Microstructure and mechanical properties of two uranium-containing high-entropy alloys

Journal Pre-proof Microstructure and mechanical properties of two uranium-containing high-entropy alloys Jie Shi, He Huang, Guichao Hu, Pengguo Zhang, Chunli Jiang, Haiyan Xu, Chao Luo

PII:

S0925-8388(20)34658-2

DOI:

https://doi.org/10.1016/j.jallcom.2020.158295

Reference:

JALCOM158295

To appear in: Journal of Alloys and Compounds Received date: 23 September 2020 Revised date: 16 November 2020 Accepted date: 10 December 2020 Please cite this article as: Jie Shi, He Huang, Guichao Hu, Pengguo Zhang, Chunli Jiang, Haiyan Xu and Chao Luo, Microstructure and mechanical properties of two uranium-containing high-entropy alloys, Journal of Alloys and Compounds, (2020) doi:https://doi.org/10.1016/j.jallcom.2020.158295 This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier.

Microstructure

and

mechanical

properties

of

two

uranium-containing

high-entropy alloys Jie Shi a,*, He Huang a, Guichao Hu a, Pengguo Zhang b, Chunli Jiang a, Haiyan Xu b, Chao Luob,** a

Science and Technology on Surface Physics and Chemistry Laboratory, P. O. Box Nos, 9-35,

Huafengxincun, Jiangyou, Sichuan, 621908, China b

Institute of Materials, China Academy of Engineering Physics, P. O. Box 9071, No.9

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Huafengxincun, Jiangyou, Sichuan, 621907, China

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Abbreviations1

-p

Abstract: This paper reports the microstructure and mechanical properties of two uranium-containing high-entropy alloys (HEAs), i.e., UMoNbTaHf and UMoNbTaTi. Both these

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alloys formed a simple solid solution without intermediate compounds in the solid state, indicating that the uranium-containing HEAs conform to the law of solid-solution phase formation and

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confirming that actinides can form HEAs. The UMoNbTaHf alloy achieved a body-centered cubic (BCC) structure (a = 332.1 pm), whereas the UMoNbTaTi alloy achieved a dual BCC structure

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comprising two BCC phases (a1 = 333.2 pm and a2 = 328.0 pm). By replacing the Hf in UMoNbTaHf with Ti, its room-temperature compressive yield strength decreased from 1147 MPa

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to 985 MPa, and its breaking strain increased from 7.7% to 39.5%. Further, its strength and toughness were balanced because of the formation of the dual BCC phase. UMoNbTaTi exhibited better strength and toughness than UMoNbTaHf. In addition, this study expands the application of HEAs design to actinide materials.

Keywords: uranium; high-entropy ; microstructure; mechanical properties.

1

BCC

Body-centered cubic

EDS

Energy dispersive spectroscopy

FCC

Face-centered cubic

HEA

High-entropy alloys

ROM

Rule-of-mixture

SEM

Scanning electron microscope

XRD

X-ray diffraction

1. Introduction The objective of material design is to enhance the material properties, including physical, chemical, and mechanical properties. Alloy designs based on multi-principal elements have emerged as powerful alternatives to develop novel materials. The multiple-component solid alloys are referred to as high-entropy alloys (HEAs)[1]. HEAs typically include at least four principal elements with equiatomic or near-equiatomic ratios which in conjunction with solid solutions can be obtained because of their high-mix configurational entropy. Recently, two main HEAs families

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have attracted considerable research attention because of their microstructure and good

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mechanical properties. These families include (1) alloys based on a composition of CoCrFeNi. Three-dimensional (3d) transition metal elements, such as Al

[2–4]

, Cu [5], and Mo [6], are added to

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these alloys. Such alloys exhibit a simple face-centered cubic (FCC) structure and high room-temperature compressive strength. (2) The refractory HEAs systems include Hf [7], Mo [8], [9]

, V [10], W

[11]

, and Zr

[12]

re

Nb

. They have a body-centered cubic (BCC) structure and exhibit

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specific strength noticeably greater than those of the commercial refractory alloys. Almost all transition metals have been employed in HEAs; however, to date, only some studies

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have considered lanthanides or actinides such as uranium [13]. Actinides differ from lanthanides in terms of their complex electronic structure, wherein the 5f, 6d, 7s, and 7p orbitals exhibit relatively comparable energies

[14]

. Therefore, uranium highly reacts with different elements to

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form intermetallic compounds. Metallic uranium exists in three phases: α (orthorhombic), β (tetragonal), and γ (BCC). Only some elements exhibit considerable solid solubility at high temperatures; however, the addition of elements, such as Ti[15], Nb [16], Mo[17], and Zr[18], makes them extensively soluble in the high-temperature γ-phase (20%–100%), much less soluble in the intermediate-temperature β-phase (<1%), and almost insoluble in the low-temperature α-phase (<0.3%) [14]. Uranium exhibits a wide range of applications because of its high density (19.1 × 103 kg/m3) and unique nuclear properties[19].There has been an ongoing research to qualify LEU(low-enrichment uranium,<20 at.% 235U) fuels for substituting HEU (high-enriched uranium) fuels[20]. Uranium is often alloyed (1-2 elements) to improve its resistance to oxidation and corrosion, and to increase its strength and phase stabilization [14]. The increase in the strength and toughness of the material can improve the resistance to radiation swelling[21] and reduce the

difficulty of thermal processing[22]. Among all innovation concepts, alloying design based on multi-principle elements has been used to design uranium alloys. Some high-entropy alloys have high phase stability[23] and mechanical properties can be improved by changing the constituent phases [24-26]. This has resulted in several advantages, both in extending the field of HEAs and the understanding of multiprincipal uranium-containing alloys. Based on the concept of HEAs, in this study, we developed and characterized two novel uranium-containing HEAs. The U-Mo-Nb-Ta system was considered to be the base composition,

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and Ti and Hf were considered to be the alloying elements. The as-cast microstructures, phase

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formation, and mechanical properties (Young’s modulus, microhardness, and compressive properties) of the developed UMoNbTaHf and UMoNbTaTi were obtained. In addition, we

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propose atomic models to describe the phase formation process of UMoNbTaTi and discuss the

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relation between microstructures and mechanical properties.

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2. Material and methods

We used commercial elemental bulk materials with a purity of more than 99.9% (wt%) as the

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starting materials to fabricate the UMoNbTaHf and UMoNbTaTi alloy ingots in an equiatomic fraction by arc melting. The arc-melted ingots weighing approximately 30 g were fabricated under a Ti-gettered argon atmosphere in a water-cooled copper hearth. The homogeneity was improved

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by melting all the ingots four times. The diameter and height of the ingots were approximately 18 and 6 mm, respectively.

The crystalline structure of the as-cast UMoNbTaHf and UMoNbTaTi alloys was analyzed by

X-ray diffraction (XRD) using a TD3500 diffractometer with monochromatic Cu Kα radiation. The scanning angles were 20°–90°, and a scanning rate of 2°/min was adopted. The microstructure of the as-cast alloy was examined using a Series 200 scanning electron microscope (SEM) (FEI, Eindhoven,

The

Netherlands)

and

a

LEXT

OLS4000

laser

scanning

confocal

microscope(Olympus, USA). The experimental compositions were analyzed by energy dispersive spectroscopy (EDS) using an SEM. The sample was etched using nitric acid, hydrofluoric acid, and distilled water (HNO3:HF:H2O = 2:1:7) to observe its microstructure.

The Vickers hardness measurements were performed on the nonetched cross-sectional surface of the alloy specimen using the hardness-testing machine equipped with the 136° Vickers diamond pyramid under a load of 200 g for 20 s. The samples were mechanically ground with SiC abrasive papers of 800–2000 grits; subsequently, they were polished with 2.5- and 1-μm diamond paste. Then, nanoindentation tests were performed on the fine-polished surface using a nanomechanical testing instrument (Hysitron TI-950 US) with the Berkovich indenter to characterize the hardness and Young’s modulus of the constituent phases. The loads were applied at a rate of 1.6 mN/s, and

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the maximum load was maintained for 2 s. The room-temperature compressive properties were evaluated using a computer-controlled testing machine. The strain rate was 1 × 10−3 s−1. The test

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specimens were cylindrical (Φ4 mm × 6 mm). The microstructure and fracture surfaces were

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observed using an SEM. 3. Results

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3.1 Microstructural characterization

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Fig. 1 shows the XRD patterns of the as-cast UMoNbTaHf and UMoNbTaTi alloys. As shown in the figure, only one BCC phase was observed in the as-cast UMoNbTaHf alloy, whereas two

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BCC phases could be observed in the UMoNbTaTi alloy. The peaks of BCC1 could be observed below the Bragg angle, indicating that its lattice parameter is greater than that of the BCC2 phase. In both the as-cast alloys, no super lattice diffraction peaks of crystal ordering or other peaks were

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observed. Combining the Bragg equation and the equation of the inter-plane spacing of the crystal planes, the lattice parameter a of the two BCC phases was calculated as follows :

a

 2 sin 

h2  k 2  l 2

(1)

where λ is the wavelength of x-ray radiation (0.1542 nm) and θ is the diffraction angle of the (hkl) planes. XRD results of UMoNbTaHf

show that the shapes of the four peaks are symmetric. The

segregation does not cause any new phases with a different crystal structure and noticeably different lattice constants. The material can be regarded as a continuous BCC solid solution in the entire composition. The lattice parameter of the BCC phase was determined to be a = 332.1 pm. The lattice parameter of the UMoNbTaTi alloy was 333.2 pm for the BCC1 phase and 328.0 pm for the BCC2 phase. Fig. 1 shows that the intensity of the diffraction peaks with a large angle is

generally weak because the alloy contains more elements. The elements corresponding to different atomic radii result in large lattice distortions of the alloy. In this work, volume fraction of two phases in UMoNbTaTi is calculated from the XRD results[27,28]:

fM 

I

I

HKL ,1

HKL ,1

(2)

 I hkl , 2

where IHKL,M and Ihkl, A denote the integrated intensities of BCC1 phase with plane HKL and BCC2

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phase with plane hkl, respectively. Due to the weak diffraction of BCC2 at 2θ>75°,only (110), (200) and (211) are taken into account in Eq.(2). The volume fractions of BCC1 phase and BCC2

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re

-p

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phase are listed in Table 1.

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Fig. 1 X-ray diffraction patterns of the as-cast UMoNbTaHf and UMoNbTaTi alloys

Fig. 2 shows the microstructure of the as-cast UMoNbTaHf and UMoNbTaTi alloys obtained

from the middle parts of the ingots. The figure reveals that the UMoNbTaHf alloy, which exhibits a typical columnar crystal morphology, has a structure comprising slightly elongated grains with an average width of 30-60 μm. However, the SEM results clearly show segregations in the alloy. This indicates that UMoNbTaHf alloy has two phases with the same crystal structure (BCC) and extremely similar lattice parameters that cannot be distinguished by XRD(Fig.1). The matrix is named zone B and segregation area is named zone A. The chemical compositions of the two zones characterized by EDS are shown in Table 1. Ta and Hf were rich in zone B while U was rich in zone A. Only Nb and Mo do not show evident different in the two zones. The compositions of A zone were U28Mo19Nb20Ta15Hf17 and the B zone were U18Mo19Nb20Ta21Hf22. Fig. 3 shows the elemental mapping results of the UMoNbTaTi alloy. After etching, typical dendritic and

interdendritic structures were observed. The dendritic region in the UMoNbTaTi alloy was rich in Mo, Nb, and Ta, whereas the interdendritic region in the UMoNbTaTi alloy was rich in U and Ti. Mo, Nb, and Ta solidified into the dendritic arms, whereas Ti and U segregated into the interdendritic regions. The chemical compositions of the dendritic and interdendritic regions were studied via EDS, and the results are presented in Table 1. As shown in the table, the composition of the interdendritic regions was U40Mo20Nb14Ta11Ti15 and that of the dendritic arms was U11Mo18Nb21Ta28Ti22 corresponding to the BCC1 and BCC2 peaks observed in the XRD analysis,

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respectively. Conversely, according to the U–Ta binary phase diagram, U–Ta would decompose into U- and Ta-rich phases at a high temperature of approximately 2800 K, increasing the

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re

-p

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segregation of the alloy constituents.

Fig. 2. SEM images of the as-cast (a) UMoNbTaHf and (b) UMoNbTaTi alloys, showing two phases with distinct

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morphologies and compositions, i.e., BCC1 and BCC2

Fig. 3. Elemental mapping with EDS for each component of the UMoNbTaTi HEA, showing elemental segregation in dendritic (BCC2) and interdendritic (BCC1) regions.

Table 1. Chemical compositions of the as-cast UMoNbTaHf and UMoNbTaTi alloys (at.%) Alloy

Volume

Region in microstructure

U

DR(BCC2)

10.64

18.4

27.95

21.13

21.88

72.5%

ID(BCC1)

39.76

19.78

11.37

13.95

15.14

27.5%

Area A

28.03

19.58

15.2

20.49

16.7

Area B

18.51

19.08

21.13

19.78

21.5

Mo

Ta

Nb

Ti

Hf

fraction

UMoNbTaTi

UMoNbTaHf

Based on the XRD and EDS results, the UMoNbTaTi alloy can be identified as BCC1 and

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BCC2 phases, respectively. The difference between the composition of the two phases resulted in slight difference in the lattice parameter. Based on the element concentration in each BCC phase,

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the lattice parameter amix of the ideal disordered solid solutions of the two BCC phases can be

-p

calculated using the rule of mixture (ROM) or Vegard’s law [29].

(3)

re

amix   ci ai

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where ci and ai are the atomic fraction and lattice parameter of the ith element, respectively. The solid Mo, Ta, and Nb exhibited BCC phases. Solid uranium exhibits α-phase (orthorhombic) at

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temperatures of lower than 941 K and γ-phase (BCC) at temperatures of greater than 1068 K. The lattice parameters at room temperature can be extrapolated from those at elevated temperatures using the linear thermal expansion coefficient

[21]

. The lattice parameters of U, Ti, and Hf at high

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and room temperature are presented in Table 2. The calculated lattice parameter for the UMoNbTaHf alloy was 334.9 pm, which is approximately 0.84% greater than the measured one. According to the EDS data, the compositions of BCC1 and BCC2 in the UMoNbTaTi alloy were U40Mo20Nb14Ta11Ti15 and U11Mo18Nb21Ta28Ti22, respectively. The calculated amix values for the BCC1 and BCC2 phases in UMoNbTaTi were 332.0 and 328.3 pm, respectively. The calculated value for the BCC1 phase was less than the measured value by approximately 0.36%, whereas that of the BCC2 phase was greater than the measured value by approximately 0.09%. The experimental and calculated values of a were similar, indicating that the lattice parameter of the alloys followed the rule of mixture. This indicates that the BCC and dual BCC structures are close to the fully disordered solid solution.

Table 2 Crystsal structure ,atomic radius, vacancy electron concentration, and melting temperature of the constituent elements of the studied alloys.

High temperature

Crystsal structure

Room temperature High

Lattice

temperature

parameter,a,(pm)

Room temperature

U

Mo

Nb

Hf

Ta

Ti

BCC

BCC

BCC

BCC

BCC

BCC

orthorhombic

BCC

BCC

HCP

BCC

HCP

347.2

-

-

355.9

-

330.6

343.3

314.7

330.1

333.9

330.3

327.6

13.9×10−6

-

-

linear thermal

9×10−6

-

10.9×10−6

5

4

5

4

2896

2750

2509

3268

1941

139.0

142.9

157.8

143.0

146.2

Valence electron

-p

coefficient,(K-1) 3

5

1135

Tm, (K)

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3.2 Hardness analysis

157.0

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Atomic radius, r, (pm)

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concentration (VEC) Melting temperature,

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expansion

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Element

Fig. 4 shows the load–displacement curves under nanoindentations for the interdendritic (BCC1 phase) and dendritic regions (BCC2 phase) in the UMoNbTaTi alloy. The hardness (H) and

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contact modulus (Er) were determined based on the loading and unloading curves using the procedure of Oliver and Pharr [30]. The elastic modulus (E) and indentation hardness (HIT) can be evaluated using the following equations:

H IT 

Pmax Ac

1 1  2 1  i2   Er E Ei

(4)

(5)

where Pmax is the maximum indentation load and Ac is the projected contact area for which the second approximation Ac = 24.5hc2 + 2400hc was adopted, where hc is the contact depth. Er is the reduced modulus, and Ei and νi are the Young’s modulus and Poisson’s ratio of the indenter, with

values of 1140 GPa and 0.07, respectively. Each matrix was measured five times to obtain the average elastic modulus and hardness. The calculated elastic modulus and hardness are presented in Table 3. The UMoNbTaHf alloy exhibited the highest hardness of 8.44 GPa, whereas the BCC2 phase of the UMoNbTaTi alloy exhibited a much lower hardness of 4.68 GPa, which is almost half of that of UMoNbTaHf alloy. The ROM approach was used to predict the theoretical hardness values (Hvmix) of the alloys as follows: (6)

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Hmix   ci ( H )i

where ci and Hvi are the atomic fraction and hardness of element i, respectively. The theoretical

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hardness values based on both the designed and analyzed compositions were calculated, as listed

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in Table 3. The directly measured hardness values are approximately 1.2 to 3.4 times greater than the theoretical values. The Hv values of the BCC1 and BCC2 phases of UMoNbTaTi alloy were

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350.09 and 490.03 kg/mm2, respectively, which were lower than those of the UMoNbTaHf alloy. This can be attributed to the presence of the solid-solution strengthening effect via elemental

for hardness.

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interaction. In addition, the elastic moduli of the two alloys follow the same trend as that observed

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Elasticity and plasticity can be obtained based on the load–displacement curves under nanoindentations, which can be used to characterize the relative plastic/elastic behavior of materials under external stress and strain. The fraction of energy dissipation (rd) and elastic recovery work (re) can be defined as follows [31]:

rd 

re 

hf hm

(hm  h f ) hm

(7)

(8)

where hm is the penetration depth of the maximum load and hf is the residual depth measured when the load becomes zero during unloading. The results are presented in Table 3. A low re of 28% and a high rd of 72% were obtained for the BCC1 phase of UMoNbTaTi alloy, indicating that the

phase exhibits good plasticity and poor elasticity. The plasticity of the alloys was in the order of

-p

ro

of

UMoNbTaTi (BCC1) > UMoNbTaTi (BCC2) > UMoNbTaHf.

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Fig. 4 P–h curves under nanoindentation for the UMoNbTaHf alloy and the dendritic and interdendritic regions of

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the UMoNbTaTi alloy tested with a Berkovich indenter.

Table 3. Elastic modulus (E), indentation hardness, theoretical hardness (Hvmix), and experimental hardness (Hv)

Alloy

Structure

E (GPa)

HIT (GPa)

Hv (kg/mm2)

Hvmix (kg/mm2)

rd

re

BCC

171.14

8.44

529.05

183.46

65%

35%

BCC1

100.02

4.68

350.09

233.65

72%

28%

BCC2

165.33

7.52

490.03

145.67

67%

33%

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UMoNbTaHf

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for the UMoNbTaHf and UMoTNbTaTi alloys

UMoNbTaTi

3.3 Compressive properties and fractography Room-temperature compression tests were conducted to investigate the effect of the constituent elements and the structure of the as-cast UMoNbTaHf and UMoNbTaTi alloys on their mechanical properties. Fig. 5 shows the typical engineering stress–strain curves of the alloys. The yield strength σy of the UMoNbTaHf alloy at room temperature was 1147 MPa, and the peak strength was 1505 MPa. The samples exhibited an apparent plastic strain εp of 7.7% before failure. The yield and fracture strengths of the UMoNbTaTi alloy at room temperature were 985 and 1812 MPa, respectively. The maximum compressive strain εp was approximately 39.5%. Thus, the

plasticity of the UMoNbTaTi alloy was considerably greater than that of the UMoNbTaHf alloy, indicating that Ti plays a critical role in improving the mechanical properties of the investigated U-Mo-Nb-Ta system. Fig. 6 shows the fracture surfaces of the two alloys. The fracture surface of UMoNbTaHf showed cleavage steps and river patterns. Fewer cleavage features were observed on the surface of the UMoNbTaTi alloy compared with that of the UMoNbTaHf alloy. The fracture surface of the UMoNbTaTi alloy was covered by fan-shaped cleavage and dimple patterns. Dimples were

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observed along the edge region of the cleavage feature on the surface. The cleavage cracks

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nucleated at a certain point in the new grain, gradually propagated outward in a fan-shaped manner, and expanded to all the grains. Based on the composition of the two BCC phases,

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cleavage and dimple features can be identified for the BCC2 and BCC1 phases. The BCC1 phase

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exhibited larger shear deformation and higher fracture resistance than the BCC2 phase before the

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fracture occurred. The fracture morphologies agree well with the plasticity.

Fig.5 Compressive engineering stress–strain curves of the as-cast UMoNbTaHf and UMoNbTaTi alloys at room temperature

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Fig. 6 SEM images of the fracture surfaces of (a) the UMoNbTaHf alloy, (b) zoom-in image of the blocked area in

4. Discussion

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(a), (c) the UMoNbTaTi alloy, and (d) zoom-in image of the blocked area in (c).

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4.1 Phase formation

Based on the Hume–Rother rules[32], the atomic size difference δ play dominant roles in

controlling the phase selection in HEAs

[33,34].

From the experimental results, solid solutions of

HEAs are favored when −15 < ΔHmix < 5 kJ/mol and δ < 6.6%, and intermetallic compounds are formed when ΔHmix < −15 kJ/mol and δ > 6.6%

[35]

. Yang and Zhang [36] proposed a parameter Ω,

indicating the ratio between the entropy and the enthalpy contributions of a given system at the melting temperature Tm. The solid solution phase can be obtained when Ω ≥ 1.1 and δ ≤ 6.6. The above parameters can predict the possibility of forming solid solutions; however, they cannot be used to differentiate between the structures of these random solid solutions. The introduction of an electronic criterion in HEAs based on VEC was proposed by Guo et al. [37], which provides the basis for the design of solid solution structures. The alloys with VEC < 6.87 seem to promote the stable solid-solution phase of BCC, whereas those with VEC > 8 promote a stable solute solution.

The ΔHmix, VEC, δ, and Ω for the uranium-containing alloys studied here are listed in Table 4. For the UMoNbTaHf and UMoNbTaTi alloys, δ ≤ 5.46 and Ω ≥ 29.9, which approximately satisfy the criterion for the formation of solid solution phases. The VEC is 4.6, which satisfies the boundary condition of the BCC case. Based on the experimental data obtained here, the UMoNbTaHf alloy formed a BCC solute solution phase. However, dual BCC could be observed in the UMoNbTaTi alloy; thus, the ΔHmix, δ, and Ω could not be used to accurately predict the phase selection in the uranium-containing alloy system.

△Hmix

UMoNbTaHf

BCC

−0.48

BCC1 +

BCC2

−0.96

Δ × 100

Ω

4.6

5.46

59.5

4.6

4.67

29.9

re

UMoNbTaTi

VEC

ro

Structure

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Alloys

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Table 4. The calculated parameters △Hmix, VEC, δ, and Ω of the studied alloys

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To interpret the phase formation of the dual phase alloy, fig. 7 shows the forming process of the BCC1 phase (U-rich) and the BCC2 phase (U-poor) found in the UMoNbTaTi alloy. The

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formation process can be divided into three stages. In the first stage, the matrix UMoNbTaTi forms a stable BCC phase when the U levels are low and each atom in the phase randomly occupies the crystal lattice (Fig. 7(a)). Then, the local compressive strain in the matrix continues

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to increase as the U content increases, resulting in large distortion energy in the lattice. At this point, a portion of the U atoms can no longer be incorporated in the matrix; thus, it forms a new phase (U-rich phase). Then, the distortion energy in the matrix is released (Fig. 7(b)). Finally, both the U-rich and U-poor phases exist in the system (Fig. 7(c)). This hypothesis was indirectly supported by EDS maps, because of the EDS maps showing the dual BCC phases were U-rich and Mo, Nb, Ta-rich(refer to Fig. 3). The

BCC1 phase(U-rich) was determined to be

U40Mo20Nb14Ta11Ti15, and the BCC2 phase(U-poor) was U11Mo18Nb21Ta28Ti22. The two phases continued to increase in the system. To further expound upon the mechanism, the lattice distortions near each element in UMoNbTaHf and UMoNbTaTi alloy were calculated. In multi-component alloys, each atom occupies the crystal lattice site and can be considered as a solution atom. Thus, the variations in

the size of these atoms can generate elastic distortion of the lattice. Then, the lattice distortion δai (per atom pair) is estimated as the average of the atomic size difference of this element with respect to its neighbors. Each solute in the BCC crystal lattice has eight nearest-neighbor atoms, forming a nine-atom cluster. Then, the lattice distortion δai (per atom pair) near an element i is estimated as an average of the atomic size difference of this element with its neighbors [9].

 ai 

9  c j aij 8

(9)

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where cj is the atomic fraction of the j element in the alloy and δaij = 2(ri − rj)/(ri + rj) is the atomic size difference with respect to the elements i and j. Tables 5 and 6 present the lattice distortions

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near each element in the UMoNbTaHf and UMoNbTaTi alloys. In case of the UMoNbTaHf alloy,

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smaller elements, including Mo, Ta, and Nb, produce local tensile strain, whereas the larger elements, such as U and Hf, produce local compressive strain (δai = 0.06–0.07). In the

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UMoNbTaTi alloy, Hf was replaced by Ti. The radius of Hf is approximately 10% larger than that

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of Ti. As expected, the smaller elements, i.e., Mo, Nb, Ti, and Ta, produced local tensile strain. Conversely, the largest element, U, produced local compressive strain (δai = 0.09). Uranium atoms

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have large lattice strain in UMoNbTaTi. The crystal lattice exhibits considerable lattice distortion energy, which reduces the matrix stability. Table 5. Relative atomic size difference and δaij of the alloying element pairs for the UMoNbTaHf alloy

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i

U

Mo

Nb

Ta

Hf

δai

U

0

0.12

0.094

0.094

-0.013

0.06

Mo

-0.12

0

-0.028

-0.028

-0.13

-0.06

Nb

-0.094

0.028

0

0

-0.1

-0.03

Ta

-0.094

0.028

0

0

-0.1

-0.03

Hf

0.013

0.13

0.1

0.1

0

0.07

j

Table 6. Relative atomic size difference and δaij of the alloying element pairs for the UMoNbTaTi alloy j

U

Mo

Nb

Ta

Ti

δai

U

0

0.12

0.094

0.094

-0.013

0.09

Mo

-0.12

0

-0.028

-0.028

-0.05

-0.05

Nb

-0.094

0.028

0

0

-0.023

-0.02

Ta

-0.094

0.028

0

0

-0.023

-0.02

Ti

-0.074

0.05

0.023

0.023

0

0.005

i

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Fig. 7 Formation process of the BCC1 and BCC2 phases in the UMoNbTaTi alloy

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4.2 Relation between the microstructure and mechanical properties of the alloys

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In the UMoNbTaHf alloy, each atom can be considered as a solution atom. The radius of the U and Hf atoms are larger than those of other elements in the alloy system; thus, the lattice distortion

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is increased. The entire solute matrix would result in a high solution-hardening effect. In addition, the mixing enthalpy of Hf and Mo with other elements are more negative than that of Ti with the

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four elements, indicating that the binding energy of Hf and U with Mo, Nb and Ta are high (Table 7). This also results in a strong hardening effect. The decrease in ductility can be attributed to the

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effect of increased strength, which hinders plastic deformation. However, further study is required to clarify this mechanism. Based on the hardness analysis, the BCC1 phase is softer than the BCC2 phase in UMoNbTaTi

alloy. The yield strength could be obtained from the equation developed by Pavlina and Van Tyne[38] , in which the yield strength of an alloy is related with the Vickers hardness: σy (MPa) = −90.7 + 2.876 × Hv (kgf/mm2). In this study, ROM was used to analyze the contribution of the dual phase of the UMoNbTaTi alloy as σymix ≈ f1σy1 + f2σy2 = 1213 MPa, where f1=0.275, σy1 =916MPa , f2=0.725, σy2=1318 MPa. The number is about 22% higher than the experimentally measured one of 985 Mpa. This can be considered as a good agreement. According to the deformation state of the constituent phases, the inhomogeneous deformation of two-phase materials can be classified into three stages [39]. First, the constituent phases are in the elastic stage; second, one of the constituent phases is in the plastic stage, whereas the other phases remain in the

elastic stage; third, the constituent phases are in the plastic stage. The stress and strain in the BCC1 and BCC2 phases were almost the same in the first stage because there was no large difference between the Young’s modulus values of the constituent phases. In the second stage, BCC1 is plastically deformed, whereas BCC2 remains elastically deformed because the BCC1 phase is softer than the BCC2 phase. The third stage begins when the stress in the BCC2 phase becomes greater than its yield strength. Consequently, both the phases deform plastically. Table 7. Mixing enthalpy △Hmix (kJ/mol) of different atom pairs U

Nb

Hf

Mo

0

4

−1

2

-

0

4

−6

Hf

-

-

0

Mo

-

-

-

Ti

-

-

-

Ta

-

-

-

Ta

0

3

2

0

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U Nb

Ti

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△Hmix

0

−2

0

−4

−5

-

0

1

-

-

0

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−4

Inhomogeneous deformation can be generally observed in deforming materials.The fractured

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UMoNbTaTi sample was cut parallel to the compression direction; the morphology and location of microholes and microcracks are shown in Fig. 8, microcracks in the BCC2 phase (see arrows in

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the Fig.8(a)) and ductile microholes at the phase interface (see circles in the Fig.8(a)). Microcracks appeared in the BCC2 phase when there was no large deformation zone in the BCC1

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phase. Additionally, the separation of the two-phase interface was observed. A slight deformation would cause cracks in the BCC2 phase because of its poor plasticity. After crack formation, its tip passes through the BCC2 phase and eventually propagates and connects to each other, resulting in brittle fracture(see crack in Fig.8(b) and Fig.8(c)). The inhomogeneous deformation of the two phases causes poor coordination of the phase interface and the formation of ductile holes. These types of ductile holes do not propagate easily; thus, UMoNbTaTi exhibits relative high plasticity (see the dimples at the fracture; Fig. 6(d)).

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Fig. 8 Morphology and location of microholes and microcracks in the UMoNbTaTi alloy

We present the nucleation, growth, and connection process of the microcracks and microholes during the deformation of the UMoNbTaTi alloy to explain its failure mechanism, as shown in Fig.

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9. From the above discussion based on the characteristics of the UMoNbTaTi alloy, the BCC2 phase is not completely continuously distributed in the BCC1 phase. In the early stage of the compression process, the BCC1 phase is plastically deformed before the BCC2 phase and bears a larger amount of deformation. As the stress increases, it would be difficult for the BCC2 phase to deform continuously in space. The small deformations in the BCC2 phase would be hindered by the BCC1 phase, making the stress concentration not to be relaxed effectively , therefore, in the region of stress concentration, a large number of microvoids can be observed in the BCC2 phase before the matrix breaks (Fig. 9(b)). The fracture of the specimen is mainly caused by the connection of microcracks in the direction of stress concentration, and these crack tips pass through the BCC2 phase in a cleavage fracture mode. They eventually expand and connect to each other, resulting in the brittle fracture of the specimen.

Fig. 9 Cracks and microholes in the UMoNbTaTi alloy during the compression process

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5. Conclusions Two uranium-containing HEAs, i.e., UMoNbTaHf and UMoNbTaTi, were prepared with equal

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molar ratios. Based on the obtained analysis results, the following conclusions are drawn.

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(1) The two alloys formed a solid solution. The as-cast UMoNbTaHf alloy has a BCC

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structure with a lattice parameter of 332.1 pm. The local compressive stress of the U atoms in the crystal lattice of the UMoNbTaTi alloy is large, resulting in the formation of BCC1 (U-rich) and

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BCC2 (U-poor) phases in the matrix. The measured components of the two phases are U40Mo20Nb14Ta11Ti15 and U11Mo18Nb21Ta28Ti22, and the lattice parameters of these components

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are 333.2 and 328.0 pm, respectively.

(2) Based on the nanoindentation experimental measurement, E = 171.14 GPa and HIT = 8.44

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GPa for the UMoNbTaHf alloy. The local compressive stress of the UMoNbTaTi alloys resulted in E = 100.02 GPa and HIT = 4.68 GPa for the BCC1 phase and E = 165.33 GPa and HIT = 7.52 GPa for the BCC2 phase. Based on the elasticity and plasticity indexes under stress and strain, both the alloys exhibited high plasticity and low elasticity. The plastic deformation capacity of the alloys is in the following order

UMoNbTaTi (BCC1) > UMoNbTaTi (BCC2) > UMoNbTaHf.

(3) The room-temperature compressive yield strengths of the UMoNbTaHf and UMoNbTaTi alloys were 1147 and 985 MPa, respectively, and the fracture strains were 7.7% and 39.5%, respectively. The strength and plasticity of the UMoNbTaTi alloy were better than those of the UMoNbTaHf alloy. The fracture surface of the former showed a mixture of shallow dimples and cleavage features, whereas that of the latter exhibited typical cleavage features. (4) The deformation process of the UMoNbTaTi alloy was conducted under the coordination of

BCC1 and BCC2. Thus, the plastic deformation ability of the BCC1 phase was better than that of the BCC2 phase, and the main source of cracks in the alloy was the brittle crack of the BCC2 phase. Acknowledgement

The authors would like to thank Dongli Zou and ruiwen Li for their as-sistance, and Yanzhi Zhang ,Min Wang and Ce Ma for helpful discussions. This work was supported by the Fund of the

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Key Laboratory of Surface Physics and Chemistry (XKFZ201902) and the Innovation Fund of

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Materials Research of the Chinese Academy of Engineering Physics (CX201909).

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Author statement

Jie Shi: Writing-Original Draft preparation, Validation.

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He Huang: Methodology, Editing. Guichao Hu: Validation, Editing.

Chunli Jiang: Methodology.

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Haiyan Xu: Conceptualization, Methodology.

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Pengguo Zhang: Validation.

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Chao Luo: Conceptualization, Methodology, Supervision, Editing.

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

High lights 1. The effect of Ti and Hf on the microstructure and mechanical properties in UMoNbTaX is determined. 2. Microstructure evolves from single BCC to dual BCC phase with Hf replaced by Ti in UNbMoTaHf alloy.

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3. High strength with promising ductility was acquired in as-cast UMoNbTaTi alloy.

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4. Microcracks propagation in the BCC2 phase rather than the BCC1 phase.