Alloying and Hardness of Eutectics with Nb_ss and Nb₅Si₃ in Nb-silicide Based Alloys

Abstract

In Nb-silicide based alloys, eutectics can form that contain the Nb_ss and Nb₅Si₃ phases. The Nb₅Si₃ can be rich or poor in Ti, the Nb can be substituted with other transition and refractory metals, and the Si can be substituted with simple metal and metalloid elements. For the production of directionally solidified in situ composites of multi-element Nb-silicide based alloys, data about eutectics with Nb_ss and Nb₅Si₃ is essential. In this paper, the alloying behaviour of eutectics observed in Nb-silicide based alloys was studied using the parameters ΔH_mix, ΔS_mix, VEC (valence electron concentration), δ (related to atomic size), Δχ (related to electronegativity), and Ω (= T_m ΔS_mix/|ΔH_mix|). The values of these parameters were in the ranges −41.9 < ΔH_mix <−25.5 kJ/mol, 4.7 < ΔS_mix < 15 J/molK, 4.33 < VEC < 4.89, 6.23 < δ < 9.44, 0.38 < Ω < 1.35, and 0.118 < Δχ < 0.248, with a gap in Δχ values between 0.164 and 0.181. Correlations between ΔS_mix, Ω, ΔS_mix, and VEC were found for all of the eutectics. The correlation between ΔH_mix and δ for the eutectics was the same as that of the Nb_ss, with more negative ΔH_mix for the former. The δ versus Δχ map separated the Ti-rich eutectics from the Ti-poor eutectics, with a gap in Δχ values between 0.164 and 0.181, which is within the Δχ gap of the Nb_ss. Eutectics were separated according to alloying additions in the Δχ versus VEC, Δχ versus <Si>, δ versus <Si>, and VEC versus <Si> maps, where <Si> = Al + Ge + Si + Sn. Convergence of data in maps occurred at δ ≈ 9.25, VEC ≈ 4.35, Δχ in the range ≈ 0.155 to 0.162, and <Si> in the range ≈ 21.6 at.% to ≈ 24.3 at.%. The convergence of data also indicated that the minimum concentration of Ti and maximum concentrations of Al and Si in the eutectic were about 8.7 at.% Ti, 6.3 at.% Al, and 21.6 at.% Si, respectively, and that the minimum concentration of Si in the eutectic was in the range 8 < Si < 10 at.%.

1. Introduction

Nb-silicide based alloys (also known as Nb-silicide in situ composites) are multi-element high temperature alloys. They can offer a balance of properties, and meet property goals to enable future aero engines to comply with new environmental and performance targets [1]. Alloying additions that have been reported in Nb-silicide based alloys include Al, B, Cr, Fe, Ga, Ge, Hf, Ho, Mo, Si, Sn, Ta, Ti, V, W, Y or Zr. The desirable phases in these Nb-Si based alloys are the bcc Nb solid solution (Nb_ss) and tetragonal Nb₅Si₃ silicide. Other phases also can be present, such as for example C14-NbCr₂ Laves and A15-Nb₃X intermetallic phases.

In current aero engines, columnar grained and single crystal blades that were manufactured from Ni-based superalloys are used. Eutectic alloys with unusual highly anisotropic microstructures and properties can be manufactured. The properties of directionally solidified (DS) eutectic alloys depend on the regularity and directionality of the microstructure. DS in situ composites can be used at high stress levels at high homologous temperatures, and are capable of meeting the needs of different applications. The evaluation of DS eutectic Nb-silicide in situ composites is desirable.

In situ composites can be produced via liquid-to-solid and solid-to-solid phase transformations. In binary systems with eutectic and eutectoid reactions, in situ composites of the binary eutectics and eutectoids have been studied. The directional solidification of alloys of eutectic composition can produce in situ composites with one or more high strength phases (which are often referred to as reinforcing phases) in a metal matrix. The interface between the matrix and the reinforcing phase is formed at close to equilibrium conditions, and is stable. Microstructures can be stable at high homologous temperatures. Eutectics have been grown with ductile metal matrices and reinforcing whiskers with strengths in excess of 7 GPa [2].

Aligned composites are desirable for high-temperature applications. Those that are grown from the melt have inherent advantages compared with other types of aligned composites, because adequate bonding and low reactivity between the phases is achieved, and there are no lay-up problems or fibre matrix interactions during fabrication.

Aligned in situ composites of near eutectic composition can be fabricated. In binary alloys of compositions well removed from the eutectic, in situ composites have been grown under high G/R ratios, where G is the temperature gradient, and R is the growth rate [3,4]. Multi-component alloys can be grown with a plane front and an aligned composite structure, provided that the interface kinetics do not pose too great a barrier to growth, the G/R ratio is sufficiently high, and the convection is sufficiently low.

DS materials are sensitive to changes in R, G, and composition. Reactions with the mould and core(s) may be a serious problem at low R values. Elements (impurities) of low concentration C_o may influence (i) the stability and (ii) the properties of the DS structure. The effects of such elements may be large (i) because they can cause a macroscopically planar S/L interface to become morphologically unstable. A degeneration of an S/L interface to a non-planar configuration is more pronounced at high R values that produce finer and stronger structures, or low G values. Two ratios, which depend on the processing and alloy parameters, are important. The first is the ratio G/(RC_o), which must be greater than some critical value to produce a controlled DS eutectic. The second is the ratio (RΔT_o/D), where ΔT_o is the freezing range of the alloy, and D is the diffusivity in the melt. For G < (RΔT_o/D), the S/L interface becomes morphologically unstable. The value of ΔT_o depends on composition. ΔT_o is small when the alloy has the eutectic composition and when the impurity concentration C_o is low. Off-eutectic alloys have larger ΔT_o values, and impurities also increase ΔT_o. The effects of growth rate fluctuations are minimized for an alloy of eutectic composition. In off-eutectic alloy compositions, growth rate fluctuations cause changes in volume fractions of phases. If the fluctuation in growth rate is large enough, the volume fraction of one phase may go to zero. Thus, knowledge about the composition of the eutectic and element(s) with low concentration (impurities) is essential for regular DS composites. In other words, composites without irregularities in the DS structure, such as change(s) in the cross-section during DS casting, can also change R and G, and thus cause the breakdown of the regular structure.

Research in the early 1970s on titanium matrix eutectics, where Ti was reinforced with an intermetallic phase, reported that reinforcement with 31 vol % Ti₅Si₃ fibres gave a considerable improvement of the Young’s modulus, compressive yield strength, and creep strength compared with existing commercial alloys [5,6].

The development of Nb-silicide based alloys has concentrated almost exclusively on cast and heat-treated alloys. Powder metallurgy (PM) alloys also have been made [7]. The non-consumable electrode arc melting of small elemental charges (0.01 kg to 0.6 kg) of pure elements in water cooled copper crucibles has been the preferred processing route for the large majority of cast alloys, owing to the limited available facilities and resources for alloy making and processing worldwide.

In the Nb–Si binary phase diagram [8], there are eutectic and eutectoid reactions (see below in this section), which, in principle, make it possible to produce in situ Nb–Si composites via liquid-to-solid and solid-to-solid phase transformations. Research has sought to utilize these reactions for the development of Nb-silicide based alloys [9]. In the 1990s, it was demonstrated that DS in situ Nb–Si composites can be grown [1,9]. DS Nb-silicide based alloys have been produced using (i) the Bridgman method with liquid metal cooling [10,11,12,13], (ii) homemade DS facilities [14,15,16], and (iii) optical floating zone (OFZ) processing [17,18,19,20,21,22]. Typical microstructures of DS Nb-silicide based alloys produced using (i) to (iii) are shown in [10,11,12,13,14,15,17,21].

The fabrication of aligned Nb_ss and Nb₅Si₃ in situ composites of multi-element Nb-silicide based alloys is highly desirable. Aligned microstructures with Nb_ss and Nb₅Si₃ could be produced using the directional solidification of eutectics that contain these phases. For the solidification processing of such in situ eutectic composites, data about the eutectics with Nb_ss and Nb₅Si₃ that can form in Nb-silicide based alloys is required. The following discussion will highlight that such data is currently either non-available or severely limited.

Why it is possible to fabricate in situ composites of Nb-silicide based alloys? Why is there interest in eutectics with Nb_ss and Nb₅Si₃? To answer these questions, one needs to revisit what is known about eutectic(s) and eutectoid reactions in the Nb–Si binary system. In the Nb-rich part of the equilibrium Nb–Si binary phase diagram, the eutectic and eutectoid reactions are L → Nb_ss + Nb₃Si (stable eutectic), and Nb₃Si → Nb_ss + αNb₅Si₃, respectively [8]. The latter is very sluggish. In binary Nb–Si alloys, the former reaction can be suppressed under rapid solidification conditions, and replaced by the metastable eutectic reaction L → Nb_ss + βNb₅Si₃ [23,24,25]. The phase diagram used in [23] to show the metastable extension of the Nb₅Si₃ liquidus to form the metastable eutectic indicated stable eutectic for a liquid composition at Si = 18.7 at.%, and a metastable eutectic at Si ≈ 20 at.%. For the stable eutectic in the binary phase diagram, the reported values of the Si concentration of the liquid are in the range 15.3 at.% to 18.7 at.% [26,27]; in other words there is disagreement about the composition of the stable eutectic. There is also disagreement about the temperature of the eutectoid reaction for which the high and low temperatures of 2043 K and 1939 K, respectively, have been reported [28,29]. The concentration of Si in the metastable eutectic estimated from the metastable extension of the Nb₅Si₃ liquidus depends on the Nb–Si binary phase diagram that is used.

The tetragonal Nb₅Si₃ silicide is preferred for Nb-silicide based alloys owing to its superior properties compared with Nb₃Si and hexagonal γNb₅Si₃. The two phase Nb + αNb₅Si₃ area in the Nb–Si binary has a composition range from 0.6 at.%. to 37.5 at.%. This gives flexibility to form Nb + Nb₅Si₃ composites that are stable above the envisaged surface temperature of the new alloys in service (T_service ≤ 1673 K) and with different volume fractions of the phases.

Nb-silicide based alloys have been developed that have met the toughness or creep property goals or significantly closed the gap with the oxidation property goal. These are multi-element Nb–Si-based alloys. Some of the alloying additions provide solid solution strengthening to the Nb_ss (for example, Mo, Ta, Ti, and W). Meanwhile, other elements suppress pest oxidation and improve oxidation at high temperatures (for example, Al, B, Cr, Fe, Ge, Hf, Sn, and Ti); other elements suppress the stable eutectic and replace it with the metastable one (for example, Al, Mo, Sn, Ta, and W), and other elements stabilise tetragonal Nb₅Si₃ (for example, Al, Cr, Mo, Ta, and W) and improve creep (Mo, Ta, and W). Phase diagrams provide data about eutectic and eutectoid reactions. However, for the design and development of Nb-silicide based alloys, such data is limited. For example, there are no phase diagrams for the Nb-Si-Ta, Nb-Si-Y ternary systems [30], no or limited data about the liquidus projections of the Nb-Si-Al, Nb-Si-Hf, Nb-Si-Mo, Nb-Si-V, Nb-Si-W, Nb-Si-Zr ternary systems [30], and there are disagreements about the Nb-Ti-Si and Nb-Cr-Si liquidus projections [31,32,33,34,35,36,37].

Recently, the alloying of Nb_ss and tetragonal Nb₅Si₃ was reported in [38,39]. The study of the solid solution [38] used the parameters ΔH_mix (enthalpy of mixing), ΔS_mix (entropy of mixing (VEC (valence electron concentration), δ (parameter related to atomic size), Δχ (parameter related to electronegativity) and Ω = T_m ΔS_mix/|ΔH_mix|. The capital letter Q was used instead of Ω for the ratio T_mΔS_mix/|ΔH_mix|in [38] to avoid confusion with the term Ω_ij in the definition of ΔH_mix. The above parameters are used in the study of the so-called high entropy alloys. References for publications on high entropy alloys are given in [38]. In [38], the alloying behaviour of the solid solution was described well by the parameters δ, Δχ, and VEC. The study of tetragonal Nb₅Si₃ [39] also showed that the parameters Δχ and VEC described its alloying behaviour, and that the changes of the hardness of the alloyed Nb₅Si₃ were related to the VEC parameter.

What can we learn about the Si concentration of eutectics that contain Nb_ss and Nb₅Si₃ from the available data for Nb-silicide based alloys? For these eutectics, would it be possible to deduce (i) the maximum and minimum concentrations of Si in the eutectic, (ii) the total concentration of simple metal and metalloid elements in the eutectic, (iii) the minimum and maximum concentrations of other alloying additions in the eutectic (see the discussion about C_o and ΔT_o earlier in this section), (iv) the dependence of the concentration of refractory metals on the Si concentration in the eutectic, and (v) whether the hardness of the eutectics is related to the VEC parameter?

The motivation for the research presented in this paper was to answer the above questions. The structure of the paper is as follows. First, the values of the aforementioned parameters will be given for eutectics with Nb_ss and Nb₅Si₃, and compared with data for Nb-silicide based alloys and their solid solutions. Then, the relationships between them will be discussed. The focus will then be on relationships between parameters, and the concentration of simple and metalloid elements in the eutectic. Next, the relationships between the concentrations of solute additions and the Si concentration in the eutectic will be discussed. Finally, the hardness of the eutectics will be considered.

2. Methodology

The available experimental data for the eutectics with Nb_ss and Nb₅Si₃ in Nb-silicide based alloys from [40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56] was used to seek out relationships between the parameters ΔH_mix, ΔS_mix, VEC, δ, Δχ, and Ω, and between these parameters and the hardness of eutectics. The actual compositions of eutectics with Nb_ss and Nb₅Si₃ were the essential requirement in order to calculate the parameters of the eutectic. The equations that were used to calculate the parameters H_mix, S_mix, VEC, δ, Δχ and Ω were given in [38]. The data for the properties of elements was from the same sources as in [38].

All of the eutectics studied in this paper were observed in the cast microstructures of Nb-silicide based alloys that had been prepared using arc melting with non-consumable tungsten electrodes in an inert atmosphere with water-cooled copper crucibles. The phases in the cast microstructures of the alloys were identified using XRD (Siemens D5000, Hiltonbrooks Ltd., Crewe, UK) and JCPDS data (International Centre for Diffraction Data), and quantitative microanalysis [40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]. For the latter, electron probe microanalysis (EPMA) was used in a JEOL 8600 EPMA (JEOL Ltd., Tokyo, Japan) equipped with energy-dispersive and wavelength-dispersive spectrometers and the Oxford Link INCA software (Oxford Instruments plc, Abingdon, UK). Carefully polished standards of high purity of Nb, Si, and the other alloying element additions (Al, Cr, Fe, Ge, Hf, Mo, Sn, Ta, Ti, V, W, Y, and Zr) were used. At least 10 analyses were performed for each eutectic area in an alloy. Each specimen had been carefully polished, and was not etched. The hardness of eutectics was measured using a CV-430 AAT automatic hardness-testing machine. The load that was used was 10 kg, and was applied for 20 seconds. The indentations were made only on the eutectic areas, and covered a larger area relative to inter-lamellar spacing. At least 10 measurements were taken for each phase. The hardness measurements were taken from eutectics with similar inter-lamellar spacing in the order of micrometres. No new experimental data were created during the course of this study.

Eutectics with Nb_ss and Nb₅Si₃ have been observed in Nb-silicide based alloys with/out Ti addition, and with simple metal and metalloid element additions and other transition and refractory metal additions. The alloys belong in different alloy systems. Eutectics with Nb_ss and Nb₅Si₃ have been reported in ternary Nb-Si-X (X = Ga, Ge, Mo, Sn) [43,45,57,58]; quaternary Nb-Si-Hf-X (X = Al, Cr, Sn, W) [40,42,49], Nb-Si-Mo-X (X = Al, W) [21,42], Nb-Si-Ge-X (X = Al, Cr) [47,48], Nb-Ti-Si-X (X = Al, Ge, Sn) [46,59]; quinary Nb-Si-Hf-Sn-Al [49], Nb-Si-Hf-Mo-Ta [41], Nb-Ti-Si-Al-Cr [59], Nb-Ti-Si-Sn-X (X = Al, Cr, Fe, Hf) [44,51,52], Nb-Ti-Si-Al-X (X = Ge, Hf) [48], and Nb-Ti-Si-Mo-W [41,42] alloys; and higher order alloys, such as for example Nb-Ti-Si-Al-Cr-X (X = Ge, Hf, Sn, Ta) [10,12,13,15,19,50,53,60], Nb-Ti-Si-Hf-Mo-W [61], Nb-Ti-Si-W-Ge-Sn-X (X = Mo, Ta) [50,53], Nb-Ti-Si-Al-Cr-Mo-W-Ge-Sn [50,53], Nb-Ti-Si-Al-Cr-Ge-Y [55], Nb-Ti-Si-Al-Cr-Hf-B-Y [14,16], and Nb-Ti-Si-Al-Cr-Hf-Ta-Ho [20] alloys. Eutectics with Nb_ss and Nb₅Si₃ have been observed in boron containing Nb-silicide based alloys, but there is no data for the chemical composition of such eutectics (see discussion of Figures 6 and 13 in the next section).

Both Nb_ss and Nb₅Si₃ in Nb-silicide based alloys can be alloyed; for example, Nb-32.4Ti-1.4Si-5.8Cr-2.5Al-2.8Fe-4.9Sn-1.3Hf and Nb-34.1Si-20.7Ti-9.6Hf-3.7Al-1.8V-0.4Cr-0.4Sn are actual average chemical compositions (at.%) respectively of a solid solution and a Nb₅Si₃ silicide in two different Nb-silicide based alloys. Some of the alloying additions partition preferably to one of these phases (for example, Sn partitions to the Nb_ss [43,44] and Ge partitions to the Nb₅Si₃ [45,46,47,48]) and other elements partition to both phases (for example, Hf and Ti). Depending on alloying additions, other phases also can form, for example A15-Nb₃X (X = Al, Ge, Sn, Si) and C14-NbCr₂ Laves. These phases also are alloyed; for example, Nb-25.4Ti-2.3Cr-0.7Fe-0.3Hf-10.9Sn-5.1Si-2.4Al [52] and Nb-6.6Ti-6.9Ta-4.4W-1.1Hf-44.2Cr-8.7Si-6Al-1Ge-0.6Sn [50] are actual average chemical compositions (at.%) respectively of an A15 and a Laves phase in two different Nb-silicide based alloys.

The A15 phases are observed next to the Nb_ss, and the Laves phases form in the last to solidify Cr-rich melt in between Nb_ss and Nb₅Si₃ dendrites [59,60]. Under backscatter electron (BSE) imaging conditions, the contrasts of Nb_ss and A15-Nb₃X phase are similar. Ti-rich areas can form in Nb_ss and Nb₅Si₃. Nb_ss/Nb₅Si₃ interfaces also can be Ti-rich. In Hf and Ti-containing alloys, the increase of the concentration of Ti in Nb_ss and/or Nb₅Si₃ is accompanied by an increase of the concentration of Hf. In alloys with Mo and W additions, the partitioning of these elements and Ti in the Nb_ss also creates problems with contrast, as Mo and W “do not like Ti in the Nb_ss”, meaning that as the concentrations of Mo and W increase, that of Ti decreases. The variations in contrast that arise from the partitioning of solutes and the fine microstructures of the eutectics sometimes made it very difficult to confirm whether a binary Nb_ss + Nb₅Si₃ or a ternary eutectic between Nb_ss and Nb₅Si₃ and A15-Nb₃X or C14-NbCr₂ Laves had formed in alloys with three or more phases. In the great majority of the alloys studied in this paper binary, Nb_ss + Nb₅Si₃ eutectics were observed. All of the eutectics studied in this paper contained Nb_ss and Nb₅Si₃. No eutectics that contained Nb_ss and Nb₃Si were studied in this paper.

The experimental data [40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56] about the actual average chemical compositions of the eutectics with Nb_ss and Nb₅Si₃ observed in alloys of the aforementioned systems was used to study the alloying behaviour of the eutectic. Compositions of eutectics with Nb_ss and Nb₅Si₃ are given in [40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56]. The eutectics had 1.9 < Al < 6.4 at.%, 1.3 < Cr < 7.7 at.%, 1.2 < Ge < 7.8 at.%, Hf < 8.6 at.%, 1.2 < Mo < 11.3 at.%, 8.1 < Si < 24.4 at.%, 1.2 < Sn < 5.4 at.%, 8.2 < Ti < 36.8 at.%, and 2 < W < 5.8 at.%. The total concentration of simple element and metalloid element additions in the eutectic is given in this paper as <Si> = Al + Ge + Si + Sn; i.e., the <Si> (at.%) includes the additions of Al, Ge, Si, and Sn, depending on whether Al, Ge, and Sn were present individually or simultaneously in the alloy.

3. Results and Discussion

The ranges of the values of the aforementioned parameters for the eutectics with Nb_ss and Nb₅Si₃ are given in

Table 1. Values of the parameters ΔH_mix, ΔS_mix, valence electron concentration (VEC), δ, Δχ, and Ω for all of the Nb-silicide based alloys and their solid solutions, and for the eutectics with Nb_ss and Nb₅Si₃.

Material	Parameter
	ΔHmix /(kJ/mol)	ΔSmix (J/molK)	VEC	δ	Δχ	Ω +
Nb-silicide based alloys [62]	−32.7 to –44.8	8.3–14.7	4.37–4.9	8.1–14.3	0.12–0.237	0.57–0.95
Nbss in Nb-silicide based alloys [38]	−2 to –15.9	5.8–14.5	4.4–5.4	2.4–9.7	0.039–0.331 with a gap in the range 0.13 to 0.179	1.55–8.9
Eutectics with Nbss and Nb5Si3	−25.5 to –41.9	4.7–15	4.33–4.89	6.23–9.44	0.118–0.248 with a gap in the range 0.164 to 0.181	0.38–1.35

+ The capital letter Q was used instead of Ω for the ratio T_mΔS_mix /|ΔH_mix|in [38].

, where they are compared with those of the Nb-silicide based alloys [62] and Nb_ss in all of the alloys [38]. As was the case in [62], the parameters were not used to predict whether the eutectics are HEAs (high entropy alloys) or whether the solid solution and/or intermetallic(s) will be stable. They were used to study alloying behaviour in the eutectics, discover if there are relationships between parameters and between parameters and solute concentrations in eutectics, and find out if the hardness of eutectics is related to specific properties. Compared with Nb-silicide based alloys [62], the eutectics had wider ranges of ΔH_mix, ΔS_mix, Δχ, and Ω values, the VEC range was essentially the same, the range of δ values was narrow, and some eutectics had δ values that were lower than those in the Nb-silicide based alloys. Compared with Nb solid solutions [38], the eutectics had more negative ΔH_mix values with a wider range, the ΔS_mix range was slightly wider, the ranges of the VEC, Δχ, and δ values were narrow and in the ranges of the values of Nb_ss in all of the alloys, and the Ω values were smaller and outside the Ω range of the solid solution.

Figure 1 and Figure 2 show the relationship between the parameters ΔS_mix and Ω, and ΔS_mix and VEC of the eutectics, respectively. Figure 1 shows that the ΔS_mix increases with Ω. All of the available data exhibits a linear fit with R² = 0.8133, and the data subsets of the eutectics that contain only Sn (meaning <Si> = Al + Si + Sn) or only Ge (<Si> = Al + Ge + Si) exhibit better linear fits with R² values of 0.8754 and 0.9863, respectively. Such a relationship was not exhibited by the ΔS_mix and Ω parameters of the Nb_ss.

Figure 2 shows that the VEC parameter increases with the decreasing ΔS_mix of the eutectic. The data in this figure is for eutectics in alloys with only a Ge or only an Sn addition. All of the data exhibits a linear fit with R² = 0.8346. The linear fit for the eutectics with only Sn (green circles) or only Ge (brown circles), respectively, gives R² = 0.8966 and R² = 0.8183. Similar behaviour was not observed for the parameters VEC and ΔS_mix of the Nb_ss.

The ΔH_mix of the Nb_ss decreases (becomes more negative) as the parameter δ increases [38]. The same trend was found for the eutectics, see Figure 3. In Figure 3, the linear fit of all of the data is good (R² = 0.8925), the data for the eutectics follows the trend of the data for the Nb_ss, and the gap in the ΔH_mix values is shown by the horizontal dashed lines. There was also good correlation of the data in ΔH_mix versus Ω (R² = 0.8485), and Ω versus Δχ (R² = 0.8515) plots (Figures not shown) for eutectics where Ge and Sn were present simultaneously (meaning <Si> = Al + Ge + Si + Sn).

The δ versus Δχ map of the eutectics is shown in Figure 4. The partitioning of Ti in the Nb-silicide based alloys is important for the chemical composition and properties of the Nb_ss and Nb₅Si₃. For example, Ti and Cr, and Ti and Hf “like each other” in the Nb_ss and Nb₅Si₃ (meaning the concentrations of Cr and Hf increase with increasing Ti concentration in the solid solution and the silicide) but not Ti, Mo, and W in the Nb_ss, in which as the Ti concentration increases, those of Mo and W decrease. The δ versus Δχ map separates the Ti-rich eutectics from the Ti-poor ones, and shows a gap in Δχ values between the two groups (note that in cast Nb-silicide based alloys with Ti additions, it is possible to form Ti-rich Nb_ss and Ti-rich Nb₅Si₃, [59,60]). The gap in Δχ values of the eutectics falls in the gap of Δχ values of the Nb_ss (Table 1). However, the δ versus Δχ map cannot separate the contributions made by different groups of alloying additions. This is possible in the Δχ versus VEC map of the eutectics, which is shown in Figure 5. The eutectics, whose data points fall in the gap of the Δχ values of the Nb_ss, belonged in alloys where only normal Nb_ss was formed [38]. The alloying elements in each data series in Figure 5 are indicated in the figure caption. In the series a, as well as in the series c to f, there is no Fe; there is no Ge in series f; there is no Mo in series a, b, and g; there is no Ta in series a, b, e, and g; there is no V in series a, b, e, and g; there is no W in series a, b, f, and g; and Zr is only in series c. It should be noted that the linear fits of the data “converge” to VEC ≈ 4.35 and Δχ ≈ 0.162. The “convergence” of the data suggested that alloying elements in the eutectics in Nb-silicide based alloys might have minimum and maximum concentrations. This was confirmed by further analysis of the data for the eutectics, as shown below.

The dependence of the parameter Δχ on the <Si> of the eutectics is shown in Figure 6. The data falls in different subsets, the alloying elements of which are given in the figure caption. All of the subsets “converge” to <Si> ≈ 21.6 at.% and Δχ ≈ 0.155. Series b and e have no Fe; there is no Mo, no Ta and no W in series a, b and e; the elements V and Zr are only in series c, and Y is only in series a and e. The trend between Δχ and <Si> for series c and d is the same as that of the parameter Δχ, and the sum of simple metal and metalloid element additions in Nb₅Si₃, as shown in Figure 7. Figure 7 has data for the Nb₅Si₃ in Nb-silicide based alloys with/out eutectics, not for Nb₅Si₃ in eutectics. It should be noted that (i) the data in Figure 7 includes boron-containing silicides (their data falls on the same trend as for the other simple metal and metalloid elements) and (ii) there is no data for the chemical composition of eutectics with Nb_ss and Nb₅Si₃ in boron-containing alloys (see Section 2). The data for the Δχ and <Si>_Nbss of the Nb_ss, where <Si>_Nbss = Al + Ge + Si + Sn, showed that the Δχ of the Nb_ss can increase or decrease with increasing <Si>_Nbss, depending on alloying element additions. This would suggest that in the eutectics of the series c and d in Figure 6, the composition of the eutectics was “controlled” by the silicide. Similarities between the alloying elements in the different series in Figure 5 and Figure 6 should be noted.

The dependence of δ on the <Si> of the eutectic is shown in Figure 8. The data falls in different subsets, the alloying elements of which are given in the figure caption. Series b and d have no Fe, there is no Mo in series d, there is no Ta in series a, there is no V in series d, and Y and Zr are only present in series c. All of the series “converge” to <Si> ≈ 24.35 at.% and δ ≈ 9.25 The parameter δ increases with increasing <Si> for all of the series. Similarities between the alloying elements in the different series in Figure 5, Figure 6 and Figure 8 should be noted.

Titanium is an important addition in Nb-silicide based alloys, because it improves oxidation and toughness, and reduces density. It partitions to Nb_ss and Nb₅Si₃ [59,60] where its concentration affects that of other elements. Both phases can have Ti-rich areas that persist only in the silicide after exposure to high temperatures [59,60]. The relationship between the Ti and Si concentrations of the eutectics is shown in Figure 9. The data falls into four subsets, of which series d has no Al and Cr. All four series “converge” to Si ≈ 21.6 at.% and Ti ≈ 8.7 at.%, and show that the Si concentration in the eutectic decreases as the Ti concentration increases. The latter was also the case for the Ti and Si concentrations in Nb₅Si₃ in Nb-silicide based alloys with/out eutectics, but not for the Nb_ss where the Si concentration increases as the Ti concentration increases.

Aluminium is added at low concentrations in Nb-silicide based alloys because of its adverse effect on their toughness. It reduces density and contributes to the improvement of oxidation resistance with additions of B, Ge, or Sn. It partitions to Nb_ss and Nb₅Si₃, where its concentration depends on other alloying elements [59,60]. Figure 10 shows the relationship between the Al and Si concentrations of the eutectics. The data falls in three subsets, with the alloying elements in each series indicated in the figure caption. All of the subsets of data show that as the Si concentration in the eutectic decreases, the Al content increases, which is in agreement with the data for Nb₅Si₃ in Nb-silicide based alloys with/out eutectics, but not with the data for the Nb_ss. The data “converges” to Al ≈ 6.3 at.% and Si ≈ 8 at.%. Similarities between the alloying elements in the different series in Figure 9 and Figure 10 should be noted.

In Nb-silicide based alloys, Hf is added to improve the oxidation and toughness and scavenge oxygen to form hafnia. Hafnium partitions to both the Nb_ss and Nb₅Si₃, and its concentration is related to that of Ti in the two phases. The Hf concentration decreases with decreasing Si concentration in eutectics, and the data “converges” to Hf ≈ 1 at.% and Si ≈ 10 at.%. The trend of the data (figure not shown) is the same as that of the Hf and Si concentrations in the Nb_ss in Nb-silicide based alloys with/out eutectics. There is no correlation between the Hf and Si concentrations in Nb₅Si₃.

The “convergence” of data that was shown earlier would suggest that (i) the alloying elements have maximum and minimum concentrations in the eutectics, and (ii) the maximum concentrations of Al and Si in the eutectic are about 6.3 at.% and 21.6 at.%, respectively. The minimum concentration of Ti in the eutectic is about 8.7 at.%, and the minimum concentration of Si in the eutectic is in the range of 8 at.% to 10 at.%.

The refractory metals Mo, Ta, and W can be present in the eutectics, and can stabilise their lamellar microstructure at high temperatures, depending on the other alloying additions in the Nb-silicide based alloy [41,42,50,53,60,61]. Their concentration in the eutectic also is related to the Si concentration of the latter. Molybdenum is chosen to demonstrate this relationship in this paper. Figure 11 shows that the Mo concentration of the eutectics decreases as the Si concentration increases. This is consistent with the data for the Nb_ss in Nb-silicide based alloys with/out eutectics, which shows the same trend, and also with the partitioning behaviour of Ti and Mo in the solid solution where, as the Ti concentration increases, the Mo concentration decreases.

Data for the hardness of eutectics with Nb_ss and Nb₅Si₃ is available for the Nb-silicide based alloys without the addition of Ti, and are shown in Figure 12. The eutectics were observed in alloys of the following systems: Nb-Si-Sn, Nb-Si-Ge, Nb-Si-Hf-Al, Nb-Si-Hf-Sn, Nb-Si-Ge-Al, and Nb-Si-Cr-Ge [40,43,45,47,48,49]. The eutectics in the alloys in Figure 12 had <Si> = Si + Sn, <Si> = Si + Al, <Si> = Si + Ge, or <Si> = Si + Al + Ge. The microstructures of the Sn-containing alloys consisted of three phases, namely Nb_ss, Nb₅Si₃, and A15-Nb₃Sn, and the microstructures of the alloys without Sn addition contained only Nb_ss and Nb₅Si₃. The data points for the alloys with A15-Nb₃Sn in their microstructures are indicated in the blue colour in Figure 12. Figure 12a shows that the hardness of the eutectics increased as the VEC increased. The same trend between hardness and VEC was observed for the hardness of the A15-Nb₃X phases in the Nb-silicide based alloys [63], for β(Nb,Ti)₅Si₃ (see below), and for the hardness of tetragonal Nb₅Si₃, as shown in Figure 13. Note that the data in the latter figure is for the Nb₅Si₃ in Nb-silicide based alloys, not for the Nb₅Si₃ lamellae in eutectics with Nb_ss and Nb₅Si₃ in such alloys. The elements in each data series in Figure 13 are given in the caption. Mo is only in series c; W is only in series d, which does not also have B, Ge, and Ta; V is not in series a and b; and there is no Sn in series b. Eutectics with Nb_ss and Nb₅Si₃ have been observed in boron-containing Nb-silicide based alloys. There is data for the chemical composition and hardness of the 5-3 silicide in the microstructure of the latter, but not for the eutectics (see Section 2).

The data for the alloys with A15-Nb₃Sn in Figure 12 falls on the same line as the data for the eutectics with only Nb_ss and Nb₅Si₃, and all of the data exhibits a very good linear fit (R² = 0.9686). Figure 12b shows that the hardness of the eutectics decreased as their <Si> increased. The linear fit of the hardness versus the <Si> data is also good (R² = 0.9012), but this was not the case when hardness was plotted against the concentration of Si in the eutectics, which varied from 10.3 at.% to 20 at.% for the alloys in Figure 12.

The ranking of the eutectics in Figure 12 in terms of their hardness from low to high values does not follow the ranking of the hardness of alloyed Nb₅Si₃ that was discussed in [39]. Figure 12 suggests that the VEC of the eutectic should decrease as its <Si> content increases. Indeed, this is the case as shown in Figure 14, which also confirms that the data converges to VEC ≈ 4.35 and <Si> ≈ 23 at.%. In Figure 14, there is no Cr in series c, there is no Fe in series c to e, there is no Ge in series e, there is no Mo in series b and e, and there is no Y in series a and c to e. Meanwhile, Ta is present only in series c; V is present only in series a and c; W is present only in series a, c, and d; and Zr is present only in series c. Note the similarities with the data series in Figure 14 and in Figure 6 and Figure 8. The data in Figure 6, Figure 8 and Figure 14 shows that <Si> and Δχ “converge” respectively in the ranges 21.6 at.% to 24.3 at.%, and 0.155 to 0.162.

The hardness of intermetallics has been reported to depend on the scale of their microstructure, and to follow a Hall–Petch relationship [64,65]. Intermetallics participate in eutectics; examples include the Al/Al₂Cu, Al/Al₃Ni, Nb/Nb₃Si, and Nb/Nb₅Si₃ eutectics. In a eutectic, the inter-lamellar spacing, the properties of the participating phases, and the interfaces between the lamellae are expected to define their mechanical properties. Refinement of eutectic microstructure can be affected by solidification conditions and/or alloying additions. When the eutectic spacing is refined, the role of interfaces becomes important. Lamellar interfaces are expected to play a major role in the deformation of eutectics.

The improvement of properties of directionally solidified (DS) eutectics with microstructure refinement has been related to a Hall–Petch relationship for eutectics. For Al–Si eutectics, there are different hardness versus inter-lamellar spacing relationships for different silicon morphologies [66]. Mason et al. showed that the hardness of a Mo₅Si₃/MoSi₂ eutectic depended on lamellar spacing in accordance with a Hall–Petch relationship, where the hardness was dependent upon the scale of the lamellae of MoSi₂ [67]. Dislocation pile-ups are necessary for Hall–Petch strengthening. Grain boundaries impede dislocation propagation from one grain to the next. As the dislocations pile up against a grain boundary, the stress field assists dislocations to traverse the grain boundary, and thus, deformation spreads from grain to grain. Dislocations are generated during indentation for the measurement of hardness [68]. For the Mo₅Si₃/MoSi₂ eutectic, Mason et al. suggested that the Mo₅Si₃ silicide behaved as an impenetrable barrier [67].

What is known about the deformation of lamellar microstructures consisting of alloyed Nb_ss and Nb₅Si₃? How would a strong or weak Nb_ss/Nb₅Si₃ interface behave under mechanical loading? How important is an orientation relationship between Nb_ss and Nb₅Si₃ for the deformation of a lamellar Nb_ss/Nb₅Si₃ structure? Does the morphology of Nb₅Si₃ depend on alloying additions? To answer these questions, we need to consider first microstructures based on the Nb–Si binary phase diagram, and then Nb–Si-based (i.e., alloyed) microstructures. Research on the deformation of Nb in Nb/Nb₅Si₃ micro-laminate Nb–Si binary foils [69] has highlighted the importance of layer thickness and confirmed that the deformation of Nb was dependent on the thickness of its layers in the foils. As the thickness of the latter increased, their fracture changed from ductile to brittle. This change in fracture mode was attributed to the constraint of Nb and/or changes of crack propagation rate [69]. The hardness of the Nb layers in the micro-laminate foils was 5.4 GPa, which is very close to the hardness of the 1-μm thick Nb thin films that were reported in [70], and significantly higher than the hardness of about 1.6 GPa of about 13-μm Nb particles. The high hardness of the Nb layers was attributed to “their small grain size and the narrow spaced Nb₅Si₃ layers, both of which acted to restrain dislocation motion in the Nb layers” [69]. Gavens et al. also reported that the estimated high average fracture strength of Nb₅Si₃ was typical of that of high strength ceramic fibres [69].

A study of a Nb₍₀₀₁₎/αNb₅Si₃₍₀₀₁₎ interface using a first-principles calculation showed that some of the Nb atoms at the interface become a part of Nb₅Si₃, and that the Nb–Si bonds at the interface are the likely sites for micro-cracking [71]. This study reported that the work of adhesion and fracture energy of the Nb₍₀₀₁₎/αNb₅Si₃₍₀₀₁₎ interface were 4.4 J/m² and 33.7 J/m², respectively.

In Nb-silicide based alloys, both the Nb_ss and the Nb₅Si₃ are alloyed, and the Nb_ss/Nb₅Si₃ interface can be Ti-rich (see Section 2). Also, alloying can affect the morphology of Nb₅Si₃, whose cross-sections can change from circular to polygonal as the entropy of fusion of Nb₅Si₃ increases, owing to alloying additions. The mechanical properties of [Nb_ss]₍₀₀₂₎ /[αNb₅Si₃]₍₀₀₂₎ interfaces in a directionally solidified Nb-silicide based alloy of nominal composition Nb-24Ti-15Si-4Cr-2Al-2Hf (at.%) were studied experimentally, and with finite element modelling by Guan et al. [72]. The lower work of the adhesion and fracture energy values compared with the work of Shang et al. [71] were attributed to the alloying of the [Nb_ss]₍₀₀₂₎/[αNb₅Si₃]₍₀₀₂₎ interface, as the latter would be expected to be rich in Ti and Hf on the silicide side and Ti, Hf, Al and Cr on the Nb side, and the different orientation relationship of the studied interface.

The data in Figure 12 is not for the same eutectic of one specific alloy composition, but for different eutectics with Nb_ss and Nb₅Si₃ in different alloys. In the latter, the phases that participated in the eutectics had different chemical compositions and different hardness, and the eutectics had similar inter-lamellar spacing, but not the same volume fractions of phases and different Nb_ss/Nb₅Si₃ interface chemistries. Yet, the hardness versus the VEC data for the eutectics of these different alloys followed a remarkable linear relationship with a very good R² value (=0.9686). This strong relationship is attributed to the covalent bonded intermetallic phase(s) in the eutectics, which are suggested to be the key phases that determine the hardness of the eutectics.

In the solid solution, the bonding is delocalized, and the hardness depends on grain size, grain boundaries, and contamination by interstitials (impurities). In covalent compounds, the mobilities of dislocations are low because of the localized bonding [73]. The dependence of the hardness of covalent bonded hard materials on their shear modulus is stronger than the relationship between the hardness and their bulk modulus [74]. The latter measures the resistance to volume change, which is not the case with the hardness test, and the former is a measure of the rigidity against shape change in the hardness test. Among the various shear stiffnesses, only C₄₄ represents a shape change without volume change. Thus, C₄₄ provides direct information about the electronic response to shear strain [75]. Jhi et al. [75] showed that there exists a relationship between C₄₄ and VEC, and hardness and VEC for different transition metal carbonitrides. For each carbonitride, the trend in the aforementioned relationships was the same, the C₄₄ and hardness increased with decreasing VEC to a maximum value for VEC of about 8.4. Wang and Zhou [75] showed that the C₄₄ of M₂AlC increased with increasing VEC in the order M = Ti, Nb, V, and Cr. The polynomial fit of the data indicated a maximum value of C₄₄ for a VEC of about 8.5. It was also suggested that the hardness of M₂AlC compounds could be predicted from the correlation between C₄₄ and VEC [76].

Figure 15 and Figure 16 respectively show the C44 and VEC, and hardness and VEC relationships for α(Nb,Ti)₅Si₃ and β(Nb,Ti)₅Si₃ for Ti = 0, 3.125, 6.25, 9.375, and 12.5 at.% using data for C₄₄ from [77]. Unfortunately, there is no experimental data for the hardness of (Nb,Ti)₅Si₃ silicides. In [39], it was shown that the hardness values that were calculated using the equation HV = 2[(G/B)²G]^0.585 – 3 were in better agreement with the available experimental data. The calculations of the hardness values in Figure 15 and Figure 16 used the above equation with data for shear G and bulk B moduli from [77]. Figure 15b shows that the hardness of α(Nb,Ti)₅Si₃ increases as the Ti concentration increases and the VEC decreases. Figure 16b shows that the hardness of β(Nb,Ti)₅Si₃ decreases as the Ti concentration decreases and the VEC increases. The polynomial fit of the data in Figure 15 and Figure 16a showed respectively for α(Nb,Ti)₅Si₃ and β(Nb,Ti)₅Si₃ maximum and minimum values of C₄₄ for essentially the same VEC (4.426 and 4.429, respectively). Figure 15 shows that the trends between the C₄₄ and VEC and hardness and VEC of α(Nb,Ti)₅Si₃ are the same as those reported for transition metal carbonitrides [75]. The trend between the C₄₄ and VEC of β(Nb,Ti)₅Si₃ is the same as that reported for M₂AlC compounds [76]. It should be noted that the trend between hardness and VEC is the same in Figure 12a and Figure 16b; the hardness increases as the VEC increases. Figure 16b is for β(Nb,Ti)₅Si₃. The βNb₅Si₃ is the 5-3 silicide in the metastable eutectic (see Introduction).

The eutectics in Figure 12 had 5-3 silicides where only Si was substituted by other simple metal and metalloid elements. There is no C₄₄ data for these alloyed silicides. It is suggested that their C₄₄ also correlates with VEC. It would be interesting to compare their C₄₄ versus VEC and hardness versus the VEC correlations with those of (Nb,Ti)₅Si₃ silicides.

4. Conclusions

In Nb-silicide based alloys, eutectics that contain Nb_ss and Nb₅Si₃ can form. It was shown that the alloying behaviour of the eutectics, the great majority of which are binary Nb_ss + Nb₅Si₃ eutectics, can be described using the parameters ΔH_mix, ΔS_mix, VEC, δ, Δχ, and Ω.

The values of these parameters were in the ranges −41.9 < ΔH_mix < −25.5 kJ/mol, 4.7 < ΔS_mix < 15 J/molK, 4.33 < VEC < 4.89, 6.23 < δ < 9.44, 0.38 < Ω < 1.35, and 0.118 < Δχ < 0.248, with a gap in the Δχ values between 0.164 and 0.181.

Compared with Nb-silicide based alloys, the eutectics had wider ranges of ΔH_mix, ΔS_mix, Δχ, and Ω values, the VEC range was essentially the same, the range of δ values was narrow, and some eutectics had δ values lower than the Nb-silicide based alloys.

Compared with Nb solid solutions, the eutectics had more negative ΔH_mix values within a wider range; the range of ΔS_mix values was slightly wider; the ranges of the VEC, Δχ, and δ values were narrow; and in the ranges of the values of Nb_ss in the Nb-silicide based alloys, the Ω values were smaller, and outside the range of the Ω values of the solid solution.

There were correlations between ΔS_mix, Ω, ΔS_mix, and VEC for all of the eutectics. The correlation between ΔH_mix and δ was the same as that of the Nb_ss.

Specific maps of the studied parameters could describe the alloying of the eutectics. The δ versus Δχ map separated the Ti-rich from the Ti-poor eutectics, with a gap in Δχ values between 0.164 and 0.181, which is within the Δχ gap of the Nb_ss. Eutectics were also separated according to alloying element additions in the Δχ versus VEC, Δχ versus <Si>, δ versus <Si>, and VEC versus <Si> maps where <Si> = Al + Ge + Si + Sn.

The convergence of data in maps indicated that (i) the eutectics had δ ≈ 9.25 and VEC ≈ 4.35 and Δχ in the range ≈ 0.155 to 0.162, and <Si> in the range ≈ 21.6 at.% to ≈ 24.3 at.%, (ii) the minimum concentration of Ti, and maximum concentrations of Al and Si in the eutectic were about 8.7 at.% Ti, and 6.3 at.% Al and 21.6 at.% Si, respectively and (iii) the minimum concentration of Si in the eutectic was in the range 8 < Si < 10 at.%.