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研究生:葉書佑
研究生(外文):Shu-Yu Yeh
論文名稱:定量相場模式在三接點附近界面不穏定形態之研究
論文名稱(外文):Quantitative Phase Field Modeling of Interfacial Morphology near Triple Junction
指導教授:藍崇文藍崇文引用關係
指導教授(外文):Chung-Wen Lan
口試委員:諶玉真高振宏廖英志曹恆光
口試委員(外文):Yu-Jane ShengC-Robert KaoYing-Chih LiaoHeng-Kwong Tsao
口試日期:2015-07-28
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:化學工程學研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:英文
論文頁數:133
中文關鍵詞:相場模式晶界溝槽界面失穩線張力晶界擴散三接點
外文關鍵詞:Phase field modelGrain boundary grooveInterfacial instabilityLine tensionGrain boundary diffusionTriple junction
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在多晶固化的過程中,晶界的存在對於界面不穩定有著重要的影響,晶界同時提供了一個讓溶質可以快速擴散的路徑。 本論文將利用多晶相場模式來模擬雙成份多晶的平衡形狀及垂直固化程序,並結合定量多晶適應性相場模式及抑制溶質包覆修正項來進行包含晶界的穩定界面及界面失穩模擬。 在穩定界面模擬中,晶界的存在會使得固液界面受晶界能的影響形成溝槽,而在奈米尺度下,晶界的線張力會開始影響晶界溝槽的夾角和曲率。 但是對於相場模式, 目前仍無法三維定量模擬線張力在三接點的影響。本文提出適應性定量相場模式的線張力模式對接觸角的影響。 而在晶體生長的過程中,因為溶質經由晶界擴散,固液界面會朝液體方向有輕微的變形,這樣的現象造成了當晶體生長速度大於臨界速度時,駝峰形狀的產生。 在平行晶界的方向,隨著長速的增加,也會有界面失穩的現象發生。 這和實驗的觀察有一致的結果。 但是,在處理晶界擴散時,很難避免相場模式中界面厚度對等效擴散係數的影響。 為了修正這樣的影響,吾人將提出結合了古典晶界擴散及適應性相場模式的新模式。 這個新模式有不受界面厚度影響及和古典的晶界擴散理論一致的優點。

During the polycrystalline solidification process, the existence of grain boundary plays an important role in the interface instability, and provides a fast diffusion path for the solute. In the directional solidification process, the solute diffuses into the grain boundary. Even at the pulling speed below the critical value, the interfaces beside the grain boundary groove are slightly deflected toward the melt. This supercooling and the interface deflection trigger the morphological instability as the pulling speed exceeds the critical value. As observed in the experiments, this led to the hump formation and the interface would break down in the direction parallel to the grain boundary at the higher pulling velocity. However, in dealing with the grain boundary diffusion, it is difficult to simulate the diffusion process that is independent of the interface thickness.
The equilibrium shape of the grain boundary groove is affected by the grain boundary energy. As the grain size decreasing to nanoscale, the line tension begins to play a role in the equilibrium shape.
In this thesis, a binary polycrystalline alloy during the directional solidification process is simulated by the adaptive phase field model; the orientation field is used for treating the grain boundary, and thin-interface model with anti-trapping solute current are further adopted. The line tension model coupled with the quantitative phase field model is proposed. A model that embeds a grain boundary and triple junction diffusion term in the existing adaptive phase field model are derived. The grain boundary diffusion results are in good agreement with the classical solution.


摘要 I
Abstract II
Table of Contents III
Nomenclature VI
List of Tables XV
List of Figures XVI
Chapter 1. Introduction 1
1-1 Equilibrium Shapes of Polycrystal 1
1-2 Interface Instability near Grain Boundary 6
1-3 Numerical Methods for Free Boundary Problem and Polycrystalline Simulation 11
1-4 Phase Field Model 13
1-5 Motivation 22
1-6 Organization of the Thesis 22
Chapter 2. Theory of Solidification and Grain Boundary Diffusion 25
2-1 Fundamental Theory of Solidification 25
2-2 Interface Instability in Directional Solidification of Binary Alloy 27
2-3 Grain Boundary and Triple Junction Diffusion Model 31
Chapter 3. Adaptive Phase Field Model and Numerical Methods 37
3-1 Polycrystalline Phase Field Model 37
3-2 Phase Field Model with Line Tension at Triple Junction 40
3-3 Numerical Method 42
3-3-1 Adaptive Mesh Refinement 43
3-3-2 Finite Volume Method 48
Chapter 4. Equilibrium Shape at Triple Junction 55
4-1 Grain Boundary Grooving 55
4-2 Wall Effects on the Grain Boundary Groove 58
4-3 Adaptive Phase Field Model with Line Tension at Triple Junction 61
4-4 Phase Field Model on Anisotropic Wetting 63
4-4-1 Wetting on Single Stripe 64
4-4-2 Wetting on Multiple Stripes 66
4-4-3 Wetting on Microgrooves 68
Chapter 5. Interface Instability near Grain Boundary and Triple Junction 71
5-1 1D Diffusion Problem with a Constant Moving Velocity 71
5-2 2D Directional Solidification of a Binary Alloy Polycrystalline 73
5-2-1 Effect of Pulling Velocity 75
5-2-2 Hump Formation 80
5-3 3D Interface Instability near the Grain Boundary 85
5-4 Sample Thickness Effects on the Interface Instability near the Grain Boundary 92
Chapter 6. Grain Boundary and Triple Junction Diffusion Model with Phase Field Model 95
6-1 Modified Grain Boundary Diffusion Model 95
6-2 Benchmarks of Modified Grain Boundary Diffusion Model 100
6-3 3D Grain Boundary and Triple Junction Diffusion Model 104
Chapter 7. Conclusion and Outlook 107
Bibliography 109
Appendix A : Gibbs-Thomson equation with line tension 121
Appendix B : Line tension effects on contact angle 125
Appendix C : Thermodynamics Approach of Phase Field Model with Line Tension Effects 127
Appendix D : Curriculum Vitae 133


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