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研究生:蔡坤佑
研究生(外文):Tsai, Kun-Yo
論文名稱:高熵合金之高熵效應及緩慢擴散效應探討
論文名稱(外文):On High Entropy Effect and Sluggish Diffusion Effect of High-Entropy Alloys
指導教授:葉均蔚
指導教授(外文):Yeh, Jien-Wei
學位類別:博士
校院名稱:國立清華大學
系所名稱:材料科學工程學系
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:2013
畢業學年度:102
語文別:英文
論文頁數:177
中文關鍵詞:高熵合金高熵效應緩慢擴散效應
外文關鍵詞:High-entropy alloyHigh entropy effectSluggish diffusion effect
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高熵合金具有四個核心效應:高熵、嚴重晶格扭曲、緩慢擴散及雞尾酒效應,而本論文主旨在於探討高熵效應及緩慢擴散效應。由於高熵效應可促進固溶相的形成,但較大的混合焓及原子尺寸差會促進有序相的形成,為瞭解此一競爭,本研究設計兩個參數分析高熵合金的成份與相型態之間的關聯。其一為熱力學參數ε,代表合金中混合熵與混合焓之間的競爭關係;其二為拓樸學參數δ,代表合金中不同元素原子尺寸的差異。利用此二參數分析已知的高熵合金,結果發現可清楚界定出形成單純無序固溶相合金及生成有序相的條件。當δ較小,且混合熵的效應大於混合焓(即ε > 1.1)時,會傾向形成無序固溶相。當混合焓的效應大於混合熵(即ε < 1.1)時,合金傾向生成有序中間相。而當δ超過簡單結構所能承受的極限時,合金即會生成結構較複雜的介金屬相。此研究結果可提供未來合金設計與開發的參考。

此外,本研究藉由「擬二元擴散偶」實驗量測Co-Cr-Fe-Mn-Ni五元高熵合金中各元素的擴散參數,得到高熵合金緩慢擴散效應的直接證據。將各項擴散參數與其他FCC金屬比較,可發現隨著合金元數增加,各元素的擴散係數會隨之降低。而將各元素的活化能除以熔點標準化後,也可發現其值隨著合金元數增加而增加。本研究對這些趨勢提出理論解釋,採用準化學模型對晶格位能的差異幅度加以計算,結果發現高熵合金因主元素多,晶格屬全溶質晶格,晶格位能的差異幅度較大,因此具有許多位能相對較低的晶格位置形成原子的陷阱,使擴散活化能提高,此一理論可說是高熵合金緩慢擴散效應的主要機制。

High-entropy alloys have four core effects: high entropy, sluggish diffusion, severe lattice distortion, and cocktail. The aim of this study is to demonstrate high entropy and sluggish diffusion effects in a quantitative way. High entropy effect has been found to enhance the formation of solid solutions whereas large atomic size difference and large negative mixing enthalpy between unlike atom pairs have been found to enhance the formation of ordered phases. In order to gain more understanding of such an order-disorder competition, this study proposes two parameters to analyze the correlation between alloy compositions and phase types. One is the modified thermodynamic parameter ε which represents the competition between mixing entropy and mixing enthalpy, while the other is the topological parameter δ which represents the atomic size difference. From the analyses of these two parameters of published high-entropy alloys, the well-defined criteria for the formation of random solid solutions and ordered phases are obtained. When δ is small and ε is large (i.e. the effect of mixing entropy dominates over that of mixing enthalpy), alloys tend to form random solid solutions. On the other hands, when ε < 1.1 (i.e. the effect of mixing enthalpy dominates over that of mixing entropy), alloys tend to form ordered phases. Furthermore, when δ is too high to retain simple structures alloys will form intermetallic phases with more complex structures. These criteria could provide a useful guideline for alloy design of high-entropy alloys.

Beside, this study directly confirms the sluggish diffusion phenomenon by the measurement of diffusion parameters for the Co-Cr-Fe-Mn-Ni alloys using a quasi-binary diffusion couple method. Comparing the diffusion parameters of the five component elements measured in the present HEAs with that in the reference FCC metals, it can be found that the diffusion coefficients decrease with the number of constituent elements in the matrix, whereas the normalized activation energies Q/Tm increase with the number of constituent elements. These tendencies are certainly the direct evidences of the sluggish diffusion effect in HEAs. The mechanism behind such effect has also been proposed. The fluctuation of lattice potential energy (LPE) was calculated using quasichemical model. The larger LPE fluctuation in the whole-solute matrix of HEAs provides abundant sites with lower potential energy, which become the traps of atoms and cause higher normalized activation energies and lower diffusion rate.

摘 要 i
Abstract iii
誌 謝 v
Contents viii
List of Figures xii
List of Tables xvi
Chapter 1 Introduction 1
Chapter 2 Background: High-entropy alloys 5
2.1 Alloy concept 5
2.2 Definition of high-entropy alloy 6
2.3 Multi-principal-element effect 12
2.3.1 High entropy effect 12
2.3.1 Lattice distortion effect 14
2.3.2 Sluggish diffusion effect 18
2.3.3 Cocktail effect 20
Chapter 3 Formation Rules of Solid Solution Phases in High-Entropy Alloys 21
Abstract 21
3.1 Introduction 22
3.2 Theoretical background 25
3.2.1 Mixing enthalpy for binary alloys: Miedema’s model 25
3.2.2 Mixing enthalpy for multicomponent alloys 28
3.2.3 Mixing entropy 30
3.2.4 Prediction of phases formed in HEAs 30
3.3 Analysis methods 40
3.3.1 Thermodynamic parameter 40
3.3.2 Topological parameter 49
3.3.3 Classification of constituent phases of HEAs 51
3.4 Results and discussion 57
3.4.1 Statistic distribution analysis 57
3.4.2 Effect of the thermodynamic parameter on phase formation 79
3.4.3 Effect of the topological parameter on phase formation 80
3.4.4 Advantages of our modifications for prediction of solid solution formation 84
3.4.4.1 Using absolute values of binary mixing enthalpies 84
3.4.4.2 Using solid state for calculation and correct phase classification 87
3.4.5 Other factors controlling the phase formation 88
3.5 Summary 92
Chapter 4 Sluggish Diffusion in Co-Cr-Fe-Mn-Ni High-Entropy Alloys 95
Abstract 95
4.1 Introduction 96
4.2 Theory of diffusion 99
4.2.1 Fick’s laws 99
4.2.2 Inverse method 100
4.2.2.1 Boltzmann-Matano method 100
4.2.2.2 Sauer-Freise method 103
4.2.3 Multicomponent diffusion 103
4.2.4 Interdiffusion and intrinsic diffusion 105
4.2.5 Tracer diffusion 107
4.3 Determination of diffusion coefficients in HEA 108
4.4 Experimental procedure 113
4.4.1 Alloys design 113
4.4.2 Assembly and diffusion annealing of the diffusion couples 115
4.4.3 Analysis of concentration profiles 117
4.5 Results 118
4.5.1 Concentration profiles and diffusion coefficients 118
4.5.2 Activation energies and pre-exponential factors 124
4.6 Discussion 132
4.6.1 Quasichemical model for atomic migration 132
4.6.2 Calculation of single-bond interaction energy 135
4.6.3 Probability distributions of SBIE 139
4.6.4 Change of SBIE during atomic migration and its effect to diffusion kinetics 144
4.6.5 Other possible effect to diffusion kinetics 148
4.7 Summary 149
Chapter 5 Conclusions 151
Appendix Examples of alloy identification and classification 155
References 161

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