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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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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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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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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
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Approximating lattice similarity.

Lawrence C Andrews1, Herbert J Bernstein2, Nicholas K Sauter3

  • 1Ronin Institute, 9515 NE 137th Street, Kirkland, WA 98034-1820, USA.

Acta Crystallographica. Section A, Foundations and Advances
|July 24, 2023
PubMed
Summary
This summary is machine-generated.

A new method selects crystal unit cells to ensure maximum similarity to a reference cell. This approach accommodates variations in cell parameters and lattice centering for diverse crystal structures.

Keywords:
DelaunayDeloneNiggliSellinglattice matching

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Area of Science:

  • Crystallography
  • Materials Science
  • Computational Chemistry

Background:

  • Crystallographic data often presents unit cells in non-uniform representations.
  • Inconsistent unit cell descriptions complicate comparative analysis and data mining.

Purpose of the Study:

  • To develop a standardized method for selecting representative unit cells from a crystal structure dataset.
  • To enable robust comparison of crystal structures regardless of initial cell representation.

Main Methods:

  • A novel algorithm for unit cell selection based on similarity to a target cell.
  • Implementation accommodates variations in cell parameters (lengths, angles).
  • The method supports different lattice centering types (e.g., primitive, body-centered, face-centered).

Main Results:

  • Demonstrated ability to unify diverse unit cell representations into a consistent format.
  • The proposed method effectively minimizes differences between selected and reference unit cells.
  • Successful accommodation of cells with varying parameters and centering types.

Conclusions:

  • The developed method provides a robust solution for standardizing unit cell representation in crystallography.
  • Facilitates more accurate and efficient comparison and analysis of crystal structure databases.
  • Enhances data interoperability and reduces ambiguity in crystallographic studies.