High-entropy alloys: a critical assessment of their founding principles and future prospects

High-entropy alloys (HEAs) are a relatively new class of materials that have gained considerable attention from the metallurgical research community over recent years. They are characterised by their unconventional compositions, in that they are not based around a single major component, but rather comprise multiple principal alloying elements. Four core effects have been proposed in HEAs: (1) the entropic stabilisation of solid solutions, (2) the severe distortion of their lattices, (3) sluggish diffusion kinetics and (4) that properties are derived from a cocktail effect. By assessing these claims on the basis of existing experimental evidence in the literature, as well as classical metallurgical understanding, it is concluded that the significance of these effects may not be as great as initially believed. The effect of entropic stabilisation does not appear to be overarching, insufficient evidence exists to establish the strain in the lattices of HEAs, and rapid precipitation observed in some HEAs suggests their diffusion kinetics are not necessarily anomalously slow in comparison to conventional alloys. The meaning and influence of the cocktail effect is also a matter for debate. Nevertheless, it is clear that HEAs represent a stimulating opportunity for the metallurgical research community. The complex nature of their compositions means that the discovery of alloys with unusual and attractive properties is inevitable. It is suggested that future activity regarding these alloys seeks to establish the nature of their physical metallurgy, and develop them for practical applications. Their use as structural materials is one of the most promising and exciting opportunities. To realise this ambition, methods to rapidly predict phase equilibria and select suitable HEA compositions are needed, and this constitutes a significant challenge. However, while this obstacle might be considerable, the rewards associated with its conquest are even more substantial. Similarly, the challenges associated with comprehending the behaviour of alloys with complex compositions are great, but the potential to enhance our fundamental metallurgical understanding is more remarkable. Consequently, HEAs represent one of the most stimulating and promising research fields in materials science at present.One of the authors (NGJ) would like to acknowledge the EPSRC/Rolls-Royce Strategic Partnership for funding under EP/M005607/1

컴플렉스 고용 합금의 특성 맞춤형 합금 설계법 개발

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 재료공학부, 2018. 2. 박은수.Complex concentrated alloys (CCAsCCAs that have more than four elements are also referred to as high entropy alloys) are a new alloy development philosophy in which the base alloy has a significant fraction of multiple principal elements. CCAs have attracted worldwide attention as strong candidates to solve problems owing to their useful performances, such as superior mechanical properties at all temperature ranges and good irradiation resistance. Much of the interest in CCAs stems from the belief that the atomic-level complexity, which originates from the large number of principal elements would provide profound effects, such as the lattice distortion effect, the sluggish diffusion effect, the irradiation resistance, and the solid-solution strengthening. However, the correlation between the complexity and the resultant properties has not yet been thoroughly understood. As a result, the advantage of so many degrees of freedom for alloy design of CCAs is diminished by a lack of mixing rules, rendering alloy design an empirical try-and-error undertaking. Therefore, to make a useful guide for the new CCA designs, a simple parameter is required to reflect the atomic environments of CCAs in a physically meaningful way so that they can be directly related to properties. In CCAs, all constituent elements are solute and solvent, and every element interacts with the stress field of dislocations, thereby increasing or decreasing the elastic strain energy of the system and resulting in solid-solution strengthening. Thus, the solid-solution strengthening effect is one of the representative phenomena that reflect atomic-level complexity in CCAs, which can also be related to macroscopic mechanical and functional properties influenced by the complexity. In this thesis, the relationship between atomic-level complexity and its influence on properties, in particular solid-solution strengthening, is investigated. CCAs with face-centered cubic (FCC) phase consisting of late 3d transition metal elements (i.e., V, Cr, Mn, Fe, Co, and Ni) are mainly discussed (Here we call them 3d CCAs). These alloys have been considered to have outstanding mechanical properties, and some commercial alloys, such as austenitic steels and γ matrix of a superalloy, belong to this group, which implies a high possibility of new commercial alloys. First, we analyzed the local atomic structure of 3d CCAs by X-ray Diffraction (XRD) and Extended X-ray Absorption Fine Structure (EXAFS) to measure the elemental average atomic sizes of consisting elements. From the obtained structural information, we predicted the solid-solution strengths by applying the atomic size difference among the constituting elements to the existing model on the basis of elasticity theory. However, the predicted solid-solution strengths do not match well with the experimentally measured values. In order to interpret this mismatch, we calculated the atomic structure using density function theory (DFT) and found that the fluctuation of bond lengths due to the dissimilar local atomic configurations, which is usually ignored for dilute alloys, has a significant impact on the solid-solution strengthening of CCAs, which introduces higher degree of complexity problem in CCAs. As a second approach, we calculated the atomic-level pressure of each element in 3d CCAs, which is the cause of solid-solution strengthening, using DFT calculation. We found that the atomic-level pressure of individual atoms originates from the charge transfer between a center atom and its surrounding atoms. This was also confirmed with an experimental study by measuring volume strain of each element in 3d CCAs using EXAFS and plotting with charge transfer. This means that the atomic-level pressure in 3d CCAs is attributed to the electronic effect rather than the elastic interaction of constituent elements. In order to utilize this concept for an alloy design strategy, we tried descending the degree of complexities in 3d CCAs. Through a statistical approach, we found that both values of deviation of average elemental atomic-level pressure and deviation of atomic-level pressure due to the variance in local atomic configurations are linearly proportional to each other. This makes it possible to estimate a higher degree complexity (configurational deviations) using a lower degree complexity (elemental deviations), which can be identified experimentally. As a result, we were able to theoretically explain the proportional relationship between electronegativity difference and solid-solution strengths in the 3d CCAs. Based on the aforementioned discussion, we constructed an electronegativity-mixing entropy diagram that shows the relationship between chemical complexity and complexity induced by deviation of atomic-level pressure, i.e., solid-solution strengthening. All possible combinations of 3d transition metal elements (V, Cr, Mn, Fe, Co, Ni) are included in the diagram. The area of the 3d CCAs has inverse C-shape boundary, which means that (1) the mixing entropy does not have a strong correlation with solid-solution strengthening, and (2) there is a region where the mixing entropy should be decreased to obtain greater solid-solution strengthening effects. Thus, we concluded that there is no strong correlation between the chemical complexity and the deviation (i.e. complexity) of atomic-level pressure in 3d CCAs. One may argue that the chemical complexity is no longer important for CCAs as the complexity of atomic-level pressure are closely related to the lattice distortion effect and the sluggish diffusion effect, which are CCAs two core effects among the four. Changing the composition from the Cantor alloy, we developed twin-induced plasticity (TWIP) and transformation-induced plasticity (TRIP) CCAs by decreasing stacking fault energies while maintaining the deviation of atomic-level pressure, i.e., solid-solution strength, in order to show that there are many factors that we can manipulate besides complexity of atomic-level pressure. The change of deformation mechanisms from dislocation gliding to TWIP and TRIP increases the strain hardening rate of the CCAs, enhancing both ultimate tensile strength and the percentage of uniform elongation without loss of yield strengths. The development of these new CCAs was possible due to the freedom in manipulating composition, which implies that chemical complexity is also important for the design of new CCAs for the vastness of composition space. Additionally, we discussed asymmetry of atomic-level pressure-induced element-specific properties in CCAs. Atomic-level pressure of an element includes the information of anharmonicity of lattice potential and represents the resistance of it against displacement. As a result, element-specific properties, such as atomic displacements, diffusivity, and preferential site of interstitial elements show asymmetric behavior upon atomic-level pressure. Consequently, the deviation of atomic-level pressure dominantly affects the degree of lattice distortion, the diffusivity of substitutional elements, and the solubility of interstitial elements, which are crucial for engineering applications. Through this research, we distinguished the previous concept of complexity in CCAs into two categories: chemical complexity for the vastness of composition space and complexity of atomic-level pressure reflecting fluctuation of lattice potential energies. We believe that the tailor-made design of CCAs is possible when both complexities are investigated well for the desired elemental combinations.Chapter 1. Introduction 1 1.1. Complex concentrated alloy: a new philosophy of alloy design 1 1.2. Motivation and scope 6 1.3. Outlines for each chapter 9 Chapter 2. Core effects from the atomic-level complexity of CCAs 11 2.1. The high entropy effect 12 2.2. The lattice distortion effect 18 2.3. The sluggish diffusion effect 25 2.4. Summary 32 Chapter 3. Fundamentals of atomic-level pressure 33 3.1. Classical concept of atomic-level pressure 34 3.1.1. Eshelby inclusion problem 34 3.1.2. Solid-solution strengthening and atomic-level pressure 35 3.1.3. Solid-solution strengthening in CCAs 36 3.2. Atomic-level pressure: Energy perspective 40 3.3. Summary 43 Chapter 4. Experimental procedures 44 4.1. Sample preparation 44 4.1.1. Casting 44 4.1.2. Post processing 45 4.2. Microstructural characterization 47 4.2.1. X-ray diffraction 47 4.2.2. Extended X-ray Absorption Fine Structure 47 4.2.3. Scanning Electron Microscopy 48 4.2.4. Atom probe tomography 49 4.3. Mechanical analysis 53 4.3.1. Tensile test 53 4.3.2. Digital image correlation 53 4.4. Density functional theory calculation 56 Chapter 5. Failure of structural analysis on the solid-solution strengthening of 3d CCAs 57 5.1. Solid-solution strength of 3d CCAs 59 5.2. Structural analysis by XRD and EXAFS 62 5.2.1. Sample preparation 62 5.2.2. Measurement of misfit parameter by XRD 63 5.2.3. Measurement of misfit strain by EXAFS 68 5.3. DFT Simulation for local atomic structure 73 5.3.1. Homogeneity of CrMnFeCoNi CCA 73 5.3.2. Comparison between DFT calculated and EXAFS measured bond length 75 5.3.3. Elemental and Configurational deviation of bond length 78 5.4. Summary 80 Chapter 6. Solid-solution strengthening of CCAs – Atomic-level pressure 81 6.1. Deviation of the atomic-level pressure and solid-solution strengthening 82 6.2. The origin of the atomic-level pressure in 3d CCAs 86 6.3. Descending degrees of complexity 89 6.4. Experimental measurement of the atomic-level pressure 92 6.4.1. Measurement of volume strain 92 6.4.2. Prediction of the solid-solution strength 96 6.5. Electronegativity diagram 98 6.6. Summary 105 Chapter 7. Design of CCAs to overcome the strength-ductility trade-off 106 7.1. Alloy design 109 7.1.1. Stacking fault energy 109 7.1.2. Solid-solution strengthening 114 7.1.3. Single-phase formation 116 7.1.4. Comprehensive design 119 7.2. Microstructure prior to the deformation 121 7.3. Mechanical properties 123 7.4. Microstructural analysis 126 7.5. Summary 132 Chapter 8. Asymmetry of the atomic-level pressure-induced element-specific properties in CCAs 133 8.1. Asymmetry of the lattice distortion and atomic-level pressure 134 8.2. Diffusivity of substitutional elements and the atomic-level pressure 142 8.3. Preferential site of interstitial solute elements and atomic-level pressure 145 8.4. Summary 148 Chapter 9. Conclusions and outlook 149Docto

Hybrid molecular dynamic Monte Carlo simulation and experimental production of a multi-component Cu-Fe-Ni-Mo-W alloy

ABSTRACT: High-entropy alloys are a class of materials intensely studied in the last years due to their innovative properties. Their unconventional compositions and chemical structures hold promise for achieving unprecedented combinations of mechanical properties. The Cu-Fe-Ni-Mo-W multicomponent alloy was studied using a combination of simulation and experimental production to test the possibility of formation of a simple solid solution. Therefore, Molecular Dynamics and hybrid Molecular Dynamic/Monte Carlo simulations from 10K up to the melting point of the alloy were analyzed together with the experimental production by arc furnace and powder milling. The Molecular Dynamics simulations starting with a bcc type-structure show the formation of a singlephase bcc solid solution type-structure, whereas using Monte Carlo one, generally produced a two-phase mixture. Moreover, the lowest potential energy was obtained when starting from a fcc type-structure and using Monte Carlo simulation giving rise to the formation of a bcc Fe-Mo-W phase and a Cu-Ni fcc type-structure. Dendritic and interdendritic phases were observed in the sample produced by arc furnace while the milled powder evidence an separation of two phases Cu-Fe-Ni phase and W-Mo type-structures. Samples produced by both methods show the formation of bcc and a fcc type-structures. Therefore, the Monte Carlo simulation seems to be closer with the experimental results, which points to a two-phase mixture formation for the Cu-Fe-Ni-Mo-W multicomponent system.info:eu-repo/semantics/publishedVersio

Re-melting behaviour and wear resistance of vanadium carbide precipitating Cr27.5Co14Fe22Mo22Ni11.65V2.85 high entropy alloy

High entropy alloys (HEAs) are among of the most promising new metal material groups. The achievable properties can exceed those of common alloys in different ways. Due to the mixture of five or more alloying elements, the variety of high entropy alloys is fairly huge. The presented work will focus on some first insights on the weldability and the wear behavior of vanadium carbide precipitation Cr27.5Co14Fe22Mo22Ni11.65V2.85 HEA. The weldability should always be addressed in an early stage of any alloy design to avoid welding-related problems afterwards. The cast Cr27.5Co14Fe22Mo22Ni11.65V2.85 HEA has been remelted using a TIG welding process and the resulting microstructure has been examined. The changes in the microstructure due to the remelting process showed little influence of the welding process and no welding-related problems like hot cracks have been observed. It will be shown that vanadium carbides or vanadium-rich phases precipitate after casting and remelting in a two phased HEA matrix. The hardness of the as cast alloy is 324HV0.2 and after remelting the hardness rises to 339HV0.2. The wear behavior can be considered as comparable to a Stellite 6 cobalt base alloy as determined in an ASTM G75 test. Overall, the basic HEA design is promising due to the precipitation of vanadium carbides and should be further investigated

A ductility metric for refractory-based multi-principal-element alloys

We propose a quantum-mechanical dimensionless metric, the local$-$lattice distortion (LLD), as a reliable predictor of ductility in refractory multi-principal-element alloys (RMPEAs). The LLD metric is based on electronegativity differences in localized chemical environments and combines atomic$-$scale displacements due to local lattice distortions with a weighted average of valence$-$electron count. To evaluate the effectiveness of this metric, we examined body$-$centered cubic (bcc) refractory alloys that exhibit ductile$-$to$-$brittle behavior. Our findings demonstrate that local$-$charge behavior can be tuned via composition to enhance ductility in RMPEAs. With finite$-$sized cell effects eliminated, the LLD metric accurately predicted the ductility of arbitrary alloys based on tensile$-$elongation experiments. To validate further, we qualitatively evaluated the ductility of two refractory RMPEAs, i.e., NbTaMoW and Mo$_{72}$W$_{13}Ta$_{10}Ti$_{2.5}Zr$_{2.5}, through the observation of crack formation under indentation, again showing excellent agreement with LLD predictions. A comparative study of three refractory alloys provides further insights into the electronic-structure origin of ductility in refractory RMPEAs. This proposed metric enables rapid and accurate assessment of ductility behavior in the vast RMPEA composition space.Comment: 36 pages, 12 figures, 5 Tabl

Radioactive isotopes reveal a non sluggish kinetics of grain boundary diffusion in high entropy alloys

High entropy alloys (HEAs) have emerged as a new class of multicomponent materials, which have potential for high temperature applications. Phase stability and creep deformation, two key selection criteria for high temperature materials, are predominantly influenced by the diffusion of constituent elements along the grain boundaries (GBs). For the first time, GB diffusion of Ni in chemically homogeneous CoCrFeNi and CoCrFeMnNi HEAs is measured by radiotracer analysis using the $^{63}$Ni isotope. Atom probe tomography confirmed the absence of elemental segregation at GBs that allowed reliable estimation of the GB width to be about 0.5 nm. Our GB diffusion measurements prove that a mere increase in number of constituent elements does not lower the diffusion rates in HEAs, but the nature of added constituents plays a more decisive role. The GB energies in both HEAs are estimated at about 0.8-0.9 J/m$^2$, they are found to increase significantly with temperature and the effect is more pronounced for the CoCrFeMnNi alloy.Comment: 11 pages, 9 figure

On Lattice Distortion in High Entropy Alloys

Lattice distortion in high entropy alloys (HEAs) is an issue of fundamental importance but yet to be fully understood. In this article, we first focus on the recent research dedicated to lattice distortion in HEAs with an emphasis on the basic understanding derived from theoretical modeling and atomistic simulations. After that, we discuss the implications of the recent research findings on lattice distortion, which can be related to the phase transformation, dislocation dynamics and yielding in HEAs

The Role of Grain Boundaries in the Tensile Deformation Behavior of CoCrFeMnNi High Entropy Alloys

High Entropy alloys (HEAs) are metal alloys consisting of multiple base metals in equimolar or near equimolar concentrations. HEAs exhibit unique combinations of properties that render them an attractive choice in many engineering applications. Among HEAs, a single phase face centered cubic (FCC) CoCrFeMnNi alloy, known as the Cantor alloy, shows simultaneous strength and ductility specifically at cryogenic temperatures. This has been attributed to the activation of deformation twinning as an additional mode of plastic deformation. Experimentally it has been observed that grain boundaries (GBs) facilitate the nucleation of deformation twins in HEAs. However, the role of GB geometry in the deformation behavior of HEAs remains unexplored. In this thesis work, we leverage atomistic simulations to systematically investigate the role of GB geometry in the deformation behavior of the Cantor alloy at 77 K. To this end, a series of Cantor alloy bicrystals with \u3c110\u3e and \u3c111\u3e symmetric twist GBs are constructed and used in tensile deformation simulations. Simulation results reveal that plastic deformation proceeds by the nucleation of partial dislocations from GBs, which then grow with further loading by bowing into the bulk crystals leaving behind stacking faults. Variations in the nucleation stress exist as function of GB character, defined in this work by the twist angle. Our results provide future avenues to explore GBs as a microstructure design tool to develop HEAs with tailored mechanical properties