From Penrose tiling to quasi crystal – Chung Yuan Kung－貢中元的部落格

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)

Direct evidence for the 2-D Penrose tiling frame of 3-D quasicrystals.

Chung-Yuan Kung, Han-wen Liu, Chu-Yang Chao, Marlachi Warneke*

Department. of Electrical Engineering, National Chung Hsing University. E-mail Address: cykung@dragon.nchu.edu.tw.

*UCLA, Chemistry Dept.

Penrose tiling is 2-D geometric framework whose internal structure can change infinitely, whereas a quasicrystal is a 3-Dl phenomenon that reaching stability in growth but has not final yet stabilized. Penrose 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 issues of different dimensions are correctly related to each other is a big problem that requires logical explanation.

In this study, a detailed analysis of high-resolution transparent electron microscopy (HRTEM) images of Al-Pd-Mn quasicrystals was performed, using color difference technology techniques to distinguish surface arrays of different characteristic atomic sites on the same image (comparing the size and position correlation of HRTEM and Penrose tiling atomic points as the first step of analysis). Four basic atomic clusters with five-fold mirror symmetry were identified, three of which can be regarded as nucleation centers that coarsening with the fourth atomic clusters respectively to form a larger atomic cluster, eventually showing coupled Penrose tiling characteristics.

The spd(f)3-d(4f) electronic sublevel filling model was used to explain the possible formation of van der Waals molecules, resulting in five-fold symmetric atomic clusters with weak van der Waals bond characteristics, and explaining the 3-D liquid behavior of quasicrystals.

A coupled Penrose tile diagram was created to point-to-point match to the atomic point array of the Al-Pd-Mn HRTEM photograph. Apparently, a Penrose tile framework (lattice) structure does exist in the atomic array of a quasicrystal. A simple slanted-shift rotational stacking model is proposed to fabricate 3D (liquid) quasicrystals with relatively weak bonds between adjacent layers.

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).

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.