On the Stability of Complex Concentrated (CC)/High Entropy (HE) Solid Solutions and the Contamination with Oxygen of Solid Solutions in Refractory Metal Intermetallic Composites (RM(Nb)ICs) and Refractory Complex Concentrated Alloys (RCCAs)

In as-cast (AC) or heat-treated (HT) metallic ultra-high temperature materials often “conventional” and complex-concentrated (CC) or high-entropy (HE) solid solutions (sss) are observed. Refractory metal containing bcc sss also are contaminated with oxygen. This paper studied the stability of CC/HE Nbss and the contamination with oxygen of Nbss in RM(INb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs. “Conventional” and CC/HE Nbss were compared. “Conventional” Nbss can be Ti-rich only in AC alloys. Ti-rich Nbss is not observed in HT alloys. In B containing alloys the Ti-rich Nbss is usually CC/HE. The CC/HE Nbss is stable in HT alloys with simultaneous addition of Mo, W with Hf, Ge+Sn. The implications for alloy design of correlations between the parameter δ of “conventional” and CC/HE Nbss with the B or the Ge+Sn concentration in the Nbss and of relationships of other solutes with the B or Ge+Sn content are discussed. The CC/HE Nbss has low Δχ, VEC and Ω and high ΔSmix, |ΔHmix| and δ parameters, and is formed in alloys that have high entropy of mixing. These parameters are compared with those of single-phase bcc ss HEAs and differences in ΔHmix, δ, Δχ and Ω, and similarities in ΔSmix and VEC are discussed. Relationships between the parameters of alloy and “conventional” Nbss also apply for CC/HE Nbss. The parameters δss and Ωss, and VECss and VECalloy can differentiate between types of alloying additions and their concentrations and are key regarding the formation or not of CC/HE Nbss. After isothermal oxidation at a pest temperature (800 oC/100 h) the contaminated with oxygen Nbss in the diffusion zone is CC/HE Nbss, whereas the Nbss in the bulk can be “conventional” Nbss or CC/HE Nbss. The parameters of “uncontaminated” and contaminated with oxygen sss are linked with linear relationships. There are correlations between the oxygen concentration in contaminated sss in the diffusion zone and the bulk of alloys with the parameters ΔχNbss, δNbss and VECNbss, the values of which increase with increasing oxygen concentration in the ss. The effects of contamination with oxygen of the near surface areas of a HT RM(Nb)IC with Al, Cr, Hf, Si, Sn, Ti and V additions and a high vol.% Nbss on the hardness and Young’s modulus of the Nbss, and contributions to the hardness of the Nbss in B free or B containing alloys are discussed. The hardness and Young’s modulus of the bcc ss increased linearly with its oxygen concentration and the change in hardness and Young’s modulus due to contamination increased linearly with [O]2/3.


Introduction
The interdepended targets for performance and environmental impact of future aero engines could be met with materials that would allow high pressure turbines to operate at significantly higher than current temperatures. In other words, ultra-high temperature NICE shows that metallic UHTMs must be understood holistically and that the properties of a metallic UHTM are comprehended by studying the alloying behaviour and properties of its constituent phases. In other words, NICE proposes two complementary ways of studying alloy development using both reductionist and holistic approaches. Akin to all alloys, a RM(Nb)IC, RHEA or RCCA is a physical system with a collection of atoms of different elements with similar or different concentrations and different levels of structure (meaning the different or similar structures of elements and of the phases such as solid solution(s) and intermetallic(s) that make up the alloy microstructure with a particular "architecture" (e.g., co-continuous solid solution(s)-intermetallic(s)), influenced by internal processes (e.g., solute partitioning) or the environment (e.g., contamination with interstitials) in which the alloy is produced and/or operates. For example, partitioning of solutes can result (i) to change in crystal structure (the case of Ti partitioning to Nb 5 Si 3 and substituting Nb, thus causing a change in structure from tetragonal to hexagonal [46]) or (ii) formation of sub-grains in Nb 5 Si 3 [47], 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 [48]).
In RM(Nb)ICs, RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs and single phase or multiphase RCCAs or RHEAs the solid solution(s) will be contaminated with oxygen, and the severity of contamination will differ, depending on alloying additions and their concentrations, and exposure conditions [13]. Alloying strategies might be able to counterbalance effects of interstitial contamination on properties. For example, grain-boundary segregation of oxygen caused room-temperature brittleness of the as cast (AC) single phase solid solution NbMoTaW RHEA. Alloying with B from 400 ppm (0.04 at.%) to 8000 ppm (0.8 at.%) offset this effect of O and improved the mechanical properties at room temperature. Both strength and plasticity were improved and reached maximum values at around 5000 ppm (0.5 at.%) B addition. Specifically, the plasticity increased from <2% to >10% and the fracture strength increased from 1211 MPa to 1780 MPa, respectively, for the base RHEA and the RHEA alloyed with 5000 ppm B. However, the plasticity of the said RHEA decreased with further increase in the B concentration [49]. Contamination with oxygen can have a strong effect of the near surface properties of phases and alloy [3]. This paper will show how NICE helps the alloy developer to understand the effect of contamination with oxygen on the properties of the bcc solid solution.

Aim of This Work
HE or CC phases can co-exist with "conventional" phases and can be stable in RM(Nb)ICs, RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs [10,14]. Phase transformations of CC silicides give new simple and/or complex microstructures the importance of which for the properties of alloys has not been studied or considered in modelling research, e.g., modelling of creep [50]. Are the CC or HE bcc solid solutions stable? Is their stability dependent on alloying additions, alloy condition (meaning AC or heat treated (HT)) and contamination with oxygen? Boron or Ge and Sn have a distinctive effect on the alloying behaviour and properties of the aforementioned materials [26,[32][33][34]45] and the Nb 5 Si 3 silicide [9,14,29]. Is the stability of CC/HE Nb ss dependent on the presence of B or Ge and Sn in the alloy? Are there similarities regarding the dependence of other solute addition concentrations on the B or Ge+Sn content of solid solutions? How does the contamination of bcc Nb ss with oxygen or alloying with boron affect its properties? The motivation for this paper was to provide answers to these questions.
I shall consider some of the possible permutations of available data between aforementioned parameters and between parameters and solutes under two major headings, namely "complex concentrated bcc solid solution" and "contamination of the bcc solid solution with oxygen". There is a logic behind this approach in this paper, as I shall aim to show. The four solutes Ge, Sn, B and O will be a focus, and the latter two will be the point of reference when I shall discuss the hardness of the bcc solid solution. All four solutes are remarkably untypical in RHEAs and RCCAs studied to date (e.g., see [19]) even though they are essential additions in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs for balance of properties. The first three, Ge and Sn together and B on its own or in synergy with Ge or Sn can assist the alloy developer to obtain metallic UHTMs with a balance of properties by making use of the synergies of these three elements with Al, Cr, Hf, Si and Ti, as suggested by research on RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs, e.g., see [9,14,[32][33][34][35][36]. Oxygen is a solute the presence of which cannot be avoided in UHTMs with RM additions owing to the sensitivity of RMs to interstitial contamination (e.g., see [3] and Section 3.1 below). The contamination with oxygen has profound implications for properties of phases (this will be demonstrated for the solid solution in this paper) that (a) should not be ignored in studies of processing-microstructure-property relationships in UHTMs, as discussed in [3,19], and (b) can be used to design specific microstructures to improve properties, for example see the "design and selection of Nb-Al-Si-Hf-Ti alloys" in [37,38].
The paper is consciously selective. It does not deal with CC/HE silicides, C14 Laves and A15 compounds, eutectics and lamellar microstructures and their contamination with oxygen. It is intended to open further questions about bcc solid solutions in metallic UHTMs and to suggest future research. It is not a system of polarities (opposite characteristics) (meaning "conventional"-CC/HE, contaminated -"uncontaminated" phase) that we have to deal with but an overlapping set of interrelationships (see below) and transformations [13,16], which are viewed in the context of metallic UHTM development and provide a useful route and compass for exploring the microstructures of these materials.
Given that the analysis of data for bcc solid solutions will be based on aforementioned parameters, the calculation of which requires high quality chemical analysis data [9,10,14], this paper concentrates only on the bcc solid solutions in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs for which such data are available, and cannot include RCCAs or RHEAs, for example, like those included in the review in [19], owing to lack of data for the latter metallic UHTMs.

Complex Concentrated Bcc Solid Solution
The bcc Nb ss in RM(Nb)ICs and RM(Nb)ICs/RCCAs with nominal Si concentration 18 at.% and alloying addition of Al, B, Cr, Ge, Hf, Mo, Nb, Sn, Ta, Ti or W can be (i) "conventional" Nb ss , (ii) CC/HE Nb ss , or (iii) Nb ss with no Si and (iv) not stable after heat treatment. These types of bcc solid solution are shown schematically in Figure 1 where the colours for (i) to (iv) are dark blue, red, light purple and light blue, respectively. Note that Figure 1 has data for bcc Nb ss in AC and HT alloys. "Conventional" Nb ss can be Ti rich only in AC alloys, meaning Ti rich Nb ss is not observed in HT alloys. In B containing alloy the Ti rich solid solution is usually CC/HE Nb ss .
For presentation purposes, in Figure 1 the numbers 15, 10 and 5 have been assigned, respectively, to "conventional" Nb ss , CC/HE Nb ss and not stable Nb ss . The nominal compositions of the alloys are shown in the Appendix A. For most of the alloys in Figure 1 the CC/HE Nb ss that was formed in the AC alloy was not stable after heat treatment.
The data in Figure 1 show (a) that CC Nb ss was stable after heat treatment only in alloys where Mo and W simultaneously were in synergy with Hf and with the simultaneous addition of Ge and Sn in the alloy (compare the alloys JZ3+, JZ4, JZ5 and the OHS1), whereas (b) when Mo was substituted with Ta a higher concertation of Sn was required to stabilise the CC Nb ss in the heat treated alloy (compare the alloys JZ3+ and JZ3). The (a) is also supported by the data for the alloy JN2, which in the AC condition had "conventional" Nb ss plus two CC solid solutions and only "conventional" Nb ss in the HT condition [51]. Furthermore, (c) in the alloy JZ3+ the CC Nb ss was formed in the AC and HT conditions, whereas (d) in the alloys JZ4 and JZ5 Nb ss was not formed in the AC condition and the CC Nb ss with no Si formed after heat treatment, while (e) the opposite was the case in the alloy OHS1, where CC Nb ss was formed in the AC condition and the Nb ss was not stable after heat treatment. In the B containing TT4, TT5, TT7 and TT8 alloys and the Ta containing alloy KZ6 "conventional" and CC/HE Nb ss formed in the AC condition and only "conventional" Nb ss after heat treatment, but in the Sn containing alloys EZ8, JG6 and OHS1 the CC Nb ss was formed in the AC condition and the Nb ss was not stable after heat treatment. In the alloys EZ5 and TT6, "conventional" Nb ss formed in the AC condition and the Nb ss was not stable after heat treatment. Note that both alloys contain Sn, whereas B was present only in the alloy TT6. For presentation purposes, in Figure 1 the numbers 15, 10 and 5 have been assigned, respectively, to "conventional" Nbss, CC/HE Nbss and not stable Nbss. The nominal compositions of the alloys are shown in the Appendix A. For most of the alloys in Figure 1 the CC/HE Nbss that was formed in the AC alloy was not stable after heat treatment.
The data in Figure 1 show (a) that CC Nbss was stable after heat treatment only in alloys where Mo and W simultaneously were in synergy with Hf and with the simultaneous addition of Ge and Sn in the alloy (compare the alloys JZ3+, JZ4, JZ5 and the OHS1), whereas (b) when Mo was substituted with Ta a higher concertation of Sn was required to stabilise the CC Nbss in the heat treated alloy (compare the alloys JZ3+ and JZ3). The (a) is also supported by the data for the alloy JN2, which in the AC condition had "conventional" Nbss plus two CC solid solutions and only "conventional" Nbss in the HT condition [51]. Furthermore, (c) in the alloy JZ3+ the CC Nbss was formed in the AC and HT conditions, whereas (d) in the alloys JZ4 and JZ5 Nbss was not formed in the AC condition and the CC Nbss with no Si formed after heat treatment, while (e) the opposite was the case in the alloy OHS1, where CC Nbss was formed in the AC condition and the Nbss was not stable after heat treatment. In the B containing TT4, TT5, TT7 and TT8 alloys and the Ta containing alloy KZ6 "conventional" and CC/HE Nbss formed in the AC condition and only "conventional" Nbss after heat treatment, but in the Sn containing alloys EZ8, JG6 and OHS1 the CC Nbss was formed in the AC condition and the Nbss was not stable after heat treatment. In the alloys EZ5 and TT6, "conventional" Nbss formed in the AC condition and the Nbss was not stable after heat treatment. Note that both alloys contain Sn, whereas at.% and alloying elements Al, B, Cr, Ge, Hf, Mo, Nb, Sn, Ta, Ti, W: "conventional" Nb ss (dark blue), CC/HE Nb ss (red), (iii) Nb ss with no Si (light purple) (iv) not stable Nb ss (light blue). For presentation purposes the numbers 15, 10 and 5 have been assigned, respectively, to "conventional" Nb ss , CC/HE Nb ss and not stable Nb ss . AC = as cast, HT = heat treated. For nominal alloy compositions and references see the Appendix A. RM(Nb)ICs/RCCAs the alloys JZ3+, JZ5, TT5, ZF9, JG6, EZ8, TT7, OHS1, JZ4. HE Nb ss in TT4-AC.
In other words, considering the three elements B, Ge and Sn, which in synergy with Al, Cr, Hf and Ti, are key for improving the oxidation resistance and obtaining a balance of properties in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs [3,9,10,14,17,18,[33][34][35][36]42,[52][53][54] and (I would suggest) in RCCAs and RHEAs, it is advised that alloying with B plus Hf or Mo or Ta is unlikely to stabilise CC/HE Nb ss compared with the simultaneous addition of Ge and Sn with Hf, Mo and W in the aforementioned metallic UHTMs.
The relationship between the entropies of mixing of alloys and their bcc solid solutions is shown in Figure 2a. Data for solid solutions and alloys can be found, respectively, in the Table 1 in [28] and the Table 1 in [26] and the nominal alloy compositions are given in the Appendix A. In Figure 2a the linear fit of all the data is good (R 2 = 0.9019) and shows that the CC/HE Nb ss has high entropy of mixing (see below), and is formed in RM(Nb)ICs, and RM(Nb)ICs/RCCAs or RM(Nb)IC/RHEAs that also have high entropy of mixing (12.4 < ∆S mix alloy < 13.65 Jmol −1 K −1 ). Relationships of the solid solution parameter Ω with the solid solution enthalpy of mixing, and the parameters δ and ∆χ are shown in Figure 2b-d. The CC/HE Nb ss has low Ω (<2.4), high |∆H mix |, high and low δ and ∆χ (Pauling electronegativity) parameters (>5.7 and <0.18, respectively) and low VEC (figure not shown). In the plots of Ω ss with δ ss , ∆χ ss and VEC ss (figure not shown) only δ ss can show the effect of specific alloying additions. Indeed, in Figure 2c the blue data are for the alloying additions Al, B, Cr, Hf, Mo, Nb, Si, Sn, Ti and W, the brown data for Al, B, Cr, Ge, Hf, Mo, Nb, Si, Ta, Ti, W and the red data for Al, B, Cr, Ge, Hf, Mo, Nb, Si, Sn, Ta, Ti and W. Note that the blue and brown lines in Figure 2c are essentially parallel, and that the red line is for alloys with 24 at.% Ti and 18 at.% Si (nominal). In other words, (i) the addition of Ta and the replacement of Sn with Ge reduces both the δ ss and Ω ss parameters (shift from blue to brown line), whereas the simultaneous addition of the said elements "bridges the gap" with further decrease in Ω ss and formation of CC/HE Nb ss (red data) and (ii) the parameters δ ss and Ω ss are key in the alloy design stage for designing alloys with "conventional" and CC/HE Nb ss .
How do the values of the parameters for CC/HE Nb ss of the alloys in Figure 2  In other words, considering the three elements B, Ge and Sn, which in synergy with Al, Cr, Hf and Ti, are key for improving the oxidation resistance and obtaining a balance of properties in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs [3,9,10,14,17,18,[33][34][35][36]42,[52][53][54] and (I would suggest) in RCCAs and RHEAs, it is advised that alloying with B plus Hf or Mo or Ta is unlikely to stabilise CC/HE Nbss compared with the simultaneous addition of Ge and Sn with Hf, Mo and W in the aforementioned metallic UHTMs.
The relationship between the entropies of mixing of alloys and their bcc solid solutions is shown in Figure 2a. Data for solid solutions and alloys can be found, respectively, in the Table 1 in [28] and the Table 1 in [26] and the nominal alloy compositions are given in the Appendix A. In Figure 2a the linear fit of all the data is good (R 2 = 0.9019) and shows that the CC/HE Nbss has high entropy of mixing (see below), and is formed in RM(Nb)ICs, and RM(Nb)ICs/RCCAs or RM(Nb)IC/RHEAs that also have high entropy of mixing (12.4 < Smix alloy < 13.65 Jmol −1 K −1 ). Relationships of the solid solution parameter  with the solid solution enthalpy of mixing, and the parameters  and  are shown in Figure 2b  Relationships between the parameters ∆χ and VEC of alloys and Nb ss are shown in Figure 3, where the CC/HE Nb ss is indicated with the green data points. Note that this type of solid solution was mostly observed in AC alloys ( Figure 1). The data in Figure 3 are for the same alloys as in Figure 2. In Figure 3a the R 2 = 0.8061 is for the linear fit of all the data and R 2 = 0.8867 is for the data of the CC/HE Nb ss . Notice (i) the gap (green double arrow) in ∆χ Nbss values, in agreement with [28], which means that the CC/HE Nb ss follows the same rules as the "conventional" Nb ss [10], and (ii) that CC/HE Nb ss is found on either side of this gap. In Figure 3b all the data have R 2 = 0.628, the brown data points give R 2 = 0.8322, and the green data points give R 2 = 0.6978.
Even though the same alloying additions were in the alloys and their solid solutions represented by the green and blue data points in Figure 3, the alloys and their solid solutions indicated with the brown data points did not contain Ge and their Ti content was not fixed at 24 at.% nominal, as is the case for the alloys represented with the green data points. Instead, they were either Ti free (alloy YG8) or their Ti concentration was lower (alloys YG10, YG11). In other words, the parameter VEC ( Figure 3b) shows that not only the alloying additions but also their concentrations in an alloy are key regarding the formation or not of CC/HE Nb ss . Furthermore, only with the parameter VEC we can differentiate the data for CC/HE Nb ss and "conventional" Nb ss , as indicated with the brown and green lines compared with the blue line in Figure 3b. Thus, the co-existence of CC/HE Nb ss with "conventional" Nb ss in most alloys [14] is supported by the data in Figures 2 and 3. Additionally, Figure 3 confirms (iii) that the relationships between the alloy and solid solution parameters ∆χ and VEC, which are fundamental relationships in NICE [10], apply also for CC/HE Nb ss and (iv) that the parameters VEC alloy and VEC ss are key in the alloy design stage for designing alloys with "conventional" and CC/HE Nb ss . To summarise, the design of alloys with "conventional" and CC/HE Nb ss must make use of the relationships of the parameter ∆χ alloy with the concentrations of solute additions in NICE [10] and the relationships between the parameters VEC alloy and VEC ss and δ ss and Ω ss .
The parameters VEC, δ and ∆χ of alloys in which CC/HE Nb ss was observed are shown in Figure 4, and the parameters VEC, δ and ∆χ of the CC/HE Nb ss in the same alloys are shown in Figure 5. Figure 4a shows significantly higher values of δ alloy for B containing alloys (range 12.57 to 13.35, compared with 8.55 to 9.66 for B free alloys) and essentially similar VEC alloy values (4.403 to 4.584). Figure 4b shows small range of ∆χ alloy values (0.131 to 0.21) (also see Table 1 in [26]), and wider range and higher values of VEC CC/HE Nbss (4.51 to 5.38, Figure 5a). Significantly wider range of ∆χ CC/HE Nbss values (0.067 to 0.369) is shown in Figure 5b with strikingly lower values for B containing CC Nb ss (Figure 6a), noticeably higher values of δ CC/HE Nbss for RM(Nb)ICs/RCCAs where B was simultaneously present with Hf (alloy 11) or Ta (alloy 12) ( Figure 5a) and overall markedly lower values of δ CC/HE Nbss (4.239 to 9.69) compared with δ alloy (also see Table 1 in [28]). The parameter ∆χ CC/HE Nbss increases with increasing ∆χ alloy (Figure 6a Nbss (4.239 to 9.69) compared with alloy (also see Table 1 in [28]). The parameter CC/HE Nbss increases with increasing alloy (Figure 6a), "conventional" Nbss ( Figure 6b) and VECCC/HE Nbss ( Figure 6c). Remarkably, there is a strong correlation between the  parameters of "conventional" and CC/HE Nbss with the B concentration of the solid solution, as shown in Figure 7a.    of alloy. Colours: blue VEC, brown , green . Alloys 1 to 12 contain Al, Cr, Nb, Si, Ti plus in (1) Ge, Hf, Sn, Ta, W, in (2) Ge, Hf, Mo, Sn, W, in (3) B, Ta, in (4) Ge, Hf, in (5) Ge, Hf, Sn, Ta, W, in (6) Hf, Mo, Sn, in (7) Hf, Sn, in (8) Ta, in (9)  The co-existence of CC/HE Nb ss with "conventional" Nb ss in most alloys [14] is further supported by the data in Figure 6 that also confirm that the relationships between the alloy and solid solution parameters ∆χ and VEC, which are fundamental relationships in NICE [10], apply also for CC/HE Nb ss .
Boron, Ge and Sn are key elements for obtaining a balance of properties in metallic UHTMs but their roles regarding the stability of CC/HE Nb ss differ, see above. The CC/HE Nb ss was stable after heat treatment in alloys with simultaneous addition of Mo, W with Hf, Ge and Sn ( Figure 1). Figure 7 shows relationships of the solid solution parameter δ versus the B or Ge+Sn concentration in the solid solution. In both cases the parameter δ increases with increasing B or Ge+Sn concentration in the solid solution.
Note that in Figure 7a, the data are for "conventional" and CC/HE Nb ss , whereas in Figure 7b the data are only for CC/HE Nb ss . The co-existence of CC/HE Nb ss with "conventional" Nb ss in boron containing alloys is further supported by the data in Figure 7a. Lowest B concentration in the solid solution and thus lowest δ parameter was found when B was simultaneously present with Sn or Ta in the alloy [35]. Correlations of boron concentration in Nb ss with the parameters VEC and ∆χ are not strong (figures not shown).
Relationships between B or Ge+Sn concentration and other solute additions in CC/HE Nb ss in RM(Nb)ICs and RM(Nb)ICs/RCCAs are shown in Figures 8 and 9.  The co-existence of CC/HE Nbss with "conventional" Nbss in most alloys [14] is further supported by the data in Figure 6 that also confirm that the relationships between the R² = 0.9791  The Al, Cr, Ti, Al+Cr and Si concentrations in the CC/HE Nb ss decrease as its boron concentration increases. The Nb/Ti ratio of the CC/HE Nb ss increases with its boron concentration and decreases with its Al+Cr content. The parabolic fit of data in Figure  Note that in Figure 7a, the data are for "conventional" and CC/HE Nbss, whereas in Figure 7b the data are only for CC/HE Nbss. The co-existence of CC/HE Nbss with "conventional" Nbss in boron containing alloys is further supported by the data in Figure 7a. Lowest B concentration in the solid solution and thus lowest  parameter was found when B was simultaneously present with Sn or Ta in the alloy [35]. Correlations of boron concentration in Nbss with the parameters VEC and  are not strong (figures not shown).
Relationships between B or Ge+Sn concentration and other solute additions in CC/HE Nbss in RM(Nb)ICs and RM(Nb)ICs/RCCAs are shown in Figures 8 and 9. Whereas the Al, Cr, Ti and Al+Cr concentrations in the CC/HE Nb ss in B containing alloys decrease as the B concentration in the solid solution increases (Figure 8), the opposite is the case when the concentrations of the same solute additions are plotted versus the Ge+Sn concentration of the CC Nb ss in B free alloys (Figure 9). Note that there is no correlation between the Si and Ge+Sn concentrations in CC Nb ss . Similarly with the B containing alloys, the Nb/Ti ratio of the CC Nb ss increases with decreasing Al+Cr content (Figures 8e and 9e), but unlike the B containing Nb ss , the Nb/Ti ratio decreases with increasing Ge+Sn concentration (Figures 8f and 9f). Furthermore, there is a good correlation between the total RM concentration in CC Nb ss and its Ge+Sn content that shows the former decreasing as the latter content increases (RM = Nb + Mo + Ta + W). Note that also there are good correlations between the W and Ti content, the Ti concentration with the W/RM ratio and the Al+Cr sum with the Sn/Ge ratio of the Nb ss of B free RM(Nb)ICs and RM(Nb)ICs/RCCAs with Ge, Sn, and RM additions (see Figure 12 in [33] and Figure 12 in [34]).  (Figure 9). Note that there is no correlation between the Si and Ge+Sn concentrations in CC Nbss. Similarly with the B containing alloys, the Nb/Ti ratio of the CC Nbss increases with decreasing Al+Cr content ( Figures  8e and 9e), but unlike the B containing Nbss, the Nb/Ti ratio decreases with increasing Ge+Sn concentration (Figures 8f and 9f). Furthermore, there is a good correlation between the total RM concentration in CC Nbss and its Ge+Sn content that shows the former decreasing as the latter content increases (RM = Nb + Mo + Ta + W). Note that also there are good correlations between the W and Ti content, the Ti concentration with the W/RM ratio and the Al+Cr sum with the Sn/Ge ratio of the Nbss of B free RM(Nb)ICs and RM(Nb)ICs/RCCAs with Ge, Sn, and RM additions (see Figure 12 in [33] and Figure 12 in [34]).
In B containing RM(Nb)ICs and RM(Nb)ICs/RCCAs, the parameter Nbss increases with BNbss (Figure 7a) and the hardness of the solid solution decreases with increasing Nbss (see the descending part (green data) of the HVss versus ss data in Figure 7 in [3]). In B containing RM(Nb)ICs and RM(Nb)ICs/RCCAs, the parameter δ Nbss increases with B Nbss (Figure 7a) and the hardness of the solid solution decreases with increasing δ Nbss (see the descending part (green data) of the HV ss versus δ ss data in Figure 7 in [3]). From the two linear relationships the dependence of HV ss on B Nbss can be derived. The hardness of Nb ss in B free or B containing alloys is discussed in the next section. Note that the alloying with B has the opposite effect on the hardness of tetragonal Nb 5 Si 3 compared with the effect of Ge or Sn, meaning the hardness increases upon alloying with B (see Figure 14 in [9]).
The ductile behaviour and yield strength of bcc Nb-rich solid solution alloys with Al, Cr and Ti additions (i.e., (Nb,Ti,Cr,Al) ss ) has been studied for different Nb/Ti ratios and Al+Cr sums [55]. At low Nb/Ti ratios, brittle behaviour was observed at higher Al+Cr content compared with high Nb/Ti ratios. For example, for Nb/Ti ≈ 0.8 brittle behaviour was observed for Al+Cr higher than about 22 at.%, and for Nb/Ti ≈ 1 or 2 ductile behaviour was observed for Al+Cr less than about 20 at.% and 18 at.%, respectively,. The room temperature yield strength decreased with decreasing Nb/Ti ratio. For example, for Nb/Ti ≈ 1 and Al+Cr ≈ 20 at.% the yield strength was about 980 MPa, whereas for Nb/Ti ≈ 0.8 it was about 825 MPa for Al+Cr ≈ 22 at.%. For Nb/Ti ≈ 1 increasing the Al content gave strengthening at room temperature and weakening at high temperatures, the Cr addition gave significant strengthening at all temperatures, approximately doubling the strength at 1200 • C. Reduced Ti concentration improved the high temperature strength. Note that for B containing RM(Nb)ICs and RM(Nb)ICs/RCCAs the Nb/Ti ratio of the solid solution increases with increasing B content (Figure 8f). It is suggested that it would be possible to "ductilize" the "conventional" or CC/HE Nb ss with B addition and "fine tuning" of the Nb/Ti ratio, and the Al+Cr sum of the Nb ss in multiphase RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs (Figure 8).
Unlike the B containing RM(Nb)ICs and RM(Nb)ICs/RCCAs, currently there are no hardness data for the solid solutions in B free alloys with Ge, Sn and RM additions. Like the B-containing alloys, the latter alloys (i) exhibit exceptional oxidation resistance at pest and high temperatures with no scale spallation [33][34][35][36] and (ii) are expected to have good creep properties [14,34]. A material system suitable for high pressure turbine comprising a RCCA substrate of the Nb-Al-Cr-Ge-Hf-Mo-Si-Sn-Ti-W alloy system and a HEA bond coat of the Nb-Al-Hf-Si-Ti alloy system has been proposed using NICE [14,34].

Contamination of Nb with Interstitials
The contamination of Nb with carbon, hydrogen, nitrogen and oxygen has been reported in the literature. Pionke and Davis found out that in the temperature range 200 to 600 • C, both carbon and nitrogen had very limited solubility in Nb (<0.1 at.% (0.014 wt.%)), oxygen had slightly more (<0.6 at.%, (0.1 wt.%)) while hydrogen had very large solubility, about 10 at.% (0.1 wt.%). Unlike the other interstitial elements, the solubility of hydrogen in Nb decreased with increasing temperature. The equilibrium concentration of hydrogen was affected by pressure [56].
The use of reactive alloying elements (Hf, Ti, and Zr) in Nb tends to lower the oxygen solubility. The addition of Zr is of particular interest because Zr is an effective strengthener of Nb. Zirconium additions to Nb have the effect of lowering the apparent oxygen solubility limit but increasing the Nb solubility limit. This increase is roughly a factor of 4 for a given temperature and pressure [57].
There are conflicting reports about the solution hardening of Nb with oxygen and nitrogen. For example, Harris [58] reported that oxygen was three times more effective in solution hardening than nitrogen or carbon, whereas Seigle [59] found the latter two elements to be twice as effective as oxygen and Szkopiak ([60] and references within) reported that nitrogen was twice as effective as oxygen.
Oxygen contents as high as 0.41 wt.% increased the room temperature tensile strength of Nb from 276 MPa to 896 PMa and reduced the elongation from 30 to 10%. Contamination of Nb with oxygen increased its hardness [61] and caused embrittlement [62,63]. The latter has been attributed to screw dislocations moving through a repulsive field imposed by oxygen atoms, forming cross kinks and emitting excess vacancies in Nb which bind with oxygen and hinder dislocation motion [64].
Oxygen also affected the elevated temperature properties [62]. Tensile tests conducted on Nb with varying oxygen concentrations (10, 200 and 4300 wppm) revealed brittle failures below 400 • C for oxygen concentration of 0.43% [65]. At higher temperatures ductile failures were produced. The amount of ductility exhibited by Nb−O alloys at elevated temperatures was sensitive to strain-rate. For example, Nb containing 0.15% oxygen exhibited a decrease in the reduction in area from 90% to 30% at 467 • C due to a change in strain rate of 5 × 10 −5 to 2 × 10 −1 s −1 [66].
The DBTT of Nb depends on solute additions and increases with oxygen concentration as does the yield strength [67]. Interstitial elements have a significant effect on the DBTT, in that it can be raised as these impurities are increased. This trend in the data indicates that the interstitials progressively cause embrittlement and that the relative order of embrittlement is hydrogen (which is most potent), followed by oxygen and carbon (which is least potent). The effect of nitrogen is difficult to separate primarily because of uncertainties as to whether the solubility limit has been exceeded; however, based on very limited data, it appears to be more embrittling than either carbon or oxygen [68].
The sensitivity of the group V bcc metals to contamination with oxygen is greater compared with the group VI bcc metals Mo, W [69]. Contamination in air-reacted niobium, was similar to that in oxygen-reacted niobium, suggesting that oxygen is the primary diffusing contaminant [70]. Alloying Nb with Mo reduced the oxygen solubility, whereas alloying with Ti or Zr, respectively, increased and decreased it [71]. Contamination with hydrogen affected the shear moduli C' = (C 11 -C 12 )/2 and C 44 and the bulk (K) and Young's (E) moduli of V, Nb and Ta (group V bcc metals), of which the C' decreased, the C 44 increased, the K remained nearly constant, whereas the E of polycrystalline V or Ta with random orientation decreased and that of Nb increased with increasing hydrogen contamination. The effect on the C' of V was about four times the effect in Nb and Ta, whereas the change in C 44 with hydrogen was greatest for Nb and weakest for Ta [72]. Contamination with oxygen resulted in a small increase in C 44 and K for V, but in the case of Nb, the C' did not change with O ≤ 0.6 at.%, compared with the significant change in the C 44 with O ≤ 0.7 at.%, and both C' and C 44 increased, respectively, by 1% and 7% with O ≤10 at.%, which could be associated with precipitation of Nb oxide. Furthermore, the change in the C 44 of Nb was similar to that caused by the hydrogen contamination [72]. Hydrogen contamination increased the Young's modulus of all three group V bcc metals [73] and the increase in E 110 was very significant for Nb [74]. Contamination of Nb with oxygen (about 0.35 at.%) did not cause noticeable changes in the C' and C 44 shear moduli [75].
Regarding solid solutions of Nb with other bcc metals, contamination with oxygen affects mechanical properties. For example, for Nb-V alloys the addition of 500-ppm nitrogen and 1500-ppm (by weight) oxygen to Nb−2V and Nb−4V (wt.%) alloys caused pronounced increases in the DBTT of (Nb,V,I) ss where I = O or N. Nitrogen was found to be more potent than oxygen as a strengthener. The influence of both nitrogen and oxygen on the mechanical properties increased with increasing V content [76]. The affinity of Al, Cr, Hf, Ti and Zr for oxygen is high (for example Hf or Zr is used to scavenge oxygen in RM alloys [56]).
The bcc solid solution in RM(Nb)ICs, RM(Nb)ICs/RCCAs, RM(Nb)ICs/RHEAs, RHEAs and RCCAs is contaminated with oxygen, owing to the sensitivity of RMs on interstitial contamination and the presence of reactive elements in solution [3,10,13,[16][17][18][19]42,77]. Contamination can be severe depending on alloying elements (e.g., see Figure 17 in [13]). There are limited data for contaminated Nb ss and such data are available only for RM(Nb)ICs. These data show remarkable correlations between the parameters δ, ∆χ and VEC. The data in Figure 10 are for "conventional" Nb ss and Ti rich Nb ss in AC alloys and for the diffusion zone (DZ) and bulk of alloys after isothermal oxidation at 800 • C for 100 h. Figure 10 shows that δ Nbss increases with increasing ∆χ Nbss or VEC Nbss and that VEC Nbss increases with increasing ∆χ Nbss . The contaminated Nb ss in the DZ is CC/HE Nb ss , whereas that in the bulk of oxidised alloys can be "conventional" Nb ss or CC/HE Nb ss . The parameters of the solid solution in the AC alloys have the lowest values. There are also linear relationships between the parameters ∆χ (Figure 10d), VEC and δ (figures not shown) of the contaminated Nb ss in the bulk of alloy after isothermal oxidation at 800 • C versus the same parameter of "uncontaminated" Nb ss in AC alloy that show the same trend as in Figure 10d, meaning the parameter of the former is higher the higher the parameter of the latter.
Remarkably, strong correlations also exist for the oxygen concentration in contaminated solid solutions in the diffusion zone and the bulk of isothermally oxidised alloys at 800 • C with the parameters ∆χ Nbss (Figure 11a), δ Nbss ( Figure 11b) and VEC Nbss (Figure 11c), the values of which increase with increasing oxygen concentration in the solid solution. Note (i) that the chemical analysis data have been obtained using electron probe microanalysis [13,[16][17][18] and (b) the strong correlation with the parameter ∆χ Nbss . Moreover note that there are relationships between the concentrations of solutes in alloy and solid solution and the parameters ∆χ alloy and ∆χ ss , respectively, which are key in alloy design using NICE [10].
The co-existence of CC/HE Nb ss with "conventional" Nb ss in most alloys [14] is further supported by the data in Figure 10, which also show that such relationships between the parameters δ, ∆χ and VEC can be used in NICE to predict whether the microstructure of a designed alloys will consist of "conventional" Nb ss and CC/HE Nb ss and what the chemical compositions of such solid solutions would be. Furthermore, Figure 11 shows that contamination with oxygen affects all three parameters, which are related with atomic size, electronegativity and electron concertation in the valence band [10,28] and can account for changes in mechanical properties (creep, strength) and oxidation [9,10,14,17,18,[32][33][34]42].   Figure 10 shows that Nbss increases with increasing Nbss or VECNbss and that VECNbss increases with increasing Nbss. The contaminated Nbss in the DZ is CC/HE Nbss, whereas that in the bulk of oxidised alloys can be "conventional" Nbss or CC/HE Nbss. The parameters of the solid solution in the AC alloys have the lowest values. There are also linear relationships between the parameters  (Figure 10d), VEC and  (figures not shown) of the contaminated Nbss in the bulk of alloy after isothermal oxidation at 800 °C versus the same parameter of "uncontaminated" Nbss in AC alloy that show the same trend as in Figure 10d, meaning the parameter of the former is higher the higher the parameter of the latter.
Remarkably, strong correlations also exist for the oxygen concentration in contaminated solid solutions in the diffusion zone and the bulk of isothermally oxidised alloys at 800 °C with the parameters Nbss (Figure 11a), Nbss ( Figure 11b) and VECNbss (Figure 11c), the values of which increase with increasing oxygen concentration in the solid solution. Note (i) that the chemical analysis data have been obtained using electron probe microanalysis [13,[16][17][18] and (b) the strong correlation with the parameter Nbss. Moreover note that there are relationships between the concentrations of solutes in alloy and solid solution and the parameters alloy and ss, respectively, which are key in alloy design using NICE [10].

Hardness
Contamination of Nb with oxygen increases the Vickers hardness and yield strength of (Nb,O) ss and also increases its DBTT (Section 3.1). Contamination of the Nb solid solution in RM(Nb)ICs, RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs would affect its mechanical properties, in particular its hardness/yield strength and Young's modulus [3]. In each of these types of alloys and other RCCAs and RHEAs, for example those included in the review in [19], the contamination of the bcc solid solution will be different as it depends on the chemical composition of the solid solution, alloy condition (AC, HT) and environment of operation. For example, the contamination of the solid solution of the alloy NV1 was very sever, compared with other RM(Nb)ICs, see Figure 17 in [13]. I shall demonstrate the effects of contamination of bcc solid solution with oxygen on properties using data for the Nb ss in the RM(Nb)IC alloy NV1.
Why the alloy NV1? The high vol.% Nb ss (about 81%) in this alloy made feasible the measurement of the nanohardness of the Nb ss using nanoindentation, as discussed in [16]. Furthermore, the solute additions included key solute elements in metallic UHTMs, namely Al, Cr, Hf, Nb, Ti and V as well as Si and Sn.
The alloy NV1 was heat treated at 1500 • C for 100 h in a Ti-gettered argon atmosphere [16]. Contamination of the alloy could not be avoided even under these HT conditions. The nanohardness (nanoH, GPa) and the reduced elastic modulus E r (GPa) of the Nb ss of NV1-HT was measured from the surface of the heat-treated specimen to 2000 µm below the surface. A Hysitron TriboScope nano-mechanical testing system was used [16], with 8000 µN indenter load. A 4 × 4 testing array was created over a 50 µm × 50 µm area, 16 indents per area with 10 µm spacing. Data were collected from the surface and areas below it every 40 µm to a depth of 400 µm, then at 470 µm, then every 100 µm to 770 µm depth, and then at 940, 1070, 1220, 1390, 1590 and 2000 µm [78]. The microstructure of NV1-HT was shown in Figure 2 in [16]. The data in Figure 12a show that the nanoH ss increased to a maximum value in the area that was 570 µm below the surface, and then decreased to the "bulk" value of the HT specimen (blue data point). In Figure 12a, all the data fit to the 4th order polynomial nanoH ss = −3 × 10 −12 d 4 + 2 × 10 −08 d 3 − 3 × 10 −05 d 2 + 0.0175d + 7.4127 with R 2 = 0.921. First, there was a rapid increase in nanohardness (red data points, R 2 for linear fit of data) to about 120 µm, then the change in nanohardness with distance decreased (green data, R 2 for linear fit of data) and the nanohardness reached its maximum value in the area 570 µm below the surface, then the nanohardness decreased with distance from 570 µm to about 1220 µm (brown data points, R 2 for linear fit of data) followed with minor changes for distances greater than 1590 µm below the surface. A similar hardness profile to that shown in Figure 12a was reported in [70] for contamination of Nb with oxygen (i.e., for (Nb,O) ss ) after 1.62 h at 1000 • C, where the depth of contamination was at least 760 µm.
In Figure 12a the surface nanohardness is 7.29 GPa or 743.3 HV and corresponds to microhardness (microH) 548.2 HV based on the relationship microH Nbss = 0.7357 × nanoH Nbss (see [16]), whereas the maximum nanohardness of 10.77 GPa or 1098 HV at 570 µm below the surface corresponds to microhardness 807.9 HV. In the area 2000 µm below the surface the nanohardness was 6.1 GPa or 622 HV and corresponds to microH Nbss = 457.6 HV. This is lower than the hardness of the solid solution (523 HV) reported in [16], where the area of hardness measurement below the surface was not recorded. The surface hardness and the maximum hardness of the alloyed and contaminated with oxygen Nb ss in NV1-HT below the surface, respectively, was more than 7 and 10 times that of "uncontaminated" Nb. Up to 15 times increase in hardness has been reported for Nb contaminated with 16 at.% C, i.e., for (Nb,C) ss [79].
The hardness of the contaminated with oxygen Nb ss in NV1-HT at the surface (548 HV), and 570 µm below the surface (808 HV) was higher than the hardness of the (un-  Figure 11b give δ ss = 16.24. The ascending part of the HV ss versus δ ss data (brown data) in Figure 7 in [3] gives microH ss 600 µm = 797 HV that corresponds to nanoH ss 600 µm = 1083 HV or nanoH ss 600 µm = 10.62 GPa. The highest measured nanohardness of the Nb ss , which was for the area 570 µm below the surface (see above), and Figure 7 in [3] give δ ss = 16.66 and from Figure 11b we obtain the oxygen content of 12.96 at.%. Both oxygen concentrations are higher than the maximum solubility of oxygen in Nb (9 at.% at 1915 • C) according to the Nb-O binary phase diagram [69] and would suggest that the hardness increased with distance below the surface to the area where the Nb ss most likely became saturated with oxygen. Note (i) that the 9 at.% O solubility is for the (Nb,O) ss , (ii) that the maximum solubility of oxygen in the Nb ss of NV1 is not known, (iii) that the Nb ss in NV1 was heavily alloyed and its contamination was more severe compared with the Nb ss in other RM(Nb)ICs (see Figure 17 in [13]) and (iv) that no precipitation of a second phase in the Nb ss was observed in the areas below the surface where nanoindentation was performed. NICE has demonstrated how the relationships between parameters of alloys and their phases and between parameters and properties of alloys and their phases can assist the alloy designer to design/select new alloys worthy of R&D work [9,10,14]. Below it will be shown that it is possible to use such relationships to understand/predict how contamination with oxygen or alloying with boron affect properties of the solid solution.
Owing to contamination of Nb with oxygen the hardness and the lattice parameter of the (Nb,O) ss increase. This is well documented in the literature, for example see [60] and references within, and [61]. The effect of oxygen contamination on the hardness of Nb is given with linear relationships of the form HV ( [81]. Furthermore, they reported that the contamination of Nb with oxygen decreased the density of electronic states at the Fermi level N(0) and the "band structure" density of states N bs (0) [81], both of which correlate well with the parameter VEC of the (Nb,O) ss (Figure 13a,b). The importance of the parameter VEC for the properties (oxidation, creep) of RM(Nb)ICs was discussed in [10].

Boron Free RM(Nb)ICs
For boron free KZ series alloys (KZ series alloys are RM(Nb)ICs based on Nb-24Ti-18Si (at.%, nominal) with addition of Al, Cr individually or simultaneously, for example the alloys KZ4, KZ5 and KZ7, or with simultaneous addition of Al, Cr and Ta, for example the alloy KZ6, see Appendix A for nominal compositions) the hardness of the Nb ss depends on δ with a linear relationship of the form HV ss = aδ + b of which the constants a and b are both positive (for example, see the ascending data (brown data points) in Figure 7 in [3]). The values of these constants change when Sn or Ge is present in the alloy with/without Hf but they are still positive. The constant b is the hardness of Nb ss for which the type of solute elements and their concentrations give δ = 0 (solute additions and contamination with oxygen will change the lattice parameter). The parameter δ of the Nb ss depends on oxygen concentration with a linear relationship of the form δ = c[O] + d (Figure 11b For the Nb ss of the alloy NV1-HT, the hardness is HV ss NV1-HT = A ss NV1-HT [O] + B ss NV1-HT . If we were to assume that B ss NV1-HT is the average of the measured microhardness values of the Nb ss in the bulk of NV1-HT given in [16] and in [82] and [78] (i.e., B ss NV1-HT = 507 HV), and take into account the measured oxygen content of Nb ss in NV1-HT below the surface (see previous section) and the nanohardness data for different areas below the surface (Figure 12a), we can calculate the oxygen concentration of the Nb ss with distance below the surface of NV1-HT. This is shown in Figure 12c. Similarly with the other two parts of Figure 12, all the data for oxygen concentration as a function of distance below the surface fit to the 4th order polynomial [O] Nbss (at.%) = −4 × 10 −12 d 4 + 3 × 10 −08 d 3 − 8 × 10 −05 d 2 + 0.049d + 2.2136 with R 2 = 0.901. In Figure 12c Table 1 in [60] or about 430 HV if we take HV • Nb = 77.6 from [81]. We can also calculate the change in hardness of the Nb ss (∆HV) due to contamination with oxygen (∆HV = HV Nbss contaminated − HV Nbss bulk ) with distance d below the surface. This is shown in Figure 14a Figure 14b. Note that all the data in Figure 14b fit to a 6th order polynomial ∆HV ss = −0.1603x 6 + 3.0517x 5 − 23.073x 4 + 87.252x 3 − 163.54x 2 + 180.57x − 4.4811 with R 2 = 0.9989, shown with blue dashed line, and that at low oxygen contents the increase in ∆HV ss is parabolic (R 2 = 0.9596), followed by linear increases (R 2 = 0.9981 and R 2 = 0.9997) with increasing ∆HV ss /[O] 2/3 as the severity of contamination with oxygen increased, in agreement with [60].

Boron Containing RM(Nb)ICs
For boron containing KZ series alloys (for "definition" of these alloys see the previous section) the hardness of the solid solution also is given by a liner relationship of the form HV ss = aδ + b, where a < 0 and b > 0 (see the descending part of the data (green data points) in Figure 7 in [3]). Currently, there are no data for the change in the parameter δ with oxygen concentration in the Nb ss . Let us assume (i) that a linear relationship of the form δ = c[O] + d applies for the dependence of δ on contamination and (ii) that for an alloy 1 the hardness of its Nb ss increases with oxygen contamination, i.e., the equation HV 1

Boron Containing RM(Nb)ICs
For boron containing KZ series alloys (for "definition" of these alloys see the previous section) the hardness of the solid solution also is given by a liner relationship of the form HVss = aδ + b, where a < 0 and b > 0 (see the descending part of the data (green data points) in Figure 7 in [3]). Currently, there are no data for the change in the parameter  with oxygen concentration in the Nbss. Let us assume (i) that a linear relationship of the form δ = c[O] + d applies for the dependence of δ on contamination and (ii) that for an alloy 1 the hardness of its Nbss increases with oxygen contamination, i.e., the equation HV1 = A1[O] + B1 applies, or HVss1 = a1c1[O] + a1d1 + b1. Given that a1 < 0, the first term would be negative if c1 were to be positive. Thus, based on the aforementioned assumptions, we conclude that c1 must be negative, in other words the parameter δ of the solid solution would de- However, in the case of boron containing KZ series alloys, the parameter δ of the Nb ss depends on its boron concentration, as shown in Figure 7a, and the hardness of the solid solution decreased with increasing B concentration ( Figure 15). In other words, for these alloys the experimental evidence gives HV = C[B] + D, where C < 0, and D > 0 ( Figure 15) and δ = e[B] + f, where e > 0 and f > 0 (Figure 7a). Thus, for a boron containing alloy 1, HV ss1 = C ss1 [B] + D ss1 , HV ss1 = a 1 δ + b 1 (where a 1 < 0, see previous paragraph) or HV ss1 = a 1 (e 1 [B] + f 1 ) + b 1 or HV ss1 = a 1 e 1 [B] + a 1 f 1 + b 1 . Therefore, C ss1 = a 1 e 1 , i.e., the constant C ss1 is negative, in agreement with the experimental data ( Figure 15). The value of D ss1 = a 1 f 1 + b 1 is made of two parts, one (the constant b 1 ) is the hardness of a Nb ss with the same solute elements and concentrations that give δ = 0 and this part is positive, as was the case for B 1 (see above), and the other part, which in this case is negative, depends (i) on how changes in atomic size affect hardness (the constant a 1 < 0) owing to the alloying additions and their concentrations (excluding oxygen contamination), as was the case for B 1 , and (ii) on how alloying with boron affects atomic size (the constant f 1 > 0), differently with B 1 . a1(e1[B] + f1) + b1 or HVss1 = a1e1[B] + a1f1 + b1. Therefore, Css1 = a1e1, i.e., the constant Css1 is negative, in agreement with the experimental data ( Figure 15). The value of Dss1 = a1f1 + b1 is made of two parts, one (the constant b1) is the hardness of a Nbss with the same solute elements and concentrations that give δ = 0 and this part is positive, as was the case for B1 (see above), and the other part, which in this case is negative, depends (i) on how changes in atomic size affect hardness (the constant a1 < 0) owing to the alloying additions and their concentrations (excluding oxygen contamination), as was the case for B1, and (ii) on how alloying with boron affects atomic size (the constant f1 > 0), differently with B1.

Young's Modulus
The Young's modulus Es (GPa) of the Nbss was calculated using the data from the nano-indentation experiments (see Section 3.2.1) and Equation (1) ) 1 ( where Es and νs are the Young's modulus and Poisson's ratio of the phase, and Ei, νi are the parameters for the Berkovich indenter [83].

Young's Modulus
The Young's modulus E s (GPa) of the Nb ss was calculated using the data from the nano-indentation experiments (see Section 3.2.1) and Equation (1) where E s and ν s are the Young's modulus and Poisson's ratio of the phase, and E i , ν i are the parameters for the Berkovich indenter [83]. For the calculation of E s the values of E i and ν i that were given in the TriboScope manual [84] as 1140 GPa and 0.07, respectively, were used and the ν s was 0.38 [46,85]. Data for E s are shown in Figure 12b. The data showed that E r Nbss and E s Nbss increased to maximum values in the area 570 µm below the surface, and then decreased to the "bulk" of the HT specimen (blue data point). All the data fit to 4 th order polynomials, as follows: E r Nbss = 6 × 10 −12 d 4 + 2 × 10 −08 d 3 -0.0001d 2 + 0.1284d + 149.81 with R 2 = 0.8972 (figure not shown) and E s Nbss = 6 × 10 −12 d 4 + 3 × 10 −08 d 3 − 0.0002d 2 + 0.1501d + 147.33 with R 2 = 0.8968 (Figure 12b). First, there is a rapid increase in E s from 146 GPa at the surface to 175 GPa about 120 µm below the surface (red data points, the R 2 value is for linear fit of data), then the change in E s with distance decreases (green data, the R 2 value is for linear fit of data) and reaches its maximum value of 194 GPa in the area 670 µm below the surface, then the E s decreases with distance to about 155 GPa at 1220 µm (brown data points, the R 2 value is for linear fit of data) followed with minor changes for distances greater than 1590 µm below the surface to about 140 GPa in the bulk.
The values of the Young's modulus of the alloyed and contaminated with oxygen Nb ss in NV1-HT at 400 to 570 µm below the surface approached that of unalloyed γNb 5 Si 3 [46]. Significant increase in the Young's modulus of Nb owing to interstitial contamination has been reported for Nb contaminated with 16 at.% C (i.e., for (Nb,C) ss ), where the increase was up to three times the Young's modulus of "uncontaminated" Nb [79].
The Young's moduli of the Nb ss at the surface and the bulk of NV1-HT were higher than those of the (uncontaminated?) single phase solid solution RHEAs TiZrNbMo  Figure 14c. If we take the Young's modulus of uncontaminated and pure Nb as E • Nb = 101.9 GPa [46] and assume that the solid solution at 2000 µm below the surface was uncontaminated, we can obtain the contribution to the Young's modulus from the alloying additions (about 38.1 GPa) and then we can calculate the change in the Young's modulus of the Nb ss (∆E s ) due to contamination with oxygen with distance below the surface, as shown in Figure 14d, where ∆E s = 6 × 10 −12 d 4 + 3 × 10 −08 d 3 − 0.0002d 2 Figure 14e for which ∆E s = −0.0951x 6 + 2.0575x 5 − 16.628x 4 + 62.854x 3 − 109.2x 2 + 73.741x − 2.07 with R 2 = 0.9591. Note that at low contamination level the increase in ∆E s was linear (R 2 = 0.9773) and was followed with parabolic increases (R 2 = 0.9979 and R 2 = 0.7561) as the severity of contamination increased. As shown in the Figure 16 there is a linear relationship between the change in Vickers hardness (∆HV) and the change in Young's modulus (∆E) of the solid solution due to contamination with oxygen.

Summary
In this paper the stability of CC/HE solid solutions and the contamination with oxygen of solid solutions in (RM(INb)ICs), RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs was studied. "Conventional" solid solutions were compared with CC/HE ones. "Conventional" Nb ss can be Ti rich only in AC alloys, and Ti rich Nb ss is not observed in HT alloys. In B containing alloys the Ti rich solid solution is usually CC/HE Nb ss . The CC/HE Nb ss is stable after heat treatment in alloys with simultaneous addition of Mo, W with Hf, Ge and Sn. There is a strong correlation between the δ parameters of "conventional" and CC/HE Nb ss with the B or the Ge+Sn concentration in the solid solution. Similarities and differences between relationships of other solutes in alloys with B or Ge+Sn addition were noted and their implications for alloy design were discussed.
The CC/HE Nb ss has low ∆χ, VEC and Ω and high ∆S mix , |∆H mix | and δ parameters and is formed in alloys that also have high entropy of mixing. These parameters were compared with those of single-phase solid solution HEAs and differences in the values of ∆H mix , δ, ∆χ and Ω, and similarities in the values of ∆S mix and VEC were discussed. Relationships between the alloy and "conventional" solid solution parameters in NICE also apply for CC/HE Nb ss . The parameters δ ss and Ω ss , and VEC ss and VEC alloy can differentiate between types of alloying additions and their concentrations and are key regarding the formation or not of CC/HE Nb ss .
After isothermal oxidation at a pest temperature (800 • C/100 h) the contaminated with oxygen Nb ss in the diffusion zone is CC/HE Nb ss , whereas the solid solution in the bulk of the oxidised alloys can be "conventional" Nb ss or CC/HE Nb ss . The parameters of "uncontaminated" and contaminated with oxygen solid solutions are linked with linear relationships. There are strong correlations between the oxygen concentration in contaminated solid solutions in the diffusion zone and the bulk of isothermally oxidised alloys at 800 • C with the parameters ∆χ Nbss , δ Nbss and VEC Nbss , the values of which increase with increasing oxygen concentration in the solid solution.
Correlations between oxygen content and the parameters δ, ∆χ and VEC showed that the effects of interstitial contamination on properties can be understood and/or described with all three parameters. The boron content on the other hand correlates only with δ.
The effects of contamination with oxygen of the near surface areas of a heat-treated RM(Nb)IC with high vol.% Nb ss on the hardness and Young's modulus of the solid solution, and contributions to the hardness of the Nb ss in B free or B containing KZ series alloys were discussed. The hardness and Young's modulus of the bcc solid solution increased linearly with its oxygen concentration and the change in hardness and Young's modulus due to contamination increased linearly with [O] 2/3 .

Suggestions for Future Research
In RM(Nb)ICs/RCCAs, the CC bcc solid solutions with Ge+Sn and Al, Cr, Hf, Mo, Ti and W additions are (i) stable ( Figure 1) and (ii) Si free [33,34]. It is suggested (a) that single phase bcc solid solution RCCAs or RHEAs with above elements would be stable at high temperatures. Furthermore, given that Ge+Sn with Al, Cr, Hf, Mo and Ti improve oxidation at pest and high temperatures [32][33][34]87] it is suggested (b) that these RCCAs or RHEAs would also be oxidation resistant. For B containing RM(Nb)ICs, RM(Nb)ICs/RCCAs, RM(NB)ICs/RHEAs, RCCAs and RHEAs it is suggested to study the contamination with oxygen of their solid solutions and to find out if there is a relationship between the parameter δ and the oxygen concentration, see Boron Containing RM(Nb)ICs in Section 3.2.1.

Funding:
The support of this work by the University of Sheffield, Rolls-Royce Plc and EPSRC (EP/H500405/1, EP/L026678/1) is gratefully acknowledged.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable. Data Availability Statement: All the data for this work is given in the paper, other data cannot be made available to the public.

Acknowledgments:
The support of this work by the University of Sheffield, Rolls-Royce Plc and EPSRC (EP/H500405/1, EP/L026678/1) is gratefully acknowledged. Discussions with N Vellios, P Keating, J Uttley and O Chapman are gratefully acknowledged. For the purpose of open access, the author has applied a 'Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising.

Conflicts of Interest:
The author declares no conflict of interest.