Brian Cox with Rolfe Petschek
Understanding Quasicrystals
Quasicrystals have been observed in a variety of metallic systems and recently also in simulations of hard tetrahedral[1]. In quasicrystals atoms are arranged in such a way that the fourier transform of the positions of their centers, or indeed of any characteristic of the structure has sharp peaks at a number of points. These peaks cannot be indexed by a simple three dimensional lattice but are indexed by a higher dimensional lattice, with the height of the peak related to the index of the lattice[2,3]. Such lattices also contain many tetrahedra and dense structures of Bernal or tetrahelicies[1], in which the position and orientation of the tetetrahedra rotate in a periodic fashion. This project will examine the possibility that a better understanding of quasicrystals can be based on fourier transforms of the spherical harmonics associated with the orientation of the tetrahedral, rather than a fourier transform of the locations of the centers or corners of the tetrahedra. While all information is (in principle) contained in the position fourier transforms, these tend to be rather complicated and with many approximately equally intense peaks. If some orientation peaks have significantly higher brightnesses, this may allow a better understanding of such systems as condensed orientation waves.