Icosahedral Order in Materials Science and Geometry, Part I: Real materials

Jean Taylor, Courant Institute

November 10, 2015

The beautiful geometric structure of the Yb-Cd quasicrystal, as determined by Takakura et al, will be presented and compared to its periodic approximants. It is not a tiling and isn't really self-similar, but can be formulated (as will be explained) as a cut-and-project from a six-dimensional density determined by diffraction. Then the "why and how" will begin to be addressed, with excursions into entropy, Mackay icosahedra, gold fining as explored by Rappaz, and Cahn's Q-glass. The foundations of this talk are in my 2013 Mathematical Intelligencer article with Marjorie Senechal, who will give the independent-but-coordinated Part II seminar on December 8.

With special guest Erin Teich of Sharon Glotzer's group at the University of Michigan.