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研究生:呂季紘
研究生(外文):Chi-Hung Lu
論文名稱:運用第一原理計算搭配古典力場模型探討鋁鈷鉻鐵鎳高熵合金的析出行為及相穩定度
論文名稱(外文):First-principles Calculations and MEAM Modeling of the Precipitation Behavior and Phase Stability in the AlCoCrFeNi High-entropy Alloy
指導教授:郭錦龍
指導教授(外文):Chin-Lung Kuo
口試委員:許文東吳鉉忠李明憲
口試委員(外文):Wen-Dung HsuHsuan-Chung WuMing-Hsien Lee
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:材料科學與工程學研究所
學門:工程學門
學類:材料工程學類
論文種類:學術論文
論文出版年:2019
畢業學年度:108
語文別:英文
論文頁數:123
中文關鍵詞:高熵合金第一原理計算古典力場模型相穩定度
外文關鍵詞:high-entropy alloyfirst-principles calculationclassical modelingphase stability
DOI:10.6342/NTU201904184
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本篇論文利用第一原理搭配密度泛函理論計算及MEAM古典力場模型兩種方式來研究AlxCoCrFeNi高熵合金中隨著Al濃度變化的相穩定度。根據這兩種模擬方法的計算精準度以及它們所須耗費的計算資源,我將這兩種方法用於不同尺度、不同研究方向的計算模擬。
論文的第一部分我們運用第一原理計算搭配我們開發的逆蒙地卡羅方法來研究五元AlxCoCrFeNi高熵合金隨Al濃度變化的相穩定度。我們藉由逆蒙地卡羅方法來建構各種不同局域元素排序的結構,而經由這些結構的能量計算,我們首先發現B2-NiAl的析出是AlxCoCrFeNi合金從FCC結構轉變為BCC結構的重要關鍵,且Ni和Al的析出在能量上是自發性的反應。雖然如此,NiAl的析出物有兩種可能性,分別是L12-Ni3Al和B2-NiAl,而Al濃度的高低和Cr元素的局域分布都會顯著影響NiAl析出物會是哪一種結構。而藉由進一步的四元合金計算,我們探討了Ni和Al在合金中對相穩定度的影響,也探討了在含有Fe、Co、Ni、Al的有序BCC結構中,這四種元素傾向以何種方式排列。最後,我們進行了σ相的計算,搭配前述FCC及BCC結構的計算,我們以理論計算的角度解釋了文獻中提到過的σ相生成路徑。
在第二部分的研究中,我們修正了我們團隊原有的CoCrFeMnNi MEAM參數,並開發了一組新的AlCoCrFeNi MEAM參數,並驗證這些參數的結構、機械性質,以及異相之間的相對能量。最後,我們針對兩種高熵合金系統進行大尺度的分子動力學模擬,一方面用於驗證這兩組參數的可靠性;另一方面,我們藉由這種較大尺度的模擬來展示相分離或相轉變的過程,並提供了另一種相較於第一原理計算更大的尺度來佐證我們在第一部分研究中所提出的論點。
Density functional theory (DFT) and modified embedded atom method (MEAM), which is a classical force field, are applied in this thesis to study the relative phase stability of FCC and BCC AlxCoCrFeNi alloys when varying Al content. Due to the accuracy and the computational demands of these two atomistic approaches, they are used in different types of researches.
In the first part of this study, an algorithm by which we can construct certain atomic structures with certain local chemical ordering is developed and is combined with first-principles static calculations to study the phase stability of AlxCoCrFeNi alloys. We find out that the formation of B2-NiAl plays a key role in the phase transition from FCC to BCC, and the segregation of Ni and Al is energy favorable. However, the stable precipitates of Ni and Al can be L12-Ni3Al or B2-NiAl; both the Al concentration and atomic distribution of Cr element can affect which type of structure NiAl precipitates may form. In addition, by further study of quaternary alloys, we find how Ni and Al can affect the phase stability and the possible atomic distribution of ordered BCC structure composed of Fe, Co, Ni, and Al. Finally, by calculations of σ phase, we explain the formation paths of σ phase that have been proposed in the literature in a theoretical point of view.
In the second part of this study, two sets of MEAM atomistic potential models are developed, one of which is for CoCrFeMnNi system, and another one is for AlCoCrFeNi system. They are validated by structural properties, mechanical properties, and relative energies between structures. After that, molecular dynamics simulations are performed to demonstrate the phase separation and phase transition behaviors that have been discussed in DFT calculations and to provide another perspective about the phase transition from large-scale atomistic simulations.
論文口試委員審定書 ii
致謝 iii
摘要 iv
Abstract v
Contents vii
List of Figures x
List of Tables xiv
Chapter 1. Introduction 1
Chapter 2. Theoretical background 7
2.1 First principles calculation 7
2.2 Born-Oppenheimer approximation 7
2.3 Density functional theory (DFT) 8
2.3.1 Thomas-Fermi model 8
2.3.2 Hohenberg-Kohn theorem 9
2.3.3 Kohn-Sham equation 9
2.3.4 Exchange-correlation functional 12
2.3.5 Pseudopotential 12
2.4 Classical force field 14
2.4.1 Modified embedded atom method (MEAM) 15
2.4.2 Potential parameters optimization 18
2.5 Molecular dynamics 19
2.5.1 Verlet algorithm 19
2.5.2 Nosé-Hoover thermostat 20
2.6 Structure construction and analysis method 20
2.6.1 Common neighbor analysis (CNA) 20
2.6.2 Reverse Monte Carlo algorithm (RMC alogrithm) 22
Chapter 3. First-principles Study of the Phase Stability of AlxCoCrFeNi Alloy 26
3.1 Introduction 26
3.2 Computational details 31
3.3 Results and discussion 32
3.3.1 Homogeneous AlxCoCrFeNi solid solution 32
3.3.2 L12-Ni3Al segregated FCC and B2-NiAl segregated BCC 34
3.3.3 Prediction of thermodynamically stable structures of AlxCoCrFeNi alloys 42
3.3.4 The effects of the addition of Ni or Al on the phase stability of the CoCrFe alloy 48
3.3.5 The atomic distribution of Fe, Co, Ni, Al-rich B2 phase 55
3.3.6 The formation path of CoCrFe-rich σ phase in AlxCoCrFeNi alloy 58
3.4 Summary 62
Chapter 4. Development of MEAM Atomistic Potential Model for CoCrFeMnNi and AlCoCrFeNi High-entropy Alloys 64
4.1 Introduction 64
4.2 Methodology 66
4.2.1 MEAM parametrization 66
4.2.2 Stacking fault energy (SFE) calculation 68
4.2.3 Mechanical properties calculation 69
4.2.4 Computational detail 71
4.3 Modification of CoCrFeMnNi MEAM potential model 72
4.3.1 Validation of CoCrFeMnNi MEAM model 72
4.3.2 Molecular dynamics simulations of CoCrFeMnNi alloy 76
4.4 Development of AlCoCrFeNi MEAM potential model 82
4.4.1 Validation of homogeneous AlxCoCrFeNi alloys 82
4.4.2 Energies of NiAl-segragated AlxCoCrFeNi alloys 86
4.4.3 Energies of NixCoCrFe alloys 89
4.4.4 Molecular dynamics simulations of Al1.0CoCrFeNi alloy 90
4.4.5 Molecular dynamics simulations of Al0.5CoCrFeNi alloy 97
4.5 Summary 104
Chapter 5. Conclusions 106
Reference 108
Appendix 115
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