本文利用密度泛函理論 (Density Functional Theory, DFT)及分子動力學理論 (Molecule Dynamics, MD)模擬一維氧化鋅奈米結構的機械性質及電子特性。本文研究分成兩部份：
1.介紹一維氧化鋅奈米管在受到軸向應力拉伸時，其機械性質與電子特性。研究過程中，藉由密度泛函理論計算可以發現最高佔據軌道 (Highest Occupied Molecular Orbital, HOMO)和最低未佔據軌道 (Lowest Unoccupied Molecular Orbital, LUMO )的差值 (Gap)以及Radial Buckling會隨著應變量增加而變小。此外針對鍵長和鍵角的增減則可以知道結構隨著應變量增加而產生的變化，在電荷分布情形上，本文也採用部份電子態密度 (Partial Density of State, PDOS)、鍵級 (Bond Order, BO)以及電子密度差 (deformation density)等結果來進一步分析並了解氧化鋅奈米管在受到軸向應力拉伸時，電子特性的變化。
2.本文經由計算可以得知在以分子動力學搭配白金漢勢能函數 (Buckingham Potential)和Core-Shell 勢能函數來模擬一維氧化鋅奈米管在拉伸的過程中，各種不同的物理量，包含降伏應力、楊氏模數以及原子的滑移向量 (Slip Vector)參數來探討奈米管在受到軸向應力拉伸時的動態行為及結構變化。

In this study, we employed density functional theory (DFT) and molecular dynamics (MD) to investigate the mechanical and electronic properties of one-dimensional zinc oxide nanostructure. This study can be arranged into two parts:
In part I: We investigated the mechanical and electronic properties of one-dimensional zinc oxide nanostructure under axial mechanical deformations by density functional theory. In this case, we could find both the highest occupied molecular orbital and the lowest unoccupied molecular orbital gap (HOMO-LUMO gap) and value of radial buckling will decrease linearly with the increase of axial strain. The changes of bond lengths and bond angles show the variation of nanostructure dependence to the increase of axial strain. This study also used partial density of state (PDOS), bond order (BO) and deformation density to analyse the differences of the electronic properties between the zinc oxide nanotubes under axial strain.
In part II: This study, which employed molecular dynamics combines Buckingham and Core-Shell potentials, shows the different physical parameters, such as yield stress, young’s modulus and slip vector to research the mechanical behavior and variation of structure of nanotube under axial strain.

目錄
目錄 I
圖目錄 III
表目錄 V
中文摘要 VI
英文摘要 VII
第一章 緒論 1
1.1研究目標與動機 1
1.2單壁氧化鋅奈米管材料簡介及文獻回顧 4
1.3 本文架構 7
第二章 理論介紹 8
2.1密度泛函理論(Density Functional Theory, DFT) 8
2.1.1 電子密度(Electric Density) 8
2.1.2 湯馬士-費米模型(Thomas-Fermi model, TF model) 9
2.1.3 霍恩貝格-科恩模型(Hohenberg-Kohn model, HK model) 10
2.1.4 科恩-軒姆模型(Kohn-Sham model, KS model) 10
2.2 分子動力學理論 14
2.2.1 勢能函數(Potential Function) 14
2.2.1.1 白金漢勢能函數（Buckingham Potential Function） 15
2.2.1.2 Core-shell勢能函數 15
2.2.2 運動方程式 17
2.2.3 積分法則 18
2.2.4 時間步階選取 19
2.2.5 溫度修正 20
2.2.5.1 諾斯-胡佛恆溫法(Nosé-Hoover thermostat) 20
2.3數值統計方法 22
2.3.1 鄰近表列數值方法 22
2.3.2 原子級的應力計算方法 24
2.3.3 滑移向量(Slip Vector) 28
2.3.4 徑向分佈函數(Radial Distribution Function, RDF) 30
2.3.5 角關係函數(Angular Correlation Function, ACF) 32
第三章 結果與討論 33
3.1密度泛函理論模擬結果 33
3.1.1 單壁氧化鋅奈米管建構及參數設定 .33
3.1.2 HOMO-LUMO Gap和結構分析 36
3.1.3 電子特性分析 41
3.2分子動力學模擬結果 46
3.2.1 單壁氧化鋅奈米管建構及條件設定 46
3.2.2 在真空中的機械性質分析 46
第四章 結論與建議 56
4.1 結論 56
4.2 建議與未來展望 58
參考文獻 59

圖目錄
圖2-1截斷半徑法示意圖 17
圖2-2局部原子P0的Voronoi體積，如中間灰色區塊所示，其中P1、P2 及P3…等分別為鄰近原子，L為兩原子間之鉛垂線 27
圖2-3局部原子P0的Voronoi體積，相等於Srolovitz體積(圓的體積)，其中ai為原子平均半徑 27
圖2-4手扶型之奈米管搜尋鄰近原子之示意圖 29
圖2-5徑向、切線與軸向滑移向量之示意圖 29
圖2-6徑向分佈函數二維示意圖 31
圖2-7角關係函數三維示意圖 32
圖3-1 (4,4)扶手型單壁氧化鋅奈米管物理模型 35
圖3-2 (4,4)扶手型單壁氧化鋅奈米管應力應變曲線與HOMO-LUMO Gap變化 39
圖3-3依原子結構，將單壁氧化鋅奈米管上的鍵結與鍵角分類圖 39
圖3-4 Radial buckling、鍵長與應變之關係圖 40
圖3-5鍵角與應變之關係圖 40
圖3-6 O (30)與Zn (32)原子電荷與應變率之關係圖 43
圖3-7不同應變率下的O (30)與Zn (32)的部分電子態密度 44
圖3-8不同應變率下的鍵級與電子態密度差 45
圖3-9 (11,11)扶手型單壁氧化奈米管物理模型 49
圖3-10單壁氧化鋅奈米管應力、平均滑移向量對應變變係圖 49
圖3-11依原子結構，將單壁氧化鋅奈米管上的鍵結與鍵角分類 50
圖3-12鍵長與應變之關係圖 50
圖3-13鍵角與應變之關係圖 51
圖3-14各應變量其結構形貌圖 53
圖3-15應變量和徑向分佈函數 54
圖3-16應變量和角關係函數 55

表目錄
表2-1白金漢勢能參數 16
表2-2 Core-shell勢能參數 16
表2-3不同系統及運動形式的時間步階選取 19
表3-1扶手型單壁氧化鋅奈米管之管徑、鍵長、電荷轉移比較與鍵結能 35

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