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Related Concept Videos

Metallic Solids02:37

Metallic Solids

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.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
Crystal Growth: Principles of Crystallization01:25

Crystal Growth: Principles of Crystallization

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.
Initiating crystallization involves manipulating the concentration of the solute and the temperature of the solution. Since crystal growth occurs when the ratio of concentration and solubility of the solute in the solvent – the...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

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.
Types of Unit Cells
Imagine taking a large number of identical...
Imperfections in Crystal Structure: Point, Line and Plane Defects01:25

Imperfections in Crystal Structure: Point, Line and Plane Defects

A perfect crystal, in theory, has a uniform structure with the same unit cell and lattice points throughout. However, any deviation from this periodic arrangement is known as an imperfection or defect. These defects can be categorized into three types: point, line, and plane defects.Point defects occur when there is a deviation from the ideal due to missing atoms, displaced atoms, or additional atoms. These imperfections might occur due to imperfect packing during crystallization or because of...
Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...

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Flocking as a continuous phase transition in self-aligning active crystals.

Marco Musacchio1, Alexander P Antonov1, Hartmut Löwen1

  • 1Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.

The Journal of Chemical Physics
|May 18, 2026
PubMed
Summary
This summary is machine-generated.

Active crystals with self-aligning units transition from disorder to flocking. This study presents the first microscopic theory, mapping dynamics to a Landau-Ginzburg model and predicting a continuous phase transition.

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Area of Science:

  • Physics
  • Soft Matter Physics
  • Statistical Mechanics

Background:

  • Active matter systems exhibit emergent behaviors like flocking.
  • Self-alignment mechanisms in active units can drive collective motion.
  • Understanding phase transitions in these systems is crucial for predicting their dynamics.

Purpose of the Study:

  • To develop a microscopic theory for flocking transitions in two-dimensional active crystals.
  • To analytically map the crystal dynamics onto a Landau-Ginzburg model.
  • To quantitatively predict transition points and velocity correlations.

Main Methods:

  • Derivation of a Landau-Ginzburg model from microscopic active crystal dynamics.
  • Analytical calculation of velocity-dependent effective free energy.
  • Comparison of theoretical predictions with simulation results.

Main Results:

  • The theory analytically describes the transition from a disordered to a flocking state.
  • A velocity-dependent effective free energy transitions from a single-well to a Mexican-hat profile.
  • Quantitative prediction of the transition point and spatial velocity correlations.

Conclusions:

  • Flocking in self-aligning active crystals represents a continuous phase transition (BKT type in 2D, second-order in 3D).
  • The findings provide a theoretical foundation for experimentally observed flocking in active granular particles and migrating cells.
  • This work advances the understanding of collective behavior and phase transitions in active matter.