本研究主要以多尺度模擬方法，藉由第一原理分子動力學(FPMD)所計算之材料性質，結合有限元素法(FEM)計算於高溫作用下熔融鹽電解質熱電池之熱/質傳巨觀性能，評估熱電池在不同操作溫度下對電池性能之影響；後續參考國外文獻所提供之實驗結果，以驗證本研究模型之正確性與可行性，進而建立一套具多尺度且完整的模擬工具，期能達到開發新式熔融鹽電解質熱電池之性能預測與最佳化目的。
熱電池又稱為熱激發電池，屬熔融鹽電池的一種，主要特徵為使用之電解質由共晶混合鹽所組成，當外部點火器啟動給予熱源時，透過各單電池的上下熱片傳遞大量的熱，迅速使電解質呈熔融態，並使熱電池開始作電化學反應。本研究首先從熔鹽電解質之二元(binary)材料出發，建構微觀尺度模型，利用量子力學計算原子分布/組成、勢能模型及離子擴散性等，並輔以分子動力學計算離子傳導率、熱傳導率、比熱與熔點等性質；接著運用有限元素分析法建構巨觀尺度模型及代入微觀尺度模型所計算之性質，求解溫度分布及濃度場，並導入電化學理論，進而探討熱電池放電性能最佳化分析與評估熱效應造成之影響。
有別於傳統LiCl-KCl二元(binary)電解質，本研究尚提出具備成本低、安全性佳且不易造成環境破壞等優點之LiCl-LiBr-based三元(ternary)、四元(quaternary)新型電解質材料，並從模擬結果中顯示它們可大幅提升電池性能。其中，三元(ternary)材料擁有較大之比功率，約為傳統二元(binary)材料之1.5倍；此外，四元(quaternary)材料不但可有效降低操作溫度(低熔點)，減少電池失效機率，亦可延長電池作用時間(壽命)。本研究成果，除可有效降低熱電池研發成本，大幅縮減研發時程，可作為未來研發設計新型熱電池之重要參考依據，從而提升台灣國防科技國機國造之競爭力。

This research aims to develop some novel ternary and quaternary molten electrolytes to enhance the overall performance of high-temperature molten salt batteries. The methodology in this study is based on the multi-scale simulation technique, combining first principle molecular dynamics (FPMD) to obtain material properties with the finite element method (FEM) to predict heat/mass transfer and electrochemical performance in macro-scale performance of molten-salt thermal batteries at different operating temperatures. The simulation result will be compared with reference and experimental result from foreign literature, in order to verify the correctness and feasibility of this research.
Our objective is to optimize the novel electrolytes with the greatest ionic conductivity and lowest melting point, also to develop the multi-cell system with the optimized I-V performance without thermal run-away and short-circuit. The finite element method is used to solve the temperature distribution and concentration field on the LiCl-KCl electrolyte thermal battery at operating temperatures. Besides, the electrochemical theory is needed to analysis the thermal effects of the internal electrolyte, ionic transport phenomena, and the discharge performance. In addition, the internal heat source is carried out to detailed studies, in order to predict the failure of batteries which is caused by two main reasons: thermal runaway and short-circuit.
Finally, this study also predicts macroscopic performances of LiCl-LiBr-based ternary and quaternary systems. All these simulation techniques provide a low cost alternative to experiments and are able to optimize the battery design at the realistic operating conditions.

摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 VII
表目錄 IX
符號定義 X
第一章 緒論 1
1.1 前言 1
1.2 熱電池簡介 1
1.2.1 熱電池基本結構 2
1.2.2 電極材料 4
1.2.2 電解質 10
1.2.3 火工材料與絕緣材料 12
1.3 文獻回顧 13
1.3.1 分子動力學 13
1.3.2 巨觀分析 14
1.4 研究動機與目的 15
第二章 第一原理分子動力學模擬材料性質 16
2.1 研究方法 16
2.1.1第一原理分子動力學(First Principle Molecular Dynamics, FPMD) 16
2.1.2 密度泛函理論 (Density functional theory, DFT) 17
2.1.3 交換相關能 22
2.1.4 Hellmann-Feynman Theorem 23
2.1.5 邊界條件 25
2.1.6 溫控器 27
2.2 模型建構與模擬方法 29
2.2.1 模擬流程 29
2.2.2 模擬工具 30
2.2.3 數據後處理 31
第三章 熱電池系統之熱/質傳與性能模擬 34
3.1 熱電池系統 34
3.2 統御方程式 35
3.1.1 熱傳輸(Heat transport) 35
3.1.2 Li離子質傳(Li-ion transport) 38
3.1.3 電荷傳輸(Charge transport) 40
3.3 基本假設 40
3.4 邊界條件與初始條件 41
3.5 自然對流下熱對流係數 42
3.6 電化學性能計算 44
3.6.1 平均電流密度 44
3.6.2 操作電壓和功率 45
3.7 有限單元法(Finite Element Method) 48
3.7.1 函數空間(Functional Space) 49
3.7.2 弱解形式(Weak Formulation) 49
3.7.3 離散化與Galerkin Method 53
3.7.4 牛頓拉森法(Newton-Raphson Method) 55
3.8 模擬進行 57
3.8.1 系統模型網格建構 57
3.8.2 模擬流程與參數設置 59
第四章 結果與初步討論 63
4.1 第一原理分子動力學(FPMD) 63
4.1.1 初始結構模型 63
4.1.2 徑向分布函數(Radial distribution function, RDF) 65
4.1.3 均方位移(Mean square displacement, MSD) 66
4.1.4 擴散係數 67
4.1.5 離子傳導率 69
4.2 有限元素分析(FEM) 70
4.2.1 溫度場 70
4.2.2 離子濃度場 86
4.2.3 收斂性測試 92
4.3 電化學性能計算(Electrochemistry) 93
第五章 總結與未來工作建議 102
5.1 總結 102
5.1.1 微觀尺度 102
5.1.2 巨觀尺度 103
5.2 未來工作建議 105
參考文獻 106

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