A surface-stacking structural model for icosahedral quasicrystals

An original structural model for the description of icosahedral quasicrystals is proposed. This novel theoretical approach is based on a surface-stacking image of icosahedral quasicrystals and is in concert with the step-terrace morphology observed in many experimental investigations of real icosahedral surfaces. According to this model, the infinite icosahedral structure is constructed by stacking two arrangements of quasi-periodic surfaces along each of the 5-fold axis of the icosahedral symmetry. In this stacking order, the spacings between the layered surfaces are governed by Fibonacci sequence. The proposed model operates within the real physical (Euclidean) space and provides a direct three-dimensional visual representation of the icosahedral superstructure, which can be instrumental for conducting different modes of experimentations, analyses, and fabrication strategies; eliminating a major roadblock for researchers especially outside the fields of crystallography and material science. More importantly, understanding the long-range surface-stacking logic of the icosahedral structure will hopefully provide a deeper understanding of the structure of quasicrystals at an atomic scale and help achieve improved control over material compositions and structure.