臺灣博碩士論文加值系統

本論文採用平衡分子動力學數值工具來研究碲化鉍單晶系統及具雙晶界之系統的聲子色散關係、聲子態密度及晶格熱傳導係數。原子間的交互作用力考慮了二體勢能函數、三體勢能函數及庫倫勢能函數。
在單晶系統的模擬中，於聲子色散關係的部份，考慮三體勢能會使聲頻支斜率增加，並使得低頻區聲子態密度分佈範圍增加，庫倫勢能則不會造成明顯影響。晶格熱傳導係數乃透過Green-Kubo relation求得，並以擬合函數得相關時間常數。研究發現熱傳導係數隨溫度上升而下降，且有明顯的非等向性。有考慮三體勢能時所得的熱傳導係數較大，額外添加庫倫勢能則略微降低熱傳能力。
在雙晶界系統的模擬中，發現具Te1原子層雙晶界之系統其界面能量改變不明顯，而具Te2及Bi原子層雙晶界之系統其界面能量略為上升，但對於聲子色散關係及聲子態密度的影響不大，僅多出一些橫波光頻支。與單晶系統相比，雙晶界會造成熱傳導係數在in plane及cross plane方向上約有20%~40%的下降，表示雙晶界會增加聲子的散射機會。其中，以具Te2及Bi原子層雙晶界之系統有較Te1雙晶界系統大的下降幅度；隨著雙晶界週期變小，熱傳導係數有降低的趨勢。

This thesis employs the equilibrium molecular dynamics (EMD) simulation method to calculate the phonon dispersion relations, the phonon density of states (DOS) and the lattice thermal conductivity of bismuth telluride which has either a single crystal structure or is embedded with twin boundaries. We consider the two-body potential, the three-body potential and the coulomb potential to describe the interactions between atoms. Effects of the latter two are studied.
In the simulations of Bi2Te3 single crystal, the group velocities of acoustic phonons are larger and the low-frequency region of the DOS spectrum becomes broader when the three-body potential is taken into consideration. However, the Coulomb potential has no significant impact on the vibration modes. We obtain the lattice thermal conductivity in use of the Green-Kubo relation; a low-frequency filtering process, and an exponential fitting process with two time scales are utilized. The calculation results show that the thermal conductivity is anisotropic and decreases with increasing temperature. The thermal conductivities become larger when the three-body potential is included and drop a little by the Coulomb force.
When embedded with Te1 twin boundaries, the interfacial energy of the system does not change obviously, when embedded with Te2 or Bi twin boundaries, the interfacial energy of the system increases slightly, but the phonon dispersion relation and DOS are barely affected except the presence of a few new optical branches. Compared to the simulations of the single crystal, both the in-plane and cross-plane thermal conductivities decrease about 20%-40% by the twin boundaries, especially, the Te2 and the Bi twin boundaries. Furthermore, the thermal conductivities decrease as the period of twin boundaries decreases.

誌謝 I
中文摘要 II
Abstract III
目錄 V
表目錄 VII
圖目錄 VIII
符號說明 XI
第一章 緒論 1
1-1 研究背景 1
1-2 文獻回顧 1
1-2-1 實驗量測 2
1-2-2 理論模型 3
1-2-3 分子動力學模擬 3
1-3 研究動機與目的 6
1-4 論文架構 6
第二章 碲化鉍材料、分子動力學理論與數值方法 8
2-1 碲化鉍材料 8
2-2 勢能函數 9
2-2-1 Qiu和Ruan勢能函數及參數 10
2-2-2 Huang和Kaviany勢能函數及參數 10
2-2-3 庫倫勢能及Ewald method 11
2-3 無因次化 13
2-4 初始與邊界條件 15
2-4-1初始位置與速度 15
2-4-2週期性邊界條件 16
2-5 溫度控制 16
2-6 運動方程式 17
2-7 平衡分子動力學 18
2-7-1聲子色散關係 18
2-7-2聲子態密度 19
2-7-3 Green-Kubo relation 19
2-8 模擬之收斂測試規劃 21
第三章 碲化鉍材料之能量傳輸性質 23
3-1 Ewald method測試及參數最佳化 23
3-1-1測試模型及流程簡介 23
3-1-2測試結果 23
3-2 模擬系統設置 25
3-3 穩態判斷 26
3-4 聲子色散關係 27
3-5 聲子態密度 28
3-6 原子位置徑向分佈函數 29
3-7 熱傳導係數與時間常數 30
3-7-1熱流自相關函數及Green-Kubo relation 30
3-7-2不同溫度下的熱傳導係數與時間常數 31
第四章 雙晶界對於碲化鉍材料的影響 34
4-1雙晶界模型及模擬設置 34
4-2穩態判斷 34
4-3聲子色散關係 35
4-4聲子態密度 36
4-5熱傳導係數與時間常數 36
第五章 結論與未來展望 39
5-1 結論 39
5-2 未來展望 40
參考文獻 41
圖表 45

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