Refractory Metal (Nb) Intermetallic Composites, High Entropy Alloys, Complex Concentrated Alloys and the Alloy Design Methodology NICE—Mise-en-scène Patterns of Thought and Progress

The paper reflects on the usefulness of the alloy design methodology NICE (Niobium Intermetallic Composite Elaboration) for the development of new Nb-containing metallic ultra-high-temperature materials (UHTMs), namely refractory metal (Nb) intermetallic composites (RM(Nb)ICs), refractory high entropy alloys (RHEAs) and refractory complex concentrated alloys (RCCAs), in which the same phases can be present, specifically bcc solid solution(s), M5Si3 silicide(s) and Laves phases. The reasons why a new alloy design methodology was sought and the foundations on which NICE was built are discussed. It is shown that the alloying behavior of RM(Nb)ICs, RHEAs and RCCAs can be described by the same parameters. The practicality of parameter maps inspired by NICE for describing/understanding the alloying behavior and properties of alloys and their phases is demonstrated. It is described how NICE helps the alloy developer to understand better the alloys s/he develops and what s/he can do and predict (calculate) with NICE. The paper expands on RM(Nb)ICs, RHEAs and RCCAs with B, Ge or Sn, the addition of which and the presence of A15 compounds is recommended in RHEAs and RCCAs to achieve a balance of properties.


Introduction
The targets given to the aerospace industry by international regulatory authorities regarding the environmental impact (noise, emissions) of aircraft in the future could be met with changes in airframes and aeroengines. The contribution of the latter to meet the targets is the reduction of CO 2 by 30% and of the NO x certification metric by 75% [1]. New materials are considered necessary to manufacture components that would enable critical parts of future aeroengines to operate at significantly higher temperatures (≥1850 • C) than those currently possible in high-pressure turbines (HPT) where coated and internally cooled single crystal Ni-based superalloy blades are used with turbine entry temperatures (TETs) not exceeding 1600 • C. In other words, there is a need for ultra-high-temperature materials (UHTMs) with capabilities beyond those of Ni-based superalloys [1][2][3].
In this paper, I reflect on the utility of NICE to design and develop new metallic UHTMs with Nb one of the alloying additions, drawing on my recent publications [1,3,[7][8][9][10][11] and, where it is appropriate, on papers that I have co-authored with members of the research group. I discuss (i) why a new alloy design methodology was sought for metallic UHTMs and the foundations on which NICE was built, (ii) how NICE helps one to understand better the alloys s/he develops, and (iii) what one can do and predict (calculate) with NICE. In this paper, I do not cover the processing, oxidation and fracture toughness of metallic UHTMs, about which the interested reader could refer to [3]. In addition, I do not compare the properties of RM(Nb)ICs with those of the RHEAs and RCCAs that were reviewed by Senkov et al. in [13]; an interested reader could consult the ref [3]. However, in this paper, I expand on RM(Nb)ICs with B, Ge or Sn additions, some of which are also RHEAs and RCCAs [19], and in doing so, I confirm that the above elements are key additions in RHEAs and RCCAs to achieve a balance of properties.
In this paper, my approach to the subject matter is to provide a brief coverage/review of the alloying of RM(Nb)ICs (discussed in the refs [7][8][9][10][11] that dealt closely with issues that pertain to the alloys and their phases) and to show how my ideas that were instigated from these studies, despite their having been conceived and organized separately over many years, converged and were unified in NICE [1] to give a perspicuous and straight-forward account of a new alloy design methodology that is useful both for RM(Nb)ICs and for RHEAs and RCCAs [1,3,[19][20][21]24,25]. I use this opportunity to draw attention to RM(Nb)ICs and RCCAs with B, Ge or Sn additions and expand on the data presented in [1,3,[7][8][9][10][11] and, most recently, in [19,26]. The structure of the paper is as follows: First, we return to the alloying behavior of metallic UHTMs and their phases, then an overview of properties of alloys and phases and of relationships between alloys and their phases is given, and finally, the alloy design/selection methodology NICE is revisited.

Alloying Behavior of RM(Nb)ICs, RHEAs and RCCAs and Their Phases
Alloying elements mentioned in the previous section fall in different groups in plots (a) of diffusivity versus atomic size r i or Pauling electronegativity χ i [7], (b) of functions of elastic constants C ij (e.g., the Zener anisotropy constant) versus r i or χ i or the number of valence electrons per atom filled into the valence band (VEC) [8] (see also Figure 1) and (c) of Young's modulus versus r i or χ i [8]. Remarkably, in (a) and (c), where B is included in the data, the B always belongs in specific groups with/without the elements Al, Cr, Ge, Hf, Si, Sn, Ti and with/without RMs [7,8]. The elements Al, B, Cr, Ge, Hf, Si, Sn, Ti are key additions for improving the oxidation resistance of RM(Nb)ICs, meaning suppressing pest oxidation and improving oxidation resistance at high temperatures [1,3], and suppressing scale spallation [1,3,[19][20][21]25,26]. To the author's knowledge, additions of B, Ge or Sn have not been reported in RHEAs, and RCCAs studied to date and were not reported for the RCCAs reviewed in [13], but they have been used only in RM(Nb)ICs some of which are also RHEAs or RCCAs, e.g., [3,[19][20][21]25]. We return to these three elements as alloying addition(s) in metallic UHTMs below in this section and in the following sections.    Figure 1 shows plots of elastic constants C ij , shear modulus G and bulk modulus B versus atomic size r i , Pauling electronegativity χ i and VEC of cubic (Figure 1a,d) and hexagonal ( Figure 1d) symmetry elements. Note that Fe currently is not used as elemental addition in RHEAs or RCCAs [13] and that in Figure 1a the group and R 2 value do not significantly change if Fe were to be excluded. In Figure 1d, note (i) that the elements Hf, Nb, Mo, W or Hf, Ti, Al, Cr, Si, Ge could be grouped together (see Figure 1e), (ii) that the latter six elements improve oxidation resistance in RM(Nb)ICs [1] as well as in RM(Nb)ICs that are also RCCAs [3,19,26,27] and suppress pest oxidation [27], (iii) that the former four elements are key additions (a) in RM(Nb)ICs for bcc solid solution strength and alloy strength [3] and for meeting the creep goal [3,12] and (b) in RCCAs for enhanced strength [3,13] and for improved oxidation resistance when added together with Al, Cr, Ti and Si [13]. Recently, our research group suggested that RM(Nb)ICs, RHEAs and RCCAs of the Nb-Mo-W-Ti-Cr-Hf-Al-Ge-Si-Sn system are worthy of development owing to their promise to meet property goals and/or offer a balance of properties [19]. Such metallic UHTMs could be protected by environmental coatings (ECs) of the bond coat (BC)/thermally grown oxide (TGO)/top coat (TC) type with BC consisting of αAl 2 O 3 scale forming HEAs of the Nb-Ti-Si-Al-Hf system [19][20][21] (compatible with the metallic UHTM substrate) with/without αAl 2 O 3 or Cr 2 O 3 and SiO 2 scale forming Si-rich intermetallic alloys of the Al-Cr-Fe-Nb-Si-Ti system [28] that are also compatible with the aforementioned HEA BC [28,29]. We return to ECs for metallic UHTMs in Section 5.
Metallurgists have used atomic size, electronegativity, the heat of mixing ∆H mix , the entropy of mixing ∆S mix and VEC to study alloys prior to HEAs, for example, for the study of rapidly solidified (RS) alloys and metallic glasses. The role of the researcher is not so much to collect and analyze data as to bring "trained judgment" to bear on the data. One often needs to capture similarities as well as differences (s) in his/her data. Consideration (i) of the alloying behavior of RM(Nb)ICs using the same parameters, namely ∆χ (based on Pauling electronegativity), δ (based on atomic size), VEC, ∆H mix , ∆S mix , Ω that are used (1) for the study of HEAs [23] and (2) to compare the latter with BMGs, e.g., [30], and (ii) of the (a), (b) and (c) in the first paragraph of this section and Figure 1, necessitated scrutiny of our work from a new perspective. We did not just consider "what do these parameters refer to?" but "how do we use these parameters?" what roles may possibly have in alloy design and how these roles change, overlap, and can be shown/demonstrated. This experience confronted me with new ways of interpreting our work that exceeded the limits of what can be perceived and visualized in familiar terms and made possible (A) the classification of the RM(Nb)ICs (and RCCAs) in groups, (B) new ways of presenting data (Figure 2, also see [8] and Figure 19 in [3]), and (C) the comparison of RM(Nb)ICs with RCCAs [3] and with HEAs and metallic glasses (Table 1). To sift and assess raw data required some form of visual representation and thus an element of informed subjectivity. After assessing the data, it was decided to separate all the alloys with boron addition, and in doing so, it was discovered that these alloys formed a separate group (group C) in parameter maps, see Figure 2. This then steered scrutiny of the data of the boron-free alloys, and in doing so, it was discovered that alloys that meet or have the potential to meet the creep property goal could form a separate group (group B) in parameter maps, see Figure 2. The grouping of alloys shown in Figure 2 considered RM(Nb)ICs based on the alloys KZ5, and YG8 with nominal compositions, respectively Nb-24Ti-18Si-5Al-5Cr [31] and Nb-20Si-5Hf-5Mo-3 W [32], of which the former meets the toughness goal, and the latter is close to meeting the creep goal [3,12], with additions of other TMs, RMs and simple metal (SM) and metalloid (Met) elements. with/out Laves phase, Group B alloys based on YG8 with Nb ss and Nb 5 Si 3 , Group C alloys based on KZ series alloys [31,33] with B addition. There are no boron-containing alloys in areas A and B. Alloys with RMs, Al, Cr, Sn and Ge are in all three areas. The alloys KZ5 and YG8 are indicated by asterisks. For the alloys of series 2 to 8, see Table 1 in [8], where also the values of the parameters ∆χ, δ, VEC, ∆H mix , ∆S mix , Ω are given. Figure 2 fall within the areas occupied by RCCAs in similar maps, for example, the ∆χ versus δ map in Figure 19 in [3] (otherwise stated, the RHEAs and RCCAs include some RM(Nb)ICs), (b) oxidation-resistant metallic UHTMs can be found in all three groups A, B and C in Figure 2 and (c) some of the RM(Nb)ICs in group C are also RHEAs and RCCAs (see below and following sections) with exceptional oxidation resistance [3]. In essence, (i) the alloying behavior of RM(Nb)ICs, RHEAs and RCCAs can be presented in ∆χ versus δ, ∆H mix versus VEC and VEC versus δ maps and (ii) there are RHEAs and RCCAs with B, Ge or Sn addition that are also RM(Nb)ICs [1,3,19] (or to put it in another way, some RM(Nb)ICs with B, Ge or Sn addition can also be RHEAS and RCCAs).

Remarkably, (a) groups A and B in
If the alloying of metallic UHTMs can be described using the parameters ∆χ, δ, VEC, ∆H mix , ∆S mix , Ω, why the phases that are present in the microstructures of these materials were not studied using these parameters before the publication of [7,[9][10][11]? A reasonable answer is that it is partly a matter of where researchers "point their instruments" to collect data and partly a matter of what they instructed their instruments to find for them. In our research group, we used reliable quantitative chemical analysis data (EPMA and EDS with standards) for RM(Nb)ICs and their phases and created maps for their bcc solid solutions ( Figure 3) [7][8][9][10][11]. In RM(Nb)ICs, three types of bcc Nb solid solution (Nb ss ) can form, namely "normal" Nb ss , Si-free Nb ss and Ti-rich Nb ss [7]. In RCCAs, one or more solid solutions can form [13]. The Ti-rich Nb ss is observed in as-cast (AC) RM(Nb)ICs. Figure  3a shows the VEC ss versus δ ss map for all the bcc solid solutions in AC and heat-treated (HT) RM(Nb)ICs (the chemical compositions of the solid solutions in this figure were given in table 1 in [7]) and would suggest that VEC ss decreases as δ ss increases, like the parameter (∆H mix ) ss in the (∆H mix ) ss versus δ ss map [3,7]. Figure 3b shows that the Si-free Nb ss has δ ss less than approximately 5, which is also the case in the (∆H mix ) ss versus δ ss map for RM(Nb)ICs [7], whereas the solid solutions of RCCAs have 4 < δ < 6 [3]. The parameter ∆χ ss would suggest that there exist no bcc Nb solid solutions in RM(Nb)ICs for 0.13 < ∆χ ss < 0.18 (Figure 4a), and that the Si-free Nb ss has ∆χ > 0.24 ( Figure 4b). The same gap exists in the case of solid solution RCCAs [3], and there is also a gap in the ∆χ values of eutectics with Nb ss and Nb 5 Si 3 [11]. Are these gaps "real" or just "an upshot of the available experimental data"? My response to this question is as follows: "There is actually a certain value in not finding data in some part of a map, in other words in having gaps in parameter values. They are some of those areas where the absence of evidence currently is evidence".  Valence electron concentration (VEC) versus δ maps for the bcc Nb ss in Nb-silicide-based alloys, (a) all data and (b) data for Si-free Nb ss and for Nb ss rich in Ti. In (a) the series 2 data are for Nb ss with RMs and Sn and no Al, the series 3 is for Nb ss with RMs, Ge and Sn and with/out Al and Cr, the series 4 is for Nb ss with Al, Cr, with/out Hf, no RMs and no B, Ge, Sn, the series 5 is for Nb ss with Al, B, Cr with/out Hf, the series 6 is for Nb ss with Al, Cr, with/out Ge or Sn or B, the series 7 is for Nb ss with RMs, with/out Al and with no B, Cr, Ge, Sn and the series 8 is for Nb ss with TMs, Al with/out RMs, B or Sn and no Ge. In (b) the series 2 is for Nb ss rich in Ti, and series 3 is for Si-free Nb ss . RM = Mo,Ta,W, TM = Cr,Hf,Ti. For the chemical composition of the solid solutions, see Table 1 in [7]. For dashed line in (b), see text. Note that the solid solutions included in this figure belong to the alloys for which data are given in Figure 2.
The alloys and their solid solutions can also be presented together in maps of the aforementioned parameters [8], and they can be separated into distinctly different groups in VEC versus ∆H mix , ∆χ versus δ ( Figure 5), and ∆χ versus ∆H mix and ∆χ versus Ω maps [8] in which the B-containing alloys and solid solutions occupy separate groups. Basically, (i) the alloying behavior of solid solutions in RM(Nb)ICs, and solid solution RHEAs and RCCAs can be presented in ∆χ versus δ, ∆χ versus VEC, ∆H mix versus δ and VEC versus δ maps [1,3] and (ii) the data includes solid solutions in RM(Nb)ICs with B, Ge or Sn addition that are (the alloys) also RHEAs and RCCAs [1,3,19,26].  for Si-free Nb ss and Nb ss rich in Ti. In (a) the series 2 data are for Nb ss with RMs and Sn and no Al, the series 3 is for Nb ss with RMs, Ge and Sn and with/out Al and Cr, the series 4 is for Nb ss with Al, Cr, with/out Hf, no RMs and no B, Ge, Sn, the series 5 is for Nb ss with Al, B, Cr with/out Hf, the series 6 is for Nb ss with Al, Cr, with/out Ge or Sn or B, the series 7 is for Nb ss with RMs, with/out Al and with no B, Cr, Ge, Sn and the series 8 is for Nb ss with TMs, Al with/out RMs, B or Sn and no Ge. In (b) the series 2 is for Nb ss rich in Ti, and series 3 is for Si-free Nb ss . RM = Mo,Ta,W, TM = Cr,Hf,Ti. For the chemical composition of the solid solutions, see Table 1 in [7]. For dashed lines and ellipses, see text. Note that the solid solutions included in this figure belong to the alloys for which data are given in Figure 2.
The alloying behavior of Nb 5 Si 3 is shown in Figure 6. The substitution of Si by Sn in Nb 5 (Si,Sn) 3 increases both VEC and ∆χ, these parameters increase further when Si is substituted by Ge in Nb 5 (Si,Ge) 3 (shown by the black arrow in Figure 6), whereas the substitution of Si by B in Nb 5 (Si,B) 3 has the opposite effect, causing a significant decrease of VEC and a small decrease of ∆χ (shown by the green arrow). The substitution of Nb by Ti in the silicide decreases VEC and slightly increases ∆χ in (Nb,Ti) 5 Si 3 (blue arrow) and the changes of VEC and ∆χ are enhanced in (Nb,Ti) 5 (Si,Ge) 3 and (Nb,Ti) 5 (Si,Sn) 3 (purple and red arrows, respectively), whereas, for the Nb 5 Si 3 alloyed with B and Ti, the VEC is decreased further compared with the Nb 5 (Si,B) 3 . Similarly, with the RM(Nb)ICs alloyed with B, which, as we have seen, occupy a separate area (C) in parameter maps (Figure 2), the alloyed 5-3 silicide with the addition of B also occupies a distinct, separate area in Figure 6. The effect of B on the alloying behavior of Nb 5 Si 3 is also shown in Figure 7, where the data are for RM(Nb)ICs based on KZ5 (Nb-24Ti-18Si-5Al-5Cr, nominal composition [31]) with additions of B, Ge, Hf or Sn. Note (a) the remarkable linear fit of data and (b) that the diamond data points correspond to RM(Nb)ICs that are also RCCAs.
The alloying behavior of the C14-NbCr 2 Laves phase and A15-Nb 3 X compounds (X = Al, Ge, Si, Sn) was discussed in [10] and of eutectics with Nb ss and Nb 5 Si 3 in [11]. In the refs [10,11], maps of the aforementioned parameters can be found. The data in Figure 8 shows that the parameter ∆χ of A15-Nb 3 X (i) decreases with increasing <X> = Al + Ge + Si + Sn, (ii) is in the range 0.855 to 1.04 for the alloyed Nb 3 X where Nb is substituted by Cr, Fe, Hf, Mo, Ti or W and (iii) does not deviate significantly from the trend established by the data for the unalloyed Nb 3 Al, Nb 3 Ge, Nb 3 Sn. A similar decrease of the parameter ∆χ of C14-NbCr 2 occurs with alloying, but in the case of the Laves phase, the substitution of Nb and Cr by alloying additions shifts the data to higher ∆χ values compared with the unalloyed Laves phase [10]. Remarkably, there is a gap (from 4.628 to 4.721) in the values of the parameter VEC of alloyed A15-Nb 3 X even though the data point for Sn rich Nb 3 Sn falls in this gap ( Figure 9). The same gap was shown in the ∆χ versus VEC map in [10]. Essentially, the alloying behavior of the intermetallics that can be stable in the microstructures of RM(Nb)ICs, some of which are also RHEAs or RCCAs, can be described using maps of the aforementioned parameters. Unfortunately, there is no data for the Laves phases and M 5 Si 3 silicides that are observed in the RHEAs and RCCAs that were reviewed in [13] to enable the construction of maps and to compare them with those of the intermetallic compounds in RM(Nb)ICs.  Table 1 in [7], and the series 2a to 8a data are for Nb silicide-based alloys in Table 1 in [8]. The series 2 and 2a data are for alloys with RMs, TMs, and Sn, but no Al, the series 3 and 3a data are for alloys with RMs, TMs, Ge and Sn and with/without Al and Cr, the series 4 and 4a data are for alloys with TMs, Al, with/without Hf, no RMs and no B, Ge, Sn, the series 5 and 5a data are for alloys with TMs, Al and B, with/without Hf, the series 6 and 6a data are for alloys with TMs, Al and with/without B, Ge, Hf and Sn, the series 7 and 7a data are for alloys with RMs, TMs with/without Al and with no B, Ge, Sn and the series 8 and 8a data are for alloys with TMs, Al with/without RMs, B or Sn and no Ge.  . Data about the densities and room temperature strength of these alloys is given in [3]. Nominal compositions (at.%) of B-containing RM(Nb)ICs-RCCAs 37Nb-24Ti-18Si-6B-5Al-5Cr-5Hf, 39Nb-24Ti-18Si-6B-5Al-4Cr-4Sn. For nominal compositions of other alloys, see Appendix A Table A1.  The ∆χ versus VEC maps of the phases in RM(Nb)ICs are shown in Figure 10. These and the ∆χ versus VEC map in Figure 16 in [3] are the "master maps" of metallic UHTMs (excluding RM(Mo)ICs). Note (a) that Figure 10 is a correction of Figure 5 in [1], in which by mistake, the labels for the A15-Nb 3 X and C14-NbCr 2 phases were swapped, (b) that the B-containing Nb ss and Nb 5 Si 3 "sit" in the left-hand side of the map in Figure 10a, (c) that eutectics with Nb ss and Nb 5 Si 3 are positioned in the area between approximately 0.12 < ∆χ < 0.25 and 4.3 < VEC < 4.9 that is also occupied by the bcc solid solution (Figure 10b), (d) that the data for the bcc solid solution RCCAs studied by Senkov et al. [13] and the HEA Nb ss and HEA eutectics with Nb ss and Nb 5 Si 3 in RM(Nb)ICs that satisfy the standard definition of HEAs fall in the area of the Nb ss and eutectics with Nb ss and Nb 5 Si 3 in Figure 10b, as discussed in [3].  ) show maps of ∆χ versus VEC. In (a), the data are for the Nb ss (blue triangles), Nb 5 Si 3 (green diamonds), C14-NbCr 2 Laves (purple diamonds) and A15-Nb 3 X (red diamonds) phases, and the boron-containing Nb ss and Nb 5 Si 3 are shown in light blue and light green. In (b), the data are for the Nb ss (blue triangles), Nb 5 Si 3 (green diamonds), eutectics with Nb ss and Nb 5 Si 3 (orange circles), C14-NbCr 2 Laves (purple diamonds) and A15-Nb 3 X (red diamonds) phases. The data for the bcc solid solution RCCAs studied by Senkov et al. [13], and HEA Nb ss and HEA Nb ss and Nb 5 Si 3 eutectics in RM(Nb)ICs that satisfy the "standard definition" of HEAs fall in the area of the solid solution and eutectics data in (b), as shown in Figure 16 in [3]. Note that both parts of this figure are the same as those in Figure 5 in [1], in which by mistake, the labels for the A15-Nb 3 X and C14-NbCr 2 phases were swapped.
The parameters ∆χ, δ, VEC, ∆H mix , ∆S mix , Ω can be seen as being nothing more than guidelines to make alloys. This they do with a certain monotonous consistency. In this sense, they are like the keys of the piano, each playing a single note, but combine them (in NICE as we discuss below) as you would combine piano keys, and you can create "melodies of infinite variety". Put all these parameters together (in NICE as we discuss below), and you have "the great symphony of RM(Nb)ICs, HEAs, RHEAs, RCCAs".

Alloying Behavior of RM(Nb)ICs, RHEAs and RCCAs and Properties of Alloys and Phases
The Vickers hardness of RM(Nb)ICs, some of which are also RCCAs, increases with increasing (∆H mix ) alloy , (∆S mix ) alloy or ∆χ alloy (Figure 11a,c). Only the parameter VEC alloy can separate the hardness of RM(Nb)ICs-RCCAs with B, Ge or Sn addition, which increases with VEC alloy , from the hardness of RM(Nb)ICs that are not RCCAs, which decreases with VEC alloy (Figure 11d). The latter trend was also exhibited in the room temperature strength (calculated from hardness) versus the VEC alloy plot discussed in [3], where it should be noted that the data includes Ti-free RM(Nb)ICs.   Figure 12 shows that the G/B ratio (Pugh's ratio) of the bcc solid solution formed in RM(Nb)ICs without B addition, respectively, increases and decreases with the parameters δss and Δχss of the solid solution (the ratio G/B of the Nbss also decreases with VECss, figure not shown). Pugh [35] predicted ductile behavior for G/B < 0.5. Figure 13 Figure 12 shows that the G/B ratio (Pugh's ratio) of the bcc solid solution formed in RM(Nb)ICs without B addition, respectively, increases and decreases with the parameters δ ss and ∆χ ss of the solid solution (the ratio G/B of the Nb ss also decreases with VEC ss , figure not shown). Pugh [35] predicted ductile behavior for G/B < 0.5. Figure 13 shows the Vickers hardness of solid solutions (HV ss ) formed in RM(Nb)ICs versus the parameters (a) Ω ss , (b) (∆H mix ) ss and (c) ∆χ ss . The HV ss decreases with Ω ss , (∆H mix ) ss or ∆χ ss for the solid solutions with Al, Cr, Ge, Hf, Mo, Nb, Si, Sn, Ti or W and increases with ∆χ ss for solid solutions that contain B and Ta, but not Ge. None of the solid solutions in this figure is a HEA/RHEA/RCCA, but the two solid solutions that belong in RM(Nb)ICs that are also RCCAs were formed in alloys with B addition. Note that the hardness HV ss of Nb ss in B-free as-cast RM(Nb)ICs increases with δ ss [3]. The effect of alloying additions on the hardness of Nb 5 Si 3 was discussed in [9], where it was shown (i) that among the elements that substitute Si, the addition of Ge has the strongest effect regarding the increase of hardness, whereas Al, B and Sn decrease the hardness, and (ii) that among the elements that substitute Nb the addition of Cr, Hf and Ti has the opposite effect reducing the hardness compared with the binary Nb 5 Si 3 [36,37]. Figure 14 shows that the Vickers hardness of alloyed Nb 5 Si 3 decreases with VEC Nb5Si3 for RM(Nb)ICs without B addition that is not RCCAs (Figure 14a), whereas the HV Nb5Si3 increases with VEC Nb5Si3 for RM(Nb)ICs with B addition (Figure 14b). Note that the data in Figure 14b (a) does not include alloys with simultaneous addition of B and Ge, but (b) includes data for Nb 5 Si 3 in RM(Nb)ICs that are also RCCAs (red diamonds). In RM(Nb)ICs, the Vickers hardness of eutectics with Nb ss and Nb 5 Si 3 increases with VEC eutectic [11] and decreases with increasing ∆χ eutectic or δ eutectic in Ti-free RM(Nb)ICs, respectively with Al, Cr, Ge, Hf, Nb, Si, Sn and Cr, Ge, Hf, Nb, Si, Sn alloying elements ( Figure 15).  In RM(Nb)ICs, the Vickers hardness of alloyed A15-Nb 3 X (X = Al, Ge, Si or Sn) increases with increasing ∆χ A15 or VEC A15 [10]. The increase of the creep rate of alloyed Nb 5 Si 3 compared with the binary silicide [1] is linked with the shift of the position of Nb 5 Si 3 in parameter maps ( Figure 6, and [9]), namely with changes in the parameters ∆χ Nb5Si3 and VEC Nb5Si3 . Furthermore, there are relationships between the creep rate of RM(Nb)ICs and the parameters δ alloy , ∆χ alloy or VEC alloy [1]. Unfortunately, there is no data about the creep of RHEAs and RCCAs and about the properties of the M 5 Si 3 and Laves phase(s) that are observed in these UHTMs. No RHEAs and RCCAs with A15-Nb 3 X compounds have been studied to date outside our research group [19,25,26].
Weight changes of alloys in isothermal oxidation are also linked with changes of the aforementioned parameters [1,19,26,27,38]. Figure 16 shows the weight change in isothermal oxidation at 1200 • C in the air of RM(Nb)ICs that are also RCCAs (data from Table 4 in [19]). Note (a) that the scale formed on the RM(Nb)ICs-RCCAs EZ8, JG6, ZF9 spalled off [19] (for the nominal composition of alloys see Table A1) and (b) that Bcontaining RM(Nb)ICs and RM(Nb)ICs-RCCAs do not experience pest oxidation at 800 • C and scale spallation at 1200 • C [3]. The arrows in Figure 16 indicate "direction of change" with alloying. The red arrow shows the effect on ∆W/A of removing Mo from its synergy with Al, Cr, Hf and Sn in the alloy JG6 [39] and having Ge in synergy with Al, Cr and Hf in ZF9 [34] or Sn in synergy with Al, Cr and Hf in EZ8. The brown and pink arrows show the shift towards the Hf-free alloy OHS1 [26], where Ge and Sn were in synergy with Al and Cr. The blue arrow shows the change owing to having Ge and Sn in synergy with Al, Cr, Hf and Ta (JZ3+ [25]) or Mo (JZ5 [19]). The purple arrow shows the effect of adding to OHS1 the elements Hf and Ta (JZ3 [25]) or Hf and Mo (JZ4 [19]), and the green arrow shows the effect of increasing the Ti concentration (JZ5). Note that the alloys JZ5 and JZ4 belong in the Nb-Mo-W-Ti-Cr-Hf-Al-Ge-Si-Sn system (see the second paragraph of Sections 2 and 5). The densities of RM(Nb)ICs, RM(Nb)ICs with B addition and RM(Nb)ICs-RCCAs with B addition, respectively are in the ranges 6.27 < ρ < 8.67 g/cm 3 , 6.41 < ρ < 6.87 g/cm 3 and 6.46 < ρ < 6.87 g/cm 3 [3] whereas the densities of RM(Nb)ICs-RCCAs with Ge or Sn or Ge + Sn and with/without Hf addition are in the range 6.78 < ρ < 7.94 g/cm 3 [19]. The densities of the RCCAs reviewed in [13] were in the range 5.6 < ρ < 13.8 g/cm 3 with those with Al, or Cr with/without Si, Ti, V or Zr addition having ρ < 9.08 g/cm 3 whereas the RCCAs with high strength at T ≥ 1200 • C have ρ > 10 g/cm 3 . The room temperature specific strength of RM(Nb)ICs with B addition and RM(Nb)ICs-RCCAs with B addition calculated from hardness, respectively, is in the ranges 315.8 < σ HV /ρ < 376.5 MPa cm 3 g -1 and 340.2 < σ HV /ρ < 383.6 MPa cm 3 g -1 [3], while that of the alloys JZ4 and JZ5 with Ge + Sn addition, respectively was 387 and 396 MPa cm 3 g -1 [19], higher than the specific strength of multiphase RHEAs and RCCAs that is less than about 308 MPa cm 3 g -1 [13]. In other words, RM(Nb)ICs-RCCAs with the addition of Be, Ge, or Sn have superior room temperature strength and specific strength and do not experience pest oxidation and scale spallation compared with RHEAs and RCCAs without these solutes.

Alloying Behavior of RM(Nb)ICs, RHEAs and RCCAs, Relationships Between Alloys and Their Phases
In view of the relationships between properties of the alloys and the aforementioned parameters (Figures 11-16), one would expect that the latter can also link alloys and their phases. Indeed, this is the case. Figure 17 shows (i) that the parameter VEC can link alloys and their Nb ss and Nb 5 Si 3 and (ii) that the parameter ∆χ links alloys and their eutectics with Nb ss and Nb 5 Si 3 (relationships also exist with the parameter δ, not shown in this paper). As the Al content in the alloy increases, the VEC alloy decreases (Figure 18a), and the VEC ss decreases (Figure 17a) as the Al of the Nb ss increases (Figure 18b). Note that in Figure 18a, the rectangle defines the area for alloys with different Ti/Si ratios [3] and alloying element additions. In this area, the B-containing RM(Nb)ICs and RM(Nb)ICs-RCCAs are close to the lower bound, whereas RM(Nb)ICs are closer to the upper bound.
Both Hf and Ti partition to the Nb 5 Si 3 , where they substitute Nb [9]. Ti-rich Nb 5 Si 3 is also rich in Hf compared with the "normal" Nb 5 Si 3 [9]. The partitioning of Hf with Ti in Ti-rich Nb 5 Si 3 contributes to the decrease of VEC alloy (Figure 17b) owing to the decrease of the VEC Nb5Si3 (Figure 18c). Ti (and Hf) rich Nb 5 Si 3 can form in as-cast RM(Nb)ICs and, unlike Ti-rich Nb ss , can be present after heat treatment. The partitioning of Ti and Hf (and other solute additions) in Nb 5 Si 3 affects its hardness ( Figure 14). Changes in VEC Nb5Si3 are also linked with changes in ∆χ Nb5Si3 (Figure 6), which together with changes in ∆χ ss [1,3,7], can affect the properties of eutectics with Nb ss and Nb 5 Si 3 . For the latter, the parameter ∆χ eutectic can increase or decrease with <Si> = Al + Ge + Si + Sn depending on the alloying additions [11]. For the alloying additions given in the caption of Figure 17c, the increase of ∆χ eutectic with ∆χ alloy is linked with a decrease of <Si> [11] and thus with an increase of VEC eutectic and HV eutectic [11].  for B-containing RM(Nb)ICs that are also RCCAs, blue line (R 2 = 0.9013) for alloying elements Al, B, Cr, Ge, Hf, Mo, Nb, Si, Sn, Ta, Ti, or W, circles for RM(Nb)ICs, diamonds for RM(Nb)ICs that are also RCCAs, green color for B-containing alloys, (c) VEC Nb5Si3 versus the concentration of Hf in Nb 5 Si 3 , green circle for Ti rich Nb 5 Si 3 , blue circle for normal Nb 5 Si 3 , for all data R 2 = 0.8853, diamonds for RM(Nb)ICs that are also RCCAs, green diamonds for B-containing alloys, alloying elements Al, B, Cr, Ge, Hf, Nb, Si, Sn, Ti, linear fit for data for RM(NB)ICs that are also RCCAS has R 2 = 0.9209. For the rectangular area in (a), see text.
Given that the aforementioned parameters connect alloys and their phases (Figures 11-18), one would expect relationships that link solute additions in alloys and their phases. In actual fact, this is the case. The concentrations of Ti, Al or W in the bcc solid solution(s) in RM(Nb)ICs increase with the Ti, Al or W concentrations in the alloy (e.g., Figure 19b and [1]). As Ti partitions to the solid solution, it "pulls" with it Al and Cr (Figure 19c,d and [40]) and "pushes away" W [19,25,41]. The changes of the solute concentrations in the alloy and its solid solution(s) are associated with changes in parameters (e.g., Figure 17a, Figure 18a,b and Figure 19a) and properties of the solid solution (e.g., Figures 12 and 13).
In the same way, as there are relationships between parameters and solutes in the bcc solid solution in RM(Nb)ICs and RCCAs (Figure 19a), and between solutes in the solid solution (Figure 19b,d), there are relationships between solutes in Nb 5 Si 3 and ∆χ Nb5Si3 (Figure 2 in [9] for B, Ge and Sn), between Ti Nb5Si3 and B, Ge, Sn (Figure 1 in [9]), Al and Si in Nb 5 Si 3 (Figure 8 in [42]), between Hf and Nb in Nb 5 Si 3 (Figure 8 in [42]). Figure 20 shows data for Al, Cr and Si in Nb 5 Si 3 . Note that this figure includes data for RM(Nb)ICs that are also RCCAs. Furthermore, note that, as was the case for the bcc solid solution, the data for RCCAs follows the same trend as that for RM(Nb)ICs (remember that Ti "pulls" with it Hf in Nb 5 Si 3 ). The changes of the solute concentrations in the alloy and its 5-3 silicide are associated with changes in parameters (e.g., Figures 17b and 18c) and properties of the silicide (Figure 14).
In addition, there exist relationships between solutes in the C14-NbCr 2 Laves phase that can form in RM(Nb)ICs and RM(Nb)ICs-RCCAs. Figure 21 shows such relationships for Al and Si. Note that data for Laves phase in oxidized alloys are also included in this figure. As the Cr concentration in the Laves increases, the concentrations of Al and Si, respectively, decrease and increase. The rectangular area in Figure 21b indicates the range of Si and Cr concentrations in C14-NbCr 2 Laves with upper (R 2 = 0.8309) and lower (R 2 = 0.9344) bands for RM(Nb)ICs and RM(Nb)ICs-RCCAs with RM = Mo,Nb,Ta,W, TM = Cr,Hf,Ti and SM-Met = Al,Ge,Si,Sn. The changes in solute concentrations in the Laves phase result in changes of its parameters VEC C14-NbCr2 and ∆χ C14-NbCr2 and its properties [10].

The Alloy Design/Selection Methodology NICE
The above-mentioned interrelationships of alloys and their phases regarding (i) alloying behavior, (ii) properties and (iii) solute concentrations are captured in the alloy design methodology NICE, the development of which was based on data for RM(Nb)ICs and was expanded to include data for RM(Nb)ICs that are also HEAs, RHEAs and RCCAs. The aforementioned parameters of alloys and their phases were calculated for those alloys for which reliable chemical analysis data (EPMA and EDS with standards) was available [1,3]. The database is updated as new data becomes available. The framework of NICE was discussed first in [1] and then in [3]. In the ref. [3] the RM(Nb)ICs that were included in [1] and the RCCAs reviewed in [13] were compared.
The choice of method and procedure in NICE was not content-neutral but closely bound with the identification of difficulties with experimental, modeling and ab-initio research [1,3,13]. The different components in the conception support and reinforce one another. Basically, NICE is a "goal-driven" alloy design approach that leads to the selection of metallic UHTMs worthy of development owing to promising oxidation or creep properties. NICE does not consider toughness. In NICE, the design of an alloy combines constraint(s), say desirable alloying elements and/or phases or RM/TM, or SM/Met ratios in the alloy (e.g., see [19][20][21]25]), with a property goal, say a creep rate (έ) target or an oxidation weight change (∆W/A) target, e.g., [19,25,43]. The alloy design starts with the calculation of the alloy composition. This is done using the relationship between, say,έ and ∆χ alloy to calculate the latter and then relationships of ∆χ alloy with the concentration of each element i (C i alloy ) are used to calculate C i alloy [1]. Clearly, elements with C i alloy < 0 cannot be present in the alloy composition. The calculated alloy composition can be consistent with an RM(Nb)IC or an RM(Nb)IC-RHEA/RCCA. The next step is to calculate first the parameters δ alloy , VEC alloy , ∆H mix alloy , ∆S mix alloy and Ω alloy for the alloy composition [1] and then alloy properties, for example, room temperature strength [3] and hardness (e.g., Figure 11). From the alloy composition, one can also calculate the macrosegregation of Si (MACSi) if the alloy were to be produced using liquid route processing [19,[24][25][26]34,38,[42][43][44]. Then one proceeds to calculate the composition of the bcc solid solution. First, the ∆χ Nbss is calculated from the relationship between ∆χ alloy and ∆χ Nbss [1]. The chemical composition of the solid solution is calculated from relationships between C i Nbss and ∆χ Nbss (there are also relationships between C i Nbss and δ Nbss or VEC Nbss , e.g., Figure 18b). Properties of the solid solution, for example, hardness, are then calculated [3] ( Figure 13). The solid solution is considered not to be stable in the alloy if 0.13 < ∆χ Nbss < 0.18 (Table 1, Figure 4). The type of solid solution, for example, Si-free Nb ss , is predicted from the δ Nbss value. The latter is calculated from the δ alloy versus δ Nbss relationship [1]. Si-free Nb ss is predicted to be stable in the alloy if δ Nbss < 5 ( Figure 3). The chemical composition of intermetallic compounds is calculated following a similar approach. For example, for Nb 5 Si 3 , the ∆χ Nb5Si3 is calculated from the relationship between ∆χ alloy and ∆χ Nb5Si3 and then the concentration of each element i (C i Nb5Si3 ) is calculated from relationships between C i Nb5Si3 and ∆χ Nb5Si3 [1]. The formation or not of a eutectic with Nb ss and Nb 5 Si 3 and whether the eutectic would be Ti-rich or Ti-poor [11] can be predicted using relationships between ∆χ alloy and ∆χ eutectic [1]. Similar to the alloy and phases, properties of the eutectic, for example hardness, can be calculated (e.g., see Figure 15). The vol. % of solid solution [19,25] and other properties also can be calculated. For example, mass changes (∆W/A) after isothermal oxidation for 100 h at 800 or 1200 • C and steady-state creep ratesέ for different temperatures and stresses are calculated using relationships between the alloy parameters and ∆W/A orέ [1]. Regarding creep, for a given temperature and stress, for each of the parameters δ, ∆χ or VEC, NICE calculates the steady-state creep rateέ [1] (attributed to intrinsic resistances to dislocation mobility [1,3]) and how the concentration of each alloying element affects the creep rate (e.g., Figure 22). Similarly, for oxidation resistance, NICE calculates the alloy weight change for each of the parameters δ, ∆χ and VEC for isothermal oxidation at 800 • C or 1200 • C [1,3,19,[25][26][27]43].  To summarize, NICE can calculate the composition of an alloy and the compositions of its solid solution(s) and intermetallic compound(s) (e.g., [19,25,43]), and can predict room temperature properties of an alloy and its phases (hardness, strength), Si macrosegregation, weight changes ∆W/A in isothermal oxidation and steady-state creep rateέ for a given temperature and stress (e.g., [3,19,21,25,27,28,34,43]). Owing to the relationships betweeń ε or ∆W/A and ∆χ alloy , δ alloy or VEC alloy in NICE [1,3], the latter also helps the alloy designer to understand the role/importance/contribution of each of the above parameters towards achieving the property goals and the contributions alloying additions make towards oxidation or creep properties, e.g., Figure 22 and [1]. For example, increasing the concentration of Al or Ti in the alloy increases the creep rate (Figure 22a,b), whereas increasing the concentrations of Mo and Si has the opposite effect (Figure 22c,d). Al and Ti are key additions for improving oxidation, reducing alloy density [1,3] and "balancing" properties of solid solution and intermetallic compounds; Si is important for reducing density, balancing vol.% of phases and properties of solid solution(s) and intermetallic compound(s), for improving oxidation resistance and for "balancing" the mechanical properties of the alloy. Mo is a key addition for room and high-temperature strength [3], oxidation [45], creep and alloy density [3]. Obviously, the calculations/predictions of NICE about the composition of alloys and phases and properties can be verified or not experimentally [19][20][21]25,43].
The search for metallic UHTMs that meet all three property goals simultaneously may be Sisyphean [46], but the search for creep resistance or oxidation resistance or toughness does not have a Sisyphean structure i.e., it must not be endlessly laborious or futile. According to NICE, to meet the creep goal or the oxidation goal, the alloy should have, respectively, high and low VEC alloy values, whereas the opposite is the case for the parameter δ alloy [1,24,[26][27][28]38]. (Valence electrons also play a role regarding the ductility of solid solution RCCAs [47] and the toughness of Nb-Ti-Cr solid solutions [48]). For increased creep resistance, alloy design should aim to increase the parameter ∆χ alloy [1]. To put this another way, NICE recommends low VEC alloy to suppress pest oxidation and improve oxidation resistance at high temperatures and high VEC alloy for high-temperature strength and resistance to creep. Thus, it is unlikely that RM(Nb)ICs and RM(Nb)ICs-RHEAS/RCCAs could meet both the oxidation and creep goals simultaneously. The same was concluded by Bewlay et al. for RM(Nb)ICs [49]. Consequently, it is essential for alloy developers also to consider the development of ECs to offer environmental protection to creep-resistant metallic UHTMs. NICE can help the alloy developer to design BC alloy(s) of ECs. Indeed, NICE has been used to design alumina forming HEAs for BCs for RM(Nb)ICs, e.g., [20,21] and to construct maps for the selection of oxidation-resistant BC HEAs or intermetallic alloys, e.g., [20,21,26]. Figure 23 shows parameter maps for HEAs of the Nb-Ti-Si-Al-Hf system and RM(Nb)ICs-RHEAs/RCCAs with/without B, or Sn or Ge or Ge + Sn or B + Sn addition, some of which belong in the Nb-Mo-W-Ti-Cr-Hf-Al-Ge-Si-Sn system (see Section 2). The B-containing alloys do not suffer from pest oxidation and scale spallation at 800 and 1200 • C [3]. Data for the weight change ∆W/A of the B-free RM(Nb)ICs-RHEAs/RCCAs and HEAs included in Figure 23 is given in Figure 16. In Figure 23, note (i) that the B-containing RM(Nb)ICs-RHEAs/RCCAs are found in distinct different areas in the VEC alloy versus δ alloy and ∆χ alloy versus δ alloy maps (Figure 23b,c), (ii) that the HEAs also are in separate areas in the three maps, (iii) that the RM(Nb)ICs-RHEAs/RCCAs with Ge + Sn addition are in distinct areas in the VEC alloy versus ∆χ alloy and ∆χ alloy versus δ alloy maps and (iv) the linear fit of the data (R 2 = 0.9971) for the HEAs and RM(Nb)ICs-RHEAs/RCCAs, respectively of the Nb-Ti-Si-Al-Hf and Nb-Mo-W-Ti-Cr-Hf-Al-Ge-Si-Sn systems in the VEC alloy versus ∆χ alloy map.
The above brief discussion and [1,3] show that NICE fashions comprehensive conceptions by linking the aforementioned parameters. Each one is to some extent independent, but they are also "in line with" one another's requirements to form a coherent whole. NICE shapes and is shaped by the idea of alloy design, and its rational procedures are ratified by the satisfactory results they deliver. We need to distinguish two main ideas ("theses") about the relationships between data and NICE, (i) the relevant data about the alloying behavior of alloys and their phases is necessary for NICE and (ii) reliable data are a necessary "constituent element" of NICE.
NICE is (a) internally consistent, (b) responsive (to a particular property or set of properties, and to the complexities of metallic UHTMs), (c) value-relative through and through (responds to needs of the designer of metallic UHTMs and is assessed in accordance with its success in doing this), (d) self-enhancing (reminds the alloy designer that its predictions are conditional and that further work remains to be done) and (e) practical (can address specific needs of the alloy designer, makes useful and helpful contributions), and (f) gives emphasis to attention to particularity (i.e., to be exact and detailed). Users of NICE become more discriminating, more confident and more reliable in their choice of alloys that are selected for further study.
I use the "metaphor of the rope" [50] to account for the capabilities ("strength") of NICE. A rope is made of many filaments, but not a single filament goes through the rope's entire length. It is the way the filaments overlap and their properties that give the rope its strength. Now think of NICE as a rope and the aforementioned parameters its filaments. The capability of NICE to predict room temperature strength, hardness, isothermal oxidation behavior in the pest oxidation regime and at high temperatures, and steady-state creep rates for different temperatures and stresses, and its capacity to calculate compositions of alloys and their phases are found in (results from) the overlap of the aforementioned parameters.

Summary and Comments About Future Research
This paper considered metallic UHTMs (excluding RM(Mo)ICs) that are under development as potential replacements of Ni-based superalloys for critical applications in aeroengines and must comply with specific property goals. The approach to creating the alloy design methodology NICE [7][8][9][10][11] was revisited.
The same phases can be present in the microstructures of RM(Nb)ICs, and RHEAs and RCCAs with Nb addition, namely solid solution(s) and intermetallics(s) such as M 5 Si 3 silicides and Laves phases. Together with Nb, the other alloying elements essentially can be the same in these metallic UHTMs and include B, Ge or Sn.
The alloying behavior of RM(Nb)ICs, RHEAs and RCCAs can be described by the same parameters, namely ∆χ, δ, VEC, ∆H mix , ∆S mix , Ω. The practicality of parameter maps inspired by NICE for describing/understanding the alloying behavior and properties of alloys and their phases was demonstrated.
The relevance of NICE for the design of RM(Nb)ICs, some of which are also RHEAs and RCCAs, was highlighted. Particular emphasis was given to the alloying additions B, Ge or Sn that are suitable for RM(Nb)ICs as well as for RHEAs and RCCAs to achieve a balance of properties. To date, RHEAs and RCCAs with B, Ge or Sn additions and with A15 compounds have not been studied outside the author's research group.
A recommendation for the development of bond coat HEAs of the Nb-Ti-Si-Al-Hf system and RM(Nb)ICs-RHEAs/RCCAs substrates of the Nb-Mo-W-Ti-Cr-Hf-Al-Ge-Si-Sn system that was made in [19][20][21] was highlighted in this paper. It was proposed that future research could investigate the effects of B, Ge or Sn additions on the properties of metallic UHTMs.
In my opinion, the present state of understanding of metallic UHTMs may reflect either the scarcity of key data, for example, how contamination by interstitial elements affects phase equilibria or mechanical properties [3,13] or information overload that may actually inhibit the conversion of information into knowledge and the reflection required to acquire understanding [3].
The creative practices of the international materials science and engineering community have stimulated technological innovation in metallic UHTMs, namely RMICs and RHEAs/RCCAs. Our thinking is formed not purely in the laboratory but also through discussions with an extensive circle of research colleagues and many hours of reading each other's work. Collaboration between the research groups that strive for the same thing in different ways within the technological context of their time can be powerful. Efforts to match capabilities to challenges and collaboration between laboratories infused with innovative thinking should be encouraged. Researchers should take inspiration from each other's practice. They observe, record, and act from different perspectives with the same goals and through different means-complementary perspectives perhaps, but sometimes divergent, answering to competing pulls of subjectivity and objectivity [3]. They must point to new research questions to seek a comprehensive understanding of the new materials and motivate new research for the provision of answers. The big picture emerges from the small details, from what we say to each other and what has come from this dialog.
I hope that in this paper and in the refs [1,3], I have shown by my account of NICE as much as by what it does succeed in doing, how hard and yet how exciting it is to study refractory metal alloys.

Acknowledgments:
The support of this work by the University of Sheffield, Rolls-Royce Plc and EPSRC (EP/H500405/1, EP/L026678/1) and discussions with all the members (current and past) of the research group and with partners in the EU-F5 ULTMAT project are gratefully acknowledged. where c i , r i , χ i , (VEC) i and T mi, respectively, are atomic percentage, atomic radius, Pauling electronegativity, VEC and melting point of the ith element, ∆ mix AB is the mixing enthalpy of binary liquid AB alloy and R is the gas constant.