以第一原理計算探討鋰於鈮摻雜二氧化鈦之嵌入與擴散路徑

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高思穠(Szu-Nung Kao) 查詢紙本館藏

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化學工程與材料工程學系

論文名稱

以第一原理計算探討鋰於鈮摻雜二氧化鈦之嵌入與擴散路徑
(Investigating Lithium Intercalation and Diffusion in Nb-Doped TiO2 by First Principles Calculations)

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★ 以第一原理計算探討鋰離子於鐵摻雜磷酸鋰鈷之塊材與表面附近之擴散路徑

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至系統瀏覽論文 (2025-6-30以後開放)

摘要(中)

近年來二氧化鈦
因為其較高的理論電容值、安全性、化學穩定性與容易取得等特
點成為了鋰離子電池負極材料的熱門人選。然而，在實際情況下，二氧化鈦卻存在著
高能隙所造成之低電導率以及受限的鋰離子擴散表現等缺點。為了改善上述的缺點，
許多實驗團隊選擇在二氧化鈦中摻雜其他元素來提升其電池上的表現，其中，鈮金屬
為所摻雜元素中的熱門選擇。
本研究將銳鈦礦 (anatase) 、金紅石 (rutile) 與單斜晶系二氧化鈦 (TiO2(B)) 三種常見於鋰離子負極材料的二氧化鈦晶型皆列入考慮，並以第一原理之計算來分析摻雜鈮金屬後在稀薄鋰離子濃度情況下對鋰離子嵌入與擴散的影響。在摻雜鈮金屬後，三種晶型之二氧化鈦皆出現晶格膨脹的現象，其歸因於Nb5+的離子半徑大於Ti4+的緣故。為了觀察鈮金屬對於鋰離子擴散上的影響，考量了距離鈮金屬較近與較遠的兩條路徑，鋰離子分別被置於三種晶相中較可能之嵌入點位，而所有結構之鋰離子嵌入能相較無改質之二氧化鈦皆有明顯下降的趨勢，其中金紅石 (Rutile) 下降最為劇烈。而鋰離子之擴散移動路徑則是藉由CI-NEB (Climbing Image Nudged Elastic Band) 方法由穩定嵌入點位移動至鄰近的穩定嵌入點位計算所得。三種晶相的擴散能障皆有些微上升的情況，而距離鈮較近的路徑上升幅度又較為明顯，其原因為摻雜鈮金屬後產生的極化子與鋰離子產生強作用力所導致。此外，三種結構之電子結構也進行了計算分析，結果顯示在摻雜鈮金屬後價帶 (valence band) 都有往費米能階 (Fermi level) 移動的趨勢，使得能隙值下降，幫助提升電導率。

摘要(英)

In recent years, titanium dioxide has become a popular anode material for Lithium batteries (LIBs) anode due to its high theoretical specific capacity, safety, chemical stability and easy availability. However, practical application faces difficulties such as low electronic conductivity caused by high band gap and restricted lithium diffusion performance. To overcome the shortcoming above-mentioned, many studies decided to improve the performance of titanium dioxides in lithium batteries by doping with different elements, including niobium which has drawn a great deal of attention.
Our study took three commonly used polymorphs of titanium dioxides in LIBs into consideration: anatase, rutile and TiO2(B). First principles calculation based on density functional theory (DFT) was employed for lithium intercalation and diffusion behavior in Nb-doped TiO2 at dilute lithium concentrations. The lattice parameters of all three polymorphs indicated lattice expansion, which was attributed to the ionic radius of Nb5+ greater than the ionic radius of Ti4+. In order to investigate the effect of niobium on the diffusion of lithium ion near to or far from niobium metal diffusion pathways were considered. Lithium was placed at the most suitable intercalation site for the calculation. Compared with pristine TiO2, lithium insertion energies in Nb-doped TiO2 have significant downward trend, among which rutile had the sharpest decline. The CI-NEB (Climbing Image Nudged Elastic Band) method was performed from the most stable intercalation site to adjacent intercalation site. The activation barriers of three polymorphs increased slightly and the energy barrier of near diffusion pathway was higher than far diffusion pathway. This is attributed to the polaron generated by niobium and lithium which results in strong interaction with lithium. In addition, the electronic structure of three structures were calculated and analyzed. The results showed that valence band tended to move towards the Fermi level, which reduced the band gap and facilitated improvement of electronic conductivity.

關鍵字(中)

★ 二氧化鈦
★ 摻雜
★ 鋰擴散路徑
★ 密度泛函理論
★ 鋰離子電池
★ 廣義梯度近似

關鍵字(英)

★ TiO2
★ Lithium batteries
★ Doped
★ Lithium diffusion
★ Niobium
★ Density functional theory
★ DFT
★ GGA+U

論文目次

Table of content
中文摘要 ................................................................................................................................................... i
Abstract .................................................................................................................................................... ii
Chapter 1 Background ............................................................................................................................. 1
1.1 Introduction ................................................................................................................... 1
1.2 Illustration of LIBs ........................................................................................................ 3
1.3 Titanium dioxides (TiO2) as an anode material of LIBs ............................................... 4
1.3.1 Titanium dioxides (TiO2) .............................................................................................. 5
1.3.2 Modified titanium dioxide........................................................................................... 12
1.3.3 Experimental Study on doped tiatnium dioxides LIBs ............................................... 15
1.3.4 Computational study on titanium dioxides.................................................................. 18
1.3.5 Computational study on Nb-doped titanium dioxides ................................................. 22
1.4 Motivation ................................................................................................................... 25
2 Theory and method........................................................................................................................ 26
2.1 First principles calculation .......................................................................................... 26
2.2 Density functional theory ............................................................................................ 27
2.3 Hohenberg-Kohn Theorem ......................................................................................... 28
2.4 Kohn-Sham equation ................................................................................................... 28
2.5 Local-density Approximation ..................................................................................... 29
2.6 Generalized gradient approximation ........................................................................... 30
2.7 DFT+U correction ....................................................................................................... 30
2.8 Bloch’s theorem .......................................................................................................... 31
2.9 k-points ........................................................................................................................ 31
2.10 Spin-polarization ......................................................................................................... 32
2.11 Basis set & Cutoff energy ........................................................................................... 32
2.12 Pseudopotetnail & Plane wave .................................................................................... 33
2.13 Electronic structure ..................................................................................................... 35
ix
2.14 Geometry optimization................................................................................................ 35
2.15 Material Studio & CASTEP ........................................................................................ 36
Chapter 3 Computational details ........................................................................................................... 37
3.1 Pristine TiO2 ................................................................................................................................ 38
3.2 Niobium-doped TiO2 ................................................................................................................... 40
3.3 The lithium intercalation sites of TiO2 and Niobium-doped TiO2 .............................................. 43
3.4 The lithium diffusion pathway of TiO2 and Niobium-doped TiO2 ............................................. 45
Chapter 4 Results and discussions ........................................................................................................ 49
4-1 Lattice parameters of niobium-doped TiO2 ................................................................................ 49
4-2 Electron density difference mapping .......................................................................................... 52
4-2-1 Pristine titanium dioxides .................................................................................................... 52
4-2-2 Polarons and Nb-doped titanium dioxides ........................................................................... 54
4-3 Lithium intercalation energy ....................................................................................................... 59
4-3-1 Pristine TiO2 ........................................................................................................................ 59
4-3-2 Niobium-doped TiO2 ........................................................................................................... 60
4-4 Diffusion path of lithium atom ................................................................................................... 63
4-4-1 Diffusion path of lithium atom in pristine TiO2 .................................................................. 63
4-4-2 Diffusion path of lithium atom in Nb-doped TiO2 .............................................................. 64
4-5 Electronic structure ..................................................................................................................... 72
Chapter 5 Conclusion ............................................................................................................................ 77
References ......................................................................................................................................... 79
Appendix ............................................................................................................................................... 86

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指導教授

謝介銘張博凱(Chieh-Ming Hsie Bor Kae Chang)

審核日期

2020-7-28

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