Weirdest Martensite: Smectic Liquid Crystal Microstructure and Weyl-Poincaré Invariance.

Phys Rev Lett

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853-2501, USA.

Published: April 2016

AI Article Synopsis

  • Smectic liquid crystals exhibit unique microstructures formed by ordered patterns like ellipses and hyperbolas, presenting a complex challenge in filling three-dimensional space under certain conditions.
  • A set of strict compatibility rules for concentric circle domains at 2D smectic interfaces has been developed, as these rules dictate the arrangement and interactions between different domains.
  • The research employs numerical simulations to create a clustering algorithm that effectively identifies and analyzes the boundaries between various domains, and it proposes methods to extend this analysis to the three-dimensional smectic structures.

Article Abstract

Smectic liquid crystals are remarkable, beautiful examples of materials microstructure, with ordered patterns of geometrically perfect ellipses and hyperbolas. The solution of the complex problem of filling three-dimensional space with domains of focal conics under constraining boundary conditions yields a set of strict rules, which are similar to the compatibility conditions in a martensitic crystal. Here we present the rules giving compatible conditions for the concentric circle domains found at two-dimensional smectic interfaces with planar boundary conditions. Using configurations generated by numerical simulations, we develop a clustering algorithm to decompose the planar boundaries into domains. The interfaces between different domains agree well with the smectic compatibility conditions. We also discuss generalizations of our approach to describe the full three-dimensional smectic domains, where the variant symmetry group is the Weyl-Poincaré group of Lorentz boosts, translations, rotations, and dilatations.

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http://dx.doi.org/10.1103/PhysRevLett.116.147802DOI Listing

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