臺灣博碩士論文加值系統

近年來隨著動力機械與3C產品之快速發展，對於鋰電池續航力和電流密度的需求持續增加，使得現有石墨負極之鋰容量漸顯不足。在目前所有可能的替代材料中，矽基材料因擁有相當高的鋰容量而被認為是最有可能取代石墨作為次世代鋰電池之負極材料。然而，矽基材料的應用仍有許多問題需要克服。例如，在充放電過程中，鋰原子進出系統會造成電極體積劇烈的變化，因而使得矽基電極之機械與循環性質產生不可逆的損耗。此外，鋰-矽合金系統之低導電率也是實際應用上亟需克服之障礙。針對這些問題，目前可能的解決方案是將此系統混摻入其他元素形成合金，亦或是改變系統之微結構，例如使用矽的奈米線或奈米顆粒做為基材。雖然這些方法多少有些成效，其離實際商業應用尚有一段距離。如欲改進矽基材料作為鋰電池負極之實用性，我們必須對其原子層級結構與各種基本性質作更深一層的了解。
本研究利用第一原理計算與分子動態模擬來探討液態與非晶質鋰矽合金在不同成分下的原子層級結構、動力學、以及各種電子性質。我們首先使用適當的升溫與持溫程序來產生合理之鋰矽液態合金，再經由嚴謹的降溫程序以建構接近真實的非晶相鋰矽合金模型。根據此原子結構模型，我們得以對鋰矽合金系統的微結構以及各項基本性質作更深入的瞭解。本研究分為二個部份：在第一部份中我們針對不同組成之鋰矽液態合金進行各項性質分析，而在第二個部分則為針對其降溫所形成之非晶質結構進行各種探討。
在第一部份的研究中，我們主要探討原子比例和系統溫度對液態合金之結構、動力學、與電性的影響。我們的結果顯示，即使在矽原子濃度偏低的系統中，液態合金裡仍然有相當比例的矽原子形成共價鍵結，其平均鍵長不受矽濃度的影響。此外，在液態合金中矽原子間的鍵結並無固定的形式，其通常是以大小不同的原子團簇存在。當系統中的矽濃度達到一定程度時，矽原子間可能會進一步鍵結形成接近連續體的網狀結構，而隨溫度的上升，矽原子團簇的平均大小也會隨之減小。我們也分析了液態合金系統的動力學性質。我們所推算之鋰、矽原子擴散係數與先前的研究大致符合。關於液態合金的電子性質，我們的結果顯示在液態系統中，鋰的電子會轉移至矽原子以填滿其殼層軌域；在鋰濃度較低的環境中，雖然可提供的電子不足以填滿所有矽原子之殼層軌域，矽原子間仍可透過形成共價鍵以共享電子之方式滿足八隅體。藉由電子能態密度的分析，我們觀察到隨著鋰濃度的增加，矽原子的鍵結與非鍵結軌域會逐漸分離，其代表了系統內部矽原子間的連結度降低，與結構分析的結果一致。另外，我們亦計算了各種組成之液態合金的導電率，並成功重現實驗上所觀察到之現象：當矽原子之濃度在某個範圍內，電阻率並不會隨系統組成的改變而有顯著的變化(即：resistivity plateau)。這是由於矽-矽共價鍵的形成，使得費米能附近的電子被侷限在較低能階的鍵結軌域或矽的孤對電子，使得系統載子濃度較低。然而，當矽的含量繼續增加時，由於矽的配位缺陷也隨之增加，其導電率會在矽濃度超過一定比例時上升。
在本研究的第二個部分，我們將前述所得的液態合金進行適當的降溫程序，再經過結構最適化處理後得到非晶質的鋰矽合金模型。我們分別對不同組成的非晶質鋰矽合金進行結構與電性分析。結果顯示，在固化過程中，系統密度約較液態合金增加約10~15%。此外，非晶質結構擁有與液態合金相似之短程微結構特徵，且同樣缺乏可明確定義之聚合陰離子。當矽濃度達到一定值以上時，系統內部的矽原子亦會形成連續網狀結構，而針對非晶相的鋰矽合金，我們亦能看到如液相合金中所呈現之電阻率平台(resistivity plateau)等有趣現象。

This thesis consists of two main focuses. In the first part, we investigated the structures and properties of the liquid Li-Si alloys, while in the second part we studied those of their amorphous structures. We employed first-principles calculations and molecular dynamic simulations to generate realistic structural models of the liquid and amorphous alloys within various compositions. Based on the generated structural models, we subsequently examined the structures, dynamics, and thermodynamics, as well as the electronic properties of the Li-Si alloy system.
Our results showed that Si atoms usually tend to form covalent bonding in the liquid alloys even when the Si content is very low. Unlike the crystalline systems, Si atoms do not form any specific polyanions in the liquid alloys but form various types of segments containing a wide range of local configurations. Moreover, the average size of Si clusters was found to increase steadily with increasing the Si content, and eventually they turn into a continuous bond network as the Si concentration exceeds a critical value. As the temperature increases, there is no significant change in the average distances between different atom pairs though the size of the Si cluster may drop significantly. The change in the local structures was also manifested in the vibrational spectra in which the high frequency vibrational modes of Si were significantly reduced as the system was at very high temperature.
The calculated dynamic property of the liquid alloys showed that the diffusivities of Li and Si atoms at 1050 K both decrease with increasing the Si content, but the diffusivities of Si atoms appear to be independent of the alloy composition as the temperature is raised above 1500K. Furthermore, the Bader charge analysis showed that there are residual metallic Li atoms in the highly-lithiated liquid alloys, resulting in higher conductivity for those systems. As the Si concentration increases, all the valence electrons of Li in the liquid alloys are ionized by the Si atoms, leading to lower conductivity due to the depletion of free charge carriers in the system.
The structures and electronic properties of the amorphous Li-Si alloys at various compositions were also examined in this study. Our results showed that the short-range order in the amorphous structures is in close resemblance to the liquid alloys at 1050K, but the densities of the amorphous alloys are about 10~15% higher than their liquid phases. Moreover, the configurations of polyanions in the amorphous alloys are similar to those in the liquid states but their average cluster sizes are slightly larger than those in the liquids. On the other hand, we also observed a resistivity plateau at a specific range of composition for the amorphous alloys, which is similar to that found in the liquid phases but the resistivity of the amorphous alloys is slightly higher.

誌謝 I
摘要 II
Abstract IV
Index VI
Index for Figures VIII
Index for Tables XI
Chapter 1: Introduction 1
1.1 Lithium ion battery 1
1.1.1 Development history of Li-ion battery 1
1.1.2 C-based materials as anodes 2
1.1.3 Si-based anode materials 3
1.1.4 “Zintl-like compounds” and Li-Si system 4
1.2 Motivation and objective 12
Chapter 2: Methodology 14
2.1 First-principles calculations 14
2.2 Density functional theory (DFT) 14
2.2.1 Thomas-Fermi model 15
2.1.2 Hohenberg-Kohn theorems 16
2.1.3 Kohn-Sham DFT 16
2.1.4 Exchange-correlation energy: LDA & GGA 18
2.1.5 Pseudopotential 19
2.3 Molecular dynamics 21
2.3.1 Verlet algorithm 21
2.3.2 First-principles MD 22
2.3.3 Nosé-Hoover thermostat 22
Chapter 3: Computational details 24
Chapter 4: Results and Discussion 28
4.1 Analysis of the liquid 28
4.1.1 Structure analysis 29
4.1.2 Dynamic properties 54
4.1.3 Electronic properties 66
4.2 Analysis of the amorphous solid: comparison with liquid structures 83
4.2.1 Volume of the alloys 83
4.2.2 Structures of the systems 84
4.2.3 Electronic properties 90
Chapter 5: Conclusion 95
Reference 97

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