本研究將透過分子動力學模擬探討鐵-鉻-鉬-碳(Fe-Cr-Mo-C)塊材金屬玻璃之機械與結構性質，並選用第二最鄰近修正式原子鑲嵌法(second-nearest neighbor modified embedded-atom method, 2NN MEAM) 勢能函數描述鐵-鉻-鉬-碳原子之間的相互作用。再者，透過密度泛函理論計算勢能函數所需之參考數據並且結合force-matching(FM)方法擬合出適合的Fe54Cr16Mo12C18 塊材金屬玻璃的勢能參數。藉由所取得準確的勢能參數結合 basin-hopping(BH)方法便可建構Fe54Cr16Mo12C18 之非晶模型，之後再利用分子動力學理論去模擬此塊材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訊。
從應力應變曲線可求得楊氏模數約為139 GPa，且曲線也透露出該塊材金屬玻璃具有很大的塑性變形區間，顯示此研究材料具良好的延展性。由局部應力分析看出該塊材金屬玻璃材料受張力變形時，剪切帶的形成非常均勻，且受拉伸破壞後的斷裂角度 (θT) 為50°，與實驗預測拉伸斷裂角度 45°~ 90° 區間相符合。最後再用HA鍵型指數法(Honeycutt-Andersen index,HA index)來分析 Fe54Cr16Mo12C18 塊材金屬玻璃材料受到張應力時的結構變化以及塑性行為。

The mechanical properties and structural properties of Fe-Cr-C-Mo bulk metallic glasses have been investigated by molecular dynamics (MD) simulation with the 2NN modified embedded-atom method (2NN MEAM) potential which be used to model the atomic interactions among Fe, Cr, C, and Mo atoms. Furthermore, the reference data were obtained from the density functional theory (DFT) calculations. The parameter sets of binary element of Fe-Cr, Fe-Mo, Fe-C, Cr-Mo, Cr-C and Mo-C were fitted by force-matching (FM) method. Finally, these parameter sets of MEAM were further applied in generating Fe54Cr16Mo12C18 amorphous structures by basin-hopping (BH) method for conducting tensile simulations to get the stress-strain profiles. The mechanical properties and deformation mechanism, such as elastic modulus, plastic/elastic deformation mechanism and local strain distribution at different strains, were further investigated by the MD simulation.
According to stress-strain profiles, the estimated Young’s modulus of Fe54Cr16Mo12C18 bulk metallic glass is about 139 GPa. It also shows that this bulk metallic glass possess excellent ductility because of large plastic region. Local strain distribution was used to analyze the deformation mechanism, and the results reveal that shear bands form homogeneously and the tensile fracture angle (θT) is about 50 degree which is agreement with experimental result of 45°< θT < 90°. Finally, Honeycutt-Andersen (HA) index were used to investigate the plastic/elastic deformation mechanism of Fe54Cr16Mo12C18 BMG under the tensile test.

誌謝 i
中文摘要 ii
Abstract iii
目錄 iv
圖次 vii
表次 ix
第一章 緒論 I
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電子密度 10
2.1.2湯瑪士-費米理論 (Thomas-Fermi Theory) 10
2.1.3霍恩貝格-科恩理論 (Hohenberg-Kohn Theory) 10
2.1.4科恩-沈方程式 (Kohn–Sham equation) 11
2.1.5交換相關函數(Exchange-Correlation Function) 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 15
2.2.3 Basin-Hopping (BH) method 16
2.3分子靜力學理論 18
2.3.1 LBFGS法 18
2.3.2火炎演算法 20
2.3.3共軛梯度法 21
2.4分子動力學理論 23
2.4.1積分法則 23
2.4.2諾斯-胡佛恆溫法(Nosé-Hoover thermostat) 24
2.4.3時間步階選取 25
2.5結構分析 27
2.5.1 HA鍵型指數法 27
2.5.2原子級應力分析 28
2.5.3區域應變分析 31
2.6週期邊界的處理 32
2.7鄰近原子表列數值方法 33
2.7.1截斷半徑法 33
2.7.2 Verlet List表列法 34
2.7.3 Cell Link表列法 36
2.7.4 Verlet List結合Cell Link表列法 37
2.8 模擬流程 38
第三章 結果與討論 41
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 參數擬合結果 54
3.2 模型建立及分析 58
3.2.1 試驗之物理模型建構 58
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 65
3.3.1 拉伸模型建立 65
3.3.2 試驗結果分析 66
第四章 結論與建議 73
4.1 結論 73
4.2 建議與未來展望 75
參考文獻 76

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