On the Nb₅Si₃ Silicide in Metallic Ultra-High Temperature Materials

Abstract

Refractory metal (RM) M₅Si₃ silicides are desirable intermetallics in metallic ultra-high temperature materials (UHTMs), owing to their creep properties and high Si content that benefits oxidation resistance. Of particular interest is the alloyed Nb₅Si₃ that forms in metallic UHTMs with Nb and Si addition. The choice of alloying elements and type of Nb₅Si₃ that is critical for achieving a balance of properties or meeting a property goal in a metallic UHTM is considered in this paper. Specifically, the different types of alloyed “normal” Nb₅Si₃ and Ti-rich Nb₅Si₃, namely “conventional”, “complex concentrated” (CC) or “high entropy” (HE) silicide, in metallic UHTMs with Nb and Si addition were studied. Advanced metallic UHTMs with additions of RMs, transition metals (TMs), Ge, Sn or Ge + Sn and with/without Al and with different Ti, Al, Cr, Si or Sn concentrations were investigated, considering that the motivation of this work was to support the design and development of metallic-UHTMs. The study of the alloyed silicides was based on the Nb/(Ti + Hf) ratio, which is key regarding creep, the parameters VEC and Δχ and relationships between them. The effect of alloying additions on the stability of “conventional”, CC or HE silicide was discussed. The creep and hardness of alloyed Nb₅Si₃ was considered. Relationships that link “conventional”, CC or HE bcc solid solution and Nb₅Si₃ in the alloy design methodology NICE (Niobium Intermetallic Composite Elaboration) were presented. For a given temperature and stress, the steady state creep rate of the alloyed silicide, in which TMs substituted Nb, and Al and B substituted Si, depended on its parameters VEC and Δχ and its Nb/(Ti + Hf) ratio, and increased with decreasing parameter and ratio value, compared with the unalloyed Nb₅Si₃. Types of alloyed Nb₅Si₃ with VEC and Δχ values closest to those of the unalloyed Nb₅Si₃ were identified in maps of alloyed Nb₅Si₃. Good agreement was shown between the calculated hardness and chemical composition of Nb₅Si₃ and experimental results.

1. Introduction

Metallic ultra-high temperature materials (UHTMs) could replace Ni-based superalloys in high-pressure turbines (HPT) if they could meet property goals for fracture toughness, creep and oxidation or offer a balance of properties [1,2]. Metallic UHTMs currently under development are refractory metal (RM) intermetallic composites (ICs) (i.e., RMICs), RM high entropy alloys (RHEAs) and RM complex concentrated alloys (RCCAs) [1,3,4,5,6,7] (see Appendix A for abbreviations). Like the Ni-based superalloys, in an HPT the new metallic UHTMs will be part of a material system that consists of a metallic UHTM substrate plus environmental coating, most likely of the bond coat/thermally grown oxide/top coat type [2,8,9,10,11,12,13,14,15,16,17,18,19]. A route to selecting substrate alloys and bond coat alloys for environmental coatings for metallic UHTMs was discussed in [2] and the design of bond coat alloys that form the α-Al₂O₃ scale was discussed in [15,16].

The aforementioned metallic UHTMs can be single-phase or multiphase materials. The RMICs are multiphase materials with microstructures that consist of bcc solid solution(s) and intermetallic(s) [1,2,20,21,22,23,24,25,26,27,28], whereas the RHEAs and RCCAs can be single-phase bcc solid solution alloys or multiphase alloys with microstructures that consist of solid solution(s) and intermetallic(s), e.g., [3], or only intermetallics, e.g., [15,16]. For the said categories of metallic UHTMs, the M₅Si₃ silicides (M = transition metal (TM), RM), in particular the Nb₅Si₃ and Mo₅Si₃ silicides, have attracted the interest of alloy designers and developers [1,3,13,24] owing to their creep properties and high Si content that benefits oxidation resistance [29,30,31,32,33,34,35,36,37,38,39,40]. Other intermetallics that can improve the properties of these three categories of metallic UHTMs are M₃Si silicides, Laves phases and A15 compounds, as well as the MoSi₂ and NbSi₂ disilicides [1,3,24,41,42,43,44,45,46]. Eutectics and lamellar microstructures that consist of bcc solid solution and intermetallics also can be present in the microstructures of metallic UHTMs [46,47,48,49,50,51,52,53,54], for example, see the Table 11 in [51]. The reader who is interested to know why other intermetallics in addition to M₅Si₃ are included in the microstructures of metallic UHTMs could consult [1,24,27,30,42,46].

In the microstructure of multiphase metallic UHTMs, the aforementioned phases can be “conventional” and/or “high entropy” (HE) or “complex concentrated” (“compositionally complex”), i.e., CC. The “conventional”, HE and/or CC phases can co-exist in as cast (AC) and/or heat-treated (HT) alloys [24,50,51,52,53,54,55,56,57,58]. This has been demonstrated for RMICs based on Nb (i.e., RM(Nb)ICs), some of which also are RHEAs or RCCAs (i.e., RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs, see Appendix A) because they meet the definition of the latter two categories of metallic UHTMs [2,7,50,51,56]. Indeed, HEAs and HE phases are those alloys and phases where the maximum and minimum concentrations of elements are not above or below, respectively 35 and 5 at.%, whereas RCCAs alloys and CC phases are those where the maximum and minimum concentrations of elements are above 35 at.% (up to about 40 at.%) and below 5 at.% [1,3,27].

RMICs based on Nb (i.e., RM(Nb)ICs) also are referred to as Nb silicide-based composites or Nb silicide-based in situ composites because in these metallic UHTMs, the alloyed Nb₅Si₃ is formed in situ [1,31,59]. The volume fraction and spatial and size distributions of the aforementioned silicide is key for achieving a balance of properties or meeting a property goal in RM(Nb)ICs, see [1,24,40]. The interested reader can find a detailed background on Nb₅Si₃ silicides and their use in metallic UHTMs in [1,24,27,40].

All three categories of metallic UHTMs with Nb and Si plus other TMs, RMs and simple metal and metalloid element additions can be designed using the alloy design methodology NICE (Niobium Intermetallic Composite Elaboration) [24]. The “engine room” in NICE consists of the parameters ΔH_mix, ΔS_mix, δ, Δχ, VEC and Ω, which are the same parameters that are used to study HEAs [60], and relationships between these parameters and properties of alloys and phases. In NICE, the linking of the alloying behaviour and properties of phases with the said parameters forms the infrastructure that determines/supports the superstructure of metallic UHTMs that can be B free or B containing, Ti free or Ti containing and can have different Ti/Si or Nb/(Ti + Hf) ratios. The reader who is interested to know why B and Ti additions and the Ti/Si and Nb/(Ti + Hf) ratios are important could consult [1,2,24,61,62]. Metallic UHTMs are designed with NICE to meet individual property goals or to offer a balance of properties [1,2,24,56,61,62].

The Nb₅Si₃ that forms in metallic UHTMs can be “conventional” or CC [51] depending on its chemical composition (see above) and can co-exist with “conventional” or CC or HE bcc Nb_ss [56] or other CC or HE intermetallics (e.g., see the Table 11 in [51]). In the Nb₅Si₃, TMs and RMs substitute Nb (e.g., Cr, Fe, Hf, Mo, Ta, Ti, V, W and Zr) and simple metals and metalloid elements substitute Si (e.g., Al, B, Ge and Sn) [40]. Research has confirmed that the aforementioned alloying elements in metallic UHTMs are key for improving important properties, namely yield strength, creep and oxidation resistance, for example, see [1,3,5,6,7,8,9,17,20,21,22,24,26,36,42,50,52,53,54,57,58,59,61,62]. Simultaneous use of the aforesaid solutes is not essential, the alloy design methodology NICE can guide the alloy designer regarding the choice of alloying additions and their concentrations in a metallic UHTM, for example, see [2,15,16,17,24,27,62].

The alloyed Nb₅Si₃ silicide can be “normal” and/or Ti and Hf rich in the AC and HT alloy according to the partitioning of solutes [24,40] (also the bcc solid solution can be “normal” or Ti rich or Si free, according to the partitioning of solutes [1,24,55]), can have high or low Nb/Ti or Nb/(Ti + Hf) ratios [40], its crystal structure can be tetragonal or hexagonal depending on alloying additions and interstitial contamination [40,51,63,64,65,66,67]. For B-free RM(Nb)ICs, the Nb/(Ti + Hf) ratio is important for (i) the creep properties of the alloy (the ratio must be higher than 1.4) [35], (ii) the crystal structure of the silicide [68] and (iii) the design of bond coat alloy(s) for an environmental coating [16].

Since the classification of new alloys as HEAs or CCAs, excellent mechanical properties have been reported for some of the single-phase solid solution materials [60]. Similarly, outstanding mechanical properties (e.g., yield strength) have been reported for some RCCAs and RHEAs [3] and for multiphase RMICs [1,2,27], with properties (e.g., specific strength and oxidation resistance) of some of the latter alloys and properties (e.g., hardness) of their bcc solid solutions greater than those of the former alloys [1,27,56,61,62,67]. In addition, the creep of some RMICs is close to the creep property goal for metallic UHTMs [1]. Furthermore, some RMICs have outstanding (for RM alloys) oxidation in the pest temperature range and simultaneously at high temperatures, e.g., see [27,62,65], which, to the author’s knowledge, currently is not the case for RCCAs and RHEAs [3].

In RMICs, the key phases, namely bcc solid solution and 5–3 silicide [24,27,40,44,49], can be “conventional”, CC or HE, see above and [51,56]. Recently, the stability of CC or HE Nb_ss in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs was studied in [56]. A similar study for the Nb₅Si₃ silicide is missing. This paper aspires to address this oversight. In particular, some key questions regarding the Nb₅Si₃ in metallic UHTMs, which are important for the design of these materials, will be considered. In RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs the type of stable Nb₅Si₃, meaning “conventional”, CC or HE, is determined by (dependent on) alloying additions. Are there relationships between (a) the parameters (i) of the alloyed Nb₅Si₃ (ii) of alloy and alloyed Nb₅Si₃ (iii) of silicide and bcc solid solution and (b) the parameters and the Nb/(Ti + Hf) ratio of the silicide? How do alloying additions affect the creep of alloyed Nb₅Si₃? Can the alloy developer select alloying elements and type of Nb₅Si₃ (meaning “conventional”, CC or HE) that are desirable for the “best” creep properties of the silicide?

In this paper, I shall deliberate on the type of Nb₅Si₃ (“conventional” or CC/HE) in different groups of alloys to consider, for the first time, the effect of specific alloying additions, whether TMs, RMs or simple metal and metalloid element in (Nb, Ti, Cr)₅(Si, Al)₃ and discuss the hardness of the silicide. With guidance from NICE, relationships between parameters, and parameters and solutes will be sought and the effect of alloying additions on the creep of Nb₅Si₃ will be discussed. I shall classify Nb₅Si₃ silicides as “conventional” or CC/HE, using published data about the chemical composition of Nb₅Si₃ silicides in RMICs, and with this data I shall also present, for the first time, the relationships between parameters and discuss the importance of the Nb/Ti and Nb/(Ti + Hf) ratio of the silicide. Moreover, I shall suggest creep experiments on tetragonal Nb₅Si₃ with specific alloying elements substituting Si or Nb and Si, which in my opinion are essential to understand better how alloying affects the creep of Nb₅Si₃.

HE or CC ceramics and silicides have been studied as single-phase materials, e.g., [69,70,71,72]. Single-phase materials are not considered in this paper. Scarce data about the chemical composition of phases in multiphase RHEAs or RCCAs with Nb and Si addition shows that their phases can be “conventional”, CC or HE, for example, see (i) the RHEA alloy NbCrMoTiVAl₀.₅Si₀.₃ in [52] where the solid solution is CC, the Nb₅Si₃ is HE and the eutectic of these two phases is also HE and (ii) the RHEA alloy Mo₀.₅NbHf₀.₅ZrTiSi_x in [53] where the eutectic is HE. The aforementioned RHEAs in the references [52,53] in which they were referred to as high entropy composite and refractory high entropy (Mo₀.₅NbHf₀.₅ZrTi)_BCC/M₅Si₃ in situ compound, respectively, and classified as RHEAs in [3], strictly speaking, are refractory metal high entropy intermetallic composites (i.e., RMICs/RHEAs).

There are no systematic studies of M₅Si₃ silicides in RHEAs or RCCAs that would allow one to answer the questions asked above for alloyed 5–3 silicides in these metallic UHTMs, in particular the dependence of the type of alloyed Nb₅Si₃ on alloying additions, and how alloying additions affect the creep of alloyed Nb₅Si₃. Thus, owing to the lack of such studies of alloyed Nb₅Si₃ silicides in multiphase RCCAs or RHEAs, the focus of this paper will be alloyed Nb₅Si₃ silicides only in RM(Nb)ICs, RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs that have been studied systematically in our research group and which can be arranged in different groups/sets depending on the “basis” alloy. The chemical compositions of the alloys are given in Appendix B, where also are given references where the interested reader can find the experimental data about the structure and chemical analysis of alloyed Nb₅Si₃ silicides. In this paper, the alloys are arranged in four groups/sets, as discussed in the next section, in order to show the effect of alloying, meaning the substitution of Nb or Si by specific solutes, on the type of Nb₅Si₃ silicide.

2. Complex Concentrated Nb₅Si₃

RM(Nb)ICs, RHEAs and RCCAs not only use the same alloying elements [1,2,27] and their phases can be displayed in the same Δχ versus VEC map [2], but also can be presented together in the same Δχ versus δ map [1,2,73]. In the latter map, the alloys with B addition are found in a distinctly different location from KZ series alloys with/without RM and simple metal and metalloid element additions [73] (KZ series alloys are based on Nb-24Ti-18Si (at.%, nominal) with the addition of Al and/or Cr (each at 5 at.%, nominal)).

To study the effects of specific alloying additions on the type (meaning “conventional”, CC/HE) and stability of Nb₅Si₃, I shall (i) make use of maps in which (a) alloys will be grouped together using a different “basis” alloy and (b) different colours will be employed for different alloy conditions, namely dark colours for the AC condition and light colours for the HT condition, (ii) use blue colour for “normal” Nb₅Si₃ and red colour for Ti rich Nb₅Si₃ and (iii) give (only for presentation purposes to enable comparison of silicides in different alloys) the “values” 15 and 10, respectively for “conventional” Nb₅Si₃ and CC Nb₅Si₃ to schematically distinguish (separate) the two silicides, see Figure 1, Figure 2, Figure 3 and Figure 4. Note that in this paper, the Nb₅Si₃ silicide is studied in alloys in which the bcc solid solution Nb_ss recently was studied as “conventional”, CC or HE, see [56], i.e., in alloys where “conventional”, CC/HE Nb_ss and Nb₅Si₃ co-exist. It will be shown that there exist relationships between Nb_ss and Nb₅Si₃, in addition to relationships between parameters of Nb₅Si₃. For the calculation of the parameters VEC and Δχ of the silicide, the reader should refer to [40].

The “normal” Nb₅Si₃ of an alloy can be “conventional” or CC in both the AC and HT conditions, in which case, its y-axis “value” in Figure 1a, Figure 2a, Figure 3a and Figure 4a will be 15 or 10, respectively, and the silicide will be shown with dark blue colour in the AC condition and light blue colour in the HT condition. Alternatively, the silicide could be Ti rich and “conventional” or CC in the AC and HT conditions, in which case its y-axis “value” would be 15 or 10, respectively, and the Ti-rich Nb₅Si₃ will be shown with dark red colour in the AC condition and light pink colour in the HT condition.

In the first group/set of Nb₅Si₃, shown in Figure 1a, the basis alloy is the alloy KZ5 and the group is made up of silicides in the RM(Nb)ICs KZ5, KZ6, JG2, JG3, JN1, TT4, ZF6 and ZX8 (see the Appendix B for the nominal alloy compositions and references, note that the chemical analysis data was obtained using EPMA or EDS with standards). These alloys were chosen to show the effect of the addition of B, Ge, Hf, Mo, Sn or Ta to KZ5 (the basis alloy) on the type (“conventional” or CC) of Nb₅Si₃ or, in other words, to show the effect of the synergy of Al, Cr and Ti in (Nb, Ti and Cr)₅(Si and Al)₃ (i.e., the 5–3 silicide in the basis alloy, where Nb is substituted with Cr and Ti, and Si with Al) with B, Ge, Hf, Mo, Sn or Ta (the specific alloying addition) in the silicide in the aforementioned RM(Nb)ICs. In Figure 1a each solute addition to the basis alloy is indicated in parenthesis.

In the basis alloy KZ5, the “normal” Nb₅Si₃ and Ti-rich Nb₅Si₃ (dark blue and red colours—AC condition) was “conventional” (the y-axis “value” is 15) in both the AC and HT (lighter blue and pink colours) conditions. With each addition to the basis alloy, the Ti rich Nb₅Si₃ became CC (the y-axis “value” is 10). With the addition of Ge, Hf or Sn, the status (rank) of the “normal” silicide as “conventional” did not change. With the addition of B, the Ti rich Nb₅Si₃ was not stable after HT. The Mo addition in the alloys JG2 and JG3 (note the lower Mo content in JG3, see the Appendix B) showed that the Mo concentration in the alloy is important regarding the promotion or not of CC Nb₅Si₃. The addition of Ta was more effective regarding the formation of CC Nb₅Si₃ in the AC alloy compared with the addition of Mo when the latter was at low concentration, otherwise Mo and Ta were equally effective at high (about 5 to 6 at.%) concentrations in the alloy.

The partitioning of Ti to Nb₅Si₃ affects the Nb/Ti or Nb(Ti + Hf) ratio of the “conventional” and CC silicide (Figure 1b). The effect depends on alloying addition, for example, it was severe for the Ti-rich Nb₅Si₃ (CC silicide) with the addition of Hf in the alloy (compare the silicide in the alloys KZ5 and JN1). Compared with the AC condition, in the HT condition, the said ratio of the Ti-rich Nb₅Si₃ (CC silicide) was lower and higher when Mo or Hf and Ge or Ta, respectively, were added to the basis alloy (compare the silicide in the alloys JN1 and JG3, and the alloys ZF6 and KZ6). Only with the addition of Sn the said ratio of the “conventional” Nb₅Si₃ increased in the HT condition (alloy ZX8). Furthermore, the Nb/(Ti + Hf) ratio of the Ti-rich silicide (CC Nb₅Si₃) in the alloy JN1 was less than one (hexagonal silicide [68]).

The alloying additions to the basis alloy also affect the parameters VEC and Δχ of the Nb₅Si₃, see Figure 1c,d. Compared with the basis alloy KZ5, the changes of the parameters VEC and Δχ were more severe, respectively with the addition of Hf (Figure 1c, silicide in alloy JN1) and B or Ta (Figure 1d, silicide in the alloys TT4 and KZ6). Compared with the AC condition, in the HT condition, the parameter VEC of the Ti-rich Nb₅Si₃ (CC silicide) decreased and increased, respectively with the addition of Hf or Mo and Ge or Ta (Figure 1c, silicide in the alloys JN1, JG2 and JG3 and the alloys ZF6 and KZ6). With the exception of the B addition in the alloy TT4, the value of the parameter VEC of the “conventional” “normal” Nb₅Si₃ exceeded 4.4. In the alloy TT4, the Ti-rich Nb₅Si₃ (CC Nb₅Si₃) had the lowest VEC (about 4.27).

The parameter Δχ of the “conventional” Nb₅Si₃ decreased in the HT condition compared with the AC condition in the basis alloy and with the addition of Ge, Hf, 5 at.% Mo, Sn or Ta, but increased when the concentration of Mo was decreased to 2 at.% (Figure 1d, silicide in the alloys KZ5, JN1, JG2, KZ6, ZX8, ZF6 and the alloy JG3). In contrast, the parameter Δχ of the CC Nb₅Si₃ increased in the HT condition compared with the AC condition in the basis alloy and with the addition of Ge (Figure 1d, silicide in the alloys KZ5 and ZF6), and decreased with the addition of B, Hf, Mo, Sn or Ta (silicide in the alloys TT4, JN1, JG2, JG3, ZX8, KZ6). Note that the change of the Mo concentration in the alloy affected only the parameter Δχ of the “conventional” silicide. Moreover, note that the lowest and highest Δχ values for “conventional” and CC Nb₅Si₃ were with the addition of B and Ge (silicide in the alloys TT4 and ZF6).

The trends of the VEC versus Δχ data of the Nb₅Si₃ for the addition of B, Ge, Hf, Mo, Sn or Ta to the basis alloy KZ5 are shown in the map in Figure 1e. Note (i) similar trends for the addition of Ge or Sn, Ta or B and Hf or Mo, (ii) that with the addition of B or Ta, the parameter Δχ is less than about 0.31, whereas with the addition of Hf, Mo or Sn, the Δχ was higher and in the range 0.3 to 0.41, (iii) the narrow Δχ range with the addition of Ge, (iv) maxima with the addition of B (0.2546, 4.338), Hf (0.3757, 4.429), Mo (0.3589, 4.435) or Ta (0.2676, 4.421) and (v) minima with the addition of Ge (0.4038, 4.294) and Sn (0.3618, 4.356), where in parenthesis is given the corresponding Δχ and VEC of maximum or minimum. The relationship between the Nb/Ti or Nb/(Ti + Hf) ratio and the parameter VEC of Nb₅Si₃ is shown in Figure 1f. High ratio values link with high VEC values of the silicide.

In the second group/set of Nb₅Si₃, shown in Figure 2a, the basis alloy is the alloy JN1 (i.e., KZ5 + Hf) and the group is made up of the alloys JN1, JG4, TT7, ZF9 and EZ8 (see the Appendix B for the nominal alloy compositions and references). These alloys were chosen to show the effect of the synergy of Hf with the addition of B, Ge, Mo or Sn on the type (“conventional” or CC) of Nb₅Si₃ or, in other words, to show the effect of the synergy of Al, Cr, Hf and Ti in (Nb, Ti, Cr, Hf)₅(Si, Al)₃ (note this is different from the (Nb, Ti, Cr)₅(Si, Al)₃ of the first group/set owing to substitution of Nb with Hf, as well as with Cr and Ti) in the basis alloy with the addition of B, Ge, Mo or Sn (the specific alloying addition) in the aforementioned RM(Nb)ICs and RM(Nb)ICs/RCCAs. In Figure 2a, each solute addition to the basis alloy is indicated in parenthesis. Note that in this group the alloys EZ8, TT7 and ZF9 are RM(Nb)ICs/RCCAs.

Figure 1. Data for Nb₅Si₃ in RM(Nb)ICs with basis alloy KZ5 (Nb-24Ti-18Si-5Al-5Cr, at.%, nominal) and alloying additions B, Ge, Hf, Mo, Sn or Ta (shown in parentheses in (a,d)). Alloys KZ5, KZ6, JG2, JG3, JN1, TT4, ZF6 and ZX8. For nominal alloy compositions and references, see the Appendix B. (a) Type of Nb₅Si₃ (“conventional” or CC), dark and lighter colours, respectively for AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” Nb₅Si₃ and CC Nb₅Si₃. (b) Nb/Ti or Nb/(Ti + Hf) ratio of Nb₅Si₃, (c) VEC of Nb₅Si₃, (d) Δχ of Nb₅Si₃, (e) VEC versus Δχ of Nb₅Si₃ and (f) Nb/Ti or Nb/(Ti + Hf) ratio versus VEC of Nb₅Si₃. See text for hatched data in (c,d) and for the arrow in (f). In (d,e), the parameter Δχ is based on the Pauling electronegativity. In (f), the light colour data is for “conventional” silicide. In (e), JZ2 = KZ5 + 5 Mo and JG3 = KZ5 + 2 Mo (at.%). (g) Nb/(Ti + Hf) versus Δχ of Nb₅Si₃. In (g), lighter colours indicate “conventional” Nb₅Si₃ and darker colours CC Nb₅Si₃, parabolic fit of green data gave R² = 0.9092, all other R² values are for linear fit of data. In (g), blue data is for the alloys KZ5, KZ6, TT4, ZX8, black data for the alloys KZ5, KZ6, TT4, ZX8 plus JG3, green data for the alloys KZ5, JG2, JG3, JN1, ZF6, ZX8 and brown data for the alloys KZ5, JG2, JN1, ZF6, i.e., no B, Sn or Ta additions in brown data, no B or Ta in green data, no Ge or Hf in black data and no Ge, Hf or Mo in blue data.

Figure 1. Data for Nb₅Si₃ in RM(Nb)ICs with basis alloy KZ5 (Nb-24Ti-18Si-5Al-5Cr, at.%, nominal) and alloying additions B, Ge, Hf, Mo, Sn or Ta (shown in parentheses in (a,d)). Alloys KZ5, KZ6, JG2, JG3, JN1, TT4, ZF6 and ZX8. For nominal alloy compositions and references, see the Appendix B. (a) Type of Nb₅Si₃ (“conventional” or CC), dark and lighter colours, respectively for AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” Nb₅Si₃ and CC Nb₅Si₃. (b) Nb/Ti or Nb/(Ti + Hf) ratio of Nb₅Si₃, (c) VEC of Nb₅Si₃, (d) Δχ of Nb₅Si₃, (e) VEC versus Δχ of Nb₅Si₃ and (f) Nb/Ti or Nb/(Ti + Hf) ratio versus VEC of Nb₅Si₃. See text for hatched data in (c,d) and for the arrow in (f). In (d,e), the parameter Δχ is based on the Pauling electronegativity. In (f), the light colour data is for “conventional” silicide. In (e), JZ2 = KZ5 + 5 Mo and JG3 = KZ5 + 2 Mo (at.%). (g) Nb/(Ti + Hf) versus Δχ of Nb₅Si₃. In (g), lighter colours indicate “conventional” Nb₅Si₃ and darker colours CC Nb₅Si₃, parabolic fit of green data gave R² = 0.9092, all other R² values are for linear fit of data. In (g), blue data is for the alloys KZ5, KZ6, TT4, ZX8, black data for the alloys KZ5, KZ6, TT4, ZX8 plus JG3, green data for the alloys KZ5, JG2, JG3, JN1, ZF6, ZX8 and brown data for the alloys KZ5, JG2, JN1, ZF6, i.e., no B, Sn or Ta additions in brown data, no B or Ta in green data, no Ge or Hf in black data and no Ge, Hf or Mo in blue data.

In the basis alloy JN1, the “normal” Nb₅Si₃ and Ti-rich Nb₅Si₃ (dark blue and red colours-AC condition), respectively “conventional” and CC (the y-axis “values”, respectively are 15 and 10) in both the AC and HT (lighter blue and pink colours) conditions. The “status” (rank) of the silicide did not change with the addition of 2 at.% Mo (alloy JG4), but with the addition of B or Ge the “normal” and Ti-rich Nb₅Si₃ were CC in both the AC and HT conditions (silicide in the alloys TT7 and ZF9), whereas with the addition of Sn the CC Nb₅Si₃ in the alloy, EZ8-AC changed to “conventional” silicide after the heat treatment (Figure 2a). With all solute additions to the basis alloy, the “status” (rank) of the Ti-rich Nb₅Si₃ did not change, i.e., it was CC. The synergy of Hf with the low concentration of Mo (alloy JG4) was less effective than the synergy of B with Hf regarding the conversion of the “conventional” Nb₅Si₃ to CC. For the former synergy, this effect was attributed to Hf for the latter was attributed to B (compare with Figure 1a). Furthermore, the synergy of Ge and Hf was more effective than the synergy of Hf and Sn regarding the conversion of the “conventional” Nb₅Si₃ to CC (compare with Figure 1a).

The Nb/(Ti + Hf) ratio of the “conventional” silicide increased in the HT condition in the basis alloy and with the addition of Ge, Mo or Sn (Figure 2b), and was higher than 1.5 (tetragonal silicide [68]) in the basis alloy JN1 and with the addition of Mo or Sn. However, this ratio was lower than one (indicative of hexagonal structure [68]) for the Ti rich Nb₅Si₃ (CC) in the basis alloy, and with the addition of B, Ge, Mo or Sn in the alloys TT4, ZF6, JG4 and ZX8. Furthermore, the Nb/(Ti + Hf) ratio of the Nb₅Si₃ alloyed with Hf and B, Ge, Mo or Sn did not exceed 1.9, and was lower than that of the silicide in the alloys with KZ5 as their basis (compare Figure 1b and Figure 2b).

Figure 2. Data for Nb₅Si₃ in RM(Nb)ICs and RM(Nb)ICs/RCCAs with basis alloy JN1 (Nb-24Ti-18Si-5Al-5Cr-5Hf, at.%, nominal) and alloying additions B, Ge, Mo or Sn (shown in parenthesis). Alloys JN1, JG4, TT7, ZF9 and EZ8. For nominal alloy compositions and references, see the Appendix B. (a) Type of Nb₅Si₃ (“conventional” or CC), dark and lighter colours, respectively for AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” Nb₅Si₃ and CC Nb₅Si₃. (b) Nb/(Ti + Hf) ratio of Nb₅Si₃, (c) VEC of Nb₅Si₃, (d) Δχ of Nb₅Si₃, (e) VEC versus Δχ of Nb₅Si₃ and (f) Nb/(Ti + Hf) ratio versus VEC of Nb₅Si₃. In (d,e), the parameter Δχ is based on the Pauling electronegativity. See text for hatched data in (d) and for the arrow in (f). In (f), the light colour data is for “conventional” silicide. In (e), the R² values are for parabolic fit of data. RM(Nb)ICs/RCCAs the alloys EZ8, TT7 and ZF9.

Figure 2. Data for Nb₅Si₃ in RM(Nb)ICs and RM(Nb)ICs/RCCAs with basis alloy JN1 (Nb-24Ti-18Si-5Al-5Cr-5Hf, at.%, nominal) and alloying additions B, Ge, Mo or Sn (shown in parenthesis). Alloys JN1, JG4, TT7, ZF9 and EZ8. For nominal alloy compositions and references, see the Appendix B. (a) Type of Nb₅Si₃ (“conventional” or CC), dark and lighter colours, respectively for AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” Nb₅Si₃ and CC Nb₅Si₃. (b) Nb/(Ti + Hf) ratio of Nb₅Si₃, (c) VEC of Nb₅Si₃, (d) Δχ of Nb₅Si₃, (e) VEC versus Δχ of Nb₅Si₃ and (f) Nb/(Ti + Hf) ratio versus VEC of Nb₅Si₃. In (d,e), the parameter Δχ is based on the Pauling electronegativity. See text for hatched data in (d) and for the arrow in (f). In (f), the light colour data is for “conventional” silicide. In (e), the R² values are for parabolic fit of data. RM(Nb)ICs/RCCAs the alloys EZ8, TT7 and ZF9.

The highest VEC values (about 4.4) were for the “conventional” silicide of the basis alloy in the AC and HT conditions and after the addition of Mo (alloy JG4), and in the alloy EZ8-HT (addition of Sn), Figure 2c. These VEC values were lower than the highest VEC values of silicides in the alloys with KZ5 as their basis (compare with Figure 1c). The parameter VEC of the CC Ti rich Nb₅Si₃ decreased after heat treatment, with the exception of the alloy ZF9 (addition of Ge) where it did not change. The lowest VEC value (4.173), which was for the CC Nb₅Si₃ in the alloy TT7-HT (addition of B), was lower than the lowest VEC of the alloys considered in Figure 1.

The parameter Δχ of the silicide decreased with the addition of B, Mo or Sn to the basis alloy JN1, with the exception of the CC Ti rich Nb₅Si₃ in the alloy TT7-AC (B addition) and did not change significantly with the addition of Ge (Figure 2d). Both the lowest Δχ value (0.128), which was for the CC Nb₅Si₃ in the alloy TT7-HT (B addition), and the highest Δχ value (0.4) that was for the “conventional” silicide in the alloy JN1-AC (basis alloy), were lower than the parameter Δχ of the silicide in the alloys considered in Figure 1. In other words, the synergy of Hf with Al, Cr and Ti plus B, Ge, Mo or Sn in Nb₅Si₃ decreased the parameters VEC and Δχ compared with the Hf-free Nb₅Si₃ (the parameter VEC changed from the range 4.452 to 4.266 to the range 4.402 to 4.173 and the parameter Δχ changed from the range 0.415 to 0.224 to the range 0.399 to 0.128).

The map of the parameters VEC and Δχ of the Nb₅Si₃ in the alloys with JN1 as their basis is shown in Figure 2e. Note (i) similar trends for the basis alloy JN1 and for the additions of B (alloy TT7) or Mo (alloy JG4), (ii) similar trends for the additions of Ge (alloy ZF9) or Sn (alloy EZ8), (iii) maxima for the additions of B (0.296, 4.3025) or Mo (0.312, 4.399) and the basis alloy (0.376, 4.429) and (iv) that the B, Ge, Mo or Sn addition reduced the parameters Δχ and VEC. Compared with the Hf free Nb₅Si₃ in the alloys considered in Figure 1, the B and Mo maxima shifted, respectively to higher and lower Δχ and VEC values in the case of B addition, and to both lower Δχ and VEC values in the case of Mo addition. The relationship between the Nb/(Ti + Hf) ratio and the parameter VEC of Nb₅Si₃ is shown in Figure 2f. High ratio values link with high VEC values of the silicide. The figure confirms the lower range of the parameter VEC for the second group of alloys. Note that the slope of the line in Figure 2f is less than that in Figure 1f.

In the third group/set of Nb₅Si₃, shown in Figure 3a, the basis alloy is the alloy TT4 (i.e., KZ5 + B) and the group is made up of the alloys TT4, TT5, TT6, TT7 and TT8 (see the Appendix B for the alloy compositions and references). These alloys were chosen to show the effect of the synergy of B with the Hf, Mo, Sn or Ta additions on the type (“conventional” or CC) of tetragonal T2-Nb₅(Si, B)₃ or, in other words, to show the effect of the synergy of Al, Cr, B and Ti in T2-(Nb, Ti, Cr)₅(Si, Al, B)₃ (note this is different from (Nb, Ti, Cr)₅(Si, Al)₃ of the first group owing to the substitution of Si with B as well as with Al) in the basis alloy with the addition of Hf, Mo, Sn or Ta (the specific alloying addition) in the aforementioned RM(Nb)ICs and RM(Nb)ICs/RCCAs. Each solute addition to the basis alloy is indicated in parenthesis. Note that in this group, the alloys TT5, TT6 and TT7 are RM(Nb)ICs/RCCAs.

In the basis alloy TT4-AC, the “normal” T2 and Ti-rich T2 (dark blue and red colours-AC condition), respectively was “conventional” and CC (the y-axis “values”, respectively are 15 and 10) and both were CC in the HT (lighter blue and pink colours) condition (Figure 3a). The Mo addition did not promote the conversion of “conventional” T2 to CC after heat treatment, and the Sn addition did not prevent the CC silicide from converting to “conventional” after heat treatment. This behaviour was the same as that observed for the synergies of Hf and Mo and Hf and Sn (compare Figure 2a and Figure 3a). On the contrary, with the additions of Hf or Ta, the CC silicide (“normal” or Ti rich) in the AC alloys was stable after HT (silicide in the alloys TT5-HT and TT7-HT). In other words, the “conventional” T2 was stable after heat treatment when the silicide was alloyed with Mo or Sn.

Figure 3. Data for tetragonal T2-Nb₅(Si, B)₃ in RM(Nb)ICs and RM(Nb)ICs/RCCAs with basis alloy TT4 (KZ5 + B) and alloying additions Hf, Mo, Sn or Ta (shown in parenthesis). Alloys TT4, TT5, TT6, TT7 and TT8. For nominal alloy compositions and references, see the Appendix B. (a) Type of T2 silicide (“conventional” or CC), dark and lighter colours, respectively for the AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” T2 and CC T2. (b) Nb/Ti or Nb/(Ti + Hf) ratio of T2, (c) VEC of T2, (d) Δχ of T2 and (e) VEC versus Δχ of T2. See text for hatched data in (c,d). In (d,e), the parameter Δχ is based on the Pauling electronegativity. In (e), the R² values are for the parabolic fit of data. Poor fit of data for the Ta addition. RM(Nb)ICs/RCCAs are the alloys TT5, TT6 and TT7.

Figure 3. Data for tetragonal T2-Nb₅(Si, B)₃ in RM(Nb)ICs and RM(Nb)ICs/RCCAs with basis alloy TT4 (KZ5 + B) and alloying additions Hf, Mo, Sn or Ta (shown in parenthesis). Alloys TT4, TT5, TT6, TT7 and TT8. For nominal alloy compositions and references, see the Appendix B. (a) Type of T2 silicide (“conventional” or CC), dark and lighter colours, respectively for the AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” T2 and CC T2. (b) Nb/Ti or Nb/(Ti + Hf) ratio of T2, (c) VEC of T2, (d) Δχ of T2 and (e) VEC versus Δχ of T2. See text for hatched data in (c,d). In (d,e), the parameter Δχ is based on the Pauling electronegativity. In (e), the R² values are for the parabolic fit of data. Poor fit of data for the Ta addition. RM(Nb)ICs/RCCAs are the alloys TT5, TT6 and TT7.

For the “conventional” T2 silicide, the synergy of B with Mo in the AC and HT alloy TT8 resulted in a similar Nb/Ti ratio with the basis alloy TT4-AC (Figure 3b). The Nb/Ti and Nb/(Ti + Hf) ratio of the CC T2 in the AC alloys TT4, TT8 and TT6 was higher than one and lower than one when B was in synergy with Hf or Ta (silicide in the alloys TT7-AC and TT5-AC). The said ratio of the CC T2 was higher than one in the HT alloys TT5, TT6 and TT8 (i.e., when B was in synergy with Ta, Sn or Mo) and less than one in TT7-HT. The range of values of the Nb/Ti and Nb/(Ti + Hf) ratios was slightly higher compared with the second group of alloys, namely 1.9 to 0.67 compared with 2.12 to 0.76 (Figure 2b and Figure 3b).

Compared with the silicide in the alloy TT4-AC, the synergy of B with Hf gave the highest VEC (4.324) in the CC T2 in the alloy TT7-AC, and the highest VEC (4.362) in the “conventional” T2 in the alloy TT8-HT (synergy of B with Mo), see Figure 3c. The parameter VEC was less than 4.2 only when B was in synergy with Hf, Mo or Sn, respectively in CC T2 (in the alloy TT7-HT), CC Ti-rich T2 (alloy TT8-AC) and CC Ti-rich T2 (alloy TT6-HT). The range of the parameter VEC of T2 was 4.362 to 4.107, compared with the ranges 4.452 to 4.266 and 4.402 to 4.173, respectively for the Nb₅Si₃ in the first group and the second group of alloys, i.e., it was wider but with smaller high and low values than these groups (compare Figure 1c, Figure 2c and Figure 3c).

Compared with the silicide in the basis alloy, the parameter Δχ of the CC T2 silicide in the AC alloys TT7 (Hf addition), and TT5 (Ta addition) increased and decreased in the alloy TT6-AC (Sn addition) and the alloy TT8-AC (Mo addition) (Figure 3d). The range of the values of the parameter Δχ of T2 was 0.3512 to 0.1034, compared with the ranges 0.4153 to 0.2241, and 0.399 to 0.128, respectively for the Nb₅Si₃ in the first group and the second group of alloys, i.e., it was wider only than the first group of alloys and had smaller high and low values than these groups (compare Figure 1d, Figure 2d and Figure 3d).

The map of the parameters VEC and Δχ of the T2 silicide in the alloys with the alloy TT4 as their basis is shown in Figure 3e. Note (i) similar trends for the basis alloy TT4 and for the additions of Hf, Sn or Ta, (ii) the maxima for Hf (0.296, 4.303) and Sn (0.190, 4.311) and for the basis alloy TT4 (0.2546, 4.338), (iii) that only with the addition of Hf or Ta the parameter Δχ exceeds 0.3 and (iv) that only with the addition of Mo or Ta the parameter VEC exceeds 4.35.

The fourth group/set of Nb₅Si₃ is for advanced RM(Nb)ICs and RM(Nb)ICs/RCCAs with additions of RM, TMs, Ge, Sn or Ge + Sn (meaning simultaneous addition of Ge and Sn), with/without Al addition and with different Ti, Al, Cr, Si or Sn concentrations. The reader who is interested to know why Ge, Sn or Ge + Sn additions are important for metallic UHTMs could refer to [1,2,24,27,65,66,67]. Data for this group is shown in Figure 4. In Figure 4a, the data for the Nb₅Si₃ in the alloys JN4 and JG6 shows the effect of the presence of Al in an alloy where Hf, Mo and Ti are in synergy with Sn (the “conventional” silicide is converted to CC), whereas the simultaneous addition of Ge and Sn in the alloy OHS1 could reverse the effect of Al in the cast microstructure in the absence of Hf and Mo in the alloy (compare the silicide in the alloys JN4, JG6 and OHS1-AC). The data for Nb₅Si₃ in the alloys JN2 and JN3 shows that in the absence of Al in the alloy, its Cr concentration is important as lower Cr concentrations promote “conventional” Nb₅Si₃ and Ti-rich Nb₅Si₃.

The data for the Nb₅Si₃ in the alloys JZ4 and JZ5 shows the effect of Ti concentration in the alloy and that higher Ti concentration promotes the CC silicide, whereas the data for the Nb₅Si₃ in the alloys OHS1 and JZ5 shows that the synergy of Hf, Mo, Ti and W with Ge + Sn also promotes the CC silicide as seen in Figure 4a. In other words, in RM(Nb)ICs/RCCAs the type of Nb₅Si₃, meaning “conventional” or CC, can be controlled via the Ti concentration, the simultaneous addition of Ge and Sn and the synergy of these solutes with the simultaneous addition of Al, Cr, Hf, Mo, Ti and W, which are solute additions that contribute to achieving a balance of properties [2,27]. Is the choice of RMs important?

Comparison of the data for the alloys JZ3 and JZ4 shows that the substitution of Mo with Ta stabilised the “conventional” Nb₅Si₃ after heat treatment and converted the “conventional” Ti-rich Nb₅Si₃ in the cast alloy to CC, whereas a comparison of JZ4 with JZ3+ shows that the increase in the Sn concentration in the latter converted the “conventional” Ti-rich Nb₅Si₃ to CC in the alloy [JZ3+]-AC, as seen in Figure 4a. In other words, the choice of RMs is important. In RM(Nb)ICs/RCCAs with simultaneous addition of Al and Cr (each at 5 at.%, nominal), Ge, Hf and Sn with Ti and RMs, the type of Nb₅Si₃ (“conventional” or CC) can be controlled with (i) the concentrations of Sn and/or Ti, and (ii) and the choice of the RM that would be in synergy with W in the alloy.

The synergies of solute additions had a strong effect on the Nb/Ti or Nb/(Ti + Hf) ratio of Nb₅Si₃, as seen in Figure 4b. For example, with the decrease in the Cr concentration in the alloy JN3, the Nb/(Ti + Hf) ratio of the “conventional” Nb₅Si₃ increased compared with the alloy JN2, whereas with the addition of Al in the alloy JG6, the Nb/(Ti + Hf) ratio not only decreased to less than two, compared with the alloy JN4 but also the ratio was less than one for the CC Ti-rich Nb₅Si₃ in both the AC and HT conditions (hexagonal structure [68]). Similarly, the Nb/(Ti + Hf) ratio of CC Nb₅Si₃ decreased below two when the concentration of Ti in the alloy JZ5 increased compared with the alloy JZ4, in which the “conventional” Nb₅Si₃ had Nb/(Ti + Hf) higher than four. Furthermore, the substitution of Mo with Ta gave higher Nb/(Ti + Hf) ratios for the silicide in the alloy JZ3-HT compared with JZ4, but with the increase in the Sn concentration in the alloy [JZ3+]-HT, the said ratio was essentially the same as for the Nb₅Si₃ in the alloy JZ4-HT. In other words, the choice of solute additions and their concentrations is important not only for the type of Nb₅Si₃ but also for its Nb/(Ti + Hf) ratio.

Concentrations of solutes and synergies of the latter in advanced alloys affect the values of the parameters VEC and Δχ of Nb₅Si₃, Figure 4c,d. For example, with the addition of Al in the alloy JG6, the CC Ti-rich Nb₅Si₃ not only was hexagonal but also its parameter VEC decreased compared with the “normal” CC silicide in the same alloy and the “conventional” silicide in the alloy JN4, Figure 4c. However, the effect on VEC of the decrease in the Cr concentration in the alloy JN3 was minimal compared with the alloy JN2. The addition of Hf, Mo and W in JZ5 increased the parameter VEC of Nb₅Si₃ compared with the alloy OHS1, and the decrease in Ti concentration in JZ4 increased the parameter VEC further, as seen in Figure 4c. Changes of the parameter VEC of Nb₅Si₃ were marginal when the Mo was substituted with Ta in the alloy JZ3 compared with the alloy JZ4, but the increase in the Sn concentration in the alloy JZ3+ resulted to small decrease in the VEC of the CC silicide. The VEC range was from 4.584 for the “conventional” Nb₅Si₃ in the alloy JZ4-AC to 4.218 for the CC hexagonal Nb₅Si₃ in the alloy JG6-HT.

The parameter Δχ changed from 0.2055 for the CC Nb₅Si₃ in the alloy JG6-AC to 0.479 for the “conventional” Ti-rich Nb₅Si₃ in the alloy JN3, Figure 4d. The parameter Δχ was higher for the Al-free alloys JN2 and JN3, in which the Cr concentration had a noticeable effect on the parameter Δχ of the “conventional” Ti-rich Nb₅Si₃ in the alloy JN3. The simultaneous addition of Ge and Sn in the Hf free alloy OHS1 increased the parameter Δχ of Nb₅Si₃ compared with the alloys JN4 and JG6, and the addition of Mo and W increased further the parameter Δχ. However, the increase in Δχ was marginal when the Ta was in synergy with W in the alloys JZ3 and JZ3+, even when the concentration of Sn was increased in the latter alloy.

The relationships between the parameters VEC and Δχ in Nb₅Si₃ in the alloys considered in Figure 4a are shown in the map in Figure 4e. Note (i) similar trends of the data for the alloys JN2 and JN4 (the lines are essentially parallel, with a shift to significantly lower Δχ in the W free and less rich in Cr alloy JN4), (ii) similar trends of the data for the alloys JG6, OHS1, JZ4 and JZ5, and JN3 with (a) a significant shift to higher VEC and Δχ values as the concentration of Cr was reduced and Al was removed from the alloy JN3 compared with the alloy JG6, (b) a gradual shift to higher VEC and Δχ values with Ge + Sn in the absence of Hf and Mo (alloys JG6 and OHS1), and when Hf, Mo and W were added to the alloys JZ4 and JZ5 with the simultaneous addition of Ge and Sn, (iii) opposite trend of the data when Mo was substituted with Ta in the alloys JZ3 and JZ3+, (iv) maxima in the data for JG6 (0.2506, 4.352), OHS1 (0.3061, 4.413), JZ4 and JZ5 (0.3343, 4.522), JN3 (0.4342, 4.556) and minimum (0.2841, 4.408) for the data of the alloys JZ3 and JZ3+. The relationship between the Nb/Ti or Nb/(Ti + Hf) ratio and the parameter VEC of Nb₅Si₃ is shown in Figure 4f. High ratio values link with high VEC values of the silicide, as was noted earlier in Figure 1f and Figure 2f. Note the higher slope of the data for the Ta-containing alloys JZ3 and JZ3+ in Figure 4f, in the same way as the data for the alloy TT5 (Ta addition) in the Nb/Ti or Nb/(Ti + Hf) versus VEC map of alloys with TT4 as basis.

Figure 4. Data for Nb₅Si₃ in RM(Nb)ICs and RM(Nb)ICs/RCCAs with additions of RM, TMs, Ge, Sn or Ge + Sn, with/without Al addition and with different Ti, Al, Cr or Sn concentrations. Alloys JN2, JN3, JN4, JN4, JG6, JZ3, JZ3+, JZ4, JZ5 and OHS1. For nominal alloy compositions and references, see the Appendix B. (a) Type of Nb₅Si₃ (“conventional” or CC) and dark and lighter colours, respectively for the AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” Nb₅Si₃ and CC Nb₅Si₃. (b) Nb/Ti or Nb/(Ti + Hf) ratio of Nb₅Si₃, (c) VEC of Nb₅Si₃, (d) Δχ of Nb₅Si₃, (e) VEC versus Δχ of Nb₅Si₃ and (f) Nb/Ti or Nb/(Ti + Hf) ratio versus VEC of Nb₅Si₃. In (e), linear fit of data for the alloys JN2 and JN4, and the R² values are for parabolic fit of data. In (f), R² = 0.6902 for all data, R² = 0.9809 for the alloys JN4 and JG6, R² = 0.8093 for the alloys JN2 and JN3, R² = 0.9193 for the alloys JZ3 and JZ3+, R² = 0.6894 for the alloys OHS1, JZ5 and JZ4. In (d,e), the parameter Δχ is based on the Pauling electronegativity. See text for hatched data in (c,d) and for the arrow in (f). RM(Nb)ICs/RCCAs the alloys JG6, JZ3+, JZ4, JZ5 and OHS1.

Figure 4. Data for Nb₅Si₃ in RM(Nb)ICs and RM(Nb)ICs/RCCAs with additions of RM, TMs, Ge, Sn or Ge + Sn, with/without Al addition and with different Ti, Al, Cr or Sn concentrations. Alloys JN2, JN3, JN4, JN4, JG6, JZ3, JZ3+, JZ4, JZ5 and OHS1. For nominal alloy compositions and references, see the Appendix B. (a) Type of Nb₅Si₃ (“conventional” or CC) and dark and lighter colours, respectively for the AC and HT conditions. For presentation purposes, the “values” 15 and 10 have been assigned, respectively to “conventional” Nb₅Si₃ and CC Nb₅Si₃. (b) Nb/Ti or Nb/(Ti + Hf) ratio of Nb₅Si₃, (c) VEC of Nb₅Si₃, (d) Δχ of Nb₅Si₃, (e) VEC versus Δχ of Nb₅Si₃ and (f) Nb/Ti or Nb/(Ti + Hf) ratio versus VEC of Nb₅Si₃. In (e), linear fit of data for the alloys JN2 and JN4, and the R² values are for parabolic fit of data. In (f), R² = 0.6902 for all data, R² = 0.9809 for the alloys JN4 and JG6, R² = 0.8093 for the alloys JN2 and JN3, R² = 0.9193 for the alloys JZ3 and JZ3+, R² = 0.6894 for the alloys OHS1, JZ5 and JZ4. In (d,e), the parameter Δχ is based on the Pauling electronegativity. See text for hatched data in (c,d) and for the arrow in (f). RM(Nb)ICs/RCCAs the alloys JG6, JZ3+, JZ4, JZ5 and OHS1.

2.1. Creep

In the microstructures of RM(Nb)ICs, RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs, the Nb₅Si₃ silicide is desirable because of its creep properties and its high Si content, which is expected to benefit oxidation resistance. As we discussed in the previous section, in the aforementioned metallic UHTMs, the Nb₅Si₃ is alloyed, and its alloying behaviour is described by its parameters VEC and Δχ [40]. TMs and RMs substitute Nb and simple metal and metalloid elements substitute Si [40]. Experiments have confirmed that the alloying of Nb₅Si₃ affects its creep properties [30,31,32,35,36,40].

Data for the creep of Nb₅Si₃ is limited. In the Norton plot of Nb₅Si₃ (Figure 12 in [40] and Figure 7 in [24]), the experimental data shows that the steady-state creep rate (έ) of Nb₅Si₃ increases with alloying additions and that the alloying of Nb₅Si₃ causes the Norton line to shift upwards and to the left, i.e., towards higher creep rate at lower stress. In Figure 5, lnέ is plotted versus the parameter Δχ or VEC of the silicide and the data is for unalloyed Nb₅Si₃ and 3 alloyed silicides for which experimental data is available. The data is (i) for Nb₅Si₃ silicides where Nb is substituted either by Ti or by Ti and other TMs, and the Si is not substituted or is substituted with Al and B, i.e., the data is for (Nb, TM)₅(Si, X)₃, where TM = Cr, Hf, Ti and X = Al, B (see figure caption) and (ii) for a particular temperature and stress (T = 1200 °C and σ = 140 MPa). The arrow points in the direction of increasing creep rate for the specific T and σ. The data shows that the creep rate of (Nb, TM)₅(Si, X)₃ would increase as the alloying of Nb₅Si₃ changes the crystal structure of the silicide from tetragonal to hexagonal (the crystal structure of the T2 silicide is tetragonal and of the D8₈ silicide is hexagonal).

The arrow in Figure 5 points from the unalloyed past (purple square) towards the alloyed future of Nb₅Si₃ in metallic UHTMs, as in some sequences where Ti and Ti plus other TMs and RMs, such as Cr, Hf, Mo, Ta, V or W, substitute Nb, and Al, B, Ge or Sn substitute Si, owing to these additions in multiphase metallic UHTMs [1,2,24,40,73]. Note that previously the direction of change of the alloying behaviour of Nb₅Si₃ was represented with arrows in the Δχ versus VEC map in Figure 6 in [27]. The arrows showed in which direction the parameters of the silicide changed when different solutes substituted Nb or Si in the silicide.

In Figure 5, the arrow points in the direction of increasing creep rate for (Nb, TM)₅(Si, X)₃ at the given temperature and stress. There is no experimental data about the creep of Nb₅Si₃ where only Si is substituted by Ge or Sn, i.e., for Nb₅(Si, Y)₃, where Y = Ge, Sn. In this case, we know that the Δχ versus VEC map shows a different alloying behaviour of the latter silicides, meaning the change of alloying behaviour is in the opposite direction compared with the Ti-alloyed Nb₅Si₃ (see Figure 6 in [27] and Figure 11 in [40]). Currently, there is no experimental data for the creep of Nb₅(Si, Y)₃ silicides. In other words, we do not know whether the creep rate of these silicides also would increase with increasing temperature and stress. If creep experiments were to confirm this not to be the case, then I would like to suggest that further experimental work on the creep of tetragonal Nb₅Si₃ where Si is substituted with other simple metal and metalloid elements, namely with Al or with Al plus Ge or Sn, Ge + Sn or Al + Ge + Sn, and Nb with RMs (Mo, Ta, W) or Cr but not Hf or Ti, is essential.

The arrows in Figure 1f, Figure 2f and Figure 4f show that as the Nb/(Ti + Hf) ratio increases the parameter VEC increases. For RM(Nb)ICs, the said ratio has been shown to be important for their creep [24,35]. In alloys where the Nb/(Ti + Hf) ratio of the alloy and silicide is less than one, the creep rate is poor owing to hexagonal silicides being stable in the microstructure [68]. Low creep rates require the alloy Nb/(Ti + Hf) ratio to be higher than 1.4. Figure 1c,d, Figure 2c,d and Figure 4c,d show how the Nb/(Ti + Hf) ratio links (connects) with the parameters VEC and Δχ of the silicide. Below we shall see that the silicide can also link with the alloy and the solid solution via these parameters.

In Figure 1, Figure 2, Figure 3 and Figure 4, the silicides with VEC and Δχ values closest to those of the unalloyed Nb₅Si₃ are shown with hatched data (the parameter VEC for the “conventional” silicide in the alloys KZ5-AC and ZX8-HT in Figure 1c, the parameter Δχ for the “conventional” silicide in the alloy ZX8-HT in Figure 1d, the parameter Δχ for the CC silicide in the alloy EZ8-AC and “conventional” silicide in the alloy EZ8-HT in Figure 2d, the parameter VEC for the “conventional” silicide in the alloy TT8-HT in Figure 3c, the parameter Δχ for the “conventional” silicide in the alloy TT8-AC in Figure 3d, the parameter VEC for the “conventional” silicide in the alloys JZ4-AC and [JZ3+]-AC in Figure 4c, the parameter Δχ for the “conventional” silicide in the alloy OHS1-AC and CC silicide in the alloy [JZ3+]-AC in Figure 4d). Note (i) that the solute additions in the aforementioned alloys are Al, B, Cr, Ge, Hf, Mo, Sn, Ta, Ti and W, all of which play a key role in the creep and oxidation of RM(Nb)ICs, RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs [1,2,24], (ii) that all the silicides in the alloys with basis the alloy JN1 have VEC lower than that of the unalloyed Nb₅Si₃ (Figure 2c) and (iii) the high Nb/(Ti + Hf) ratio of the hatched “conventional” silicides in the alloys [JZ3+]-AC and JZ4-AC (compare Figure 4a,b with c,d). With NICE, it is possible to design a material system consisting of a metallic UHTM substrate with the elements Al, Cr, Ge, Hf, Mo, Nb, Si, Sn, Ti and W and an environmental coating the bond coat of which would be alloy(s) of the Al-Cr-Hf-Nb-Si-Ti alloy system [2,15,16,17,67].

Why is the above important for the development of metallic UHTMs? Our research group has shown that NICE makes it possible to design a metallic UHTM to meet a specific property target, say creep or oxidation, with/without other constraints, for example, constraints about solute elements, solute element ratios and hardness [2,15,16,17,24,27,50,51,62,64,66,67,75,76,77,78,79]. NICE also allows the alloy designer to consider alloying additions (meaning type and concentration) in the alloy to “move” its Nb₅Si₃ in a direction of change closer to or away from the creep properties of unalloyed Nb₅Si₃ or Ti-alloyed Nb₅Si₃, even to change the crystal structure of Nb₅Si₃. In other words, data about alloying behaviour and creep can be used to guide alloy design because the “bread and butter” of NICE are the relationships between solutes, between solute concentrations and alloy parameters, between alloy parameters and phase parameters and between alloy or phase parameters and their properties, where phase includes “conventional” and CC and/or HE phases (bcc solid solution, 5–3 silicides, C14-Laves phases, A15 compounds, eutectics of solid solutions and silicides) and alloy means RMIC, RCCA or RHEA with Nb and Si additions [1,2,15,16,17,24,27,40,44,49,51,58,61,62,66,67,80].

2.2. Hardness

According to the alloy design methodology NICE, the hardness of Nb₅Si₃ can be expressed as a function of its parameter VEC with the linear relationship HV_Nb5Si3 = a₁VEC_Nb5Si3 + b₁ (e.g., see Figure 14 in [27]). Guided by NICE, relationships of the parameter VEC with key solutes in the Nb₅Si₃ were sought in order to find out if the hardness of the silicide can be written down as a function of solute additions in metallic UHTMs. It was discovered that the parameter VEC of Nb₅Si₃ is related to its Nb/(Ti + Hf) ratio with a linear relationship [Nb/(Ti + Hf)]_Nb5Si3 = a₂VEC_Nb5Si3 + b₂, where the constants a₂ and b₂ depend on the basis alloy (see Figure 1f, Figure 2f and Figure 4f). For the basis alloy KZ5, the constants are a₂ > 0 and b₂ < 0. For KZ series alloys (for example, see the alloys in [58,64,76,80,81,82,83]), a₁ < 0 and b₁ > 0 (Figure 14a in [27]), i.e., the hardness of the silicide decreases as its parameter VEC increases. (Note that the hardness of carbides, nitrides and carbo-nitrides of TMs decreases with their parameter VEC [84] and that the hardness of Ti-alloyed Nb₅Si₃, i.e., of (Nb, Ti)₅Si₃, decreases and increases with its parameter VEC, respectively for α(Nb, Ti)₅Si₃ and β(Nb, Ti)₅Si₃ (see Figures 15 and 16 in [49])).

The hardness of Nb₅Si₃ can be written as a linear function of the ratio X_Nb5Si3 = Nb/(Ti + Hf), i.e., HV_Nb5Si3 = (a₁[X_Nb5Si3 − b₂]/a₂) + b₁ or HV_Nb5Si3 = f₁(X_Nb5Si3). Given that in NICE the concentrations of the solute elements in Nb₅Si₃ are related to the concentration of Hf or Ti in the silicide with linear relationships, e.g., Si = c₁Ti + d_1, Hf = c₂Ti + d₂ or Hf = c₃Nb + d₃, where the constants c_i and d_i can be positive or negative (e.g., see [24,40,76]), the ratio X_Nb5Si3 can be written as a function of the concentration of a specific solute and, therefore, the hardness of Nb₅Si₃ can also be written as a function of the concentration of a specific solute element in the silicide. In other words, the dependence of the hardness of Nb₅Si₃ on its parameter VEC allows one to calculate the HV_Nb5Si3 (attributed to VEC) for the specific concentration(s) of a specific solute.

Furthermore, as a consequence of the relationships between the parameters VEC and Δχ of the silicide (Figure 1e, Figure 2e, Figure 3e and Figure 4e), and thus between X_Nb5Si3 = Nb/(Ti + Hf) and Δχ_Nb5Si3, and, therefore, X_Nb5Si3 = a₃Δχ_Nb5Si3 + b_3, where a₃ and b₃ can be positive or negative (e.g., for KZ5 as the basis alloy see Figure 1g). NICE hinted that electronegativity is also important for the hardness of the silicide. Indeed, HV_Nb5Si3 = (a₁[X_Nb5Si3 − b₂]/a₂) + b₁ or HV_Nb5Si3 = f(Δχ_Nb5Si3) = (a₁[a₃Δχ_Nb5Si3 + b₃ − b₂]/a₂) + b₁. The hardness of Nb₅Si₃ can increase or decrease with increasing parameter Δχ depending on the solute elements. Given that the Ti content of Nb₅Si₃ depends on its parameter Δχ_Nb5Si3 (i.e., Δχ_Nb5Si3 = g(Ti_Nb5Si3)) with linear relationships, Δχ_Nb5Si3 = a₄Ti + b₄ where a₄ and b₄ can be positive or negative, and the hardness HV_Nb5Si3 = (a₁[a₃(a₄Ti + b₄) + b₃ − b₂]/a₂) + b₁ (in other words, the HV_Nb5Si3 is a function of its Ti content). Owing to the relationships of the concentrations C_i^Nb5Si3 of solutes i in Nb₅Si₃ with its Ti content (i.e., C_i^Nb5Si3 = g_i(Ti_Nb5Si3)) (e.g., Si = c₁Ti + d_{1, etc.}, see above), the hardness of alloyed Nb₅Si₃ for different solutes can be calculated. Actually, the dependence of the hardness of Nb₅Si₃ on its parameter Δχ allows one to calculate the HV_Nb5Si3 (attributed to Δχ) for the specific concentration(s) of a specific solute.

The experimental Vickers hardness of unalloyed βNb₅Si₃ is 1360 HV [40]. First principles calculations have shown that the substitution of Nb by Ti in the β(Nb, Ti)₅Si₃ reduces the hardness [40,85]. The experimental Vickers hardness of the β(Nb, Ti, Cr)₅(Si, Al)₃ in KZ5-AC was 1131 HV [76] of the β(Nb, Ti, Cr, Hf)₅(Si, Al)₃ in JN1-HT was 1124 HV [76] and of the β(Nb, Ti, Cr)₅(Si, Al, Ge)₃ in ZF6-HT was 1576 HV [64]. To put it in another way, the alloying of the silicide and the synergies of solutes in the alloys KZ5, JN1 and ZF6, respectively reduced and increased the hardness of the alloyed βNb₅Si₃ in these alloys. The concentrations of solutes in Nb₅Si₃ in the aforementioned alloys are known (determined using EPMA, see [64,76,81]), thus it is possible to calculate the hardness of the silicide (attributed to VEC or Δχ) for the concentration (at.%) range of each solute, see

Table 1. Calculated with NICE contributions of solutes to the Vickers hardness of alloyed βNb₅Si₃ attributed to the parameters Δχ and VEC for the silicide in the alloys KZ5-AC, JN1-HT and ZF6-HT (for the concentration ranges of each solute see the EPMA data in Table 2).

Alloy and Parameter		Solute
		Al	Cr	Ge	Hf	Nb	Si	Ti
KZ5-AC	Δχ	1234–1279	1220–1350	-	-	1013–1326	1176–1225	1024–1469
	VEC	1385–1411	1403–1471	-	-	793–1398	1270–1311	1185–1495
JN1-HT	Δχ	1216–1341	1265–1321	-	955–1528	922–1576	1303–1365	887–1563
	VEC	1331–1390	1359–1409	-	1155–1263	1213–1578	1263–1301	1253–1525
ZF6-HT	Δχ	1174–1315	1252–1403	1328–1707	-	845–1158	1204–1297	1135–1658
	VEC	1385–1434	1418–1475	1448–1558	-	1102–1421	1397–1436	1365–1566

and

Table 2. Measured with EPMA (range and average) and calculated with NICE concentrations (at.%) of solutes in the alloyed βNb₅Si₃ in the alloys KZ5-AC, JN1-HT and ZF6-HT. EPMA data from [64,76,81].

Alloy	Method	Solute
		Al	Cr	Ge	Hf	Nb	Si	Ti
KZ5-AC	EPMA	3.1–4	1.2–2.7	-	-	36.7–46.8	30.8–33.2	16.7–25.2
		3.5	2	-	-	41.9	31.8	23.9
	NICE	3.6	0.7	-	-	40.7	30.8	24.2
JN1-HT	EPMA	1.6–3.3	0.4–1.3	-	4.5–9.5	27.1–41.5	31.4–33.6	17.9–26.7
		3.1	1.2	-	9.3	27.3	32.5	26.6
	NICE	3.5	0.5	-	8.1	31.8	32.8	23.3
ZF6-HT	EPMA	3.1–5.2	1.5–2.8	7–8.1	-	35.9–43.4	20.8–24.4	20.5–29.7
		4.8	2.7	7.8	-	37.6	21	26.1
	NICE	3.9	1.1	7.7	-	35.4	25.2	26.8

. The calculated hardness of alloyed βNb₅Si₃ is given in Table 1 and the concentration ranges of each solute in the silicide that were determined using EPMA are given in Table 2.

For example, in the case of the β(Nb, Ti, Cr)₅(Si, Al)₃ in KZ5-AC, we have 16.7 < Ti < 25.2 at.%, 30.8 < Si < 33.2 at.%, 3.1 < Al < 4 at.%, 1.2 < Cr < 2.7 at.% and 36.7 < Nb < 46.8 at.% [81], and for each element, the calculated Vickers hardness (i) attributed to the parameter VEC is in the range 1185 to 1495, 1270 to 1311, 1385 to 1411, 1403 to 1471 and 793 to 1398 HV, respectively for Ti, Si, Al, Cr and Nb, and (ii) attributed to the parameter Δχ is 1024 to 1469, 1176 to 1225, 1234 to 1279, 1220 to 1350 and 1013 to 1326, respectively for Ti, Si, Al, Cr and Nb. Compared with the unalloyed βNb₅Si₃, on account of VEC and Δχ, the decrease in the hardness can be attributed, respectively to the solutes Nb, Si and Ti, and to all solutes among which Al, Cr and Si have a strong effect. Note that the average hardness calculated using the low hardness contribution of each element that is attributed to Δχ and VEC is 1133.4 and 1207.2, respectively (average 1170.3), compared with the measured hardness 1131 ± 54.

In the case of the alloy JN1-HT, the data in Table 1 shows that, compared with the unalloyed βNb₅Si₃ and taking into consideration the parameters VEC and Δχ, the decrease in the hardness can be attributed, respectively to the solutes Nb, Si, Ti and Hf, and to all solutes among which Ti and Nb have a strong effect. However, the hardening attributed by the parameter Δχ to Hf can be significant at lower Hf concentrations. Note that the average hardness calculated using the low hardness contribution of each element that is attributed to the parameters Δχ and VEC is 1091.3 and 1262.3, respectively (average 1176.8), compared with the measured hardness 1124 ± 58. Regarding the alloy ZF6-HT, the data in Table 1 shows that, compared with the unalloyed βNb₅Si₃ and taking into account VEC and Δχ, the increase in the hardness can be attributed, respectively to all solutes, in particular, Ge, and to Cr, Ge and Ti, with Ge having a noticeable hardening effect at high concentration, attributed to electronegativity (Δχ). Note that the average hardness calculated using the high hardness contribution of each element that is attributed to the parameters Δχ and VEC is 1423 and 1481.7, respectively (average 1452.4), compared with the measured hardness 1576 ± 60.

In [40], it was discussed that different alloying additions affect in a different way the solubility ranges in Nb₅Si₃. Compared with the silicide in the basis alloy KZ5, the data in Table 2 shows that with the addition of Hf in the alloy JN1, the Ti and Si concentration ranges increased while those of Al, Cr and Nb decreased, whereas with the addition of Ge in the alloy ZF6, the Ti, Al and Cr concentrations ranges increased and those of Si and Nb decreased. These changes also contributed to the changes in the Vickers hardness of the alloyed βNb₅Si₃ in the alloys JN1 and ZF6, along with the alloying with Hf or Ge.

The relationships of the hardness of Nb₅Si₃ with its parameter Δχ (HV_Nb5Si3 = f(Δχ_Nb5Si3)) and of Δχ_Nb5Si3 with the Ti concentration in Nb₅Si₃ (Δχ_Nb5Si3 = g(Ti_Nb5Si3)) in different RM(Nb)ICs, RM(Nb)ICs or RM(Nb)ICs/RHEAs, and the correlations of the concentrations C_i of solutes i with the Ti concentration in Nb₅Si₃ (C_i^Nb5Si3 = g_i(Ti_Nb5Si3)) allow us to calculate the chemical composition of the silicide using the measured hardness in the relationship between HV_Nb5Si3 = f₁(X_Nb5Si3) and the HV_Nb5Si3 = f(Δχ_Nb5Si3) and Δχ_Nb5Si3 = g(Ti_Nb5Si3) and C_i^Nb5Si3 = g_i(Ti_Nb5Si3) relationships in NICE. For the alloyed βNb₅Si₃ in the alloys KZ5-AC, JN1-HT and ZF6-HT, the measured chemical composition range and average concentration, and the calculated composition of each solute are given in Table 2. For each alloy, the agreement between measured and calculated concentrations of solutes in the silicide is good with the exception of the concentration of Cr that was underestimated by NICE for each alloy and the overestimated concentrations of Si and Nb in the alloys ZF6-HT and JN1-HT, respectively.

Given that X_Nb5Si3 = [Nb/(Ti + Hf)]_Nb5Si3 = a₂VEC_Nb5Si3 + b₂ = a₃Δχ_Nb5Si3 + b₃, the relationship between the parameters VEC and Δχ of the silicide is Δχ_Nb5Si3 = (a₂VEC_Nb5Si3 + b₂ − b₃)/a₃. For the basis alloy KZ5, the data gives 4.213 < VEC_Nb5Si3 < 5.902 for Δχ_Nb5Si3 > 0. Figure 1g is shows the extension of the brown data linear fit. The intercepts of the linear fits of the blue and black data, black and brown data and blue and brown data, respectively are (0.353, 2.859), (0.354, 2.891) and (0.355, 2.874), and the intercept of the linear fit of the dark green colour data (i.e., the data for CC Nb₅Si₃, see Figure 1g caption) of the green parabola is (0.354, 1.959). Note that data converge to similar Δχ (about 0.354) and that the ratio values (about 2.9 and 2) correspond to high VEC in Figure 1f. From Δχ_Nb5Si3 = 0.354 and the linear fits of data in Figure 1g (i.e., the blue, black and brown lines), we get the ratio [Nb/(Ti + Hf)]_Nb5Si3 and using Figure 1f, we calculate the parameter VEC_Nb5Si3 = 4.513. When we use the linear fits of the dark green colour data (i.e., the data for CC Nb₅Si₃, see Figure 1g caption) of the green parabola, we get the VEC_Nb5Si3 values 4.382 and 4.422, respectively for the linear fit with positive and negative slope. Parabolic fits of the blue and brown data, and of the black and brown data gave R² = 0.9056 and R² = 0.8863, respectively. The maxima for these parabolas and for the green data, respectively are (0.3163, 2.651), (0.3592, 2.5248) and (0.3628, 1.7128), and give VEC_Nb5Si3 values 4.49, 4.48 and 4.4, respectively. Note that the VEC_Nb5Si3 for the silicides in KZ5-AC and ZX8-HT shown with hatched data in Figure 1c was 4.45.

2.3. Alloy Design

As discussed in [2,51,56] and in this paper, in RM(Nb)ICs, RM(Nb)ICs/RCCAs or RM(Nb)ICs/RHEAs “conventional” phases can co-exist with CC or HE phases. NICE can design the aforementioned metallic UHTMs with said phases owing to relationships between parameters of alloys and phases [24]. Such relationships are characteristic of the approach to alloy design put into practise with NICE. Figure 6 shows examples of such relationships between the parameter VEC of alloy and “conventional” silicide (Figure 6a), between the parameters Δχ and VEC of CC silicide (Figure 6b), and between the parameter VEC of CC Nb_ss and Nb₅Si₃ (Figure 6c).

Figure 6. Relationships between the parameters (a) VEC of alloy versus VEC of “conventional” Nb₅Si₃, (b) Δχ versus VEC of CC Nb₅Si₃ and (c) VEC of CC Nb₅Si₃ versus VEC of CC Nb_ss. In (a), AC alloys JN1, JN2, JN3, JN4, JZ3, JZ3+, OHS1, TT4, TT8 and ZF6, in (b) AC alloys EZ8, JN1, JG6, JZ3, JZ3+, KZ6, OHS1, TT4, TT5, TT7, TT8, ZF6 and ZF9 and in (c), AC alloys EZ8, JG6, JZ3, JZ3+, KZ6, TT4, TT5, TT7 and ZF9, and HT alloys JZ5 and TT5. In all three parts, the red data is for alloys with Ge and/or Sn addition. Black R² values are for all data. Parabolic fits of data in (a,c). For nominal alloy compositions and references, see the Appendix B.

Figure 6. Relationships between the parameters (a) VEC of alloy versus VEC of “conventional” Nb₅Si₃, (b) Δχ versus VEC of CC Nb₅Si₃ and (c) VEC of CC Nb₅Si₃ versus VEC of CC Nb_ss. In (a), AC alloys JN1, JN2, JN3, JN4, JZ3, JZ3+, OHS1, TT4, TT8 and ZF6, in (b) AC alloys EZ8, JN1, JG6, JZ3, JZ3+, KZ6, OHS1, TT4, TT5, TT7, TT8, ZF6 and ZF9 and in (c), AC alloys EZ8, JG6, JZ3, JZ3+, KZ6, TT4, TT5, TT7 and ZF9, and HT alloys JZ5 and TT5. In all three parts, the red data is for alloys with Ge and/or Sn addition. Black R² values are for all data. Parabolic fits of data in (a,c). For nominal alloy compositions and references, see the Appendix B.

Regarding phases other than the Nb₅Si₃ silicide and their properties, for example, the bcc solid solution(s) or eutectics consisting of bcc solid solution and Nb₅Si₃, and properties of RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAs, for example, oxidation, creep, hardness or specific strength, other “arrows of alloying” also link with other properties.

For example, the hardness of the solid solution (HV_ss) increased and decreased as its parameter δ_ss increased, respectively for B-free and B-containing RM(Nb)ICs and RM(Nb)ICs/RCCAs, see Figure 4 in [2]. We could choose the “arrow of hardness” of the bcc solid solution to point, respectively, in the direction of increase and decrease in HV_ss with δ_ss for the alloys in Figure 4 in [2]. In the case of B-free alloys, the δ_ss increased with increasing (Ge + Sn)_ss (Figure 7b in [56]). Note that Ge and Sn are two solutes that play a key role in the oxidation of metallic UHTMs with Nb and Si addition [1,2,65,66,67]. We could choose the “arrow of alloying” to point in the direction of increase in δ_ss in Figure 7b in [56]. However, because the (Ge + Sn)_ss sum links with the concentrations of other solute additions (see Figure 9 in [56]), the “arrow of alloying” also “targets” other solute additions. Furthermore, because δ_ss increased with increasing [O]_ss (see Figure 11 in [56]), the effect of the contamination of the bcc solid solution on its hardness also can be taken into account via the “arrow of alloying”. In the case of B-containing alloys, the δ_ss increased with increasing boron in the solid solution, B_ss (Figure 7a in [56]). Note that B is another solute that plays a key role in the oxidation of metallic UHTMs with Nb and Si addition [1,2,61,62]. We could choose the “arrow of alloying” to point in the direction of increase in δ_ss in Figure 7a in [56]. Similarly, with the (Ge + Sn)_ss sum, the B_ss is linked with the concentrations of other solute additions (Figure 8 in [56]), and thus the “arrow of alloying” also “targets” other solute additions. Note the opposite trends regarding relationships of solute concentrations with (Ge + Sn)_ss or B_ss (compare Figures 8 and 9 in [56]).

The hardness of RM(Nb)ICs and RM(Nb)ICs/RCCAs with B, Ge or Sn addition (HV_alloy) increased with the parameter VEC_alloy (Figure 11 in [27]). Additionally, the room temperature-specific strength of RM(Nb)ICs and RM(Nb)ICs/RCCAs decreased with increasing VEC_alloy (Figure 6 in [2]). Furthermore, there are relationships between the steady-state creep rate of RM(Nb)ICs at a specific temperature and stress and the parameters VEC_alloy, Δχ_alloy or δ_alloy (Figure 10 in [24]). We could choose the “arrow of alloy hardness” to point in the direction of increase in VEC_alloy for alloys with B, Ge or Sn addition, the “arrow of alloy specific strength” to point in the direction of decrease in VEC_alloy and the arrow that shows the change of alloy creep to point in the direction of increasing VEC_alloy or Δχ_alloy and decreasing δ_alloy. “Arrows of oxidation” were shown in the VEC_alloy versus (ΔW/A)_alloy in Figure 16 in [27] ((ΔW/A)_alloy is the mass change in isothermal oxidation in air at 1200 °C of RM(Nb)ICs and RM(Nb)ICs/RCCAs). The parameter VEC_alloy links with solute concentrations in the alloy and bcc solid solution, for example, see the VEC_alloy versus Al_ss and Al_alloy versus Al_ss relationships in Figure 19 in [27] and the VEC_alloy versus Al_alloy and VEC_ss versus Al_ss relationships in Figure 18 in [27], and relationships between solute concentrations and alloy steady-state creep rate for the creep goal conditions, as seen in Figure 22 in [27]. In each of the aforementioned figures, we could assign an “arrow of alloying”. Furthermore, we could give “arrows of alloying” for the relationships between VEC_alloy and VEC_ss or VEC_Nb5Si3 in Figure 17 in [27].

The hardness of eutectics with bcc solid solution and Nb₅Si₃ (HV_eutectic) increased with increasing parameter VEC_eutectic (Figures 12 and 13 in [49]) and decreased with increasing parameter Δχ_eutectic or δ_eutectic (Figure 15 in [27]). We could choose the “arrow of eutectic hardness” to point in the direction of increase in VEC_eutectic or decrease in Δχ_eutectic or δ_eutectic. “Arrows of alloying” can be assigned to the relationships between VEC_eutectic and <Si>_eutectic (Figure 14 in [49]), between δ_eutectic and <Si>_eutectic (Figure 8 in [49]), between Δχ_eutectic and <Si>_eutectic (Figure 6 in [49]), where <Si>_eutectic = Al + Ge + Si + Sn, between Δχ_eutectic and VEC_eutectic (Figure 5 in [49]) and Δχ_eutectic and Δχ_alloy (Figure 17 in [27]).

The “arrows of alloying” and arrows of properties, for example, in Nb₅Si₃ steady-state creep rate, solid solution hardness, eutectic hardness, alloy hardness, alloy specific strength, alloy steady-state creep rate and alloy oxidation, by having specific properties such as their “targets”, point the alloy developer to the direction of appropriate and trustworthy paths and guide him/her along these paths in an alloy development roadmap/”landscape”. The starting point in NICE is always a property goal or property goals if a balance of properties were to be the desirable outcome of alloy design/development [24].

NICE informs (warns) the alloy developer (a) that it is unrealistic to seek to develop an alloy that meets simultaneously the three specific property goals for toughness, creep and oxidation [1,2], (b) that there is no point in arbitrarily choosing some elements from the periodic table and putting them to “work together” (be in synergy) at some arbitrarily chosen concentrations [27] because synergies differ (e.g., see Figure 4e,f) and chemical composition and element identity matter because they “bring into being” parameter values [1,2,24,27,40,44,49,55,73] and (c) that the development of metallic UHTMs should work closely together with the development of environmental coatings [1,2,15,16,17,27,78,79].

3. Conclusions

Different types of alloyed “normal” Nb₅Si₃ and Ti-rich Nb₅Si₃, namely “conventional”, CC or HE, can form in metallic UHTMs with Nb and Si addition, i.e., in RM(Nb)ICs, RM(Nb)ICs/RCCAs and RM(Nb)ICs/RHEAS. Alloying behaviour and properties of the silicides can be studied using their Nb/(Ti + Hf) ratios, the parameters VEC and Δχ and relationships between them.

• Ti-rich (Nb, Ti, Cr)₅(Si, Al)₃, is converted from “conventional” to CC when it is alloyed with B, Ge, Hf, Mo, Sn or Ta. With the exception of the B addition, the “conventional” Nb₅Si₃ has VEC > 4.4. The “conventional” and CC Nb₅Si₃ has the lowest and highest Δχ when it is alloyed with B or Ge.
• Ti rich (Nb, Ti, Cr, Hf)₅(Si, Al)₃ is CC when alloyed with B, Ge, Mo or Sn and with the addition of B or Ge the “normal” and Ti rich silicide changes to CC in both the AC and HT conditions. The alloying of (Nb, Ti, Cr, Hf)₅(Si, Al)₃ with B, Ge, Mo or Sn gives Nb/(Ti + Hf) < 1.9.
• Regarding the alloyed tetragonal T2-(Nb, Ti, Cr)₅(Si, Al, B)₃, the “conventional” T2 is stable in the HT condition when alloyed with Mo or Sn. When alloyed with Hf or Ta the T2 has Δχ > 0.3 and when alloyed with Mo or Ta, it has VEC > 4.35.
• In advanced metallic-UHTMs where Hf, Mo and Ti are in synergy with Sn, (i) the addition of Al converts the “conventional” silicide to CC, whereas (ii) lower Cr concentration promotes “conventional” Nb₅Si₃ and Ti-rich Nb₅Si₃ in the absence of Al in the alloy. Furthermore, in advanced metallic-UHTMs where Al, Cr, Hf, RMs and Ti are in synergy with Ge + Sn the type of Nb₅Si₃ depends (iii) on the concentrations of Sn and/or Ti, and (iv) the choice of RM that is in synergy with W in the alloy, in particular the substitution of Mo with Ta stabilizes the “conventional” Nb₅Si₃ after HT and converts the “conventional” Ti rich Nb₅Si₃ to CC.
• The steady-state creep rate of the alloyed silicide can be related to its parameters VEC and Δχ, and its Nb/(Ti + Hf) ratio. For a given temperature and stress, the steady-state creep rate of the alloyed silicide, in which TMs substitute Nb and Al and B substitute Si, increases with decreasing parameter and ratio value, compared with the unalloyed Nb₅Si₃.
• Relationships of the hardness of alloyed Nb₅Si₃ with its parameter VEC, relationships of the latter with the silicide parameter Δχ and Nb/(Ti + Hf) ratio and relationships of the concentrations of solutes in the silicide with its Ti concentration enable the alloy designer/developer (i) to calculate the hardness of alloyed Nb₅Si₃, attributed to VEC or Δχ for a specific solute and its concentration range and (ii) to calculate the average chemical composition of Nb₅Si₃ from its hardness.