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Related Concept Videos

Crystal Growth: Principles of Crystallization01:25

Crystal Growth: Principles of Crystallization

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Crystallization is a phase transformation process in which crystals are precipitated from a supersaturated solution or formed from other sources. During crystallization, atoms or molecules arrange themselves into a well-defined, rigid crystal lattice to minimize energy.
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Recrystallization is a purification technique used to separate impurities from solid compounds. In this technique, no chemical reactions occur. Instead, it exploits physical properties only, specifically, the solubility differences between the desired compound and impurities, either at a single temperature or at different temperatures, and under other selected conditions. The solid-solution equilibrium (solubility equilibrium) of each component in the solution represents a binary phase...
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Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
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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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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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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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Growing Protein Crystals with Distinct Dimensions Using Automated Crystallization Coupled with In Situ Dynamic Light Scattering
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Emerging crystallization in one dimension.

Lila Bouzar1, René Messina2

  • 1University of Science and Technology Houari Boumediene (USTHB), Materials Physics Laboratory, BP 32 Bab Ezzouar, 16111 Algiers, Algeria.

Physical Review. E
|November 18, 2025
PubMed
Summary
This summary is machine-generated.

We analytically found a universal solidlike phase in one-dimensional hard-sphere systems. This reveals quasi-long-range order and provides criteria for detecting solid order in confined systems.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Theoretical Physics

Background:

  • One-dimensional systems exhibit unique properties distinct from higher dimensions.
  • Understanding phase transitions and emergent order in constrained geometries is crucial.

Purpose of the Study:

  • To analytically uncover the emergence of a universal solidlike phase in one-dimensional hard-sphere systems (Tonks gas).
  • To establish a theoretical framework for crystallization in 1D and define criteria for incipient solid order.

Main Methods:

  • Analytical derivation of the pair distribution function.
  • Analysis of correlation length and decay regimes.

Main Results:

  • Identified algebraic decay of the pair distribution function, indicating quasi-long-range order.
  • Determined a correlation length ξ∼ℓ/(1-ϕ)^{2} beyond which exponential decay sets in.
  • Pinpointed the onset of solidlike behavior near packing fraction ϕ^{*}≃0.8, where ξ≈ℓ.

Conclusions:

  • Established a theoretical framework for emergent crystallization in 1D hard-sphere systems.
  • Introduced criteria for detecting incipient solid order in constrained geometries.