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研究生:賴力行
研究生(外文):Li-Hsing Lai
論文名稱:運用第一原理計算方法來研究鈦酸鋇系統之物理性質
論文名稱(外文):Study the physic properties of BaTiO3 system by the First-principles calculations
指導教授:雷健明
指導教授(外文):Chien-Ming Lei
學位類別:碩士
校院名稱:中國文化大學
系所名稱:材料科學與奈米科技研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:中文
論文頁數:106
中文關鍵詞:第一原理計算六方晶鈦酸鋇聲子振動模式
外文關鍵詞:first-principles calculationhexagonal BaTiO3phononvibration mode
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我們成功的使用ABINIT完成Cubic、Tetragonal、Hexagonal三種不同結構BaTiO3的態密度、能帶結構、聲子頻譜與振動模式的第一原理計算。
Cubic結構BaTiO3的計算結果顯示,聲子能譜有虛頻率出現,這意味著Cubic為較不安定的結構。實驗結果與相關文獻比較聲子頻率,雖然不同文獻中所使用的計算程式與參數不盡相同,但整體趨勢上計算結果與文獻並不會有太大的差距。
根據結果分析Cubic結構具15種振動模式,將振動模式分為五類,第一類為鋇、鈦、氧原子都往同一方向振動;第二類為鋇原子振動方向與其他原子相反;第三類為鈦氧面的氧與鋇氧面的氧振動方向相反;第四類為鈦氧面的鈦與氧振動方向相反;第五類為鋇氧面的氧與鈦氧面的鈦與氧振動方向相反。
Tetragonal結構的計算結果顯示,聲子頻譜上未出現虛頻率,可以推斷Tetragonal為較安定的結構相。在聲子頻譜上Γ點有不連續的情況出現,此不連續發生是因為在Γ點發生的LO-TO分裂所導致。
Hexagonal結構的態密度計算結果在費米面附近有能隙(energy gap)存在,能帶結構的結果也與電子態密度的結果相符。Hexagonal結構具有30個unit cell,故聲子頻譜線非常的密集,有多條頻譜線有簡併現象發生。比較中發現文獻中的聲子頻率在550至620(cm-1)的範圍內都沒有頻率出現,而我們的計算也有相同的現象,同時由計算的結果聲子頻率在650至720(cm-1)的範圍內無聲子吸收,由實驗中也發現,確定無吸收。
經由實驗結果分析,我們先將Hexagonal的90種振動模式依振動的原子種類分為七大類。第一類為鋇、鈦、氧原子都有振動;共有5種模式、第二類為只有氧有振動,共有36種模式;第三類為只有鋇原子有振動,共有10種模式;第四類為只有鈦原子有振動;第五類為只有氧與鈦原子有振動,共有31種模式;第六類為只有氧與鋇原子有振動,共有2種模式;第七類為只有鋇與鈦原子有振動,共有6種模式。
In this thesis, we are studied the density of state, energy band structure, phonon dispersion relation and vibration modes of cubic, tetragonal and hexagonal structure of BaTiO3 by ab initio calculation.
Our first-principles calculation result shows that the existence of imaginary phonon of cubic BaTiO3 corresponds to a structural instability under ambient condition. The density of state and phonon band structures of the cubic BaTiO3 system is consistent with several literatures although those literatures are using several different lattices parameters with this thesis.
Based on the group theorem, there are 15 vibration modes of cubic structure BaTiO3. The vibration modes can be classified five types; the first type is moving modes. The second type is that the vibration direction of Ba-atoms is opposite to others atoms. The third type is the vibration direction of Oxygen atoms on Ti-O planes are opposite to the Oxygen atoms on Ba-O planes. The fourth type is the Ba and O in the Ba-O plane, which are vibrated in opposite ways. The other type is that the vibration directions of Oxygen atoms on Ba-O planes are opposite to the Oxygen atoms and Ti-atom on Ti-O planes.
The first-principles calculation result shows that there is no the existence the imaginary phonon of tetragonal BaTiO3 phase, which means the tetragonal phase is more stable than the cubic phase. Because of the LO-TO energy splitting, there are discontinued of phonon band structure at Γ point.
The calculation result shows that the hexagonal structure BaTiO3 is existence the energy band of the Fermi surface. The unit cell of hexagonal BaTiO3 is included 30 atoms, there are 90 vibration modes in the hexagonal BaTiO3, which is due to the phonon bands are very high density and degeneracy. The results are predicted that there is no mode existence during 550-620cm-1 and 650-720cm-1, which is consistent with the literature report.
Those 90 modes can be label as 7 kinds. The first kind is movement modes that are included 5 modes. The second kind is only Oxygen vibrations that are included 36 modes. The third kind is only Ba-atoms vibrations that are included 10 modes. The fourth kind is only Ti-atoms vibration that is only 1 mode. The fifth kind is only Oxygen and Ti-atoms vibration, which are included 31 modes. The sixth kind is only Oxygen and Ba-atoms vibration that are included 2 modes. The seventh kind is only Ba-atoms and Ti-atoms vibrations, which are included 6 modes.
摘要 I
Abstract III
謝誌 IV
目錄 V
圖目錄 VIII
表目錄 XI
第一章 導論 1
1-1 前言 1
1-2鐵電材料 2
1-2-1鐵電材料之特性簡述 2
1-2-2電滯曲線 6
1-2-3相變溫度 8
1-2-4鐵電晶體的分類 9
1-3鈦酸鋇(BaTiO3)基本性質 11
第二章 基本理論與模擬方法 15
2-1材料模擬方法導論 15
2-2量子物理第一原理 15
2-3密度泛函理論概述 16
2-3-1 從波函數到電子密度 16
2-3-2 Hohenberg-Kohn定理:多體理論 18
2-3-3 Kohn-Sham方程式: 有效單體理論 19
2-3-4 交換相關能量泛函 20
2-3-5 LDA 與 GGA 21
2-3-6 週期性邊界條件 22
2-3-7 k點取樣與截止能量E cut 22
2-3-8 虛位勢 23
2-4 密度泛函微擾理論與聲子計算 25
2-5 電子與聲子的交互作用與Migdal- Eliashberg理論 26
2-6 ABINIT 與其他第一原理計算軟體 28
2-7 拉曼光譜與紅外線吸收光譜 30
第三章 計算流程 32
3-1 計算流程簡介 32
3-2參數輸入與測試 33
3-2-1 Cubic結構之截止能量與k點取樣測試 33
3-2-2 Tetragonal結構之截止能量與k點取樣測試 35
3-2-3 Hexagonal結構之截止能量與k點取樣測試 36
3-3 基態計算 38
3-4 態密度、能帶結構計算 38
3-5 聲子計算 38
第四章 BaTiO3之聲子計算 40
4-1 Cubic結構之鈦酸鋇聲子計算 40
4-1-1 基態計算與態密度、能帶結構計算 40
4-1-2 聲子計算 43
4-2 Tetragonal結構之鈦酸鋇聲子計算 46
4-2-1基態計算與態密度、能帶結構計算 46
4-2-2 聲子計算 49
4-3 Hexagonal結構之鈦酸鋇聲子計算 52
4-3-1基態計算與態密度、能帶結構計算 52
4-3-2 聲子計算 55
第五章 結論 69
參考文獻 72
附錄 78
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