石墨是碳元素在自然界中(常溫常壓下)所具有的最穩定結構。它不同於鑽石，有趣的鍵結方式也表現在其化學與物理特性上。使用近年發展出的 DFT-D 修正，對石墨結構略加改造後，我們進行了一系列的聲子計算，分析形成石墨結構的各種可能條件。由此工作獲得的經驗，相信對於往後碳元素相關材料在結構及物性的分析，或新材料設計方面將有助益。

Graphite structure is the most stable allotrope of carbon in normal temperature and pressure. The special layer by layer structure make it so different from diamond on many chemical and physical properties. Benefit by DFT-d correction, we investigate the details of graphite-like systems by performing phonon calculations. The results of this research improve our understanding about graphitic materials.

目錄
第一章、緒論________________________________1
1.1簡介_____________________________________1
1.2研究目的_________________________________2
1.3名詞解釋_________________________________2
第二章、研究方法____________________________4
2.1研究途徑_________________________________4
2.2相關理論簡介_____________________________5
2.3計算參數設置_____________________________8
第三章、結果與討論__________________________9
3.1石墨結構聲子譜特徵_______________________9
3.1.1碳、矽、鍺的石墨聲子譜比較_____________9
3.1.2矽碳交錯的石墨結構____________________11
3.1.3小結__________________________________12
3.2硼／碳石墨結構增減電子__________________15
3.2.1碳石墨結構減電子的聲子譜特徵比較______15
3.2.2硼石墨結構加電子的聲子譜特徵比較______17
3.2.3小結__________________________________19
3.3使用DFT+U對鍵結的影響___________________20
3.3.1雙原子分子加U系列計算_________________20
3.3.2石墨加U計算___________________________24
3.3.3小結__________________________________25
第四章、結論與議___________________________26
4.1總結____________________________________26
4.2建議____________________________________26
參考文獻___________________________________28
附錄Ａ、利用Jmol看聲子振動_________________30
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圖目錄
Fig3.1.1碳／矽／鍺石墨結構聲子譜___________10
Fig3.1.2碳石墨結構光學聲子與聲學聲子_______10
Fig3.1.3碳、矽交錯排列石墨結構聲子譜_______13
Fig3.1.4碳矽合金石墨結構．聲子振動mode_____14
Fig3.2.1碳石墨結構減電子聲子譜變化趨勢_____15
Fig3.2.2碳減電子聲子譜與對應DOS對照________16
Fig3.2.3硼加電子聲子譜與對應DOS對照________18
Fig3.3.1碳／氧雙原子分子+U系列計算DOS比較__22
Fig3.3.2 C2 &C2 +U(0.4eV)聲米能階附近佔據態軌域比較_23
Fig3.3.3碳+U系列計算聲子譜與對應DOS對照____24
Fig3.3.4碳+U系列計算聲子譜層狀特徵弱化對照_25
Fig4.1SiO2與CO2晶體聲子譜對照______________27
FigA.1連上Jmol官方網站．尋找下載link_______30
FigA.2下載正確檔案示意圖___________________30
FigA.3測試電腦環境_________________________31
FigA.4執行Jmol_____________________________32
FigA.5開啟檔案(1)__________________________32
FigA.6開啟檔案(2)__________________________33
FigA.7開啟指令稿___________________________33
FigA.8指令範例(1)__________________________34
FigA.9指令範例(2)__________________________35
FigA.10指令範例(3)_________________________35
FigA.11指令範例(4)_________________________36
FigA.12指令範例(5)_________________________36
FigA.13觀看聲子振動mode操作(1)_____________37
FigA.14觀看聲子振動mode操作(2)_____________37
FigA.15觀看聲子振動mode操作(3)_____________38
FigA.16觀看聲子振動mode操作(4)_____________38
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表目錄
Table2.1GGA計算石墨結構與加入DFT-D後計算之晶胞邊長比較___8
Table3.1.1碳／矽／鍺石墨結構．幾何結構最佳化後基本資料___9
Table3.1.2三種碳矽交錯排列石墨結構．幾何結構最佳化後基本資料___11
Table3.3.1B2、C2、N2、O2、F2、Si2 +U系列計算鍵能、鍵長、鍵級總表___20

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