臺灣博碩士論文加值系統

結晶發生在自然現象與工業過程中。在多數的科學研究及應用，產生高品質的晶體是必要的。一個例子是利用X射線晶體學來確定蛋白質晶體的3-D結構。由溶液產生的晶體品質與成核率有關，成核率通常是由經典成核理論(Classical nucleation theory)解釋，依據此理論在溶液中密度擾動是形成臨界核的瓶頸之假設。
近來，模擬計算研究提出二階段成核過程之假說，在此假說中密度擾動與局部鍵結方向秩序為核叢集形成的兩關鍵機制。在這些模擬研究中，核叢集是依據Steinhardt等人提出的局部鍵結方向秩序參數w_4、w_6的標準決定。然而，在簡單流體中由W標準決定的無序叢集結構與BCC、FCC和HCP晶體結構的相似度仍須檢驗。本文中，根據局部鍵結方向秩序的概念引入一個新參數，局部結構相似性。用此參數來檢驗由W標準定義的叢集結構與相對應的晶體結構之間的相似性。

Crystallizations occur in natural phenomena and industrial processes. To generate crystals in good quality is essential for many scientific researches and applications. An example is the generation of protein crystals for the X-ray crystallography to determine their 3-D structure. The quality of the crystals generated from solutions depends on the nucleation rates, which were usually addressed by the classical nucleation theory (CNT) based on the assumption that density fluctuations in a solution are the bottleneck for the occurrence of critical nuclei.
Recently, computer simulation studies proposed the two-step nucleation hypothesis, in which both density fluctuation and local bond-orientational order are crucial mechanisms for the appearance of nucleus clusters. In these simulation studies, the nucleus clusters were determined by the criterions on W4 and W6, the local bond-orientational order parameters introduced by Steinhardt, et al. However, it still needs to examine the extent of the similarity between the structures of disordered clusters determined by the W-criterions in simple fluids and the BCC, FCC, and HCP crystals. In this paper, we introduce a new order parameter, the local-structure similarity, which also defined according to the concept of the local bond-orientational order. By using this newly defined order parameter, we examine the similarity between the cluster structures determined by the W-criterions and the corresponding crystal structures.

中文摘要 i
Abstract ii
誌謝 iii
目錄 iv
表格目錄 vi
圖表目錄 vii
壹、 緒論 1
貳、 理論 3
一、 局部鍵結方向秩序參數(Local bond-orientation order parameter) 3
二、 平均局部鍵結方向秩序參數(Averaged bond-orientational order parameter) 6
三、 局部結構相似性(Local structure similarity) 7
四、 剛體座標(Body frame) 9
I. 叢集體座標 9
II. 晶體結構叢集體座標 10
III. 歐拉旋轉矩陣 19
參、 系統模擬及結構分析 20
一、 Lennard-Jones systems 20
二、 模擬方法 21
三、 系統結構分析 23
I. 徑向分佈函數(Radial distribution function) 23
II. 靜態結構因子(Static Structure factor) 26
III. 鍵角分佈函數(Bond angle distribution) 27
IV. 配位數(Coordination number) 29
V. 局部鍵結方向秩序參數分佈 30
四、 歐拉角改變量選擇 33
肆、 結果與討論 35
一、 用w ̅_4、w ̅_6定義分類類似固態叢集 35
二、 利用局部結構相似性檢驗w ̅_4、w ̅_6分類結果 38
I. 叢集與不同晶體相似度 38
II. 叢集與不同晶體的相似比例 43
三、 以局部結構相似性(X)定義叢集 46
四、 檢驗X分類結果 48
I. X定義叢集與不同晶體相似度 48
II. 叢集於w ̅_4-w ̅_6平面之分佈 52
III. 叢集於q_4-q_6平面之分佈 56
IV. 叢集於q ̅_4-q ̅_6平面之分佈 60
伍、 結論 64
參考文獻 65

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