系統識別號 | U0002-1902200815444800 |
---|---|
DOI | 10.6846/TKU.2008.00581 |
論文名稱(中文) | 微波介電材料La(Mg1/2,Ti1/2)O3的聲子計算:密度泛函微擾理論之研究 |
論文名稱(英文) | Phonon calculations on microwave dielectric material La(Mg1/2,Ti1/2)O3:Density-Functional Perturbation Theory Study |
第三語言論文名稱 | |
校院名稱 | 淡江大學 |
系所名稱(中文) | 物理學系碩士班 |
系所名稱(英文) | Department of Physics |
外國學位學校名稱 | |
外國學位學院名稱 | |
外國學位研究所名稱 | |
學年度 | 96 |
學期 | 1 |
出版年 | 97 |
研究生(中文) | 李維崇 |
研究生(英文) | Way-Chung Lee |
學號 | 694180273 |
學位類別 | 碩士 |
語言別 | 繁體中文 |
第二語言別 | |
口試日期 | 2008-01-23 |
論文頁數 | 80頁 |
口試委員 |
指導教授
-
林諭男
委員 - 薛宏中 委員 - 陳宜君 |
關鍵字(中) |
La(Mg1/2,Ti1/2)O3 第一原理 拉曼光譜 紅外光光譜 羅倫茲模型 |
關鍵字(英) |
La(Mg1/2,Ti1/2)O3 First-Principles Raman FTIR Lorentz model |
第三語言關鍵字 | |
學科別分類 | |
中文摘要 |
利用第一原理模擬計算La(Mg1/2,Ti1/2)O3材料,以密度泛函微擾理論及線性響應的方式,來研究微波介電材料La(Mg1/2,Ti1/2)O3在Γ點上的聲子行為,並以羅倫茲模型對於材料介電特性跟材料的晶格振盪的關係,來探討利用拉曼光譜實驗及紅外光光譜實驗於La(Mg1/2,Ti1/2)O3材料的結果輔以第一原理模擬計算所得到的資訊,來研究La(Mg1/2,Ti1/2)O3材料的聲子行為與介電特性的關係。 |
英文摘要 |
We use first-principles to begin the simulation on the microwave dielectric material La(Mg1/2,Ti1/2)O3. In our calculations, we use the Density-Functional Perturbation Theory and linear response method to get the phonons at Γ point. And then, we make a few experimental observations like Raman spectrum and FTIR spectrum on the microwave dielectric material La(Mg1/2,Ti1/2)O3. According to our calculations, the calculated eigenvalues and corresponding eigenvectors of each vibration mode at Γ point provide a great help on assignment of our experimental observations. Finally, we use the Lorentz model to study the relation between vibration modes and dielectric properties on the microwave dielectric material La(Mg1/2,Ti1/2)O3. |
第三語言摘要 | |
論文目次 |
第一章 緒論..............................................1 1.1 研究動機..........................................1 1.2 論文架構..........................................3 第二章 計算理論及模擬方法................................4 2.1密度泛函理論(Density Functional Theory)............4 2.1.1 Hohenberg-Kohn 理論.........................4 2.1.2 Kohn-Sham Equation..........................6 2.1.3 交換相干能..................................7 2.1.4 週期邊界條件................................8 2.1.5 k點取樣.....................................8 2.1.6 虛位勢.....................................9 2.2 密度泛函微擾理論................................10 2.2.1 線性響應及晶格動力學......................11 2.2.2 振動模式介電貢獻..........................13 2.3 介電機制.........................................13 2.4 拉曼(Raman) 與(傅力葉轉換紅外光吸收光譜) FTIR 光 譜...............................................18 2.4.1 拉曼(Raman)光譜...........................18 2.4.2 傅力葉轉換紅外光吸收光譜(FTIR)光譜.......20 第三章 實驗方法與步驟...................................22 3.1 La(Mg1/2,Ti1/2)O3 材料製備........................22 3.1.1 固態反應法................................22 3.1.2 檸檬酸鹽法................................23 3.2 特性分析..........................................26 3.2.1 X-Ray 分析................................26 3.2.2 Raman 光譜分析............................30 3.2.3 FTIR 紅外光光譜分析.......................31 3.2.4 SEM微結構觀察.............................34 第四章 計算結果與討論...................................36 4.0 計算軟體介紹及計算流程...........................36 4.1 La(Mg1/2,Ti1/2)O3晶格結構介紹....................38 4.2 電子結構的計算...................................41 4.3 La(Mg1/2,Ti1/2)O3材料在Γ點上的聲子計算...........48 第五章 結論.............................................77 參考文獻................................................79 圖表目錄 圖1-1 立方晶系鈣鈦礦結構的氧化物結構圖…………………………2 圖2-1 虛位勢示意圖…………………………………………………..10 圖2-2 物質中常見的四種極化………………………………………..17 圖2-3 介電常數實部對頻率之頻譜圖………………………………..17 圖2-4 史托克斯散射、反史托克斯散射及瑞立散射示意圖………..20 圖3-1 固態反應法製備LMT材料流程圖...........................................23 圖3-2 檸檬酸鹽法製備LMT材料流程圖...........................................25 圖3-3 固態反應法LMT粉末X-Ray繞射圖...........................................27 圖3-4 固態反應法LMT塊材X-Ray繞射圖...........................................28 圖3-5 檸檬酸鹽法P.H.值為7之LMT粉末X-Ray繞射圖..................28 圖3-6 檸檬酸鹽法P.H.值為9之LMT粉末X-Ray繞射圖..................29 圖3-7 檸檬酸鹽法P.H.值為11之LMT粉末X-Ray繞射圖..................29 圖3-8經1550℃燒結4小時的LMT塊材X-Ray繞射圖.......................30 圖3-9 La(Mg1/2,Ti1/2)O3塊材的Raman光譜圖.....................................31 表3-1 Raman光譜所得La(Mg1/2,Ti1/2)O3材料之active g mode振動模..............................................................................................................31 圖3-10 La(Mg1/2,Ti1/2)O3塊材的FTIR光譜圖....................................32 圖 3-11 La(Mg1/2,Ti1/2)O3塊材由FTIR光譜計算所得介電常數(a)實部與(b)虛部............................................................................................33 表3-2 FTIR光譜所得La(Mg1/2,Ti1/2)O3材料之active u mode振動模 ..................................................................................................................34 圖3-12 以固態法製備之LMT材料樣品SEM表面微結構圖...............35 圖3-13 以檸檬酸鹽法製備之LMT材料樣品SEM表面微結構圖.........35 圖4-1 第一原理基態計算流程圖……………………………………..37 圖4-2聲子計算流程圖…………………………………………………38 圖4-3 unit cell 中的LMT結構圖(a)1 unit cell (b) (b)跟鄰近晶格中O 原子所構成八面體示意圖……………………………………………..40 表4-1 來自文獻上的LMT晶格結構…………………………………41 圖4-4 結構穩定性的測試……………………………………………..43 圖4-5 鬆弛(relax)後的LMT結構(a)單一個unit cell (b) Top view of 3x3 unit cell…………………………………………………………….44 圖4-6 LMT結構(a)電子態密度(electronic DOS) (b)以VASP軟體算出來的電子態密度(c)p-DOS圖………………………………..………...45 圖4-7 LMT能帶結構計算在布里淵區走的路徑由Z經Γ、A、B、D至E點…………………………………………………………………..46 圖4-8 LMT材料的能帶結構—在各能量上的分布…………………..48 圖4-9 La(Mg1/2,Ti1/2)O3材料的FTIR光譜……………………………54 圖4-10 La(Mg1/2,Ti1/2)O3材料的Raman光譜………………………...54 圖4-11 以固態法製備的La(Mg1/2,Ti1/2)O3材料的FTIR光譜………55 表4-2 計算得到之g mode頻率與Raman實驗所得頻率…………...55 表4-3 計算所得之u mode頻率與FTIR實驗所得頻率…………….56 表4-4 計算所得之mode effective charge……………………….........57 表4-5 每個模式相對介電貢獻………………………………………..59 表4-6 計算所得之各振動模式……………………………………60~74 表4-7 利用FTIR光譜及第一原理計算所得之介電常數……………75 圖4-12 利用FTIR光譜算出之固態法與檸檬鹽法製備樣品之Qxf 值………………………………………………………………75 表4-8 以FTIR光譜得到介電常數虛部之頻率、強度、半高寬及介電 常數……………………………………………………………..75 |
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