本文用分子動力學研究Ti60Zr10Ta15Si15金屬玻璃的機械與結構性質。為了模擬這個四元的合金系統，文中同時使用了兩種勢能函數，因鉭矽這個組合經過電子密度分析之後，顯示出較薄弱的共價鍵特性，故使用Tight-binding函數用來模擬金屬原子間以及鉭與矽之間的交互作用。Tersoff 函數則用來模擬矽與鋯、矽與鈦、矽與矽之間的作用。而為了可以正確的描述這些原子間的作用，我們將密度泛函理論計算出來的彈性模數、鍵結能與原子間的作用力當作參考的目標值，並擬合適和Ti60Zr10Ta15Si15金屬玻璃材料的勢能參數。
得到準確的勢能參數後，基於這些勢能參數建立出Ti60Zr10Ta15Si15金屬玻璃的模型，並利用分子動力學理論去模擬此金屬玻璃受到張應力下的結構變化以及得到應力應變的資料，從應力應變曲線可求得楊氏模數大約為93GPa與實驗值88GPa相近，且曲線也透露出該金屬玻璃具有延展性而由局部應力分析看出該BMG受張力變形時，剪切帶的形成非常均勻，沒有主要方向，故提升了延展性。之後再用Voronoi tessellation analysis 以及 HA 指數 來分析Ti60Zr10Ta15Si15 金屬玻璃材料受到張應力時的結構變化以及塑性行為，發現到正二十面體以及矽周圍的結構在變形時變動最為劇烈。

The mechanical and structural properties of Ti60Zr10Ta15Si15 bulk metallic glasses have been investigated by molecular dynamics (MD) simulation. In order to simulate the Ti-Zr-Ta-Si systems, two potential functions were employed. The tight binding (TB) potential was used to model the interactions between metallic elements (Ti,Zr,Ta) and the Ta-Si pair which showed less covalency based on the electron density analysis. The modified Tersoff potential was used to model the interactions between Si-Zr, Si-Ti and Si-Si pairs. All parameters of TB and modified Tersoff potentials were fitted on the basis of several reference data including the binding energies, atomic forces of structures at equilibrium, elastic constants of pure Zr, Ti, Si, the binary intermetallic compound structures. These reference data were obtained from DFT calculations and experimental results, and the fitted parameters can reflect the properties of all reference data.
These parameters of TB and modified Tersoff were further applied in generating the structure of Ti60Zr10Ta15Si15 bulk metallic glass and then the molecular dynamic simulation was performed to do the tension test and get the stress-strain profiles. According to stress-strain profiles, Ti60Zr10Ta15Si15 bulk metallic glass is ductile and the estimated Young’s modulus is about 93GPa which is close to the experimental value. Local strain distribution was used for analyzing the deformation mechanism, and results show that shear band develops homogeneously which enhances the plasticity.
The Voronoi tessellation analysis and HA index were used for further investigating the plastic/elastic deformation mechanism. The results show that icosahedral local structure and the structure around Si atoms undergo a severe variation during the tension process.

Keywords: Bulk metallic glasses, Molecular dynamics, Density Functional Theory, mechanical properties,Tight-Binding potential, Tersoff potential

論文審定書 i
誌謝 ii
中文摘要 iii
英文摘要 iv
目錄 vi
圖次 ix
表次 xi
第一章 緒論 1
　1.1 研究背景與介紹 1
　1.2 文獻回顧 5
　1.3 研究目的 7
　1.4 論文架構 8
第二章 理論基礎及方法. 9
　2.1 密度泛函理論(DENSITY FUNCTIONAL THEORY) 9
　　2.1.1 Thomas-Fermi 理論 9
　　2.1.2 Hohenberg-Kohn 理論 10
　　2.1.4 Kohn-Sham 方程式 10
　　2.1.5 交換相關函數(Exchange-Correlation Function) 11
　　2.1.6 電子密度 12
　2.2 勢能函數 13
　　2.2.1 原子間作用勢能 13
　　2.2.2 擬合勢能參數 16
　　2.2.3 Big-Bang (BB) method 17
　　2.2.4 Basin-Hopping (BH) method . 18
　2.3 分子靜力學理論 19
　　2.3.1 LBFGS 法 20
　　2.3.2 火炎演算法 22
　　2.3.3 共軛梯度法 23
　2.4 分子動力學理論 24
　　2.4.1 積分法則 24
　　2.4.2 諾斯-胡佛恆溫法(Nosé-Hoover thermostat) 25
　　2.4.3 時間步階選取 27
　2.5 結構分析 28
　　2.5.1 HA 鍵型指數法 28
　　2.5.2 Vonronoi 指數分析 29
　　2.5.3 原子級應力分析 29
　　2.5.4 區域應變分析 32
　2.6 週期邊界的處理 33
　2.7 鄰近原子表列數值方法 34
　　2.7.1 截斷半徑法 34
　　2.7.2 Verlet List 表列法 35
　　2.7.3 Cell Link 表列法 . 37
　　2.7.4 Verlet List 結合Cell Link 表列法 37
　2.8 模擬流程 39
第三章 結果與討論. 42
　3.1 擬合勢能參數 42
　　3.1.1 尋找最佳DFT 設定及建立reference data 42
　　3.1.2 選擇適合的勢能描述原子間作用力 53
　　3.1.3 參數擬合結果 55
　3.2 模型建立及分析 59
　　3.2.1 試驗之物理模型建構 59
　　3.2.2 試驗之物理模型分析 59
　3.3 拉伸試驗與機械性質探討 67
　　3.3.1 拉伸模型建立 67
　　3.3.2 試驗結果分析 67
第四章 結論與建議. 76
　4.1 結論 76
　4.2 建議與未來展望 78
參考文獻 79

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