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研究生:雷文騰
研究生(外文):Wen-Teng Lei
論文名稱:第一原理計算研究類氮化矽結構之硼碳氮化合物機械性質
論文名稱(外文):Mechanical Properties of Boron Carbon Nitride Compounds with Si3N4-like Structure: The Ab initio Study
指導教授:劉柏良劉柏良引用關係
口試委員:李明憲洪銘聰
口試日期:2017-07-28
學位類別:碩士
校院名稱:國立中興大學
系所名稱:精密工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2017
畢業學年度:105
語文別:中文
論文頁數:81
中文關鍵詞:第一原理碳化矽硼碳氮化合物彈性常數體積模數剪切模數楊氏模數
外文關鍵詞:ab initiofirst-principlesboron carbon nitrideelastic constantsbulk modulusshear modulusYoung’s modulus
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本論文利用第一原理計算研究基於α相氮化矽、β相氮化矽以及γ相氮化矽的硼碳氮化合物之晶格結構與機械性質,研究過程採用已被廣泛應用的α相氮化矽、β相氮化矽與較高硬度的γ相氮化矽之晶格結構作為基礎,將硼原子、碳原子和氮原子置換氮化矽原子模型中的氮原子和矽原子而形成基於氮化矽結構之α相硼碳氮化合物、β相硼碳氮化合物與γ相硼碳氮化合物。計算結果顯示硼碳氮化合物具有六方晶系P-6空間群、三方晶系P31c空間群以及四方晶系P-4m2空間群之結晶相,並且藉由Born穩定性準則判斷晶格結構之穩定性。對於晶格結構穩定的硼碳氮化合物則利用Voigt-Reuss-Hill近似法計算硼碳氮化合物之機械性質,其中三方晶系P31c空間群之硼碳氮化合物具有最佳的體積模數320.57 GPa、剪切模數372.68 GPa以及楊氏模數804.48 GPa。
In this study, the ab initio calculation was performed to investigate the crystal structure and mechanical properties of boron carbon nitride (BCN) compounds with basic α-, β-, and γ-Si3N4 structure while Si and N atoms were systematically replaced by boron, carbon, and nitrogen to find out the best geometry. The results of geometry optimization show that the space group of BCN compounds would be P-6, P31c or P-4m2. The following calculation on elastic constants was carried out to verify the stability of different models according to the Born stability criteria. The best mechanical properties of BCN compounds calculated by Voigt-Reuss-Hill approximation can have bulk modulus of 320.57 GPa, high shear modulus of 372.68 GPa, and high Young’s modulus of 804.48 GPa.
致謝 i
摘要 ii
Abstract iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 1
1.3 論文架構 5
第二章 文獻回顧 12
2.1 超硬材料 12
2.2 鑽石與立方結構氮化硼 12
2.3 氮化矽與氮化碳 15
2.4 硼碳氮化合物 16
第三章 計算方法與理論 21
3.1 前言 21
3.2 第一原理簡介 21
3.3 Hohenberg-Kohn Theorem 22
3.4 Kohn-Sham Equation 24
3.5 Local Density Approximation 25
3.6 Generalized Gradient Approximation 25
3.7 贗勢 26
3.8 Born Stability Criteria 27
3.9 Voigt-Reuss-Hill Approximation 28
3.10 各向異性 30
第四章 六方結構硼碳氮化合物之機械性質 32
4.1 計算模型與設定 32
4.2 結果與討論 33
4.3 結論 36
第五章 立方結構硼碳氮化合物之機械性質 59
5.1 計算模型與設定 59
5.2 結果與討論 59
5.3 結論 61
第六章 總結論 73
參考文獻 75
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