Co-Fe-Ge三元合金系統具有許多應用潛能的化合物，如 Co2FeGe是具有觸媒應用潛力的赫斯勒化合物(Heusler compound)。赫斯勒化合物是由三個元素(XYZ)組合而成，藉由替換XYZ當中的特定元素就能組合出許多不同特性的化合物。相圖是基礎的材料知識，對材料製備與性質的探討非常重要。相圖可透過實驗測定或是利用Calphad(Calculation of phase diagram)方式的計算來獲得。本研究探討Co-Fe-Ge三元系統的相圖，以提供Co-Fe-Ge三元材料的基礎知識。
探討Co-Fe-Ge三元系統的相圖，須先了解其組成的二元系統相圖。Co-Fe-Ge包含了Co-Fe、Co-Ge與Fe-Ge三個二元組成系統。文獻中已有可靠的Co-Fe與Co-Ge二元系統的相圖實驗量測與Calphad熱力學敘述，本研究將直接引用評估後的文獻，然而Fe-Ge二元系統有實驗量測的相圖，但是卻欠缺Calphad的熱力學模型敘述。本研究將進行Fe-Ge二元系統的Calphad熱力學模型建立，並用實驗的方法進行Co-Fe-Ge在950 ℃的相圖量測，並進行Co-Fe-Ge三元系統的熱力學模型建立與相圖計算。
Calphad的方法，包括建立熱力學模型與參數及相圖計算，是採用商用軟體Thermo-cal與Pandat進行。相平衡的實驗是以純元素製備合金試樣，將樣品封於石英管中，置於950℃的高溫爐中。經過兩周至七個月的時間後，取出樣品淬冷於水中。針對合金試樣，分析其存在的穩定相，包括利用掃描式電子顯微鏡(SEM, Scanning Electron Microscope)做金相分析，X光粉末繞射儀(XRD, X-Ray Diffractometer)進行材料結構的分析、電子探針分析儀(EPMA, Electron Probe Micro Analyzer)做組成分析。
依據實驗的結果，推定在950℃ 的Co-Fe-Ge三元相圖有六個單相區、八個兩相區與三個三相區，八個兩相區分別為β-(Co,Fe)5Ge3+Liquid、CoGe+Liquid、CoGe+ β-(Co,Fe)5Ge3、β-(Co,Fe)5Ge3+(αCo,γFe)、β-(Co,Fe)5Ge3+εFe3Ge、εFe3Ge+(αCo,γFe)、εFe3Ge+ αFe、αFe+(αCo,γFe)。而六個單相區則為: Liquid相、CoGe相、β-(Co,Fe)5Ge3相、(αCo,γFe)相、α-Fe相和ε-Fe3Ge相。三相區則是β-(Co,Fe)5Ge3+CoGe+Liquid、β-(Co,Fe)5Ge3+ εFe3Ge+(αCo,γFe)、εFe3Ge+(αCo,γFe)+ α-Fe。有了以上的結果可確定Co-Fe-Ge三元系統的相邊界，建構出Co-Fe-Ge三元系統相圖。
Fe-Ge二元系統的純元素性質是引用SGTE(Scientific Group Thermodata Europe)資料庫的數據。將Fe-Ge系統中的相分成三類，包括了(1)一般的溶液模型(solution model) :液相、FCC(γFe)相、BCC(αFe)相、D03相。(2)線化合物模型(line compound):εFe3Ge相、η相、Fe6Ge5相、FeGe相、FeGe2相。(3)缺陷模型 (defect model) :Beta相。以Redlich-Kister 多項式描述溶液相的過剩吉布斯自由能(excess Gibbs free energy)，如溶液相中的D03相。對於介金屬化合物(intermetallic compound)中的線化合物(line compound)則是透過加入a+bT表示式於自由能的描述中，而參數a與b則會透過商用軟體Thermo-cal與Pandat的優化(optimization)獲得。對於具有寬組成範圍 (wide compositional homogeneity range)的缺陷模型Beta相，則引入具有兩個sublattice 的模型:(Fe,Ge)0.625:(Fe,Ge)0.375來描述。透過給予Fe-Ge系統當中的相適當的熱力學模型與自由能描述再加上參數優化的結果，得到描述每個相的熱力學參數，成功地建立出Fe-Ge二元系統的計算相圖。
接著再將Fe-Ge計算相圖結合文獻已有的Co-Ge、Co-Fe二元系統的熱力學參數，建構出完整的Co-Fe-Ge三元系統計算相圖。比較實驗與計算結果，由於沒有引入三元系統的交互作用，使得計算出來的結果與實驗結果仍有一點落差，其中液相與Beta相的關係一致，雖然定量的相區位置有差異但仍可與實驗的結果相互應證，證明實驗的正確性。本研究最終用實驗與計算的方式建構出Co-Fe-Ge於950℃之等溫橫截面相圖，可做為赫斯勒化合物的基礎材料知識，並提供Co-Fe-Ge三元系統材料的熱力學資訊。

Co-Fe-Ge is an important ternary material system. Various alloys in this ternary systems have unique properties. For example, Co2FeGe is a Heusler compound of catalytic application importance. The composition of Heusler compound is described as XYZ by three different elements. Valuable properties of compound can be made by replacing the certain element. In order to deeply understand the material characteristic of Heusler compound, we need to rely on the assistance of phase diagram. Knowledge of phase equilibria is fundamentally important for materials development and application. Phase diagrams describe phase equilibria information concisely and can be determined by experimental measurements and calculation using the Calphad (calculation of Phase Diagram) approach.
In order to deeply study about Co-Fe-Ge ternary phase diagram, it is necessary to understand their three binary system, including Co-Fe, Co-Ge, Fe-Ge. Those phase diagram experiment and Calphad thermodynamics description of Co-Fe and Co-Ge binary systems are well established in the literature, this study will adopt them directly.However, there is no thermodynamics model description about Fe-Ge binary system so far although its experimental phase diagram is established. In this study, constructing appropriate thermodynamics model to describe Fe-Ge binary system by using commercial software: Thermo-cal and pandat.And using experimental method to determine Co-Fe-Ge ternary isothermal section at 950°C.
The Co-Fe-Ge 950℃ isothermal section is experimentally determined. Co-Fe-Ge alloys were prepared with pure constituent elements and equilibrated at 950℃. According to the phase boundary of three binary phase diagram : Co-Ge, Co-Fe, Fe-Ge respectively, labeling the phase boundary in Co-Fe-Ge 950℃ isothermal section ternary phase diagram. The equilibrium time is about two weeks to seven months. There are three analysis methods used to determine the phase. Using SEM to observe microstructures of alloy. Using XRD diffraction peak to check alloy structure (qualitative analysis), EPMA for composition analysis (quantitative analysis). There are six stable single-phase regions, Liquid, CoGe, β-(Co,Fe)5Ge3, (αCo,γFe) , α-Fe, and ε-Fe3Ge. There are eight two phase regions determined in phase diagram , β-(Co,Fe)5Ge3+Liquid, CoGe+Liquid , CoGe+β-(Co,Fe)5Ge3, β-(Co,Fe)5Ge3+(αCo,γFe), β-(Co,Fe)5Ge3+εFe3Ge, εFe3Ge+(αCo,γFe), εFe3Ge+ αFe, αFe+(αCo,γFe)。There are three phase regions found in phase diagrams, β-(Co,Fe)5Ge3+ CoGe+Liquid, β-(Co,Fe)5Ge3+ εFe3Ge+(αCo,γFe), εFe3Ge+(αCo,γFe)+ αFe. From the above results, the phase boundaries can be successfully determined.
In the calculation of Fe-Ge binary system, the functions of Gibbs energies of pure elements are taken from SGTE database. Before doing calculation, it is necessary to classfy each phase for their different models.There are three groups of this system, solution, line compound, intermetallic compound with homogeneity range.(1) Solution model: Liquid, FCC(γFe), BCC(αFe), D03 phases.(2)Line compound:εFe3Ge,η, Fe6Ge5,FeGe,FeGe2 phases.(3)Intermetalic compound with homogeneity range: Beta phase. Using Redlich-Kister polynomial to describe their thermodynamic properties for the excess Gibbs free energy term in solution phase, such as D03 phase. For line compound, adding a+bT in Gibbs free energy of thermodynamics description. Parameter a and b can assess in optimization by using commercial software Thermo-cal and Pandat. For intermetallic compound with wide homogeneity range, introducing two sublatticce model (Fe,Ge)0.625:(Fe,Ge)0.375 to describe Beta phase. Choose suitable model to satisfy Fe5Ge3 with homogeneity range, and the solution phase of D03. By the optimization result, getting the thermodynamics parameters to describe each phase. Finishing calculation phase diagram of Fe-Ge binary system.
Combining the thermodynamics description of Co-Ge ,Co-Fe in literatures and Fe-Ge system to construct calculation phase diagram of Co-Fe-Ge ternary system completely.Compare the experimental result and calculation result, there are a little bit different between them because there is no interaction parameter induced in ternary system. The relation of Liquid and Beta phase are correct although there are some difference in position, the calculation result still can prove the accuracy for experiment.
In this research using experimental method and Calphad method to construct ternary isothermal section of Co-Fe-Ge at 950℃. This research, as the basic material knowledge of Hesler compounds will provide thermodynamic information of Co-Fe-Ge ternary system materials.

摘要 i
Abstract iii
第 1 章 前言 1
第 2 章 文獻回顧與探討 3
2-1 赫斯勒合金 3
2-2 相圖 7
2-3 相圖計算 11
2-3-1 Calphad介紹 11
2-3-2 Calphad法的熱力學模型 12
2-3-3 Calphad法的步驟 13
2-4 Co-Fe-Ge 三元系統相圖 16
2-4-1 Co-Fe相圖 16
2-4-2 Co-Fe計算相圖 19
2-4-3 Co-Ge相圖 24
2-4-4 Co-Ge計算相圖 26
2-4-5 Fe-Ge相圖 38
第 3 章 研究方法與步驟 41
3-1 合金製備 41
3-1-1 配置合金 41
3-1-2 電弧熔融合金 41
3-1-3 前處理 42
3-2 相平衡實驗 42
3-3 金相樣品製備與分析 42
3-3-1 研磨樣品 43
3-3-2 金相分析(SEM) 44
3-3-3 定量分析(EPMA) 44
3-3-4 定性分析(XRD) 45
第 4 章 結果與討論 46
4-1 Co-Fe-Ge三元系統950oC等溫橫截面圖 46
4-1-1 CoGe+Liquid 兩相區 52
4-1-2 β(Co,Fe)5Ge3+Liquid 兩相區 60
4-1-3 β(Co,Fe)5Ge3+(αCo,γFe) 兩相區 74
4-1-4 Liquid 單相區 81
4-1-5 CoGe 單相區 88
4-1-6 β(Co,Fe)5Ge3單相區 91
4-1-7 (αCo,γFe)單相區 96
4-1-8 Liquid+CoGe+ β(Co,Fe)5Ge3三相區 104
4-1-9 β(Co,Fe)5Ge3+(αCo,γFe)+εFe3Ge三相區 107
4-1-10 (αCo,γFe)+εFe3Ge+BCC三相區 108
4-1-11 Co-Fe-Ge三元系統950°C等溫橫截面圖 109
4-2 Fe-Ge二元系統之計算相圖 111
4-2-1 液體混合焓與活性 111
4-2-2 找尋適當的熱力學模型 114
4-3 Co-Fe-Ge三元系統之計算相圖 121
第5章 結論 129
第6章 參考資料 131

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