Speakers - 2026 Speakers

Title: The direct evidence of relation between Penrose tiling and Quasi crystal

Abstract

Penrose tiling is a mathematical problem of trigonometric geometric drawing, and other one, quasicrystal HRTEM images is a physics problem of not consistent with traditional understanding of the crystal structure. The only correlation between these two problems is that they both have five-fold rotational symmetric inner structure. How to prove that these two issues are correctly related to each other is a big question that requires precise logical explanation. In this report, we first consider the Penrose tiling as a uniform space partitioning framework and consider a quasicrystal as a combination of van der Waals compounds that are balanced bonding in the liquid state.

We will then analyze and compare the features of the dodecahedral network arrays observed by Binary decagonal Penrose tiling and the features of the dodecahedral network array atomic sites on the AlMnPd quasicrystal atomic sites observed by high-resolution transmission electron microscopy (Ref. 1) to understand the similarities and differences in the formation of the array patterns and thus to more accurately understand the relationship between them. Four potential nucleation sites associated with Pd atoms were identified. In this demonstration, we also selected an atomic array of AlMnPd quasicrystal observed by HAADF STEM (reference 2) for point-to-point fitting, proving that the atomic positions of the quasicrystal match the vertices of the Penrose tiling well. We also attempted to establish a three-dimensional model of the Penrose tiling and quasicrystal. Some unresolved issues will also be discussed.