本研究藉由密度泛函理論與模擬退火法建立非結晶鎂銅釔金屬玻璃合金，並利用分子靜力學探討非結晶鎂銅釔金屬玻璃合金於奈米壓痕及奈米刮痕下的機械性質。
　　本研究中所需之部分勢能參數由擬合所得到，建立結構後所得的體積模數44.81GPa、楊氏係數53.49GPa和X-ray繞射曲線圖，這三個性質和實驗文獻比對非常相近，數值上的誤差皆在10%以內，驗證了本研究擬合勢能的正確性。
　　在模擬奈米壓痕過程，探針的力量-位移曲線和影響深度曲線被計算，此外滑移向量參數和Honeycutt-Andemen index也被利用去探討材料局部結構的變形機制及鍵型變化。於本研究的模擬結果，其非結晶鎂銅釔金屬玻璃合金硬度是6.984GPa，並且執行壓痕過程中，發現當探針壓至銅原子居多的局部結構時，會因為阻擋原子之擴散行為而造成硬度上升。此外，外力造成鎂銅釔合金結構的組成仍為非晶態，其原因由探針附近的局部結構，與FCC和HCP相關的鍵型指數1421，有36%轉變為與非晶態相關的鍵型指數1431。可能形成結晶型態的機率，因外力的影響而降低。
　　在模擬奈米括痕過程，兩個不同刮痕深度(5Å與15Å)的奈米刮痕被探討，並分析探針的側向力量-刮痕距離曲線。此外滑移向量參數也被利用去探討材料局部結構的變形機制。我們發現在刮痕深度5Å，刮痕距離14Å處與刮痕深度15Å，刮痕距離6Å處，還有10Å至13Å，均有側向力曲線突然升高或異常平滑，這是因為探針接觸到銅原子團，導致銅原子團變形，進而影響側向力的變化。經由壓痕與刮痕相對照後，可發現探針受力情況與原子活動狀況皆因銅原子團所影響。

Amorphous Mg-Cu-Y metallic glasses are established by density functional theory and simulated annealing method in this study. The mechanical properties of amorphous Mg-Cu-Y metallic glasses are investigated by molecular statics simulations for the nano-indentation and the nano-scratch process.
In this study, some potential energy parameters are obtained by fitting for describing the Mg-Cu-Y system. The bulk modulus, the Young’s modulus and X-ray structure of the Mg-Cu-Y system are calculated. Our results are within 10% error compared with experimental values, which prove the correctness of fitted potential parameters.
For the cases of nanoindentations, the indentation force-displacement and the influenced depth are calculated. The mechanical properties are obtained are close to experimental results. The both “slip vector” and Honeycutt-Andemen index (HA index) parameters are also used to study the deformation behavior and bond-type of a group of atoms. Our results indicate that the influenced depths can be affected by the tip indentation and the gather of copper atoms. The gather of copper atoms can provide the resistance and strengthen the mechanical properties of Mg-Cu-Y material. On the other hand, our results indicate that the amorphous structure of Mg-Cu-Y metallic glasses cannot be transferred to crystal structure during nano-indentation process by analysis of HA index.
For the cases of nano-scratch, two different scratch depth (5Å and 15Å) are investigated to understand the understand the depth effect. the scratch force-displacement curve is also obtained. As the same with nano-indentation results, the scratch force will increase because the gather of copper atoms and provide the resistance.

目錄 i
圖目錄 iii
表目錄 v
摘要 vi
Abstract viii
第一章　緒論 1
1.1 研究目的與動機 1
1.2 文獻回顧 3
1.3 論文架構 8
第二章 理論基礎 9
2.1 密度泛函理論(Density functional theory, DFT) 9
2.1.1 Thomas-Fermi模型與Hohenberg-Kohn模型 9
2.1.2 Kohn-Sham方程式 10
2.2 勢能函數 11
2.2.1 擬合勢能參數 11
2.2.2 基板原子間作用勢能 12
2.2.3 基板原子與碳原子間作用勢能 13
2.3 模擬退火法 14
2.4 最佳化理論 15
第三章 數值模擬方法 18
3.1 週期性邊界條件 18
3.2 鄰近原子表列數值方法 19
3.2.1 截斷半徑法(Cut-off method) 20
3.2.2 維理表列法(Verlet list) 21
3.2.3 巢室表列法(Cell link) 22
3.2.4 維理表列結合巢室表列法(Verlet list combine cell link) 23
第四章　結果與討論 25
4.1 建立基板結構 26
4.1.1 擬合基板原子間的勢能參數 26
4.1.2 探針對基板原子的勢能參數 29
4.1.3 藉由模擬退火法建立結構 30
4.2 奈米壓痕 34
4.2.1 壓痕物理模型之建構 34
4.2.2 壓痕深度與影響深度之關係及材料機械性質分析 35
4.2.3 HA鍵型指數法分析壓痕深度對結構之影響 42
4.3 奈米刮痕 47
4.3.1 刮痕物理模型之建構 47
4.3.2 刮痕距離與側向力之關係 48
第五章　結論與建議 56
參考文獻 57

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