From Penrose tiling to quasi crystal –
a directed evidence of a large area correction between Penrose tiling to quasi crystal
Chung-Yuan Kung (last name Kung)
Corresponding author : Chung-Yuan Kung (last name Kung), Department. of Electrical Engineering, National Chung Hsing University. 145 Xingda Road., South Dist. Taichung City 40227. Taiwan. Telephone: 886-4-22850359, E-mail Address: cykung@dragon.nchu.edu.tw.
The van der Waals radius, rw, According to the arrangement of electrons in Al, Fe, and Pd metal atoms, Al a
toms are the main electron contributors. Each Al contributes 3 electrons (1 from the 3p energy level and 2 from the 3s energy level). Fe and Mn atoms are Basic electron absorber, atom. Fe (tetravalent vacancy) and Mn (pentavalent vacancy)..However, the absorption of electron from the 4 s level may lower down more energy.
•根據Al、Fe、Pd金屬原子中電子的排列，Al原子是主要的電子貢獻者。每個Al貢獻3個電子（1個來自3p能階，2個來自3s能階）。 Fe和Mn原子是鹼性電子吸收劑原子。 Fe（四價空位）和 Mn（五價空位）.然而，從4s能階吸收電子可能會降低更多的能量。Several initial Van der Waal molecules such as , Al-Mn,Al-Al, Al-Pd, Al-Pd-Mn, were fromed at very begining, then four nuclei, that are 5-fold and mirror symmetric were genereated on 2-D plane. In fact, these nuclei were three D atom clusters, with several extra Al atoms on up layer and down layer plane.
幾個初始范德華分子，如 Al-Mn、Al-Al、Al-Pd、Al-Pd-Mn，是從一開始就形成的，然後在 2- 上生成 4 個 5 倍且鏡像對稱的核。平面。事實上，這些原子核是三個D原子簇，在上層和下層平面上還有幾個額外的Al原子
ABSTRACTPenrose tiling is a mathematical problem of triangular geometry drawing, while quasicrystal HRTEM images are a physical problem that is inconsistent with the understanding of traditional crystal structures. The only correlation between the two problems is that they both have five-fold rotationally symmetric internal structures. How to prove that these two questions are correctly related to each other is a big question that requires logical explanation.
In this research, we conducted a detailed analysis of the Al-Pd-Mn quasicrystal high resolution transparent electron microscope (HRTEM) photos and used color difference technology to distinguish the surface array of atomic sites with different features on the same photos. (Apply the size and position correlation comparison of HRTEM and Penrose tiled atomic points for the first step of analysis). We were able to identify four basic atomic clusters of five-fold and mirror symmetry, three of which could serve as nucleation centers, coarsening the other clusters to form a larger cluster, showing coupled Penrose tiling features. The possible formation of van der Waals molecules is explained using the spd(f) 3-d(4f) electron sub-level filling model, which accordingly produces five-fold symmetric atomic clusters; weak van der Waals bonds account for the liquid behavior of quasicrystals.
A coupled Penrose tile diagram was created that matched point-to-point to the atomic point array of the HRTEM photograph. Apparently, a Penrose tile framework (lattice) structure does exist in quasicrystals. A simple slanted-shift rotational stacking model is proposed to fabricate 3D quasicrystals with relatively weak bonds between adjacent layers.
Conclusion: a direct evidence of Penrose tiling (frame work) corrected to quasi crystal will be presented in detailed.
BIOGRAPHY
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 department since 1991 to 2016 (retired).
留言列表
