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Related Concept Videos

Structures of Solids02:22

Structures of Solids

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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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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

Crystal Field Theory - Octahedral Complexes

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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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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
Imagine taking a large number of identical...
15.5K
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

49.7K
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,...
49.7K
Network Covalent Solids02:18

Network Covalent Solids

16.5K
Network covalent solids contain a three-dimensional network of covalently bonded atoms as found in the crystal structures of nonmetals like diamond, graphite, silicon, and some covalent compounds, such as silicon dioxide (sand) and silicon carbide (carborundum, the abrasive on sandpaper). Many minerals have networks of covalent bonds.
To break or to melt a covalent network solid, covalent bonds must be broken. Because covalent bonds are relatively strong, covalent network solids are typically...
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Updated: Apr 1, 2026

Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis
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Quantitative Atomic-Site Analysis of Functional Dopants/Point Defects in Crystalline Materials by Electron-Channeling-Enhanced Microanalysis

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Topological framework for local structure analysis in condensed matter.

Emanuel A Lazar1, Jian Han2, David J Srolovitz3

  • 1Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104; mLazar@seas.upenn.edu.

Proceedings of the National Academy of Sciences of the United States of America
|October 14, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a novel topological framework using Voronoi cells to classify local structure in materials. This method offers a powerful and practical approach to understanding both ordered and disordered systems.

Keywords:
Voronoi topologyatomic systems visualizationstructure classification

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Fabrication of Spatially Confined Complex Oxides
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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Materials Science

Background:

  • Understanding the atomic and particle-level structure of physical systems is crucial in condensed matter research.
  • Real-world materials deviate from perfect crystalline order due to thermal vibrations and defects, complicating structural analysis.
  • Liquids and glasses exhibit complex structures, making a unified description challenging.

Purpose of the Study:

  • To propose a unified mathematical framework for classifying local structure in both ordered and disordered systems.
  • To demonstrate the advantages of a topological description over continuous methods for structural analysis.
  • To explore the framework's applicability to real-world materials and complex structural phenomena.

Main Methods:

  • Development of a unified mathematical framework based on the topology of the Voronoi cell of a particle.
  • Analysis of the underlying reasons for the superiority of topological descriptions in structural analysis.
  • Application of the framework to model crystalline structure under thermal stress and identify defects.

Main Results:

  • A powerful and practical topological framework for classifying local structure in diverse physical systems.
  • Explanation of why topological descriptions are better suited for structural analysis than continuous methods.
  • Demonstration of the framework's ability to analyze compromised crystalline structures at elevated temperatures.

Conclusions:

  • The proposed topological framework provides a unified and effective method for characterizing local structure in materials.
  • This approach offers significant advantages for analyzing defects, complex structures, and disordered systems.
  • The framework has broad potential applications in materials science and condensed matter research.