本論文是以分子動力模擬在非平衡狀態，二元合金固液體在快速冷卻固化過程中系統受一個拉的速度（V），其固-液界面區模擬濃度、溫度、密度和擴散系數的變化。
在快速冷卻中，控制固化速度為本文重要的變數（固化速度為系統受一個拉速度所轉化），速度(V)值會受原子勢能、系統溫度和密度的影響而產生出不同的變化，因此系統雖然是受一個固定拉速度，但系統每一個原子的速度卻不為一個常數，而速度V也會逐漸的轉換成溶質分離和陷落的驅動力。
在分離（segregation）的狀態控制下，我們可以重新得到一個液體區溶質的濃度分佈，而溶質的陷入或靜止則取決於V的增加或減少，因此我們可以從理論性的Aziz模型（J.Appl.Phys.53,1158~1981）來映證本文答案。

We use molecular dynamics to simulate the rapid directional solidification of binary alloy solid-liquid interface in the non-equilibrium state. In the pulling fixed velocities, we report the temperature, density, and diffusion coefficient of the interface.
In cooling fast, controlling the velocities of solidification for the important parameter of this text，it produces different changes that velocity value will be affected by atom potential energy and system temperature and density，though the system is pulling a fixed velocities, that the speed of every atom of the system is all not constant .The velocity will be changed into the driving force that the solute will be separated and trapped.
In the segregation regime, we recover the exponential form of the concentration profile within the liquid phase. Solute trapping is shown to settle in progressively as V is increased or reduction and our results are in good agreement with the theoretical predictions of Aziz.

第一章 序論
1.1 前言……………………………………………………… 1
1.2 文獻回顧………………………………………………… 3
第二章 固化理論
2.1 凝固簡介………………………………………………… 6
2.2 二元合金的凝固模式…………………………………… 7
2.3 凝固過程中溶質再分配………………………………… 9
第三章 分子動力學
3.1 基本原理………………………………………………… 14
3.2 勢能函數………………………………………………… 19
3.2.a Lennard-Jones potential…………………………… 22
3.2.b Morse potential……………………………………… 23
3.3 運動方程式
3.3.a Verlet algorithm……………………………………… 24
3.3.b Leap-Frog algorithm………………………………… 25
3.3.c Beeman algorithm……………………………………… 26
3.4 截斷勢能………………………………………………… 27
3.5 週期性幾何邊界條件…………………………………… 28
3.5.a 最小映象法……………………………………………… 28
3.6 Rescaling 溫度修正…………………………………… 30
3.7 分子動力學數值方法
3.7.a Verlet List 表列法…………………………………… 33
3.7.b Cell Link 表列法……………………………………… 34
3.7.c Verlet List 表列法結合Cell Link 表列法………… 36
3.7.d 無因次化……………………………………………… 37
3.8 系統熱力性質和動力特性……………………………… 39
第四章 建立物理模型
4.1 物理模型簡介…………………………………………… 40
4.2 模型物理參數…………………………………………… 41
4.3 模擬控制………………………………………………… 42
4.4 初始的系統濃度分配和二元相圖的運用……………… 46
第五章 模擬結果
5.1 分離的效應（segregation coefficient）…………… 51
5.2 對流速度………………………………………………… 53
第六章 結論與未來展望
6.1 結果與討論……………………………………………… 56
6.2 未來展望和建議………………………………………… 57
參考文獻………………………………………………………… 58

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