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Related Concept Videos

Metallic Solids02:37

Metallic Solids

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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....
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Crystal Field Theory - Octahedral Complexes02:58

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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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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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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...
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Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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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
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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.
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Topological states from topological crystals.

Zhida Song1,2, Sheng-Jie Huang3,4, Yang Qi5,6,7

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We introduce topological crystals, a new class of states formed from lower-dimensional topological states. This framework provides a complete classification for topological crystalline insulators in three dimensions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Topology in Physics

Background:

  • Symmetry-protected topological states are crucial in modern physics.
  • Understanding these states requires classifying them under combined onsite and spatial symmetries.
  • Topological crystalline insulators are a key area of research.

Purpose of the Study:

  • To develop a scheme for constructing and classifying topological states protected by both onsite and spatial symmetries.
  • To introduce and define the concept of "topological crystals."
  • To provide a comprehensive classification of topological crystalline insulators.

Main Methods:

  • Adiabatic deformation of symmetry-protected topological states into topological crystals.
  • Explicit construction and enumeration of topological crystals.
  • Classification based on combined onsite and spatial symmetries for noninteracting time-reversal symmetric electronic insulators.

Main Results:

  • All symmetry-protected topological states can be deformed into topological crystals.
  • Topological crystals are real-space assemblies of lower-dimensional topological states.
  • A full classification of topological crystalline insulators is achieved for all 230 space groups.

Conclusions:

  • The concept of topological crystals unifies the understanding of various topological states.
  • This work establishes a complete classification for topological crystalline insulators.
  • The findings pave the way for discovering new quantum materials with exotic topological properties.