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中文論文名稱 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
英文論文名稱 Phonon calculations on microwave dielectric material La(Mg1/2,Ti1/2)O3:Density-Functional Perturbation Theory Study
校院名稱 淡江大學
系所名稱(中) 物理學系碩士班
系所名稱(英) Department of Physics
學年度 96
學期 1
出版年 97
研究生中文姓名 李維崇
研究生英文姓名 Way-Chung Lee
學號 694180273
學位類別 碩士
語文別 中文
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
中文關鍵字 La(Mg1/2,Ti1/2)O3  第一原理  拉曼光譜  紅外光光譜  羅倫茲模型 
英文關鍵字 La(Mg1/2,Ti1/2)O3  First-Principles  Raman  FTIR  Lorentz model 
學科別分類 學科別自然科學物理
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.
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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