Mistakes in Quasilattices

Abstract

We studied a class of mistakes or faults in quasilattices. The effect of a random distribution of mistakes on the diffraction of 1D, and a special class of 3D, quasilattices is calculated exactly. Mistakes change the diffraction pattern qualitatively: Some Bragg peaks decrease in intensity as expected, but some are enhanced. As a result some spots disappear and some new ones appear. The diffuse scattering is also calculated. Results are given comparing calculated diffraction patterns in fivefold, threefold, and twofold symmetry directions for a 3D quasicrystal with and without mistakes.