High entropy alloys

Atomic structure model of fcc CoCrFeMnNi[1]

High-entropy alloys (HEAs) are alloys that are formed by mixing equal or relatively large proportions of (usually) five or more elements. Prior to the synthesis of these substances, typical metal alloys comprised one or two major components with smaller amounts of other elements. For example, additional elements can be added to iron to improve its properties, thereby creating an iron based alloy, but typically in fairly low proportions, such as the proportions of carbon, manganese, and the like in various steels.[2] Hence, high entropy alloys are a novel class of materials.[1][2] The term “high-entropy alloys” was coined because the entropy increase of mixing is substantially higher when there is a larger number of elements in the mix, and their proportions are more nearly equal.[3]

These alloys are currently the focus of significant attention in materials science and engineering because they have potentially desirable properties.[2] Furthermore, research indicates that some HEAs have considerably better strength-to-weight ratios, with a higher degree of fracture resistance, tensile strength, as well as corrosion and oxidation resistance than conventional alloys. Although HEAs have been studied since the 1980s, research substantially accelerated in the 2010s.[2][4][5][6][7][8]

## Contents

* 1 Early development
* 2 Definition
* 3 Alloy design
* 3.1 Phase formation
* 3.2 Thermodynamic mechanisms
* 3.3 Kinetic mechanisms
* 3.4 Other properties
* 4 Synthesis
* 5 Modeling and simulation
* 6 Phase Diagram Generation
* 7 Properties and potential uses
* 7.1 Mechanical
* 7.2 Electrical and magnetic
* 7.3 Other
* 8 See also
* 9 References

## Early development

Although HEAs were considered from a theoretical standpoint as early as 1981[9] and 1996,[10] and throughout the 1980s, in 1995 Jien-Wei Yeh came up with his idea for ways of actually creating high-entropy alloys in 1995, while driving through the Hsinchu, Taiwan, countryside. Soon after he decided to begin creating these special metal alloys in his lab. With Taiwan being the only region researching these alloys for over a decade, most other countries in Europe, the United States and other parts of the world lagged behind in the development of HEAs. Significant research interest from other countries did not develop until after 2004 when Jien-Wei Yeh and his team of Taiwanese scientists invented and built the world's first high-entropy alloys that can withstand extremely high temperatures and pressures. Potential applications include use in state-of-the-art race cars, spacecraft, submarines, nuclear reactors, jet aircraft, nuclear weapons, long range hypersonic missiles and so on.[11][12]

A few months later, after the publication of Jien-Wei Yeh's paper, another independent paper on high entropy alloys was published by another team from the United Kingdom composed of Brian Cantor, I. T. H. Chang, P. Knight and A. J. B. Vincent. Yeh was also the first to coin the term "high-entropy alloy" when he attributed the high configurational entropy as the mechanism stabilizing the solid solution phase.[13] Cantor did the first work in the field in the late 1970s and early 1980s, though he did not publish until 2004. Not knowing of Yeh's work, he did not describe his new materials as "high-entropy" alloys, preferring the term "multicomponent alloys". The base alloy he developed, equiatomic FeCrMnNiCo, has been the subject of considerable work in the field, and is known as the "Cantor alloy", with similar derivatives known as Cantor alloys.[14]

Before the classification of high entropy alloys and multi-component systems as a separate class of materials, nuclear scientists had already studied a system that can now be classified as a high entropy alloy: within nuclear fuels Mo-Pd-Rh-Ru-Tc particles form at grain boundaries and at fission gas bubbles.[15] Understanding the behavior of these '5 metal particles' was of specific interest to the medical industry as Tc-99m is an important medical imaging isotope.

## Definition

There is no universally agreed-upon definition of a HEA. The originally defined HEAs as alloys containing at least 5 elements with concentrations between 5 and 35 atomic percent.[13] Later research however, suggested that this definition could be expanded. Otto et al. suggested that only alloys that form a solid solution with no intermetallic phases should be considered true high-entropy alloys, as the formation of ordered phases decreases the entropy of the system.[16] Some authors have described 4-component alloys as high-entropy alloys[17] while others have suggested that alloys meeting the other requirements of HEAs, but with only 2–4 elements[18] or a mixing entropy between R and 1.5R[19] should be considered "medium-entropy" alloys.[18]

## Alloy design

In conventional alloy design, one primary element such as iron, copper, or aluminum is chosen for its properties. Then, small amounts of additional elements are added to improve or add properties. Even among binary alloy systems, there are few common cases of both elements being used in nearly-equal proportions such as Pb-Sn solders. Therefore, much is known from experimental results about phases near the edges of binary phase diagrams and the corners of ternary phase diagrams and much less is known about phases near the centers. In higher-order (4+ components) systems that cannot be easily represented on a 2-dimensional phase diagram, virtually nothing is known.[14]

### Phase formation

Gibbs' phase rule, F=C−P+2, can be used to determine an upper bound on the number of phases that will form in an equilibrium system. In his 2004 paper, Cantor created a 20-component alloy containing 5 at% of Mn, Cr, Fe, Co, Ni, Cu, Ag, W, Mo, Nb, Al, Cd, Sn, Pb, Bi, Zn, Ge, Si, Sb, and Mg. At constant pressure, the phase rule would allow for up to 21 phases at equilibrium, but far fewer actually formed. The predominant phase was a face-centered cubic solid solution phase, containing mainly Fe, Ni, Cr, Co, and Mn. From that result, the FeCrMnNiCo alloy, which forms only a solid solution phase, was developed.[14]

The Hume-Rothery rules have historically been applied to determine whether a mixture will form a solid solution. Research into high-entropy alloys has found that in multi-component systems, these rules tend to be relaxed slightly. In particular, the rule that solvent and solute elements must have the same crystal structure does not seem to apply, as Fe, Ni, Cr, Co, and Mn have 4 different crystal structures as pure elements (and when the elements are present in equal concentrations, there can be no meaningful distinction between "solvent" and "solute" elements).[16]

### Thermodynamic mechanisms

Phase formation of HEA is determined by thermodynamics and geometry. When phase formation is controlled by thermodynamics and kinetics are ignored. ΔGmix (Gibbs free energy of mixing) is defined as:

ΔGmix = ΔHmix - TΔSmix

Where Hmix is defined as enthalpy of mixing, T is temperature and Smix is entropy of mixing respectively. ΔHmix and TΔSmix continuously competing to determine the phase of the HEA material. Another factor that needs to be considered include atomic size of each individual element within the HEA where Hume – Rothery Rule and Inoue's three empirical rules for bulk metallic glass plays a role.

Disordered solid were form when atomic size different is small and ΔHmix is not negative enough. This is due to each atom is around the same size where it can easily substitute one another and ΔHmix is not low enough to form a compound. The more ordered HEAs are formed as the size difference between each element gets larger and ΔHmix to be more negative. When the size different of each individual element become to large, bulk metallic glasses would form instead of HEAs. High temperature and high ΔSmix would also promote the formation of HEA since it significantly lower ΔGmix, making the HEA easier to form since it is more stable than other phases such as intermetallic.[20]

The multi-component alloys Yeh developed also consisted mostly or entirely of solid solution phases, contrary to what had been expected from earlier work in multi-component systems, primarily in the field of metallic glasses.[13][21] Yeh attributed this result to the high configurational, or mixing, entropy of a random solid solution containing numerous elements. The mixing entropy for a random ideal solid solution can be calculated by:

ΔSmix=−R∑i=1Nciln⁡ci

where R is the ideal gas constant, N is the number of components, and ci is the atomic fraction of component i. From this it can be seen that alloys in which the components are present in equal proportions will have the highest entropy, and adding additional elements will increase the entropy. A 5 component, equiatomic alloy will have a mixing entropy of 1.61R.[13][22]

Parameter  | Design guideline

|

∆Smix | Maximized
∆Hmix | > -10 and < 5 kJ/mol
Ω  | ≥ 1.1
δ  | ≤ 6.6%
VEC  | ≥ 8 for fcc, <6.87 for bcc
Empirical parameters and design guidelines for forming solid solution HEAs

However, entropy alone is not sufficient to stabilize the solid solution phase in every system. The enthalpy of mixing (ΔH), must also be taken into account. This can be calculated using:

ΔHmix=∑i=1,i≠jN4ΔHABmixcicj

where ΔHABmix is the binary enthalpy of mixing for A and B.[23] Zhang et al. found, empirically, that in order to form a complete solid solution, ΔHmix should be between -10 and 5 kJ/mol.[22] In addition, Otto et al. found that if the alloy contains any pair of elements that tend to form ordered compounds in their binary system, a multi-component alloy containing them is also likely to form ordered compounds.[16]

Both of the thermodynamic parameters can be combined into a single, unitless parameter Ω:

Ω=TmΔSmix|ΔHmix|

where Tm is the average melting point of the elements in the alloy. Ω should be greater than or equal to 1.1 to promote solid solution development.[24]

### Kinetic mechanisms

The atomic radii of the components must also be similar in order to form a solid solution. Zhang et al. proposed a parameter δ representing the difference in atomic radii:

δ=∑i=1Nci(1−rir¯)2

where ri is the atomic radius of element i and r¯=∑i=1Nciri. Formation of a solid solution phase requires a δ≤6.6%, but some alloys with 4%<δ≤6.6% do form intermetallics.[22][24]

### Other properties

For those alloys that do form solid solutions, an additional empirical parameter has been proposed to predict the crystal structure that will form. HEAs are usually FCC, BCC, HCP, or a mixture of the above structure, and each structure have their own advantages and disadvantages in terms of mechanical properties. There are many methods to predict the structure of HEA. Valence electron concentration (VEC) can be used to predict the stability of the HEA structure. The stability of physical properties of the HEA is closely associated with electron concentration (this is associated with the electron concentration rule from the Hume – Rothery rules).

When HEA is made with casting, only FCC structures are formed when VEC is larger than 8. When VEC is between 6.87 and 8, HEA is a mixture of BCC and FCC, and while VEC is below 6.87, the material is BCC. In order to produce certain crystal structure of HEA, certain phase stabilizing elements can be added. Experimentally, adding elements such as Al and Cr and help the formation of BCC HEA while Ni and Co can help forming FCC HEA.[20]

## Synthesis

High-entropy alloys are difficult to manufacture using extant techniques as of 2018[update], and typically require both expensive materials and specialty processing techniques.[25]

High-entropy alloys are mostly produced using methods that depend on the metals phase - if the metals are combined while in a liquid, solid, or gas state.

* Most HEAs have been produced using liquid-phase methods include arc melting, induction melting, and Bridgman solidification.[24]
* Solid-state processing is generally done by mechanical alloying using a high-energy ball mill. This method produces powders that can then be processed using conventional powder metallurgy methods or spark plasma sintering. This method allows for alloys to be produced that would be difficult or impossible to produce using casting, such as AlLiMgScTi.[24][6][26]
* Gas-phase processing includes processes such as sputtering or molecular beam epitaxy (MBE), which can be used to carefully control different elemental compositions to get high-entropy metallic[27] or ceramic films.[24]

Other HEAs have been produced by thermal spray, laser cladding, and electrodeposition.[24][28]

## Modeling and simulation

The atomic-scale complexity presents additional challenges to computational modelling of high-entropy alloys. Thermodynamic modeling using the CALPHAD method requires extrapolating from binary and ternary systems.[29] Most commercial thermodynamic databases are designed for, and may only be valid for, alloys consisting primarily of a single element. Thus, they require experimental verification or additional ab initio calculations such as density functional theory (DFT).[30] However, DFT modeling of complex, random alloys has its own challenges, as the method requires defining a fixed-size cell, which can introduce non-random periodicity. This is commonly overcome using the method of "special quasirandom structures," designed to most closely approximate the radial distribution function of a random system,[31] combined with the Vienna Ab-initio Simulation Package. Using this method, it has been shown that results of a 4-component equiatomic alloy begins to converge with a cell as small as 24 atoms.[32][33] The exact muffin-tin orbital method with the coherent potential approximation has also been employed to model HEAs.[32][34] Other techniques include the 'multiple randomly populated supercell' approach, which better describes the random population of a true solid solution (although is far more computationally demanding).[35] This method has also been used to model glassy/amorphous (including bulk metallic glasses) systems without a crystal lattice.[36][37]

Further, modeling techniques are being used to suggest new HEAs for targeted applications. The use of modeling techniques in this 'combinatorial explosion' is necessary for targeted and rapid HEA discovery and application.

Simulations have highlighted the preference for local ordering in some high entropy alloys and, when the enthalpies of formation are combined with terms for configurational entropy, transition temperatures between order and disorder can be estimated.[38] \- allowing one to understand when effects like age hardening and degradation of an alloy's mechanical properties may be an issue.

The transition temperature to reach the solid solution (miscibility gap) was recently addressed with the Lederer-Toher-Vecchio-Curtarolo thermodynamic model.[39]

## Phase Diagram Generation

CALPHAD (calculation of phase diagrams) method with reliable thermodynamic data base can be an effective tool when searching for single phase HEAs. However, this method can be limited since it needs to extrapolate from known binary of ternary phase diagram, this method also does not take account into the process of material synthesis. Also this method can only predict equilibrium phases.[40] The phase diagram of HEA can be explored experimentally via High throughput experimentation (HTE). This method rapidity producing hundreds of samples allowing the researcher to explore a region of composition in one step thus can used to quickly map out the phase diagram of the HEA.[41] Another way to predict the phase of the HEA is via enthalpy concentration. This method take account for specific combination of single phase HEA and reject similar combination that have been tried show not to be single phase.  This model uses first principle high throughput density functional theory to calculation the enthalpies. Thus required no experiment input, and it has shown excelled agreement with reported experimental result.[42]

## Properties and potential uses

### Mechanical

The crystal structure of HEAs has been found to be the dominant factor in determining the mechanical properties. bcc HEAs typically have high yield strength and low ductility and vice versa for fcc HEAs. Some alloys have been particularly noted for their exceptional mechanical properties. A refractory alloy, VNbMoTaW maintains a high yield strength (>600 MPa (87 ksi)) even at a temperature of 1,400 °C (2,550 °F), significantly outperforming conventional superalloys such as Inconel 718\. However, room temperature ductility is poor, less is known about other important high temperature properties such as creep resistance, and the density of the alloy is higher than conventional nickel-based superalloys.[24]

CoCrFeMnNi has been found to have exceptional low-temperature mechanical properties and high fracture toughness, with both ductility and yield strength increasing as the test temperature was reduced from room temperature to 77 K (−321.1 °F). This was attributed to the onset of nanoscale twin boundary formation, an additional deformation mechanism that was not in effect at higher temperatures. At ultralow temperatures, inhomogenous deformation by serrations has been reported.[43] As such, it may have applications as a structural material in low-temperature applications or, because of its high toughness, as an energy-absorbing material.[44] However, later research showed that lower-entropy alloys with fewer elements or non-equiatomic compositions may have higher strength[45] or higher toughness.[46] No ductile to brittle transition was observed in the bcc AlCoCrFeNi alloy in tests as low as 77 K.[24]

Al0.5CoCrCuFeNi was found to have a high fatigue life and endurance limit, possibly exceeding some conventional steel and titanium alloys. But there was significant variability in the results, suggesting the material is very sensitive to defects introduced during manufacturing such as aluminum oxide particles and microcracks.[47]

A single-phase nanocrystalline Al20Li20Mg10Sc20Ti30 alloy was developed with a density of 2.67 g cm−3 and microhardness of 4.9 – 5.8 GPa, which would give it an estimated strength-to-weight ratio comparable to ceramic materials such as silicon carbide,[6] though the high cost of scandium limits the possible uses.[48]

Rather than bulk HEAs, small-scale HEA samples (e.g. NbTaMoW micro-pillars) exhibit extraordinarily high yield strengths of 4-10 GPa —one order of magnitude higher than that of its bulk form—and their ductility is considerably improved. Additionally, such HEA films show substantially enhanced stability for high-temperature, long-duration conditions (at 1,100 °C for 3 days). Small-scale HEAs combining these properties represent a new class of materials in small-dimension devices potentially for high-stress and high-temperature applications.[27][17]

In 2018, new types of HEAs based on the careful placement of ordered oxygen complexes, a type of ordered interstitial complexes, have been produced. In particular, alloys of titanium, halfnium, and zirconium have been shown to have enhanced work hardening and ductility characteristics.[49]

Bala et al. studied the effects of high-temperature exposure on the microstructure and mechanical properties of the Al5Ti5Co35Ni35Fe20 high-entropy alloy. After hot rolling and air-quenching, the alloy was exposed to a temperature range of 650-900 °C for 7 days. The air-quenching caused γ′ precipitation distributed uniformly throughout the microstructure. The high-temperature exposure resulted in growth of the γ′ particles and at temperatures higher than 700 °C, additional precipitation of γ′ was observed. The highest mechanical properties were obtained after exposure to 650 °C with a yield strength of 1050 MPa and an ultimate tensile yield strength of 1370 MPa. Increasing the temperature further decreased the mechanical properties.[50]

Liu et al. studied a series of quaternary non-equimolar high-entropy alloys AlxCo15Cr15Ni70-x with x ranging from 0 to 35%. The lattice structure transitioned from FCC to BCC as Al content increased and with Al content in the range of 12.5 to 19.3 at%, the γ′ phase formed and strengthened the alloy at both room and elevated temperatures. With Al content at 19.3 at%, a lamellar eutectic structure formed composed of γ′ and B2 phases. Due to high γ′ phase fraction of 70 vol%, the alloy had a compressive yield strength of 925 MPa and fracture strain of 29% at room temperature and high yield strength at high temperatures as well with values of 789, 546, and 129 MPa at the temperatures of 973, 1123, and 1273K.[51]

In general, refractory high-entropy alloys have exceptional strength at elevated temperatures but are brittle at room temperature. The HfNbTaTiZr alloy is an exception with plasticity of over 50% at room temperature. However, its strength at high temperature is insufficient. With the aim of increasing high temperature strength Chien-Chuang et al. modified the composition of HfNbTaTiZr, and studied the mechanical properties of the refractory high-entropy alloys: HfMoTaTiZr and HfMoNbTaTiZr. Both alloys have simple BCC structure. Their experiments showed that the yield strength of HfMoNbTaTiZr had a yield strength 6 times greater than HfNbTaTiZr at 1200 °C with a fracture strain of 12% retained in the alloy at room temperature.[52]

### Electrical and magnetic

CoCrCuFeNi is an fcc alloy that was found to be paramagnetic. But upon adding titanium, it forms a complex microstructure consisting of fcc solid solution, amorphous regions and nanoparticles of Laves phase, resulting in superparamagnetic behavior.[53] High magnetic coercivity has been measured in a BiFeCoNiMn alloy.[28] Superconductivity was observed in TaNbHfZrTi alloys, with transition temperatures between 5.0 and 7.3 K.[54]

### Other

The high concentrations of multiple elements leads to slow diffusion. The activation energy for diffusion was found to be higher for several elements in CoCrFeMnNi than in pure metals and stainless steels, leading to lower diffusion coefficients.[55] Some equiatomic multicomponent alloys have also been reported to show good resistance to damage by energetic radiation.[56] High entropy alloys are investigated for hydrogen storage applications.[57][58]

## See also

* Amorphous metal
* Nanocrystalline material
* Hume-Rothery rules

## References

1. ↑ 1.0 1.1 Wang, Shaoqing (13 December 2013). "Atomic Structure Modeling of Multi-Principal-Element Alloys by the Principle of Maximum Entropy". Entropy 15 (12): 5536–5548. doi:10.3390/e15125536. Bibcode: 2013Entrp..15.5536W.
2. ↑ 2.0 2.1 2.2 2.3 Tsai, Ming-Hung; Yeh, Jien-Wei (30 April 2014). "High-Entropy Alloys: A Critical Review". Materials Research Letters 2 (3): 107–123. doi:10.1080/21663831.2014.912690.
3. ↑ Ye, Y.F.; Wang, Q.; Lu, J.; Liu, C.T.; Yang, Y. (July 2016). "High-entropy alloy: challenges and prospects". Materials Today 19 (6): 349–362. doi:10.1016/j.mattod.2015.11.026.
4. ↑ Lavine, M. S. (4 September 2014). "A metal alloy that is stronger when cold". Science 345 (6201): 1131. doi:10.1126/science.345.6201.1131-b. Bibcode: 2014Sci...345Q1131L.
5. ↑ Shipman, Matt (December 10, 2014). "New 'high-entropy' alloy is as light as aluminum, as strong as titanium alloys". Phys.org. http://phys.org/news/2014-12-high-entropy-alloy-aluminum-strong-titanium.html.
6. ↑ 6.0 6.1 6.2 Youssef, Khaled M.; Zaddach, Alexander J.; Niu, Changning; Irving, Douglas L.; Koch, Carl C. (9 December 2014). "A Novel Low-Density, High-Hardness, High-entropy Alloy with Close-packed Single-phase Nanocrystalline Structures". Materials Research Letters 3 (2): 95–99. doi:10.1080/21663831.2014.985855.
7. ↑ Yarris, Lynn (4 September 2014). "A Metallic Alloy That is Tough and Ductile at Cryogenic Temperatures". News Center. https://newscenter.lbl.gov/2014/09/04/a-metallic-alloy-that-is-tough-and-ductile-at-cryogenic-temperatures/.
8. ↑ Gludovatz, B.; Hohenwarter, A.; Catoor, D.; Chang, E. H.; George, E. P.; Ritchie, R. O. (4 September 2014). "A fracture-resistant high-entropy alloy for cryogenic applications". Science 345 (6201): 1153–1158. doi:10.1126/science.1254581. PMID 25190791. Bibcode: 2014Sci...345.1153G. https://zenodo.org/record/1230932.
9. ↑ Vincent AJB; Cantor B: part II thesis, University of Sussex (1981).
10. ↑ Huang KH, Yeh JW. A study on multicomponent alloy systems containing equal-mole elements [M.S. thesis]. Hsinchu: National Tsing Hua University; 1996.
11. ↑ Wei-han, Chen (10 June 2016). "Taiwanese researcher gets special 'Nature' coverage - Taipei Times". The Taipei Times. http://www.taipeitimes.com/News/taiwan/archives/2016/06/10/2003648301.
12. ↑ Yeh, Jien Wei; Chen, Yu Liang; Lin, Su Jien; Chen, Swe Kai (November 2007). "High-Entropy Alloys – A New Era of Exploitation". Materials Science Forum 560: 1–9. doi:10.4028/www.scientific.net/MSF.560.1.
13. ↑ 13.0 13.1 13.2 13.3 Yeh, J.-W.; Chen, S.-K.; Lin, S.-J.; Gan, J.-Y.; Chin, T.-S.; Shun, T.-T.; Tsau, C.-H.; Chang, S.-Y. (May 2004). "Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes". Advanced Engineering Materials 6 (5): 299–303. doi:10.1002/adem.200300567.
14. ↑ 14.0 14.1 14.2 Cantor, B.; Chang, I.T.H.; Knight, P.; Vincent, A.J.B. (July 2004). "Microstructural development in equiatomic multicomponent alloys". Materials Science and Engineering: A 375-377: 213–218. doi:10.1016/j.msea.2003.10.257.
15. ↑ Middleburgh, S. C.; King, D. M.; Lumpkin, G. R. (April 2015). "Atomic scale modelling of hexagonal structured metallic fission product alloys". Royal Society Open Science 2 (4): 140292. doi:10.1098/rsos.140292. PMID 26064629. Bibcode: 2015RSOS....2n0292M.
16. ↑ 16.0 16.1 16.2 Otto, F.; Yang, Y.; Bei, H.; George, E.P. (April 2013). "Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys". Acta Materialia 61 (7): 2628–2638. doi:10.1016/j.actamat.2013.01.042. Bibcode: 2013AcMat..61.2628O. https://zenodo.org/record/1258678.
17. ↑ 17.0 17.1 Zou, Yu; Maiti, Soumyadipta; Steurer, Walter; Spolenak, Ralph (February 2014). "Size-dependent plasticity in an Nb25Mo25Ta25W25 refractory high-entropy alloy". Acta Materialia 65: 85–97. doi:10.1016/j.actamat.2013.11.049. Bibcode: 2014AcMat..65...85Z.
18. ↑ 18.0 18.1 Gali, A.; George, E.P. (August 2013). "Tensile properties of high- and medium-entropy alloys". Intermetallics 39: 74–78. doi:10.1016/j.intermet.2013.03.018. https://zenodo.org/record/1259071.
19. ↑ Miracle, Daniel; Miller, Jonathan; Senkov, Oleg; Woodward, Christopher; Uchic, Michael; Tiley, Jaimie (10 January 2014). "Exploration and Development of High Entropy Alloys for Structural Applications". Entropy 16 (1): 494–525. doi:10.3390/e16010494. Bibcode: 2014Entrp..16..494M.
20. ↑ 20.0 20.1 Gao, Michael C, et al., editors (2018). HIGH-ENTROPY ALLOYS: Fundamentals and Applications.. Springer. ISBN 9783319800578.
21. ↑ Greer, A. Lindsay (December 1993). "Confusion by design". Nature 366 (6453): 303–304. doi:10.1038/366303a0. Bibcode: 1993Natur.366..303G.
22. ↑ 22.0 22.1 22.2 Zhang, Y.; Zhou, Y. J.; Lin, J. P.; Chen, G. L.; Liaw, P. K. (June 2008). "Solid-Solution Phase Formation Rules for Multi-component Alloys". Advanced Engineering Materials 10 (6): 534–538. doi:10.1002/adem.200700240.
23. ↑ Takeuchi, Akira; Inoue, Akihisa (2005). "Classification of Bulk Metallic Glasses by Atomic Size Difference, Heat of Mixing and Period of Constituent Elements and Its Application to Characterization of the Main Alloying Element". Materials Transactions 46 (12): 2817–2829. doi:10.2320/matertrans.46.2817.
24. ↑ 24.0 24.1 24.2 24.3 24.4 24.5 24.6 24.7 Zhang, Yong; Zuo, Ting Ting; Tang, Zhi; Gao, Michael C.; Dahmen, Karin A.; Liaw, Peter K.; Lu, Zhao Ping (April 2014). "Microstructures and properties of high-entropy alloys". Progress in Materials Science 61: 1–93. doi:10.1016/j.pmatsci.2013.10.001.
25. ↑ Johnson, Duane; Millsaps, Laura (1 May 2018). "Ames Lab takes the guesswork out of discovering new high-entropy alloys". Ames Laboratory News (U.S. Dept. of Energy). https://www.ameslab.gov/news/news-releases/ames-lab-takes-the-guesswork-out-discovering-new-high-entropy-alloys. "high-entropy alloys are notoriously difficult to make, requiring expensive materials and specialty processing techniques. Even then, attempts in a laboratory don’t guarantee that a theoretically possible compound is physically possible, let alone potentially useful."
26. ↑ Ji, Wei; Wang, Weimin; Wang, Hao; Zhang, Jinyong; Wang, Yucheng; Zhang, Fan; Fu, Zhengyi (January 2015). "Alloying behavior and novel properties of CoCrFeNiMn high-entropy alloy fabricated by mechanical alloying and spark plasma sintering". Intermetallics 56: 24–27. doi:10.1016/j.intermet.2014.08.008.
27. ↑ 27.0 27.1 Zou, Yu; Ma, Huan; Spolenak, Ralph (10 July 2015). "Ultrastrong ductile and stable high-entropy alloys at small scales". Nature Communications 6 (1): 7748. doi:10.1038/ncomms8748. PMID 26159936. Bibcode: 2015NatCo...6.7748Z.
28. ↑ 28.0 28.1 Yao, Chen-Zhong; Zhang, Peng; Liu, Meng; Li, Gao-Ren; Ye, Jian-Qing; Liu, Peng; Tong, Ye-Xiang (November 2008). "Electrochemical preparation and magnetic study of Bi–Fe–Co–Ni–Mn high entropy alloy". Electrochimica Acta 53 (28): 8359–8365. doi:10.1016/j.electacta.2008.06.036.
29. ↑ Zhang, Chuan; Zhang, Fan; Chen, Shuanglin; Cao, Weisheng (29 June 2012). "Computational Thermodynamics Aided High-Entropy Alloy Design". JOM 64 (7): 839–845. doi:10.1007/s11837-012-0365-6. Bibcode: 2012JOM....64g.839Z.
30. ↑ Gao, Michael; Alman, David (18 October 2013). "Searching for Next Single-Phase High-Entropy Alloy Compositions". Entropy 15 (12): 4504–4519. doi:10.3390/e15104504. Bibcode: 2013Entrp..15.4504G.
31. ↑ Zunger, Alex; Wei, S.-H.; Ferreira, L. G.; Bernard, James E. (16 July 1990). "Special quasirandom structures". Physical Review Letters 65 (3): 353–356. doi:10.1103/PhysRevLett.65.353. PMID 10042897. Bibcode: 1990PhRvL..65..353Z. https://zenodo.org/record/1233887.
32. ↑ 32.0 32.1 Niu, C.; Zaddach, A. J.; Oni, A. A.; Sang, X.; Hurt, J. W.; LeBeau, J. M.; Koch, C. C.; Irving, D. L. (20 April 2015). "Spin-driven ordering of Cr in the equiatomic high entropy alloy NiFeCrCo". Applied Physics Letters 106 (16): 161906. doi:10.1063/1.4918996. Bibcode: 2015ApPhL.106p1906N.
33. ↑ Huhn, William Paul; Widom, Michael (19 October 2013). "Prediction of A2 to B2 Phase Transition in the High-Entropy Alloy Mo-Nb-Ta-W". JOM 65 (12): 1772–1779. doi:10.1007/s11837-013-0772-3. Bibcode: 2013JOM....65l1772H.
34. ↑ Tian, Fuyang; Delczeg, Lorand; Chen, Nanxian; Varga, Lajos Karoly; Shen, Jiang; Vitos, Levente (30 August 2013). "Structural stability of NiCoFeCrAlx high-entropy alloy from ab initio theory". Physical Review B 88 (8): 085128. doi:10.1103/PhysRevB.88.085128. Bibcode: 2013PhRvB..88h5128T.
35. ↑ Middleburgh, S.C.; King, D.M.; Lumpkin, G.R.; Cortie, M.; Edwards, L. (June 2014). "Segregation and migration of species in the CrCoFeNi high entropy alloy". Journal of Alloys and Compounds 599: 179–182. doi:10.1016/j.jallcom.2014.01.135.
36. ↑ King, D.J.M.; Middleburgh, S.C.; Liu, A.C.Y.; Tahini, H.A.; Lumpkin, G.R.; Cortie, M.B. (January 2015). "Formation and structure of V–Zr amorphous alloy thin films". Acta Materialia 83: 269–275. doi:10.1016/j.actamat.2014.10.016. Bibcode: 2015AcMat..83..269K.
37. ↑ Middleburgh, S.C.; Burr, P.A.; King, D.J.M.; Edwards, L.; Lumpkin, G.R.; Grimes, R.W. (November 2015). "Structural stability and fission product behaviour in U3Si". Journal of Nuclear Materials 466: 739–744. doi:10.1016/j.jnucmat.2015.04.052. Bibcode: 2015JNuM..466..739M.
38. ↑ King, D. M.; Middleburgh, S. C.; Edwards, L.; Lumpkin, G. R.; Cortie, M. (18 June 2015). "Predicting the Crystal Structure and Phase Transitions in High-Entropy Alloys". JOM 67 (10): 2375–2380. doi:10.1007/s11837-015-1495-4. Bibcode: 2015JOM...tmp..273K.
39. ↑ Lederer, Yoav; Toher, Cormac; Vecchio, Kenneth S.; Curtarolo, Stefano (October 2018). "The search for high entropy alloys: A high-throughput ab-initio approach". Acta Materialia 159: 364–383. doi:10.1016/j.actamat.2018.07.042. Bibcode: 2018AcMat.159..364L.
40. ↑ Gao, M. C.; Carney, C. S.; Doğan, Ö. N.; Jablonksi, P. D.; Hawk, J. A.; Alman, D. E. (2015-11-01). "Design of Refractory High-Entropy Alloys" (in en). JOM 67 (11): 2653–2669. doi:10.1007/s11837-015-1617-z. ISSN 1543-1851. Bibcode: 2015JOM....67k2653G. https://doi.org/10.1007/s11837-015-1617-z.
41. ↑ Ruiz-Yo, Benjamine (2016). "The Different Roles of Entropy and Solubility in High Entropy Alloy Stability.". ACS Combinatorial Science 18 (9): 596–603. doi:10.1021/acscombsci.6b00077. PMID 27494349.
42. ↑ Troparevsky, M. Claudia (2015). "Criteria for Predicting the Formation of Single-Phase High-Entropy Alloys.". Physical Review X 5 (1): 011041. doi:10.1103/PhysRevX.5.011041. Bibcode: 2015PhRvX...5a1041T.
43. ↑ Naeem, Muhammad; He, Haiyan; Zhang, Fan; Huang, Hailong; Harjo, Stefanus; Kawasaki, Takuro; Wang, Bing; Lan, Si et al. (27 March 2020). "Cooperative deformation in high-entropy alloys at ultralow temperatures". Science Advances 6 (13): eaax4002. doi:10.1126/sciadv.aax4002. PMID 32258390. Bibcode: 2020SciA....6.4002N.
44. ↑ Otto, F.; Dlouhý, A.; Somsen, Ch.; Bei, H.; Eggeler, G.; George, E.P. (September 2013). "The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy". Acta Materialia 61 (15): 5743–5755. doi:10.1016/j.actamat.2013.06.018. Bibcode: 2013AcMat..61.5743O. https://zenodo.org/record/1258680.
45. ↑ Wu, Z.; Bei, H.; Otto, F.; Pharr, G.M.; George, E.P. (March 2014). "Recovery, recrystallization, grain growth and phase stability of a family of FCC-structured multi-component equiatomic solid solution alloys". Intermetallics 46: 131–140. doi:10.1016/j.intermet.2013.10.024.
46. ↑ Zaddach, A.J.; Scattergood, R.O.; Koch, C.C. (June 2015). "Tensile properties of low-stacking fault energy high-entropy alloys". Materials Science and Engineering: A 636: 373–378. doi:10.1016/j.msea.2015.03.109.
47. ↑ Hemphill, M.A.; Yuan, T.; Wang, G.Y.; Yeh, J.W.; Tsai, C.W.; Chuang, A.; Liaw, P.K. (September 2012). "Fatigue behavior of Al0.5CoCrCuFeNi high entropy alloys". Acta Materialia 60 (16): 5723–5734. doi:10.1016/j.actamat.2012.06.046. Bibcode: 2012AcMat..60.5723H.
48. ↑ Shipman, Matt. "New 'high-entropy' alloy is as light as aluminum, as strong as titanium alloys". Phys.org. http://phys.org/news/2014-12-high-entropy-alloy-aluminum-strong-titanium.html.
49. ↑ "Enhanced strength and ductility in a high-entropy alloy via ordered oxygen complexes". Phys.org. https://phys.org/news/2018-11-strength-ductility-high-entropy-alloy-oxygen.html.
50. ↑ Bała, Piotr; Górecki, Kamil; Bednarczyk, Wiktor; Wątroba, Maria; Lech, Sebastian; Kawałko, Jakub (January 2020). "Effect of high-temperature exposure on the microstructure and mechanical properties of the Al5Ti5Co35Ni35Fe20 high-entropy alloy". Journal of Materials Research and Technology 9 (1): 551–559. doi:10.1016/j.jmrt.2019.10.084.
51. ↑ Liu, Dajin; Yu, Pengfei; Li, Gong; Liaw, P.K.; Liu, Riping (May 2018). "High-temperature high-entropy alloys AlxCo15Cr15Ni70−x based on the Al-Ni binary system". Materials Science and Engineering: A 724: 283–288. doi:10.1016/j.msea.2018.03.058.
52. ↑ Juan, Chien-Chang; Tsai, Ming-Hung; Tsai, Che-Wei; Lin, Chun-Ming; Wang, Woei-Ren; Yang, Chih-Chao; Chen, Swe-Kai; Lin, Su-Jien et al. (July 2015). "Enhanced mechanical properties of HfMoTaTiZr and HfMoNbTaTiZr refractory high-entropy alloys". Intermetallics 62: 76–83. doi:10.1016/j.intermet.2015.03.013.
53. ↑ Wang, X.F.; Zhang, Y.; Qiao, Y.; Chen, G.L. (March 2007). "Novel microstructure and properties of multicomponent CoCrCuFeNiTix alloys". Intermetallics 15 (3): 357–362. doi:10.1016/j.intermet.2006.08.005.
54. ↑ Vrtnik, S.; Koželj, P.; Meden, A.; Maiti, S.; Steurer, W.; Feuerbacher, M.; Dolinšek, J. (February 2017). "Superconductivity in thermally annealed Ta-Nb-Hf-Zr-Ti high-entropy alloys". Journal of Alloys and Compounds 695: 3530–3540. doi:10.1016/j.jallcom.2016.11.417.
55. ↑ Tsai, K.-Y.; Tsai, M.-H.; Yeh, J.-W. (August 2013). "Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys". Acta Materialia 61 (13): 4887–4897. doi:10.1016/j.actamat.2013.04.058. Bibcode: 2013AcMat..61.4887T.
56. ↑ Granberg, F.; Nordlund, K.; Ullah, Mohammad W.; Jin, K.; Lu, C.; Bei, H.; Wang, L. M.; Djurabekova, F. et al. (1 April 2016). "Mechanism of Radiation Damage Reduction in Equiatomic Multicomponent Single Phase Alloys". Physical Review Letters 116 (13): 135504. doi:10.1103/PhysRevLett.116.135504. PMID 27081990. Bibcode: 2016PhRvL.116m5504G.
57. ↑ Sahlberg, Martin; Karlsson, Dennis; Zlotea, Claudia; Jansson, Ulf (10 November 2016). "Superior hydrogen storage in high entropy alloys". Scientific Reports 6 (1): 36770. doi:10.1038/srep36770. PMID 27829659. Bibcode: 2016NatSR...636770S.
58. ↑ Karlsson, Dennis; Ek, Gustav; Cedervall, Johan; Zlotea, Claudia; Møller, Kasper Trans; Hansen, Thomas Christian; Bednarčík, Jozef; Paskevicius, Mark et al. (February 2018). "Structure and Hydrogenation Properties of a HfNbTiVZr High-Entropy Alloy". Inorganic Chemistry 57 (4): 2103–2110. doi:10.1021/acs.inorgchem.7b03004. PMID 29389120.

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