AN ALLOY

Abstract

An alloy consisting of, in atomic percent: aluminium: 20 to 35%; zirconium: 16.7% or less; vanadium: 7% or less; tungsten: 35% or less; chromium: 35% or less; iron: 10% or less; nickel: 5% or less; titanium: 40% or less; tantalum: 35% or less; niobium: 20% or less; molybdenum: 35% or less; cobalt: 5% or less; manganese: 10% or less; copper: 5% or less; hafnium: 10% or less; silicon: 5% or less; platinum: 5% or less; palladium: 5% or less; ruthenium: 10% or less; rhodium: 5% or less; iridium: 5% or less; rhenium: 35% or less provided ARe≤(35−ATa)+(35−AW)+(20−ANb) and where ARe, ATa, AW and ANb are the amounts in atomic percent of rhenium, tantalum, tungsten and niobium respectively; and incidental impurities less than 1 at % in sum; wherein the following equations are satisfied where xi is the atomic fraction of element i in the alloy, VECi is the number of valence electrons associated with an atom of element i and R is the universal gas constant.

Description

FIELD OF THE DISCLOSURE

The present invention relates to a complex concentrated alloy (CCA) designed for high temperature applications. The alloy has a unique combination of a high ductility, high temperature mechanical strength and resistance to oxidation at high temperature. This can be achieved in combination with a low density and reasonable alloy cost.

BACKGROUND

Conventional alloys for high mechanical strength at high temperature usually rely upon a main principal component. Alloys with very high melting points are often based upon the refractory elements, molybdenum, tungsten, niobium and tantalum. Although these alloys have very high melting points and high strength they do not have tolerance to environmental damage. They also often have extremely high density which limits their potential application to rotating machinery, particularly in aerospace applications where the significant weight penalty is undesirable. Alternatively platinum group metal (PGM) alloys can often combine a high melting point and environmental resistance. However, the high cost of the PGM alloys and the relative scarcity of these materials means it is not economically viable to use these alloys in many commercial applications.

To address this challenge there has been recent development activity in the field of complex concentrated alloys (CCAs) and refractory complex concentrated alloys (RCCAs). However, the alloys which have currently been proposed do not achieve the desired combination of high melting point, high temperature strength, high oxidation resistance at high temperature combined with low density and reasonable cost to reach commercial application in fields such as gas turbine technology, jet turbine technology and rocket propulsion. Examples of alloys which have been commonly researched are shown in Table 1. (Cao et al. Effects of Al and Mo on high temperature oxidation behaviour of refractory high entropy alloys, Trans. Nonferrous Met. Soc. China 29 (2019) 1476-1483; Gorr et al., High-Temperature Oxidation Behaviour of Refractory High-Entropy Alloys: Effect of Alloy Composition, Oxid. Met. (2017) 88:339-349; Miracle et al., Mechanical Properties of Nb₂₅Mo₂₅Ta₂₅W₂₅ and V₂₀Nb₂₀Mo₂₀Ta₂₀W₂₀ Refractory High-Entropy Alloys (PREPRINT), July 2011, Air Force Research Laboratory Materials and Manufacturing Directorate, Wright-Patterson Air Force Base, OH45433-7750 Air Force Materiel Command United States Air Force). [1]-[3]

TABLE 1
Nominal composition in at % of previously studied
high temperature complex concentrated alloys.
Alloy
(at %)	Al	Cr	Mo	Nb	Ta	Ti	V	W	Zr
Gorr 1	20	20	20	0	0	20	0	20	0
Gorr 2	20	20	20	20	0	20	0	0	0
Gorr 3	20	20	20	0	20	20	0	0	0
Miracle 1	0	0	25	25	25	0	0	25	0
Miracle 2	0	0	20	20	20	0	20	20	0
Cao 1a	0	0	0	28.57	14.29	28.57	0	0	28.57
Cao 1b	0	0	0	27.76	16.88	30.75	0	0	24.61
Cao 2a	22.22	0	0	22.22	11.11	22.22	0	0	22.22
Cao 2b	19.35	0	0	22.48	12.59	23.5	0	0	22.08
Cao 3a	20	0	10	20	10	20	0	0	20
Cao 3b	18.82	0	8.67	21.55	10.2	21.87	0	0	18.89

SUMMARY

The present invention provides an alloy consisting of, in atomic percent: aluminium: 20 to 35%; zirconium: 16.7% or less; vanadium: 7% or less; tungsten: 35% or less; chromium: 35% or less; iron: 10% or less; nickel: 5% or less; titanium: 40% or less; tantalum: 35% or less; niobium: 20% or less; molybdenum: 35% or less; cobalt: 5% or less; manganese: 10% or less; copper: 5% or less; hafnium: 10% or less; silicon: 5% or less; platinum: 5% or less; palladium: 5% or less; ruthenium: 10% or less; rhodium: 5% or less; iridium: 5% or less; rhenium: 35% or less provided A_Re≤(35−A_Ta)+(35−A_W)+(20−A_Nb) and where A_Re, A_Ta, A_W and A_Nb are the amounts in atomic percent of rhenium, tantalum, tungsten and niobium respectively; and incidental impurities less than 1 at % in sum; wherein the following equations are satisfied:

$4.6\ge \sum _i{x}_i·{\mathrm{VEC}}_i\mathrm{and}$ $13.38\le -R·\sum _i{x}_i·\ln \left(x_i\right)$

where x_i is the atomic fraction of element i in the alloy and VEC_i is the number of valence electrons associated with an atom of element i and R is the universal gas constant.

In an embodiment, in order to reduce the change of intermetallic phase formation the following equation is fulfilled:

$0.7\ge \frac{A_{\mathrm{Zr}}}{A_{\mathrm{Al}}}\mathrm{preferably}$ $0.45\ge \frac{A_{\mathrm{Zr}}}{A_{\mathrm{Al}}}\mathrm{more}\mathrm{preferably}$ $0.3\ge \frac{A_{\mathrm{Zr}}}{A_{\mathrm{Al}}}$

• • where A_W and A_Zr are the amounts in atomic percent of aluminium and zirconium respectively.

In an embodiment, in order to increase oxidation resistance by reducing spalling the following equation is fulfilled:

$2.\ge {\sum }_i{x}_i·R_{\mathrm{PB}}^i\mathrm{preferably}1.98\ge {\sum }_i{x}_i·R_{\mathrm{PB}}^i\mathrm{more}\mathrm{preferably}1.95\ge {\sum }_i{x}_i·R_{\mathrm{PB}}^i$

where x_i is the atomic fraction of element i in the alloy and R_PBⁱ is the Pilling-Bedworth ratio for pure element i.

In an embodiment, in order to reduce the density of the alloy the following equation is fulfilled:

$10.0\ge \sum _i{x}_i{\rho }_i\mathrm{preferably}$ $9.\ge \sum _i{x}_i{\rho }_i\mathrm{more}\mathrm{preferably}$ $8.\ge \sum _i{x}_i{\rho }_i$

where x_i is the atomic fraction of element i in the alloy and ρ_i is the density for pure element i.

In an embodiment, in order to increase the high temperature strength of the alloy the following equation is fulfilled:

$$\begin{gathered} \begin{array}{cc}1800\le {\sum }_i{x}_i·T_{\mathrm{mi}}\text{ \\ preferably⁢2000≤∑i⁢xi·Tmi⁢ \\ more⁢preferably⁢2100≤∑i⁢xi·Tmi⁢ \\ more⁢preferably⁢2200≤∑i⁢xi·Tmi⁢ \\ more⁢preferably⁢2400≤∑i⁢xi·Tmi⁢ \\ more⁢preferably⁢2500≤∑i⁢xi·Tmi}& \left(1\right)\end{array} \end{gathered}$$

• • where x_i is the atomic fraction of element i in alloy bulk composition and T_mi is the melting point of pure element i.

In an embodiment, in order to increase the stability of the solid solution the following equation is fulfilled:

$13.5\le -R·\sum _i{x}_i·\ln \left(x_i\right)\mathrm{preferably}$ $13.8\le -R·\sum _i{x}_i·\ln \left(x_i\right)$

where x_i is the atomic fraction of element i in alloy bulk composition.

In an embodiment, in order to reduce the cost of the alloy the following equation is fulfilled:

$14.\ge 0.048x_{\mathrm{Al}}+1.933x_{\mathrm{Co}}+0.489x_{\mathrm{Cr}}+0.381x_{\mathrm{Cu}}+0.024x_{Fe}+0.100x_{\mathrm{Mn}}+3.848x_{\mathrm{Mo}}+6.829x_{\mathrm{Nb}}+0.816x_{\mathrm{Ni}}+666.621x_{\mathrm{Re}}+55.189x_{\mathrm{Ta}}+0.543x_{\mathrm{Ti}}+18.899x_V+6.490x_W+3.320x_{\mathrm{Zr}}\mathrm{preferably}$ $12.\ge 0.048x_{\mathrm{Al}}+1.933x_{\mathrm{Co}}+0.489x_{\mathrm{Cr}}+0.381x_{\mathrm{Cu}}+0.024x_{\mathrm{Fe}}+0.100x_{\mathrm{Mn}}+3.848x_{\mathrm{Mo}}+6.829x_{\mathrm{Nb}}+0.816x_{\mathrm{Ni}}+666.621x_{\mathrm{Re}}+55.189x_{\mathrm{Ta}}+0.543x_{\mathrm{Ti}}+18.899x_V+6.490x_W+3.320x_{\mathrm{Zr}}\mathrm{more}\mathrm{preferably}$ $10.\ge 0.048x_{\mathrm{Al}}+1.933x_{\mathrm{Co}}+0.489x_{\mathrm{Cr}}+0.381x_{\mathrm{Cu}}+0.024x_{\mathrm{Fe}}+0.100x_{\mathrm{Mn}}+3.848x_{\mathrm{Mo}}+6.829x_{\mathrm{Nb}}+0.816x_{\mathrm{Ni}}+666.621x_{\mathrm{Re}}+55.189x_{\mathrm{Ta}}+0.543x_{\mathrm{Ti}}+18.899x_V+6.490x_W+3.320x_{\mathrm{Zr}}\mathrm{even}\mathrm{more}\mathrm{preferably}$ $8.\ge 0.048x_{\mathrm{Al}}+1.933x_{\mathrm{Co}}+0.489x_{\mathrm{Cr}}+0.381x_{\mathrm{Cu}}+0.024x_{\mathrm{Fe}}+0.100x_{\mathrm{Mn}}+3.848x_{\mathrm{Mo}}+6.829x_{\mathrm{Nb}}+0.816x_{\mathrm{Ni}}+666.621x_{\mathrm{Re}}+55.189x_{\mathrm{Ta}}+0.543x_{\mathrm{Ti}}+18.899x_V+6.490x_W+3.320x_{\mathrm{Zr}}\mathrm{even}\mathrm{more}\mathrm{preferably}$ $6.5\ge 0.048x_{\mathrm{Al}}+1.933x_{\mathrm{Co}}+0.489x_{\mathrm{Cr}}+0.381x_{\mathrm{Cu}}+0.024x_{\mathrm{Fe}}+0.100x_{\mathrm{Mn}}+3.848x_{\mathrm{Mo}}+6.829x_{\mathrm{Nb}}+0.816x_{\mathrm{Ni}}+666.621x_{\mathrm{Re}}+55.189x_{\mathrm{Ta}}+0.543x_{\mathrm{Ti}}+18.899x_V+6.490x_W+3.320x_{\mathrm{Zr}}\mathrm{most}\mathrm{preferably}$ $5.\ge 0.048x_{\mathrm{Al}}+1.933x_{\mathrm{Co}}+0.489x_{\mathrm{Cr}}+0.381x_{\mathrm{Cu}}+0.024x_{\mathrm{Fe}}+0.100x_{\mathrm{Mn}}+3.848x_{\mathrm{Mo}}+6.829x_{\mathrm{Nb}}+0.816x_{\mathrm{Ni}}+666.621x_{\mathrm{Re}}+55.189x_{\mathrm{Ta}}+0.543x_{\mathrm{Ti}}+18.899x_V+6.490x_W+3.320x_{\mathrm{Zr}}$

• • where x_x is the atomic fraction of element x in the alloy

In an embodiment, in order to reduce the cost of the alloy the following equation is satisfied:

$75\ge A_V+3A_{\mathrm{Ta}}\mathrm{preferably}64\ge A_V+3A_{\mathrm{Ta}}\mathrm{more}\mathrm{preferably}53\ge A_V+3A_{\mathrm{Ta}}\mathrm{Even}\mathrm{more}\mathrm{preferably}42\ge A_V+3A_{\mathrm{Ta}}\mathrm{Even}\mathrm{more}\mathrm{preferably}34\ge A_V+3A_{\mathrm{Ta}}\mathrm{Most}\mathrm{preferably}26\ge A_V+3A_{\mathrm{Ta}}$

where A_V and A_Ta are the amounts in atomic percent of vanadium and tantalum respectively.

In an embodiment the alloy includes 21 to 35 at % aluminium, preferably 22 to 35 at % aluminium, more preferably 23 to 35 at % aluminium. Such an alloy has superior oxidation resistance.

In an embodiment the alloy includes 33 at % or less aluminium, preferably 31 at % or less aluminium. Such an alloy has increased high temperature strength. In an embodiment the alloy includes 11.1 at % or less zirconium, preferably 10 at % or less zirconium, most preferably 9% or less zirconium. Such an alloy has reduced chance of intermetallic phase formation.

In an embodiment the alloy includes 2 at % or more zirconium, preferably 4 at % or more zirconium, more preferably 6 at % or more zirconium, more preferably 8 at % or more zirconium, most preferably 10 at % zirconium or more. Such an alloy has reduced VEC leading to higher ductility and also a reduction in the chance of spalling which can lead to reduced oxidation resistance.

In an embodiment the alloy includes 5.1 at % or less vanadium, preferably 3 at % or less vanadium. Such an alloy has better corrosion resistance.

In an embodiment the alloy includes 2 at % or more vanadium, preferably 5 at % or more vanadium. Such an alloy has reduced density and improved high temperature strength.

In an embodiment the alloy includes 26.8 at % or less tungsten, preferably 25.1 at % or less tungsten, more preferably 20.0 at % or less tungsten, preferably 19.0 at % or less tungsten, preferably 10 at % or less tungsten. Such an alloy has reduced density.

In an embodiment the alloy includes 2 at % or more tungsten, preferably 5 at % or more tungsten, preferably 8 at % or more tungsten, more preferably 11 at % or more tungsten. Such an alloy has increased high temperature strength. In an embodiment the alloy includes 25 at % or less chromium, preferably 20 at % or less chromium and most preferably 15 at % or less chromium or even 10 at % or less chromium. Such an alloy is less likely to develop detrimental laves or other Cr-rich phases.

In an embodiment the alloy includes 7 at % or less iron, preferably 5 at % or less iron. Such an alloy has reduced VEC leading to improved ductility.

In an embodiment the alloy includes 0.5 at % or more iron, preferably 2 at % or more iron, more preferably 4 at % or more iron. Such an alloy has superior printability.

In an embodiment the alloy includes 4 at % or less nickel, preferably 3 at % or less nickel, more preferably 1 at % or less nickel. Such an alloy has increased ductility due to lower VEC.

In an embodiment the alloy includes 0.5 at % or more nickel, preferably 1 at % or more nickel, more preferably 2 at % or more nickel. Such an alloy has increased oxidation resistance due to lower likelihood of spalling.

In an embodiment the alloy includes 35 at % or less titanium, preferably 33 at % or less titanium, more preferably 30 at % or less titanium, more preferably 25 at % or less titanium, even more preferably 20 at % or less titanium. Such an alloy has improved oxidation resistance.

In an embodiment the alloy includes 5 at % or more titanium, preferably 8 at % or more titanium, more preferably 13 at % or more titanium, most preferably 20 at % or more titanium. Such an alloy has increased high temperature strength. In an embodiment the alloy includes 33.3 at % or less tantalum, preferably 25 at % or less tantalum, more preferably 21.3 at % or less tantalum, even more preferably 17.7 at % or less tantalum, more preferably 14 at % or less tantalum, more preferably 11.3 at % or less tantalum, most preferably 8.7 at % or less tantalum. Such an alloy has reduced density and cost.

In an embodiment the alloy includes 2 at % or more tantalum, preferably 5 at % or more tantalum, preferably 10 at % or more tantalum, more preferably 15 at % or more tantalum, most preferably 20 at % or more tantalum. Such an alloy has improved high temperature strength.

In an embodiment the alloy includes 16 at % or less niobium, preferably 13 at % or less niobium to reduce the chance of pesting.

In an embodiment the alloy includes 5 at % or more niobium, preferably 8 at % or more niobium, more preferably 10 at % or more niobium. Such an alloy has increased strength.

In an embodiment the alloy includes 20 at % or less molybdenum, preferably 15 at % or less molybdenum, more preferably 12 at % of less molybdenum, even more preferably 7 at % or less molybdenum. This improved oxidation resistance. In an embodiment the alloy includes 2 at % or more molybdenum, preferably 4 at % or more molybdenum, more preferably 6 at % or more molybdenum. This helps increase high temperature strength.

In an embodiment the alloy includes 3 at % or less cobalt, preferably 2 at % or less cobalt. This increases ductility by reducing VEC.

In an embodiment the alloy includes 0.5 at % or more cobalt, preferably 1 at % or more cobalt, more preferably 2 at % or more cobalt, even more preferably 3 at % or more cobalt, most preferably 4 at % or more cobalt. This helps reduce density and cost, as well as increasing oxidation resistance by reducing spalling.

In an embodiment the alloy includes 4 at % or less copper, preferably 3 at % or less copper. This increases ductility by reducing VEC.

In an embodiment the alloy includes 0.5 at % or more copper, preferably 1 at % or more copper, more preferably 2 at % or more copper. This helps increase oxidation resistance by reducing spalling.

In an embodiment the alloy includes 7 at % or less manganese, preferably 5 at % or less manganese. This increases ductility by reducing VEC and improves oxidation performance.

In an embodiment the alloy includes 0.5 at % or more manganese, preferably 2 at % or more manganese, more preferably 4 at % or more manganese. This helps reduce density of the alloy.

In an embodiment the alloy includes 20 at % or less rhenium, preferably 15 at % or less rhenium, more preferably 10 at % or less rhenium, most preferably 5 at % or less rhenium. This reduces cost and improves oxidation resistance by reducing spalling.

In an embodiment the alloy includes 3 at % or more rhenium, preferably 5 at % or more rhenium. This increases high temperature strength.

In an embodiment, in order to improve ductility the following equation is fulfilled:

$4.4\ge \sum _i{x}_i·{\mathrm{VEC}}_i\mathrm{preferably}$ $4.05\ge \sum _i{x}_i·{\mathrm{VEC}}_i$

In an embodiment, in order to reduce densitythe following equation is satisfied:

$A_W+0.8A_{\mathrm{Ta}}\le 37.8\mathrm{preferably}$ $A_W+0.72A_{\mathrm{Ta}}\le 26.8\mathrm{more}\mathrm{preferably}$ $A_W+0.6A_{\mathrm{Ta}}\le 20$

where A_Ta and A_W are the atomic percent of tantalum and tungsten, respectively, in the alloy.

In an embodiment, in order to improve ductility the following equation is satisfied:

$A_{\mathrm{Al}}+A_{\mathrm{Zr}}+A_{\mathrm{Ti}}\ge 41\mathrm{preferably}{A}_{\mathrm{Al}}+A_{\mathrm{Zr}}+A_{\mathrm{Ti}}\ge 60$

where A_Al, A_Zr and A_Ti is are the atomic percent of aluminium, zirconium and titanium respectively in the alloy.

In an embodiment, in order to improve ductility the following equation is satisfied:

$A_{\mathrm{Zr}}+A_{\mathrm{Ti}}\ge 6$

where A_Zr and A_Ti are the amounts in atomic percent of zirconium and titanium respectively.

In an embodiment, in order to improve high temperature oxidation resistance the following equation is satisfied:

$A_V+1.15A_W\le 28.9$

where A_V and A_W are the amounts in atomic percent of vanadium and tungsten respectively.

In an embodiment, in order to improve high temperature oxidation resistance the following equation is satisfied:

$A_{\mathrm{Nb}}+0.83A_{\mathrm{Ta}}\le 42.5$

where A_Nb and A_Ta are the amounts in atomic percent of niobium and tantalum respectively.

In an embodiment the alloy includes 1 at % or more chromium, preferably 2 at % or more chromium, more preferably 3 at % or more chromium, even more preferably 5 at % or more chromium, most preferably 10 at % or more chromium. Such an alloy has superior corrosion resistance.

In an embodiment, in order to improve high temperature strength the following equation is satisfied:

$\begin{array}{cc}& 10\le A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\\ \mathrm{preferably}& \\ & 13\le A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\\ \mathrm{more}\mathrm{preferably}& \\ & 26\le A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\\ \mathrm{even}\mathrm{more}\mathrm{preferably}& \\ & 39\le A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\\ \mathrm{most}\mathrm{preferably}& \\ & 50\le A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\end{array}$

where A_W, A_Ta, A_Mo and A_Nb are the amounts in atomic percent of tungsten, tantalum, molybdenum and niobium respectively.

In an embodiment, in order to improve high temperature strength the following equation is satisfied:

$\begin{array}{cc}& A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\ge 10\\ \mathrm{preferably}& \\ & A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\ge 0.75A_{\mathrm{Al}}-4.75\\ \mathrm{more}\mathrm{preferably}& \\ & A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\ge 0.75A_{\mathrm{Al}}+8.75\\ \mathrm{even}\mathrm{more}\mathrm{preferably}& \\ & A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\ge 0.8A_{\mathrm{Al}}+23\\ \mathrm{most}\mathrm{preferably}& \\ & A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}\ge 1.25A_{\mathrm{Al}}+21.25\end{array}$

where A_Al, A_W, A_Ta, A_Mo and A_Nb are the amounts in atomic percent of aluminium, tungsten, tantalum, molybdenum and niobium respectively.

The term “consisting of” is used herein to indicate that 100% of the composition is being referred to and the presence of additional components is excluded so that percentages add up to 100 atomic percent. Unless stated otherwise, all amounts are given in atomic percent (at %). A_i is atomic percent of element i in the alloy and x_i is atomic fraction of element i in the alloy. The invention will be more fully described, by way of example only, with reference to the accompanying drawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1a-FIG. 1j is plots of Co, Cu, Fe, Mn, Ni, Pt, Pd, Ru, Rh and Ir on the y axes vs VEC on the x-axis for all alloys in the space defined in table 2 except that zirconium may be present up to 35 at % with no further restrictions;

FIG. 2 is SEM micrographs of the surface layer of experimental samples along with V and O contents in EDS maps;

FIG. 3 shows vanadium concentration for certain alloys and whether or not a mixed oxide outer layers or a pure vanadium oxide outer layer formed;

FIG. 4a-FIG. 4b plots Pilling-Bedworth ratio of alloys with variations in W and V in FIG. 4a and variations in Ta and Nb in FIG. 4b for the whole alloy space of table 2, excluding hafnium, silicon, platinum, palladium, ruthenium, iridium and rhodium;

FIG. 5a-FIG. 5c plots density of alloys as a function of W and Ta content. Lines are drawn for density≤10, ≤9 and ≤8 g/cm³ in FIGS. 5a, 5b and 5c respectively. The alloy space is the elemental space as defined in claim 1, excluding hafnium, silicon, platinum, palladium, ruthenium, iridium and rhodium, and including the constraints VEC≤4.6 and entropy≥13.38;

FIG. 6 plots VEC on the y axis against Al equivalent (sum of Al, Zr and Ti). The alloys plotted are those falling within claim 1 and also including the constraints VEC≤4.6, entropy≥13.38, Pilling-Bedworth ratio<2 and density<10, and excluding hafnium, silicon, platinum, palladium, ruthenium, iridium and rhodium;

FIG. 7 shows zirconium concentration and whether or not Al—Zr intermetallics are present;

FIG. 8 shows SEM and EDS images for samples 2D and 2E and proves the absence of Zr—Al precipitates;

FIG. 9a-FIG. 9e plots melting temperature as a function of tungsten equivalent (W_eq, sum of tungsten, tantalum, molybdenum and niobium) vs at % aluminium. The alloy space is the elemental space as defined in claim 1 and also including the constraints VEC≤4.6 and entropy≥13.38, and excluding hafnium, silicon, platinum, palladium, ruthenium, iridium and rhodium. FIGS. 9a-9e plot alloys with a melting temperature of greater than 1800, 2000, 2200, 2400 and 2500 K respectively; for all alloys FIG. 10 shows the density vs melting point trade off for all alloys as defined in claim 1 and also including the constraints VEC≤4.6 and entropy≥13.38; and

FIG. 11a-FIG. 11f shows cost vs Ta and V concentrations. The alloy space is the elemental space as defined in claim 1 and also including the constraints VEC≤4.6 and entropy≥13.38, and excluding hafnium, silicon, platinum, palladium, ruthenium, iridium and rhodium.

DETAILED DESCRIPTION OF THE INVENTION

Traditionally, high performance alloy materials have been designed through empiricism. Thus their chemical compositions have been isolated using time consuming and expensive experimental development, involving small-scale processing of limited quantities of material and subsequent characterisation of their behaviour. The alloy composition adopted is then the one found to display the best, or most desirable, combination of properties.

In the field of CCA's and RCCA's the removal of a principal element results in an extremely large number of possible alloying combinations, therefore modelling techniques provide novel insight that can be applied to isolate improved alloys.

A modelling-based approach used for the isolation of optimised CCA's is described here, termed the “Alloys-By-Design” (ABD®) method. This approach utilises a framework of computational materials models to estimate design relevant properties across a very broad compositional space. In principle, this alloy design tool allows the so-called inverse problem to be solved; identifying optimum alloy compositions that best satisfy a specified set of design constraints.

The first step in the design process is the definition of an elemental list along with the associated upper and lower compositional limits. The compositional limits for each of the elemental additions considered in this invention-referred to as the “alloy design space”—are detailed in Table 2.

The starting point is that at least three different elements should be present (though at least four elements are likely to be needed to ensure high enough entropy) meaning that each element can be present up to 35 at %. Titanium was allowed to increase up to 40 at % because of its importance in reducing VEC. The only elements which reduce VEC are aluminium, zirconium and titanium. However excessive amounts of aluminium can lead to a loss in high temperature strength as it has a much lower melting point that the other two alloys. Zirconium is limited in order to reduce the chance of intermetallic phase formation. Thus titanium is the only of these elements which can be used in very high amounts to reduce VEC. If a very high entropy alloy is desired, the amount of titanium can be reduced to 35 at % or less.

Certain elements are restricted below 35 at % based on an understanding on their likely effect in practice, particularly on oxidation behaviour. In order to produce a continuous alumina scale, a substantial aluminium content in the alloy is used. Based on the known properties of prior art alloys, a minimum aluminium content of 20 at % is used as this will allow for an equivalent oxidation resistance to the alloys in Gorr et al. High-Temperature Oxidation Behaviour of Refractory High-Entropy Alloys: Effect of Alloy Composition, Oxid. Met. (2017) 88:339-349. Any increases in aluminium content beyond this level are desirable because they will increase the supply of aluminium atoms for scale formation and hence minimise the duration of the vulnerable transient period during which oxide is forming. Increases in aluminium content to 21 at. % or more or 22 at. % or more are preferred to increase oxidation resistance further. More preferably the minimum aluminium content of the present invention is 23 at. %, because this will allow for a superior oxidation resistance and exceed the levels in Cao et al Effects of Al and Mo on high temperature oxidation behaviour of refractory high entropy alloys, Trans. Nonferrous Met. Soc. China 29 (2019) 1476-1483.

High levels of niobium have been observed to correlate with severe pesting oxidation in the ternary system Al—Nb—Ti, which is a representative system of the wider RCCA design space. It has been reported that severe pesting oxidation occurs for niobium content of 42 wt % and higher (Chen et al., Oxidation of Intermetallic Alloys in Ti—Al—Nb Ternary System, Corrosion-Vo. 48, No. 11, 1992, National Association of Corrosion Engineers). This is equivalent to 20 at % for these alloys. This invention encompasses alloys with 20 at % or less niobium. A reduced amount of niobium of 16 at % or less will further reduce the chance of pesting. Much lower mass gain due to pesting oxidation is reported for niobium as low as 30 wt %, equivalent to 13 at %. It is preferable for this reason that niobium levels to be equal to or less than 13 at %.

In addition to having intrinsic ductility, the present invention also encompasses alloys with a low volume fraction of detrimental intermetallics. The presence of zirconium is known to lead to the formation of intermetallics with aluminium (Soni et al., Phase stability as a function of temperature in a refractory high-entropy alloy, J. Mater, Res., 2018; Tsai et al., Intermetallic Phases in High-Entropy Alloys: Statistical Analysis of their Prevalence and Structural Inheritance, Metals 2019, 9, 247). On this basis, an upper limit of 16.7 at % zirconium content is applied in this invention.

Hafnium is not a principal element in the composition space due to being difficult to source, but it's ability to scavenge oxygen and lower ductile-to-brittle transition temperature make it able to impart useful properties on a RCCA (Tsakiropoulos, 2022). Based on the Hf—Nb phase diagram, above 10.0 at % hafnium, it will promote the formation of second, hafnium-rich, phase. It is therefore required for hafnium to be present in levels of 10.0 at % or lower. The high temperature niobium alloy, C103, has composition of Nb-10Hf-1Ti (wt %), which is equivalent to 5.5 at % hafnium. It is therefore preferable for hafnium to be present in levels of 5.5 at % or lower. Preferably hafnium is present at levels of 1.0 at. % or less. In an embodiment it is preferable for hafnium to be absent (e.g. at the level of incidental impurities).

The main refractory elements in this invention (Mo, Nb, Re, Ta, Ti, V, W and Zr) have a low solubility for silicon (3, 5, 10, 5, 5, 7, 4, 0 at %, respectively). Beyond the solubility limit, silicide phases, e.g. M3Si, can form. At low volume fractions, these silicide phases can increase yield strength substantially. However, the silicides fracture in a brittle manner, so a high volume fraction or continuous network of the phase through a microstructure are severely detrimental to fracture toughness. To avoid excessive formation of silicides, Si concentration should be kept below 5.0 at %, as this corresponds to the limits for Nb, Ta and Ti. Preferably silicon will be 3.0 at % or lower, even more preferably 1.0 at % or lower, most preferably 0 at % (e.g. at the level of incidental impurities), as this will remove any possibility of very brittle silicides forming.

TABLE 2
Alloys design space in at % searched using the
“Alloys-by-Design” method.
	Element (at %)	Min	Max
	Al	20	35
	Co	0	35
	Cr	0	35
	Cu	0	35
	Fe	0	35
	Hf	0	10
	Ir	0	35
	Mn	0	35
	Mo	0	35
	Nb	0	20
	Ni	0	35
	Pd	0	35
	Pt	0	35
	Re	0	35
	Rh	0	35
	Ru	0	35
	Si	0	5
	Ta	0	35
	Ti	0	35
	V	0	35
	W	0	35
	Zr	0	16.7

The selection of alloys relies upon calculating merit indices for the alloys within the alloy composition space. Examples of these merit indices include entropy (which relates to the propensity for the elements within the alloy to form a solid solution structure and so relates to strength and creep resistance), valence electron concentration (which relates to the resistance to intermetallic phase formation and so good ductility), Pilling-Bedworth index, melting point index, density and cost.

In the second stage, the calculated merit indices over the whole space defined in table 2 are compared with limits for required behaviour for configurational entropy and valence electron concentration and these design constraints are considered to be the boundary conditions to the problem. All compositions which do not fulfil the boundary conditions are excluded. At this stage, the alloy space will be reduced in size.

In the third stage the dataset of remaining compositions was analysed and example compositions which have favourable merit indices compared to prior art alloys were prepared. Further limits to the alloy scope were made as a result of experimental observations.

Merit Index Descriptions

The example merit indices are now described.

The first merit index is the entropy index. A sufficiently high entropy of mixing for solid solution enhances stability of the solid solution, relative to the formation of intermetallic phases. This stability often extends to elevated temperatures and can increase ease of processing. Entropy is given by

$\begin{array}{cc}\mathrm{Entropy}=-R·{\sum }_i{x}_i·\ln \left(x_i\right)& \left(2\right)\end{array}$

where x_i is the atomic fraction of element i in the alloy and R is the universal gas constant.

The solid solution structure of RCCAs is stabilised by the high entropy effect, which simplifies the microstructure significantly, compared with what would be expected of the constituent binary and ternary systems. Entropy of RCCAs is dominated by configurational entropy. There exist a number of competing definitions of the threshold of configurational entropy at which an alloy is considered a high-entropy-alloy, benefitting from the high entropy effect. The first definition is for configurational entropy of a value of 1.5R (12.47) or greater, where R is the universal gas constant, with value 8.3145 J K⁻¹ mol⁻¹. (Murty et al., 2019) [4] A further definition is for configurational entropy of a value of ln (5) R (13.38) or greater, based on an alloy composed of five or more principal elements in equiatomic ratios [5]. Some studied HEA compositions have been 5 element equiatomic, including but not limited to Gorr 1, 2, 3 and Miracle 2 in Table 1. These compositions have been reported to benefit from the high entropy effect, and their configurational entropy is thus a promising starting point from which to improve. [2], [3] Thus the present invention requires a configurational entropy of 13.38 or more. To further improve these properties, this invention more preferably requires entropy equal to or greater than 13.5 to promote even greater stability of the solid solution as well as increase lattice distortion and sluggish diffusion, which increase strength and creep resistance, respectively. As can be seen from table 9 below, alloys with configurational entropies of 13.8 and above have been designed and these are preferred.

The second merit index is the valence electron concentration index. The Valence Electron Concentration describes the number of electrons in the outer electron shell of an atom given by

$\mathrm{VEC}=\sum _i{x}_i·{\mathrm{VEC}}_i$

where x_i is the atomic fraction of element i in the alloy bulk composition and VEC_i is the valence electron concentration of element i. [6] A low VEC is indicative of an alloy which is predominantly BCC phase resulting in an alloy with high ductility. The number of electrons in the outer shell is given in table 3 below:

TABLE 3
Element VECi
Al      3
Co      9
Cr      6
Cu      11
Fe      8
Hf      4
Ir      9
Mn      7
Mo      6
Nb      5
Ni      10
Pd      10
Pt      10
Re      7
Rh      9
Ru      8
Si      4
Ta      5
Ti      4
V       5
W       6
Zr      4

Valence Electron Concentration is reported to be a good predictor of crystal structure in high entropy alloys (Tsai et al., Criterion for sigma phase formation in Cr- and V-containing high-entropy alloys. Mater. Res. Lett. 2013, 1, 207-212), where VEC<6.87 corresponds to predominantly BCC phase, sigma-free alloys. It has also been reported [8] that further restriction of VEC can promote intrinsic ductility in single-phase BCC high entropy alloys. Brittle behaviour was absent for VEC<4.6 and this is a design requirement for the present invention. A preferable VEC is 4.4 or less as this ensures ductile behaviour.

The third merit index is the Pilling-Bedworth index. This is an indicator of the volume of the oxide relative to the volume of the underlying alloy. The alloy of the present invention is required to have excellent oxidation resistance at temperatures exceeding 1100° C. In this regime a passivating alumina oxide scale (Al₂O₃) is a suitable means of protecting the alloy against further oxidation damage. During the initial stages of oxidation, multiple elements react simultaneously to form a mixed oxide. In this stage, the oxide mechanical stability is determined by the relative volume of the oxide scale to the alloy substrate, as described by the Pilling Bedworth ratio. A high Pilling Bedworth ratio indicates oxide volume is much larger than alloy volume, inducing compressive stresses in the oxide, promoting spallation. Repeated spallation exposes unprotected metal to the atmosphere, preventing a continuous protective alumina layer from forming.

For high values of P—B index (>2) the oxide is likely to spall, due to it's large volume relative to the alloy. For low values (<1) the oxide is likely to be too thin to provide protection to the underlying alloy. The Pilling-Bedworth index is given by

$\begin{array}{cc}\stackrel{\_}{R_{\mathrm{PB}}}={\sum }_i{x}_i·R_{\mathrm{PB}}^i& \left(3\right)\end{array}$

where x_i is the atomic fraction of element i in the alloy and R_PBⁱ is the Pilling-Bedworth ratio for element i. The Pilling-Bedworth ratio depends on stoichiometry and density of oxide. For elements with multiple oxide species, the most stable was used. Table 4 sets out the Pilling-Bedworth ratios for the elements in the alloy:

	TABLE 4
		Oxide
	Element	species	RPBi
	Al	Al2O3	1.279603
	Co	CoO	1.754464
	Cr	Cr2O3	2.013115
	Cu	CuO	1.776089
	Fe	Fe3O4	2.176389
	Hf	HfO2	1.621499
	Ir	IrO2	2.256926
	Mn	Mn3O4	2.059621
	Mo	MoO2	2.118827
	Nb	Nb2O5	2.665129
	Ni	NiO	1.699602
	Pd	PdO	1.666654
	Pt	PtO2	2.442192
	Re	Re2O7	4.480021
	Rh	Rh2O3	1.866379
	Ru	RuO2	2.351768
	Si	SiO2	2.264630
	Ta	Ta2O5	2.486122
	Ti	TiO2	1.777194
	V	V2O5	3.190773
	W	WO3	3.390671
	Zr	ZrO2	1.550566

The fourth merit index is the melting point index. For high temperature application, melting of the alloy should be avoided, so a high melting point is required. In addition, high temperature strength and creep resistance is best when melting point is high. Melting point T_m is given by

$\begin{array}{cc}\mathrm{Tm}={\sum }_i{x}_i·T_{\mathrm{mi}}& \left(4\right)\end{array}$

where x_i is the atomic fraction of element i in alloy bulk composition and T_mi is the melting point of pure element i. Table 5 gives the melting points of the elements in the alloy:

TABLE 5
Element Tmi
Al      933
Co      1768
Cr      2136
Cu      1358
Fe      1811
Hf      2504
Ir      2720
Mn      1519
Mo      2896
Nb      2742
Ni      1728
Pd      1828
Pt      2042
Re      3459
Rh      2236
Ru      2607
Si      1687
Ta      3293
Ti      1943
V       2183
W       3695
Zr      2128

The fifth merit index is density. The density, ρ was calculated using a simple rule of mixtures and a correctional factor, where, ρ_i, is the density for a given element and x_i is the atomic fraction of the alloy element. Table 6 gives the densities of the elements involved.

$\begin{array}{cc}\rho ={\sum }_i{x}_i{\rho }_i& \left(7\right)\end{array}$

TABLE 6
Element ρi
Al      2.7
Co      8.9
Cr      7.22
Cu      8.96
Fe      7.874
Hf      13.3
Ir      22.7
Mn      7.47
Mo      10.22
Nb      8.57
Ni      8.902
Pd      12.0
Pt      21.1
Re      21
Rh      12.5
Ru      12.4
Si      2.3
Ta      16.65
Ti      4.508
V       6.11
W       19.3
Zr      6.52

The sixth merit index is cost. In order to estimate the cost of each alloy a simple rule of mixtures was applied, where the atomic fraction of the alloy element, x_i, was multiplied by the current (2021) raw material cost for the alloying element, c_i, in USD/mol.

$\begin{array}{cc}\mathrm{Cost}={\sum }_i{x}_i{c}_i& \left(8\right)\end{array}$

The estimates assume that processing costs are identical for all alloys, i.e. that the product yield is not affected by composition. Table 7 gives the costs of all elements involved:

TABLE 7
Element ci
Al      0.048
Co      1.933
Cr      0.489
Cu      0.381
Fe      0.024
Hf      160.6
Ir      10735.3
Mn      0.100
Mo      3.848
Nb      6.829
Ni      0.816
Pd      5267.8
Pt      5423.3
Re      666.621
Rh      15127.1
Ru      1061.2
Si      0.0
Ta      55.189
Ti      0.543
V       18.899
W       6.490
Zr      3.320

On the basis of initial modelling results, the present inventors realised that table 2 encompasses alloys with a volume fraction of detrimental intermetallics at a level which would detrimentally influence ductility. On this basis, the ratio of zirconium to aluminium content (in at %) was used to gauge intermetallic phase formation. Thermodynamic calculations predict the formation Al₃Zr₂, Al₄Zr₅, Al₂Zr₃, Al₃Zr₅, in the alloy space shown in Table 2. These have Zr/Al ratios of ˜0.7, 1.2, 1.5, 1.7, respectively. With a Zr/Al ratio equal to or less than 0.7, supplying the optimal stoichiometry of Zr and Al for the formation of the predicted intermetallics can be avoided. This is the seventh merit index. Reducing the Zr/Al ratio even further reduces the chance of Al_xZr_y intermetallic formation even further and so a Zr/Al ratio of 0.45 or less is preferred, or even more preferably the Zr/Al ratio is 0.3 or less.

The ABD method described above was used to isolate alloy compositions which met the required entropy and VEC criteria described above and which showed promising other characteristics as defined by the third to seventh merit indices.

Cobalt, copper, iron, manganese, nickel, platinum, palladium, ruthenium, rhodium and iridium have the highest VEC of the elements in Table 2. FIG. 1 is a series of plots showing the alloys in the space of table 2. Plotted on the y-axis is the amount of certain elements and on the x-axis the VEC. As can be seen, in order to achieve a VEC of 4.6 or less these elements need to be kept below the following concentrations in the alloy to ensure ductility:

• • A_Co<5; A_Cu<5; A_Fe<10; A_Mn<10; A_Ni<5; A_Pt<5; A_Pd<5; A_Ru<10; A_Rh<5; A_Ir<5;

Where A_Co, A_Cu, A_Fe, A_Mn, A_Ni, A_Pt, A_Pd, A_Ru, A_Rh, A_Ir are the atomic percent of cobalt, copper, iron, manganese, nickel, platinum, palladium, ruthenium, rhodium and iridium in the alloy, respectively. It is even more preferable to further reduce the content of the elements, to reach even lower VEC levels. Thus copper is preferably kept at a level of 3 at % or less, or even 0 at %. Manganese is preferably kept at a level of 7 at % or less or even 5 at % or less, or even 0 at %. Cobalt is kept at 3 at % or less in a preferred embodiment and at 2 at % or less in a further preferred embodiment, or even 0 at %. Iron is preferably reduced to 7 at % or less or even 5 at % or less to reduce VEC, or even 0 at %. For the same reason nickel is preferably kept low, for example to 4 at % or less or 3 at % or less or even 1at % or less nickel, or even 0 at %. Platinum is preferably kept below 3 at % or even 0 at %. Palladium is preferably kept below 3 at % or even 0 at %. Ruthenium is preferably kept below 10 at % or 8 at % or 5 at % or even 3 at %. In an embodiment it would be preferable for ruthenium to be absent other than in trace amounts. Rhodium is preferably kept below 3 at % or even 0 at %. Iridium is preferably kept below 3 at % or even 0 at %.

The modelling results indicate that for Al, V, W, Cr, Ti, Ta, Mo, Zr, Nb, Hf, Si VEC≤4.6 is achievable throughout the ranges of table 2 and so these were assumed to be allowable.

Rhenium has a higher melting point than Ta and Nb, and higher melting point than W. Due to this, rhenium can impart similar high temperature strength on an alloy, so can substitute for Ta, W and Nb. Therefore, 35 at % or less of rhenium is permitted, provided A_Re≤(35−A_Ta)+(35−A_W)+(20−A_Nb) and where A_Re, A_Ta, A_W and A_Nb are the amounts in atomic percent of rhenium, tantalum, tungsten and niobium respectively. Rhenium is very difficult to source, resulting is a high elemental cost, it also has high density and elemental Pilling-Bedworth ratio, meaning an oxide is more likely to spall. For this reason, it is preferable for rhenium content to be 20 at % or less, more preferably 15 at % or less, or most preferably 10 at % or less or even 5 at % or less. To achieve particularly high melting point, a minimum rhenium content of 3 at % or even 5 at % or more is preferred, at the expense of cost, density and oxidation resistance, as described above.

Table 8 and 9 set out compositions of prior art alloys and some example alloys and the calculated merit indices.

TABLE 8
Nominal compositions in at % of the newly designed refractory complex
concentrated alloys, compared with the alloys listed in Table 1.
Alloy
(at %)	Al	Co	Cr	Cu	Fe	Mn	Mo	Nb	Ni	Ta	Ti	V	W	Zr
Gorr 1	20	0	20	0	0	0	20	0	0	0	20	0	20	0
Gorr 2	20	0	20	0	0	0	20	20	0	0	20	0	0	0
Gorr 3	20	0	20	0	0	0	20	0	0	20	20	0	0	0
Miracle 1	0	0	0	0	0	0	25	25	0	25	0	0	25	0
Miracle 2	0	0	0	0	0	0	20	20	0	20	0	20	20	0
Cao 1a	0	0	0	0	0	0	0	28.57	0	14.29	28.57	0	0	28.57
Cao 1b	0	0	0	0	0	0	0	27.76	0	16.88	30.75	0	0	24.61
Cao 2a	22.22	0	0	0	0	0	0	22.22	0	11.11	22.22	0	0	22.22
Cao 2b	19.35	0	0	0	0	0	0	22.48	0	12.59	23.5	0	0	22.08
Cao 3a	20	0	0	0	0	0	10	20	0	10	20	0	0	20
Cao 3b	18.82	0	0	0	0	0	8.67	21.55	0	10.2	21.87	0	0	18.89
RHG2A	30	0	0	0	0	0	11	15	0	9	23	0	7	5
RHG2B	30	0	0	0	0	0	11	19	0	5	23	0	7	5
RHG2D	22	0	5	0	0	0	0	19	0	5	35	0	5	9
RHG2E	22	0	5	0	0	0	0	19	0	5	33	0	7	9
RHG2G	30	0	0	0	0	0	11	15	0	7	23	0	9	5
RHG2H	30	0	0	0	0	0	7	15	0	9	29	0	5	5
RHG2I	27	0	0	0	0	0	13	15	0	9	27	0	0	9
RH2400	20	0	0	0	0	0	20	6	0	30	9	0	0	15
RHG100A	35	0	0	0	0	0	7	9	0	9	25	0	0	15
RHG100B	30.8	0	0	0	0	0	5	0	0	25	5	5	24.2	5
RHG100C	33	0	5	0	5	0	0	5	5	27	15	0	0	5
RHG100D	28	0	0	0	0	0	15	7	0	25	5	5	0	15
RHG100E	33	0	0	0	0	0	0	5	0	5	25	5	17	10
RHG100F	27.6	0	0	0	0	0	5	17	0	23	20	0	7.4	0
RHG100G	21.6	0	0	0	0	0	17	9	0	15	25	0	7.4	5
RHG100H	33.8	0	5	0	5	5	0	5	0	19	0	0	12.2	15
RHG100I	25.6	0	0	0	0	0	5	5	0	25	0	5	19.4	15
RHG100J	34.2	1	0	0	0	0	5	17	0	22	12.5	0	0	8.3
RHG100K	34.7	1	0	3	0	0	0	17	0	11	25	0	0	8.3
RHG100L	32.7	4.5	0	1	0	0	0	17	0	0	25	0	11.5	8.3
RHG2M	29	29	13	0	5	0	5	0	5	0	0	7	7	0
RHG2C	30	0	0	0	0	0	7	23	0	5	25	0	5	5
RHG1C	33.2	0	14.2	0	13.8	0	10.7	0	14.0	0	0.1	0	0.0	14.0
RHG1F	27.0	10.5	3.6	0	0	7.0	7.0	0.1	3.2	0	36.0	0.2	1.5	3.8
RHG1H	3.6	0.2	1.6	0	0.2	0.3	21.2	17.2	0	0	2.6	0	53.2	0
RHG1R	34.6	0	4.8	5.1	0	4.0	21.8	0	0	0	14.0	5.1	5.4	5.2

TABLE 9
Calculated merit indices made with the “Alloys-by-Design”
software. Results for conventional RCCAs listed in Table 1 and
newly designed RCCAs compared with the alloys listed in Table 1.
Alloy	Sconfig	ρ	Tm	VEC	RPB	RZr, Al	Cost
Gorr 1	13.38	9.13	1878	5.00	2.12	0	2.28
Gorr 2	13.38	6.90	1832	4.80	1.97	0	2.35
Gorr 3	13.38	8.81	1950	4.80	1.94	0	12.02
Miracle 1	11.53	14.30	1911	5.50	2.67	—	18.09
Miracle 2	13.38	12.96	2321	5.40	2.77	—	18.25
Cao 1a	11.24	8.28	2417	4.43	2.06	—	10.94
Cao 1b	11.34	8.49	2438	4.45	2.08	—	12.20
Cao 2a	13.15	7.20	2087	4.11	1.89	1.00	8.52
Cao 2b	13.20	7.44	2138	4.16	1.91	1.14	9.35
Cao 3a	14.53	7.50	2168	4.30	1.92	1.00	8.05
Cao 3b	14.53	7.52	2181	4.30	1.93	1.00	8.18
RHG2A	14.79	7.77	2118	4.30	1.96	0.17	7.17
RHG2B	14.49	7.42	2096	4.30	1.97	0.17	5.24
RHG2D	13.99	6.86	2054	4.22	1.94	0.41	4.91
RHG2E	14.28	7.14	2089	4.26	1.97	0.41	5.02
RHG2G	14.79	7.79	2126	4.32	1.98	0.17	6.20
RHG2H	14.19	7.25	2045	4.18	1.91	0.17	6.92
RHG2I	14.05	7.00	2052	4.23	1.86	0.33	6.95
RH2400	13.93	9.48	2412	4.56	1.98	1.98	18.29
RHG100A	13.45	6.04	1877	3.97	1.74	0.43	6.50
RHG100B	13.73	11.03	2462	4.58	2.27	0.16	16.71
RHG100C	14.57	8.02	2016	4.59	1.87	0.15	15.57
RHG100D	14.62	8.56	2236	4.39	1.97	0.54	16.34
RHG100E	14.08	7.52	2045	4.16	2.02	0.30	5.63
RHG100F	13.79	8.87	2288	4.37	2.09	0.00	14.65
RHG100G	15.15	8.47	2300	4.51	2.02	0.23	10.34
RHG100H	15.15	8.97	2121	4.60	2.00	0.44	12.16
RHG100I	14.53	10.82	2489	4.58	2.24	0.59	17.05
RHG100J	13.83	7.75	2092	4.20	1.91	0.24	13.87
RHG100K	13.43	6.25	1873	4.19	1.81	0.24	7.69
RHG100L	13.75	6.72	1952	4.37	1.93	0.25	2.43
RHG2M	15.01	7.54	1794	6.23	1.90	0	2.65
RHG2C	13.98	7.07	2055	4.22	1.96	0.17	5.24
RHG1C	14.24	6.27	1715	5.56	1.70	0.42	1.08
RHG1F	14.74	5.68	1738	4.94	1.72	1.72	1.01
RHG1H	10.73	14.29	3181	5.68	2.85	2.85	5.47
RHG1R	15.50	6.59	1880	4.82	1.85	1.85	2.47

The RHG2 alloys were manufactured and their properties investigated. On the basis of experimental results, the following further limitations are imposed on the inventive alloy.

The addition of vanadium is beneficial for raising configuration entropy without detrimentally affecting the other merit indices due to its moderate valence electron concentration (described above), low density and high melting point. In corrosive environments the formation of VO_x, particularly the V₂₀₅ oxide phase has detrimental effects on the alloy. The oxide species can form a low melting point eutectic which accelerates corrosion [10]. Thus, a lower vanadium content is preferable. In RHG2M a continuous layer of VO_x was observed to form during the early stages of oxidation (FIG. 2). Two alloys (RHG1F and RHG1R) with lower vanadium content show no evidence of a dense VO_x layer during the early stages of oxidation, just a mixed oxide, which is not detrimental to corrosion resistance. RHG1F and RHG1R contain 0.2 and 5.1 at % vanadium, respectively, as measured using ICP-OES. These alloys are outside the main claim of the invention, due to their high VEC. This relates to alloy ductility, as described above. Despite this, their oxidation behaviour is representative of the invention due to a combination of high aluminium and refractory content. Further alloys with high vanadium content (Table 10) have similarly been observed to form V₂O₅, as captured in FIG. 3. Alloys L1, L2 and L3 were oxidised for 20 h at 1300° C., and alloy E1 was oxidised at 900° C. [9], All alloys which formed V₂O₅ contain greater than or equal to 7 at % vanadium. To avoid VO_x layer formation, this invention encompasses alloys with a vanadium content of 7 at % or lower, preferably 5.1 at % or lower, even more preferably 3.0 at % or lower.

TABLE 10
Nominal composition in at % of alloys referenced in FIG. 3 (V limit)
Alloy
(at %)	Al	Cr	Mo	Nb	Ti	V	W	Zr	Si	Mn	Cu	Co	Ni	Fe
RHG1F	27.0	3.6	7	0.1	36	0.2	1.5	3.8	0	7.1	0	10.5	3.2	0
RHG1R	34.6	4.8	21.8	0	14	5.1	5.4	5.2	0	4	5.1	0	0	0
RHG2M	29	13	5	0	0	7	7	0	0	0	0	29	5	5
L3	6.96	16.95	17.14	17.68	18.26	17.32	0	0	5.69	0	0	0	0	0
L2	8.15	18.92	18.08	18.35	18.12	18.38	0	0	0	0	0	0	0	0
L1	10.15	23.04	22.16	22.50	0	22.15	0	0	0	0	0	0	0	0
E1	25	25	0	0	25	25	0	0	0	0	0	0	0	0

Preferably the Pilling Bedworth ratio is a value of 2.000 or less, in order to certainly form a mechanically stable oxide. The elements W, V, Ta and Nb form oxides with high Pilling Bedworth ratios, so promote spallation more than the other elements in Table 2.

The calculations to derive the data in FIGS. 4 to 6, 9 and 11 and the associated relationships described below hafnium, silicon, platinum, palladium, ruthenium, iridium and rhodium additions from the possible alloys. Therefore in a preferred embodiment, the alloy does not have any hafnium, silicon, platinum, palladium, ruthenium, iridium and rhodium additions and the relationships described below apply throughout such an alloy range.

FIG. 4 are plots in the alloy space of table 2 showing Pilling Bedworth ratio as grey scale for varying W and V (upper) and Ta and Nb (lower) concentration. The lines in FIG. 4 upper and lower show the position of alloys with a PB ratio of 2.000. For a value less than or equal to 2.000, the following relationships should be obeyed:

$A_V+1.15A_W\le 28.9,\mathrm{resulting}\mathrm{in}{A}_W\le 25.1\mathrm{at}\%\mathrm{in}\mathrm{the}\mathrm{absence}\mathrm{of}\mathrm{vanadium}\mathrm{and}\le 19.\mathrm{when}\mathrm{vanadium}\mathrm{is}\mathrm{limited}\mathrm{to}7\mathrm{at}\%.$ $A_{\mathrm{Nb}}+0.83A_{\mathrm{Ta}}\le 42.5$

Reducing PB ratio to lower values, below 2.000 is preferable because the difference between oxide and alloy volume is even lower, so even less compressive stress is induced in the oxide, reducing probability of spallation. Thus the PB ratio is preferably 1.98 or lower or even 1.95 or lower.

The addition of chromium is beneficial for corrosion resistance in certain applications, such as industrial gas turbines. In these cases, this invention contains some chromium, for example at least 1 at % or 2 at % or even 3 at % and the alloy preferably has chromium levels greater than 5 at % or even 10 at % or more. Further increasing chromium levels increases the supply of chromium atoms to the surface, further improving corrosion resistance. Excessive chromium can promote the formation of Laves and Cr-rich phases, so reduction in chromium levels will reduce likelihood of formation. An upper limit of 25 at %, 20 at % or even 15 at % is preferable. Most preferably chromium is limited to 10 at % or less.

The addition of titanium is beneficial for lowering Valence Electron Concentration, but excess titanium can promote rapid growth of an external TiO₂ layer, which reduces the capability of forming protective alumina layer, and removes titanium from the matrix, destabilising the microstructure. Titanium content is therefore preferably 33 at % or lower, more preferably 30 at % or lower. Further reduction of titanium beyond these levels is even more beneficial because it reduces the supply of titanium atoms available to form TiO₂ on the surface. Thus titanium is present in an amount of 25 at % or less in one embodiment and at 20 at % or less in another embodiment.

The addition of molybdenum is beneficial for raising the melting point of the alloy, but in high quantities there is a high probability of forming volatile oxide species, such as MoO₃, which is detrimental for oxidation. Mass loss behaviour, due to volatilisation of MoO₃, has been recorded for alloys Ma1, Ma2, Ma3, Ma4 and Z1, which have compositions defined in Table 11. [11], [12] Further to this, alloys Mu1, Mu2 and Mu3, have demonstrated destruction of oxide due to MoO₃ volatilisation. All of these oxides reported to form MoO₃ have molybdenium content of 20 at % of greater. [13] It is therefore preferable for molybdenum content to be 20 at % or lower or even 15 at % or lower. Even more preferably molybdenum is present in an amount of 12 at % or less even 7 at % or less.

TABLE 11
Nominal composition in at % of Mo-containing alloys
	Alloy
	(at %)	Mo	Al	Cr	Ti	Nb	Ta
	Ma1	100	0	0	0	0	0
	Ma2	75	25	0	0	0	0
	Ma3	20	80	0	0	0	0
	Ma4	27	73	0	0	0	0
	Z1	30.8	7.7	30.8	30.8	0	0
	Mu1	20	20	20	20	20	0
	Mu2	25	25	25	0	25	0
	Mu3	25	25	25	0	0	25

It is desirable to minimise the density. This is done by controlling the content of additions of elements with high atomic mass, particularly tungsten and tantalum. The relationship between the levels of these two elements and predicted alloy density is shown in FIGS. 5a-c. A maximum target alloy density of 10 g/cm³ or less, to be lower than FS85, is achieved when:

$A_W+0.8A_{\mathrm{Ta}}\le 37.8\mathrm{at}\%$

Where A_W and A_Ta and the content of tungsten and tantalum in the alloy, respectively, in atomic percent. More preferably the alloy density is 9 g/cm³ or less, to be lower than C103, as this results in lighter parts which require less creep strength when used in rotating applications. This is achieved when:

$A_W+0.72A_{\mathrm{Ta}}\le 26.8\mathrm{at}\%$

This requires A_W to be less than 26.8. Most preferable maximum alloy density is 8 g/cm³ or less, to be lower than CMSX-4, corresponding to:

$A_W+0.6A_{\mathrm{Ta}}\le 20\mathrm{at}\%$

This requires A_Ta and A_W to be less than 33.3 and 20, respectively.

Of the elements in the invention design space, aluminium, zirconium and titanium are the only constituents with an elemental VEC lower than the target of 4.6 for the alloy, excluding hafnium and silicon. A minimum quantity of these elements is required to meet the VEC target of 4.6 or lower as well as the entropy target, the Pilling-Bedworth target and the density target, as shown in FIG. 6. When the design space is restricted in that way the requirement for these lower VEC elements is:

$A_{\mathrm{Al}}+A_{\mathrm{Zr}}+A_{\mathrm{Ti}}\ge 41\mathrm{at}\%$ $\mathrm{As}\mathrm{Al}<35\%,\mathrm{Zr}+\mathrm{Ti}\mathrm{are}\mathrm{preferably}\ge 6\mathrm{at}\%.$

It is preferred that aluminium, zirconium and titanium levels are increased to levels even higher than those above, to reach even lower VEC, making ductility even better. For example, to achieve a VEC of 4.05 or lower, the following is required:

$A_{\mathrm{Al}}+A_{\mathrm{Zr}}+A_{\mathrm{Ti}}\ge 60\mathrm{at}\%$

FIG. 7 shows three regions in zirconium content. The plotted points are labelled T1, T2, T3 . . . , corresponding to alloys in Table 11, as defined in Metals 2019 article. [14] Additional plotted points are labelled 2D, 2E, corresponding to alloys RHG2D and RHG2E, respectively, as defined in Table 8. RHG2D and RHG2E were both found to be absent of Al—Zr-based intermetallics, as shown in FIG. 8. All alloys reported to form Zr—Al intermetallics contain greater than or equal to 16.7 at % zirconium. This invention encompasses alloys with zirconium content equal to or less than 16.7 at %, to avoid Zr—Al intermetallic formation. T7, RHG2D and RHG2E all contain both Al and Zr, but Zr—Al intermetallics were not observed. It is therefore preferable for the alloys encompassed by this invention to contain less than or equal to 11.1 at % zirconium or even 10 at % or less zirconium. Preferably, like examples 2E and 2D where Al—Zr intermetallics are absent, zirconium is present at 9 at % or less.

TABLE 11
Nominal composition in at % of alloys referenced in FIG. 7 (Zr limit)
Alloy
(at %)	Al	Zr	V	Cr	Fe	Ni	Ti	Ta	Nb	Mo	Mn
T1	20	0	0	20	0	0	20	0	20	20	0
T2	10	0	10	20	0	0	40	0	20	0	0
T3	16.7	16.7	16.7	16.7	0	0	16.7	0	16.7	0	0
T4	12.3	0	0	0	34.0	17.0	5.66	0	0	0	31.1
T5	20	20	0	0	0	0	20	10	20	10	0
T6	20	20	0	0	0	0	20	20	20	0	0
T7	22.2	11.1	22.2	0	0	0	33.3	0	11.1	0	0
T8	20	20	20	0	0	0	20	0	20	0	0
T9	27.3	18.2	18.2	0	0	0	18.2	0	18.2	0	0

The alloy of the invention is designed to have good ductility, but also good mechanical strength and creep resistance at elevated temperature. Strength correlates with both entropy (as mentioned earlier) and melting point, meaning melting point should be maximised. In addition, creep rate becomes most severe at homologous temperatures exceeding 0.6:

$\mathrm{Homologous}\mathrm{temperature},\frac{T}{T_m}>0.6$

Where T is the environmental temperature and T_m is the melting point. In order to reduce the homologous temperature, and thus the creep rate, T_m can be maximised. This can be achieved by maximising the melting temperature index (defined earlier). As can be seen from table 9, this invention encompasses alloys with melting temperatures index exceeding 1800K or even 2000K and even above 2100K and 2200K and these are preferred limits. Alloys with a melting temperature index of 2400K or more and even 2450K (or 2500K) or more are also shown to be possible and in one embodiment are preferred. These correspond to a minimum quantity of refractory elements in the alloy, see FIG. 9, defined by a W-equivalent, where A_W, A_Ta, A_Mo, A_Nb are the concentration of tungsten, tantalum, molybdenum and niobium in the alloy in atomic percent:

$W_{\mathrm{eq}}=A_W+A_{\mathrm{Ta}}+A_{\mathrm{Mo}}+A_{\mathrm{Nb}}$

For melting point index to exceed 1800K, 2000K, 2200K, 2400K and 2500K, W_eq must roughly exceed 10, 13, 26, 39 and 50, respectively, and the following equations should be obeyed (derived through FIG. 9). More accurately, for melting point index greater than:

$1800K,W_{\mathrm{eq}}\ge 10$ $2000K,W_{\mathrm{eq}}\ge 0.75A_{\mathrm{Al}}-4.75$ $2200K,W_{\mathrm{eq}}\ge 0.75A_{\mathrm{Al}}+8.75$ $2400K,W_{\mathrm{eq}}\ge 0.8A_{\mathrm{Al}}+23$ $2500K,W_{\mathrm{eq}}\ge 1.25A_{\mathrm{Al}}+21.25$

A trade-off also exists between melting point and density, shown in FIG. 10. As the melting point lower limit is raised, the lowest achievable density is also raised. Similarly, as density upper limit is lowered, the maximum achievable melting point is lower. Balancing these properties is part of the invention because high density induces higher stresses during rotation, but reducing density corresponds to a reduction in melting point, which will lower the strength and creep strength, reducing the ability of the alloy with withstand the loading.

It is desirable for the present invention to be competitive on a cost basis with existing refractory and nickel-based superalloys. Maximum elemental alloy cost is desirably less than 8.00 USD/mol, corresponding to an elemental cost lower than FS85, C103 and CMSX-4, preferably elemental cost will be lower than 6.50 USD/mol and more preferably it will be lower than 5.00 USD/mol. Vanadium and tantalum are the elements with the highest elemental cost. The relationship between the levels of these two elements and alloy cost is shown in FIG. 11 and leads to a model that can be described as follows:

$f\left(\mathrm{cost}\right)=A_V+3A_{\mathrm{Ta}}$

• • where A_V and A_Ta are the atomic percent of vanadium and tantalum in the alloy, respectively. f(cost) is a numerical value which must be 75 or lower in order to lead to a cost index of 14.00 or less, requiring A_Ta to be less than 25. Preferably f(cost) is 64 or lower for a cost index of 12.00 or less, requiring A_Ta to be less than 21.3. More preferably f(cost) is 53 or lower for a cost index of 10.00 or less, requiring A_Ta to be less than 17.7. Even more preferably f(cost) is 42 or lower for a cost index of 8.00 or less, requiring A_Ta to be less than 14. Even more preferably f(cost) is 34 or lower for a cost index of 6.50 or less, requiring A_Ta to be less than 11.3. Most preferably f(cost) is 26 or lower for a cost index of 5.00 or less, requiring A_Ta to be less than 8.7.

The addition of aluminium is beneficial for oxidation resistance, as described above, but excessive aluminium lowers the melting point of the alloy, reducing strength at high temperature. For this reason, an upper limit of 33 at % or even 31 at % is preferable.

Whilst increased zirconium content can lead to the formation of zirconium-based intermetallics, it's addition is also beneficial in lowering Valence Electron Concentration, increasing ductility. Other benefits are a reduction in Pilling Bedworth ratio, and reduction in density. For these reasons, an increased zirconium content of 2 at % or more or even 4 at % or more is preferred. Even higher levels lead to further improvements so that a level of 6 at % or more or even 8 or 10 at % or more is most preferred if high ductility and low density are desired.

A high vanadium content can be detrimental to corrosion resistance, as described above, however in low levels it's unique combination of high melting point and low density can simultaneously improve high temperature strength capability, and reduce rotational loads, respectively. For these reasons, increasing the vanadium content may be preferred. Thus vanadium at levels of 2 at % or more, preferably 5.0 at % or more is preferred.

The high density and Pilling Bedworth ratio of tungsten mean it can be sensible to reduce it's content. However, tungsten has the highest melting point of any element in the invention, meaning increasing the content can result in a large temperature and strength capability increase. Thus preferred lower limits for the amount of tungsten are 2 at % or even 5 at % or even 8 at %. At 11 at % or more tungsten high temperature strength is superior and this is preferred if that property is desired.

Iron has a moderate impact on properties such as Pilling Bedworth ratio, and melting point, not greatly improving or deteriorating performance. Increasing iron reduces density, and having small additions of a larger number of elements allows higher alloy entropy to be achieved, stabilising the microstructure. It's addition, particularly in conjunction with chromium, can also improve printability during laser powder bed fusion additive manufacture. For these reasons, increasing iron levels to 0.5 at % or more or 2 at % or more or even 4 at % or more is preferred.

Increasing nickel content has the impact of lowering Pilling Bedworth ratio, reducing spallation of the oxide scale and improving protection it can offer the alloy under high temperature oxidation. If these properties are desired, including nickel in an amount of 1 at % or more or even 2 at % or more is desirable.

Additions of titanium to an alloy are beneficial in preventing oxide spallation in the initial stages of oxidation, because titanium has a low Pilling Bedworth ratio. It also has a substantial impact on reducing density. It is preferable to increase titanium levels to 5 at % or more for these reasons. Even larger amounts of titanium can be beneficial in certain applications and in some embodiments the alloy has 8 at % or more titanium or even 13 at % or more or 20 at % or more titanium.

Tantalum is costly due to difficulty sourcing the metal from conflict-free regions. This, in addition to having a high density and promoting oxide spallation due to high Pilling Bedworth ratio, mean it is preferable to reduce levels in this invention. Tantalum significantly increases high temperature strength due to it's melting point, so higher levels are preferred, for example 2 at % or more, preferably 5 at % or more or even 10 at % or more. Levels of 15 at % or more or even 20 at % or more are preferred where high strength is desired.

Niobium additions raise melting point, improving high temperature strength. Whilst the effect is not as strong as some other elements, such as tungsten, this is an advantage for some alloy processing methods, such as arc melting, where extremely high melting point elements may be difficult to incorporate into the alloy melt. Thus in some embodiments niobium is present in an amount of 5 at % or more or 8 at % or more and most preferably 10 at % or more.

Provided molybdenum levels are kept low enough to avoid the formation of volatile MoO₃, it's addition can be beneficial in increasing alloy high temperature strength, by raising melting point. Unlike elements with a similar impact on melting point, it does not significantly raise the Pilling Bedworth ratio, so spallation is not as big a concern. For these reasons, increasing molybdenum levels to 2 at % or more, for example, can be beneficial. In some embodiments molybdenum is present in an amount of 4 at % or more or even 6 at % or more.

Cobalt additions reduce likelihood of oxide spallation by reducing Pilling Bedworth ratio below the critical level of 2, or preferably lower. Cobalt has a moderate impact on density, cost and melting point. Small additions result in an increase in entropy, stabilising microstructure. For these reasons, increasing cobalt content to 0.5 at % or more, for example, can be beneficial. In some embodiments cobalt is present in an amount of 1 at % or more to take advantage of these effects. Even more preferably cobalt is present in an amount of 2 at % or more, or even 3 at % or more. Most preferably cobalt is present in an amount of 4 at % or more.

Copper promotes the formation of oxides with low likelihood of spallation due to lowering effect on Pilling Bedworth ratio. It is preferable to increase levels of copper to 0.5 at % or more, or even 1 at % or more or 2 at % or more.

Manganese additions can be detrimental to oxidation performance due to a tendency to form rapidly-growing Mn-based oxides. Reducing the manganese levels reduces the supply of manganese atoms, avoiding this problem. The low density of manganese can be beneficial to reduce self-loading, so increasing the levels to 0.5 at %, or more can be beneficial. In some embodiments manganese is present at higher levels, for instance 2 at % or more or even 5 at % or more.

Summary of Composition Limits

					Most	Most
Element			Preferable	Preferable	Preferable	Preferable
(at %)	Min	Max	Min	Max	Min	Max
Al	20	35	21	33	21	31
Co	0	5	0	3	0	2
Cr	0	35	1	25	3	15
Cu	0	5	0	4	0	3
Fe	0	10	0	7	0	5
Hf	0	10	0	5.5	0	0
Ir	0	5	0	3	0	0
Mn	0	10	0	7	0	5
Mo	0	35	0	20	0	7
Nb	0	20	5	20	10	20
Ni	0	5	0	3	0	1
Pd	0	5	0	3	0	0
Pt	0	5	0	3	0	0
Re	0	35	0	25	0	15
Rh	0	5	0	3	0	0
Ru	0	10	0	3	0	0
Si	0	5	0	3	0	0
Ta	0	35	2	33.9	2	10
Ti	0	40	5	40	13	40
V	0	7	0	5.1	0	3
W	0	35	0	26.8	2	10
Zr	0	16.7	2	11.1	6	10

• [1] Y. Cao, Y. Liu, B. Liu, W. Zhang, J. Wang, and M. Du, “Effects of Al and Mo on high temperature oxidation behavior of refractory high entropy alloys,” Trans. Nonferrous Met. Soc. China, vol. 29, no. 7, pp. 1476-1483, 2019, doi: 10.1016/S1003-6326 (19) 65054-5.
• [2] B. Gorr et al., “High-Temperature Oxidation Behavior of Refractory High-Entropy Alloys: Effect of Alloy Composition,” Oxid. Met., vol. 88, no. 3-4, pp. 339-349, 2017, doi: 10.1007/s11085-016-9696-y.
• [3] D. B. Miracle, O. N. Senkov, J. M. Scott, G. B. Wilks, and F. Approved, “Mechanical properties of Nb 25 Mo 25 Ta 25 W 25 AND V 20 Nb 20 Mo 20 Ta 20 W 20 refreactory high-entropy alloys,” 2011.
• [4] B. S. Murty, J. W. Yeh, S. Ranganathan, and P. P. Bhattacharjee, “Chapter 2: High-entropy alloys: basic concepts,” High-Entropy Alloy., pp. 13-30, 2019, doi: 10.1016/b978-0-12-816067-1.00002-3.
• [5] J. W. Yeh, “Alloy design strategies and future trends in high-entropy alloys,” Jom, vol. 65, no. 12, pp. 1759-1771, 2013, doi: 10.1007/s11837-013-0761-6.
• [6] D. B. Miracle and O. N. Senkov, “A critical review of high entropy alloys and related concepts,” Acta Mater., vol. 122, pp. 448-511, 2017, doi: 10.1016/j.actamat.2016.08.081.
• [7] M. H. Tsai, K. Y. Tsai, C. W. Tsai, C. Lee, C. C. Juan, and J. W. Yeh, “Criterion for sigma phase formation in Cr- and V-Containing high-entropy alloys,” Mater. Res. Lett., vol. 1, no. 4, pp. 207-212, 2013, doi: 10.1080/21663831.2013.831382.
• [8] S. Sheikh et al., “Alloy design for intrinsically ductile refractory high-entropy alloys,” J. Appl. Phys., vol. 120, no. 16, pp. 1-5, 2016, doi: 10.1063/1.4966659.
• [9] C. M. Liu, H. M. Wang, S. Q. Zhang, H. B. Tang, and A. L. Zhang, “Microstructure and oxidation behavior of new refractory high entropy alloys,” J. Alloys Compd., vol. 583, pp. 162-169, 2014, doi: 10.1016/j.jallcom.2013.08.102.
• [10] M. Esmaily, Y. Qiu, S. Bigdeli, M. B. Venkataraman, A. Allanore, and N. Birbilis, “High-temperature oxidation behaviour of AlxFeCrCoNi and AlTiVCr compositionally complex alloys,” npj Mater. Degrad., vol. 4, no. 1, pp. 1-10, 2020, doi: 10.1038/s41529-020-00129-2.
• [11] T. Maruyama, B. X. Fang, and K. Nagata, “Aluminized molybdenum by pack cementation and its resistance to high-temperature oxidation.” 1991.
• [12] R. Zhang, J. Meng, J. Han, K. Tulugan, and R. Zhang, “Oxidation resistance properties of refractory high-entropy alloys with varied AlxCrTiMo content,” J. Mater. Sci., 2020, doi: 10.1007/s10853-020-05480-y.
• [13] F. Muller et al., “On the oxidation mechanism of refractory high entropy alloys,” 2019, doi: 10.1016/j.corsci.2019.108161.
• [14] M. H. Tsai, R. C. Tsai, T. Chang, and W. F. Huang, “Intermetallic phases in high-entropy alloys: Statistical analysis of their prevalence and structural inheritance,” Metals (Basel)., vol. 9, no. 2, pp. 1-18, 2019, doi: 10.3390/met9020247.

Claims

1. An alloy consisting of, in atomic percent: aluminium: 20 to 35%;zirconium: 16.7% or less; vanadium: 7% or less;tungsten: 35% or less;chromium: 35% or less;iron: 10% or less;nickel: 5% or less;titanium: 40% or less;tantalum: 35% or less;niobium: 20% or less;molybdenum: 35% or less;cobalt: 5% or less;manganese: 10% or less;copper: 5% or less;hafnium: 10% or less;silicon: 5% or less;platinum: 5% or less;palladium: 5% or less;ruthenium: 10% or less;rhodium: 5% or less;iridium: 5% or less;rhenium: 35% or less provided ARe≤(35−ATa)+(35−AW)+(20−ANb) and where ARe, ATa, AW and ANb are the amounts in atomic percent of rhenium, tantalum, tungsten and niobium respectively; andincidental impurities less than 1 at % in sum;wherein the following equations are satisfied:

2. The alloy of claim 1, wherein the following equation is fulfilled:

3. The alloy of claim 1, wherein the following equation is fulfilled:

4. The alloy of claim 1, where in the following equation is fulfilled:

5. The alloy of any of claims 1 to 4claim 1, wherein the following equation is fulfilled:

6. (canceled)

7. The alloy of any of claims 1 to 6claim 1, wherein the following equation is fulfilled:

8-9. (canceled)

10. The alloy of claim 1, including 33 at % or less aluminium.

11. (canceled)

12. The alloy of claim 1, including 2 at % or more zirconium.

13. (canceled)

14. The alloy of claim 1, including 2 at % or more vanadium.

15. (canceled)

16. The alloy of claim 1, including 2 at % or more tungsten.

17-20. (canceled)

21. The alloy of claim 1, including 0.5 at % or more nickel.

22. (canceled)

23. The alloy of claim 1, including 5 at % or more titanium.

24. (canceled)

25. The alloy of claim 1, including 2 at % or more tantalum.

26. (canceled)

27. The alloy of claim 1, including 5 at % or more niobium.

28. (canceled)

29. The alloy of claim 1, including 2 at % or more molybdenum.

30. (canceled)

31. The alloy of claim 1, including 0.5 at % or more cobalt.

32-34. (canceled)

35. The alloy of claim 1, including 0.5 at % or more manganese.

36-37. (canceled)

38. The alloy of claim 1, wherein the following equation is fulfilled:

39. The alloy of claim 1, wherein the following equation is satisfied:

40. (canceled)

41. The alloy of claim 1, wherein the following equation is satisfied:

42. The alloy of claim 1, wherein the following equation is satisfied:

43-53. (canceled)