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研究生:洪千晴
研究生(外文):Cain-Cing Hung
論文名稱:以第一原理計算探討鉭摻雜對於二氧化鈦作為鈉離子陽極材料之影響
論文名稱(外文):First-Principles Calculations to Investigate the Effect of Tantalum Doping on Titanium Dioxide as a Sodium-ion Anode Material
指導教授:謝介銘
指導教授(外文):Chieh-Ming Hsieh
學位類別:碩士
校院名稱:國立中央大學
系所名稱:化學工程與材料工程學系
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:2023
畢業學年度:111
語文別:中文
論文頁數:106
中文關鍵詞:密度泛函理論鉭摻雜二氧化鈦銳鈦礦金紅石TiO2(B)
外文關鍵詞:density functional theorytantalum-dopedtitanium dioxideanataserutileTiO2(B)
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鈉離子電池由於成本上的絕對優勢及豐沛的天然資源,是替代鋰離子電池成為大規模儲能系統最合適候選人,尋求具有高壽命極高理論容量的陽極材料是主要的挑戰之一。二氧化鈦擁有毒性低、化學穩定度高,易取得且高理論電容量,因此被認為是有前途的鈉離子電池陽極材料,但卻有著高帶隙所導致的低電導率,先前的實驗文獻表明,摻雜6at%的鉭原子可以有效的改善電池的電化學性能及循環性能。
在這本篇研究中,我們基於第一性原理計算,利用density functional theory (DFT)以微觀的角度探討鈉離子在摻雜鉭原子前後之嵌入及擴散行為,並且我們也分析了Hirshfeld分布、電子密度差圖及電子結構。首先我們對三種常見的二氧化鈦晶型:銳鈦礦、金紅石及TiO2(B),進行全幾何結構優化計算,並且比較摻雜鉭原子分布遠、近之能量,以找到最有利的鉭摻雜分布。然後,根據不同的擴散環境,設計了兩個不同的擴散路徑,即鈉離子擴散時是否經過兩個相鄰的鉭原子之間,同時利用climbing image nudged elastic band (CI-NEB)方法計算比較不同路徑和鉭摻雜的影響。計算結果表明,鉭原子由於尺寸效應和較高的Hirshfeld電荷,因此並不利於鈉離子的傳輸,在銳鈦礦及金紅石的系統中,相較於鈉離子嵌入未經過兩個相鄰鉭原子的路徑,恰好經過兩個相鄰的鉭原子之間時擴散能障的增加量最多高達9倍之多,相反的,相較於鈉離子嵌入原始二氧化鈦,鉭摻雜TiO2(B)擴散能障些微下降0.168和0.175eV。最後,從電子結構的角度來看,鉭的摻雜產生了上自旋極化,形成新的局域態,有效的降低了銳鈦礦及 TiO2(B) 的帶隙,促進了電化學性能,我們認為鉭摻雜的銳鈦礦和 TiO2(B) 複合材料,並且適量的摻雜維持了鈉離子擴散性能的穩定性,奠定了鉭摻雜二氧化鈦作為鈉離子電池的潛力。
Sodium ion battery is the most suitable candidate to replace lithium ion battery as a large-scale energy storage system due to its absolute cost advantage and abundant natural resources, and the search for anode materials with high lifetime and high theoretical capacity is one of the major challenges. Titanium dioxide is considered as a promising anode material for sodium ion batteries because of its low toxicity, high chemical stability, easy availability and high theoretical capacity, but it has low conductivity due to high band gap.
In this study, we used density functional theory (DFT) to investigate the intercalation and diffusion behavior of sodium ions before and after doping with tantalum atoms from a microscopic perspective based on first principles calculations, and we also analyzed the Hirshfeld population, electron density difference map, and electronic structure. To find the most favorable tantalum doping distribution, we first performed full geometric optimization calculations for three common titanium dioxide polymorphs: anatase, rutile, and TiO2(B). Then, two different diffusion paths were designed according to different diffusion environments, i.e., whether the sodium ion passes through two neighboring tantalum atoms during diffusion, and the effects of different paths and tantalum doping were compared using the climbing image nudged elastic band (CI-NEB) method. The results show that tantalum dopants are not favorable for sodium ion transport due to size effects and higher Hirshfeld charges, and that in the case of anatase and rutile systems, the enhancement of the diffusion energy barrier is up to 9 folds when the sodium ion passes between two neighboring tantalum atoms compared to the pathway where the sodium ion is intercalated without passing through two neighboring tantalum atoms. On the contrary, the diffusion barrier of tantalum-doped TiO2(B) decreases slightly by 0.168 and 0.175 eV compared to that of sodium-intercalated pristine titanium dioxide.
Finally, from the perspective of electronic structure, tantalum doping generates upper spin polarization and forms new localized states, which effectively reduces the bandgap of anatase and TiO2(B) and promotes the electrochemical performance. We suggest that tantalum-doped anatase and TiO2(B) composite materials, and appropriate amount of doping maintains the stability of the diffusion performance of sodium ions, and establishes the potential of tantalum-doped titanium dioxide as a sodium-ion battery.
中文摘要 i
Abstract ii
致謝 iv
目錄 v
圖目錄 viii
表目錄 ix
第一章 緒論 1
1-1. 前言 1
1-2. 鈉離子電池組成 2
1-3. 常見鈉離子陰極、陽極材料 4
1-3-1. 陰極材料 (Cathode) 4
1-3-2. 陽極材料 (Anode) 4
1-4. 二氧化鈦作為鈉離子電池陽極材料 6
1-4-1. 銳鈦礦 (Anatase) 7
1-4-2. 金紅石 (Rutile) 9
1-4-3. 單斜晶系二氧化鈦 (TiO2(B)) 11
1-4-4. 二氧化鈦作陽極材料實驗文獻探討 13
1-4-5. 二氧化鈦作陽極材料理論計算探討 16
1-5. 研究動機 22
第二章 理論方法 23
2-1. 第一計算原理 (First-principles calculation) 23
2-2. 密度泛函理論 (Density functional theory, DFT) 23
2-3. Hohenberg-Kohn 定理 24
2-4. Kohn-Sham 方程式 25
2-5. 局部密度近似 (Local density approximation, LDA) 26
2-6. 廣義梯度近似 (Generalized gradient approximation, GGA) 26
2-7. GGA+U 近似修正 (Hubbard-like U) 27
2-8. 自洽場 (Self-consistent field, SCF) 27
2-9. Bloch’s 定理 28
2-10. 準位能 (Pseudopotential) 28
2-11. 截止能量 (Cut-off energy) 30
2-12. K-point 30
2-13. 自旋極化 (Spin-polarization) 31
2-14. Climbing image nudged elastic band method (CI-NEB) 31
2-15. 電子密度差圖 (Electron density difference map, EDDM) 31
第三章 計算細節 33
3-1. 模型建構 36
3-1-1. 二氧化鈦原始之結構 (Pristine TiO2) 36
3-1-3. 鉭摻雜二氧化鈦之結構 (Ta-TiO2) 37
3-1-4. 鈉離子嵌入二氧化鈦及其鉭摻雜後結構之位點 39
3-1-5. 鈉離子於二氧化鈦擴散路徑 40
第四章 計算結果與討論 42
4-1. 單位晶胞晶格參數 (Unit cell lattice parameter) 42
4-2. 鈉離子嵌入能 (Sodium intercalation energy) 44
4-2-1. 鈉離子嵌入二氧化鈦及其鉭摻雜結構之嵌入能 44
4-3. 鈉離子於二氧化鈦擴散路徑 (Diffusion path of sodium atom) 46
4-3-1. 鈉離子於二氧化鈦之擴散路徑 46
4-3-2. 鈉離子於鉭摻雜二氧化鈦之擴散路徑 46
4-4. 自旋極化與極化子分析 (Spin-polarization and polarons analysis) 53
4-5. 電子結構 (Electronic Structure) 62
第五章 結論 65
參考文獻 66
附錄一 鋰離子嵌入原始二氧化鈦及鉭摻雜二氧化鈦之模型建構 73
A1-1. 鋰離子嵌入二氧化鈦及其鉭摻雜後結構之位點 73
A1-2. 鋰離子於二氧化鈦之擴散路徑 73
附錄二 鋰離子嵌入原始二氧化鈦及鉭摻雜二氧化鈦之結果與討論 75
A2-1. 鋰離子嵌入二氧化鈦及其鉭摻雜結構之嵌入能 75
A2-2. 鋰離子嵌入二氧化鈦及其鉭摻雜結構之擴散能障 76
A2-3. 自旋極化與極化子分析 (Spin-polarization and polarons analysis) 82
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