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Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
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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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Turing Instability in the Solid State: Void Lattices in Irradiated Metals.

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|May 9, 2020
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Turing instabilities, previously observed in liquids, can explain pattern formation like void superlattices in metals. This mechanism, driven by differing diffusion rates, offers new insights into solid-state pattern development.

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Area of Science:

  • Solid-state physics
  • Materials science
  • Chemical kinetics

Background:

  • Turing instabilities explain pattern formation in reaction-diffusion systems, like animal coat patterns.
  • The phenomenon requires significantly different diffusion rates, limiting its observation primarily to liquid-phase systems.
  • In solids, differing mobilities of defects and impurities are common due to temperature-dependent migration barriers.

Purpose of the Study:

  • To investigate the applicability of the Turing mechanism to pattern formation in solid-state systems.
  • To demonstrate that Turing instabilities can explain the formation of void superlattices in irradiated metals.
  • To propose a generic model applicable to various solid-state pattern phenomena.

Main Methods:

  • Development of a minimal theoretical model based on Cahn-Hilliard equations for interstitial and vacancy concentrations.
  • Coupling of the equations to include generation and annihilation terms.
  • Validation of analytical results using phase field simulations.

Main Results:

  • The study shows that Turing instabilities can indeed drive pattern formation in solids.
  • Void superlattices in irradiated metals are identified as a potential emergent pattern explained by this mechanism.
  • The generic nature of the model suggests broad applicability to other solid-state systems.

Conclusions:

  • The Turing mechanism provides a viable explanation for void superlattice formation in irradiated metals.
  • The findings extend the understanding of Turing instabilities beyond liquid-phase systems into solid-state materials.
  • This mechanism could be a key factor in the structure and pattern formation observed in diverse solid-state systems.