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 will first analyze and explain the characteristics of pentagonal arrays and circular (embedded 10 atomic groups) arrays observed on Penrose tiled atomic sites and atomic points on quasicrystal (HRTEM) observations, in order to understand the similarities or differences in how the array patterns are formed, the different relationships between them can be more accurately understood. In this demonstration, we selected a specific AlPdMn quasicrystal HRTEM that removes the dark areas and leaves remaining spots that are easier to analyze. The application of two schemes proves that quasicrystals have good matching with Penrose tiling. Some unresolved issues will also be discussed.

Dr. Kung graduated from National Tsing Hua University 1969 and 1972 with BS and MS degree in physics, university of Alabama in Huntsville 1974 in physics and Northwestern university 1979 in material science. Post doctor at Georgia Tech and research science at Lawrence laboratory. With about 6 years experiences in US industries Fairchild and National Semiconductor and work for ITRI (Taiwan) since 1987 and worked for National Chung-Hsing University electric engineering.