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Related Concept Videos

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...
Lattice Centering and Coordination Number02:33

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 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,...
Crystallographic Point Groups01:29

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
Structures of Solids02:22

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...
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...

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Related Experiment Video

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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

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

Published on: September 26, 2014

Dirac cones in two-dimensional systems: from hexagonal to square lattices.

Zhirong Liu1, Jinying Wang, Jianlong Li

  • 1College of Chemistry and Molecular Engineering, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, and Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871, China. LiuZhiRong@pku.edu.cn.

Physical Chemistry Chemical Physics : PCCP
|October 3, 2013
PubMed
Summary
This summary is machine-generated.

Lattice symmetry significantly impacts Dirac cones. Conventional Dirac fermions are challenging to realize in square lattices due to symmetry constraints, unlike in hexagonal systems.

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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:

  • Condensed matter physics
  • Materials science
  • Solid-state physics

Background:

  • Dirac cones are crucial for understanding exotic electronic properties in 2D materials.
  • Lattice symmetry plays a fundamental role in determining electronic band structures.
  • Graphene serves as a prime example exhibiting Dirac cones due to its hexagonal lattice.

Purpose of the Study:

  • To investigate how lattice symmetry influences the formation of Dirac cones.
  • To derive criteria for Dirac cone existence in different 2D systems.
  • To compare Dirac cone formation in hexagonal and square lattice structures.

Main Methods:

  • Theoretical derivation of a criterion for Dirac cone existence using a tight-binding approximation.
  • Analysis of a general 2D atomic crystal with two atoms per unit cell.
  • Modeling a 2D electron gas (2DEG) under a periodic muffin-tin potential.

Main Results:

  • A criterion for Dirac cone existence in atomic crystals was established.
  • The probability of observing Dirac cones decreases with the transition from hexagonal to square lattices.
  • In a square lattice 2DEG, Dirac points exhibit parabolic, not linear, dispersion, differing from conventional Dirac fermions.

Conclusions:

  • Achieving conventional Dirac fermions, similar to graphene, is difficult in highly symmetric square lattices.
  • Lattice symmetry is a critical factor in the realization of Dirac physics.
  • The findings provide insights into designing materials with specific electronic properties.