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Title:
MEDIUM TO HIGH ENTROPY ALLOYS AND METHODS OF MAKING THE SAME
Document Type and Number:
WIPO Patent Application WO/2023/091595
Kind Code:
A1
Abstract:
Medium to high entropy alloys and methods for producing the same are disclosed herein. In accordance with a first aspect, provided is a method for producing a medium to high entropy alloy. The method may comprise mixing a feed composition to obtain a metal oxide mixture, wherein the feed composition comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides, or a combination of two or more thereof; and reducing the metal oxide mixture to produce a medium to high entropy alloy.

Inventors:
CHAN HELEN M (US)
KUNDU ANIMESH (US)
GIANELLE MADISON (US)
Application Number:
PCT/US2022/050295
Publication Date:
May 25, 2023
Filing Date:
November 17, 2022
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
UNIV LEHIGH (US)
International Classes:
C22C1/04; B22F9/02; C23C14/34; C23C14/58; C22C30/00
Domestic Patent References:
WO2020142125A22020-07-09
Foreign References:
US5348592A1994-09-20
US20170209908A12017-07-27
US20200392613A12020-12-17
Attorney, Agent or Firm:
HEBLE, Nikhil A. et al. (US)
Download PDF:
Claims:
CLAIMS

What is Claimed is:

1. A method for producing a medium to high entropy alloy, the method comprising: mixing a feed composition to obtain a metal oxide mixture, wherein the feed composition comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides, or a combination of two or more thereof; heat treating of the metal oxide mixture by annealing at a temperature of about 900 to about 1600 °C for an annealing time of about 10 to about 260 hours in an atmosphere comprising hydrogen and at least one of nitrogen, argon, or a combination thereof.

2. The method according to claim 1, wherein the feed composition comprises four or more metal oxides selected from a cobalt oxide, a nickel oxide, an iron oxide, a chromium oxide, a manganese oxide, a titanium oxide, a vanadium oxide, a zinc oxide, a copper oxide, a magnesium oxide, and a combination of two or more thereof.

3. The method according to claim 1 or claim 2, wherein the feed composition comprises a chromium oxide, a manganese oxide, a cobalt oxide, a nickel oxide, and an iron oxide.

4. The method according to any foregoing claim further comprising: milling the metal oxide mixture prior to heat treatment for about 1 to about 30 hours.

5. The method according to any foregoing claim, wherein the temperature is about 900 to about 1,500 °C, optionally about 1,000 to about 1,400 °C, about 1,000 to about 1,300 °C, about 1,100 to about 1600 °C, about 1150 to about 1300 °C, or about 1180 to about 1600 °C.

6. The method according to any foregoing claim, wherein the annealing time is about 20 to about 180 hours, preferably about 24 to about 180 hours, preferably about 24 to about 150 hours, or preferably about 24 to about 120 hours.

7. The method according to any foregoing claim, wherein the atmosphere for the heat treatment is non-flammable and comprises of about 1 to 4.5 mol.% of hydrogen and about 95.5 mol.% or more of argon, nitrogen, or a combination thereof.

8. The method according to any foregoing claim, wherein the reduction temperature is about 1200 °C or less, and the high entropy alloy comprises a microstructure having about 2 mol.% to about 16 mol.% of a Mn metal phase.

9. The method according to any foregoing claim further comprising: forming a pellet from the metal oxide mixture prior to the heat treatment.

10. The method according to any foregoing claim, wherein the medium to high entropy alloy has a micro structure comprising a metal phase, a metal oxide phase, or a combination thereof.

11. The method according to claim 10, wherein the micro structure comprises FCC metal phase.

12. The method according to claim 10, wherein the micro structure comprises a single phase.

13. The method according to any foregoing claim, wherein the medium to high entropy alloy has metal oxides uniformly dispersed throughout.

14. The method according to any foregoing claim, wherein the medium to high entropy alloy comprises metal oxide layer and metal layer.

15. A medium to high entropy alloy comprising: a composition comprising a plurality of metals comprising four or more metals present in a mass fraction of about 0.05 or more; and a micro structure comprising a metal phase, a metal oxide phase, or a combination thereof.

16. The medium to high entropy alloy of claim 15, wherein the mass fraction of each of the four or more metals is from about 0.05 to about 0.35.

17. The medium to high entropy alloy of claim 15 or claim 16, wherein the mass fraction of at least two of the four or more metal is from about 0.10 to about 0.35, optional from about 0.15 to about 0.3, or optionally from about 0.2 to about 0.3.

18. The medium to high entropy alloy of any one of claims 15 to 17, wherein the medium to high entropy alloy has a first section comprising a first microstructure and a second section comprising a second microstructure, the second microstructure being different than the first microstructure.

19. The medium to high entropy alloy of claim 18, wherein the first micro structure has a larger volumetric fraction of a FCC metal phase than the second microstructure.

20. The medium to high entropy alloy of claim 18 or claim 19, wherein the second microstructure phase has a large volumetric fraction of metal oxide phases than the first microstructure.

21. The medium to high entropy alloy of any one of claim 18 to claim 20, wherein the first section is a first layer and the second section is a second layer.

22. The medium to high entropy alloy of any one of claim 18 to claim 20, wherein the first section is a shell layer and the second section is a core, wherein the first shell layer at least partially surrounds the core.

23. The medium to high entropy alloy of any one of claim 18 to claim 22, wherein the medium to high entropy alloy comprises metal oxide layer and metal layer.

24. The medium to high entropy alloy of any one of claim 15 to claim 17, wherein the microstructure has metal oxides uniformly dispersed throughout.

25. The medium to high entropy alloy of any one of claim 15 to claim 17, wherein the microstructure comprises a single phase.

26. The medium to high entropy alloy of any one of claim 18 to claim 23, wherein the first section has an average thickness of about 100 to about 300 |im, preferably about 115 to about 280 μm, preferably about 130 to about 270 μm, preferably about 145 to about 260 μm, preferably about 160 to about 240 μm, or preferably about 170 to about 220 μm.

27. The medium to high entropy alloy of any one of claim 15 to claim 23, wherein the microstructure comprises a FCC metal phase having a lattice parameter of about 3.3 to about 3.9 A, preferably about 3.4 to about 3.8 A, preferably about 3.4 to about 3.7 A, preferably about 3.5 to about 3.7 A, or preferably about 3.55 to about 3.6 A.

28. The high entropy alloy according to any of claim 15 to claim 25, wherein the composition of the high entropy alloy further comprises a cobalt oxide, a nickel oxide, an iron oxide, or a combination of two or more thereof.

29. The high entropy alloy according to any of claim 15 to claim 25, wherein the composition of the high entropy alloy further comprises a cobalt oxide, a nickel oxide, and an iron oxide.

30. A method for producing a medium to high entropy alloy, the method comprising: mixing a feed composition to obtain a metal oxide mixture, wherein the feed composition comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides, or a combination of two or more thereof; and reducing the metal oxide mixture to produce a medium to high entropy alloy.

31. The method according to claim 30, wherein the metal oxide mixture is partial reduced.

32. The method according to claim 30, wherein the metal oxide mixture is completely reduced.

33. The method according to any one of claims 1 to 14 and 30 to 32, wherein the metal oxide mixture comprises a manganese oxide, wherein the metal oxide mixture is reduced by annealing at an annealing temperature that less than the melting temperature of the manganese oxide.

34. The method according to any one of claims 30 to 33, wherein the metal oxide mixture is reduced in an atmosphere that is non-flammable and comprises of about 1 to 4.5 mol.% of hydrogen and about 95.5 mol.% or more of argon, nitrogen, or a combination thereof.

35. The method according to claim 34, wherein the atmosphere comprises of about 1 to 4.5 mol.% of hydrogen and about 95.5 mol.% or more of argon.

36. The method according to claim 34, wherein the atmosphere consists of about 1 to 4.5 mol.% of hydrogen and about 95.5 mol.% or more of argon.

37. The method according to any one of claims 1 to 14 and 30 to 32, wherein the metal oxide mixture comprises a chromium oxide, wherein the metal oxide mixture is reduced by annealing at an annealing temperature that less than the melting temperature of the chromium oxide.

Description:
MEDIUM TO HIGH ENTROPY ALLOYS AND METHODS OF MAKING THE SAME

CROSS- REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of U.S. Provisional Patent Application No. 63/280,688, entitled “Solid State Processing of the Cantor Alloy CoCrFeMnNi by Oxide Reduction,” filed November 18, 2021, the entire disclosure of which is hereby incorporated herein by reference.

BACKGROUND

[0002] High entropy alloys (HEAs), also known as multi-principal elemental alloys (MPEAs) or multicomponent alloys (MCAs), are a relatively new class of materials. A high entropy alloy often refer to a multi-component single phase alloys formed by the reduction of total free energy of the solid solution single phase due to a significant increase in configuration entropy of the multi- component system, prohibiting the formation of intermetallic compounds. In other words, a high- entropy alloy refers not to an intermetallic compound or an amorphous alloy, but to a stable single- phase multi-component alloy.

[0003] From a compositional standpoint, high entropy alloys differ from conventional alloys in that they incorporate a high number of elemental components in significant (near equiatomic) proportions. Study of high entropy alloys, therefore, represents a radical departure from conventional alloy design strategies, which focus on a single primary component, with the addition of minor quantities of other elements. It is clear that one significant consequence of the HEA concept is the astronomically high number of possible compositions.

[0004] High entropy alloys are typically produced by arc-melting, although methods for forming a layer of high entropy alloy using a laser beam have been a recent focus of developed. The arc- melting process has merits in that it is easy to form a homogenous solid solution, the generation of contaminant elements, such as oxides and voids, is minimized compared to a sintering process, and the ductility-brittleness transition temperature (DBTT) of the composition is relatively lower in the arc-melting process than in the sintering process, thus increasing the rupture time.

[0005] Another method for producing high entropy alloys includes casting processes, in which the raw-material metal is melted, and high temperature/high pressures are used for sintering, such as spark plasma sintering or hot isostatic pressing of raw materials. The raw material for casting processes are typically highly pure metal powders.

[0006] Overall, the production of high entropy alloys has proven challenging at least partially because of the compositions used for producing high entropy alloys.

BRIEF SUMMARY

[0007] This summary is intended merely to introduce a simplified summary of some aspects of one or more implementations of the present disclosure. Further areas of applicability of the present disclosure will become apparent from the detailed description provided hereinafter. This summary is not an extensive overview, nor is it intended to identify key or critical elements of the present teachings, nor to delineate the scope of the disclosure. Rather, its purpose is merely to present one or more concepts in simplified form as a prelude to the detailed description and brief description of the drawings provided below.

[0008] Aspects of the invention are directed to medium to high entropy alloys and methods for producing the same. In accordance with an aspect, a method is provided for producing a medium to high entropy alloy, the method comprising mixing a feed composition to obtain a metal oxide mixture, wherein the feed composition comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, and post-transition metal oxides; and heat treating of the metal oxide mixture by annealing at a temperature of about 900 to about 1600 °C for an annealing time of about 10 to about 260 hours in an atmosphere comprising hydrogen and at least one of nitrogen, argon, or a combination thereof.

[0009] According to another aspect, provided is a medium to high entropy alloy having a composition comprising a plurality of metals; and a micro structure comprising a metal phase, a metal oxide phase, or a combination thereof. The plurality of metals of the composition comprises four or more metals present in a mass fraction of about 0.05 or more.

[0010] In accordance with another aspect, a method is provided for producing a medium to high entropy alloy, the method comprising mixing a feed composition to obtain a metal oxide mixture, wherein the feed composition comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides, or a combination of two or more thereof; and reducing the metal oxide mixture to produce a medium to high entropy alloy.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The present invention will become more fully understood from the detailed description and the accompanying drawings, wherein like elements are labeled similarly and in which:

[0012] FIG. 1A is an image of the microstructure of an example medium to high entropy alloy in accordance with aspects of the invention;

[0013] FIG. IB is an image of the microstructure of another example medium to high entropy alloy having a metal layer and a metal oxide layer according to aspects of the invention;

[0014] FIG. 2 is an image of a compositional Energy Dispersive X-ray Spectroscopy map of a further example medium to high entropy alloy in accordance with aspects of the invention;

[0015] FIG. 3 is a graph of a representative X-ray diffraction spectra obtained from two example medium to high entropy alloys having a metal layer and a metal oxide layer according to aspects of the invention; and

[0016] FIG. 4 is an image of a compositional Energy Dispersive X-ray Spectroscopy map of an example medium to high entropy alloy in accordance with aspects of the invention.

[0017] It should be understood that the various aspects of the invention are not limited to the arrangements and instrumentality shown in the drawings.

DETAILED DESCRIPTION

[0018] The features and benefits of the invention are illustrated and described herein by reference to exemplary (“example”) embodiments. This description of exemplary embodiments is intended to be read in connection with the accompanying drawings, which are to be considered part of the entire written description. Accordingly, the disclosure expressly should not be limited to such exemplary embodiments illustrating some possible non-limiting combination of features that may exist alone or in other combinations of features.

[0019] In the description of embodiments disclosed herein, any reference to direction or orientation is merely intended for convenience of description and is not intended in any way to limit the scope of the present invention. Relative terms such as “lower,” “upper,” “horizontal,” “vertical,” “above,” “below,” “up,” “down,” “top,” and “bottom” as well as derivative thereof (e.g., “horizontally,” “downwardly,” “upwardly,” etc.) should be construed to refer to the orientation as then described or as shown in the drawing under discussion. These relative terms are for convenience of description only and do not require that the apparatus be constructed or operated in a particular orientation. Terms such as “attached,” “affixed,” “connected,” “coupled,” “interconnected,” and similar terms refer to a relationship wherein structures are secured or attached to one another either directly or indirectly through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise.

[0020] As used throughout, ranges are used as shorthand for describing each and every value that is within the range. Any value within the range can be selected as the terminus of the range. Thus, a range from 1-5, includes specifically 1, 2, 3, 4 and 5, as well as subranges such as 2-5, 3-5, 2-3, 2-4, 1-4, etc.

[0021] The term “about” when referring to a number means any number within a range of 10% of the number. For example, the phrase “about 2 wt.%” refers to a number between and including 1.8 wt.% and 2.2 wt.%.

[0022] All references cited herein are hereby incorporated by reference in their entireties. In the event of a conflict in a definition in the present disclosure and that of a cited reference, the present disclosure controls.

[0023] As used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural references unless the context dictates otherwise. The singular form of any class of the ingredients refers not only to one chemical species within that class, but also to a mixture of those chemical species. The terms “a” (or “an”), “one or more” and “at least one” may be used interchangeably herein. The terms “comprising”, “including”, and “having” may be used interchangeably. The term “include” should be interpreted as “include, but are not limited to”. The term “including” should be interpreted as “including, but are not limited to”.

[0024] The abbreviations and symbols as used herein, unless indicated otherwise, take their ordinary meaning. The symbol “°” refers to a degree, such as a temperature degree or a degree of an angle. The symbols “hr”, “min”, “mL”, “nm”, and “μm” refer to hour, minute, milliliter, nanometer, and micrometer, respectively. The abbreviation “rpm” means revolutions per minute. When referring to chemical structures, and names, the symbols “C”, “H”, and “O” mean carbon, hydrogen, and oxygen, respectively. [0025] Any member in a list of species that are used to exemplify or define a genus, may be mutually different from, or overlapping with, or a subset of, or equivalent to, or nearly the same as, or identical to, any other member of the list of species. Further, unless explicitly stated, such as when reciting a Markush group, the list of species, compounds, components, and/or elements that define or exemplify the genus is open, and it is given that other species may exist that define or exemplify the genus just as well as, or better than, any other species listed.

[0026] The phrases, “a mixture thereof,” “a combination thereof,” or a combination of two or more thereof’ do not require that the mixture include all of A, B, C, D, E, and F (although all of A, B,

C, D, E, and F may be included). Rather, it indicates that a mixture of any two or more of A, B, C,

D, E, and F can be included. In other words, it is equivalent to the phrase “one or more elements selected from the group consisting of A, B, C, D, E, F, and a mixture of any two or more of A, B, C, D, E, and F.” Likewise, the term “an oxide thereof’ also relates to “oxides thereof.” Thus, where the disclosure refers to “an element selected from the group consisting of A, B, C, D, E, F, an oxide thereof, and a mixture thereof,” it indicates that that one or more of A, B, C, D, and F may be included, one or more of an oxide of A, an oxide of B, an oxide of C, an oxide of D, an oxide of

E, and an oxide of F may be included, or a mixture of any two of A, B, C, D, E, F, an oxide of A, an oxide of B, an oxide of C, an oxide of D, an oxide of E, and an oxide of F may be included.

[0027] All components and elements positively set forth in this disclosure can be negatively excluded from the claims. In other words, the medium to high entropy alloys of the instant disclosure can be free or essentially free of all components and elements positively recited throughout the instant disclosure. In some instances, the medium to high entropy alloys of the present disclosure may be substantially free of non-incidental and/or non-trace amounts of the ingredient(s) or compound(s) described herein. A non-incidental and/or non-trace amount of an ingredient or compound is the amount of that ingredient or compound that is added into the composition of the medium to high entropy alloys by itself.

[0028] Some of the various categories of components identified may overlap. In such cases where overlap may exist and the medium to high entropy alloy includes both components (or the composition includes more than two components that overlap), an overlapping compound does not represent more than one component.

[0029] High entropy alloy conventionally applies to alloys having a high level of internal disorder that occurs when the principal elements of such alloys are mixed. Typically, when several metals are combined, enthalpy drives them towards forming intermetallic compounds that are hard and brittle. By increasing the relative proportions of the elements and introducing more internal entropy, the formation of such compounds becomes energetically much less favorable, which is conventionally believed to give the resultant alloys improved physical properties without the drawbacks of conventional mixtures.

[0030] The inventors discovered that desirable medium to high entropy alloys could be produced from a feed composition comprising metal oxides using methods disclosed herein. Surprisingly and advantageously, certain methods disclosed herein can reduce one or more metal oxides of the feed composition at processing conditions (such as melting temperature) that would traditionally be believed impossible to reduce such metal oxide(s). Without being limited to any specific theory, it is believed that certain embodiments disclosed herein can reduce one or more of the metal oxides at processing conditions (such as melting temperature) that such metals cannot be individually reduced at due at least partially to a synergistic effect of a feed composition comprising certain metal oxides using particular method steps. For instance, as further described below, the inventors discovered that certain methods can reduce feed compositions comprising a manganese metal oxide at processing conditions that would be expected to be unable to reduce such manganese metal oxide. By way of another example, it was discovered that certain methods can reduce feed compositions comprising a chromium metal oxide at processing conditions that would be expected to be unable to reduce such chromium metal oxide.

[0031] Aspects of the invention are directed to medium to high entropy alloys and methods for producing the same. As used herein, a medium to high entropy alloy refers to an alloy comprising four or more metal components, where none of the metal components comprise more than 50 wt.% of the alloy and at least four of the metal components are present in an amount of more than 5 wt.%, based on the total weight of the medium to high entropy alloy. In accordance with an aspect, a method is provided for producing a medium to high entropy alloy, the method comprising mixing a feed composition to obtain a metal oxide mixture, wherein the feed composition comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides, or a combination of two or more thereof; and heat treating of the metal oxide mixture by annealing at a temperature of about 900 to about 1600 °C for an annealing time of about 10 to about 260 hours in an atmosphere comprising hydrogen and at least one of nitrogen, argon, or a combination thereof. [0032] According to another aspect, provided is a medium to high entropy alloy having a composition comprising a plurality of metals, the plurality of metals comprising four or more metals present in a mass fraction of about 0.05 or more; and a micro structure comprising a metal phase, a metal oxide phase, or a combination thereof.

[0033] In accordance with a further aspect, a method is provided for producing a medium to high entropy alloy, the method comprising mixing a feed composition to obtain a metal oxide mixture, wherein the feed composition comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides or a combination of two or more thereof; and reducing the metal oxide mixture to produce a medium to high entropy alloy.

[0034] The feed composition of the method typically comprises four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides, and a combination of two or more thereof. While the feed composition typically comprises four or more metal oxides, in some embodiments the feed composition includes a plurality of metal oxides comprising five, six, seven, eight, nine, or any range or subrange formed therefrom, of metal oxides. For instance, the feed composition may comprise a plurality of metal oxides comprising from 4 to 9, 4 to 8, 4 to 7, 4 to 6, 4 or 5; from 5 to 9, 5 to 8, 5 to 7, 5 or 6; from 6 to 9, 6 to 8, or 6 or 7 of metal oxides.

[0035] The feed composition may be comprised of about 50 wt.% or more of metal oxides, based on the total weight of the feed composition. For example, the feed composition may be comprised of about 60 wt.% or more, about 70 wt.% or more, about 80 wt.% or more, about 85 wt.% or more, about 88 wt.% or more, about 90 wt.% or more, about 92 wt.% or more, about 94 wt.% or more, about 96 wt.% or more, or about 98 wt.% or more of metal oxides, based on the total weight of the feed composition. In some embodiments, the feed composition comprises about 99 wt.% or about 100 wt.%, with or without trace elements, of metal oxides.

[0036] The feed composition may include a plurality of metal oxides of four or more metal oxides selected from alkali metal oxides, alkaline earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, post-transition metal oxides, and a combination of two or more thereof. One or more of the metal oxides may be selected from the same group of earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, or post-transition metal oxides. For instance, at least two, at least three, or at least four of the plurality of metal oxides may be selected from same group of earth metal oxide, lanthanoid oxide, actinoid oxide, transition metal oxide, or post-transition metal oxide. Additionally or alternatively, two or more of the metal oxides may be selected from a different groups of earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, or post-transition metal oxides. In some embodiments, at least three, at least four, at least five of the plurality of metal oxides may be selected from different groups of earth metal oxides, lanthanoid oxides, actinoid oxides, transition metal oxides, or post-transition metal oxides.

[0037] The plurality of metal oxides of the feed composition may include at least one metal oxide of lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), francium (Fr), or a combination of two or more thereof. In some embodiments, the plurality of metal oxides may include at least one metal oxide of Na, K, Rb, Cs, Fr, or a combination of two or more thereof.

[0038] Additionally or alternatively, the plurality of metal oxides may include at least one metal oxide of beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), radium (Ra), or a combination of two or more thereof. In some embodiment, the plurality of metal oxides may include at least one metal oxide of Mg, Sr, Ba, Ra, or a combination of two or more thereof.

[0039] The plurality of metal oxides may include at least one metal oxide of lanthanum (Ln), cerium (Ce), praseodymium (Pr), neodymium (Nd), promethium (Pm), samarium (Sm), europium (Eu), gadolinium (Gd), terbium (Tb), dysprosium (Dy), holmium (Ho), erbium (Er), thulium (Tm), ytterbium (Yb), lutetium (Lu), or a combination of two or more thereof.

[0040] The plurality of metal oxides may, additionally or alternatively, include at least one metal oxide of actinium (Ac), thorium (Th), protactinium (Pa), uranium (U), neptunium (Np), plutonium (Pu), americium (Am), curium (Cm), berkelium (Bk), californium (Cf), einsteinium (Es), fermium (Fm), mendelevium (Md), nobelium (No), lawrencium (Lr), or a combination of two or more thereof. In some embodiments, the plurality of metal oxides may include at least one metal oxide of Ac, Th, Pa, Np, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr, or a combination of two or more thereof. [0041] In some instances, the plurality of metal oxides may include at least one metal oxide of scandium (Sc), titanium (Ti), vanadium (V), chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), copper (Cu), zinc (Zn), yttrium (Y), zirconium (Zr), niobium (Nb), molybdenum (Mo), technetium (Tc), ruthenium (Ru), rhodium (Rh), palladium (Pd), silver (Ag), cadmium (Cd), hafnium (Hf), tantalum (Ta), tungsten (W), rhenium (Re), osmium (Os), iridium (lr), platinum (Pt), gold (Au), mercury (Hg), rutherfordium (Rf), dubnium (Db), seaborgium (Sg), bohrium (Bh), hassium (Hs), meitnerium (Mt), darmstadtium (Ds), roentgenium (Rg), copemicium (Cn), or a combination of two or more thereof. For example, the plurality of metal oxides may include at least one metal oxide of Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, W, Pt, Au, Hg, Rf, Mt, Ds, Rg, Cn, or a combination of two or more thereof. In some instances, the plurality of metal oxides may include at least one metal oxide of Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Mo, Rh, Pd, Ag, Hf, W, Pt, Au, or a combination of two or more thereof. In at least one embodiment, the plurality of metal oxides may include at least one metal oxide of Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Mo, Pd, Ag, W, Pt, Au, or a combination of two or more thereof. [0042] Additionally or alternatively, the plurality of metal oxides may include at least one metal oxide of indium (In), aluminum (Al), lead (Pb), gallium (Ga), bismuth (Bi), Thallium (TI), tin (Sn), polonium (Po), or a combination of two or more thereof. For example, the plurality of metal oxides may include at least one metal oxide of In, Al, Pb, Ga, TI, Sn, or a combination of two or more thereof. In some cases, the plurality of metal oxides may include at least one metal oxide of Al, Pb, Sn, or a combination of two or more thereof.

[0043] The method may include a feed composition having certain metal oxides depending on the desired application of the medium to high entropy alloy and/or the desired properties thereof. For instance, the plurality of metal oxides of the feed composition may comprise 4 and 9 metal oxides selected from metal oxides of Co, Ni, Fe, Cr, Mn, Ti, V, Zn, Cu, Mg, Al, Mo, Ir, Nb, Ga, Ge, Sr, Y, Zr, Rh, Pd, Ag, Sn, Sb, Hf, Ta, Pt, Au, and a combination of two or more thereof. In at least one embodiment, the feed composition comprises 4 and 9 metal oxides chosen from oxides of Cr, Fe, V, Al, Si, Mn, Mo, Ti, Ni, and a mixture of two or more thereof. In at least another embodiment, the feed composition comprises a plurality of metal oxides selected from oxides of Co, Ni, Cu, Rh, Ir, Zr, and a combination of two or more thereof.

[0044] In at some preferred embodiments, the four or more metal oxides are selected from a cobalt oxide, a nickel oxide, an iron oxide, a chromium oxide, a manganese oxide, a titanium oxide, a vanadium oxide, a zinc oxide, a copper oxide, a magnesium oxide, and a combination of two or more thereof. For example, the feed composition may comprise a chromium oxide, a manganese oxide, a cobalt oxide, a nickel oxide, an iron oxide, or a combination of two or more thereof. As another example, the feed composition may comprise cobalt oxide, chromium oxide, iron oxide, nickel oxide, niobium oxide, or a combination of two or more thereof. The manganese oxides may be selected from MnO, Mn 2 O 3 , Mn 3 O 4 , MnO 2 , Mn 5 O 8 , or a combination of two or more thereof. Examples of chromium oxides include CrO, Cr 2 O 3 , CrO 2 , CrO 3 , CrO 5 , Cr 8 O 21 , or a combination of two or more thereof. Examples of nickel oxide include NiO, Ni 2 O 3 , or a combination of two or more thereof. Examples of cobalt oxides include CoO, CO 2 O, CO 3 O, or a combination of two or more thereof. Examples of iron oxides include FeO, Fe 3 O 4 , Fe 4 O 5 , Fe 5 O 6 , Fe 5 O 7 , Fe 25 O 32 , Fe 13 O 19 , α-Fe 2 O 3 , β-Fe 2 O 3 , γ-Fe 2 O 3 , ε-Fe 2 O 3 , or a combination of two or more thereof.

[0045] The metal oxides may individually be present in the feed composition in an amount from about 5 to about 35 wt.%, based on the total weight of the feed composition. For example, the metal oxides may be individually present in the feed composition in an amount from about 5 to about 35 wt.%, about 5 to about 32 wt.%, about 5 to about 29 wt.%, about 5 to about 27 wt.%, about 5 to about 25 wt.%, about 5 to about 23 wt.%, about 5 to about 21 wt.%, about 5 to about 19 wt.%, about 5 to about 17 wt.%; from about 10 to about 35 wt.%, about 10 to about 32 wt.%, about 10 to about 29 wt.%, about 10 to about 27 wt.%, about 10 to about 25 wt.%, about 10 to about 23 wt.%, about 10 to about 21 wt.%, about 10 to about 19 wt.%, about 10 to about 17 wt.%; from about 12 to about 35 wt.%, about 12 to about 32 wt.%, about 12 to about 29 wt.%, about 12 to about 27 wt.%, about 12 to about 25 wt.%, about 12 to about 23 wt.%, about 12 to about 21 wt.%, about 12 to about 19 wt.%, about 12 to about 17 wt.%; from about 14 to about 35 wt.%, about 14 to about 32 wt.%, about 14 to about 29 wt.%, about 14 to about 27 wt.%, about 14 to about 25 wt.%, about 14 to about 23 wt.%, about 14 to about 21 wt.%, about 14 to about 19 wt.%; from about 16 to about 35 wt.%, about 16 to about 32 wt.%, about 16 to about 29 wt.%, about 16 to about 27 wt.%, about 16 to about 25 wt.%, about 16 to about 23 wt.%, about 16 to about 21 wt.%; from about 18 to about 35 wt.%, about 18 to about 32 wt.%, about 18 to about 29 wt.%, about 18 to about 27 wt.%, about 18 to about 25 wt.%, about 18 to about 23 wt.%; from about 20 to about 35 wt.%, about 20 to about 32 wt.%, about 20 to about 29 wt.%, about 20 to about 27 wt.%, about 20 to about 25 wt.%, about 20 to about 23 wt.%; from about 22 to about 35 wt.%, about 22 to about 32 wt.%, about 22 to about 29 wt.%, about 22 to about 27 wt.%, or any range or subrange formed thereof, based on the total weight of the feed composition. Preferably, each of the plurality of metal oxides in the feed composition is present in an amount from about 5 to about 35 wt.%, including any of the ranges discussed in above, based on the total weight of the feed composition. [0046] The feed composition may be formulated to have a plurality of metal oxides in certain weight ratios. For instance, the feed composition may be formulated such that each metal oxide has a weight ratio of about 1:3 to about 3:1, relative to any other individual metal oxide. In some embodiments, the weight ratio of each metal oxide to any other individual metal oxide of the plurality of metal oxides is about 1:3 to about 3:1, about 1:2 to about 3:1, about 1:1 to about 3:1; about 1:3 to about 2:1, about 1:3 to about 1:1, or any range or subpage thereof.

[0047] The methods for producing a medium to high entropy alloy typically comprise mixing a feed composition to obtain a metal oxide mixture. The feed composition may be mixed by milling, blending, and/or stirring the feed composition. For example, the feed composition may be mixed by milling, including ball milling.

[0048] The methods may further comprise reducing the metal oxide mixture. The metal oxide mixture may be reduced completely or partially. For instance, the method may be adapted to produce a medium to high entropy alloy having a micro structure comprising a metal oxide, whereby the method is adapted to partially reduce the metal oxide mixture. In some embodiments, however, the method is adapted to completely reduce the metal oxide mixture and produce a medium to high entropy alloy having a micro structure that is free or essentially free of metal oxides. The methods may be adapted to partially reduce the metal oxide mixture, such about 30 to about 95%, of the metal oxides in the metal oxide mixture is reduced. The method may partially reduce the metal oxide mixture, such that about 40 to about 95%, about 50 to about 95%, about 60 to about 95%, about 70 to about 95%; about 40 to about 85%, about 50 to about 85%, about 60 to about 85%; about 40 to about 75%, about 50 to about 75%, about 60 to about 75%; about 40 to about 65%, about 50 to about 65%, or any range or subrange formed therefrom, of the metal oxides in the metal oxide mixture is reduced.

[0049] The metal oxide mixture may be reduced by heat treating of the metal oxide mixture. In at least one preferred embodiment, the heat treatment is an isothermal heat treatment, such that the method comprises isothermal heat treating of the metal oxide mixture. The methods may include heat treating of the metal oxide mixture by annealing at a temperature of about 900 to about 1600 °C for an annealing time of about 10 to about 260 hours in an atmosphere comprising hydrogen and at least one of nitrogen, argon, or a combination thereof. The annealing may be at a temperature of about 900 to about 1600 °C, about 900 to about 1500 °C, about 900 to about 1400 °C, about 900 to about 1300 °C, about 900 to about 1200 °C, about 900 to about 1100 °C; from about 1,000 to about 1600 °C, about 1,000 to about 1500 °C, about 1,000 to about 1400 °C, about 1,000 to about 1300 °C, about 1,000 to about 1200 °C, about 1,000 to about 1100 °C; from about 1,050 to about 1600 °C, about 1,050 to about 1500 °C, about 1,050 to about 1400 °C, about 1,050 to about 1300 °C, about 1,050 to about 1200 °C, about 1,050 to about 1100 °C; from about 1,100 to about 1600 °C, about 1,100 to about 1500 °C, about 1,100 to about 1400 °C, about 1,100 to about 1300 °C, about 1,100 to about 1200 °C; from about 1,150 to about 1600 °C, about 1,150 to about 1500 °C, about 1,150 to about 1400 °C, about 1,150 to about 1300 °C, about 1,150 to about 1200 °C; from about 1,200 to about 1600 °C, about 1,200 to about 1500 °C, about 1,200 to about 1400 °C, about 1,200 to about 1300 °C; from about 1,300 to about 1600 °C, about 1,300 to about 1500 °C, about 1,300 to about 1400 °C; from about 1,400 to about 1600 °C, about 1,500 to about 1600 °C, or any range or subrange thereof. For example, in some embodiments, the method may include annealing at a temperature of about 900 to about 1,500 °C, about 1,000 to about 1,400 °C, about 1,000 to about 1,300 °C, about 1,100 to about 1600 °C, about 1150 to about 1300 °C, or about 1180 to about 1600 °C.

[0050] The annealing may occur for an amount of time that may vary, but typically in the range of from about 10 to about 260 hours, including terminal endpoints. In some embodiments, the method includes an annealing time of about 10 to about 260 hours, about 10 to about 220 hours, about 10 to about 180 hours, about 10 to about 140 hours, about 10 to about 120 hours, about 10 to about 100 hours, about 10 to about 80 hours, about 10 to about 60 hours, about 10 to about 48 hours, about 10 to about 36 hours, about 10 to about 24 hours; from about 20 to about 260 hours, about 20 to about 220 hours, about 20 to about 180 hours, about 20 to about 140 hours, about 20 to about 120 hours, about 20 to about 100 hours, about 20 to about 80 hours, about 20 to about 60 hours, about 20 to about 48 hours, about 20 to about 36 hours; from about 30 to about 260 hours, about 30 to about 220 hours, about 30 to about 180 hours, about 30 to about 140 hours, about 30 to about 120 hours, about 30 to about 100 hours, about 30 to about 80 hours, about 30 to about 60 hours, about 30 to about 48 hours; from about 50 to about 260 hours, about 50 to about 220 hours, about 50 to about 180 hours, about 50 to about 140 hours, about 50 to about 120 hours, about 50 to about 100 hours, about 50 to about 80 hours; from about 70 to about 260 hours, about 70 to about 220 hours, about 70 to about 180 hours, about 70 to about 140 hours, about 70 to about 120 hours, about 70 to about 100 hours, about 70 to about 80 hours; from about 90 to about 260 hours, about 90 to about 220 hours, about 90 to about 180 hours, about 90 to about 140 hours, about 90 to about 120 hours; from about 110 to about 260 hours, about 110 to about 220 hours, about 110 to about 180 hours, about 110 to about 140 hours; from about 150 to about 260 hours, about 150 to about 220 hours, about 150 to about 180 hours; from about 190 to about 260 hours, about 190 to about 220 hours, or any range or subrange thereof. In some embodiments, the method includes an annealing time of about 20 to about 180 hours, about 24 to about 180 hours, about 24 to about 150 hours, or about 24 to about 120 hours.

[0051] The method typically includes annealing of the metal oxide mixture in an atmosphere comprising hydrogen and at least one of nitrogen, argon, or a combination thereof. In some embodiments, the atmosphere for annealing consists of one or more of hydrogen and at least one of nitrogen, argon, or a combination thereof, with or without trace elements. In some embodiments, the method includes annealing of the metal oxide mixture in an atmosphere comprising about 1 to 4.5 mol.% of hydrogen and about 95.5 mol.% or more of argon and/or nitrogen. For instance, the annealing of the metal oxide mixture may be in an atmosphere having from about 1 to 4 mol.%, about 1 to 3.5 mol.%, about 1 to 3 mol.%, about 1 to 2.5 mol.%; from about 1.5 to 4.5 mol.%, about 1.5 to 4 mol.%, about 1.5 to 3.5 mol.%, about 1.5 to 3 mol.%, about 1.5 to 2.5 mol.%; from about 2 to 4.5 mol.%, about 2 to 4 mol.%, about 2 to 3.5 mol.%, about 2 to 3 mol.%; from about 2.5 to 4.5 mol.%, about 2.5 to 4 mol.%, about 2.5 to 3.5 mol.%; from about 3 to 4.5 mol.%, about 3 to 4 mol.%, or any range or subrange thereof, of hydrogen, based on the total composition of the atmosphere for annealing of metal oxide mixture, with the remainder being argon and/or nitrogen, with or without trace elements. Additionally or alternatively, the annealing of the metal oxide mixture may be in an atmosphere having about 95.5 mol.% or more, about 96 mol.% or more, about 96.5 mol.% or more, about 97 mol.% or more, about 97.5 mol.% or more, about 98 mol.% or more, about 98.5 mol.% or more of argon and/or nitrogen, with or without trace elements. In some embodiments, the atmosphere for annealing consists of hydrogen in any of the amounts discussed above and argon in any of the amount discussed above, with or without trace elements. Although the atmosphere for annealing generally includes hydrogen and at least one of argon, nitrogen, or a combination thereof, in some embodiments the atmosphere consists of hydrogen.

[0052] The methods disclosed herein may optionally include shaping the metal oxide mixture prior to heat treating. For instance, the method may include disposing the metal oxide mixture into a container having a predetermined shape prior to the heat treatment to ultimately produce a medium to high entropy alloy having a form corresponding to the predetermined shape. The metal oxide can be positioned in a container having a shape that is substantially geometric or geometric (e.g., as a square, rectangle, orthogonal, rhombus, trapezoid, spherical, or the like) or a shape corresponding to a pellet, a bar, a sheet, or the like. In at least some embodiments, the method is adapted to produce a medium to high entropy alloy in the form of a pellet, a bar, a sheet, a powder, or the like.

[0053] Additionally or alternatively, the methods disclosed herein may include sintering at least a section of the metal material during the heat treatment. For example, the method may include a heat treatment that sinters a section (e.g., a layer) of the metal oxide material undergoing heat treatment, e.g., such that the medium to high entropy alloy includes at least one section that underwent sintering. In some embodiments, however, the method includes sintering the whole metal oxide material during heat treatment to produce a medium to high entropy alloy that underwent sintering. The section and/or amount of the medium to high entropy alloy that was sintered during the method may depend on the form/shape of the material during heat treatment.

[0054] In some embodiments, the method may include producing a medium to high entropy alloy having a first section and a second section that is different from the first section. For example, the method may include producing a medium to high entropy alloy in the form of a sheet, wherein the medium to high entropy alloy has a first layer and a second layer that is different from the first layer. In some embodiments, the first section and/or first layer has a microstructure comprising a metal phase and the second section and/or second layer has a microstructure comprising a metal oxide phase.

[0055] According to another aspect, provided is a medium to high entropy alloy. The medium to high entropy alloy may be produced according to the methods described herein. The medium to high entropy alloys disclosed herein, including those produced according to the methods described herein, may be adapted for aerospace materials, nuclear reactor materials, electronic components and/or materials, circuitry components and/or materials, biomedical components, and the like.

[0056] The medium to high entropy alloy typically comprises a composition having a plurality of metals comprising four or more metals present in a mass fraction of about 0.05 or more. Although the medium to high entropy alloy typically comprises four or more metal, in some embodiments the composition of the medium to high entropy alloy comprises five, six, seven, eight, nine, or any range or subrange formed therefrom, of metals. For instance, the composition may comprise a plurality of metal comprising from 4 to 9, 4 to 8, 4 to 7, 4 to 6, 4 or 5; from 5 to 9, 5 to 8, 5 to 7, 5 or 6; from 6 to 9, 6 to 8, or 6 or 7 metals.

[0057] The medium to high entropy alloy may have a composition including a plurality of metals selected from alkali metals, alkaline earth metals, lanthanoids, actinoids, transition metals, post- transition metal, oxides thereof, a carbide thereof, a nitride thereof, or a combination of two or more thereof. For instance, the medium to high entropy alloy may comprise one or more (e.g., at least two, at least three, or at least four) of the metals selected from the same group of earth metals, lanthanoids, actinoids, transition metals, post-transition metals, an oxide thereof, a carbide thereof, a nitride thereof, or a combination of two or more thereof. Additionally or alternatively, the medium to high entropy alloy may comprise two or more of the metals selected from a different group of earth metals, lanthanoids, actinoids, transition metals, post-transition metals, oxides thereof, or a mixture of two or more thereof.

[0058] The composition of the medium to high entropy alloy may include one or more metal selected from Li, Na, K, Rb, Cs, Fr, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. In some embodiments, the medium to high entropy alloy includes at least one metal selected from Na, K, Rb, Cs, Fr, an oxide thereof, a carbide thereof, a nitride thereof, and a combination thereof. Additionally or alternatively, the medium to high entropy alloy may include at least one metal selected from Be, Mg, Ca, Sr, Ba, Ra, an oxide thereof, a carbide thereof, a nitride thereof, and a combination thereof. In some embodiments, the medium to high entropy alloy includes at least one of Mg, Sr, Ba, Ra, an oxide thereof, a carbide thereof, a nitride thereof, or a combination thereof.

[0059] Additionally or alternatively, the composition of the medium to high entropy alloy may include a metal selected from Ln, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. The composition of the medium to high entropy alloy may include one or more metals selected from Ac, Th, Pa, U, Np, Pu, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. In some embodiment, the medium to high entropy alloy includes at least one metal selected from Ac, Th, Pa, Np, Am, Cm, Bk, Cf, Es, Fm, Md, No, Lr, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof.

[0060] Additionally or alternatively, the composition of the medium to high entropy alloy may include one or more metals selected from Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, lr, Pt, Au, Hg, Rf, Db, Sg, Bh, Hs, Mt, Ds, Rg, Cn, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. For example, the medium to high entropy alloy may include at least one metal of Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, W, Pt, Au, Hg, Rf, Mt, Ds, Rg, Cn, an oxide thereof, a carbide thereof, a nitride thereof, or a combination of two or more thereof. In some instances, the medium to high entropy alloy includes at least one metal selected from Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Mo, Rh, Pd, Ag, Hf, W, Pt, Au, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. In at least one embodiment, the medium to high entropy alloy includes at least one metal of Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Mo, Pd, Ag, W, Pt, Au, an oxide thereof, a carbide thereof, a nitride thereof, or a combination of two or more thereof.

[0061] Additionally or alternatively, the medium to high entropy alloy may include at least one metal selected from In, Al, Pb, Ga, Bi, TI, Sn, Po, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. For example, the medium to high entropy alloy may include at least one metal selected from In, Al, Pb, Ga, TI, Sn, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. In at least one embodiment, the medium to high entropy alloy includes at least one metal selected from Al, Pb, Sn, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. In some embodiments, the composition of the medium to high entropy alloy includes one or more metals selected from Co, Ni, Fe, Cr, Mn, Ti, V, Zn, Cu, Mg, Al, Mo, Ir, Nb, Ga, Ge, Sr, Y, Zr, Rh, Pd, Ag, Sn, Sb, Hf, Ta, Pt, Au, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. In at least one embodiment, the composition of the medium to high entropy alloy comprises 4 and 9 metals chosen from Cr, Fe, V, Al, Si, Mn, Mo, Ti, Ni, an oxide thereof, a carbide thereof, a nitride thereof, and a mixture of two or more thereof. In at least another embodiment, the medium to high entropy alloy comprises one or more metals selected from Co, Ni, Cu, Rh, Ir, Zr, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof.

[0062] In at some preferred embodiments, the medium to high entropy alloy includes one or more metals selected from Co, Ni, Fe, Cr, Mn, Ti, V, Zn, Cu, Mg, an oxide thereof, a carbide thereof, a nitride thereof, and a combination of two or more thereof. For example, the composition of the medium to high entropy alloy may comprise Cr, Mn, Co, Ni, Fe, an oxide thereof, a carbide thereof, a nitride thereof, or a combination of two or more thereof. As another example, the medium to high entropy alloy may comprise Co, Cr, Fe, Mo, Nb, an oxide thereof, a carbide thereof, a nitride thereof, or a combination of two or more thereof.

[0063] The composition of the medium to high entropy alloy typically comprises a composition having a plurality of metals comprising four or more metals present in a mass fraction of about 0.05 or more. The four or more metal present in a mass fraction of about 0.05 or more are sometimes referred to herein as principal metals. For example, the mass fraction of the four or more principal metals may be from about 0.05 to about 0.35. In some embodiment, at least one of the four or more principal metals may be present in a mass fraction amount from about 0.05 to about 0.35, about 0.05 to about 0.33, about 0.05 to about 0.31, about 0.05 to about 0.29, about 0.05 to about 0.27, about 0.05 to about 0.25, about 0.05 to about 0.23, about 0.05 to about 0.21, about 0.05 to about 0.19; from about 0.1 to about 0.35, about 0.1 to about 0.33, about 0.1 to about 0.31, about 0.1 to about 0.29, about 0.1 to about 0.27, about 0.1 to about 0.25, about 0.1 to about 0.23, about 0.1 to about 0.21, about 0.1 to about 0.19; from about 0.13 to about 0.35, about 0.13 to about 0.33, about 0.13 to about 0.31, about 0.13 to about 0.29, about 0.13 to about 0.27, about 0.13 to about 0.25, about 0.13 to about 0.23, about 0.13 to about 0.21, about 0.13 to about 0.19; from about 0.16 to about 0.35, about 0.16 to about 0.33, about 0.16 to about 0.31, about 0.16 to about 0.29, about 0.16 to about 0.27, about 0.16 to about 0.25, about 0.16 to about 0.23, about 0.16 to about 0.21; from about 0.19 to about 0.35, about 0.19 to about 0.33, about 0.19 to about 0.31, about 0.19 to about 0.29, about 0.19 to about 0.27, about 0.19 to about 0.25, about 0.19 to about 0.23; from about 0.21 to about 0.35, about 0.21 to about 0.33, about 0.21 to about 0.31, about 0.21 to about 0.29, about 0.21 to about 0.27, about 0.21 to about 0.25; from about 0.23 to about 0.35, about 0.23 to about 0.33, about 0.23 to about 0.31, about 0.23 to about 0.29, about 0.23 to about 0.27; from about 0.25 to about 0.35, about 0.25 to about 0.33, about 0.25 to about 0.31, about 0.25 to about 0.29; from about 0.28 to about 0.35, about 0.28 to about 0.33, about 0.28 to about 0.31; from about 0.3 to about 0.35, about 0.3 to about 0.33, or any range or subrange, based on the total mass of the composition of the medium to high entropy alloy. In some embodiments, the mass fraction of at least two of the four or more principal metal is from about 0.10 to about 0.35, optional from about 0.15 to about 0.3, or optionally from about 0.2 to about 0.3. In further embodiments, each of the four principal metals are present in the medium to high entropy alloy in a mass fraction of about 0.05 to about 0.35, including any of the ranges listed above with respect to at least one of the four or more principal metals.

[0064] The medium to high entropy alloys typically includes a micro structure comprising a metal phase, a metal oxide phase, or a combination thereof. The micro structure may include a metal that is a BCC metal phase or an FCC metal phase. The micro structure may comprise a plurality of phases selected from metal phases, metal oxide phases, or combinations thereof. For instance, the microstructure may comprise two, three, four, five, six, seven, eight, nine, ten, or any range or subrange formed therefrom of phases. In some embodiments, the medium to high entropy alloy comprises from 2 to 9, 2 to 8, 2 to 7, 2 to 6, 2 to 5, 2 to 4; from 3 to 9, 3 to 8, 3 to 7, 3 to 6; from 4 to 9, 4 to 8, 4 to 7, 4 to 6, 4 or 5; from 5 to 9, 5 to 8, 5 to 7, 5 or 6; from 6 to 9, 6 to 8, or 6 or 7, of phases in the micro structure.

[0065] Although the medium to high entropy alloys may comprise one or more microstructures, in some embodiments, the medium to high entropy alloy may comprise a single micro structure. The components, particles, and/or phases of the microstructure may be uniformly or substantially uniformly dispersed throughout the medium to high entropy alloy. As used herein, substantially uniform dispersion and substantially uniformly dispersed refer to a component (e.g., metal and/or metal oxide) being dispersed within 10% of a uniform dispersion. The uniformity of the microstructure may be measured using devices including, e.g., X-ray fluorescence (XRF) analyzers, scanning electron microscopes (SEM), and/or energy dispersive X-ray spectroscopy (EDS) apparatuses.

[0066] The medium to high entropy alloy may be configured to have a form, preferably adapted for the desired use and/or application. For example, the medium to high entropy alloy may be configured to have a form and/or shape that is geometric or substantially geometric (e.g., such as a square, rectangle, orthogonal, rhombus, trapezoid, spherical, or the like). In some embodiments, the medium to high entropy alloy is configured to have the form and/or shape of a pellet, a bar, a sheet, or the like.

[0067] Additionally or alternatively, the medium to high entropy alloys may comprise a first section comprising a first micro structure and optionally a first composition and a second section comprising a second microstructure and optionally a second composition. Typically, the second microstructure, when present, is different from the first microstructure. For example, the medium to high entropy alloy may include a first section having a first micro structure comprising a metal phase and a second section having a second microstructure comprising a metal oxide phase.

[0068] The first microstructure may have a larger volumetric fraction of an FCC and/or BCC metal phase than the second micro structure. For instance, the first micro structure of the first section may have a total volume fraction of metal phase(s) that is larger than the total volume of metal phases of the second micro structure of the second section by about 7 % or more, about 14 % or more, about 21 % or more, about 28 % or more, about 35 % or more, about 45 % or more, about 55 % or more, about 75 % or more, about 100 % or more, about 140 % or more, or about 180 % or more. In some embodiment, the medium to high entropy alloy has a first section having a first microstructure and a second section having a second microstructure, where the first microstructure has a total volume fraction of metal phase(s) that is larger than the total volume of metal phases of the second microstructure by about 7 % to about 140%, about 7 % to about 100%, about 7 % to about 75 %, about 7 % to about 55 %, about 7 % to about 45 %, about 7 % to about 35 %, about 7 % to about 25 %, about 7 % to about 15 %; from about 17 % to about 140%, about 17 % to about 100%, about 17 % to about 75 %, about 17 % to about 55 %, about 17 % to about 45 %, about 17 % to about 35 %; from about 27 % to about 140%, about 27 % to about 100%, about 27 % to about 75 %, about 27 % to about 55 %, about 27 % to about 45 %; from about 47 % to about 140%, about 47 % to about 100%, about 47 % to about 75 %; from about 67 % to about 140%, about 67 % to about 100%; from about 90 % to about 140 %, or any range or subrange thereof.

[0069] The second micro structure phase may have a larger volumetric fraction of metal oxide phases than the first microstructure. For instance, the second micro structure of the second section of the medium to high entropy alloy may have a total volume fraction of metal oxide(s) that is larger than the total volume fraction of metal oxide(s) of the first micro structure of the first section by about 7 % or more, about 14 % or more, about 21 % or more, about 28 % or more, about 35 % or more, about 45 % or more, about 55 % or more, about 75 % or more, about 100 % or more, about 140 % or more, or about 180 % or more. In some embodiment, the medium to high entropy alloy has a first section having a first micro structure and a second section having a second microstructure, where the second microstructure has a total volume fraction of metal oxide phase(s) that is larger than the total volume of metal oxide phases of the first micro structure by about 7 % to about 140%, about 7 % to about 100%, about 7 % to about 75 %, about 7 % to about 55 %, about 7 % to about 45 %, about 7 % to about 35 %, about 7 % to about 25 %, about 7 % to about 15 %; from about 17 % to about 140%, about 17 % to about 100%, about 17 % to about 75 %, about 17 % to about 55 %, about 17 % to about 45 %, about 17 % to about 35 %; from about 27 % to about 140%, about 27 % to about 100%, about 27 % to about 75 %, about 27 % to about 55 %, about 27 % to about 45 %; from about 47 % to about 140%, about 47 % to about 100%, about 47 % to about 75 %; from about 67 % to about 140%, about 67 % to about 100%; from about 90 % to about 140 %, or any range or subrange thereof.

[0070] In some embodiments, the medium to high entropy alloy has a first section that is in the form of a first layer and a second section that is in the form of a second layer. The medium to high entropy alloy may be configured to have a first section (e.g., a first layer) adapted for bonding, coupling, and/or attachment to a metal substrate and a second section (e.g., a second layer) adapted for bonding, coupling, and/or attachment to a ceramic substrate. For example, the medium to high entropy alloy may be configured to have a metal layer adapted for coupling to a metal substrate and a metal oxide layer adapted for coupling to ceramic substrate. Additionally or alternatively, the medium to high entropy alloy may be configured to have a first section (e.g., a first layer) that has an electrical resistance that is different from the electrical resistance of a second section (e.g., a second layer) of the medium to high entropy alloy. In some embodiments, the medium to high entropy alloy has a first section that is in the form of a shell layer and a second section that is in the form of a core, wherein the first shell layer at least partially surrounds the core. The shell layer may completely surround or encapsulate the core in some embodiments.

[0071] The medium to high entropy alloy may be configured such that the first section and/or the second section have an average thickness of about 100 to about 300 μm. In some embodiments, the average thickness of the first section, the second section, or both the first and the second section is about 100 to about 280 μm, 115 to about 280 μm, 115 to about 270 μm, about 130 to about 270 μm, about 130 to about 260 μm, about 160 to about 260 μm, about 160 to about 240 μm, about 170 to about 240 μm, about 170 to about 220 μm, or any range or subrange formed therefrom.

EXAMPLES

Example 1

[0072] Six non-limiting example high entropy alloys (Examples A-F) were prepared in accordance with aspects of the invention. Examples A-F were prepared from the following feed oxide powders: Co(OH)2 (99.9%), Cr2O3 (99.0%), Fe2O3 (99.998%), NiO (99.998%), and MnO2 (99.9%). While Co(OH)2 was used as the source of Co in this Example, it is contemplated that medium to high entropy alloys can be prepared using CoO. The powders were weighed and mixed together in the proportion, such that assuming complete reduction, the high entropy alloy composition would be an equimolar Cantor composition, CoCrFeNiMn. [0073] The feed oxide powders were mixed together and ball milled for a minimum of 12 hours in 200 proof ethanol with alumina milling media to ensure homogeneous mixing of the component oxides. After milling, the mixture of feed oxide powders were sieved to remove the milling media, washed using ethanol, and subsequently dried under vacuum. The dried mixture of feed oxide powders was then compacted in steel dies to cylindrical pellets (~20 x 7 mm) by uniaxial pressing at 2500 psi. The pellets were embedded in graphite powder and subjected to isothermal reduction heat treatment at various temperatures ranging from 1000 °C to 1185 °C for different time periods from 24 to 120 hours in a flowing 3 mol.% H 2 balanced argon atmosphere to produce Examples A-F, which were in the form of a pellet. The gas atmosphere used in this Example was forming gas (5 mol.% H 2 - N 2 ) to circumvent the possible formation of nitrides. A summary of the reduction heat treatments used in the production of Examples A-F is shown in Table 1.

Table 1

Example 2

[0074] Phase identification for the pellets of Examples A-F was carried out utilizing powder X- ray diffraction (XRD, Malvern Panalytical Empyrean, Bragg -Brentano geometry, Cu-Kα source, 1.54184 A, 40 kV, 45 mA). Each data set was calibrated with a NIST silicon standard where the X-ray diffraction (XRD) patterns of the silicon and the samples were collected at the same time under identical conditions. The XRD patterns were acquired at high resolution, with a 29 step size of -0.01°. XRD patterns from the surfaces as well as the cores of the samples were collected.

[0075] The cores were exposed by grinding off the surface layers. Cross-sections of the samples of Examples A-F were prepared for further characterizations using standard metallographic techniques. The microstructures of the samples were characterized using scanning electron microscopy (SEM, Hitachi S-4300 FESEM, FEI Scios FIB). Elemental maps of selected regions of the samples were collected with the aid of Energy Dispersive X-ray Spectroscopy (EDS, FEI Scios FIB equipped with an EDAX-Ametek silicon drift detector). These results were complemented by electron microprobe analysis (JEOL JXA-8900) of regions of interest in the samples. The microprobe was operated at 15 kV accelerating voltage and 30 nA current to obtain accurate measurements of the samples.

Example 3

[0076] The densification of the pellets of Examples A-F was evaluated, and the results are presented in Table 2.

Table 2

[0077] The density of the pellets of Examples A-F increased monotonically as the annealing temperature and annealing time was increased. The maximum density observed was 6.0 g/cm 3 for a heat treatment at a temperature of 1185 °C for 120 hours, which is considerably lower than the theoretical density of a Cantor alloy (7.964 g/cm 3 ).

[0078] Note that for complete reduction of all of the metal oxides to a metallic alloy, a theoretical weight loss of 31.7% was expected, hence the results suggest that the reduction process was incomplete. However, if one considers only the reduction of the Fe 2 O 3 , Co(OH) 2 , and NiO to their metallic form (with Cr 2 O 3 and MnO 2 remaining as oxides), then the expected weight loss is about 18.0%. Since all the samples had mass reduction percentages that exceeded this value, it was inferred that these three components had reduced to their metallic form (Fe, Co, Ni), which was confirmed as discussed in the following Examples.

Example 4

[0079] SEM examination of polished and sectioned samples of the pellets of Examples A-F revealed complex, multiphase microstructures. For the samples of the pellets of Examples A-C, which underwent reduction annealing at temperatures of 1000 and 1100 °C, the samples of the pellets consisted of a fine mixture of metallic and ceramic phases. FIG. 1A shows the microstructure (back-scattered electron contrast) of a sample of the pellet of Example A, which was heat-treated for 24 hours at a temperature of 1000 °C (3 mol.% H 2 -Ar). The metallic regions exhibit bright contrast (due to their higher average atomic number) and are distributed throughout the sample. It can be seen that in some areas, coarsening has occurred, resulting in larger metallic grains.

[0080] Sample pellets of Examples D-F, which had a higher reduction temperatures (e.g., 1150 or 1185 °C), developed a core-shell microstructure having a core comprising a mixture of oxide and metallic phases and a metallic outer shell layer. The outer shell layer exhibited significantly less porosity than the core, and based on EDS compositional maps, was determined to be primarily metallic in nature. The pellet of Example D, which underwent reduction at a temperature of 1150 °C for 24 hours, had an outer shell layer that was discontinuous. The pellet of Example E, which underwent reduction at a temperature of 1185 °C for 24 hours, had an outer shell layer that was continuous. The outer shell layer of the pellet of Example E had a thickness ranging from 11 pm to 147 μm as seen in FIG. IB). The volume fraction of metallic phase is clearly much higher in the sample of the pellet of Example E than for the sample of the pellet of Example A, which was reduced at the temperature of 1000°C. Without being limited to any particular theory, it is believed that increasing the duration of annealing time to 120 hours, promoted the formation of a shell layer having a thickness that was more uniform and increased the thickness of the shell layer to about 194 pm.

Example 6

[0081] X-ray EDS elemental maps of the sample of the pellet of Example F were produced. FIG. 2 is an image of the X-ray EDS elemental maps of the sample of the pellet of Example F. The X- ray EDS elemental map was of an area that encompassed both the core and shell layer regions of the sample of the pellet of Example F.

[0082] As seen in FIG. 2, the dense outer shell layer of the sample of the pellet of Example F contains iron, cobalt, nickel, chromium and manganese, and is essentially devoid of oxygen. The core of the sample of the pellet of Example F contained a mixture of oxide and metallic phases similar to the observations of Example E in FIG. IB. As seen most clearly in the coarsened regions, the metal is enriched in Fe, Co and Ni, and deficient in Cr and Mn. From the Mn map it is also apparent that the core of the sample of the pellet of Example F had a higher concentration of Mn rich oxide phases.

Example 7

[0083] X-ray diffraction (XRD) spectra were obtained from both the near surface and interior of the samples of the pellets of Examples A-F. Three distinct phases were detected from the XRD spectra, namely an FCC phase, a manganese chromate (MnCr 2 O 4 ) phase, and a chromium (III) oxide (Cr 2 O 3 ) phase. The relative fraction of the different phases was estimated from the area of the XRD peaks, and the results are presented in Table 3 for the sample pellets that had undergone reduction for 24 hours at different temperatures.

Table 3

[0084] In agreement with the SEM observations, it can be seen that for the sample of the pellet of Example A, there is little difference between the phase make-up of the core and outer shell layer, i.e., about 58% metal, by volume, and about 42% metal oxide, by volume. The volume fractions for the microstructure phases can be calculated from area fraction measurements. Additionally, the fraction of the various phases of the core for the samples of Examples A, B, D, and E remained relatively constant irrespective of the reduction temperature. In contrast, at the surface of the samples of Examples A, B, D, and E, the volume fraction of metallic phase increased with increasing reduction temperature, and was estimated to be about 95%, by volume, for the sample pellet of Example E. There was a corresponding decrease in the volume fraction of MnCr 2 O 4 and Cr 3 O 3 in the outer shell layer, which is indicative of the increasing extent of reduction of the Cr and Mn oxides. Representative XRD spectra taken from the sample of the pellets of Examples E and F are shown in FIG. 3.

[0085] For the exterior of the sample from the pellet of Example F only peaks corresponding to an FCC phase were detected (see FIG. 3). This corresponds to the metallic shell observed in the SEM. The lattice parameter of this phase was determined to be 3.580 A. By way of comparison, the lattice parameter of the equimolar Cantor alloy is 3.59 A. For the sample of the pellet of Example E, the exterior was mainly FCC metal, but peaks corresponding to a small volume fraction of MnCr 2 O 4 were also visible (see FIG. 3). The core of the sample of the pellet of Example E showed a lesser degree of reduction, with peaks corresponding to FCC metal, MnCr 2 O 4 , and Cr 2 O 3 . These results illustrate the progression of the reduction, and support the SEM observations. [0086] Without being limited to any specific theory, it is believed that the development of the core- shell structure is at least partially dependent on the heat treatment being at certain temperatures. For instance, as can be seen from Table 2, samples heat-treated at a temperature of 1000 °C exhibited a distribution of phases that was essentially uniform through the thickness. However, at the higher reduction temperatures (e.g., at a temperature of 1150 °C or 1185 °C), it is believed that the increased rate of diffusion in the metallic constituents results in sintering of the metallic regions and the formation of a shell of high density. Once the shell is formed, it is believed that the reduction of the interior regions can only take place if there is inward diffusion of hydrogen, and the outward transport of H 2 O; of these two processes, the latter is most likely the rate limiting due to steric considerations. The shell formation thus results in a local increase in the pO 2 in the core region. Due to the resulting slowing of the reduction kinetics, there is increased time for the residual MnO and Cr 2 O 3 to react to form MnCr 2 CO 4 . Additionally, one of the factors that determines whether a core-shell structure develops is the relative kinetics of sintering of the metallic product versus oxide reduction.

Example 8

[0087] The micro structure of the shell region of the samples discussed in Examples 1-7 was examined at higher magnification. Corresponding compositional maps for the sample pellet of Example F are depicted in FIG. 4. It can be seen in FIG. 4 that the outer shell layer of the sample of the pellet of Example F was a poly crystalline metallic layer, which contained all five constituents of the Cantor alloy, namely Fe, Ni, Co, Cr and Mn. These elements were distributed homogeneously within the interior of the grains of the shell layer of the pellet of Example F, although there was evidence of Cr depletion in the grain boundary regions and relative enrichment of the Fe, Co and Ni. It is postulated without being limited to any particular theory that the depletion resulted from the net outward diffusion of Cr atoms, driven by the thickness gradient in pO 2 through the pellet. The higher oxygen activity at the grain boundaries is believed to promote the formation of isolated precipitates of Cr 2 O 3 . An alternate explanation is that the oxide precipitates formed during cooling, since at lower temperatures, the conditions are less reducing. Example 9

[0088] In order to quantitatively determine the chemistry of the shell layer, the samples of the pellets of Examples A-F were examined in the electron microprobe using wavelength dispersive spectroscopy (WDS). The compositional makeup of the pellets was quantified utilizing elemental standards, and the results were corrected for x-ray absorption effects. The results shown in Table 4, which represent the average of values obtained from 372 analyzed areas, were taken from the shell layer of the pellet of Example F.

Table 4

[0089] The analyzed regions spanned from the center to the edge of the sample pellet, and to a depth of about 100 pm from the surface. A total of 400 areas were originally examined, however regions that encompassed the grain boundaries or contained precipitates were removed from analysis as they were not representative of the bulk composition of the shell. A point to be noted here is that because each elemental concentration is determined separately using a standard, the total concentration of all the elements may deviate from 100%.

[0090] The WDS results showed that the composition of the shell layer was fairly homogeneous at any given depth in the pellets. The concentrations of Fe and Mn exhibited a slight compositional gradient through the thickness of the shell of the pellets. More specifically, the manganese concentration varied from 0.079 atom fraction at the surface to 0.085 atom fraction at a depth of about 100 μm, while the iron concentration varied from 0.254 at the surface to 0.250 atom fraction. [0091] Converting the values in Table 3 from weight percentages (wt.%) to atomic percentages (atomic% or mol.%), the average composition of the shell layer of the pellet samples of Example F was determined to be Co 0.25 Cr 0.19 Fe 0.25 Ni 0.23 Mn 0.08 . Compared to the composition of the conventional Cantor alloy (equimolar CoCrFeNiMn), the processed high entropy alloy of Example F was deficient in manganese, with corresponding excess of iron, cobalt and nickel.

Example 10

[0092] The reduction of manganese oxides in the samples of the pellets of Examples A-F was further evaluated in view of the difficulty of reducing manganese oxides. The reduction of manganese (IV) oxide (MnO 2 ) is a complex process, whereby a series of intermediate oxides is formed with progressively lower oxygen content: MnO 2 → Mn 2 O 3 → Mn 3 O 4 → MnO → Mn. Whereas reduction from MnO 2 to MnO can be achieved relatively easily at pO 2 values of approximately 10 -4 , MnO is very stable. At the reduction temperature of 1185°C, which was utilized during the heat treatment process for the preparation of Examples E and F, the equilibrium oxygen partial pressure for the reduction of manganese oxide (MnO) to metallic manganese was calculated to be approximately 10 -20 . This very low value is consistent with the general recognition that reduction of MnO to Mn is not achievable at temperatures below the melting point of Mn, using either hydrogen or CO gas mixtures. It was, thus, surprising, because certain pellets of Examples A-F showed a significant reduction to Mn did occur, resulting in an high entropy alloy containing about 8 mol % of Mn.

[0093] To test whether there was some additional factor at work during our fabrication process, an additional experiment was conducted whereby a comparative sample consisting solely of manganese (IV) oxide (MnO 2 ) was prepared according to the same steps as an example high entropy alloy prepared from a mixture of the same MnO 2 along with Fe 2 O 3 , Co(OH) 2 , Cr 2 O 3 and NiO. Specifically, the comparative sample and the example high entropy alloy were prepared using a procedure similar to that described in Example 1, with the reduction conditions being at a temperature of 1185 °C for 24 hours in an atmosphere of 3% H 2 with the remainder being Ar. Both the comparative sample and the example high entropy alloy both developed a core- shell structure with a shell.

[0094] Notably, the comparative sample prepared from the MnO 2 powder contained a MnO phase. Moreover, for the comparative sample, no other phases were identified in the powder x-ray diffraction measurements. Thus, the MnO 2 powder was only reduced to MnO for the comparative sample. The example high entropy alloy, however, developed a core-shell structure with a metallic shell containing a phase of Mn. This result strongly suggests that there is a synergistic effect that promotes the reduction of MnO to its metallic state for the example high entropy alloy prepared according to the methods described in this Example and Example 1.

[0095] Without being limited to any specific theory, it is believed that the increased entropy of the product high entropy alloy plays a beneficial role. Using standard thermodynamic data at a temperature of 1185 °C (1458 K), the values of the AG of reaction for the reduction of each of the component oxides can be determined (ΔG red ) assuming that reduction occurs by a reaction of the formula:

[0096] Further, since the final composition of the high entropy alloy was determined to be Co0.25Cr0.19Fe0.25Ni0.23Mn0.08, these values can be weighted and summed according to the number of moles of each metal required to produce one mole of the high entropy alloy. It turns out that the net result is slightly positive, namely + 17.8 kJ mol 1 for the high entropy alloy, which suggests that taken as a whole, the set of reduction reactions is not thermodynamically favorable. However, in the oxide reduction process, the end product is not the individual metallic elements, but a solid solution high entropy alloy. The total free energy change during the reaction (ΔG tot ) can thus be considered as follows:

[0097] To take into account the effect of the free energy change related to the formation of the solid solution (ΔG mix ), we need to consider the enthalpy (ΔH mix ) and entropy of mixing (ΔS mix ). The configurational entropy of mixing is readily determined from the following:

[0098] The value calculated for ΔS mix of the actual high entropy alloy composition was ΔS mix of about 12.9 J mol 1 K 1 ; which at 1458 K corresponds to a contribution to ΔG mix of about - 18.8 kJ mol 1 . It would seem, therefore, for an ideal solution where ΔH mix is about 0, that the additional contribution of ΔS mix can provide a plausible rationale for the successful reduction of MnO. Any further contribution due to a negative value of ΔH mix would make the reaction to form the high entropy alloy even more favorable, whereas a highly positive ΔH mix would make it unfavorable. Using the method of Gao et al., and the binary enthalpy of mixing values provided by Takeuchi and Inoue, ΔH mix for the Cantor related HEA was estimated to be -3.75 kJ mol 1 . This value is consistent, therefore, with the successful reduction to form the high entropy alloy. See M.C. Gao, J.W. Yeh, P.K. Liaw, Y. Zhang, editors. “High-Entropy Alloys: Fundamentals and Applications,” Basel: Springer; 2016 and Takeuchi and A. Inoue, “Calculations of Mixing Enthalpy and Mismatch Entropy for Ternary Amorphous Alloys,” Mat. Trans. JIM 41 (2000) 1372-1378, both of which are incorporated herein in their entireties for all purposes.