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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.
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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...
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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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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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Molecular and Ionic Solids02:54

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Crystalline solids are divided into four types: molecular, ionic, metallic, and covalent network based on the type of constituent units and their interparticle interactions.
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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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Crystal Field Theory
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Updated: Oct 21, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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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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Direct Correlation Function of a Crystalline Solid.

S-C Lin1, M Oettel1, J M Häring2

  • 1Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany.

Physical Review Letters
|September 3, 2021
PubMed
Summary
This summary is machine-generated.

Researchers calculated the direct correlation function (DCF) for hard sphere crystals. This reveals crucial differences from liquid DCFs, highlighting the impact of vacancies on solid properties and elastic constants.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Direct correlation functions (DCFs) are vital for describing matter, especially in ordered phases.
  • DCFs encode local structure, defects, and thermodynamic properties of crystalline solids.

Purpose of the Study:

  • To numerically calculate the DCF of a hard sphere crystal for the first time.
  • To compare the solid DCF with its liquid counterpart and analyze differences.

Main Methods:

  • Employed a demanding numerical approach based on the fundamental measure concept.
  • Explicitly calculated the DCF for a hard sphere crystal.

Main Results:

  • The DCF of a hard sphere crystal significantly differs from its liquid counterpart in shape and magnitude.
  • Vacancies dominate the solid DCF at coexistence.
  • Traditional use of liquid DCFs in free energy expansions is conceptually flawed.

Conclusions:

  • The study provides the first explicit calculation of a solid's DCF.
  • Accurate calculation of elastic constants requires using solid-specific DCFs, showing good agreement with simulations.