Understanding Fivefold Symmetry in Electron-Diffraction Patterns

Abstract: The electron-diffraction patterns with 5-fold rotational symmetry of the experimental Al-Mn alloy phase reported by Shechtman et al. are assumed to be produced by a periodic structure. A three-dimensional periodic structure is presented based on two kind polyhedrons. The structure can be used as an atomic model to describe the alloy phase. The Fourier-transform patterns of the model are simulated along six “symmetry directions”. The chemical composition of the model is similar to that of the Al-Mn alloy phase. Details of the motivations and approaches that lead to these models are discussed. This study suggests that non classical periodic structures are also well candidates to describe quasicrystals