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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.
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Crystal Field Theory
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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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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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Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
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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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Atomic pair distribution functions from textured polycrystalline samples: fundamentals.

Zizhou Gong1, Songsheng Tao2, Simon J L Billinge2

  • 1Department of Physics, Columbia University, New York, NY 10027, USA.

Acta Crystallographica. Section A, Foundations and Advances
|September 18, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces the bond orientational distribution function (BODF) to analyze textured polycrystalline, nanocrystalline, and amorphous materials. The BODF provides detailed structural insights beyond conventional crystallographic texture analysis.

Keywords:
BODFODFPDFbond orientation distribution functioncrystallographic texturenanostructure determinationorientation distribution functionpair distribution functionpreferred orientationtotal scattering

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Area of Science:

  • Materials Science
  • Crystallography
  • Condensed Matter Physics

Background:

  • Conventional crystallographic texture studies analyze the orientational distribution of crystal lattices.
  • These methods may not fully capture the structural nuances of nanocrystalline or amorphous materials.

Purpose of the Study:

  • To formulate equations for the reduced structure function and atomic pair distribution function (PDF) of textured polycrystalline samples.
  • To introduce a new function, the bond orientational distribution function (BODF), for analyzing materials with complex orientational distributions.

Main Methods:

  • Derivation of equations relating material functions to the orientational distribution function (ODF).
  • Definition and formulation of the bond orientational distribution function (BODF) based on interatomic vector orientations.

Main Results:

  • Equations for reduced structure function and PDF are expressed using ODF and single crystallite structure function.
  • The BODF is shown to be sensitive to orientational distributions of interatomic vectors.

Conclusions:

  • The BODF offers a method to obtain detailed structural information from experimental data for known crystallite structures.
  • This approach extends structural analysis capabilities to nanocrystalline and amorphous samples, surpassing conventional texture studies.