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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...
Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
X-ray Crystallography02:18

X-ray Crystallography

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.
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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...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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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,...
Unit Cells01:18

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A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...

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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Binary crystals in two-dimensional two-component Yukawa mixtures.

Lahcen Assoud1, René Messina, Hartmut Löwen

  • 1Institut fur Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universitat Dusseldorf, Universitatsstrasse 1, D-40225 Dusseldorf, Germany.

The Journal of Chemical Physics
|December 3, 2008
PubMed
Summary
This summary is machine-generated.

This study reveals diverse stable crystal structures in binary mixtures of like-charge particles. These findings are relevant for experiments with colloids and dusty plasmas.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Materials science

Background:

  • Understanding phase diagrams is crucial for predicting material properties.
  • Binary mixtures of charged particles exhibit complex behaviors due to electrostatic interactions.

Purpose of the Study:

  • To calculate the zero-temperature phase diagram of binary mixtures of like-charge particles.
  • To identify stable crystal structures as a function of composition and charge ratio.

Main Methods:

  • Minimizing potential energy using Lekner summation for screened Coulomb interactions.
  • Analyzing candidate two-dimensional crystal structures.

Main Results:

  • Identification of various stable crystal structures: A, B, AB(2), A(2)B, and AB(4).
  • Elementary cells based on triangular, square, or rhombic lattices with complex particle arrangements.
  • Absence of intermediate crystals for small charge asymmetry, except for pure A and B triangular crystals.

Conclusions:

  • The study predicts a rich variety of stable crystal structures in binary mixtures of like-charge particles.
  • These predicted structures are experimentally verifiable in confined colloidal or dusty plasma systems.