**Microstructure and Room Temperature Mechanical Properties of Different 3 and 4 Element Medium Entropy Alloys from HfNbTaTiZr System**

**Jiˇrí Zýka 1,\*, Jaroslav Málek 1, Jaroslav Veselý 1, František Lukácˇ 2,3, Jakub Cˇ ížek 3, Jan Kuriplach <sup>3</sup> and Oksana Melikhova <sup>3</sup>**


Received: 12 December 2018; Accepted: 15 January 2019; Published: 26 January 2019

**Abstract:** Refractory high entropy alloys (HEA) are promising materials for high temperature applications. This work presents investigations of the room temperature tensile mechanical properties of selected 3 and 4 elements medium entropy alloys (MEA) derived from the HfNbTaTiZr system. Tensile testing was combined with fractographic and microstructure analysis, using scanning electron microscope (SEM), wavelength dispersive spectroscope (WDS) and X-Ray powder diffraction (XRD). The 5 element HEA alloy HfNbTaTiZr exhibits the best combination of strength and elongation while 4 and 3 element MEAs have lower strength. Some of them are ductile, some of them brittle, depending on microstructure. Simultaneous presence of Ta and Zr in the alloy resulted in a significant reduction of ductility caused by reduction of the BCC phase content. Precipitation of Ta rich particles on grain boundaries reduces further the maximum elongation to failure down to zero values.

**Keywords:** refractory high entropy alloys; medium entropy alloys, mechanical properties; microstructure

#### **1. Introduction**

High entropy alloys (HEAs) attract attention of a growing number of scientists and researchers. A concept of mixing of 5 or more elements in equimolar or near equimolar concentrations is used in order to explore central regions of multicomponent alloy phase space [1]. This approach is driven by possibility to get stable solid solution microstructure of the alloy with favourable mechanical properties (high strength and good ductility) as well as other physical properties, for example, good corrosion resistance [2]. Microstructure stability shall be provided by high configurational entropy of the system, supposing random arrangement of alloying elements [3,4]. Although increased configurational entropy may in principle stabilize solid solution its stabilizing effect is usually found insufficient to counteract driving forces for formation of intermetallic phases [5,6].

Since the pioneering work of Yeh [4], original concept has been evolved and widened. The term HEA is connected mainly with approach utilizing high configurational entropy to get single phase solid solution of multiple elements. Multiple principal element alloys (MPEA) represent a broader approach when the main motivation is exploring of a vast composition space of multi-principal element alloys without primary concern about the magnitude of the configurational entropy [1]. MPEAs with multi-phase microstructures are denoted complex concentrated alloys (CCA) [1].

Different elements are used to fabricate HEAs. Although the number of possible 4 or 5 elements combinations is enormous five basic metallic HEA groups can be distinguished: FCC HEAs based on the Cantor alloy, BCC refractory metal HEAs, light element HEAs, HCP HEAs and precious functional HEAs [7]. Ceramic HEAs have been established as well [8,9].

Our attention was attracted by the refractory HEA group, which is composed of elements from IV, V and VI groups of the periodic table of elements [10]. These elements are characterized by prevailing good mutual miscibility and high melting points. The melting point of titanium (1668 ◦C) is the lowest among them. Therefore HEAs composed of these elements are intended for high temperature applications. Moreover some of these elements are biocompatible [11]. Therefore some of these alloys can be attractive for bioimplant related materials research. Note that β-Ti alloys used in bioimplant research are usually composed of this group of elements [12]. Several biocompatible HEAs have been already studied [13–16]. Also, hard ceramic composites were produced from the metals from IV, V and VI groups of the periodic table [17].

Original definition of HEAs with single phase solid solution microstructure and good room temperature mechanical properties, especially ductility, is beneficial also for use in human medicine. Inspiration can be found also in other materials used for production of bioimplants which are used or have been used in other parts of material research, for example, TiAl6V4 in aerospace, CoCrMo in aero engines.

Our first attempt in research of HEAs was therefore related to HfNbTaTiZr refractory metal alloy [18]. Our research was inspired by Senkov [19] and confirmed our expectations. Ingots produced by vacuum arc melting possessed single phase solid solution microstructure, with a high room temperature tensile strength and ductility.

Some of the elements used in the HfNbTaTiZr alloy are very similar to each other with very similar chemical behaviour; Nb is chemically similar to Ta and Zr to Hf. Therefore a question has emerged whether it is necessary to use all of these elements in order to get random solid solution and good mechanical properties (high strength and sufficient ductility).

The design of the present experiment was as follows. First, we reduced the original HfNbTaTiZr alloy system by removing Hf, which is almost identical to Zr from the chemical point of view, then we distracted Ta, which is very similar to Nb; thus getting NbTiZr alloy with equiatomic concentrations. Then we produced also other 3 element combinations containing Ti, namely TaTiZr and NbTaTi. Based on the observed results; 4 element alloys containing Ti and Ta with different Nb to Zr ratio were produced as well to explore the influence of chemical composition on elongation.

NbTaTiZr [14] and NbTiZr [20,21] studies have already been reported. No reports about TaTiZr and NbTaTi were found in literature.

One can notice that set of the produced element combinations is not complete. The motivation for element selection was as follows. Titanium was used in all combination because it is element with the lowest density. Hafnium was not used since it is very reactive in ambient atmosphere and it is hard to get Hf free of impurities. Both hafnium and tantalum are high density and high price element; thus less suitable for practical use.

#### **2. Materials and Methods**

Experimental alloys were prepared by vacuum arc melting in water cooled copper crucible. Chemical purity of inserted elements was 99.9%. Final cast ingot has approximately 100 mm in length, 30 mm in width, 10 mm in height and 400 g in weight. Casting was performed 8x times and flipped for each melt to mix the elements thoroughly and suppress chemical heterogeneity. All investigated alloys were prepared at the same equipment under the same conditions. Nor HIP, nor other heat treatment was applied to the cast material.

Tensile test bodies 5 mm in diameter and 25 mm of measured length were strained with the strain rate of 2 × <sup>10</sup>−<sup>4</sup> <sup>s</sup>−<sup>1</sup> using Instron 1185 testing machine equipped with video extensometer.

Metallographic sections perpendicular to the length of the casting were prepared. Vickers hardness HV30 was measured using Zwick ZHU 250 Topline universal testing machine.

Fractography analysis of broken specimen surfaces was carried out on a scanning electron microscope (JEOL JSM 7600F).

Microstructure was examined by scanning electron microscope (FEI Quanta 200F) equipped with wavelength dispersive X-ray spectroscope (WDS) for local chemical composition analysis.

In order to determine phase composition and structures of phases in the alloys, powder X-ray diffraction (PXRD) analysis was performed. A Bruker D8 Discover diffractometer, CuKα radiation and 1D detector were used. Lattice parameters and phase composition were determined by Rietveld analysis of PXRD diffraction patterns using TOPAS V5 code [22].

*Ab-initio* quantum Monte Carlo (MC) simulation was performed to obtain atomic configuration of the 5 element HfNbTaTiZr alloy. Hf, Nb, Ta, Ti, Zr ions were distributed randomly in equimolar concentration into a 250 atom BCC supercell. This initial state was relaxed with respect to ion positions until minimum of the total free energy was reached. The equilibrium configuration corresponding to minimum free energy was obtained using a Metropolis MC algorithm at 300 K (room temperature). The details of the simulation and more complete results will be published elsewhere.

#### **3. Results**

#### *3.1. Chemical Composition*

Chemical compositions of investigated alloys in atomic percentages are given in Table 1. Important HEA related parameters are listed in Table 2. Valence electron concentration—VEC, mixing enthalpy−ΔHmix, difference in atomic radii−δ, Ω parameter, mixing entropy−Smix are calculated in accordance with literature [1], where Tm is a calculated average melting point. According to entropy-based definition HEAs are characterized by the configurational entropy higher than 1.61 *R* [1]. Hence, according to this definition, only HfNbTaTiZr alloy is high entropy alloy. The other alloys studied in the present work are medium entropy alloys.


**Table 1.** Chemical composition of investigated alloys in at.%, including important properties of individual elements.


**Table 2.** Important high entropy alloy (HEA) related parameters if investigated alloys calculated using data from Table 1.

#### *3.2. Mechanical Properties*

Tensile curves of investigated alloys performed at room temperature are shown in Figure 1. Results of tensile tests performed and hardness measurements performed at room temperature are given in Table 3.

**Figure 1.** Tensile curves of investigated alloys at room temperature. Curves for brittle alloys TaTiZr, Nb1.5TaTiZr0.5 and Nb0.5TaTiZr1.5 were shifted horizontally to make them visible.


**Table 3.** Room temperature mechanical properties of the alloys studied.

The 5 element HEA HfNbTaTiZr alloy has the best tensile properties among the alloys studied, both regarding the strength and elongation. The 4 element NbTaTiZr alloy has similar strength and

hardness as HfNbTaTiZr but elongation is reduced to 6.4%. The NbTaTi has low strength, half of that for HfNbTaTiZr but the highest elongation. The NbTiZr alloy has strength values below 1000 MPa but elongation is relatively high (14.2%). The TaTiZr alloy exhibited brittle behaviour, breaking before reaching the yield point. The Nb0.5TaTiZr1.5 alloy performed very similarly, breaking also before reaching yield point but a little bit later than TaTiZr alloy. The Nb1.5TaTiZr0.5 alloy reached the yield point (822 MPa) but the elongation was 0.33% only.

Highest hardness (HV30 = 485) values were measured in the most brittle alloys TaTiZr and Nb0.5TaTiZr1.5. Hardness of the 4 and 5 element equimolar alloy was very similar to each other, lower by ≈130 HV compared to the brittle alloys. Hardness of the NbTiZr and Nb1.5TaTiZr0.5 are slightly lower than 300 HV. The most ductile alloy NbTaTi exhibited the lowest hardness of 246 HV.

#### *3.3. Fractographic Analysis*

Fracture surfaces of specimen broken during tensile test were subjected to fractographic analysis, see Figure 2. Both transgranular and intergranular ductile fracture can be found on fracture surfaces of the NbTiTaZr alloy, see Figure 2a–c. Elongated particles were observed on the intergranular ductile fracture surface. Ductile dimples of different diameters were found on the transgranular fracture surface of NbTaTi alloy, see Figure 2d. Transgranular ductile fracture was found also in the case of NbTiZr alloy (Figure 2f). On the other hand, fracture surface of TaTiZr alloy is dominantly flat and brittle and containing number of needle like particles, see Figure 2e. River-like pattern is present as well (not shown). Nb1.5TaTiZr0.5 specimen fracture surfaces are composed of transgranular ductile fracture and intergranular fracture, see Figure 2g. A lot of particles are present on the intergranular part of the fracture surface. Nb0.5TaTiZr1.5 fracture surfaces (Figure 2h–i) are similar to those of Nb1.5TaTiZr0.5 and NbTaTiZr alloy but without presence of particles on the intergranular part of the fracture surface.

**Figure 2.** Scanning electron microscopy (SEM) image of investigated fracture surfaces: (**a**), (**b**), (**c**) NbTaTiZr alloy; (**d**) NbTaTi alloy (**e**) TaTiZr alloy; (**f**) NbTiZr alloy; (**g**) Nb1.5TaTiZr0.5 alloy; (**h**), (**i**) Nb0.5TaTiZr1.5 alloy; where TG denotes transgranular ductile fracture and IG intergranular ductile fracture.

#### *3.4. Microstructure*

Microstructure of the investigated alloys is shown in Figure 3. Grains size was estimated by light microscopy on metallographic specimens with mirror-like polished and slightly etched surface using the linear intercept procedure [23]. It revealed grain size around 0.5 mm which is similar for all alloys. All alloys, except of NbTiZr alloy, exhibited dendritic segregation.

**Figure 3.** SEM image of investigated alloys microstructure: (**a**) NbTaTiZr alloy; (**b**) NbTaTi alloy; (**c**) TaTiZr alloy; (**d**) NbTiZr alloy; (**e**) Nb1.5TaTiZr0.5 alloy; (**f**) Nb0.5TaTiZr1.5 alloy.

Small submicron precipitates were found on grain boundaries of TaTiZr, Nb1.5TaTiZr0.5 and Nb0.5TaTiZr1.5 alloys, see Figure 4. WDS analysis of these precipitates revealed that they are rich in Ta. For example the average Ta concentration in the precipitates in TaTiZr alloy is (52 ± 1) at.% while the Ta content in the matrix of this alloy was found to be (38 ± 1) at.%.

**Figure 4.** SEM image of investigated alloys microstructure: (**a**), (**b**) TaTiZr alloy; (**c**) Nb1.5TaTiZr0.5 alloy; (**d**) Nb0.5TaTiZr1.5 alloy.

Figure 5 illustrates existence of two phases. One of them appears brighter because of higher average Z number while the second one appears darker due to lower average Z number. Phase separation into these two phases occurs on the length scale of ~20 μm. The only exception is NbTiZr alloy, which shows no phase segregation, see Figure 5d. WDS line analysis showed enhanced concentration of Zr and Ti in the dark phase and Ta and Nb in the bright phase, see Table 4.

**Figure 5.** WDS line analysis of: (**a**) NbTaTiZr alloy; (**b**) TaTiNb alloy; (**c**) TaTiZr alloy; (**d**) NbTiZr alloy; (**e**) Nb1.5TaTiZr0.5 alloy; (**f**) Nb0.5TaTiZr1.5 alloy.


**Table 4.** Chemical composition in atomic % of bright and dark phase in investigated alloys. Uncertainties of concentrations (one standard deviation) are given in parenthesis.

#### 3.4.1. XRD Analysis

XRD patterns in Figure 6 exhibit peaks in positions corresponding to reflection of a BCC phase but with different extent of broadening. HfNbTaTiZr [18], NbTaTi and NbTiZr alloys consist of single BCC phase. Rietveld refinement of XRD patterns suggested existence of two BCC phases with slightly different lattice parameters in case of NbTaTiZr and TaTiZr alloys (Table 5). This corresponds to the previously observed presence of the dendritic microstructure in the feedstock powder particles [24]. The regions that solidify earlier were enriched in Nb, Ta, thereby triggering a measurable change in the respective lattice parameters of the BCC regions as compared to the interdendritic regions with increased Zr, Ti content. Rietveld refinement suggested even three BCC phases in case of Nb1.5TaTiZr0.5, Nb0.5TaTiZr1.5 with similar lattice parameters (Table 5). Grain size cannot be calculated from XRD data since the broadening of XRD reflections caused by finite grain size was found to be negligible. It means the average grain size of the alloys studied is higher than 100 nm which is consistent with metallographic and SEM observations. Dominant source of peak broadening is chemical heterogeneity, that is, local changes of lattice parameter due to spatial variations of chemical composition.

**Figure 6.** X-ray diffraction (XRD) patterns of investigated alloys. Reflections of the BCC phases are marked by labels.

**Table 5.** Phase composition of investigated alloys. The lattice parameter (a) and phase content were obtained using Rietveld refinement fitting.


Note: Error of the last digit is shown in the parentheses.

#### 3.4.2. Monte Carlo Simulation of Microstructure

*Ab-initio* MC simulation was performed to evaluate the microstructure stability of investigated alloys. Simulation was performed for the 5 element HfNbTaTiZr alloy, because it contains all elements considered in investigated alloys.

Hf, Nb, Ta, Ti, Zr ions were distributed randomly in equimolar concentration into a 250 atom BCC supercell. This initial state was relaxed with respect to ion positions until minimum of the total free energy was reached. The equilibrium configuration corresponding to minimum free energy was obtained using a Metropolis MC algorithm at 300 K (room temperature). The details of the simulation and more complete results will be published elsewhere. Figure 7 shows the equilibrium atomic configuration corresponding to the minimum of total energy. The most apparent effect is a rather one-dimensional Ta object ('wire') along the <100> direction. The Ta wire is surrounded predominantly by Nb ions. The rest of the simulation box is filled up by the mixture of Ti, Zr and Hf. The latter two elements appear to be well separated from the Ta and Nb region. Hence, this preliminary result indicates inhomogeneity of the HfNbTaTiZr alloy. Such inhomogeneities–though they need to be yet verified experimentally–could affect physical properties of the alloy.

**Figure 7.** Equilibrium atomic configuration of simulated HfNbTaTiZr alloy.

#### **4. Discussion**

Mechanical properties tests have revealed that combination of Ta and Zr reduces elongation. Microstructure analysis revealed existence of dark and bright phases because of Ta-Zr segregation. This kind of dendritic segregation was reported elsewhere [25–27]. It was shown [25] that Ta with Nb segregates during solidification to the solid and Zr with Ti to the liquid.

Figure 8a shows relation between the elongation to failure, A and the total atomic fraction of Ta and Zr. All alloys studied exhibit linear relationship of A on the Ta + Zr concentration. The only exception is Nb1.5TaTiZr0.5 alloy not following the linear relationship because, it is brittle despite of relatively low Ta + Zr content. In the latter alloy Nb probably plays similar role as tantalum. Figure 8b shows the content of the BCC1 phase as a function of the total concentration of is Ta and Zr. Obviously it obeys similar linear relationship with the net concentration of Ta and Zr as the elongation.

Intergranular nanosized precipitates were found on grain boundaries of brittle alloys with zero or almost zero elongation, namely TaTiZr, Nb1.5TaTiZr0.5 and Nb0.5TaTiZr1.5. XRD analysis revealed 2 BCC phases (BCC1, BCC2) which are probably caused by the microsegregation [24]. In two cases small amount of third BCC phase (BCC3) was detected, it can be connected with the intergranular precipitation. However, it was not investigated in detail in the present study.

Usually relations between the misfit parameter δ [1] and strength or hardness are reported, since rising δ shall indicate higher solid solution strengthening. Since in the present case we have single phase solid solution only in 3 alloys out of 7 investigated, the relation between hardness and δ is more complicated than simple linear dependence. Indeed if we exclude two most brittle alloys, indicated by red symbols in Figure 9a, the dependence of hardness and δ becomes rather close to

the linear relationship. In elongation and δ relationship NbTaTi alloy, the most ductile one, destroys possible correlation as well, Figure 9b.

**Figure 8.** (**a**) Relation of the total elongation to failure A on the sum of Ta and Zr atomic concentration, (**b**) the concentration of the BCC1 phase plotted as a function of the sum of Ta and Zr content. Data for Nb1.5TaTiZr0.5 alloy are indicated by red symbols and were excluded from linear regression.

**Figure 9.** Relation of δ and: (**a**) HV30; (**b**) elongation.

A relation between the elongation and the VEC parameter was reported in case of refractory HEAs [28]. Alloys with VEC lower than 4.4 shall be ductile, alloys with VEC higher than 4.6 shall be brittle. Figure 10a shows relation between elongation of investigated alloys and their VEC parameters. VEC values are close to the boundary value of 4.5. Brittle alloys TaTiZr (VEC = 4.329), Nb0.5TaTiZr1.5 (VEC = 4.375 ) and ductile alloy NbTaTi (VEC = 4.663) do not follow the reported rule. However, these alloys are MEAs and not HEAs. Brittle alloys with VEC lower than 4.5 are not single phase systems but contain 2 or 3 BCC phases and intergranular precipitates. NbTaTi is ductile because of absence of Ta-Zr combination in the alloy. The NbTiZr alloy exhibits similar behaviour. The HfNbTaTiZr alloy is also ductile, despite the fact that it contains Ta-Zr combination. Although MC simulation showed segregation of Ta, any mark of such segregation, was detected in experiment. When plotting the total elongation A as a function of the BCC1 phase content one can observe a clear linear relationship, see Figure 10b. Hence, there is a positive correlation between the total elongation and the BCC1 phase content. This is not surprising since both the total elongation and the BCC1 phase content decrease with Ta + Zr concentration, see Figure 8. The only exception is Nb1.5TaTiZr0.5 alloy which does not follow this trend.

The presence of other BCC phases influences also fracture mechanisms and fracture surfaces of tensile specimens.

**Figure 10.** Relation of the elongation to failure and: (**a**) the VEC parameter; (**b**) the content of BCC 1 phase.

It is important to investigate the question of existence of 2 or more BCC phases in our alloys. In HEA related research a lot of work has been done to establish connection between chemical composition or related parameters and microstructure, especially existence of single phase or intermetallics or amorphous microstructure. Satisfying δ < 0.066 and ΔHmix > − 11.6 kJ/mol, however, is necessary but not sufficient conditions to form solid solutions in HEAs. Checking the binary phase diagrams among constituent elements can give some further guidance in designing solid solutions forming HEAs [28]. All our alloys satisfy these two conditions but some of them are not single phase. Thus binary diagram analysis is needed.

Mixing enthalpies of element pairs relevant to the investigated alloys is shown in Table 6. Some mixing enthalpies are zero (Ti-Zr, Ti-Hf, Zr-Hf and Ta-Nb – pairs of elements from the same group) or almost zero (Ti-Ta, Ti-Nb), which is ideal for solid solution forming. Other mixing enthalpies are little bit higher (Ta-Zr, Ta-Hf, Nb-Zr, Nb-Hf – pairs from different but neighbouring groups). Above zero mixing enthalpies can cause existence of miscibility gaps in respective binary diagrams. Binary equilibrium phase diagrams of pairs with higher mixing enthalpies are shown in Figure 11. No intermetallic phases are present but large miscibility gaps can be found. Although in case of Ta-Zr diagram miscibility gap is in the range between 800 ◦C and 1780 ◦C, see Figure 10a, we found two BCC phases at room temperature.


**Table 6.** Mixing enthalpies of element pairs relevant to the investigated alloys [29].

**Figure 11.** Binary phase diagrams: (**a**) Ta-Zr. Reprinted from [30] with permission of Springer Nature; (**b**) Nb-Zr. Reprinted from [31] with permission of Springer Nature; (**c**) Ta-Hf. Reprinted from [32] with permission of Springer Nature; (**d**) Nb-Hf. Reprinted from [33] with permission of Springer Nature.

It is not clear whether presence of BCC phases in our less ductile alloys is due to stabilizing by rapid cooling during vacuum arc melting or due to differences between binary alloy and 3, 4 or 5 element alloys.

Existence of two BCC phases was reported in similar RHEA system with Mo and V instead of Ta and Nb [34]. CALPHAD simulation of the HfNbTaTiZr was performed, too [35]. A mixture of BCC and HCP phases with Ta Zr segregation was predicted. Experimental observation was performed on cold deformed and heat treated alloy in combination with high pressure torsion (HPT) and isothermal annealing in the range 300 ◦C–1100 ◦C and BCC + HCP phases were identified. Combination of two BCC phases and HCP was detected in a HfNbTaTiZr specimen annealed at 500 ◦C for 100 h. On contrary we observed only a single BCC phase in as-cast state.

System HfNbTaTi, similar to our NbTaTiZr alloy was calculated by CAPLHAD method [36]. Also combination of BCC + HCP phases was found to be stable at room temperature the BCC2 phase appeared between 750 ◦C and 1000 ◦C.

In Ref. [25] equimolar NbTaTiZr was modified by adding Ti and removing Ta and results similar to the present work were observed. The elongation to failure increased with rising titanium content. Dendritic segregation came from solidifying, segregation of Ta and Zr and intergranular precipitates were formed after 1200 ◦C/8 h annealing. But only single BCC phase was found in the as-cast state. Stabilizing of BCC phase by reduction of Ta content and rising Ti content was proposed [25]. A clear

correlation between strength or elongation and the misfit parameter δ were established. It is probably due to single phase microstructure.

Table 7 shows comparison of tensile properties of the alloys studied in the present work with MEAs reported in literature. There is a good agreement in ultimate tensile strength of NbTaTiZr alloy but referred rupture strength is higher and elongation much lower than in case alloy studied in this work.

Elongation, A calc., based on tantalum and zirconium combined content using equation from Figure 8a was calculated. There is a good correlation in higher Ti contents in case of alloys referred. But there is important difference in lower Ti content, although single phase solid solution for all compositions was reported [25].


**Table 7.** Tensile properties of present and reported medium entropy alloys (MEAs) [25].

\* Values estimated from the figure [25]

This difference corresponds with important change in elongation with Ti fraction. No clear explanation of this phenomenon was given [25]. Comparing experimental details of the present study with Ref. [25] one can recognize that dimensions of ingots were different. Ingots of alloys studied in the present work were larger and thereby solidifies and cools slower than ingots in Ref. [25]. Therefore NbTaTiZr alloy containing 100% of the BCC1 phase reported in Ref. [25] was likely due to higher cooling rate; while in the present work the same alloy exhibits a mixture of BCC1 and BCC2 phases, see Table 4. On the contrary in Ref. [25] the NbTaTiZr is referred as brittle, we measured 6.4% elongation, see Table 3, however, fracture mechanism has changed from transgranular with ductile dimples to intergranular, see Figure 2. Different interstitials element content may cause the difference in deformation of nominally same alloy.

In this study we use the same furnace and the same size of ingots in case of all investigated alloys. Therefore it is solely the effect of Ta + Zr content what affects the stability of the BCC1 phase. The cooling rate was high enough to produce 100% BCC1 microstructure in case of 5 element HfNbTaTiZr alloy but not in the 4 element alloy NbTaTiZr.

Intensive precipitation at grain boundaries was observed in the brittle TaTiZr alloy, see Figure 4. This alloy contains highest combined content of Ta + Zr and a low amount of the BCC1 phase.

Similar microstructures were found in Refs. [37,38]. These works investigated the influence of middle temperature annealing on the 5 element HEA HfNbTaTiZr in deformed and homogenisation annealed state. Combination of BCC and HCP phases were detected, at specific conditions (longer annealing temperatures and longer times) Ta rich BCC and Zr rich HCP phase precipitates were formed. Similarity of the microstructures and phases suggests that these effects have similar origin, namely Ta+Zr content, partial decomposition of the BCC1 phase to the BCC2 because of relatively high Ta-Zr mixing enthalpy and resulting miscibility gap.

The 5 element HfNbTaTiZr alloy was studied in Refs. [35,36]. It has lower Ta + Zr content than NbTaTiZr, Nb0.5TaTiZr1.5 and TaTiZr studied in the present work. Ingots used in Refs. [35,36] were smaller compared to that prepared in the present work, thus gaining higher cooling rate. The ingots were also annealed for homogenization and water quenched, thus metastable BCC1 solid solution was obtained. However, subsequent mid temperatures annealing caused decomposition of the BCC1 solid solution.

In our study, alloys are destabilized by higher Ta + Zr content and the cooling rate was slower than in other studies, therefore the BCC1 phase decomposition took place already during cooling. The MC simulation revealed segregation of Ta in the equilibrium state of the HfNbTaTiZr alloy. This supports the idea of Ta + Zr destabilizing HEAs also during ageing annealing. Thus single phase BCC1 structure is metastable in the 5 element HfNbTaTiZr HEA alloy at room temperature and can be preserved after high temperature annealing by rapid cooling. The role of rapid cooling has been discussed in the review [1].

The alloys containing the BCC2 phase are free of Hf. An HCP phase was predicted and confirmed experimentally in Hf containing alloys [35–38]. It means that Hf acts as an element stabilizing HCP phase.

Further research shall be focused on detail investigations of the BCC2 and BCC3 phases and intergranular precipitates detected in some alloys. Destabilising effect of Ta + Zr on the BCC phase stability during manufacturing ingots and ageing annealing shall be verified and utilised in future research. Stabilising effect of Hf on the HCP phase formation during mid temperature ageing shall be verified as well. Influence of the cooling rate on phase composition of HEAs shall be investigated, too.

Further investigation of the NbTiZr MEA alloy with promising results shall be performed.

Obtained results can be used in evolution of other variants of the investigated system HfNbTaTiZr, for example, for reduction of high temperature oxidation [39] or in research of ageing behaviour of similar RHEAs, especially containing both Ta and Zr.

#### **5. Conclusions**

Investigations of mechanical properties and microstructure of different MEAs derived from the HfNbTaTiZr alloy system has been performed. It has been shown that ductility is significantly reduced by simultaneous presence of Ta and Zr in the alloy, which leads to reduction of the BCC1 phase content. These elements segregate during solidifying. Because of the miscibility gap in the Ta-Zr equilibrium phase diagram two BCC phases are found after cooling to room temperature. Clear correlation between the BCC1 phase content and the total elongation to failure of the alloy was found. Precipitation of Ta rich precipitates on grain boundaries reduces the elongation to almost zero values. No correlation was found between the tensile mechanical properties and microstructure related parameters in investigated set of alloys. The 5 element HEA alloy exhibits the best combination of strength and elongation. 4 and 3 element MEAs have lower strength to various extent. Some of them are ductile (NbTaTiZr, NbTaTi, NbTiZr) but some of them are brittle (TaTiZr, Nb1.5TaTiZr0.5, Nb0.5TaTiZr1.5) depending on microstructure.

Obtained results on microstructure stability and related mechanical properties can be useful also for long term aging annealing of HEA alloys. The Monte Carlo simulation performed pointed out, that single solid solution of 5 element HfNbTaTiZr alloy is a metastable state at room temperature. Stabilizing effect of Hf on the HCP phase formation during mid temperature aging was proposed.

**Author Contributions:** Conceptualisation, J.Z.; Resources, J.V. and J.M.; Investigation, J.Z., F.L., O.M. and J.K.; Formal analysis, J.Z.; Writing—original draft, J.Z., J.C. and J.M.; Writing—review and editing, J.Z. and J.C.; supervision, J.C.

**Acknowledgments:** This research was funded by the Czech Science Foundation, project 17-17016S.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Effects of Mo, Nb, Ta, Ti, and Zr on Mechanical Properties of Equiatomic Hf-Mo-Nb-Ta-Ti-Zr Alloys**

**Ko-Kai Tseng 1, Chien-Chang Juan 1, Shuen Tso 2, Hsuan-Chu Chen 2, Che-Wei Tsai 1,2 and Jien-Wei Yeh 1,2,\***


Received: 30 November 2018; Accepted: 21 December 2018; Published: 25 December 2018

**Abstract:** Nowadays refractory high-entropy alloys (RHEAs) are regarded as great candidates for the replacement of superalloys at high temperature. To design a RHEA, one must understand the pros and cons of every refractory element. However, the elemental effect on mechanical properties remains unclear. In this study, the subtraction method was applied on equiatomic HfMoNbTaTiZr alloys to discover the role of each element, and, thus, HfMoNbTaTiZr, HfNbTaTiZr, HfMoTaTiZr, HfMoNbTiZr, HfMoNbTaZr, and HfMoNbTaTi were fabricated and analyzed. The microstructure and mechanical properties of each alloy at the as-cast state were examined. The solid solution phase formation rule and the solution strengthening effect are also discussed. Finally, the mechanism of how Mo, Nb, Ta, Ti, and Zr affect the HfMoNbTaTiZr alloys was established after comparing the properties of these alloys.

**Keywords:** high-entropy alloys; refractory high-entropy alloys; alloys design; elevated-temperature yield strength; solid solution strengthening effect

#### **1. Introduction**

Refractory elements, including Rhenium (Re), Molybdenum (Mo), Niobium (Nb), Tantalum (Ta), and Tungsten (W) [1] are very important for improving mechanical properties in advanced alloys such as Titanium alloys and Nickel-base superalloys. Generally, elements with a melting point higher than Titanium (Ti), such as Chromium (Cr), Hafnium (Hf), Osmium (Os), Ruthenium (Ru), Vanadium (V), and Zirconium (Zr) are also classified as refractory elements. In Titanium alloys, refractory elements, especially Mo and W, are all beta stabilizers and possess a strong solid solution strengthening characteristic [2]. Nb forms Ni3Nb *γ* phase in Nickel-base superalloys such as Inconel 718 [3]. The improved creep resistance of the sixth generation superalloy TMS-238 mainly results from Re and Ru additions [4]. Refractory alloys also play significant roles in industry. In the second generation nuclear power plants, the most-used materials for fuel cladding are Zircoloy 2 and Zircoloy 4. The Niobium alloy C103 is used for the nozzle extension of satellites [5]. Refractory alloys are also known as having the great potential for elevated-temperature applications because of their high strength at elevated temperature. According to thermodynamics, thermal efficiency of a turbine engine could be enhanced by increasing the turbine inlet temperature. However, the melting point of Nickel-base superalloy limits the application itself above 1200 ◦C. Therefore, it is necessary to develop new refractory alloys, especially for applications at temperatures higher than 1200 ◦C.

In 2004, Professor Yeh and his group published the concept of high-entropy alloys (HEAs) [6]. He defined high-entropy alloys (HEAs) as having five or more major elements beneath 5–35 at.%, and minor elements below five at.%. In 2006, he also established four core effects of HEAs [7]:

High-entropy, severe-lattices-distortion, sluggish-diffusion, and the cocktail effect. With the new concepts, scientists are able to develop and expand alloys without restrictions [8–12]. Some HEAs have been found to have attractive properties on diffusion [13], oxidation [14], corrosion [15], fatigue [16], creep [17], fracture toughness [18], and elevated-temperature strength [19]. High-entropy superalloys (HESAs) [20], eutectic HEAs (EHEAs) [21], light-weight HEAs (LWHEAs) [22], refractory high-entropy alloys (RHEAs) [23], etc. have been proposed and attract increased attention. In 2010, Senkov and Miracle first published RHEAs, MoNbTaW and MoNbTaVW [23,24]. These two alloys possess body-centered cubic (BCC) structure and have excellent elevated-temperature yield strength which is around 400 MPa at 1600 ◦C. But their density is much higher, and the room temperature compressive ductility is very low. In 2012, they published the equiatomic composition of HfNbTaTiZr, which possesses excellent compressive ductility up to 50%, lower density but poor elevated-temperature yield strength [25,26]. From then on, there were over 150 papers published concerning RHEAs [19].

There are some researches working on the addition of Al [27,28], Mo [29], Ti [30], V [31], or Zr [32], but few of them focus on the elevated-temperature mechanical performance and the overall effect of the constituent elements. To understand the elemental effect on mechanical properties, equiatomic HfMoNbTaTiZr alloy is firstly designed as a base alloy by adding the high modulus refractory element Mo to HfNbTaTiZr. Then the subtraction method is used to analyze each elemental effect in the equiatomic HfMoNbTaTiZr. Thus, in this study, six alloys HfMoNbTaTiZr, HfNbTaTiZr, HfMoTaTiZr, HfMoNbTiZr, HfMoNbTaZr, and HfMoNbTaTi are investigated and compared on their microstructure. Further, the compressive properties at room temperature and at elevated temperature are investigated. By comparing HfMoNbTaTiZr and HfNbTaTiZr, the influence of the addition of Mo can be understood. Likewise, the influence of the addition of Nb, Ta, Ti, or Zr can be articulated. In addition, promising compositions were found and further improved design is suggested. The solid solution phase formation rule and the solid solution strengthening effect will be discussed.

#### **2. Materials and Methods**

The experimental Hf-Mo-Nb-Ta-Ti-Zr alloy series was prepared by vacuum-arc melting. The purity of raw elements including Hf, Mo, Nb, Ta, and Zr was 99.9 wt.%, and that of Ti was 99.99 wt.%. The melting points of each constituent element used in alloys are shown in Table 1. These pure metals were stacked together in the sequence of low melting point to high melting point from bottom to top. The stacked metals were melted together in a water-cool copper mold and solidified therein. The ingot of each alloy was flipped and re-melted, at least, four times to improve the chemical homogeneity. The crystal structure of the alloy samples taken from the portion near the copper mold was examined with the Shimadzu XRD-6000 X-ray diffractometer (SHIMADZU CORPORATION, Kyoto, Japan), operated at 30 kV and 20 mA with a scanning rate of 4◦/min from 20◦ to 100◦. JEOL JSM-5410 (JEOL Ltd., Tokyo, Japan) scanning electron microscope (SEM) and JXA-8500F FE-EPMA (JEOL Ltd., Tokyo, Japan) was used to analyze the samples in backscattering electron (BSE) mode. Energy dispersive spectrometry (EDS) was also used to confirm the chemical compositions. The cylindrical samples for the compression test were 3.6 mm in diameter and 6 mm in height. The room temperature compression tests were conducted with Instron 4468 (INSTRON, Norwood, MA, USA) universal testing machine, and the high temperature compression tests were performed on Gleeble-3500 (DYNAMIC SYSTEMS INC, Poestenkill, NY, USA) thermal–mechanical simulator. All tests were examined at the crosshead speed of 0.36 mm/min, which imposed the strain rate of 10−<sup>3</sup> s−<sup>1</sup> on the samples.


**Table 1.** Results of scanning electron microscope-energy dispersive spectrometry (SEM-EDS) analysis (at. %). Nominal composition means the designed composition. DR means the dendritic region. ID means the interdendritic region.

#### **3. Results**

Figure 1a–f are BSE images of experimental Hf-Mo-Nb-Ta-Ti-Zr alloys. A typical dendritic structure is observed. Their compositions as obtained from SEM-EDS are shown in Table 1. It is noted that the dendritic area is rich in Ta and Mo which have the highest two melting points. This is expected since high melting point elements tend to crystalize first during solidification. By contrast of dendritic structure is poor in HfMoNbTiZr alloy as observed in the BSE image. This means the partition between dendrite and interdendrite is small and the coring phenomenon was less obvious. This is due to the subtraction of the highest melting point element Ta which would solidify first with a Ta-rich solid solution.

Figure 2 shows the X-Ray diffraction patterns. The main phase of the Hf-Mo-Nb-Ta-Ti-Zr alloy series is a BCC disordered solid solution. The asymmetry of (200) and (211) peaks are shown in the diffraction pattern results from the cored dendritic structure. The composition variation of dendritic and interdendritic areas causes a little difference in the lattice constant. The lattice constants of the Hf-Mo-Nb-Ta-Ti-Zr alloy series listed in Table 2 are in the range of 3.305 to 3.400 Å calculated by the Nelson–Riley extrapolation function. Referring to the phase diagrams of each binary alloy between Hf, Mo, Nb, Ta, Ti, and Zr, Hf-Mo, and Mo-Zr binary alloys form Mo2Hf and Mo2Zr, respectively, in a certain range of composition even at high temperature. However, these two intermetallic compounds or others do not show up in Hf-Mo-Nb-Ta-Ti-Zr alloys, which means the high entropy effect has a significant benefit in forming simple BCC solid solution in this alloy system especially at high temperature.

**Figure 1.** Backscattering electron (BSE) images of (**a**) HfMoNbTaTiZr, (**b**) HfNbTaTiZr, (**c**) HfMoTaTiZr, (**d**) HfMoNbTiZr, (**e**) HfMoNbTaZr, and (**f**) HfMoNbTaTi. All the alloys show the dendritic structure except HfMoNbTiZr.

**Figure 2.** X-ray diffraction patterns of Hf-Mo-Nb-Ta-Ti-Zr alloy series.


**Table 2.** The lattice constants (Å) of the Hf-Mo-Nb-Ta-Ti-Zr alloy series. Cal. means the value calculated from Vegard's Law. Exp. means the value calculated by Nelson–Riley extrapolation function based on X-ray diffraction pattern.

Figure 3 shows the compression test results of Hf-Mo-Nb-Ta-Ti-Zr alloy series. At room temperature, the yield strength of HfMoNbTaTiZr alloy was 1512 MPa, and ultimate strength was 1828 MPa when the strain was 11%. The compression tests for HfMoNbTaTiZr alloy were also conducted at 800 ◦C, 1000 ◦C, and 1200 ◦C, respectively. At 800 ◦C, the yield strength of HfMoNbTaTiZr alloy was 1007 MPa and ultimate strength was 1489 MPa when the strain was 19%, which shows obvious work hardening. At 1000 ◦C and 1200 ◦C, the results of yield strength were 814 MPa and 556 MPa, respectively, but the strength kept decreasing from the yield point to the end of the test, showing the work softening behavior. No crack was observed at 1000 ◦C and 1200 ◦C.

**Figure 3.** Engineer compressive stress–strain curve of (**a**) HfMoNbTaTiZr, (**b**) HfMoTaTiZr, (**c**) HfMoNbTiZr, (**d**) HfMoNbTaZr, and (**e**) HfMoNbTaTi.

When an element is removed from HfMoNbTaTiZr, the behavior is changed. The subtraction of Nb gives HfMoTaTiZr alloy. At room temperature, the yield strength of HfMoTaTiZr alloy was 1600 MPa, and the ultimate strength was 1743 MPa when the strain was 3%. At 800 ◦C, the yield strength was 1045 MPa, and the ultimate strength was 1446 MPa when the strain was 23%. As for the HfMoNbTaTiZr alloy, the stress–strain curve of HfMoTaTiZr alloy shows obvious work hardening effect. The results of yield strength were 855 MPa and 404 MPa at 1000 ◦C and 1200 ◦C, respectively. The strength kept decreasing from the yield point to the end of the test. No crack was observed at 1000 ◦C and 1200 ◦C.

The subtraction of Ta from HfMoNbTaTiZr gives HfMoNbTiZr. At room temperature, the yield strength of alloy was 1351 MPa, and the ultimate strength was 1698 MPa when the strain was 17%. This alloy performs with better toughness than HfMoNbTaTiZr and HfMoTaTiZr does at room temperature. At 800 ◦C, the yield strength was 829 MPa and the ultimate strength was 1244 MPa when the strain was 18%. At 1000 ◦C, yield strength was 721 MPa, and the strength kept decreasing when the strain increased. At 1200 ◦C, the yield strength was 301 MPa. The strength of the alloy was almost constant after the yield point to the end of the test. The strain softening effect was balanced by the strengthening effect.

Ti was removed in sequence. At room temperature, the yield strength of HfMoNbTaZr alloy was 1524 MPa, and the ultimate compress strength was 1963 MPa when the strain was 13.5%. At 800 ◦C, the compressive yield strength was 1005 MPa, and the ultimate strength was 1991 MPa when the strain was 24%. As with HfMoNbTaTiZr, there is an obvious work hardening effect shown at 800 ◦C in the stress–strain diagram. The yield strength was 927 MPa at 1000 ◦C. There was still a work hardening effect at the beginning of the test. The ultimate strength was 1336 MPa when the strain was 11%, but the strength decreased drastically to 464 MPa at the end of the test. At 1200 ◦C, the yield strength was 694 MPa, but the strength decreased to 289 MPa when the test stopped at 30% strain. At 1400 ◦C, the yield strength was 278 MPa, and the strength barely decreased during the test. Except for 800 ◦C, no fracture was observed during the test at elevated temperatures.

Finally, Zr was removed. At room temperature, the yield strength of HfMoNbTaTi alloy was 1369 MPa, and the ultimate compress strength was 2094 MPa when the strain was 25%. The yield strength at 800 ◦C was 822 MPa, and the ultimate strength was 1998 MPa when the strain was 29%. An obvious work hardening effect can be observed in the stress–strain curve. At 1000 ◦C, the yield strength was 778 MPa, and there was still work hardening effect at the beginning of the test until the ultimate strength 1454 MPa, at 27.5% strain. The results of yield strength were 699 MPa and 367 MPa at 1200 ◦C and 1400 ◦C, respectively. Both stress–strain diagrams show a steady decrease in strength after yield points. No fracture was observed at 1000 ◦C, 1200 ◦C, and 1400 ◦C.

The Tables 3 and 4 summarize the results of compressive tests. Comparing the performance at room temperature, HfMoTaTiZr alloy has the best yield strength 1600 MPa; HfMoNbTaTi has the highest 27% fracture strain; comprehensively, HfMoNbTaTi has the best mechanical properties (yield strength 1369 MPa and 27% fracture strain). The fracture strain increases from 4% for the HfMoTaTiZr alloy to 12% for HfMoNbTaTiZr. The presence of Ta can increase the yield strength but decrease the toughness. Ti seems to have no significant influence on strength, but it has a negative effect on toughness. Zr increases the strength; however, it strongly deteriorates the toughness at room temperature, because the fracture strain decreases from 27% for the HfMoNbTaTi alloy to 12% for HfMoNbTaTiZr. The presence of Mo, which has the highest shear modulus, increases the yield strength at room temperature from 929 MPa to 1512 MPa significantly. Nevertheless, the toughness decreases tremendously, fracture strain declines from > 50% to 12%. However, the presence of Nb decreases the yield strength only slightly from room temperature to 1000 ◦C and increases the yield strength by 38% at 1200 ◦C, but largely improves the room temperature fracture strain. This indicates that more Nb could be added for higher ductility.


**Table 3.** The room temperature compressive yield strength and fracture strain of the Hf-Mo-Nb-Ta-Ti-Zr alloy series.



The melting point of the elements in the alloy affects the strength performance at elevated temperature. For instance, at 1200 ◦C, HfMoTaTiZr alloy and HfMoNbTiZr alloy which have lower melting-point elements (Ta, Mo, Nb) have less strength; HfMoNbTaZr alloy and HfMoNbTaTi alloy which have higher melting-point elements (Ti, Zr) have better strength. Moreover, all the alloys with Mo present have much better strength than HfNbTaTiZr does. Therefore, Mo makes a significant contribution to strength at elevated temperature.

The elevated temperature yield strength versus temperature of Hf-Mo-Nb-Ta-Ti-Zr alloys is shown in Figure 4a. Except at 800 ◦C, the strength of the above mentioned Hf-Mo-Nb-Ta-Ti-Zr alloys is better than the commercial nickel base superalloys, CMSX-4 and Inconel 718. Additionally, Hf-Mo-Nb-Ta-Ti-Zr alloys also have better resistance to softening at elevated temperature. Figure 4b is the specific strength of Hf-Mo-Nb-Ta-Ti-Zr alloys, HfNbTaTiZr alloy, CMSX-4, and Inconel 718 at different temperatures. Below 900 ◦C, CMSX-4 and Inconel 718 perform better; at 1000 ◦C, Hf-Mo-Nb-Ta-Ti-Zr alloys, except for HfNbTaTiZr, are better than CMSX-4 and Inconel 718. At temperatures above 1200 ◦C, HfMoNbTaTi alloy has the highest specific strength.

Comprehensively speaking, Hf-Mo-Nb-Ta-Ti-Zr alloys have a potential application at elevated temperature.

**Figure 4.** (**a**) Elevated temperature yield strength and (**b**) elevated temperature specific yield strength versus temperature between Hf-Mo-Nb-Ta-Ti-Zr alloy series, CMSC-4, and Inconel 718 [3]. The elevated temperature yield strength of HfNbTaTiZr is from Reference [26].

#### **4. Discussion**

#### *4.1. Phase Formation Rule*

The solid solution phase formation rules were checked with the microstructure and crystal structure of the alloys in this study. First are the criterion based on thermodynamic parameters and atomic size parameter [33,34]. The thermodynamic parameters are mixing entropy Δ*Smix*, mixing enthalpy Δ*Hmix*, and Ω, respectively:

$$
\Delta S\_{\rm mix} = -\sum c\_i \ln c\_i \tag{1}
$$

$$
\Delta H\_{\rm mix} = \sum 4 \Delta H\_{\rm ij} c\_i c\_j \; \text{i} \; \neq \; \text{j} \tag{2}
$$

$$
\Omega = \frac{T\_m \Delta S\_{\text{mix}}}{\Delta H\_{\text{mix}}} \tag{3}
$$

where *R* is the gas constant, *ci* is the atomic percentage of the element *i*, *cj* is the atomic percentage of the element *j*, Δ*Hij* is the enthalpy of the binary liquid state of elements *i* and *j* at an equiatomic composition from the Miedema's model [35,36], and *Tm* is the melting point of the alloy defined by rule of mixing:

$$T\_m = \sum \dot{c}\_i T\_{m,i} \tag{4}$$

where *Tm,i* is the melting point of the element *i*. The atomic size parameter is atomic size difference *δ*:

$$\delta = \sqrt{\sum c\_i \left(1 - \frac{r\_i}{\overline{r}}\right)^2} \tag{5}$$

where *ri* is the atomic radius of element *i*. *r* is the average radius of the alloy defined by rule of mixing.

$$
\overline{r} = \sum c\_i r\_i \tag{6}
$$

The second criterion determining crystal type is related to electronic parameters, valence electron concentration *VEC* [37], and the third criterion determining Laves phase is related to Allen electronegativity difference Δ*χAllen* [38]:

$$VEC = \sum c\_i VEC\_i \tag{7}$$

$$
\Delta \chi\_{\text{Allen}} = \sqrt{c\_i (1 - \frac{\chi\_i^{\text{Allen}}}{\overline{\chi}})^2} \tag{8}
$$

where *VECi* is the valence electron concentration of the element *i* [39], *χAllen <sup>i</sup>* is the electronegativity of the element *i* from Allen et al. [40], and *χ* is the average electronegativity of the alloy defined by rule of mixing:

$$\overline{\chi} = \sum c\_i \chi\_i^{Allen} \tag{9}$$

The ranges in the three criterions for predicting the phases and crystal structure of HEAs are (1) Disorder solid solution phase forms when Ω >1.1 and *δ* < 6.6% [34]; (2) face-centered cubic (FCC) is stable when *VEC* > 8, and BCC is stable when *VEC* < 6.87 [37]; and (3) Laves phase forms when Δ*χAllen* > 7% and *δ* > 5% in HEAs [41]. All the criterions mentioned above are established through statistical approach, so there is still some error especially in the boundary condition. The properties of pure elements Hf, Mo, Nb, Ta, Ti, and Zr are listed in Table 5. The BCC atomic radii of Hf, Ti, and Zr are Goldschmidt radii since all the alloys are a BCC structure. All the parameters of six alloys are calculated and listed in Table 6. From Table 5, one can observe Hf and Zr possess the largest atomic radius and smallest electronegativity, and Mo possesses the smallest atomic radius and biggest electronegativity. Furthermore, from the experiment results, all the alloys at the as-cast state form

a single BCC disorder solid solution phase and no Laves phase is observed. This indicates that the formation of a single solid solution phase is consistent with criteria (1) and (2) but not consistent with criterion (3). Base on criterion (3), Laves phase might form in all the alloys except HfNbTaTiZr which is at the margin. It is necessary to check the criterion for Laves phase formation because Mo2Hf or Mo2Zr might form according to the Hf-Mo or Mo-Zr binary phase diagram. The result shows that criterion 3 is not fulfilled in the present alloy series. The minimum value 7% seems to be lower. One can observe that the Ω parameter values of these alloys are much higher than 1.1 and the VEC values are significantly lower than 6.87. This demonstrates that the high entropy effect is significant in enhancing the formation of a solid solution when mixing enthalpy and strain energy is small.


**Table 5.** Various data of the properties of Hf, Mo, Nb, Ta, Ti, and Zr. HCP means hexagonal close-packing.

**Table 6.** The values of thermodynamics, atomic size, and electronic parameters of the Hf-Mo-Nb-Ta-Ti-Zr alloy serious.


#### *4.2. Solution Hardening Mechanism*

The solid solution strengthening effect is calculated to examine the yield strength of the alloys in this study. From the experiment results, all the alloys possess a single phase of BCC disorder solid solution. It is valuable to use the yield strength of the alloys to check the solution strengthening mechanism. The solution strengthening mechanism of HEAs was proposed by Senkov et al. and then modified by Yao et al. [25,42]. The solution strengthening value Δ*σ<sup>i</sup>* contributed by element *i* is:

$$
\Delta \sigma\_i = A \, G f\_i^{4/3} \sigma\_i^{2/3} \tag{10}
$$

where *A* is a material-dependent dimensionless constant of the order of 0.04, *G* is the shear modulus of the alloy, and *fi* is the mismatch parameter of element *i* related to shear modulus and atomic size:

$$f\_i = \sqrt{\delta\_{G,l}^2 + a^2 \delta\_{r,l}^2} \tag{11}$$

where *δG,i* and *δr,i* are the modulus mismatch parameter and atomic radius mismatch parameter, respectively as Equations (12) and (13). The value of *α* depends on the type of dislocation. For mixed dislocation, the value is designated to be nine.

$$
\delta\_{\mathbf{G},\bar{i}} = \frac{9}{8} \sum c\_{\bar{j}} \delta\_{\mathbf{G},\bar{i}\bar{j}} \tag{12}
$$

$$
\delta\_{r,i} = \frac{9}{8} \sum c\_j \delta\_{r,ij} \tag{13}
$$

where *δG,ij* and *δa,ij* are the differences between elements *i* and *j* in shear modulus and atomic radius, respectively as Equations (14) and (15). Nine is the number of atoms in the *i*-centered cluster in the BCC lattice, eight is the number of atoms neighboring with the center atom *i*.

$$\delta\_{\mathbf{G},\ddot{\mathbf{j}}} = \frac{2(\mathbf{G}\_i - \mathbf{G}\_j)}{(\mathbf{G}\_i + \mathbf{G}\_j)} \tag{14}$$

$$\delta\_{r,\vec{v}} = \frac{2(r\_i - r\_j)}{(r\_i + r\_j)}\tag{15}$$

where *Gi* and *Gj* are the shear modulus of element *i* and *j*, respectively, and *rj* is the atomic radius of element *j*. Eventually, the solution strengthening Δ*σ* contributed by all the alloying elements is obtained by summation of Δ*σi*. The calculated yield stress *σ<sup>c</sup>* is the summation of the yield stress, *σm*, by rule of mixing and Δ*σ*.

$$
\Delta \sigma = (\sum (\Delta \sigma\_i)^{3/2})^{2/3} \tag{16}
$$

$$
\sigma\_{\mathcal{L}} = \sigma\_{\mathcal{M}} + \Delta \sigma \tag{17}
$$

As the shear modulus of the HfMoNbTaTiZr alloy system is still lacking, we reasonably use the rule of mixing to calculate it since the modulus relates to the interatomic potential energy well:

$$G\_m = \sum c\_i G\_i \tag{18}$$

The calculated results are listed in Table 7 and compared in Figure 5. One can observe that the *σ<sup>m</sup>* of all the alloys is small and almost the same. In addition, the trends of Δ*σ* and *σ<sup>c</sup>* are consistent with *σ0.2*. This means that high yield strength of this alloy series all comes from solution strengthening effect despite there being some deviation, about 30%, between calculated values and experimental values. It is interesting to note that Mo, with the smallest atomic radius and the largest shear modulus, interacts frequently with other elements, thus, the HfNbTaTiZr alloy possesses the smallest yield stress without the addition of Mo. Ti, having the average atomic radius and the average shear modulus, interacts slightly with other elements, and, thus, HfMoNbTaZr alloy possess the largest Δ*σ* without the addition of Ti. As for the deviation between *σ<sup>c</sup>* and *σ0.2,* it might be due to the overestimated shear modulus. Young's modulus of HfNbTaTiZr is 81 GPa reported by Juan et al. [43], and, thus, the shear modulus can be calculated to be 31 GPa. This value is obviously smaller than the average shear modulus 43 GPa of HfNbTaTiZr. This implies that all the average shear moduli might be overestimated. If we calculated the shear modulus from the experimental *σ0.2*, by assumption that *σ<sup>c</sup>* equals to *σ0.2*, the result is shown in the *Gcal* column of Table 7. From the figure, the trend of calculated shear modulus *Gcal* is consistent with the trend of average shear modulus although significantly smaller than G*<sup>m</sup>* by ~30%. One can observe that the calculated shear modulus of HfNbTaTiZr 32 GPa is in a good agreement with the literature [43]. This indicates that severe lattice distortion in HEAs has a strong solution hardening effect, but Young's modulus was effectively lower. This is reasonable and could be related to its effect on lattice constant [11]. In the alloy series, NiCo, NiCoFe, NiCoFeCr, and NiCoFeCrMn, the lattice constant of real crystal structure has more deviation from that predicted by Vegard's law. The increased lattice constants as compared with ideal average lattice constant indicates that lattice distortion has

the effect to expand the lattice. Thus, the interatomic bonding strength is effectively lower and the shear modulus is simultaneously lower. However, in the present alloy series, the calculated lattice constants based on Vegard's law are larger than the experimental lattice constants measured from X-ray diffraction patterns as listed in Table 2, especially with the addition of Mo. This is because Mo has a strong interaction with other elements to reduce the bond length according to Δ*Hij* in Table 5. Al has the same effect and is reported in Reference [27]. However, there needs to be more research in the future to confirm the reasons for the reduced shear modulus.


**Table 7.** Comparisons of G*m*, Δ*σ*, *σm*, *σc*, *σ*0.2, and G*cal* of the present alloy series.

**Figure 5.** The trend of Hf-Mo-Nb-Ta-Ti-Zr alloy series: (**a**) Δ*σ*, *σm*, *σc*, and *σ*0.2, and (**b**) *Gm* and *Gcal*.

#### **5. Conclusions**

The equiatomic HfMoNbTaTiZr alloy was chosen to analyze the effect of each constituent elemental by the subtraction method and, thus, HfMoNbTaTiZr, HfNbTaTiZr, HfMoTaTiZr, HfMoNbTiZr, HfMoNbTaZr, and HfMoNbTaTi were studied. Among these alloys, HfMoNbTaTi has the best mechanical performance, that is, 27% compressive strain at room temperature and yield strength 367 MPa at 1400 ◦C. HfMoNbTaTi has great potential for elevated-temperature applications. As the alloy system does not contain very expensive elements such as Re and Ru, it is cost competitive for high-temperature applications like Nb-Hf-Ti alloys in space vehicles. Further modification of composition and/or anti-oxidation coatings are still required for high-temperature applications in the air.

According to the experiment results, the effects of Mo, Nb, Ta, Ti, and Zr on mechanical properties of equiatomic Hf-Mo-Nb-Ta-Ti-Zr alloys were described. For higher room-temperature strength, one should add an element which interacts frequently with the alloy, such as Mo. For higher elevated-temperature strength, one should add the elements which possess high melting points, such as Mo, Nb, or Ta. One should add more Nb for higher ductility. With Ti or Zr addition, the elevated-temperature strength and the density decreases. All these elemental effects could also be applied to all other RHEAs systems, but more research is required to confirm this premise.

The solid solution phase formation rule and the solid solution strengthening effect of RHEAs have been discussed. The high entropy effect of the present alloys is significant in enhancing the formation of a solid solution. The shear modulus of RHEAs is smaller than that predicted from mixture rule by about 30%. This reduction is attributable to severe lattice distortion.

**Author Contributions:** K.-K.T. did the writing-original draft preparation, writing-review & editing, formal analysis, and the investigation. C.-C.J. did the methodology and the data curation. S.T. and H.-C.C. did the writing-original draft preparation. C.-W.T. and J.-W.Y. did the writing-review & editing, supervision, project administration, and funding acquisition.

**Funding:** This work was financially supported by the "High Entropy Materials Center" from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) and from the Project MOST 107-3017-F-007-003 by Ministry of Science and Technology (MOST) in Taiwan.

**Acknowledgments:** The authors acknowledged Woei-Ren Wang (Industrial Technology Research Institute, Tainan, Taiwan), who provided all the high temperature compressive test with Gleeble 3500.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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*Article*
