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Related Concept Videos

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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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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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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Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

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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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Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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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...
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Derivatization of Protein Crystals with I3C using Random Microseed Matrix Screening
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An effective introduction to structural crystallography using 1D Gaussian atoms.

Emily Smith1, Gwyndaf Evans2, James Foadi2,3

  • 1Gonville and Caius College, Trinity Street, Cambridge, United Kingdom.

European Journal of Physics
|November 16, 2020
PubMed
Summary

This study introduces 1D structural crystallography using truncated Gaussian functions to model atoms in crystal lattices. The CRONE program facilitates exploring these computational crystallography concepts.

Keywords:
Fourier seriesFourier transformanomalous scatteringcomputational methods for structural crystallographycrystallography

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Area of Science:

  • Crystallography
  • Computational Science
  • Materials Science

Background:

  • Quantitative aspects of computational structural crystallography are crucial for understanding crystal structures.
  • Modeling atoms in a crystal lattice requires effective mathematical representations.

Purpose of the Study:

  • To introduce the fundamental quantitative aspects of computational structural crystallography.
  • To demonstrate the application of 1D truncated and periodic Gaussian functions for atomic representation.
  • To showcase the utility of the CRONE computer program in this field.

Main Methods:

  • Definition and utilization of 1D truncated and periodic Gaussian functions.
  • Application of these functions to represent atoms within a crystal lattice.
  • Detailed description and demonstration of 1D structural crystallography principles.

Main Results:

  • Successful representation of atoms in a crystal lattice using 1D Gaussian functions.
  • Demonstration of key quantitative aspects of computational structural crystallography.
  • Validation of the CRONE program for executing crystallographic calculations.

Conclusions:

  • 1D truncated and periodic Gaussian functions provide a satisfactory method for introducing quantitative aspects of computational structural crystallography.
  • The CRONE program enables practical application and further exploration of these methods.