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Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane...
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Wrinkling crystallography on spherical surfaces.

Miha Brojan1, Denis Terwagne2, Romain Lagrange3

  • 1Departments of Mechanical Engineering.

Proceedings of the National Academy of Sciences of the United States of America
|December 24, 2014
PubMed
Summary
This summary is machine-generated.

Wrinkling a curved elastic system creates self-organized dimple patterns. These patterns form a crystal structure with defects, offering insights into curved crystallography and systems far from equilibrium.

Keywords:
curved surfacesdefectsmechanical instabilitiespackingpattern formation

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Area of Science:

  • Materials Science
  • Physics
  • Mechanics

Background:

  • Curved elastic systems under compression can exhibit complex self-organization phenomena.
  • Understanding the crystallography of these patterns is crucial for predicting material behavior.

Purpose of the Study:

  • To experimentally investigate the crystallography of dimpled patterns formed by wrinkling a curved elastic system.
  • To analyze the structure and evolution of defects in these patterns.

Main Methods:

  • Macroscopic samples of thin hemispherical shells bonded to compliant substrates were used.
  • Compression was applied to induce wrinkling and dimple formation.
  • Three-dimensional scanning was employed to digitize the surface topography.
  • Analysis of crystalline defects, including disclinations and dislocations, as a function of system size.

Main Results:

  • A self-organized crystalline pattern of dimples was observed on the shell surface.
  • Spherical Voronoi tessellations were used to model dimple packing, revealing distorted cells.
  • Disclinations and dislocations were identified as key crystalline defects, with dislocations proliferating with system size.
  • Similarities and differences were noted compared to other curved crystal systems.

Conclusions:

  • The study reveals the self-organization of crystalline dimple patterns in curved elastic systems.
  • Defect analysis provides insights into the mechanics of wrinkling and pattern formation.
  • Findings suggest a general applicability of curved crystallography principles, even with complex interactions and non-equilibrium conditions.