The most simple icosahedral quasi-crystal with continuous phasons

Abstract

An icosahedral quasi-crystal with continuous phason modes has been constructed in the form of five perfect intergrown FCC-lattices, with a finite distance between all atoms. Five is the minimal number possible. The model is essentially unique. The pair correlation function and the Fourier intensities are calculated. An analytic expression is presented for the displacement of the atoms under a phason shift.