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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