臺灣博碩士論文加值系統

本論文利用分子動力學(MD)模擬銅奈米試片在單軸拉伸下之塑性行為，假設試片內部存在有不同幾何外型之封閉缺陷，並配合不同拉伸方向，探討其奈米線的變形機制與差排發射、移動行為對其強度之影響，原子間勢能函數則採用嵌入原子式模型(EAM)。
模擬結果顯示，當差排由內部封閉缺陷周圍發射時，其強度會比完美晶體排列的試棒低。拉伸方向為<111>時，由於彈性變形時的側向變形量較小，因此內部存在有缺陷時對強度之影響較少，亦即其缺陷敏感度較低；而拉伸方向為<110>時，彈性變形時的側向變形量在<010>方向最大，因此內部存在有缺陷時，於此方向的影響程度也最高，故整體而言，拉伸方向為<110>時，其缺陷敏感度最高。而拉伸方向為<100>時，若內部存在之缺陷具有與拉力軸平行之圓柱狀對稱的幾何性質時，則在單軸拉伸條件下，由於對稱性的差排滑移，容易形成疊差菱形柱(Stacking fault rhombic pillar)。

This study analyzes mechanical behaviors of defective Cu nanowires with three different orientations during uniaxial tension, using a molecular dynamic simulation. The investigation designs the various shapes and orientations of closed cracks inside nanowires and studies the influences of the cracks on the strength, deformation mechanism, dislocation emission. The embedded-atom-method (EAM) potential is employed to describe the atomic interactions.
Analysis results demonstrate that if the leading dislocation are emitted from cracks, the strength of the defective nanowires occur is lower than that of defect-free nanowires. When the load direction is <111>, the difference in the influence of the crack on strength between the defective nanowires and defect-free nanowires because the amount of later elastic deformation of the <111> nanowires is less than other orientations. When the <110> nanowires are under tension, the effect of the crack on strength is the highest because the later elastic deformation in <010> is the highest. Therefore, the <110> orientation is the most sensitive to the crack under tension.
For the <100> nanowires, if the cross section of the crack is circular, the dislocation mechanism easy to form the stacking fault rhombic pillar due to the symmetry of dislocation slip.

目錄
中文摘要………………………………………………………………Ⅰ
英文摘要………………………………………………………………Ⅱ
誌謝……………………………………………………………………Ⅲ
目錄……………………………………………………………………Ⅳ
表索引…………………………………………………………………Ⅷ
圖索引…………………………………………………………………Ⅸ
第1章 緒論……………………………………………………………1
1.1 研究動機及目的………………………………………1
1.2 分子動力學文獻回顧…………………………………3
第2章 分子動力學基礎理論………………………………………5
2.1 勢能函數…………………………………………………5
2.2 原子級應力、應變計算………………………………7
2.3 Verlet list 表列法…………………………………………9
2.4 Centrosymmetry參數…………………………………10
第3章 程式模擬步驟與試片模型建立…………………………12
3.1 程式模擬步驟…………………………………………12
3.1.1 初步預備(Initialization)………………………12
3.1.1.1 預備(Preliminaries)………………12
3.1.1.2 初始條件(Initialization)……………16
3.1.2 平衡(Equilibration)……………………………17
3.1.3 動態模擬(Production)…………………………18
3.2 試片模型建立…………………………………………19
3.2 蒲松比(Poisson’s ratio)之計算方式…………………….21
第4章 結果與討論…………………………………………………24
4.1 模擬結果……………………………………………24
4.1.1 <100>試棒之拉伸行為.……...……………..….…24
4.1.1.1 <100>完美晶體試棒之拉伸行為(Specimen A)………………………………………....24
4.1.1.2 <100>試棒內部包含一近似圓形缺陷之拉伸行為(Specimen B)……………………..26
4.1.1.3 <100>試棒內部包含一長軸平行於[100]方向之橢圓形缺陷拉伸行為(Specimen C)…………………………………………27
4.1.1.4 <100>試棒內部包含一長軸平行於拉力軸之橢圓形缺陷拉伸行為(Specimen D)…………………………………………28
4.1.2 <110>試棒之拉伸行為.……...……………..….…30
4.1.2.1 <110>完美晶體試棒之拉伸行為(Specimen E)………………………………………....30
4.1.2.2 <110>試棒內部包含一近似圓形缺陷之拉伸行為(Specimen F)……………………..30
4.1.2.3 <110>試棒內部包含一長軸平行於<110>之橢圓形缺陷拉伸行為(Specimen G)……..31
4.1.2.4 <110>試棒內部包含一長軸平行於拉力軸之橢圓形缺陷拉伸行為(Specimen H)…………………………………………31
4.1.2.5 <110>試棒內部包含一長軸平行於<100>之橢圓形缺陷拉伸行為(Specimen I)…...32
4.1.3 <111>試棒之拉伸行為.……...……………..….…33
4.1.3.1 <111>完美晶體試棒之拉伸行為(Specimen J)……………………………………….....33
4.1.3.2 <111>試棒內部包含一近似圓形缺陷之拉伸行為(Specimen K)……………………..33
4.1.3.3 <111>試棒內部包含一長軸平行於<110>之橢圓形缺陷拉伸行為(Specimen L)……..33
4.1.3.4 <111>試棒內部包含一長軸平行於拉力軸之橢圓形缺陷拉伸行為(Specimen M)………………………………………...34
4.1.3.5 <111>試棒內部包含一長軸平行於<112>之橢圓形缺陷拉伸行為(Specimen N)…......34
4.2 試棒之拉伸行為分析……………..………….…….…...35
4.2.1 <100>試棒之拉伸行為分析..……………….....…35
4.2.2 <110>試棒之拉伸行為分析..……………….....…38
4.2.3 <111>試棒之拉伸行為分析..……………….....…41
第5章 結論與建議…………………………………………………..44
5.1 結論……………………………………………………...44
5.2 未來研究方向與建議…………………………………...45
參考文獻………………………………………………………………..46




表索引
表2.1 銅晶體之Centrosymmetry參數值……….……………………52
表3.1 EAM模型參數表……..……………………………………….52
表3.2 物理參數無因次化換算表…………………………………….53
表3.3 Gear’s預測修正法參數與展開階數關係表………….……….54
表3.4 各項參數及條件設定………………………………….………55
表3.5 試棒編號及試棒特徵描述…………………………………….56
表4.1 Specimen B Lomer-Cottrell障壁形成反應式…….……..…….58
表4.2 Specimen D Lomer-Cottrell障壁形成反應式…………..…….59
表4.3 拉伸方向為<100>之各試棒機械性質表…...…………..…….60
表4.4 拉伸方向為<110>之各試棒機械性質表…...…………..…….61
表4.5 拉伸方向為<111>之各試棒機械性質表…...…………..…….62
表4.6 拉伸方向為<111>，試棒長度加長之各試棒強度比較...…….63

圖索引
圖2.1 原子間相對距離與鍵結能關係圖………..…………………...64
圖2.2 局部最大應力(真應力)示意圖……………..………….……...65
圖2.3 Verlet表列法示意圖.…………………………………………66
圖2.4 Centrosymmetry 參數值計算示意圖……………...…………67
圖3.1 模擬流程示意圖………….…….……………………………...68
圖3.2 試棒模型外觀………………………….…...……………….....69
圖3.3 拉伸方向為<100>試棒透試圖….………………………..…...70
圖3.4 拉伸方向為<110>試棒透試圖….………………………..…...71
圖3.5 拉伸方向為<111>試棒透試圖….………………………..…...72
圖3.6 蒲松比(Poisson’s ratio)之計算示意圖….……….………..…...73
圖4.1 Specimen A拉伸過程中型態變化圖……………………..…...74
圖4.2 Specimen A應力應變曲線圖……….……………...……..…...75
圖4.3 Specimen B拉伸過程中型態變化圖……………………..…...76
圖4.4 Specimen B應力應變曲線圖……….……………...……..…...77
圖4.5 Specimen B疊差菱形柱形成機制示意圖………………….....78
圖4.6 Specimen C拉伸過程中型態變化圖……………………..…...79
圖4.7 Specimen C應力應變曲線圖……….……………...……..…...80
圖4.8 Specimen D拉伸過程中型態變化圖……………...……..…...81
圖4.9 Specimen D應力應變曲線圖……………………...……..…...82
圖4.10 Specimen D疊差菱形柱形成機制示意圖...………..…..…...82
圖4.11 Specimen D在拉伸過程中原子排列方向之轉換….…..…...83
圖4.12 Specimen B ~ Specimen D 缺陷周圍原子在拉伸過程中變形狀態三視圖…..…………………………………………….....84
圖4.13 Specimen E拉伸過程中型態變化圖………………………...85
圖4.14 Specimen E應力應變曲線圖……...…….…………………...86
圖4.15 Specimen F拉伸過程中型態變化圖………………………...87
圖4.16 Specimen F應力應變曲線圖……...…….…………………...88
圖4.17 Specimen G拉伸過程中型態變化圖…………...…………...89
圖4.18 Specimen G應力應變曲線圖……...…….……...…………...90
圖4.19 Specimen H拉伸過程中型態變化圖……………...………...91
圖4.20 Specimen H應力應變曲線圖……...…….…………………..92
圖4.21 Specimen I拉伸過程中型態變化圖…….…………………...93
圖4.22 Specimen I應力應變曲線圖……....…….…………………...94
圖4.23 Specimen J拉伸過程中型態變化圖…….…………………...95
圖4.24 Specimen J應力應變曲線圖……...…….…………………...96
圖4.25 Specimen K拉伸過程中型態變化圖…….……………..…...97
圖4.26 Specimen K應力應變曲線圖……...…….……...…………...98
圖4.27 Specimen L拉伸過程中型態變化圖…….………...………...99
圖4.28 Specimen L應力應變曲線圖……...…….………………….100
圖4.29 Specimen M拉伸過程中型態變化圖…….…..…………….101
圖4.30 Specimen M應力應變曲線圖……...…….……...………….102
圖4.31 Specimen N拉伸過程中型態變化圖…….………..……….103
圖4.32 Specimen N應力應變曲線圖……...…….………...……….104
圖4.33 拉伸方向為<100>時，FCC滑動系統示意圖...…………….105
圖4.34 彈性變形內原子側向收縮示意圖………………………….106
圖4.35 Specimen F ~ Specimen I缺陷周圍原子在拉伸過程中變形狀態三視圖…..………………………………………………...107
圖4.36 拉伸方向為<110>時，FCC滑動系統示意圖...…………….108
圖4.37 Specimen K ~ Specimen N缺陷周圍原子在拉伸過程中變形狀態三視圖…..……………………………………………...109
圖4.38 拉伸方向為<111>時，FCC滑動系統示意圖...…………..…110

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