A Strategic Design Route to Find a Depleted Uranium High-Entropy Alloy with Great Strength

: The empirical parameters of mixing enthalpy ( ∆ H mix ), mixing entropy ( ∆ S mix ), atomic radius difference ( δ ), valence electron concentration (VEC), etc., are used in this study to design a depleted uranium high-entropy alloy (HEA). X-ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were used to assess the phase composition. Compression and hardness tests were conducted to select alloy constituents with outstanding mechanical properties. Based on the experimental results, the empirical criteria of HEAs are an effective means to develop depleted uranium high-entropy alloys (DUHEAs). Finally, we created UNb 0.5 Zr 0.5 Mo 0.5 and UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 HEAs with outstanding all-round characteristics. Both alloys were composed of a single BCC structure. The hardness and strength of UNb 0.5 Zr 0.5 Mo 0.5 and UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 were 305 HB and 1452 MPa, and 297 HB and 1157 MPa, respectively.


Introduction
The concept of high-entropy alloys (HEAs) offers a new approach to exploring materials, expanding the research scope and the compositional palette. Due to the high entropy effect, HEAs can form a simple solid solution structure with excellent properties under a high concentration of multiple components [1]. HEAs with high strength and toughness [2,3], stability at high temperatures [4,5], and corrosion resistance [4,6] have been investigated. The HEA system mainly focuses on the 3rd to 5th period, 3d electron layer elements, and other main group elements, which usually form face-centered cubic (FCC) and body-centered-cubic (BCC) structures. Meanwhile, the rare earth elements, such as Tb, Dy, Lu, Tm, and Ho, usually form a hexagonal-close-packed (HCP) structure [7,8].
Unlike uranium, depleted uranium (DU) has very little radioactivity and is often used in military applications because of its self-sharpening properties and high density [9][10][11]. There are three structures of U (Table 1), and the γ-U structure with a BCC structure has ideal symmetry and properties at high temperatures. Alloying elements Zr [12], Ti [11,13], Mo [14], Nb [15,16], amongst others, usually have a wide range of solubility in γ-U of the BCC structure. Zr and Nb can dissolve completely with U and form the γ-phase at high temperatures. Ti can dissolve in the U matrix and form the γ-phase at a temperature above 725 • C, and the maximum solubility of Mo in γ-U is 21.2 weight percent (wt.%). HEAs Table 1. Uranium allotropes and their characteristics, data from [17,18].

Allotrope
α-U β-U γ-U Temperature ( • C) <667.7 667.7~774.8 774.8~1132.3 Crystal structure Metals 2022, 12, x FOR PEER REVIEW at high temperatures. Ti can dissolve in the U matrix and form the γ-phase at a ture above 725 °C, and the maximum solubility of Mo in γ-U is 21.2 weight perce HEAs have superior properties to traditional alloys. By applying the concept o tropy to DU alloys and taking full advantage of γ-U, we can design DUHEAs w lent performance and provide more options for high-performance structural m Table 1. Uranium allotropes and their characteristics, data from [17,18].

Design Idea
HEAs design commonly includes high-throughput preparation, CALPHA diagram calculation) [19,20], and DFT (density functional theory) [21][22][23]. Gen factors considered in the calculation and simulation are ideal and are insufficien the actual casting process. In this study, we combined the solid solution formati of HEA with an experimental search for high-performance DUHEAs. The ele Mo, Ti, and Zr, which have significant solubility in U, were selected. The phy erties are listed in Table 2. Yeh et al. [27] believe that the mixing entropy (ΔSmix) is the main factor prom formation of solid solutions in HEAs. Zhang [28] extended the Hume-Rothery c HEAs and proposed δ, ΔHmix, and Ω as the factors affecting the formation of solution phases.
The mixing entropy can be calculated by the following formula [1]:

∆ ln
where R is the ideal gas constant (J·mol −1 ·K −1 ); n is the number of components in and ci is the atomic fraction of the ith component in the alloy. From Formula reaches the maximum when the atomic ratio of the elements in the alloy is equ eral, alloys are assigned to the class of HEAs when the mixing entropy is high R [29]. The parameter, δ, for the difference in atomic radius can be expressed as f

Design Idea
HEAs design commonly includes high-throughput preparation, CALPHAD (ph diagram calculation) [19,20], and DFT (density functional theory) [21][22][23]. Generally, factors considered in the calculation and simulation are ideal and are insufficient to refl the actual casting process. In this study, we combined the solid solution formation crite of HEA with an experimental search for high-performance DUHEAs. The elements N Mo, Ti, and Zr, which have significant solubility in U, were selected. The physical pro erties are listed in Table 2. Yeh et al. [27] believe that the mixing entropy (ΔSmix) is the main factor promoting formation of solid solutions in HEAs. Zhang [28] extended the Hume-Rothery criterion HEAs and proposed δ, ΔHmix, and Ω as the factors affecting the formation of HEA so solution phases.
The mixing entropy can be calculated by the following formula [1]:

∆ ln
where R is the ideal gas constant (J·mol −1 ·K −1 ); n is the number of components in the all and ci is the atomic fraction of the ith component in the alloy. From Formula (1), ΔS reaches the maximum when the atomic ratio of the elements in the alloy is equal. In g eral, alloys are assigned to the class of HEAs when the mixing entropy is higher than R [29]. The parameter, δ, for the difference in atomic radius can be expressed as follows [ at high temperatures. Ti can dissolve in the U matrix and form the γ-phase at a temperature above 725 °C, and the maximum solubility of Mo in γ-U is 21.2 weight percent (wt.%).
HEAs have superior properties to traditional alloys. By applying the concept of high entropy to DU alloys and taking full advantage of γ-U, we can design DUHEAs with excellent performance and provide more options for high-performance structural materials.

Design Idea
HEAs design commonly includes high-throughput preparation, CALPHAD (phase diagram calculation) [19,20], and DFT (density functional theory) [21][22][23]. Generally, the factors considered in the calculation and simulation are ideal and are insufficient to reflect the actual casting process. In this study, we combined the solid solution formation criteria of HEA with an experimental search for high-performance DUHEAs. The elements Nb, Mo, Ti, and Zr, which have significant solubility in U, were selected. The physical properties are listed in Table 2. Yeh et al. [27] believe that the mixing entropy (ΔSmix) is the main factor promoting the formation of solid solutions in HEAs. Zhang [28] extended the Hume-Rothery criterion to HEAs and proposed δ, ΔHmix, and Ω as the factors affecting the formation of HEA solid solution phases.
The mixing entropy can be calculated by the following formula [1]: where R is the ideal gas constant (J·mol −1 ·K −1 ); n is the number of components in the alloy; and ci is the atomic fraction of the ith component in the alloy. From Formula (1), ΔSmix reaches the maximum when the atomic ratio of the elements in the alloy is equal. In general, alloys are assigned to the class of HEAs when the mixing entropy is higher than 1.5 R [29]. The parameter, δ, for the difference in atomic radius can be expressed as follows [1]:

Design Idea
HEAs design commonly includes high-throughput preparation, CALPHAD (phase diagram calculation) [19,20], and DFT (density functional theory) [21][22][23]. Generally, the factors considered in the calculation and simulation are ideal and are insufficient to reflect the actual casting process. In this study, we combined the solid solution formation criteria of HEA with an experimental search for high-performance DUHEAs. The elements Nb, Mo, Ti, and Zr, which have significant solubility in U, were selected. The physical properties are listed in Table 2. Yeh et al. [27] believe that the mixing entropy (∆S mix ) is the main factor promoting the formation of solid solutions in HEAs. Zhang [28] extended the Hume-Rothery criterion to HEAs and proposed δ, ∆H mix , and Ω as the factors affecting the formation of HEA solid solution phases.
The mixing entropy can be calculated by the following formula [1]: where R is the ideal gas constant (J·mol −1 ·K −1 ); n is the number of components in the alloy; and c i is the atomic fraction of the ith component in the alloy. From Formula (1), ∆S mix reaches the maximum when the atomic ratio of the elements in the alloy is equal. In general, alloys are assigned to the class of HEAs when the mixing entropy is higher than 1.5 R [29]. The parameter, δ, for the difference in atomic radius can be expressed as follows [1]: where r is the average atomic radius of the alloy (Å), and r i is the atomic radius of the ith element of the alloy (Å). The mixing enthalpy of a multi-component alloy can be calculated by the following Formula [1]: where H mix AB is the mixing enthalpy of the ith and jth elements (kJ·mol −1 ); c i is the atomic percentage of the ith element in the alloy; and c j is the atomic percentage of the jth elements in the alloy. The mixing enthalpy among U, Nb, Zr, Ti, and Mo are listed in Table 3. Table 3. Mixing enthalpy between elements, data from [24][25][26] (H mix AB , kJ/mol).

U Nb Zr Ti Mo
To simplify the prediction standard of an HEA solid solution structure, Zhang [30] proposed the Ω parameter, the definition of which is expressed as follows [1]: where T m is the melting point of a multi-component alloy (K); ∆S mix is the mixing entropy of a multi-component alloy (J·K −1 ·mol −1 ); and ∆H mix is the mixing enthalpy of a multicomponent alloy (J·K −1 ·mol −1 ). To develop DUHEAs with excellent mechanical properties, Zr and Nb, which can dissolve indefinitely with γ-U at a high temperature to form a BCC solid solution structure, were added to the DU ternary alloy. Then, Ti and Mo were added to the DU ternary alloy to refine its properties. The study path is shown in Figure 1.
where ̅ is the average atomic radius of the alloy (Å), and ri is the atomic radius of the ith element of the alloy (Å). The mixing enthalpy of a multi-component alloy can be calculated by the following formula [1]: where is the mixing enthalpy of the ith and jth elements (kJ·mol −1 ); ci is the atomic percentage of the ith element in the alloy; and cj is the atomic percentage of the jth elements in the alloy. The mixing enthalpy among U, Nb, Zr, Ti, and Mo are listed in Table  3. Table 3. Mixing enthalpy between elements, data from [24][25][26] ( , kJ/mol).
To simplify the prediction standard of an HEA solid solution structure, Zhang [30] proposed the Ω parameter, the definition of which is expressed as follows [1]: where Tm is the melting point of a multi-component alloy (K); ΔSmix is the mixing entropy of a multi-component alloy (J·K −1 ·mol −1 ); and ΔHmix is the mixing enthalpy of a multi-component alloy (J·K −1 ·mol −1 ). To develop DUHEAs with excellent mechanical properties, Zr and Nb, which can dissolve indefinitely with γ-U at a high temperature to form a BCC solid solution structure, were added to the DU ternary alloy. Then, Ti and Mo were added to the DU ternary alloy to refine its properties. The study path is shown in Figure 1.

Test Method
Ingots with a mass of approximately 50 g were prepared using a Vacuum arc melting furnace and pure metals of U, Nb, Mo, Ti, and Zr (purity was higher than 99 wt.%). To ensure chemical homogeneity, the ingots were re-melted at least 4~5 times. An X-ray diffractometer (XRD, Bruker D8 Advance, Bruker AXS, Bruker AXS, Karlsruhe, Germany),

Test Method
Ingots with a mass of approximately 50 g were prepared using a Vacuum arc melting furnace and pure metals of U, Nb, Mo, Ti, and Zr (purity was higher than 99 wt.%). To ensure chemical homogeneity, the ingots were re-melted at least 4~5 times. An X-ray diffractometer (XRD, Bruker D8 Advance, Bruker AXS, Bruker AXS, Karlsruhe, Germany), with Cu Kα radiation, was used to measure the phase composition of the alloys. The scanning range was from 15 • to 90 • , and the scanning speed was 5 • /min. The micromorphologies of the alloys were observed by scanning electron microscopy (SEM, EVO18, Carl Zeiss AG, Jena, Germany) operating at 20 keV. The chemical composition was observed by energy-dispersive spectroscopy (EDS) equipped in the SEM. The standard bright-field (BF), image, and selected area electron diffraction (SAED) patterns were obtained by transmission electron microscope (TEM, Tecnai F30, FEI, Hillsboro, OR, USA) operating at 300 kV, and the TEM data were processed using the Digital Micrograph software. Hardness of the alloys was measured using the Wilson Brinell hardness meter BH3000 (Wilson, Norwood, MA, USA) under a load of 1840 N for 10 s. Room temperature compression tests were carried out by CMT5105 (Suns, Shenzhen, China). The specimen was a Φ 6 mm cylinder with a height-to-diameter ratio of between 1.5 and 2. The compression tests were performed at a compression rate of 10 −3 s −1 .

Ternary U-Nb-Zr Medium-Entropy Alloy (MEA)
Firstly, the U-Nb-Zr alloy system was studied. The thermodynamic parameters of the alloy system are listed in Table 4, and the relationship between δ-∆H and δ-Ω of the alloy is shown in Figure 2. Zr and Nb are infinitely soluble in U, indicating that the alloy system has a strong tendency to form solid solutions. From Figure 2a all alloys had a disordered solid solution phase. While in Figure 2b, UNbZr0.5 and UNb1.5Zr are in the solid solution and intermetallic compound zones, UNbZr is on the boundary of the solid solution and intermetallic compound zones, which does not tend to form a solid solution. The value of VEC for every alloy was lower than 6.87, forming a stable BCC solid solution structure [31]. The results show that the alloys have a disordered solution phase. Zeiss AG, Jena, Germany) operating at 20 keV. The chemical composition was ob by energy-dispersive spectroscopy (EDS) equipped in the SEM. The standard brig (BF), image, and selected area electron diffraction (SAED) patterns were obtai transmission electron microscope (TEM, Tecnai F30, FEI, Hillsboro, OR, USA) op at 300 kV, and the TEM data were processed using the Digital Micrograph software ness of the alloys was measured using the Wilson Brinell hardness meter BH3000 ( Norwood, MA, USA) under a load of 1840 N for 10 s. Room temperature comp tests were carried out by CMT5105 (Suns, Shenzhen, China). The specimen was a cylinder with a height-to-diameter ratio of between 1.5 and 2. The compression tes performed at a compression rate of 10 −3 s −1 .

Ternary U-Nb-Zr Medium-Entropy Alloy (MEA)
Firstly, the U-Nb-Zr alloy system was studied. The thermodynamic parameter alloy system are listed in Table 4, and the relationship between δ-ΔH and δ-Ω of th is shown in Figure 2. Zr and Nb are infinitely soluble in U, indicating that the alloy has a strong tendency to form solid solutions. From Figure 2a all alloys had a diso solid solution phase. While in Figure 2b, UNbZr0.5 and UNb1.5Zr are in the solid s and intermetallic compound zones, UNbZr is on the boundary of the solid soluti intermetallic compound zones, which does not tend to form a solid solution. The v VEC for every alloy was lower than 6.87, forming a stable BCC solid solution st [31]. The results show that the alloys have a disordered solution phase.   The XRD pattern of the medium entropy alloys are presented in Figure 3. Regardless of the uranium oxides, the phase compositions of the alloys were almost identical and were composed of a single BCC phase. In addition, the diffraction peaks appeared to shift with the change in Nb and Zr contents. Combining Bragg's Law with d hkl = a √ h 2 +k 2 +l 2 (d hkl is the interplanar spacing), the diffraction peaks shifted suggesting lattice content changes [32]. Because U, Nb, and Zr have different lattice constants, the variation of the lattice constants of the alloys is complex. According to the electron diffraction of the UNbZr alloy in Figure 4a,b, the alloy exhibited a single-phase BCC structure, which is consistent with the prediction of the alloy formation. with the change in Nb and Zr contents. Combining Bragg's Law with √ℎ (dhkl is the interplanar spacing), the diffraction peaks shifted suggesting lattice content changes [32]. Because U, Nb, and Zr have different lattice constants, the variation of the lattice constants of the alloys is complex. According to the electron dif fraction of the UNbZr alloy in Figure 4a,b, the alloy exhibited a single-phase BCC struc ture, which is consistent with the prediction of the alloy formation.  The microstructures of the medium-entropy alloys in the U-Nb-Zr system are shown in Figure 5. The microstructure of UNbZr is presented in Figure 5a. The light-colored re gion was a U-enriched interdendritic structure, while Zr and Nb formed the BCC den dritic structure of the primary phase due to their higher melting points. When the Nb content decreased, as shown in Figure 5b, the segregation of UNb0.5Zr was more pro nounced than that of UNbZr. When the Zr content decreased, the segregation of UNbZr0. decreased, as shown in Figure 5c, and the dendrite structure become finer. In Figure 5d,e the alloy compositions of UNb0.5Zr0.5 and UNb1.5Zr are uniform. The structure of the UN bZr1.5 alloy is shown in Figure 5e, which was similar to UNbZr and displayed a typical as were composed of a single BCC phase. In addition, the diffraction peaks appeared to shift with the change in Nb and Zr contents. Combining Bragg's Law with √ℎ (dhkl is the interplanar spacing), the diffraction peaks shifted suggesting lattice content changes [32]. Because U, Nb, and Zr have different lattice constants, the variation of the lattice constants of the alloys is complex. According to the electron diffraction of the UNbZr alloy in Figure 4a,b, the alloy exhibited a single-phase BCC structure, which is consistent with the prediction of the alloy formation.  The microstructures of the medium-entropy alloys in the U-Nb-Zr system are shown in Figure 5. The microstructure of UNbZr is presented in Figure 5a. The light-colored region was a U-enriched interdendritic structure, while Zr and Nb formed the BCC dendritic structure of the primary phase due to their higher melting points. When the Nb content decreased, as shown in Figure 5b, the segregation of UNb0.5Zr was more pronounced than that of UNbZr. When the Zr content decreased, the segregation of UNbZr0.5 decreased, as shown in Figure 5c, and the dendrite structure become finer. In Figure 5d,e, the alloy compositions of UNb0.5Zr0.5 and UNb1.5Zr are uniform. The structure of the UN-bZr1.5 alloy is shown in Figure 5e, which was similar to UNbZr and displayed a typical as- The microstructures of the medium-entropy alloys in the U-Nb-Zr system are shown in Figure 5. The microstructure of UNbZr is presented in Figure 5a. The light-colored region was a U-enriched interdendritic structure, while Zr and Nb formed the BCC dendritic structure of the primary phase due to their higher melting points. When the Nb content decreased, as shown in Figure 5b, the segregation of UNb 0.5 Zr was more pronounced than that of UNbZr. When the Zr content decreased, the segregation of UNbZr 0.5 decreased, as shown in Figure 5c, and the dendrite structure become finer. In Figure 5d,e, the alloy compositions of UNb 0.5 Zr 0.5 and UNb 1.5 Zr are uniform. The structure of the UNbZr 1.5 alloy is shown in Figure 5e, which was similar to UNbZr and displayed a typical as-cast dendrite structure (uniform region) with segregation of the components (U-enriched region).
The hardness and yield strength of the alloys of the U-Nb-Zr system are given in Table 5. The hardness and strength of UNbZr 0.5 and UNbZr 1.5 were lower than those of other alloys. It seems that the mechanical properties of UNb 0.5 Zr, UNbZr, and UNb 1.5 Zr were higher than those of UNb 0.5 Zr 0.5 . In particular, the organization of UNb 0.5 Zr was more homogeneous than that of UNb 0.5 Zr 0.5 (see Figure 5). However, this study aimed to utilize waste DU and improve its potential availability; therefore, UNb 0.5 Zr 0.5 was selected as the base alloy for the subsequent work.  The hardness and yield strength of the alloys of the U-Nb-Zr system are giv Table 5. The hardness and strength of UNbZr0.5 and UNbZr1.5 were lower than tho other alloys. It seems that the mechanical properties of UNb0.5Zr, UNbZr, and UNb were higher than those of UNb0.5Zr0.5. In particular, the organization of UNb0.5Zr was homogeneous than that of UNb0.5Zr0.5 (see Figure 5). However, this study aimed to u waste DU and improve its potential availability; therefore, UNb0.5Zr0.5 was selected a base alloy for the subsequent work.

Quaternary U-Nb-Zr-X HEA
From the microstructural study of the U-Nb-Zr ternary alloys, the elemental d bution of the UNb0.5Zr0.5 alloy is the most uniform, the segregation phenomenon wa obvious, and its comprehensive mechanical properties were excellent. Table 6 show thermodynamic parameters of UNb0.5Zr0.5-X (Ti/Mo) HEAs. From the relationship gram of δ-ΔH and δ-Ω in Figure 6, the studied UNb0.5Zr0.5-X (Ti/Mo) HEAs were solution phases. Based on their VEC, it was discovered that these alloys were BCC ph

Quaternary U-Nb-Zr-X HEA
From the microstructural study of the U-Nb-Zr ternary alloys, the elemental distribution of the UNb 0.5 Zr 0.5 alloy is the most uniform, the segregation phenomenon was not obvious, and its comprehensive mechanical properties were excellent. Table 6 shows the thermodynamic parameters of UNb 0.5 Zr 0.5 -X (Ti/Mo) HEAs. From the relationship diagram of δ-∆H and δ-Ω in Figure 6, the studied UNb 0.5 Zr 0.5 -X (Ti/Mo) HEAs were solid solution phases. Based on their VEC, it was discovered that these alloys were BCC phases. The XRD results of UNb 0.5 Zr 0.5 -X (Ti/Mo) HEAs presenting BCC structures are represented in Figure 7. Ignoring the uranium oxides, most of the alloys consisted of a single BCC structure, UNb 0.5 Zr 0.5 Ti and UNb 0.5 Zr 0.5 Mo HEAs forming two BCC structures. The diffraction peak changed to a higher angle as the concentrations of Ti and Mo grew, showing that the lattice constant dropped [32]. As presented in Table 2, the lattice contents of U, Mo, and Ti at room temperature are 343.3 pm, 314.7 pm, and 327.6 pm [17,26], respectively. With the addition of Ti and Mo, the lattice constant of the matrix decreased, indicating the occurrence of solid solution and the generation of lattice distortion. When the content of Mo reached the maximum, UNb 0.5 Zr 0.5 Mo was composed of two BCC structures, which was because Mo has the highest melting point of the elements.  The XRD results of UNb0.5Zr0.5-X (Ti/Mo) HEAs presenting BCC structures are sented in Figure 7. Ignoring the uranium oxides, most of the alloys consisted of a BCC structure, UNb0.5Zr0.5Ti and UNb0.5Zr0.5Mo HEAs forming two BCC structur diffraction peak changed to a higher angle as the concentrations of Ti and Mo grew ing that the lattice constant dropped [32]. As presented in Table 2, the lattice cont U, Mo, and Ti at room temperature are 343.3 pm, 314.7 pm, and 327.6 pm [17,26], tively. With the addition of Ti and Mo, the lattice constant of the matrix decreased cating the occurrence of solid solution and the generation of lattice distortion. Wh content of Mo reached the maximum, UNb0.5Zr0.5Mo was composed of two BCC tures, which was because Mo has the highest melting point of the elements.   The XRD results of UNb0.5Zr0.5-X (Ti/Mo) HEAs presenting BCC structures are represented in Figure 7. Ignoring the uranium oxides, most of the alloys consisted of a single BCC structure, UNb0.5Zr0.5Ti and UNb0.5Zr0.5Mo HEAs forming two BCC structures. The diffraction peak changed to a higher angle as the concentrations of Ti and Mo grew, showing that the lattice constant dropped [32]. As presented in Table 2, the lattice contents of U, Mo, and Ti at room temperature are 343.3 pm, 314.7 pm, and 327.6 pm [17,26], respectively. With the addition of Ti and Mo, the lattice constant of the matrix decreased, indicating the occurrence of solid solution and the generation of lattice distortion. When the content of Mo reached the maximum, UNb0.5Zr0.5Mo was composed of two BCC structures, which was because Mo has the highest melting point of the elements. The as-cast microstructures of UNb0.5Zr0.5-X (Ti/Mo) HEAs are shown in Figure 8, and the alloys all have a typical as-cast dendritic structure similar to the U-Nb-Zr system alloys. Composition segregation was obvious as the concentration of Ti and Mo increased. UNb0.5Zr0.5Ti0.2, UNb0.5Zr0.5Ti0.5, UNb0.5Zr0.5Ti, UNb0.5Zr0.5Mo0.2, and UNb0.5Zr0.5Mo0.5 consisted of a uniform region, a U-enriched region and a UOx region. Compared with  Figure 8f shows, the Mo-enriched region formed the BCC2 phase that is in line with the XRD patterns of Figure 7. Table 7 shows the Brinell hardness and yield strength of the UNb 0.5 Zr 0.5 -X HEAs. The addition of Ti significantly reduced the hardness of the alloy. When the molar ratio of Ti was 0.5, the yield strength of the alloy reached 881 MPa. While the hardness of the alloy improved dramatically as the Mo percentage increased, the yield strength decreased. This was because the hardness of Mo was higher than that of other elements. In addition, the melting point of Mo was the highest of the five elements, which will improve segregation during the solidification process. As a result, the hardness increased dramatically, and segregation of the alloy increased along with the Mo content, dramatically influencing the mechanical characteristics of the alloy.
UNb0.5Zr0.5Ti0.2 and UNb0.5Zr0.5Ti0.5, the segregation of the U-enriched region UNb0.5Zr0.5Ti was high obviously. UNb0.5Zr0.5Mo was composed of a U-enriched regio Mo-enriched region, and UOx, which was different from UNb0.5Zr0.5Mo0.2 an UNb0.5Zr0.5Mo0.5. As Figure 8f shows, the Mo-enriched region formed the BCC2 phase th is in line with the XRD patterns of Figure 7.  Table 7 shows the Brinell hardness and yield strength of the UNb0.5Zr0.5-X HEAs. T addition of Ti significantly reduced the hardness of the alloy. When the molar ratio of was 0.5, the yield strength of the alloy reached 881 MPa. While the hardness of the all improved dramatically as the Mo percentage increased, the yield strength decreased. Th was because the hardness of Mo was higher than that of other elements. In addition, t melting point of Mo was the highest of the five elements, which will improve segregati during the solidification process. As a result, the hardness increased dramatically, an segregation of the alloy increased along with the Mo content, dramatically influencing t mechanical characteristics of the alloy.

Quinary U-Nb-Zr-Ti-Mo HEAs
We can observe from the previous section on the quaternary HEAs that the propos alloys could form a stable solid solution phase of a BCC structure. The UNb0.5Zr0.5Ti UNb0.5Zr0.5Ti0.5, UNb0.5Zr0.5Mo0.2, and UNb0.5Zr0.5Mo0.5 alloys had the most uniform e mental distributions, and the segregation phenomenon was not observed. A five-eleme DUHEA was prepared by varying the ratio of Ti and Mo and choosing UNb0.5Zr0.5TixM

Quinary U-Nb-Zr-Ti-Mo HEAs
We can observe from the previous section on the quaternary HEAs that the proposed alloys could form a stable solid solution phase of a BCC structure. The UNb 0.5 Zr 0.5 Ti 0.2 , UNb 0.5 Zr 0.5 Ti 0.5 , UNb 0.5 Zr 0.5 Mo 0.2 , and UNb 0.5 Zr 0.5 Mo 0.5 alloys had the most uniform elemental distributions, and the segregation phenomenon was not observed. A five-element DUHEA was prepared by varying the ratio of Ti and Mo and choosing UNb 0.5 Zr 0.5 Ti x Mo x .
The thermodynamic properties of Nb-Zr-U-Ti-Mo HEAs are shown in Table 8. The planned UNb 0.5 Zr 0.5 Ti x Mo x HEAs were all solid solution phases, as evidenced by the relationship between δ-∆H and δ-Ω in Figure 9. Based on its VEC, we can predict that the developed alloy will be a BCC phase.   The phase composition and microstructure of the five-element DUHEA were investigated. Figure 10 shows the XRD data on the UNb0.5Zr0.5TixMox (x = 0.2, 0.5) HEA. UNb0.5Zr0.5Ti0.2Mo0.2 was composed of a single BCC structure and UNb0.5Zr0.5Ti0.5Mo0.5 formed two BCC structures. The addition of Ti and Mo contributed to the formation of BCC2. In addition, when the concentration of Ti and Mo increased, the diffraction peaks were shifted to higher angles, indicating a decrease in the lattice constants. Moreover, the diffraction peaks became broader with the increase in the Ti and Mo contents, indicating grain refinement [33],.  The phase composition and microstructure of the five-element DUHEA were investigated. Figure 10 shows the XRD data on the UNb 0.5 Zr 0.5 Ti x Mo x (x = 0.2, 0.5) HEA. UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 was composed of a single BCC structure and UNb 0.5 Zr 0.5 Ti 0.5 Mo 0.5 formed two BCC structures. The addition of Ti and Mo contributed to the formation of BCC2. In addition, when the concentration of Ti and Mo increased, the diffraction peaks were shifted to higher angles, indicating a decrease in the lattice constants. Moreover, the diffraction peaks became broader with the increase in the Ti and Mo contents, indicating grain refinement [33].  The phase composition and microstructure of the five-element DUHEA were investigated. Figure 10 shows the XRD data on the UNb0.5Zr0.5TixMox (x = 0.2, 0.5) HEA. UNb0.5Zr0.5Ti0.2Mo0.2 was composed of a single BCC structure and UNb0.5Zr0.5Ti0.5Mo0.5 formed two BCC structures. The addition of Ti and Mo contributed to the formation of BCC2. In addition, when the concentration of Ti and Mo increased, the diffraction peaks were shifted to higher angles, indicating a decrease in the lattice constants. Moreover, the diffraction peaks became broader with the increase in the Ti and Mo contents, indicating grain refinement [33],.   Figure 11. These alloys had a typical cast dendritic structure of a uniform composition region and U-enriched region between the dendritic structures. It can be observed that the structure segregation phenomenon of the alloys improved as Ti and Mo concentrations increased. This was due to the fact that Mo had a high melting point (higher than U's melting point) and element redistribution during solidification. The alloy components are equally distributed without noticeable segregation, as seen in the surface scan findings of UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 in Figure 12.
The Brinell hardness and yield strength of the UNb 0.5 Zr 0.5 Ti x Mo x HEAs are listed in Table 9. The addition of Ti and Mo promoted the hardness and yield strength of the alloys, and plasticity reduced dramatically. The mixing enthalpy of Mo with Nb, Zr, and Ti was negative, and Mo had a higher melting point, resulting in component segregation. It can be demonstrated by examining UNb 0.5 Zr 0.5 Ti 0.5 Mo 0.5 , which has a higher hardness of 350 HB than that of UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 . served that the structure segregation phenomenon of the alloys improved as Ti an concentrations increased. This was due to the fact that Mo had a high melting (higher than U's melting point) and element redistribution during solidification. Th components are equally distributed without noticeable segregation, as seen in the s scan findings of UNb0.5Zr0.5Ti0.2Mo0.2 in Figure 12.  The Brinell hardness and yield strength of the UNb0.5Zr0.5TixMox HEAs are lis Table 9. The addition of Ti and Mo promoted the hardness and yield strength of the and plasticity reduced dramatically. The mixing enthalpy of Mo with Nb, Zr, and T negative, and Mo had a higher melting point, resulting in component segregation. be demonstrated by examining UNb0.5Zr0.5Ti0.5Mo0.5, which has a higher hardness HB than that of UNb0.5Zr0.5Ti0.2Mo0.2.

Discussion
The researched alloys in the present article are all BCC solid solution structure the solid-solution formation criteria and microstructure characterization.  served that the structure segregation phenomenon of the alloys improved as Ti concentrations increased. This was due to the fact that Mo had a high meltin (higher than U's melting point) and element redistribution during solidification. T components are equally distributed without noticeable segregation, as seen in the scan findings of UNb0.5Zr0.5Ti0.2Mo0.2 in Figure 12.  The Brinell hardness and yield strength of the UNb0.5Zr0.5TixMox HEAs are Table 9. The addition of Ti and Mo promoted the hardness and yield strength of th and plasticity reduced dramatically. The mixing enthalpy of Mo with Nb, Zr, and negative, and Mo had a higher melting point, resulting in component segregatio be demonstrated by examining UNb0.5Zr0.5Ti0.5Mo0.5, which has a higher hardnes HB than that of UNb0.5Zr0.5Ti0.2Mo0.2.

Discussion
The researched alloys in the present article are all BCC solid solution structu the solid-solution formation criteria and microstructure characterization.

Discussion
The researched alloys in the present article are all BCC solid solution structures, per the solid-solution formation criteria and microstructure characterization. Figure 13 shows the concept of the DUHEA design process, which begins with the ternary U-Nb-Zr system, adds Ti and Mo elements to create the quaternary alloys and, ultimately, finishes with the quinary UNb 0.5 Zr 0.5 Ti x Mo y alloy. The mixing enthalpy of U with Nb, Ti, Zr, and Mo had a significant impact on the structure and mechanical properties of the studied alloys. The relationship between the mixing enthalpy and the mechanical characteristics of the alloys are presented in Figure 14. The compressive yield strength and hardness exhibited a rising trend as the mixing enthalpy fell. Though UNb 0.5 Zr 0.5 Ti 0.5 Mo 0.5 and UNb 0.5 Zr 0.5 Mo had higher strength, severe component segregation microstructures resulted in poor plasticity. This was due to the melting point of Mo being higher than those of other elements, resulting in component segregation and poor performance. Finally, based on our combined theoretical and experimental results, UNb 0.5 Zr 0.5 Mo 0.5 and UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 had a homogeneous structure and outstanding mechanical characteristics. hibited a rising trend as the mixing enthalpy fell. Though UNb0.5Zr0.5Ti0.5Mo0.5 and UNb0.5Zr0.5Mo had higher strength, severe component segregation microstructures resulted in poor plasticity. This was due to the melting point of Mo being higher than those of other elements, resulting in component segregation and poor performance. Finally, based on our combined theoretical and experimental results, UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 had a homogeneous structure and outstanding mechanical characteristics.

Conclusions
In this paper, we examined the composition of UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2, finding both to possess a homogeneous structure, low segregation, and outstanding mechanical properties. The alloys examined were screened during the design process from the DU ternary alloy to DUHEA according to the formation law of HEAs and based on experimental results. UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 were composed of a single BCC structure, which was in line with our theoretical calculations. The hardness and strength of UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 were 305 HB and 1452 MPa, and 297 HB and 1157 MPa, respectively. This suggests that the HEA phase- sulted in poor plasticity. This was due to the melting point of Mo being higher than those of other elements, resulting in component segregation and poor performance. Finally, based on our combined theoretical and experimental results, UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 had a homogeneous structure and outstanding mechanical characteristics.

Conclusions
In this paper, we examined the composition of UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2, finding both to possess a homogeneous structure, low segregation, and outstanding mechanical properties. The alloys examined were screened during the design process from the DU ternary alloy to DUHEA according to the formation law of HEAs and based on experimental results. UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 were composed of a single BCC structure, which was in line with our theoretical calculations. The hardness and strength of UNb0.5Zr0.5Mo0.5 and UNb0.5Zr0.5Ti0.2Mo0.2 were 305 HB and 1452 MPa, and 297 HB and 1157 MPa, respectively. This suggests that the HEA phase-

Conclusions
In this paper, we examined the composition of UNb 0.5 Zr 0.5 Mo 0.5 and UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 , finding both to possess a homogeneous structure, low segregation, and outstanding mechanical properties. The alloys examined were screened during the design process from the DU ternary alloy to DUHEA according to the formation law of HEAs and based on experimental results. UNb 0.5 Zr 0.5 Mo 0.5 and UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 were composed of a single BCC structure, which was in line with our theoretical calculations. The hardness and strength of UNb 0.5 Zr 0.5 Mo 0.5 and UNb 0.5 Zr 0.5 Ti 0.2 Mo 0.2 were 305 HB and 1452 MPa, and 297 HB and 1157 MPa, respectively. This suggests that the HEA phase-formation criteria could have a wide range of applications in the design of DUHEAs, providing promising theoretical direction for the future development of specific BCC-structured HEAs.