熱電材料為近年來為解決能源問題的重要能源材料，其可應用於吸收各式製程中的多餘廢熱並將其轉換成電能，增加能源使用的效率，被認為是具有開發價值的能源材料。近年來更因為半導體製程技術與奈米技術的發展，讓熱電材料成為熱門的研究主題；迄今，中溫型熱電材料的使用與開發，除了普遍使用的碲化鉛(PbTe, Lead telluride)與銻化鈷(CoSb3, Cobalt Triantimonide)外，Sb-Se-Pb-Sn四元系統亦是重要的熱電系統。於此系統中，PbSe及其合金、Sb2Se3及SnSe等二元金屬化合物在熱電應用上的研究受到廣泛的討論。
熱電模組之建立，需要以軟銲(soldering)方式連接。軟銲為電子構裝中重要的一環。由於Sn-Pb合金價格低廉且有較低的熔點，故為電子工業主要的銲料選材，但Pb及其化合物對於人體及環境皆具傷害性，無鉛銲料議題開始受到重視。當今無鉛銲料的使用和開發，除了普遍使用的Sn-Ag-Cu合金外，Sn-Ag-In、Sn-Ag-Zn與Sn-In-Zn三元系統皆是十分有潛力之無鉛材料，近年來更有以Sn-Ag-In-Zn四元系統作為電子銲料之相關研究，故四元相圖之探討，具有相當大的研究價值，然而，目前尚未有Ag-In-Zn三元系統之相平衡資訊。
相圖是材料之基本資料，對材料的開發與應用具有重要的價值。相圖之測定可以實驗方法進行量測探討、以及計算方法測得。在計算方法中，目前以熱力學計算相圖(CALPHAD, Calculation of Phase Diagram)方法最成熟，應用範疇亦相當廣泛，其主要以搭配系統之熱力學參數與相平衡之實驗數據，得以建立系統之熱力學模型。
本研究擬建立Sn-Ag-In-Zn與Sb-Se-Pb-Sn四元系統中較為缺乏的Ag-In-Zn、Pb-Sb-Se及Sn-Sb-Se等三元系統相圖。實驗方面，利用掃描式電子顯微鏡(SEM, Scanning Electron Microscopy)觀察合金金相，同時利用能量散佈分析儀(EDS, Energy Dispersive X-ray Spectrometer)及電子微探分析儀(EPMA, Electron Probe X-ray Microanalyzer)進行組成分析。以X光粉末繞射儀(XRD, X-ray Diffractometer)進行結構分析，最後以微差熱分析儀(DTA, Differential Thermal Analysis)判定合金的相變化溫度。計算部分，將以熱力學計算相圖方法搭配實驗制定的相平衡資訊及第一原理分子動力學(AIMD, Ab-initio Molecular Dynamics)計算出的熱力學性質，以期建立Sb-Se及Sn-Se二元系統之熱力學模型。
本研究以實驗方式完成Sn-Ag-In-Zn中的Ag-In-Zn三元無鉛銲料系統之液相線投影圖及500oC等溫橫截面圖；經由合金相分析可知，Ag-In-Zn三元系統具有(Ag)、(In)、(Zn)、Beta-(Ag3In)、Zeta-(Ag3In)、Gamma-(Ag9In4)、AgIn2、Beta-(AgZn)、Gamma-(Ag5Zn8) 與Epsilon-(AgZn3)等10個首要析出相，並未於此系統中發現三元相；此外，以熱分析制定出Liquid=(In)+AgIn2+Gamma-(Ag5Zn8)、 Liquid=Epsilon-(AgZn3)+(In)+(Zn)、 Liquid+Beta-(AgZn)=Gamma-(Ag5Zn8)+Gamma-(Ag9In4)、 Liquid+Zeta-(Ag3In)=Gamma-(Ag5In8)Beta-(AgZn)與Liquid+(Ag)+Beta-(AgZn)=Zeta-(Ag3In)等5個不變反應點(Invariant reaction)；500oC等溫橫截面圖的部分，可制定出(Ag)+Zeta-(Ag3In)+Beta-(AgZn)、 Zeta-(Ag3In)+Gamma-(Ag9In4)+Beta-(AgZn)、 Zeta-(Ag3In)+Gamma-(Ag9In4)+Liquid、Gamma-(Ag9In4)+Beta-(AgZn)+Liquid、 Beta-(AgZn)+Gamma-(Ag5Zn8)+Liquid與Gamma-(Ag5Zn8)+Epsilon-(AgZn3)+Liquid等6個縛三角形(Tie Triangle)。
Sb-Se-Pb-Sn四元系統中，已分別完成Pb-Sb-Se及Sn-Sb-Se三元熱電材料系統之液相線投影圖及400oC等溫橫截面圖。Pb-Sb-Se三元系統液相線投影圖具有(Pb)、(Sb)、(Se)、PbSe、Sb2Se3、Pb6Sb6Se17、PbSb2Se4與Pb2Sb9Se9等8個首要析出相，並存在2個互溶間隙(Miscibility gap)；此外，以熱分析制定出Liquid=PbSe+(Sb)+(Pb)、Liquid=Pb2Sb9Se9+PbSb2Se4+Sb2Se3、Liquid+(Sb)=Pb2Sb9Se9+Sb2Se3、Liquid+PbSe=PbSb2Se4+Pb2Sb9Se9與Liquid+PbSe+(Sb)=Pb2Sb9Se9等5個不變反應點；400oC等溫橫截面圖的部分，共可制定出PbSe+(Sb)+Liquid、PbSe+PbSb2Se4+(Sb)、PbSb2Se4+Pb2Sb9Se9+(Sb)、PbSb2Se4+Pb2Sb9Se9+Sb2Se3、Pb2Sb9Se9+Sb2Se3+(Sb)、PbSe+Pb6Sb6Se17+PbSb2Se4、PbSe+Pb6Sb6Se17+Liquid、Pb6Sb6Se17+PbSb2Se4+Sb2Se3與Pb6Sb6Se17+Sb2Se3+Liquid等9個縛三角形，以此可清楚了解此系統在高熱電優值的溫度400oC下之相關係。
Sn-Sb-Se三元系統液相線投影圖具有(Sn)、(Sb)、(Se)、Sb2Sn3、SbSn、SnSe、SnSe2、Sb2Se3、Sn2Sb9Se9與SnSb2Se4等10個首要析出相，並存在2個互溶間隙；此外，本研究以熱分析方式制定出Liquid+Sb2Sn3=SnSe+(Sn)、Liquid+SbSn=SnSe+Sb2Sn3、Liquid+(Sb)=SbSn+SnSe、Liquid+Sn2Sb9Se9=SnSb2Se4+Sb2Se3、Liquid+Sn2Sb9Se9+(Sb)=Sb2Se3、Liquid+(Sb)+SnSe=Sn2Sb9Se9和Liquid+Sn2Sb9Se9+SnSe=SnSb2Se4等7個不變反應點；400oC等溫橫截面圖的部分，共可制定出Liquid+SbSn+SnSe、SbSn+SnSe+(Sb)、SnSe+(Sb)+Sn2Sb9Se9、(Sb)+Sb2Se3+Sn2Sb9Se9、SnSe+Sn2Sb9Se9+SnSb2Se4、Sb2Se3+Sn2Sb9Se9+SnSb2Se4、SnSe+SnSe2+SnSb2Se4、SnSe2+SnSb2Se4+Sb2Se3和SnSe2+Sb2Se3+Liquid等9個縛三角形。值得一提的是，在制定Pb-Sb-Se及Sn-Sb-Se三元相圖的過程中，發現尚未被文獻報導之Pb2Sb9Se9與Sn2Sb9Se9三元相，並進一步統整出三元相之XRD繞射圖譜。
在相圖計算方面，本研究目前以熱力學相圖計算方法計算Sb-Se二元系統之熱力學模型；本次計算主要是以商用相圖計算軟體Pandat (version 8.1 and 2013)進行相圖計算，並選擇歐洲熱力學數據科學集團(SGTE, Scientific Group Thermodata Europe)提出的純元素熱力學資料庫為基礎，以準溶解模型(Associate solution)計算出Sb-Se熱力學模型之液相；此外，為探究Sn-Se二元系統相圖是否存在互溶間隙，將以第一原理分子動力學針對Sn-Se合金進行熱力學性質計算，並進一步將結果與熱力學計算相圖結合，建立Sn-Se二元系統之熱力學模型。

Thermoelectric materials and devices are regarded as the important energy materials have been the subject of intensive study, primarily because of their abilities of direct transformation between heat and electricity. Recently, due to the development of advanced semiconductor processes and nanotechnology, the researches of thermoelectric materials are moving into new territory. Lead telluride (PbTe) and Cobalt triantimonide (CoSb3) alloys are the most widely used mid-temperature thermoelectric materials. Additionally, the Sb-Se-Pb-Sn alloys have been recently examined among various promising thermoelectric materials. In Sb-Se-Pb-Sn system, the PbSe, Sb2Se3 and SnSe compounds are of interests to thermoelectric applications because of their outstanding performances reported by numerous groups.
Soldering plays an important role of assembly of thermoelectric devices. Sn-Pb alloys are the preferred jointing material of electronic industry owning to its attractive price and relative low melting point. Nevertheless, there are healthy and environmental issues associated with the toxicity of Pb containing solders, the researches of Pb-free solders were taken seriously. In a variety of Pb-free solder systems, Sn-Ag-Cu alloys are used widely. Besides, Sn-Ag-In, Sn-Ag-Zn, and Sn-In-Zn solder alloys are also promising Pb-free solders. Additionally, there are studies about using Sn-Ag-In-Zn quaternary alloys as electronic solders. Construction of Sn-Ag-In-Zn system is fundamentally important for designing the solder alloys with better mechanical properties and higher stability. However, the phase diagrams and thermodynamic models of Ag-In-Zn ternary system have not been constructed.
Knowledge of phase equilibria is fundamentally important for materials development and applications. Phase diagrams can be obtained by experimental determinations and calculations. The CALPHAD (Calculation of Phase Diagram) approach is the most popular calculation method. Based on the information of the thermodynamic properties and phase equilibria of system, the assessment of the thermodynamic models can be determined.
In this study, the phase diagrams of Ag-In-Zn system of Sn-Ag-In-Zn quaternary system and Pb-Sb-Se, and Sn-Sb-Se ternary systems of Sb-Se-Pb-Sn quaternary systems are determined. The microstructures, compositions, and diffraction peaks were determined using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), electron probe X-ray microanalyzer (EPMA) and X-ray diffractometer (XRD). A differential thermal analysis (DTA) was used to determine the reaction temperatures of the invariant reactions. The CALPHAD approach and AIMD (Ab-initio molecular dynamics) have been used for the assessment of the thermodynamic models of Sb-Se and Sn-Se binary systems.
The liquidus projection and isothermal section of Ag-In-Zn lead-free solder system and Pb-Sb-Se, Sn-Sb-Se thermoelectric systems are experimentally determined. There are 10 primary solidification phases: (Ag), (In), (Zn), Beta-(Ag3In), Zeta-(Ag3In), Gamma-(Ag9In4), AgIn2, Beta-(AgZn), Gamma-(Ag5Zn8), and Epsilon-(AgZn3) in the Ag-In-Zn ternary system. Moreover, there are five ternary invariant reactions: Liquid=(In)+AgIn2+Gamma-(Ag5Zn8), Liquid=Epsilon-(AgZn3)+(In)+(Zn), Liquid+Beta-(AgZn)=Gamma-(Ag5Zn8)+Gamma-(Ag9In4), Liquid+Zeta-(Ag3In)=Gamma-(Ag5In8)Beta-(AgZn) and Liquid+(Ag)+Beta-(AgZn)=Zeta-(Ag3In). In the isothermal section at 500oC, there is no ternary compound and there are 6 tie triangles : (Ag)+Zeta-(Ag3In)+Beta-(AgZn), Zeta-(Ag3In)+Gamma-(Ag9In4)+Beta-(AgZn), Zeta-(Ag3In)+Gamma-(Ag9In4)+Liquid, Gamma-(Ag9In4)+Beta-(AgZn)+Liquid, Beta-(AgZn)+Gamma-(Ag5Zn8)+Liquid and Gamma-(Ag5Zn8)+Epsilon-(AgZn3) in the 500oC isothermal section of Ag-In-Zn ternary system.
There are 8 primary solidification phases, which are (Pb), (Sb), (Se), PbSe, Sb2Se3, Pb6Sb6Se17, PbSb2Se4 and Pb2Sb9Se9 phases in the liquidus projection of Pb-Sb-Se ternary system. Among of all the primary solidification phases, the ternary compound, Pb2Sb9Se9 is the new ternary compound which has not been reported before. The XRD pattern of Pb2Sb9Se9 is determined by X-ray diffraction analysis. Furthermore, Five invariant reactions: Liquid=PbSe+(Sb)+(Pb), Liquid=Pb2Sb9Se9+PbSb2Se4+Sb2Se3, Liquid+(Sb)=Pb2Sb9Se9+Sb2Se3, Liquid +PbSe =PbSb2Se4+Pb2Sb9Se9, Liquid+PbSe+(Sb)=Pb2Sb9Se9 are determined by thermal analysis. There are 9 tie-triangles, which are PbSe+(Sb)+Liquid, PbSe+PbSb2Se4+(Sb), PbSb2Se4+Pb2Sb9Se9+(Sb), PbSb2Se4+Pb2Sb9Se9+Sb2Se3, Pb2Sb9Se9+Sb2Se3+(Sb), PbSe+Pb6Sb6Se17+PbSb2Se4, PbSe+Pb6Sb6Se17+Liquid, Pb6Sb6Se17+PbSb2Se4+Sb2Se3 and Pb6Sb6Se17+Sb2Se3+Liquid, in the 400oC isothermal section of Pb-Sb-Se ternary system.
There are 10 primary solidification phases, which are (Sn), (Sb), (Se), Sb2Sn3, SbSn, SnSe, SnSe2, Sb2Se3, Sn2Sb9Se9 and SnSb2Se4 phases in the liquidus projection of Sn-Sb-Se ternary system. It is worthy of mentioning that Sn2Sb9Se9 ternary phase is another new compound which has not been reported in the literature. The XRD pattern of Sn2Sb9Se9 is determined by X-ray diffraction analysis. Seven invariant reactions: Liquid+Sb2Sn3=SnSe+(Sn), Liquid+SbSn=SnSe+Sb2Sn3, Liquid+(Sb)=SbSn+SnSe, Liquid+Sn2Sb9Se9=SnSb2Se4+Sb2Se3, Liquid+Sn2Sb9Se9+(Sb)=Sb2Se3, Liquid+(Sb)+SnSe=Sn2Sb9Se9 and Liquid+Sn2Sb9Se9+SnSe=SnSb2Se4 are experimentally determined in this study. There are 9 tie-triangles, which are Liquid+SbSn+SnSe, SbSn+SnSe+(Sb), SnSe+(Sb)+Sn2Sb9Se9, (Sb)+Sb2Se3+Sn2Sb9Se9, SnSe+Sn2Sb9Se9+SnSb2Se4, Sb2Se3+Sn2Sb9Se9+SnSb2Se4, SnSe+SnSe2+SnSb2Se4, SnSe2+SnSb2Se4+Sb2Se3 and SnSe2+Sb2Se3+Liquid, in the 400oC isothermal section of Sn-Sb-Se ternary system.
In the calculation of Sb-Se binary system, the functions of Gibbs energies of pure elements are taken from SGTE database, and the associate model is used to describe the liquid phase. The new thermodynamic description of the Sb–Se system is proposed, and good agreement between available literature data and calculated results is found. The re-optimized thermodynamic model of Sb-Se binary system may allow the construction of calculations upon multicomponent.
Another important investigation in this study is examining the existence of miscibility gap of Sn-Se binary system by using AIMD simulations. The enthalpy of mixing in liquid phase is calculated, and the results are fitted with Redlich-Kister polynomial for obtaining the new parameters used in CALPHAD approach.

摘要 I
Abstract III
Table of Content 1
List of Table 5
List of Figure 7
1. Introduction 19
1.1 Lead-free solders 20
1.2 Thermoelectric materials 22
1.3 The phase diagrams of Sb-Se-Pb-Sn and Sn-Ag-In-Zn systems 25
2. Literature Reviews 30
2.1 Binary system of Sn-Ag-In-Zn system 30
2.1.1 Sn-Ag binary system 30
2.1.2 Sn-In binary system 32
2.1.3 Sn-Zn binary system 32
2.1.4 Ag-In binary system 35
2.1.5 Ag-Zn binary system 37
2.1.6 In-Zn binary system 37
2.2 Ternary system of Sn-Ag-In-Zn system 40
2.2.1 Sn-Ag-In ternary system 40
2.2.2 Sn-Ag-Zn ternary system 47
2.2.3 Sn-In-Zn ternary system 50
2.2.4 Ag-In-Zn ternary system 50
2.3 Quaternary system of Sn-Ag-In-Zn system 50
2.4 Binary system of Sb-Se-Pb-Sn system 54
2.4.1 Pb-Sb binary system 54
2.4.2 Pb-Se binary system 54
2.4.3 Pb-Sn binary system 57
2.4.4 Sb-Se binary system 57
2.4.5 Sb-Sn binary system 60
2.4.6 Se-Sn binary system 60
2.5 Ternary system of Sb-Se-Pb-Sn system 64
2.5.1 Pb-Sb-Se ternary system 64
2.5.2 Pb-Sb-Sn ternary system 66
2.5.3 Pb-Se-Sn ternary system 71
2.5.4 Sb-Se-Sn ternary system 73
2.6 Quaternary system of Sb-Se-Pb-Sn system 73
2.7 Calculation of phase diagram 75
2.7.1 The literature information of calculated Sb-Se binary system 78
2.7.2 The literature information of calculated Sn-Se binary system 81
3. Experimental Procedure 83
3.1 Alloy preparations 83
3.1.1 Liquidus projection 83
3.1.2 Isothermal section 83
3.2 Phase determinations 84
3.3 Thermal analysis 84
3.4 Calculation of phase diagrams 87
3.5 Details of Ab-initio molecular dynamics (AIMD) simulations 88
3.5.1 Enthalpy of mixing 88
4. Results and discussion 90
4.1 Liquidus projection of Ag-In-Zn ternary system 90
4.1.1 (Ag) primary phase regime 90
4.1.2 Zeta-(Ag3In) primary phase regime 91
4.1.3 Gamma-(Ag9In4) primary phase regime 98
4.1.4 Beta-(AgZn) primary phase regime 101
4.1.5 Gamma-(Ag5Zn8) primary phase regime 104
4.1.6 Epsilon-(AgZn3) primary phase regime 104
4.1.7 Binary boundaries construction of liquidus projection of Ag-In-Zn system 110
4.1.8 Determination of invariant reaction temperatures of Ag-In-Zn ternary system 114
4.2 Ag-In-Zn phase equilibria isothermal section at 500oC 126
4.2.1 Zeta-(Ag3In)+Gamma-(Ag9In4) two-phase regime 126
4.2.2 (Ag)+Beta-(AgZn) two-phase regime 126
4.2.3 Gamma-(Ag9In4)+Beta-(AgZn) two-phase regime 131
4.2.4 Gamma-(Ag9In4)+Liquid two-phase regime 131
4.2.5 Beta-(AgZn)+Liquid two-phase regime 135
4.2.6 Gamma-(Ag5Zn8)+Epsilon-(AgZn3)+Liquid three-phase regime 135
4.2.7 Epsilon-(AgZn3)+Liquid two-phase regime 139
4.2.8 Liquid single phase regime 139
4.2.9 Binary boundaries construction of isothermal section of the Ag-In-Zn ternary system at 500oC 142
4.3 Liquidus projection of Pb-Sb-Se ternary system 146
4.3.1 PbSe primary phase regime 146
4.3.2 (Pb) primary phase regime 153
4.3.3 (Sb) primary phase regime 153
4.3.4 Sb2Se3 primary phase regime 154
4.3.5 Pb6Sb6Se17 primary phase regime 160
4.3.6 PbSb2Se4 primary phase regime 160
4.3.7 Pb2Sb9Se9 primary phase regime 164
4.3.8 Miscibility gap 168
4.3.9 Binary boundaries construction of liquidus projection of Pb-Sb-Se system 171
4.3.10 Determination of invariant reaction temperatures of Pb-Sb-Se ternary system 175
4.4 Pb-Sb-Se phase equilibria isothermal section at 400oC 187
4.4.1 PbSe+Liquid two-phase regime 187
4.4.2 PbSe+(Sb)+Liquid three-phase regime 187
4.4.3 PbSe+(Sb) two-phase regime 188
4.4.4 PbSe+PbSb2Se4+(Sb) three-phase regime 195
4.4.5 PbSb2Se4+Pb2Sb9Se9+Sb2Se3 three-phase regime 195
4.4.6 Pb2Sb9Se9+Sb2Se3+(Sb) three phase regime 198
4.4.7 PbSe+Pb6Sb6Se17+Liquid three phase regime 198
4.4.8 Pb6Sb6Se17 single-phase regime 201
4.4.9 PbSb2Se4+ Pb6Sb6Se17+Sb2Se3 three phase region 201
4.4.10 Pb6Sb6Se17+Sb2Se3+Liquid three phase region 201
4.4.11 Binary boundaries construction of isothermal section of Pb-Sb-Se system at 400oC 206
4.5 Liquidus projection of Sn-Sb-Se ternary system 211
4.5.1 SnSe primary phase regime 211
4.5.2 SnSe2 primary phase regime 216
4.5.3 (Sb) primary phase regime 216
4.5.4 Sn2Sb9Se9 primary phase regime 216
4.5.5 SnSb2Se4 primary phase regime 223
4.5.6 Sb2Se3 primary phase regime 223
4.5.7 Miscibility gap 226
4.5.8 Binary boundaries construction of liquidus projection of Sn-Sb-Se system 228
4.5.9 Determination of invariant reaction temperatures of Sn-Sb-Se ternary system 232
4.6 Sn-Sb-Se phase equilibria isothermal section at 400oC 250
4.6.1 SnSe-SbSn-Liquid three phase regime 250
4.6.2 SnSe-SbSn-(Sb) three phase regime 250
4.6.3 SnSe-(Sb) two phase regime 251
4.6.4 SnSe-Sn2Sb9Se9-(Sb) three phase regime 251
4.6.5 Sn2Sb9Se9-(Sb) two phase regime 252
4.6.6 Sb2Se3-Sn2Sb9Se9 two phase regime 261
4.6.7 Sb2Se3-Sn2Sb9Se9-(Sb) three phase regime 261
4.6.8 SnSb2Se4-SnSe2 two phase regime 261
4.6.9 SnSe2-Sb2Se3-Liquid three phase regime 264
4.6.10 Binary boundaries construction of isothermal section of Sn-Sb-Se system at 400oC 266
4.7 Calculation of Sb-Se binary system 270
4.7.1 Thermodynamic modeling 270
4.7.2 Calculated results of Sb-Se binary system 272
4.8 Calculation of Sn-Se binary system 276
4.8.1 Experimental analysis 276
4.8.2 Enthalpy of mixing 279
4.8.3 The calculated Sn-Se phase diagrams 282
5 Conclusions 285
Reference 289

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