scattering and polarization of randomly oriented hexagonal ice crystals.
To incorporate absorption effects and advanced diffraction solutions into the model.
To provide a more accurate tool for atmospheric radiative transfer studies.

Main Methods:

Developed an improved ray-optics theory considering absorption.
Utilized the Chebyshev solution for diffraction integrals.

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Last Updated: Jun 6, 2026

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Employed vector-tracing and random sampling techniques.

Derived equivalent Snell's law and Fresnel formulas for absorbing ice crystals, obtaining two optical constants (m', m″).

Main Results:

The new model computes asymmetry factors, single-scattering albedos, and scattering phase matrix elements.
Comparison with the Takano and Liou model shows improvements in computed results.
The derived optical constants (m', m″) effectively represent the behavior of absorbing ice crystals.

Conclusions:

The developed ray-optics model is practical and significantly improved for simulating light scattering and polarization by ice crystals.
This enhanced model offers greater accuracy for applications in atmospheric science and climate modeling.
The inclusion of absorption and advanced diffraction solutions represents a key advancement in the field.