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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.
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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.
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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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An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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In designing structural elements and machine parts using ductile materials, it is crucial to ensure that these components withstand applied stresses without yielding. Yielding is initially determined through a tensile test, which evaluates the material's response to uniaxial stress. However, tensile stress is insufficient when components face biaxial or plane stress conditions This condition requires advanced criteria to predict failure.
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X-ray Powder Diffraction in Conservation Science: Towards Routine Crystal Structure Determination of Corrosion Products on Heritage Art Objects
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A necessary criterion for obtaining accurate lattice parameters by Rietveld method.

Masami Tsubota1, Jiro Kitagawa2

  • 1Physonit Inc., 6-10 Minami-horikawa, Kaita, Aki, Hiroshima, 736-0044, Japan. tsubota@physonit.jp.

Scientific Reports
|November 15, 2017
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Summary

Accurate lattice parameters require reproducible peak-shift data in Rietveld refinement. This study introduces a new criterion to improve accuracy by distinguishing experimental from analytical peak-shifts, enhancing crystallographic analysis.

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Area of Science:

  • Crystallography
  • Materials Science
  • Computational Chemistry

Background:

  • The Rietveld method is a standard technique for crystal structure refinement.
  • Accurate determination of lattice parameters is crucial for understanding material properties.
  • The conventional Rietveld method may yield homothetic, rather than true, unit cells.

Purpose of the Study:

  • To investigate the relationship between lattice parameters and peak-shift in Rietveld refinement.
  • To identify sources of error in peak-shift measurements.
  • To propose an improved criterion for accurate lattice parameter determination.

Main Methods:

  • Analysis of peak-shift, defined as the deviation from theoretical Bragg positions.
  • Distinguishing between experimental and analytical peak-shifts.
  • Development of a novel criterion based on peak-shift reproducibility.

Main Results:

  • Fitting accuracy of lattice parameters is directly correlated with peak-shift reproducibility.
  • Analytical peak-shift can erroneously reduce the reliability factor (Rwp).
  • The proposed criterion demonstrates good reproducibility of experimental peak-shift.

Conclusions:

  • The conventional Rietveld method's reliance on Rwp can be misleading.
  • An additional criterion based on peak-shift is proposed for enhanced accuracy.
  • The new method significantly improves the accuracy of determined lattice parameters.