Periodic quasicrystal

Abstract

It is shown that the icosahedral quasicrystal and the recently observed T phase are closely related to each other. The latter is a periodic stacking of two-dimensional quasilattices with mirror symmetry. Their diffraction patterns, though appearing very different, can be indexed by a set of primary vectors that are only small deformations of each other. However, because of the mirror symmetry, their quasilattices are not related by small deformations. A calculation based on the model free energy of Kalugin et al. shows that this periodic quasicrystal is very competitive with (and in fact energetically more favorable than) the icosahedral quasicrystal.