本論文以實驗及分子動力學模擬(Molecular dynamics simulation)的方法探討鋰鈣硼矽(Lithium-calcium borosilicate, LCBS)玻璃系統中成分-結構-性質三者間的關係，以及其做為燒結助劑在低溫共燒陶瓷(Low-temperature co-fired ceramics, LTCC)製程技術上的應用。
首先在論文第一章中介紹玻璃形成的結構理論、硼矽玻璃系統的成分與性質的關係；分子動力學模擬的基本流程和運算中常用的演算法；低溫共燒陶瓷製程技術簡介及其材料系統與電極之選擇；並於章節最後說明研究的背景與動機。
第二章中以成分為0.4[(1-x)Li2O-xCaO]-0.6[(1-y)B2O3-ySiO2]的LCBS玻璃為研究對象，其中x的範圍為0~1，y的範圍為0.33~0.83。利用固態核磁共振儀(SSNMR)與X光吸收光譜(XAS)做為玻璃結構的主要分析儀器，探討玻璃成分、結構與其性質三者間的關係。研究中所量測之玻璃結構與性質均會受到CaO取代量與[SiO2]/[B2O3]比例(K值)之影響，同時隨著系統中Li2O被CaO所取代，部分性質可觀察到偏離線性加成關係的混合修飾劑效應(Mixed modifier effect)。混合修飾劑效應會在導電率活化能(Eaσ)中以非加成性的正偏差呈現，以及在四配位硼分率(N4)、玻璃轉換溫度(Tg)、膨脹儀軟化溫度(Td)、易裂度(m)、維式硬度(Hv)、介電常數(ε)和介電損失(tanδ)中以非加成性的負偏差呈現；而其最大偏差量皆發生在[CaO]/([CaO]+[Li2O])=0.5時，且偏差量隨著K值的上升而增加。其中，發生在Tg、Td、m和Hv的混合修飾劑效應主要肇因於玻璃網絡結構的鍵結強度下降；而在ε、tanδ和Eaσ的混合修飾劑效應則與修飾劑在網絡結構中移動時受到阻礙有關。
第三章中使用Buckingham形式的GS勢能進行分子動力學模擬，對第二章中 LCBS玻璃之成分-結構-性質關係的實驗結果做進一步探討。模擬結果指出，相較於矽氧四面體結構的些微變化，CaO取代量與K值的改變，會對硼氧多面體的結構、修飾劑周圍環境和多面體間緊密程度造成極大的影響；這些結構上的改變會進而造成楊氏模數(E)、體積模數(K)、剪切模數(G)和玻璃轉換溫度(Tg)等玻璃性質的變化。以此方法模擬的LCBS玻璃之結構與性質皆與實驗值有著相同的趨勢，且大部分僅有些微的誤差。
第四章中以LCBS玻璃做為燒結助劑，探討其對(Ca1-xSrx)(Zr1-yMny)O3陶瓷在還原氣氛下的燒結行為以及介電性質之影響。研究中(Ca1-xSrx)ZrO3的介電性質將隨著Sr/Ca比例下降而有所提升，並可藉由0.2 mol的Mn取代Zr使介電損失大幅下降，將Q × fr提升至30500 GHz。為了降低(Ca0.9Sr0.1)(Zr0.8Mn0.2)O3 (CSZM9182)的緻密溫度使之可與銅進行共燒，我們以5~10 vol%的0.4Li2O-0.6(B2O3-SiO2) (LBS)玻璃做為助燒劑，可將緻密溫度由1500 ℃降至1030 ℃。隨著LBS玻璃中K值下降，CSZM9182的緻密性將隨之增加；然而介電性質卻會衰退。這是由於K值下降將導致CSZM9182與LBS之間介面化學反應增強，進而生成介電性質較差的CaZr4O9相。將LBS玻璃中10 mol%的Li2O以CaO進行取代，雖會使緻密性下降，卻能有效提升介電性質及化學耐久性。對於Li2O、CaO、B2O3及SiO2的成分含量分別介於30~40、0~10、20~50及10~40 mol%的CSZM9182+5~10 vol% LCBS系統而言，在7.4~7.8 GHz的共振頻率下量測獲得的介電常數約為23~29，Q × fr為2000~22000 GHz，而在25~80 ℃溫度範圍的共振頻率溫度係數為-22~-7 ppm/℃。

This thesis investigates the composition-structure-properties relationship of the lithium-calcium borosilicate (LCBS) glasses by using both the experimental method and molecular dynamics (MD) simulation, and the application of LCBS glasses as the sintering aids on low-temperature co-fired ceramics (LTCC) technic.
In chapter 1, the following background knowledge is introduced: the theory of glass formation, the composition-structure relationship of borosilicate glasses; typical process, and some widely used algorithms of MD simulation; an introduction of LTCC technic and its material and electrode system. The motivation of the study is mentioned in the last part of the chapter.
In chapter 2, the LCBS glasses, which have a composition of 0.4[(1−x)Li2O–xCaO]–0.6[(1−y)B2O3–ySiO2] with x in the range of 0~1 and y in the range of 0.33~0.83, are investigated. The glass structure is observed by using solid-state nuclear magnetic resonance (SSNMR) and X‐ray absorption spectroscopy (XAS) to reveal the composition-structure-properties relationship. The results show the glass structure and properties are affected by both the content of CaO and ratio of [SiO2]/[B2O3] (K); meanwhile, with the increasing content of CaO, some properties exist the mixed modifier effect. The mixed modifier effect manifests itself as a positive deviation from linearity in the activation energy of electrical conductivity (Eaσ) and as a negative deviation from linearity in the fraction of four‐coordinated boron (N4), glass transition temperature (Tg), dilatometric softening temperature (Td), fragility (m), Vickers microhardness (Hv), dielectric constant (ε), and dielectric loss (tanδ). Moreover, the deviation, which exhibits a maximum at [CaO]/([CaO]+[Li2O])=0.5, is enhanced with increasing K in the glass network. The observed mixed modifier effect in Tg, Td, m, and Hv are attributed to the bond weakening in the network; however, the mixed modifier effect in ε, tanδ, and Eaσ are caused by the obstruction of modifier transport in the glass network.
In chapter 3, the further investigation of the composition-structure-properties relationship of LCBS glasses is studied with the MD simulation by using the Buckingham form GS potential. The results of simulation show the effect of K and content of CaO exhibit a slight influence on the structure of silicon-oxygen tetrahedron. In contrast to the silicon-oxygen tetrahedron, the effect of K and content of CaO exhibit an obvious influence on the structure of boron-oxygen polyhedron, environment of modifier ion and the connectivity of inter-polyhedron. The above structural changes are associated with the changes of Young’s modulus (E), bulk modulus (K), shear modulus (G), and glass transition temperature (Tg).
In chapter 4, the effect of LCBS glasses as the sintering aids on the sintering behavior and dielectric properties of (Ca1−xSrx)(Zr1-yMny)O3, which fired in the reducing atmosphere, are investigated. The dielectric properties of (Ca1−xSrx)ZrO3 become better with decreasing the ratio of Sr/Ca. Substituting Zr by 0.2 mol Mn, the dielectric loss of (Ca0.9Sr0.1)ZrO3 is greatly reduced, resulting in a Q × fr value of 30500 GHz. To reduce the densification temperatures of (Ca0.9Sr0.1)(Zr0.8Mn0.2)O3 (CSZM9182) to the range cofirable with Cu electrode, 5–10 vol% 0.4Li2O-0.6(B2O3-SiO2) (LBS) glass is added and the densification temperature is lowered from 1500 °C to 1030 °C. The densification is further enhanced with decreasing K in the LBS glass; however, the dielectric properties are deteriorated. The above result is attributed to a chemical reaction taking place at the interface of CSZM9182-LBS during firing, which becomes more extensive with decreasing K in the LBS glass and tends to form a worse dielectric phase of CaZr4O9. Substituting 10 mol% of Li2O in LBS glasses by CaO, the densification is decreased; however, the dielectric properties and chemical durability are efficiently improved. For the LCBS glasses with 30~40 mol% Li2O, 0~10 mol% CaO, 20~50 mol% B2O3, and 10~40 mol% SiO2, the resulting CSZM9182 +5~10 vol% LCBS microwave ceramics have a dielectric constant of 23~29, Q × fr value of 2000~22,000 GHz at 7.4~7.8 GHz, and a temperature coefficient of resonant frequency (τf) of −22~ −7 ppm/°C in the temperature range between 25 °C and 80 °C.

第一章 簡介 1
1.1 玻璃形成的結構理論 1
1.1.1 不規則網絡模型 1
1.1.2 鍵強準則與場強度準則 3
1.2 添加修飾劑對硼矽玻璃的結構之影響 4
1.2.1鹼金屬硼酸鹽玻璃的結構 4
1.2.2 鹼金屬硼矽玻璃的結構 5
1.3 分子動力學模擬 7
1.3.1 勢能函數 8
1.3.2 運動方程式之解析 9
1.3.2.1 Verlet演算法 9
1.3.2.2 Leap-frog Verlet演算法 10
1.3.2.3 Velocity Verlet演算法 11
1.3.3 系綜(Ensemble) 11
1.3.3.1 Nosé–Hoover溫控法 12
1.3.4 週期性邊界(Periodic boundary) 13
1.3.5 運算簡化法 13
1.3.5.1 截斷半徑法 14
1.3.5.2 Verlet表列法 14
1.3.5.3 Cell link 表列法 14
1.3.5.4 Verlet+Cell link表列法 15
1.3.5.5 Ewald求和法(Ewald sum method) 15
1.4 低溫共燒陶瓷(Low-temperature co-fired ceramics, LTCC)製程技術 16
1.4.1 LTCC材料系統 18
1.4.2 LTCC電極材料 19
1.5 研究背景與動機 20
參考文獻 22

第二章 Li2O-CaO-B2O3-SiO2玻璃之成分-結構-性質關係探討 39
2.1 前言 40
2.2 實驗方法 43
2.2.1 玻璃的製備 43
2.2.2 玻璃的結構分析 44
2.2.2.1 固態核磁共振光譜(Solid state nuclear magnetic resonance spectroscopy, SSNMR) 44
2.2.2.2 X光吸收光譜(X-ray absorption spectroscopy, XAS) 44
2.2.3 玻璃的性質分析 45
2.3 結果與討論 48
2.3.1 玻璃的網絡結構 48
2.3.2 玻璃的性質分析 49
2.3.2.1 物理性質 49
2.3.2.2 電性質 52
2.3.3 混合修飾劑效應機制探討 53
2.4 結論 57
參考文獻 58

第三章 以分子動力學模擬探討Li2O-CaO-B2O3-SiO2玻璃之成分-結構-性質關係 84
3.1 前言 85
3.2 模擬方法 88
3.2.1 玻璃成形之模擬 88
3.2.2 玻璃結構之計算 89
3.2.3 玻璃性質之模擬 90
3.3 結果與討論 91
3.3.1 玻璃的結構計算 91
3.3.2 玻璃的性質模擬 94
3.4 結論 96
參考文獻 97

第四章 可低溫共燒之 CSZM+LCBS微波介電陶瓷系統在還原氣氛下的燒結行為及介電性質研究 119
4.1 前言 120
4.2 實驗方法 122
4.2.1 陶瓷粉體的製備與分析 122
4.2.2 玻璃粉體的製備與分析 122
4.2.3 陶瓷+玻璃的燒結與分析 123
4.3 結果與討論 125
4.3.1 (Ca,Sr)(Mn,Zr)O3成分最佳化之研究 125
4.3.2添加LBS玻璃對CSZM9182陶瓷燒結行為及介電性質之影響 125
4.3.3添加3L1CBS玻璃對CSZM9182陶瓷燒結行為及介電性質之影響 128
4.4 結論 131
參考文獻 132

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[52] D. Zhou, H. Wang, X. Yao, and L. X. Pang, “Microwave Dielectric Properties and Co-Firing of BiNbO4 Ceramics with CuO–WO3 Substitution,” Mater. Sci. Eng. B, 142 [2-3] 106–11 (2007).

[53] D. Zhou, H. Wang, and X. Yao, “Microwave Dielectric Properties and Co-Firing with Copper of (Bi1-xCux)(Nb1-xWx)O4 Ceramics,” Ceram. Int., 34 [4] 929–32 (2008).

[55] C. C. Chou, C. S. Chen, P. C. Wu, K. C. Feng, and L. W. Chu, “Influence of Glass Compositions on the Microstructure and Dielectric Properties of Low Temperature Fired BaTi4O9 Microwave Material with Copper Electrodes in Reducing Atmosphere,” Ceram. Int., 38S [S1] S159-62 (2012).

[56] H. Shin, S. W. Lee, and H. S. Jung, “Sintering and Dielectric Properties of Li2O–B2O3–Al2O3–SiO2 Glass-Added (Ca0.7Sr0.3O)1.03(Ti0.1Zr0.9)O2 for Copper Electrode,” Int. J. Appl. Ceram. Technol., 10 [4] 716–22 (2013).

[57] K. C. Feng, C. C. Chou, C. S. Chen, L. W. Chu, and H. Chen,“ Phase Evolution and Electrical Properties of Copper-Electrode BaTi4O9 Materials with BaO–ZnO–B2O3–SiO2 Glass System in Reducing Atmosphere,” Ceram. Int., 39 [S1] S321-4 (2013).

[58] S. H. Wang, Y. L. Tsai, and W. H. Lee, “Study on (Ba,Ca)(Ti,Zr)O3 Dielectric Cofired with Copper Electrode,” Jpn. J. Appl. Phys., 53 [14] 0615011-7 (2014).

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第二章

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第三章

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[2] 劉威廷，<以分子動力學模擬法探討表面效應對金屬奈米線機械性質之影響
>，國立成功大學材料科學工程學系101年碩士論文

[3] A. J. Connelly, K. P. Travis, R. J. Hand, and N. C. Hyatt, “Composition-Structure Relationships in Simplified Nuclear Waste Glasses: 1. Mixed Alkali Borosilicate Glasses,” J. Am. Ceram. Soc., 94 [1] 151-9 (2011).

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[21] 郭純萍，<利用分子動力學模擬全氟磺酸形態和結構構象之研究>，國立中
山大學化學系104年碩士論文

[22] 王偉儒，<以分子動力學探討鹽類離子與水團簇的結構與鍵結行為>，國立清華大學化學工程學系99年碩士論文

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第四章

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[12] K. Niwa, N. Kamehara, H. Yokoyama, K. Yokouchi, and K. Kurihara, “Multilayer Ceramic Circuit Board with Copper Conductor”; pp. 41-7 in Advances in Ceramics, Vol. 19, Multilayer Ceramic Devices. Ed. J. B. Blum and W. R. Cannon. Am. Ceram. Soc., Westerville, OH, 1986.

[13] J. H. Jean and S. C. Lin, “Low-Fire Processing of ZrO2-SnO2-TiO2 Ceramics,” J. Am. Ceram. Soc., 83 [3] 1417-22 (2000).

[14] M. Udovic, M. Valant, and D. Suvorov, “Phase Formation and Dielectric Characterization of the Bi2O3-TeO2 System Prepared in an Oxygen Atmosphere,” J. Am. Ceram. Soc., 87 [4] 591-7 (2004).

[15] A. Feteira and D. C. Sinclair, “Microwave Dielectric Properties of Low Firing Temperature Bi2W2O9 Ceramic,” J. Am. Ceram. Soc., 91 [4] 1338-41 (2008).

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