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Title: Sphericity and symmetry breaking in the formation of Frank–Kasper phases from one component materials

Frank–Kasper phases are tetrahedrally packed structures occurring in numerous materials, from elements to intermetallics to self-assembled soft materials. They exhibit complex manifolds of Wigner–Seitz cells with many-faceted polyhedra, forming an important bridge between the simple close-packed periodic and quasiperiodic crystals. The recent discovery of the Frank–Kasper σ-phase in diblock and tetrablock polymers stimulated the experiments reported here on a poly(isoprene-b-lactide) diblock copolymer melt. Thus, analysis of small-angle X-ray scattering and mechanical spectroscopy exposes an undiscovered competition between the tendency to form self-assembled particles with spherical symmetry, and the necessity to fill space at uniform density within the framework imposed by the lattice. We thus deduce surprising analogies between the symmetry breaking at the body-centered cubic phase to σ-phase transition in diblock copolymers, mediated by exchange of mass, and the symmetry breaking in certain metals and alloys (such as the elements Mn and U), mediated by exchange of charge. Similar connections are made between the role of sphericity in real space for polymer systems, and the role of sphericity in reciprocal space for metallic systems such as intermetallic compounds and alloys. These findings establish new links between disparate materials classes, provide opportunities to improve the understanding of complex crystallization by buildingmore » on synergies between hard and soft matter, and, perhaps most significantly, challenge the view that the symmetry breaking required to form reduced symmetry structures (possibly even quasiperiodic crystals) requires particles with multiple predetermined shapes and/or sizes.« less
 [1] ;  [2] ;  [2]
  1. Rensselaer Polytechnic Inst., Troy, NY (United States); Univ. of Minnesota, Minneapolis, MN (United States)
  2. Univ. of Minnesota, Minneapolis, MN (United States)
Publication Date:
OSTI Identifier:
Grant/Contract Number:
AC02-06CH11357; FG02-06ER46275
Accepted Manuscript
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 111; Journal Issue: 50; Journal ID: ISSN 0027-8424
National Academy of Sciences, Washington, DC (United States)
Research Org:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY symmetry breaking; sphericity; Frank-Kasper phases; block polymers