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研究生： 莊祐誠
Chuang, Yu-Cheng
論文名稱： 以第一原理計算探討鋰離子電池中複合層狀富鋰正極材料之充放電機制
Ab initio mechanistic study on charging/discharging behaviors of the lithium-rich layered composite cathode material in lithium-ion batteries
指導教授： 林士剛
Lin, Shih-Kang
學位類別： 碩士
Master
系所名稱： 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年： 2016
畢業學年度： 104
語文別： 中文
論文頁數： 196
中文關鍵詞： 複合層狀富鋰氧化物 、正極材料 、鋰離子電池 、密度泛函理論 、第一原理計算
外文關鍵詞： Lithium-rich composite-layered oxide, Lithium-ion batteries, Cathode material, Density functional theory, Ab initio calculation
相關次數： 點閱：122  下載：15 
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    • 隨著科技日新月異的演進，人類對於能源的需求逐漸增加，但隨之而來如石油短缺與燃燒石油所造成的二氧化碳排放問題等等也逐漸成為全人類共同關注的議題。現今，除了發展乾淨的太陽能與風能等再生能源外，世界先進國家亦積極建立能源研究中心與推動各項再生能源獎助法案。另一方面，科學家同時體會到電池儲能技術必須與再生能源並行發展，強化移動式儲能電源，以擴大再生能源應用場域。在眾多能源材料中，鋰離子電池擁有能量密度高、電池性能佳、環境污染低等優點，可視為目前最能符合綠色科技的儲能元件之一。
    複合層狀正極材料由富鋰氧化物xLi2MnO3•(1-x)LiM’O2 (M’=Ni, Co, Mn…etc)依不同組成比例而成之複合層狀材料，具有高電容量之優點。然而，此材料卻也擁有(1)首次不可逆電容量(Initial irreversible capacity)高、(2)電容量衰減(Capacity fading)快以及(3)倍率性能(Rate capability)低等問題，主要由於此材料晶體結構於充放電後形變而無法維持之缺點，嚴重掩蓋材料高電容量之優點以及影響其儲能技術之發展。
    為了解決此問題，在過去的研究中，各領域之學者多利用實驗試誤式(Trial and error)之方式針對複合層狀富鋰氧化物進行材料之探索與改良，雖然已有相當多的文獻成果，但常由於傳統實驗方法需耗費大量時間、金錢與人力，甚至因各研究者之材料合成方法、組成比例、量測儀器不一，導致報導資料散亂且其解釋相互矛盾，難以有效歸納出一致的方法來提升層狀材料的結構穩定性、電容量、循環性能以及導電率。
    本研究透過密度泛函理論(Density functional theory)與第一原理計算(Ab initio calculation)材料計算，對材料結構及其充放電機制有更深的了解。透過模擬的方式，首先建構出複合層狀富鋰氧化物之原子級模型(Atomistic model)以了解其結構組合及比例，並進一步藉由X-射線繞射計算(X-ray diffraction calculation)後與實驗結果比較確認其晶體結構。再者，透過鋰離子嵌出嵌入晶體之方式以模擬充放電曲線(Charging and discharging curve)，並利用Bader電荷分析(Bader charge analysis)來計算出各元素於過程中之價數變化，以及觀察結構變異之相轉變情形(Phase transformation)。最後，利用晶體結構中添加氧缺陷之方式，並藉由缺陷生成能(Defect formation energy)計算以了解充放電過程中鋰氧共同嵌出之競爭機制，後分析歸納出複合層狀富鋰氧化物其電容量與電壓衰退之主因，用以提供快速且精確之計算數據至實驗端，幫助開發出高容量、高電壓與高穩定性複合層狀正極材料。

    The lithium-rich composite-layered oxide, xLi2MnO3•(1-x)LiM’O2, where M’ is transition metals, is a promising cathode material with high capacity in lithium ion batteries. An unusual charge-discharge feature for this material with sloping and plateau regions in the first run has been reported; however, mechanistic interpretations for this phenomenon are controversial in literature. In this work, ab initio calculations based on density functional theory were performed to examine the lattice stability of xLi2MnO3•(1-x)Li(Ni1/3Co1/3Mn1/3)O2 composite-layered cathode materials during the first charging. The atomistic models based on both monoclinic (C2/m) and rhombohedral (R3m) structures for the pristine Li2MnO3 and Li(Ni1/3Co1/3Mn1/3)O2 phases were constructed, respectively. In addition, the atomistic models of xLi2MnO3•(1-x)Li(Ni1/3Co1/3Mn1/3)O2 with x = 0.0, 0.3, 0.5, and 0.7 were also proposed. The calculated X-ray diffraction patterns based on the optimized structures agrees closely with experiments. With these proposed atomistic models, the first charging process of the 0.4Li2MnO3•0.6Li(Ni1/3Co1/3Mn1/3)O2 cathode were investigated according to defect formation energy of Li or O vacancies and Bader charge analyses. The mechanisms of delithiation as well as oxygen evolution during the first charging process are proposed, which may provide fundamental understandings for developing novel cathode materials in energy storage technology.

    目錄 摘要 II Abstract IV 誌謝 XVI 目錄 XVII 表目錄 XX 圖目錄 XXI 第一章 前言 1 第二章 文獻回顧 3 2.1 鋰離子電池 3 2.2負極材料 6 2.3電解質 10 2.4 隔離膜 11 2.5 正極材料 12 2.5.1 鋰鈷氧化物 15 2.5.2 鋰鎳氧化物 17 2.5.3 鋰錳氧化物 18 2.5.4 鋰鎳鈷錳氧化物 19 2.5.5 過量鋰 23 2.6 複合層狀富鋰氧化物 25 2.6.1 晶體結構 25 2.6.2 充放電機制 27 2.6.3 改善方法 33 2.7 研究動機 35 第三章 計算方法 39 3.1 密度泛函理論 39 3.2 Hohenberg-Kohn定理 41 3.3 Kohn-Sham定理 42 3.4 Exchange correlation functional 44 3.5 LDA+U與GGA+U方法 45 3.6 自洽場計算方法 46 3.7 VASP軟體計算函數與參數設定 48 第四章 結果與討論 52 4.1原子級模型的建立 54 4.1.1 常見層狀氧化物原子級模型建立 54 4.1.2 塊材基準計算 56 4.1.3 複合層狀富鋰氧化物原子級模型建立 62 4.1.3.1晶體接合方式探討 63 4.1.3.2界面原子排列方式探討 68 4.1.3.3 磁性自旋方向探討 73 4.1.4 xLi2MnO3•(1-x)Li(Ni1/3Co1/3Mn1/3)O2多樣比例計算 75 4.1.4.1 結構優化分析 75 4.1.4.2 X-ray繞射圖譜分析 77 4.2 充放電程序模擬 81 4.2.1 鋰嵌出之首次充電程序模擬 81 4.2.1.1 Convex hull分析 85 4.2.1.2 充放電曲線分析 87 4.2.1.3 Bader charge分析 90 4.2.1.4 結構相轉變分析 92 4.2.2 鋰嵌出與氧空缺生成之首次充電程序模擬 94 4.2.2.1 Chemical potential分析 97 4.2.2.2 以μO = -2.105 eV代入計算之Convex hull分析 126 4.2.2.3 以μO = -2.105 eV代入計算之充放電曲線分析 129 4.2.2.4 以μO = -1.200 eV代入計算之Convex hull分析 134 4.2.2.5 以μO = -1.200 eV代入計算之充放電曲線分析 136 4.2.3鋰嵌出與氧空缺生成之第二次充電程序模擬 139 4.2.3.1 Convex hull分析 141 4.2.3.2充放電曲線分析 142 第五章 結論 143 參考文獻 145 附錄 164 表目錄 表2.1-1 常見二次電池之特性比較表[2, 16, 17] 5 表2.2-1 常見鋰離子電池負極材料比較表[23, 25, 27, 28, 30-32] 9 表2.5-1 各晶體結構正極材料比較表[19, 38-42] 14 表3.4-1 常見簡單氧化物物理性質之計算與實驗比較表[117] 45 表4.1-1 各層狀材料於不同計算functional以及U值設定下所得計算晶格常數與文獻實驗、晶格常數比較表[43, 44, 53, 62, 63, 70, 103, 118, 134-138] 60 表4.1-2 不同界面原子排列方式結構之生成能計算比較表 72 表4.1-3 不同磁性自旋方向設定之生成能計算比較表 75 表4.1-4過渡金屬均勻混合排列與複合排列之兩者生成能計算比較表 79 表C.1-1 各金屬能量計算統整表 190 表C.2-1 各氧化物能量計算統整表 191 圖目錄 圖1-1 26650圓筒型磷酸鋰鐵電池材料成本分配示意圖[3] 2 圖2.1-1常見二次電池之功率密度對能量密度特性趨勢分布圖[15] 4 圖2.1-2鋰離子電池之結構與工作原理示意圖[18] 4 圖2.2-1 樹枝狀鋰結晶結構之SEM示意圖[24] 7 圖2.2-2 矽奈米粒子於充放電過程中形成之體積膨脹與電極脆裂示意圖[29] 7 圖2.2-3 各類負極材料其電容量對電壓之關係示意圖[10] 9 圖2.5-1 各類具潛力正極材料之工作電壓對電容量分布示意圖[37] 12 圖2.5-2 LiCoO2之單位晶胞原子級模型結構示意圖[43, 44] 16 圖2.5-3 LiM’O2 (M’=Co, Ni, V)層狀氧化物結構示意圖[45] 16 圖2.5-4 LiNiO2之單位晶胞原子級模型結構示意圖[43, 44] 17 圖2.5-5 LiMnO2之單位晶胞原子級模型結構示意圖[43, 44] 18 圖2.5-6 層狀氧化物中過渡金屬選用與含量對三大特性之關係示意圖[58] 20 圖2.5-7 各類正極材料其電容量對電壓之關係示意圖[10] 20 圖2.5-8 Li(Ni1/3Co1/3Mn1/3)O2之超晶胞原子級模型結構示意圖[62] 22 圖2.5-9 Li(Ni1/3Co1/3Mn1/3)O2之過渡金屬層中陽離子排列方式示意圖[62] 22 圖2.5-10 (a) LiMnO2單位晶胞原子級模型與(b) Li2MnO3單位晶胞原子級模型之Monoclinic結構比較示意圖[43, 44] 24 圖2.5-11 Li2MnO3之充放電曲線示意圖[72] 24 圖2.6-1 複合層狀富鋰氧化物之結構組成概念示意圖[37, 73, 74] 26 圖2.6-2 複合層狀富鋰氧化物之原子級模型示意圖[75] 26 圖2.6-3 複合層狀富鋰氧化物xLi2MnO3•(1-x)LiM’O2其充放電過程與組成變化所相對應的電化學反應路徑圖[76] 28 圖2.6-4 Li2Ru1-ySnyO3其充放電過程中(a)釕離子、(b)氧離子之XPS圖譜[77] 29 圖2.6-5 xLi2MnO3•(1-x)LiM’O2於充電過程之離子遷移示意圖[81] 30 圖2.6-6 xLi2MnO3•(1-x)LiM’O2其材料Pristine(a)1nm尺度、(b)2Å尺度與首次充放電後(c) 1nm尺度、(d)2Å尺度之HAADF示意圖[84] 31 圖2.6-7 xLi2MnO3•(1-x)LiM’O2其材料首次充放電前後之HAADF示意圖[85] 31 圖2.6-8 xLi2MnO3•(1-x)LiM’O2之充放電曲線示意圖[84] 32 圖2.7-1 0.5Li2MnO3•0.5Li(N1/3Co1/3Mn1/3)O2其材料充放電曲線示意圖[99] 36 圖2.7-2 0.5Li2MnO3•0.5Li(N1/3Co1/3Mn1/3)O2其Pristine材料之(a)TEM影像圖與(b)選區繞射圖(SADE) [99] 37 圖3.6-1 自洽場計算流程示意圖[121] 47 圖3.7-1真實波函數與贋勢波函數差異比較圖[123] 49 圖3.7-2 近似理論方法之分類示意圖[11] 49 圖3.7-3 鈣鈦礦(Perovskite)結構自旋方向示意圖[126] 51 圖3.7-4 LiCoO2材料其磁矩測試方法示意圖 51 圖4-1 本研究之計算流程示意圖 53 圖4.1-1 各層狀材料(a)LiCoO2、(b)LiNiO2、(c)LiMnO2、(d)Li2MnO3與(e)Li(Ni1/3Co1/3Mn1/3)O2原子級模型以及(e) Li(Ni1/3Co1/3Mn1/3)O2之過渡金屬層排列示意圖[43, 44, 62, 128] 55 圖4.1-2複合層狀副鋰氧化物於STEM-HAADF下所顯示之層狀LiM’O2與過鋰Li2MnO3分布情形示意圖[37] 62 圖4.1-3 Li2MnO3與LiMnO2兩材料以(a)水平接合與(b)垂直接合方式示意圖 63 圖4.1-4 水平接合與垂直接合於不同單位晶胞數量對生成能差異示意圖 67 圖4.1-5 0.4Li2MnO3•0.6Li(Ni1/3Co1/3Mn1/3)O2複合層狀材料Type1界面原子排列方式之(a)完整晶體結構與(b)Bottom過渡金屬層、(c)Middle過渡金屬層、(d)Top過度金屬層示意圖 68 圖4.1-6 0.4Li2MnO3•0.6Li(Ni1/3Co1/3Mn1/3)O2複合層狀材料Type2界面原子排列方式之(a)完整晶體結構與(b)Bottom過渡金屬層、(c)Middle過渡金屬層、(d)Top過度金屬層示意圖 69 圖4.1-7 0.4Li2MnO3•0.6Li(Ni1/3Co1/3Mn1/3)O2複合層狀材料Type3界面原子排列方式之(a)完整晶體結構與(b)Bottom過渡金屬層、(c)Middle過渡金屬層、(d)Top過度金屬層示意圖 69 圖4.1-8 複合層狀材料之磁矩測試方法示意圖 70 圖4.1-9 0.4Li2MnO3-0.6Li(Ni1/3Co1/3Mn1/3)O2之鐵磁自旋方向示意圖 73 圖4.1-10 0.4Li2MnO3-0.6Li(Ni1/3Co1/3Mn1/3)O2之C-type反鐵磁自旋方向示意圖 74 圖4.1-11 0.4Li2MnO3-0.6Li(Ni1/3Co1/3Mn1/3)O2之G-type反鐵磁自旋方向示意圖 74 圖4.1-12 0.5Li2MnO3-0.5Li(Ni1/3Co1/3Mn1/3)O2複合層狀材料其經結構優化前後之結構變化俯視示意圖 76 圖4.1-13 xLi2MnO3-(1-x) Li(Ni1/3Co1/3Mn1/3)O2於x分別為0.0、0.3、0.5與0.7等不同比例之(a)實驗[76]以及(b)理論X-ray繞射圖譜比較示意圖 77 圖4.1-14 xLi2MnO3-(1-x) Li(Ni1/3Co1/3Mn1/3)O2於x比例分別為0.0、0.4與1.0之理論X-ray繞射圖譜示意圖 78 圖4.1-15 0.4Li2MnO3-0.6Li(Ni1/3Co1/3Mn1/3)O2於複合與混合等二方式建構模型之理論X-ray繞射圖譜示意圖 80 圖4.2-1 鋰離子嵌出複合層狀材料之充電程序模擬概念示意圖 81 圖4.2-2 鋰離子嵌出電極之充電程序計算流程示意圖 84 圖4.2-3 LixNi0.167Co0.167Mn0.500O2 (x=0.0~1.167) 複合層狀材料之Convex hull示意圖 86 圖4.2-4 Li1.167Ni0.167Co0.167Mn0.500O2複合層狀材料之實驗[145]與計算充放電曲線示意圖 89 圖4.2-5 各鋰濃度下結構之(a)各離子之平均計算價數變化以及(b)氧離子分布於不同晶體區塊之平均計算價數與標準差變化示意圖 91 圖4.2-6 複合層狀材料於首次充電程序中之(a) Li1.167Ni0.167Co0.167Mn0.500O2、(b) Li1.000Ni0.167Co0.167Mn0.500O2、(c) Li0.833Ni0.167Co0.167Mn0.500O2、(d) Li0.500Ni0.167Co0.167Mn0.500O2等結構與文獻之尖晶石結構[81]示意圖 93 圖4.2-7 鈦酸鉛(PbTiO3)與鈦酸鋇(BaTiO3)其化學勢能圖(Chemical-potential diagram)[148] 95 圖4.2-8 固定Li2O、NiO與CoO以及僅變動MnO、MnO2、Mn2O3與Mn3O4之μLi對μO之Chemical-potential diagram繪製程序示意圖 101 圖4.2-9固定Li2O、NiO、CoO三氧化物其μLi對μO之Chemical-potential diagram示意圖 102 圖4.2-10 各μLi對μO之Chemical-potential diagram繪製程序示意圖 103 圖4.2-11 固定Li2O、NiO、Co2O3三氧化物其μLi對μO之Chemical-potential diagram示意圖 104 圖4.2-12 固定Li2O、NiO、Co3O4三氧化物其μLi對μO之Chemical-potential diagram示意圖 104 圖4.2-13 固定Li2O、NiO、MnO三氧化物其μLi對μO之Chemical-potential diagram示意圖 105 圖4.2-14 固定Li2O、NiO、MnO2三氧化物其μLi對μO之Chemical-potential diagram示意圖 105 圖4.2-15 固定Li2O、NiO、Mn2O3三氧化物其μLi對μO之Chemical-potential diagram示意圖 106 圖4.2-16 固定Li2O、NiO、Mn3O4三氧化物其μLi對μO之Chemical-potential diagram示意圖 106 圖4.2-17 上述各化合物之μO分布範圍統計示意圖 107 圖4.2-18 固定Li2O、NiO、CoO三氧化物其μNi對μO之Chemical-potential diagram示意圖 108 圖4.2-19 固定Li2O、NiO、Co2O3三氧化物其μNi對μO之Chemical-potential diagram示意圖 108 圖4.2-20 固定Li2O、NiO、Co3O4三氧化物其μNi對μO之Chemical-potential diagram示意圖 109 圖4.2-21 固定Li2O、NiO、MnO三氧化物其μNi對μO之Chemical-potential diagram示意圖 109 圖4.2-22 固定Li2O、NiO、MnO2三氧化物其μNi對μO之Chemical-potential diagram示意圖 110 圖4.2-23 固定Li2O、NiO、Mn2O3三氧化物其μNi對μO之Chemical-potential diagram示意圖 110 圖4.2-24 固定Li2O、NiO、Mn3O4三氧化物其μNi對μO之Chemical-potential diagram示意圖 111 圖4.2-25 固定Li2O、NiO、CoO三氧化物其μCo對μO之Chemical-potential diagram示意圖 111 圖4.2-26 固定Li2O、NiO、Co2O3三氧化物其μCo對μO之Chemical-potential diagram示意圖 112 圖4.2-27 固定Li2O、NiO、Co3O4三氧化物其μCo對μO之Chemical-potential diagram示意圖 112 圖4.2-28 固定Li2O、NiO、MnO三氧化物其μMn對μO之Chemical-potential diagram示意圖 113 圖4.2-29 固定Li2O、NiO、MnO2三氧化物其μMn對μO之Chemical-potential diagram示意圖 113 圖4.2-30 固定Li2O、NiO、Mn2O3三氧化物其μMn對μO之Chemical-potential diagram示意圖 114 圖4.2-31 固定Li2O、NiO、Mn3O4三氧化物其μMn對μO之Chemical-potential diagram示意圖 114 圖4.2-32 固定Li2O2、NiO、CoO三氧化物其μLi對μO之Chemical-potential diagram示意圖 115 圖4.2-33 固定Li2O2、NiO、Co2O3三氧化物其μLi對μO之Chemical-potential diagram示意圖 115 圖4.2-34 固定Li2O2、NiO、Co3O4三氧化物其μLi對μO之Chemical-potential diagram示意圖 116 圖4.2-35 固定Li2O2、NiO、MnO三氧化物其μLi對μO之Chemical-potential diagram示意圖 116 圖4.2-36 固定Li2O2、NiO、MnO2三氧化物其μLi對μO之Chemical-potential diagram示意圖 117 圖4.2-37 固定Li2O2、NiO、Mn2O3三氧化物其μLi對μO之Chemical-potential diagram示意圖 117 圖4.2-38 固定Li2O2、NiO、Mn3O4三氧化物其μLi對μO之Chemical-potential diagram示意圖 118 圖4.2-39 固定Li2O2、NiO、CoO三氧化物其μNi對μO之Chemical-potential diagram示意圖 118 圖4.2-40 固定Li2O2、NiO、Co2O3三氧化物其μNi對μO之Chemical-potential diagram示意圖 119 圖4.2-41 固定Li2O2、NiO、Co3O4三氧化物其μNi對μO之Chemical-potential diagram示意圖 119 圖4.2-42 固定Li2O2、NiO、MnO三氧化物其μNi對μO之Chemical-potential diagram示意圖 120 圖4.2-43 固定Li2O2、NiO、MnO2三氧化物其μNi對μO之Chemical-potential diagram示意圖 120 圖4.2-44 固定Li2O2、NiO、Mn2O3三氧化物其μNi對μO之Chemical-potential diagram示意圖 121 圖4.2-45 固定Li2O2、NiO、Mn3O4三氧化物其μNi對μO之Chemical-potential diagram示意圖 121 圖4.2-46 固定Li2O2、NiO、CoO三氧化物其μCo對μO之Chemical-potential diagram示意圖 122 圖4.2-47 固定Li2O2、NiO、Co2O3三氧化物其μCo對μO之Chemical-potential diagram示意圖 122 圖4.2-48 固定Li2O2、NiO、Co3O4三氧化物其μCo對μO之Chemical-potential diagram示意圖 123 圖4.2-49 固定Li2O2、NiO、MnO三氧化物其μMn對μO之Chemical-potential diagram示意圖 123 圖4.2-50 固定Li2O2、NiO、MnO2三氧化物其μMn對μO之Chemical-potential diagram示意圖 124 圖4.2-51 固定Li2O2、NiO、Mn2O3三氧化物其μMn對μO之Chemical-potential diagram示意圖 124 圖4.2-52 固定Li2O2、NiO、Mn3O4三氧化物其μMn對μO之Chemical-potential diagram示意圖 125 圖4.2-53鋰嵌出與氧空缺生成(μO = -2.105 eV)之首次充電程序示意圖 127 圖4.2-54 Li1.167-xNi0.167Co0.167Mn0.500O2-y (0.0 ≤ x ≤ 1.167) (0.0 ≤ y ≤ 2.0)複合層狀材料之Convex hull(μO = -2.105 eV)示意圖 128 圖4.2-55 Li1.167Ni0.167Co0.167Mn0.500O2複合層狀材料之實驗[145]與計算(μO = -2.105 eV)之充放電曲線示意圖 129 圖4.2-56 Li1.167Ni0.167Co0.167Mn0.500O2之首次充電鋰嵌出與氧空缺形成(μO = -2.105 eV)路徑示意圖 130 圖4.2-57 各鋰濃度下結構之氧缺陷生成能計算示意圖 132 圖4.2-58 Li1.167Ni0.167Co0.167Mn0.500O2之實驗[145]首次充電曲線分析示意圖 133 圖4.2-59 鋰嵌出與氧空缺生成(μO = -1.200 eV)之首次充電程序示意圖 134 圖4.2-60 Li1.167-xNi0.167Co0.167Mn0.500O2-y (0.0 ≤ x ≤ 1.167) (0.0 ≤ y ≤ 2.0)複合層狀材料之Convex hull(μO = -1.200 eV)示意圖 135 圖4.2-61 Li1.167Ni0.167Co0.167Mn0.500O2複合層狀材料之實驗[145]與計算(μO = -1.200 eV)之充放電曲線示意圖 136 圖4.2-62 Li1.167Ni0.167Co0.167Mn0.500O2之首次充電鋰嵌出與氧空缺形成(μO = -1.200 eV)路徑示意圖 137 圖4.2-63 Li1.167Ni0.167Co0.167Mn0.500O2複合層狀材料之實驗[145]與計算之充放電曲線示意圖 138 圖4.2-64 鋰嵌出與氧空缺生成之第二次充電程序示意圖 140 圖4.2-65 LixNi0.167Co0.167Mn0.500O1.972 (x=0.0~1.167) 複合層狀材料之Convex hull示意圖 141 圖4.2-66 Li1.167Ni0.167Co0.167Mn0.500O2複合層狀材料之實驗[145]與計算(SOC = 42%)充放電曲線示意圖 142 圖B.1-1 LiCoO2之k-point mesh對總能收斂測試示意圖 173 圖B.1-2 LiNiO2之k-point mesh對總能收斂測試示意圖 174 圖B.1-3 LiMnO2之k-point mesh對總能收斂測試示意圖 174 圖B.1-4 Li2MnO3之k-point mesh對總能收斂測試示意圖 175 圖B.1-5 Li(Ni1/3Co1/3Mn1/3)O2之k-point mesh對總能收斂測試示意圖 175 圖B.2-1 0.5Li2MnO3-0.5LiMnO2之2單位晶胞水平接合k-point mesh對總能收斂測試示意圖 176 圖B.2-2 0.5Li2MnO3-0.5LiMnO2之4單位晶胞水平接合k-point mesh對總能收斂測試示意圖 177 圖B.2-3 0.5Li2MnO3-0.5LiMnO2之6單位晶胞水平接合k-point mesh對總能收斂測試示意圖 177 圖B.2-4 0.5Li2MnO3-0.5LiMnO2之2單位晶胞垂直接合k-point mesh對總能收斂測試示意圖 178 圖B.2-5 0.5Li2MnO3-0.5LiMnO2之4單位晶胞垂直接合k-point mesh對總能收斂測試示意圖 178 圖B.2-6 0.5Li2MnO3-0.5LiMnO2之6單位晶胞垂直接合k-point mesh對總能收斂測試示意圖 179 圖B.3-1 鋰金屬單位晶胞之k-point mesh對總能收斂測試示意圖 180 圖B.3-2 錳金屬單位晶胞之k-point mesh對總能收斂測試示意圖 181 圖B.3-3 鎳金屬單位晶胞之k-point mesh對總能收斂測試示意圖 181 圖B.3-4 鈷金屬單位晶胞之k-point mesh對總能收斂測試示意圖 182 圖B.4-1 0.4Li2MnO3-0.6Li(Ni1/3Co1/3Mn1/3)O2複合層狀材料Type1結構之k-point mesh對總能收斂測試示意圖 183 圖B.5-1 Li2O之k-point mesh對總能收斂測試示意圖 184 圖B.5-2 Li2O2之k-point mesh對總能收斂測試示意圖 185 圖B.5-3 NiO之k-point mesh對總能收斂測試示意圖 185 圖B.5-4 CoO之k-point mesh對總能收斂測試示意圖 186 圖B.5-5 Co2O3之k-point mesh對總能收斂測試示意圖 186 圖B.5-6 Co3O4之k-point mesh對總能收斂測試示意圖 187 圖B.5-7 MnO之k-point mesh對總能收斂測試示意圖 187 圖B.5-8 MnO2之k-point mesh對總能收斂測試示意圖 188 圖B.5-9 Mn2O3之k-point mesh對總能收斂測試示意圖 188 圖B.5-10 Mn3O4之k-point mesh對總能收斂測試示意圖 189 圖D.1-1鋰離子於晶體中之位置標記分布示意圖 192 圖D.2-1鎳離子於晶體中之位置標記分布示意圖 193 圖D.3-1鈷離子於晶體中之位置標記分布示意圖 194 圖D.4-1錳離子於晶體中之位置標記分布示意圖 195 圖D.5-1氧離子於晶體中之位置標記分布示意圖 196

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