# A Perspective of the Design and Development of Metallic Ultra-High Temperature Materials: Refractory Metal Intermetallic Composites, Refractory Complex Concentrated Alloys and Refractory High Entropy Alloys

## Abstract

**:**

## 1. Introduction

#### Alloy Design

## 2. Design of Metallic UHTMs

## 3. Synergy

## 4. Synergy and Entanglement: The Case for Metallic UHTMs

_{5}Si

_{3}, where M = TM) can coexist with other bcc solid solutions or other silicides (e.g., M

_{3}Si) or other compounds (e.g., Laves phase(s)) [54]. The same phases can co-exist in other alloys (see below). For example, in the case of RM(Nb)ICs, RM(Nb)IC/RCCAs or RM(Nb)IC/RHEAs (see Abbreviations), bcc solid solution(s) can be “conventional”, CC or HE according to their chemical composition, or “normal”, Ti-rich, Si-free according to solute partitioning (see the Appendix B) [7,8,9,19,20,21,55], Nb

_{5}Si

_{3}silicide(s) can be “conventional”, CC or HE according to their chemical composition, or Ti rich or Ti and Hf rich according to solute partitioning (see the Appendix B) [7,8,21,56], other compounds (e.g., A15 phases [54]) can be “conventional”, CC or HE according to their chemical composition [19] and eutectics that contain bcc solid solution and Nb

_{5}Si

_{3}[57] can be “conventional”, CC or HE according to their chemical composition [7,19,57], for example see the Figures 1–4 and 6 in [58] and the Figures 1–6 in [20]. Such intricateness (see Appendix A) of phases materialises from the correlations/relationships between elements, phases, alloys and their properties. We shall expand on this intricateness below in Section 5, where the concept of entanglement (see the Appendix A) will be introduced, and the choice of this term will become clear. It suffices to say that entanglement is a distinguishing characteristic of a metallic UHTM and its elements and phases. The quality of an alloy ensues from this entanglement. Entanglement is attributed to synergy. Entanglement enables the study of a material in a multiscale framework. Entanglement and synergy are instrumental in identifying areas where interdisciplinary research could focus.

- (a)
- The relationships/correlations between
- (i)
- (ii)
- (iii)
- (iv)
- (v)
- (vi)
- alloy parameters and processing (macrosegregation), e.g., Figure 8 in [46],

- (b)
- the “co-habitation” in parameter maps
- (vii)
- (viii)
- (ix)

- (c)
- the function/role assumed in a particular situation by each parameter separately and by parameters together to give

_{5}Si

_{3}with which it coexists (e.g., see Figure 6c in [58]). Thus, the phases in an alloy are in synergy and intricateness (entangled).

_{5}Si

_{3}silicide, C14-NbCr

_{2}Laves phase, A15-Nb

_{3}X (X = Al, Ge, Si, Sn) compounds, maps of alloys and phases, macrosegregation and maps for bond coat alloys for environmental coatings.

- (1)
- (2)
- for B containing RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs there is a gap in δ
_{ss}values, see the Figure 8a in [48]. Furthermore, in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs, - (3)
- the parameter δ
_{ss}can differentiate - (4)
- The parameter VEC can differentiate the effect of the concentrations of alloying additions on the type of bcc solid solution (meaning “conventional”, or CC/HE) in alloys, see the Figure 3b in [20]. Additionally, there are relationships between parameters of CC/HE and “conventional” bcc solid solution, see Figure 6b in [20], the parameter δ
_{ss}depends strongly on the B_{ss}and (Ge+Sn)_{ss}contents of the solid solution, see the Figure 7 in [20], and the parameters VEC_{ss}, Δχ_{ss}and δ_{ss}increase with the concentration of oxygen in the solid solution, i.e., with interstitial content, see the Figure 11 in [20].

_{5}Si

_{3}silicide in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs,

- (a)
- (b)
- (c)
- (d)

_{2}Laves phase in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs can be described (i) with parameter maps, see the Figures 2 and 3 in [54] and the Figure 17 in [61], and (ii) with solute maps, see the Figure 21 in [21], the Figures 1–4 in [54] and the Figure 18d in [61].

_{3}X (X = Al, Ge, Si, Sn) compounds in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs,

- (a)
- Their alloying behaviour can be described
- (b)
- (c)
- (d)
- they improve oxidation resistance in synergy with other phases, e.g., see the Figure 12c in [42].

_{5}Si

_{3}silicide in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs

- (1)
- Their alloying behaviour is described
- (2)
- There are gaps in the values of the parameters (ΔH
_{mix})_{eutectic}and Δχ_{eutectic}, see the Figures 3 and 4, respectively, in [57] and - (3)

- (a)
- (b)
- (c)
- (d)

_{5}Si

_{3}silicide. Another metallic UHTM with the same solute elements but at different concentrations can also contain bcc solid solution and M

_{5}Si

_{3}silicide, not necessarily of the same chemical composition as the first metallic UHTM. There is entanglement in the latter and entanglement in the second metallic UHTM (regardless of where the alloys are/were studied, by whom they are/were studied or when they are/were studied). The same would be if the second metallic UHTM with the same solute elements and different concentrations consisted of bcc solid solution, M

_{5}Si

_{3}silicide and another phase, say an A15 compound.

_{5}Si

_{3}, the Figure 15a in [46] for oxidation of alloys, and the Figure 15 in [45] that shows how alloying shifts the alloys in the δ versus VEC map in the direction of improved oxidation resistance. Other examples of outcomes of synergy and entanglement on properties of alloys and their phases and vol.% of phases are shown in the Figure 15a–c in [19], in Figures 18 and 21e in [61], the Figures 4, 5a,b and 6 in [9], the Figures 17 and 18 in [48], the Figures 11, 15 and 22 in [21] and the Figure 13c in [55].

## 5. The Alloy Design “landscape” in NICE

- (a)
- macrosegregation (MACX) of solute addition(s) X for liquid route processing of the alloy (e.g., for cold hearth melting/casting [70]), and thus can guide to some extent the alloy developer about processing,
- (b)
- properties of the alloy (hardness, density, specific strength, creep, oxidation),
- (c)
- the chemical composition of alloy phases,
- (d)
- the volume fraction of phases and
- (e)
- mechanical properties of phases, and links
- (i)
- the alloy with its phases and vice versa, and
- (ii)
- the alloy properties and phase properties.

_{i}, parameter δ), electronegativity (χ

_{i}, parameter Δχ), valence electrons (parameter VEC), enthalpy (parameter ΔH

_{mix}), entropy (parameter ΔS

_{mix}) and Ω (=T

_{m}ΔS

_{mix}/∣ΔH

_{mix}∣) [7,54,55,56,57,58,59], which are the same parameters that are used for the study of HEAs, rapidly solidified alloys, or bulk metallic glasses, e.g., [71], and the ratios sd/sp (concentration of sd over sp electronic configuration elements) and Nb/(Ti+Hf) [7,47,59,72], which (the ratios) together with the aforementioned parameters are important for properties of RM(Nb)ICs, RM(Nb)IC/RCCAs, RM(Nb)IC/RHEAs [7,8,9,10,19,20,21,47,48,59,73], and their phases [9,21,48,54,56,57,60,61,74]. (For the calculation of the said parameters for alloys and solid solutions, see [55,59], and for the calculation of the parameters Δχ and VEC of Nb

_{5}Si

_{3}, C14-NbCr

_{2}Laves phase and A15-Nb

_{3}X (X = Al, Ge, Si, Sn) compounds see [54,56]).

_{ss}) and 5-3 silicide of Nb (Nb

_{5}Si

_{3}), i.e., for RM(Nb)IC, RM(Nb)IC/RCCA or RM(Nb)IC/RHEA, and for RCCA or RHEA with Nb and Si additions. It can be expanded to include the said two phases plus other compound(s), for example, Laves phases and/or A15 compounds [54], or to be the “landscape” for a material system for an application at ultra-high temperatures, for example, a substrate alloy with an environmental coating [9]. The “landscape” in Figure 1 has “lines and paths”, “focal points”, and “transitions” shown with lines single or double arrows of different weights and colour.

- (a)
- that metallic UHTMs have organised complexity,
- (b)
- that there is entanglement and
- (c)
- that the “affairs” of alloys cannot be separated from (are linked with)
- (i)
- the “affairs” of phases and
- (ii)
- the parameters that describe
- (1)
- alloying behaviour and
- (2)
- properties of alloys and phases, and

- (iii)
- the (effects of the) environment (e.g., environmental degradation because of interstitial contamination, oxidation).

- (d)
- to uncover
- (iv)
- new things about alloys and their phases, things s/he might never have suspected, and
- (v)
- regularities and linkages, and

- (e)
- to establish
- (vi)
- relationships between different properties and
- (vii)
- a framework of understanding that is subtle and mathematical.

#### 5.1. Walk in the Superstructure of the “landscape”

_{alloy}), mass change (ΔW

_{alloy}) in oxidation and yield strength (σ

_{y}

^{alloy}). (A target for toughness has also been set by industry; this property is not included in NICE [7]). We find out that each one of the property targets correlates with alloy parameters that form the third bounded area in the “landscape” on the right-hand side of the second bounded area. The second and third bounded areas are linked with a solid green arrow. The steady-state creep rate έ

_{alloy}links with Δχ

_{alloy}, VEC

_{alloy,}and δ

_{alloy}, shown with double dashed arrows, and examples of the correlations can be found, respectively, in the Figure 10a–c in [7]. The ΔW

_{alloy}links with VEC

_{alloy}and δ

_{alloy}, shown with double dashed arrows, and examples of the correlations can be seen in the Figure 9 in [7], Figure 13a,c in [60] and Figure 15a in [46] for the former parameter, and in the Figure 13b,d in [60] and the Figure 15b in [46] for the latter parameter. The σ

_{y}

^{alloy}links with Δχ

_{alloy}, VEC

_{alloy,}and δ

_{alloy}, shown with double dashed arrows, and examples of the correlations of alloy hardness and alloy specific yield strength can be found, respectively, in the Figure 11c in [21] and the Figure 18a in [48] for the first parameter, the Figure 11d in [21], the Figure 6 in [9], the Figure 19 in [48], the Figure 8a in [60] and the Figure 8d in [60] for the second parameter, and in the Figure 18b in [48] for the third parameter.

_{alloy}= g

_{1}(Δχ

_{alloy}) we calculate Δχ

_{alloy}, from έ

_{alloy}= f

_{1}(VEC

_{alloy}) we calculate VEC

_{alloy}and from έ

_{alloy}= h

_{1}(δ

_{alloy}) we calculate δ

_{alloy}, where g

_{1}, f

_{1}and h

_{1}are mathematical functions. We also find out that the entanglement of alloy properties with alloy parameters has led to the discovery of relationships between the creep rate of a metallic UHTM with the ratios Nb/(Ti + Hf) and sd/sp, i.e., relationships of the form έ

_{alloy}= g

_{2}([Nb/(Ti + Hf)]

_{alloy}), e.g., see the Figure 19 in [7] and έ

_{alloy}= g

_{3}([sd/sp]

_{alloy}), e.g., see the Figure 20 in [7].

_{X}

^{alloy}(at.%) = p(P

_{alloy}), where P is Δχ

_{alloy}, VEC

_{alloy}or δ

_{alloy}and p is a mathematical function. We find out examples (i) for C

_{X}

^{alloy}(at.%) = p

_{1}(Δχ

_{alloy}) in the Figure 12a in [7], the Figure 10a in [19] and the Figure 9c,f,i in [60], (ii) for C

_{X}

^{alloy}(at.%) = p

_{2}(VEC

_{alloy}) in the Figure 12a in [7], Figure 18a in [21], Figure 10b in [19], Figure 9a,d,g in [60] and (iii) for C

_{X}

^{alloy}(at.%) = p

_{3}(δ

_{alloy}) in the Figure 9b,e,h in [60]. Thus, we understand that the entanglement of property goals with alloy parameters empowers one to calculate the alloy chemical composition, C

_{alloy}. There are cost issues regarding the elements that “make up the alloy”, which (the costs) result from the availability and cost of specific raw materials, as well as recyclability and sustainability interests that must be addressed together with processability matters. We move from the third bounded area in the direction of the solid brown arrow in Figure 1. While we wander inside the third bounded area, we discover that the alloy parameters also work together, i.e., they are in synergy (shown with the double blue arrows in the third bounded area). We find correlations that result from the synergy of alloy parameters in the Figure 15b in [19], Figure 16 in [48], Figure 14 in [46], Figure 15a in [44], Figure 15 in [45], Figure 19 in [8], Figure 2 in [21] and the Figures 3 and 4 in [59].

_{Nbss}, VEC

_{Nbss}and δ

_{Nbss}of the bcc Nb solid solution. We discover that parameters of the alloy link with parameters of the solid solution, i.e., with relationships of the form P

_{alloy}= q(P

_{Nbss}) where P is Δχ, VEC or δ and q is mathematical relationship. These links are shown with dashed arrows between the third and the fourth bounded areas. They are described with mathematical relationships such as (i) Δχ

_{alloy}= q

_{1}(Δχ

_{Nbss}), examples of which are found in the Figures 3a and 6a in [20], (ii) VEC

_{alloy}= q

_{2}(VEC

_{Nbss}), examples of which are shown in the Figure 17 in [7], Figure 17a in [21], Figure 3b in [20] and Figure 6a in [8] and (iii) δ

_{alloy}= q

_{3}(δ

_{Nbss}) (figures not published).

_{Nbss}= k(C

_{X}

^{Nbss}) where P is Δχ, VEC or δ, k is mathematical relationship, and C is the concentration of element X in the solid solution. We find out examples (i) for Δχ

_{Nbss}= k

_{1}(C

_{X}

^{Nbss}) in the Figure 11a in [20] and Figure A1a,c in [60], (ii) for VEC

_{Nbss}= k

_{2}(C

_{X}

^{Nbss}) in the Figure 11c in [20], Figure 18b in [21], and Figure 4d–f in [60], and (iii) for δ

_{Nbss}= k

_{3}(C

_{X}

^{Nbss}) in the Figures 7 and 11b in [20] and the Figure A1b in [60]. In other words, having entered the fourth bounded area and looked around it, we realise that the entanglement of property goals with alloy parameters P

_{alloy}and solid solution parameters P

_{Nbss}, where P is Δχ, VEC or δ, empowers one to calculate the solid solution chemical composition C

_{Nbss}. Thus, we move from the fourth bounded area in the direction of the solid red arrow in the Figure 1.

_{alloy}, the third and fourth bounded areas and the red box of C

_{Nbss,}we discover that owing to the said entanglement, there is another way to calculate the chemical composition of the solid solution, namely from relationships of the form C

_{X}

^{alloy}= m(C

_{X}

^{ss}) (shown with the thin red arrow in Figure 1), examples of which are shown in the Figure 16 in [7] and Figure 19b in [21], or from other relationships such as VEC

_{alloy}= n(C

_{X}

^{Nbss}), an example of which is shown in the Figure 19a in [21]. Furthermore, we discover that the concentrations of solutes in the solid solution are linked (the link with solute relationships is also shown with a thin red arrow in Figure 1), examples of which are shown in the Figures 8 and 9 in [20], Figure 11 in [19], Figure 16 in [61], Figure 7 in [48], Figure 4a–c in [60], Figure 12d,e in [46] and relationships linking the concentrations of Ti with specific solutes, i.e., Ti

_{ss}= d

_{1}(C

_{X}

^{ss}) shown in the Figure S4 in supplemental data in [74], Figure 12a–c in [46], Figure 12 in [45], Figure 9 in [7] and the Figure 19c,d in [19]. While we are thinking about our next step in the “landscape”, we are excited to note that the said entanglement has directed research to find out that the solid solution, which in metallic UHTMs can be “normal”, Ti-rich or Si-free according to solute partitioning [55], can also be “conventional”, CC or HE [20] according to its chemical composition, and that the research has discovered relationships that link these solid solutions, for example see the Δχ

_{”conventional” Nbss}= b(Δχ

_{CC/HE Nbss}) relationship in the Figure 6b in [20].

_{ss}= h

_{1}(δ

_{ss}), shown in the Figure 10b in [20], VEC

_{ss}= ψ

_{3}(Δχ

_{ss}), shown in the Figures 6c and 10c in [20] and Figure 8c in [48], Δχ

_{ss}=h

_{3}(δ

_{ss}), shown in Figure 10a in [20], and δ

_{ss}= h

_{4}(ΔH

_{mix})

_{ss}and Ω

_{ss}= m(ΔH

_{mix})

_{ss}, shown in the Figure 8a,b in [48].

_{Nb5Si3}and VEC

_{Nb5Si3}of the silicide. We discover that parameters of the alloy link with parameters of the 5-3 silicide with relationships of the form P

_{alloy}= t(P

_{Nb5Si3}) where P is Δχ or VEC and t is a mathematical relationship. These linkages are shown with dashed arrows between the third and fifth bounded areas. For VEC

_{alloy}= t

_{1}(VEC

_{Nb5Si3}), examples are found in the Figure 6a in [58] and Figure 17b in [21] (figures for the relationship Δχ

_{alloy}= t

_{2}(Δχ

_{Nb5Si3}) have not been published). There is also a relationship between VEC and Δχ, namely VEC

_{alloy}= t

_{3}(Δχ

_{Nb5Si3}), see Figure 7 in [21]. We discover that the chemical composition of the 5-3 silicide can be calculated from relationships of the form P

_{Nb5Si3}= r(C

_{X}

^{Nb5Si3}), where P is Δχ or VEC, r is mathematical relationship, and C is the concentration of element X in the silicide. For the relationship Δχ

_{Nb5Si3}= r

_{1}(C

_{X}

^{Nb5Si3}) examples are shown in the Figure 2b,c in [7] and Figure 5d in [60], and for VEC

_{Nb5Si3}= r

_{2}(C

_{X}

^{Nb5Si3}) see the Figure 2a in [56], Figure 18c in [21] and the Figure 5c in [60].

_{alloy}and silicide parameters P

_{Nb5Si3}, where P is Δχ or VEC, allows one to calculate the silicide chemical composition C

_{Nb5Si3}. We move from the fifth bounded area in the direction of the solid purple arrow in the Figure 1. We are excited to discover that concentrations of solutes in the silicide are linked, as was the case for the solid solution. We find examples of solute correlations in the Figure 11 in [19], Figures 12 and 13 in [61] and the Figure 13 in [45], examples of relationships linking the concentrations of Ti with specific solutes, i.e., Ti

_{Nb5Si3}= d

_{2}(C

_{X}

^{Nb5Si3}), in the Figure 1b–d in [7], Figure 8a,b in [63] and the Figure 20 in [21] and examples of relationships linking the concentrations of Nb and Hf, i.e., Nb

_{Nb5Si3}= d

_{3}(Hf

_{Nb5Si3}), in the Figure 1a in [7] and the Figure 8c in [63]. The link of the chemical composition of the silicide and solute relationships is shown also with a thin purple arrow in Figure 1.

_{alloy}of an alloy, one can calculate macrosegregation (MACX) of elements and alloy properties via the aforementioned parameters (i.e., the relationships [Property]

_{alloy}= f(P

_{alloy}), where P is Δχ, VEC or δ discussed above) and other relationships, for example, HV

_{alloy}= t

_{1}((ΔH

_{mix})

_{alloy}) and HV

_{alloy}= t

_{2}((ΔS

_{mix})

_{alloy}), as shown respectively in the Figure 11a,b in [21]. We also discover how properties depend on the volume fractions of phases, examples of which can be found in the relationships HV

_{alloy}versus vol.% Nb

_{ss}in the Figure 15e in [19], HV

_{alloy}versus vol.% A15 in Figure 22c in [61], HV

_{alloy}versus vol.% Nb

_{5}Si

_{3}in Figure 22d in [61] and [ΔW/A]

_{alloy}versus vol.% Nb

_{ss}in Figure 16a in [19].

_{y})

_{ss}= g(P

_{ss}), where P is Δχ, VEC or δ and g is mathematical relationship (for examples see the relationships HV

_{ss}= g

_{5}(Δχ

_{ss}) in the Figure 13c in [21], HV

_{ss}= f(VEC

_{ss}) in the Figure 17 in [48] and the Figure 6a–c in [60] and HV

_{ss}= h

_{2}(δ

_{ss}) in the Figure 7 in [8] and the Figure 4 in [9]) and other relationships, for example, the relationship HV

_{ss}versus Ω

_{ss}shown in the Figure 13a in [20] and HV

_{ss}= h(C

_{X}

^{ss}) shown in the Figure 7 in [60]. We also discover that the vol.% of the bcc solid solution is related to alloy parameters and the chemical composition of the solid solution, as shown with the relationships of vol.% Nb

_{ss}versus VEC

_{alloy}in the Figure 16c in [19], Figure 18a in [61], vol.% Nb

_{ss}versus Δχ

_{alloy}in Figure 16b in [19] and Figure 22b in [61] and vol.% Nb

_{ss}versus C

_{ss}in Figure 9 in [46].

_{Nb5Si3}= g(P

_{Nb5Si3}), where P is Δχ or VEC, for example, see the relationship HV

_{Nb5Si3}= f

_{7}(VEC

_{Nb5Si3}) in the Figure 5 in [9]. Similarly, with the bcc solid solution, we also discover that the volume fraction of intermetallics is related to alloy parameters, as shown with the relationships linking the volume fractions of Nb

_{5}Si

_{3}, A15-Nb

_{3}X and C14-NbCr

_{2}Laves with VEC

_{alloy}in the Figure 18b–d in [61].

#### 5.2. Walk in the Substructure of the “Landscape”

- (1)
- the clarification of three phase equilibria between Nb
_{ss}, Nb_{5}Si_{3}and C14-NbCr_{2}in the Nb-Si-Cr ternary [38], - (2)
- (3)
- precipitation of Nb
_{ss}in Nb_{5}Si_{3}in heat-treated alloys, see data for the alloys KZ7 (Nb-24Ti-18Si-5Al, [117,118]), JG1 (Nb-18Si-5Al-5Cr-5Mo, [119]), KZ5 (Nb-24Ti-18Si-5Al-5Cr), KZ6 (Nb-24Ti-18Si-5Al-5Cr-6Ta), KZ2 (Nb-24Ti-18Si-4Al-8Cr), KZ8 (Nb-24Ti-18Si-4Al-8Cr-6Ta) [118], ZF8 (Nb-18Si-5Al-5Ge) and ZF5 (Nb-24Ti-18Si-5Al-5Ge) [120] and the alloy CM1 (Nb-8Ti-21Si-5Mo-4W-1Hf) [74] (in the parentheses are given the nominal compositions, at.%), - (4)
- precipitation of A15-Nb
_{3}X in heat-treated alloys, see data for the alloys EZ5 (Nb-24Ti-18Si-5Al-5Hf-5Sn), EZ8 (Nb-24Ti-18Si-5Al-5Cr-5Hf-5Sn) [61], ZX4 (Nb-24Ti-18Si-5Cr-5Sn), ZX6 (Nb-24Ti-18Si-5Al-5Sn) [42] and JG6 (Nb-24Ti-18Si-5Al-5Cr-5Hf-2Mo-5Sn) [121] (note that in JG6-HT the Sn rich Nbss that was reported in [121] subsequently was confirmed to be the A15 compound), - (5)
- precipitation of Nb
_{ss}and/or A15-Nb_{3}X in heat treated alloys, see data or the alloys NV8 (Nb-24Ti-18Si-5Fe-5Sn) [122], NV5 (Nb-24Ti-18Si-5Cr-5Fe-5Sn) [123], JZ4 (Nb-11.5Ti-18Si-5Mo-2W-4.9Sn-4.6Ge-4.5Cr-4.7Al-1Hf), JZ5 (Nb-21Ti-18Si-6.7Mo-1.2W-4.4Sn-4.2Ge-4Cr-3.7Al-0.8Hf) [46], JZ3 (Nb-12.4Ti-17.7Si-6Ta-2.7W-3.7Sn-4.8Ge-4.7Al-5.2Cr-1Hf). JZ3+ (Nb-12.4Ti-19.7Si-5.7Ta-2.3W-5.7Sn-4.9Ge-4.6Al-5.2Cr-0.8Hf) [45], EZ4 (Nb-18Si-5Al-5Hf-5Sn) [62], ZX5 (Nb-24Ti-18Si-5Al-2Sn) and ZX7 (Nb-24Ti-18Si-5Al-5Cr-2Sn) [41], - (6)
- (7)
- (8)
- phase transformations associated with CC/HE phases [61],
- (9)
- relationships between solutes in hexagonal D8
_{8}5-3 silicide in B containing RCCAs [48], - (10)
- effects of different solute additions on the chemical composition of eutectics with Nb
_{ss}and Nb_{5}Si_{3}[61], and - (11)
- solubility range of

- (12)
- the effects of processing and alloy chemical composition on the type of Nb
_{5}Si_{3}in metallic UHTMs [62], - (13)
- subgrain formation in Nb
_{5}Si_{3}is cast and OFZ (optical floating zone) grown alloy CM1 (Nb-8Ti-21Si-5Mo-4W-1Hf) [74], and - (14)

- (15)
- alloy oxidation, which improves with the addition of Ge and/or Sn that segregate to the surface where
- (16)
- correlations of the hardness
- (17)
- (18)
- correlations of the Young’s moduli of the bcc solid solution with the concentration of oxygen owing to interstitial contamination [20],
- (19)
- (20)
- correlations of the steady-state creep of Nb
_{5}Si_{3}with the parameters VEC_{Nb5Si3}, δ_{Nb5Si3}and Δχ_{Nb5Si3}[9], - (21)
- relationships of the parameters VEC
_{ss}, δ_{ss}and Δχ_{ss}with the concentration of oxygen in the bcc solid solution owing to its interstitial contamination [20], - (22)
- correlations about the contributions of solute elements to the steady state creep of the alloy [21] and
- (23)
- creep map for alloys [9].

_{ss}solution and Nb

_{5}Si

_{3}[20,167,168]. Furthermore, the interstitial contamination of the bcc solid solution, 5-3 silicide, and A15 compounds differ, depending on solute elements in each phase and is more severe for the solid solution, e.g., Figure 17 in [19], and the severity of contamination of the aforementioned phases depends on location in the metallic UHTM, e.g., see the Figure 12c in [20]. Moreover, the parameters Δχ, δ and VEC, the hardness and Young’s modulus of the bcc solid solution increase with increasing contamination with oxygen; see Figures 11, 12d, 14c and 16 in [20]. Likewise, the parameters and properties of the 5-3 silicide depend on interstitial contamination.

## 6. Self-Regulation

## 7. Synergistic Metallurgy

## 8. Afterword

_{5}Si

_{3}and substituting Nb, thus causing a change in structure from tetragonal to hexagonal as well as changes in mechanical properties [27]) or (ii) to the formation of sub-grains in Nb

_{5}Si

_{3}[74] while change in structure also can occur with contamination with interstitials (for example, the case of hexagonal instead of tetragonal Nb

_{5}Si

_{3}stabilised in Nb-Si alloys with C contamination [169]).

_{5}Si

_{3}[56]).

## 9. Something to Think about

_{5}Si

_{3}silicide [167,168], that contamination of the solid solution is more severe than that of the silicide [167,168], and that the contamination of each phase depends on how close the phase is to the scale/substrate interface and on the solute elements in the alloy and phases [19,20,167,168].

_{5}Si

_{3}silicides with bcc solid solution(s) and/or other intermetallics, owing to the partitioning of solutes, contamination with interstitials and phase transformations of the silicide (e.g., see [45,61,62,74]) on mechanical behaviour at elevated temperatures.

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CALPHAD | Calculation of Phase Diagrams |

CC | complex concentrated (also compositionally complex) |

FOMO | fear of missing out |

HE | high entropy |

HV | hardness Vickers |

MACX | macrosegregation of element X |

NICE | Niobium Intermetallic Composite Elaboration |

RM | refractory metal |

RMIC | refractory metal intermetallic composite |

RHEA | refractory metal high entropy alloy |

RCCA | refractory metal complex concentrated alloy |

RMIC/RHEA | RMIC that also meets the definition of RHEA |

RM(Nb)IC | refractory metal intermetallic composite based on Nb |

RM(Nb)IC/RCCA | RM(Nb)IC that also meets the definition of RCCA |

RM(Nb)IC/RHEA | RM(Nb)IC that also meets the definition of RHEA |

TM | transition metal |

UHTM | ultra-high temperature material |

## Appendix A. Clarifications/“Definitions”

Citizen * | Person (see below) |

Culture * | the way of life of a particular society. For example, the people (persons, see πρόσωπον below) that lived in the ancient poleis (cities) of Athens and Sparta, i.e., the societies of Athens and Sparta, had different cultures (see polis below) |

Ecclesia * | public legislative assembly of citizens that put citizen participation at its very core and underpinned the growth of a polis. |

Entanglement | occurs when the (alloying) behaviour and properties (e.g., mechanical, environmental, thermo-physical) of a complex whole (alloy) cannot be described and understood independently from the behaviour of its parts (phases) |

Essere | to be and to exist (verb in Vulgar Latin) |

Intricateness | having many complexly interrelated parts (from intricate from Latin intricatus, which means entangled) |

Inter-subjective | opinion exists within a communication network and links the subjective opinions of many individuals. Communication network is the structure and flow of communication and information between individuals within a group [171]. |

Landscape | Land + scape, scape from Old English sceppan or scyppan, meaning to shape (e.g., landscape is human-made space on the land or an area of the Earth’s surface seen by an observer) |

Methodology | derived from the words method and logos, method from μέθοδος, which derives from the verb μετέρχομαι that means movement for some purpose, and logos from λóγος, which derives from the verb λέγω that means tell, say |

Polis * | City (here the word polis is used to describe the poleis (plural of polis) in ancient (classical age) Greece; see culture above) |

Person * | πρóσωπον in Greek. The word πρόσωπον is made up of the preposition προς (=towards) and the noun ωψ (ωπός in the genitive), which means face, thus the composite word προς-ωπον. A person (πρόσωπον) has their face towards someone or something, s/he is opposite someone or something [53] |

Synergy * | is derived from the Greek word συνεργία, which comes from syn/συν (=together) and ergon/έργον (=work), thus synergy = work together. |

Topography | from topos/τóπος (=place) + graphy/γραφή (γραφή from γράφω = write about), or description of place |

## Appendix B. Partitioning of Solutes

_{5}Si

_{3}increases with increasing Ti content, and the Nb/(Ti+Hf) ratio decreases [45,46,61,63,65,73].

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**Figure 1.**Representation of alloy design “landscape” drawn with NICE for a metallic UHTM with bcc solid solution and 5-3 silicide of Nb. VEC is valence electron concentration, r is atomic size, χ is Pauling electronegativity, ΔH

_{mix}is enthalpy of mixing, ΔS

_{mix}is entropy of mixing, ΔW is mass change in oxidation, E is Young’s modulus, σ

_{y}is yield strength, έ is steady state creep rate, Δχ parameter based on χ, δ parameter based on r, Ω is parameter based on melting temperature, ΔS

_{mix}and ΔH

_{mix}, MACX is macrosegregation of element X, and C is chemical composition.

**Figure 2.**A schematic diagram showing the link between CEMI, ETS, IRIS and ESSERE. For the links of this figure with NICE, see the text.

**Table 1.**A summary perspective of the attributes and capabilities of NICE for the design and development of metallic UHTMs.

Attributes | Composition | Properties | Links with ** | Affiliates ^{+} | |||
---|---|---|---|---|---|---|---|

N I C E | Synergy Entanglement Self-regulation | Metallic UHTM Material System * Phases | Metallic UHTM Material System Phases | Costs Energy Processing Raw materials | Risks Sustainability Recyclability Environment | IRIS CEMI ETS | E S S E R E |

^{+}see Section 3 and Section 7, ** see Section 1 and Section 5.2.

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Tsakiropoulos, P.
A Perspective of the Design and Development of Metallic Ultra-High Temperature Materials: Refractory Metal Intermetallic Composites, Refractory Complex Concentrated Alloys and Refractory High Entropy Alloys. *Alloys* **2023**, *2*, 184-212.
https://doi.org/10.3390/alloys2030014

**AMA Style**

Tsakiropoulos P.
A Perspective of the Design and Development of Metallic Ultra-High Temperature Materials: Refractory Metal Intermetallic Composites, Refractory Complex Concentrated Alloys and Refractory High Entropy Alloys. *Alloys*. 2023; 2(3):184-212.
https://doi.org/10.3390/alloys2030014

**Chicago/Turabian Style**

Tsakiropoulos, Panos.
2023. "A Perspective of the Design and Development of Metallic Ultra-High Temperature Materials: Refractory Metal Intermetallic Composites, Refractory Complex Concentrated Alloys and Refractory High Entropy Alloys" *Alloys* 2, no. 3: 184-212.
https://doi.org/10.3390/alloys2030014