臺灣博碩士論文加值系統

　　近代固態物理的發展配合高速電腦的理論計算，已成為我們研究各式新穎樣品的重要途徑，本研究即以第一原理模擬計算微波介電材料(1-x)La2/3TiO3-xLaAlO3。首先我們從0.9La2/3TiO3 -0.1 LaAlO3的晶格結構中獲得純La2/3TiO3的原子位置，接著以密度泛函微擾理論來研究該材料在Γ點上之聲子行為。從聲子的計算結果輔以實驗量測獲得的拉曼光譜與紅外光光譜，藉此探討微觀下的聲子振動行為與介電機制的關係。

At the present, the combination of high performance computation and solid-state theory provides a promising methodology to elucidate the microscopic properties of versatile materials. We use the first-principles to start the simulation on the microwave dielectric material La2/3TiO3 - LaAlO3. At first, we get the La2/3TiO3 crystal structure from the atomic position of ceramic 0.9La2/3TiO3-0.1LaAlO3 , and then we use the Density - Functional Perturbation Theory to investigate the phonons at Γ point.
According to the phonon calculation, the calculated eigenvalues and the corresponding eigenvectors of each vibrational mode at Γ point provide a great help on our experimental observations. Comparing with Raman and FTIR spectrum, we can study the dielectric properties on the microwave dielectric material La2/3TiO3 - LaAlO3.

目　錄

第一章　導論 1
　　§ 1.1 研究動機 1
　　§ 1.2 第一原理計算簡介 3
　　§ 1.3 論文架構 5

第二章　理論及模擬方法 7
　　§ 2.1 前言 7
　　§ 2.2 密度泛函理論 7
　　　 2.2.1 Hohenberg-Kohn 理論 8
　　　 2.2.2 Kohn-Sham Equation 9
　　　 2.2.3 交換相干能 11
　　 　2.2.4 週期邊界條件 12
　　　 2.2.5 k點取樣 12
　　　 2.2.6 虛位勢 13
　　§ 2.3 密度泛函微擾理論 14
　　　 2.3.1 線性響應及晶格動力學 14
　　　 2.3.2 振動模式介電貢獻 16
　　§ 2.4 介電機制 17
　　§ 2.5 拉曼與傅力葉轉換紅外光吸收光譜 21
　　　 2.5.1 拉曼光譜理論 21
　　　 2.5.2 傅力葉轉換紅外光吸收光譜 23
　　　 2.5.3 FTIR 光譜分析原理 24

第三章　材料特性與實驗分析 31
　　§ 3.1 前言 31
　　　 3.1.1 鈣鈦礦結構 31
　　　 3.1.2 La2/3TiO3-LaAlO3 材料簡介 31
　　§ 3.2 文獻回顧 34
　　　 3.2.1 製程 34
　　　 3.2.2 Series of the 18 Ceramics 36
　　§ 3.3 Raman 光譜分析 38
　　　 3.3.1 A-Series 39
　　　 3.3.2 B-Series & C-Series 40
　　　 3.3.3 D-Series 42
　　　 3.3.4 (1-x)LT-xLA-0.25 wt%Mn-180oC/hour 43
　　§ 3.4 FTIR 光譜分析 45

第四章　計算結果與討論 51
　　§ 4.1 簡介 51
　　§ 4.2 計算軟體 52
　　§ 4.3 流程 53
　　　 4.3.1 La2/3TiO3 晶格結構介紹 56
　　　 4.3.2 虛位勢選擇 58
　　　 4.3.3 原子鬆弛計算 60
　　§ 4.4 DOS & Band Structure 61
　　§ 4.5 聲子 63
　　　 4.5.1 G Mode 80
　　　 4.5.2 U Mode 87
　　　 4.5.3 介電常數 91

第五章　結論 92

參考文獻 94


圖 目 錄

Fig.1-1 立方晶系鈣鈦礦結構的氧化物陶瓷材料結構圖 6
Fig.1-2 Ion positions in cubic perovskite structure 6
Fig.2-1 k-point sampling 28
Fig.2-2 虛位勢示意圖 28
Fig.2-3 物質中常見之四種極化 29
Fig.2-4 介電常數實部對頻率之頻譜圖 30
Fig.2-5 史托克斯散射、反史托克斯散射及瑞立散射 30
Fig.3-1 立方晶系鈣鈦礦結構的BaTiO3結構圖 32
Fig.3-2 Ion substitutions in perovskite structure 33
Fig.3-3 Layered structure of La2/3TiO3 33
Fig.3-4 La2/3TiO3-LaAlO3製程流程圖 35
Fig.3-5 Raman spectra for A-Series 39
Fig.3-6 Raman spectra for A-Series 40
Fig.3-7 Raman spectra for B-Series 41
Fig.3-8 Raman spectra for C-Series 41
Fig.3-9 Raman spectra for D-Series 42
Fig.3-10 Summary of Raman spectra 44
Fig.3-11 FTIR spectra of A-Series 46
Fig.3-12 FTIR spectra of B-Series 46
Fig.3-13 FTIR spectra of 0.9LT-0.1LA-1 oC/hour 47
Fig.3-14 FTIR spectra of 0.9LT-0.1LA-3 oC/hour 47
Fig.3-15 FTIR spectra of 0.9LT-0.1LA-180 oC/hour 48
Fig.3-16 FTIR spectra of 0.9LT-0.1LA-900 oC/hour 48
Fig.3-17 A-Series介電常數虛部圖 49
Fig.3-18 B-Series介電常數虛部圖 49
Fig.3-19 A-Series品質因子 50
Fig.3-20 B-Series品質因子 50
Fig.4-1 Crystal structure of La2/3TiO3 54
Fig.4-2 第一原理計算流程圖 55
Fig.4-3 La2/3TiO3晶格結構 57
Fig.4-4 La2/3TiO3晶格結構 57
Fig.4-5 E-Cut對系統總能的收斂計算(for FHI) 59
Fig.4-6 E-Cut對系統總能的收斂計算(for PSPNC) 59
Fig.4-7 Crystal structure of La2/3TiO3 60
Fig.4-8 Electronic DOS of La2/3TiO3 61
Fig.4-9 Brillouin zone path 62
Fig.4-10 Energy band structure 62
Fig.4-11 Rigid layer shift 83
Fig.4-12 Compression 83
Fig.4-13 756 cm-1 84
Fig.4-14 Raman spectra of 0.9LT-0.1LA-1 oC/hour 84
Fig.4-15 Raman spectra of 0.8LT-0.2LA-1 oC/hour 85
Fig.4-16 Raman spectra of 0.6LT-0.4LA-1 oC/hour 85
Fig.4-17 Rotation of O atom 86
Fig.4-18 292 cm-1 系統形變示意圖 86

表 目 錄

Table.3-1 Change of crystal structure symmetry with oxygen
deficiency in the ceramic La2/3TiO3-λ 34
Table.3-2 A-Series：0.6LT-0.4LA-X wt%Mn-180oC/hour 37
Table.3-3 B-Series：0.9LT-0.1LA-0.25 wt%Mn-R oC/hour 37
Table.3-4 C-Series：0.6LT-0.4LA-0.25 wt%Mn-R oC/hour 37
Table.3-5 D-Series：0.8LT-0.2LA-0.25 wt%Mn-R oC/hour 38
Table.3-6 0.4LT-0.6LA-0.25 wt%Mn-180 oC/hour 38
Table.3-7 Lattice parameters of La2/3TiO3-LaAlO3 44
Table.4-1 Atom positions of ceramic 0.9LT-0.1LA 52
Table.4-2 Crystal data for La2/3TiO3 56
Table.4-3 計算所得之55個聲子振動模式 64
Table.4-4 Mode effective charge 78
Table.4-5 計算得到之G Mode v.s. Raman spectra 82
Table.4-6 U Mode v.s. FTIR 與相對介電貢獻 90
Table.4-7 Dielectric constant of B Series 91

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