臺灣博碩士論文加值系統

本研究藉由密度泛函理論計算(Density Functional Theory)計算銅鋯(Cu-Zr) 合金之空間群對稱性結構:FCC-Cu1Zr3、FCC-Cu2Zr2、FCC-Cu3Zr1、HCP-CuZr、B1及B2為參考結構與能量，再利用Big-Bang(BB)及Basin-Hopping(BH)計算法結合Force-matching(FM)方法擬合出Cu-Zr勢能參數。並以此參數計算Cu46Zr54、Cu50Zr50 及Cu64Zr36比例組成BMG材料之體積模數(Bulk Modulus)、剪力模數(Shear Modulus)、楊氏係數(Young’s Modulus)及柏松比(Poisson Ratio)。之後，再利用分子靜力學模擬壓縮試驗探討傾斜45及水平0角度之CuZr/Zr/CuZr 之多層膜結構變形機制及機械行為，計算壓縮過程中之應力應變曲線。水平0角度因無傾斜面只有內部Zr層所產成之差排，對於傾斜45角度因ZrCu 金屬玻璃薄膜(Thin Film Metallic Glasses, TFMGs)與Zr層界面之能量穩定度，造成滑移速度及最大應力不同主要因素。最後，本研究探討各傾斜角度，在壓縮變形過程中根據不同應變在ZrCu TFMGs所產生的剪切帶、剪力變形區及受力滑移所造成的原子分佈情形。

In this study, the mechanical properties of Cu-Zr binary bulk metallic glasses (BMG) were investigated at the nano-scale. The stable amorphous structures and corresponding energies of BMG structures are performed by density functional theory (DFT) calculation as reference data. This study will combine the Force-Matching (FM) method and Basin-Hopping (BH) method to develop a new method for fitting the Cu-Zr Tight-binding (TB) potential parameters. Moreover, the Bulk modulus, Shear modulus, Young''s modulus and Poisson ratio of Cu46Zr54, Cu50Zr50 and Cu64Zr36 structures are calculated with the fitting TB parameters. In addition, the compression process of BMG materials is simulated by the Molecular Statics. The stress and strain are obtained to investigate the deformation mechanism of CuZr/Zr/CuZr nanolaminates at 0 and 45 inclined degree.
Finally, we investigate the angle in the deformation process under different strain in the shear band, shear transformation zones (STZs) and force caused by the slip of the atomic distribution of TFMGs layer.

圖次 III
表次 VI
中文摘要 VII
ABSTRACT VIII
第一章 序論 1
1.1研究目的與動機 1
1.2文獻回顧 6
1.3論文架構 10
第二章 理論基礎及方法 11
2.1密度泛函理論(Density Functional Theory) 11
2.1.1 Thomas-Fermi 理論 11
2.1.2 Hohenberg-Kohn 理論 12
2.1.4 Kohn-Sham方程式 12
2.1.5交換相關函數(Exchange-Correlation Functions) 13
2.2最佳化理論 14
2.2.1 LBFGS法 15
2.2.2火炎演算法 17
2.2.3共軛梯度法 18
2.3最佳化結構 19
2.3.1 Big-Bang (BB) method 19
2.3.2 Basin-Hopping (BH) method 20
2.4勢能函數 22
2.4.1原子間作用勢能 22
2.4.2擬合勢能參數 24
2.5原子級應力分析 25
2.6變形分析 29
2.7週期邊界的處理 29
第三章 數值方法 31
3.1鄰近原子表列數值方法 31
3.1.1截斷半徑法 31
3.1.2維理表列法(Verlet List) 32
3.1.3巢室表列法(Cell Link) 34
3.1.4維理表列結合巢室表列法 (Verlet List Combine Cell Link) 35
3.2 模擬流程圖 36
第四章 結果與討論 37
4.1 擬合勢能參數及機械性質分析 37
4.1.1 擬合原子間之勢能參數 37
4.1.2 Cu-Zr比例機械性質分析 43
4.2 模擬壓縮試驗 47
4.2.1 壓縮試驗之物理模型建構 47
4.2.2 壓縮試驗條件環境設定 51
4.3 壓縮試驗結果分析 53
第五章 結論與建議 75
參考文獻 76

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