Use of periodic approximants in a dynamical LEED study of the quasicrystalline tenfold surface of decagonal Al-Ni-Co

The determination of quasicrystal (QC) surface structures is a challenge to current surface structure techniques. Low-energy electron diffraction (LEED) is the primary technique for the determination of periodic surface structures, but application of dynamical LEED to quasicrystals requires the use of many approximations. In this study, two different approaches were used to apply dynamical LEED to the structure of the tenfold surface of decagonal Al73Ni10Co17. One method (method 1) involves the use of a quasicrystalline model along with approximations that average over the composition and local geometries. The other method (method 2) uses periodic models that approximate the actual local QC structure (approximants) in more exact, atomistic calculations. Although the results using the two methods were consistent, the results of the approximant analysis (method 2) suggested a different way to apply the approximations in method 1, resulting in a better fit between experimental and calculated beams. Thus, periodic approximant structure models can provide a simpler and more efficient method for the determination of local geometries in QC surfaces, and may also facilitate analyses using quasicrystal models.