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A hunt for new descriptions of old quasicrystals via soft-packing

Banff International Research Station for Mathematical Innovation and Discovery

Jean Taylor, currently at University of California, Berkeley. Marjorie and I are interested in how crystals grow, especially how quasicrystals grow. In the case of multi-element alloys, it is highly likely to be by formation and then aggregation of clusters. There are many reasons to suspect icosahedral order may be important in forming many clusters; periodicity or quasiperiodicity would then arise from how these local clusters aggregate. Overlapping rhombic triacontahedra (RTs) are central to describing physical crystals with local or global icosahedral symmetry; structures derived from these overlapping RTs are a key to understanding how such crystals might grow and to unifying their presentations. Might overlapping rhombic icosahedra (RIs) also be useful to understanding how crystals and quasicrystals with local or global 5-fold symmetry can be described Perhaps they could also be a key to how they might grow I will describe both our suggestions as to how this might all work out and our search for evidence in physical crystals and quasicrystals.

Mathematics; Convex and discrete geometry; Statistical mechanics, structure of matter; Discrete mathematics

video/mp4

Author affiliation: Courant Institute, NYU [also Rutgers University]

2021-01-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/77128

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/