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研究生： 鄭繼暐
Cheng, Chi-Wei
論文名稱： 利用原子級模擬法研究奈米顆粒之燒結初期行為
Study of Initial Stage of Nano-particle Sintering by Molecular Dynamics Simulations
指導教授： 許文東
Hsu, Wen-Dung
學位類別： 碩士
Master
系所名稱： 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年： 2011
畢業學年度： 99
語文別： 中文
論文頁數： 110
中文關鍵詞： 分子動力學模擬 、二氧化鈦 、氧化鎂 、奈米燒結
外文關鍵詞： Molecular dynamic simulation, TiO2, MgO, Nanosintering
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    • 本實驗分別以氬原子模型和陶瓷模型兩部分來研究結構對燒結初期混合的影響，由氬原子 FCC 模型我們可以發現參雜奈米線和奈米球體的模型相較於單純由奈米球體組成可以得到比更好的混合結果，在經過 42奈秒之後配位數可達 6.5，大約是理論值 12 的一半；陶瓷模型以 TiO2 的Rutile 結構和 MgO 的岩鹽結構混合，我們發現氧化物的尺寸、維度以及結構穩定度對混合有很大的影響。當燒結起始物尺寸差異較大或有一方結構相對不穩定時，擴散的機制將由尺寸較小或不穩定的一方主導，雖然在模擬的結果無法觀察到 MgTiO3 的成相，但對於了解燒結初期的原子運動行為仍有很大的幫助。

    The research focuses on study initial stage of sintering of nanoparticles by Molecular Dynamics(MD) simulations. Lennard-Jones model were tested first. The results show that it is easier to have coalescence between nanowire to nanoparticle than nanoparticle to nanoparticle during sintering due to better atomic mixing. The coordination number is predicted to reach 6.5 after 42 ns of sintering, which is around half of theoretical value - 12. The simulation then carried out by simulating sintering of rutile-TiO2 and MgO nanoparticles by using Buckingham potential. The results demonstrate that size, dimensions and structural stability of oxide nanoparticles play an important role at initial stage of sintering. It is found that the diffusion is dominated by the oxide with smaller size or less stable structure. Thus simulation predicted that Ti atoms diffuse faster than Mg atoms when sintering between TiO2 nano-wire and MgO nanoparticle. On the other hand, Mg atoms diffuse faster than Ti atoms when sintering between TiO2 nanoparticle and MgO nanoparticle. Though, MgTiO3 phase was not found during such short simulation time, the outcomes provide insights to understand the atomic diffusion behavior at the initial stage of sintering.

    摘要 I ABSTRACT II 誌謝 III 總目錄 IV 表目錄 VIII 圖目錄 IX 第一章 前言 1 第二章 文獻回顧 3 2.1 微波介電材料 3 2.2 固相燒結理論 4 2.2.1 燒結基本原理 4 2.2.2 固態燒結模式 4 2.2.3 奈米陶瓷燒結行為 5 2.3 分子動力模擬燒結相關文獻 6 第三章 原子級模擬基礎理論 11 3.1 蒙地卡羅法與流程圖 11 3.2 分子動力學之基本假設與流程圖 12 3.3 勢能函數 13 3.3.1 Lennard-Jones勢能 13 3.3.2 Buckingham勢能 14 3.3.3 Direct summation法 14 3.4 週期性邊界(Periodic Boundary Condition) 16 3.5 初始條件設定 16 3.6 系綜 18 3.7 運動方程式 18 3.7.1 Verlet algorithms 18 3.7.2 Leap Frog algorithms 19 3.7.3 Velocity Verlet algorithms 20 3.7.4 溫度控制方法 20 3.8 截斷勢能 21 3.8.1 Verlet表列法 22 3.8.2 Cell Link表列法 22 3.8.3 Verlet表列法結合Cell Link表列法 23 第四章 物理模型與實驗設計 30 4.1 陶瓷結構介紹 30 4.1.1 TiO2結構 30 4.1.2 MgO結構 30 4.1.3 MgTiO3結構 31 4.2 物理模型介紹 31 4.2.1 氬原子簡化模型介紹 31 4.2.2 陶瓷模型介紹 32 4.2.3 陶瓷2nm小模型介紹 32 4.2.4 陶瓷沉積模型介紹 33 4.2.5 陶瓷2nm小模型加入MgTiO3核心 33 4.3 實驗設計與參數 34 4.3.1 氬原子固體混合 34 4.3.2 陶瓷固體混合 34 4.3.3 沉積 34 4.4 分析方法 35 4.4.1 MSD與擴散係數 35 4.4.2 迴轉半徑(gyration radius) 35 4.4.3 收縮率(shrinkage ratio) 36 4.4.4 Radial Distribution Function(RDF) 36 4.4.5 粗糙度(Roughness) 37 第五章 結果與討論 43 5.1 氬原子模型 43 5.2 陶瓷模型 45 5.2.1 TiO2、MgO、MgTiO3的勢能驗證 45 5.2.2 收縮率與迴轉半徑 47 5.2.3 MSD與總能量 49 5.2.4 RDF 50 5.3 陶瓷2nm模型 52 5.3.1 收縮率與相對迴轉半徑 52 5.3.2 MSD與總能量 53 5.3.3 RDF 54 5.4 沉積模型 55 5.4.1 覆蓋率 56 5.4.2 粗糙度 56 5.4.3 MSD與擴散係數 56 5.4.4 RDF 57 5.5 陶瓷2nm模型加入MgTiO3核心 58 5.5.1 收縮率與迴轉半徑 59 5.5.2 MSD與總能量 59 5.5.3 RDF 60 5.6 綜合討論 60 第六章 結論與未來展望 103 6.1 結論 103 6.2 未來展望 104 參考文獻 105

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