貢中元的部落格

三維原子陣列的排列方式很難用二維方法來描述，尤其是以十二面體為原子單元的五重對稱原子陣列。

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摘要
    1982年，Dan Shechtman 教授首次觀察到具有十方向對稱的電子透射衍射圖像（如圖1所示），並於1984年正式發表（參考文獻1）。這種展現五重旋轉對稱性的晶體結構，被稱為「準晶體（quasicrystal）」，是一個困擾物理界超過40年的難題，至今仍未被完全理解。事實上，早在1999年（參考文獻2）便有報導指出，研究人員已成功發現尺寸約2毫米的十二面體三維準晶體（參考文獻6）。那麼，我們是否該稱其為「固態晶體」呢？

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if the quasi becomes pseudo, real will become the truth , We have two different atomic sites models for Quasi crystals
如果,準變成偽，實則成幻,影卻成真

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貢中元準晶表面觀測
從彭羅斯圖案演變為二維準晶體圖案, ,現在不再是晶體的正常重複“晶胞”?

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Unlimited number of periodic decagonal tiling  with a2-D atom sites quasi crystal model貢中元chung yuan kung

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Unlimited number of periodic decagonal tiling (2D-crystal)
The fat and thin rhombus tiles with different acute angles of 36 and 72 degrees  can combine to form six different decagonal tiles, of different inner structures, Each decagons composed of ten rhombuses , five thin rhombus and five fat rhombus , where a, b, c, d, e, f, are marked for six different decagons respectively in Figure 1.  For the fat rhombus in the decagons of type-a, type-d, type-e and type-f are highlighted in red, purple red, yellow, and light blue, respectively. These six decagons which can be regarded (considered) as basic unit, instead of two types of rhombuses, to fabricate (infinity) tiles in this paper. And be noted that only type-a decagonal tile is five-fold symmetric and the rest decagons are only mirror symmetric.

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different unit cells in one periodic decagonal crystals 
•If there are different crystal phases inside the crystal, there must be many defects or mismatched atoms on the phase boundcrystal, there must be many defects or mismatche
ed atoms on thearies of the different phases. If there are different  phases inside the phase boundaries of the different phases,again

•In this case, new crystals are created that embed grains of different phases but sh•ow no grain boundaries.•We deliberately made some of the problematic unit cells, mad

some modifications to the internal structure, and then reassembled them. For this case, the seam connecting the parts needs to be modified somewhat and becomes another kind of different unit cell. Periodic crystals are then made using two or more of these remodified unit cells.

 

•準晶體結構必須伴隨著彭羅斯 tile結構，才能清楚感受到晶格的存在

 

•This is complete different from the traditionally understanding about solid crystals of any kind.

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所有十邊形彭羅斯瓷磚 
Celebrating the 50th anniversary of the discovery of Penrose tiling

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The five-fold symmetrical tile that can be self-coupled to build up a five-fold tiling,periodic and four-way symmetry tiles (crystals) to infinity
 

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Some smaller unit cells that form different decagonal two-dimensional crystals
Four unit cells that intercepted from a translational decagonal style crystal and form four different crystals.

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