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Related Concept Videos

The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

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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...
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Determination of Crystal Structures01:29

Determination of Crystal Structures

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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...
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Crystallographic Point Groups01:29

Crystallographic Point Groups

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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...
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X-ray Crystallography02:18

X-ray Crystallography

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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...
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Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

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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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Network Covalent Solids02:18

Network Covalent Solids

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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.
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Updated: Apr 6, 2026

X-ray Powder Diffraction in Conservation Science: Towards Routine Crystal Structure Determination of Corrosion Products on Heritage Art Objects
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Pair correlations in classical crystals: The shortest-graph method.

Stanislav O Yurchenko1, Nikita P Kryuchkov1, Alexei V Ivlev2

  • 1Bauman Moscow State Technical University, 2nd Baumanskaya str. 5, 105005 Moscow, Russia.

The Journal of Chemical Physics
|July 24, 2015
PubMed
Summary
This summary is machine-generated.

The shortest-graph method accurately calculates crystal pair correlation functions. This computational approach is especially effective for soft interactions and low temperatures, offering reliable predictions for material properties.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Chemistry

Background:

  • Calculating pair correlation functions is crucial for understanding crystal properties.
  • Existing methods may face challenges with complex interactions or specific temperature regimes.

Purpose of the Study:

  • To introduce and validate the shortest-graph method for determining crystal pair correlation functions.
  • To assess the method's accuracy across various crystal types and conditions.

Main Methods:

  • Applied the shortest-graph method, representing correlation peaks as Gaussian functions.
  • Derived analytical expressions for Gaussian parameters in 2D and 3D crystals.
  • Compared results with molecular dynamics simulations for different interparticle potentials.

Main Results:

  • The shortest-graph method shows high accuracy for soft interparticle interactions and low temperatures.
  • Demonstrated effectiveness by calculating the solid-solid transition line for Yukawa crystals.
  • Accurately predicted compressibility for inverse-power law crystals.

Conclusions:

  • The shortest-graph method provides an accurate and efficient way to compute pair correlation functions in crystals.
  • The method's accuracy is linked to minimal anharmonicity effects, making it suitable for specific conditions.
  • Offers a valuable tool for predicting thermodynamic properties and phase transitions in crystalline materials.