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Structures of Solids

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...

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...

The Seven Crystal Systems: Overview

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...

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...

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,...

Imperfections in Crystal Structure: Stoichiometric Point Defects

Imperfections in Crystal Structure: Stoichiometric Point Defects

Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...

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Updated: Jul 2, 2026

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

Optimized structures for photonic quasicrystals.

Mikael C Rechtsman¹, Hyeong-Chai Jeong, Paul M Chaikin

¹Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review Letters

|September 4, 2008

Summary

This summary is machine-generated.

Researchers developed a new method to design photonic quasicrystals with wider photonic band gaps. Optimized quasicrystals show improved performance, especially at low material contrasts, offering more isotropic gaps than traditional crystals.

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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

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Area of Science:

Photonics
Materials Science
Condensed Matter Physics

Background:

Photonic quasicrystals utilize quasiperiodic arrangements of dielectric materials to create photonic band gaps.
Designing quasicrystals for optimal photonic band gap properties remains a challenge.

Purpose of the Study:

To develop a novel computational method for designing photonic quasicrystals.
To identify quasicrystal patterns yielding the widest Transverse Magnetic (TM)-polarized photonic band gap for two-component dielectric materials.

Main Methods:

A novel method involving the computation of a finite sum of density waves was employed.
Regions were assigned to one of two dielectric constants (epsilon1 or epsilon0) based on whether the sum exceeded a predefined threshold.

Main Results:

Optimized photonic quasicrystals exhibited larger TM-polarized band gaps compared to optimized conventional crystals, particularly at low dielectric contrasts (epsilon1/epsilon0).
The designed quasicrystals demonstrated significantly more isotropic band gaps across all contrasts.
For high dielectric contrasts, optimized hexagonal crystals achieved the largest band gaps.

Conclusions:

The novel method effectively generates photonic quasicrystal designs with enhanced photonic band gap properties.
Photonic quasicrystals offer advantages in band gap width and isotropy, especially at lower material contrasts.
The findings provide a pathway for designing advanced photonic materials with tailored optical properties.