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.