臺灣博碩士論文加值系統

高溫合金是目前使用的材料進行高溫應用。最近，一種新型的合金稱為高熵合金被發現有很大的潛力，以取代高溫合金為原料的高溫應用。調查高熵合金大多由實驗這是耗時且昂貴的完成。在未來，計算方法，設計高熵合金將是非常有用的。而建構一個高階系統，必需先仰賴各低階系統的完成。
一個眾所周知的計算方法基於密度泛函理論（DFT）來預測材料的性質，從頭算，已經被證明是預測各種材料特性的一大利器。這個理論將利用第一原理計算方法去預測熱力學性值，並且將藉由此方法去增進Mo-V 和 Mo-Zr 的CALPHAD 模型建構。
Mo-V 和 Mo-Zr 二元系統的熱力學評估已經完成，其實驗結果和文獻中的利用實驗所得相圖的結果相當接近，熱力學評估之參數將被提出到high-order合金系統中，例如高熵合金。Mo-V-Zr 三元系統可藉由評估V-Zr 二元系統來開發。V-Zr二元系統之第一原理計算附於附錄 B，將V-Zr 二元系統和Mo-V以及Mo-Zr 二元系統做結合可以得到Mo-V-Zr 三元系統。此外，利用第一原理彈性性質計算來自MoNbHfTiZr的純元素和二元組成附於附錄C。從彈性性質的計算，可以更深入得到高熵合金實際的應用。第一原理計算成功的預測出體心立方結構和六方最密堆積結構的純Mo, Nb, Hf, Ti和Zr 元素的彈性性質，並比較文獻中的實驗和計算的資料。再者，由Mo, Nb, Hf, Ti 和Zr組成的十種二元合金系統的計算已經完成。

Superalloys are current used materials for high temperature application. Recently, a new type of alloy called high entropy alloys are found to have a great potential to replace superalloys as material for high temperature application. Investigation on high entropy alloys are mostly done by experiment which is time consuming and costly. In the future, computational method to design High Entropy alloys (HEAs) will be very useful. Computational method need to be done accurately for lower order system before going into high-order alloy system.
A well-known computational method to predict materials properties, ab initio calculation based on Density Functional Theory (DFT), has been proven to be a great tool for predicting various material properties. This thesis contains ab initio calculation to predict thermodynamic properties. Ab initio thermodynamic properties calculation is applied into Mo-V and Mo-Zr CALPHAD modeling to improve their thermodynamic description.
Mo, V, and Zr are common added element in refractory-HEAs. The thermodynamic description has been assessed in literature. However, experimental phase diagram data and thermochemical data are rarely available. Therefore, ab initio-aided CALPHAD modeling is employed to reassess the Mo-V and Mo-Zr binary systems.
Thermodynamic reassessment of Mo-V and Mo-Zr binary systems has been done and the results are closely agreed to the experimental phase diagram in the literature. The assessed parameters are proposed into high-order alloy systems such as HEAs. Furthermore, Mo-V-Zr ternary systems can be developed by assessing V-Zr binary system. Ab initio calculation for V-Zr binary system is presented in the appendix B for the possibility of integrated Mo-V, Mo-Zr, and V-Zr binary systems into Mo-V-Zr ternary systems. Additionally, ab initio elastic properties calculations of pure elements and binary constituents from MoNbHfTiZr HEA are presented in the appendix C. The elastic properties calculations are performed to get some insights into practical application of HEAs. Ab initio calculation successfully predict elastic properties of pure Mo, Nb, Hf, Ti, and Zr In bcc and hcp structure compared with experimental and calculated data from the literature. Furthermore, elastic properties of ten binary alloys from Mo, Nb, Hf, Ti, and Zr in bcc-SQS were calculated.

Contents
Acknowledgements ii
摘要 iii
Abstract iv
Contents vi
List of Tables viii
List of Figures ix
Chapter 1 Introduction 11
1.1 Preface 11
1.2 High Entropy Alloys (HEAs) 13
1.3 Ab initio-aided CALPHAD 19
1.3.1 CALPHAD modeling 19
1.3.2 Ab initio calculation 22
Chapter 2 Literature Review 24
2.1 Mo-V binary system 24
2.2 Mo-Zr binary system 27
Chapter 3 Methodology 30
3.1 CALPHAD thermodynamic modeling 30
3.2 Ab initio calculation 32
Chapter 4 Results and discussion 34
4.1 Mo-V binary system 34
4.1.1 Ab-initio solid solution phase 34
4.1.2 CALPHAD modeling 37
4.2 Mo-Zr binary system 38
4.2.1 Ab-initio solid solution phase 38
4.2.2 Ab initio ordered phase 42
4.2.3 CALPHAD modeling 43
Chapter 5 Summary 48
Chapter 6 Future work 49
References 50
APPENDIX A The input files used in PANDAT 58
A.1 TDB File 58
A.1.1 Mo-V binary system 58
A.1.2 Mo-Zr binary system 60
A.2 POP File 63
A.2.1 Mo-V binary system 63
A.2.2 Mo-Zr binary system 68
APPENDIX B Ab initio-aided CALPHAD modeling of V-Zr binary system 89
B.1 Literature Review 89
B.2 Methodology 91
B.3 Results and Discussion 93
APPENDIX C Ab initio elastic properties of binary alloys from HfMoNbTiZr refractory HEAs 99
C.1 Introduction 99
C.2 Methodology 100
C.3 Result and discussion 103
C.4 Summary 109

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