Mechanical behaviors of AlCrFeCuNi high-entropy alloys under uniaxial tension via molecular dynamics simulation

Abstract

Although a high-entropy alloy has exhibited promising mechanical properties, little attention has been given to the dynamics deformation mechanism during uniaxial tension, which limits its widespread and practical utility. According to the experiment, an atomic model AlCrFeCuNi HEA was built using a melting and quick quenching method. In this work, the mechanical behaviors of the AlCrFeCuNi high-entropy alloy under uniaxial tensile loading are studied using atomistic simulation to investigate the evolution of dislocation and stacking fault as well as deformation twinning. The results show that calculations for the elastic properties and stress–strain relations are in excellent agreement with recent experimental results. Above all, the AlCrFeCuNi1.4 HEA not only has high strength, but also exhibits good plasticity which is qualitatively consistent with the experiment. Similar to the mechanical properties of single-crystal metals, stress fluctuation during plastic deformation of the high-entropy alloy is always accompanied with the generation and motion of dislocation and stacking fault with the increase of strain. In addition, the dislocation–dislocation interaction, dislocation–solid solution interaction, deformation twinning and detwinning occur after the yield point. Furthermore, the dislocation gliding, dislocation pinning due to the severe lattice-distortion and solid solution, and twinning are still the main mechanisms of plastic deformation in the AlCrFeCuNi1.4 high-entropy alloy. This atomistic mechanism provides a fundamental understanding of plastic deformation in a high-entropy alloy.

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1. Introduction

Recently, the high-entropy alloy (HEA) has attracted increasing attention because of its superior strength, strong hardness and good wear resistance.^1–3 This kind of HEA is commonly composed of at least five components with each ranging from 5 to 35% in molar ratio,⁴ and usually possesses simple solid solution structures. Therefore, it is used in critical functional applications, such as aerospace materials, damage resistant materials, and tool materials from the macro-scale to micro-scale. So far, numerous studies have been aimed to understand the deformation behaviors of the HEA.^1–8

Among the investigated HEA systems, the classic systems of AlxCoCrCuFeNi have been widely studied.^3–8 For example, the fatigue behavior of an Al0.5CoCrCuFeNi HEA is demonstrated.⁹ Encouraging fatigue resistance characteristics are found due to the prolonged fatigue lives of various samples at relatively high stresses. A five-element HEA CrMnFeCoNi is examined,¹⁰ which revealed a fracture transition from planar-slip dislocation activity at room temperature to deformation by mechanical nanotwinning with decreasing temperature. Until recently, a fresh AlCrCuFeNi system is introduced into the alloy design and development of the HEAs due to cost consideration.¹¹ For example, with increasing Al content or Ni content, a FCC to BCC phase transformation in the AlxCrCuFeNix system is reported.^12,13 The phase stability, microstructural evolution, hardness, and compression performance of the as-cast and -annealed AlxCrCuFeNi2 HEAs are explored.¹² The microstructural features and tensile behaviors of the Al0.5CrCuFeNi2 HEA by cold rolling and subsequent annealing are investigated.¹⁴ Subsequently, the compression responses of the AlCrCuFeNi2 HEA under different strain rates are studied.¹⁵ In addition, anomalous solidification behavior, sunflower-like morphology, slow diffusion kinetics, and near-eutectic microstructure are also found in this alloy system.¹⁶ Recently, by means of molecular dynamics (MD) simulations, the elastic and plastic deformations of indentation in the FeCrCuAlNi HEA are studied.¹⁷ Compared with the conventional alloy, equal element addition can significantly improve the mechanical properties of the HEA.¹⁷

Just as mentioned above, previous experimental results aimed to understand the mechanical behaviors of the HEA.^4–18 In order to further study and optimize the mechanical properties of the HEA, the underlying mechanism of deformation in the HEA has become a significant challenge. It is rather difficult to directly observe the plastic deformation processes of the AlCrFeCuNi HEA by in situ experiments with nanoscale resolution,^4–18 while MD simulations could provide a powerful tool to gain deeper understanding of the deformation mechanism of the nanoscale AlCrFeCuNi HEA. To address this need, here MD simulations are used to analyze the AlCrFeCuNi1.4 HEA plastic behaviors during the uniaxial tension process.¹⁹ Additionally, the tensile behavior and strengthening mechanism of the AlCrFeCuNi1.4 HEA are discussed in detail.

2 Computational methods

2.1 Potential function

For MD simulation, reliable force fields are very important to obtain reasonable results. In the present model, the empirical embedded-atoms method (EAM) potential is adopted to describe the interactions of Cr–Fe–Ni,²⁰ Cu–Cu,²¹ and Al–Al.²² The EAM potential is expressed as a multi-body potential energy function in the following form:²³where the total energy E is the total energy of the atomistic system which comprises the sum of the embedding energy F on atom i and the short-range pair potential energy ϕ, ρ the electron density, and α, β the element types of atoms i and j. The embedding energy is the energy to put atom i in a host electron density at the site of that atom. The pair potential term ϕ is the electrostatic contributions.

However, there is no existing potential function to describe the remaining atomic interactions, including Cu–Cr, Cu–Fe, Cu–Ni, Al–Cr, Al–Fe, Al–Ni, and Cu–Al. Here, Morse potential is adopted to depict their interactions. The total energy U is expressed as:

U = D{exp[−2α(r_ij − r₀)]−2 exp[−α(r_ij − r₀)]} (2)

where D is the cohesion energy, α is a constant parameter, r_ij is the distance between the two atoms, and r₀ is the distance at equilibrium. The Morse potential parameters can be estimated using mixing rules.²⁴ The Lorentz–Berthelot mixing rule is used to estimate the interatomic Morse potential for materials A and B with parameters D, r₀, and α for a mixed pair of atoms using the following formulas:²⁴

α_A–B = (α_A + α_B)/2 (4)

σ_A,B = r_0A,B − ln 2/α_A,B (6)

where the fitted dimer energy is D_A–B, the lattice constant is α_A–B, and the equilibrium distance is r_0A–B for materials A and B. Using eqn (3)–(6), the related parameters of Morse potential are described in Table 1.

Table 1 Morse parameters of the AlCrFeCuNi HEA

Atom pair	D (eV)	α (Å^−1)	r0 (Å)
CrCu	0.38904	1.4654	2.6289
FeCu	0.37832	1.3736	2.6454
NiCu	0.37972	1.3893	2.6182
CrAl	0.34541	1.3685	2.8199
FeAl	0.33589	1.2767	2.8376
NiAl	0.33713	1.2924	2.8083
CuAl	0.30444	1.2919	2.8431

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To show the validity of the present mixing potentials, the distribution of cohesive energy with atomic density for the AlCrFeCuNi HEA with a variety of lattice parameters is plotted in Fig. 1. The different lattice parameters are chosen around the average lattice parameter which will be described later. As shown in Fig. 1, there exists a minimum cohesive energy for the FCC solid solution which is the stable phase of the alloy due to low lattice energy.^21,25 The MD results are in good agreement with the experimental results,^13–15 in which the AlCrFeCuNix HEA is composed of the FCC phase and BCC phase. According to the experiment,¹³ the AlCrFeCuNi1.4 HEA has a greater proportion of the stable FCC phase up to 51.6%, therefore, it is selected as a reasonable research object.

Fig. 1 The distribution of cohesive energy with atomic density for different crystal structures with a variety of lattice parameters around the average lattice parameter.

2.2 AlCrFeCuNi HEA model

Some experiments show that the AlCrFeCuNi1.4 HEA is synthesized by the arc melting and casting method.¹³ Using the MD method, Fig. 2 simulates the process of AlCrFeCuNi1.4 HEA preparation according to the experiment, as follows: (a) atoms of the AlCrFeCuNi1.4 HEA are randomly positioned at FCC crystal structure sites at 300 K, (b) in the melt stage, all atoms are heated at 0.04 K fs⁻¹ to 1500 K and their velocities are relaxed to a position of equilibrium at 1500 K, and (c) in the quenching stage, quick quenching is simulated by reducing the environmental temperature by quenching at 0.04 K fs⁻¹ to 300 K, and relaxed to a position of equilibrium at 300 K.

Fig. 2 The flow chart of preparation of the AlCrFeCuNi1.4 HEA.

In addition, the lattice parameter of AlCrFeCuNi1.4 can be determined as follows: (a) according to the lattice parameter of the single element (Fe, Cr, Cu, Al and Ni), the maximum value of the lattice parameter a₀ is chosen to build the initial MD model of AlCrFeCuNi1.4. Here, the length dimension along the x-direction of the MD model is L₀; (b) the MD system undergoes heating to 1500 K, maintaining at 1500 K, and fast cooling to 300 K, as shown in Fig. 2. Here, we can obtain the new model size L₁ along the x-direction; (c) the new lattice parameter of AlCrFeCuNi1.4 a₁ is a₁ = a₀L₁/L₀; (d) using the above method, we change the original size of the simulation to obtain a series of lattice parameters a_i, and calculate the average lattice parameter , which is regarded as a lattice parameter of the AlCrFeCuNi1.4 HEA.

2.3 Uniaxial tensile loading

Fig. 3 shows that the sizes of the AlCrFeCuNi1.4 HEA model are 20a × 20a × 50a (a is the lattice constant), which are much larger than any of the cut-off distances in three dimensions, causing the atom interactions to vanish. As shown in Fig. 3, the periodic boundary conditions are used in the x-, y- and z-directions. There are 8 × 10⁴ atoms in the MD simulation for the AlCrFeCuNi1.4 HEA. The temperature of the system is controlled at approximately 300 K with an isobaric–isothermal (NPT) ensemble, so that thermal effects can be eliminated. The motion equations are integrated using the Verlet leapfrog method with a time step of 1 fs. Before tensile loading, the model is firstly relaxed for 100 ps to get an equilibrium state at 300 K. The strain rate of uniaxial tensile loading along the z direction is about 1 × 10⁹ s⁻¹ in MD simulations. In this study, MD simulation is implemented in the LAMMPS,²⁶ and OVITO is adopted for visualizing the evolution of the atomic structure.²⁷

Fig. 3 Schematic of conventional tensile specimen, and schematic of the atomic AlCrFeCuNi1.4 HEA sample for MD simulations under tensile loading, in which the arrows indicate the loading directions. Cr, Fe, Ni, Cu, Al.

3. Results and discussion

3.1 Elastic deformation behavior

Fig. 4a shows the compressive stress–strain curves of the AlCrFeCuNix (x from 0.6 to 1.4) HEA with different contents of Ni at room temperature, where the curves a–e are obtained from the experimental data,¹³ and the curves f–j are obtained from the MD simulation. Comparison of the experiment and MD simulation in Al0.5CrCuFeNi2 (ref. 14) and AlCrCuFeNi2 (ref. 15) is presented in Fig. 4b and c. From Fig. 4, in the elastic stage the MD simulation results are consistent with the experimental results, while the nanostructure AlCrFeCuNix exhibits high yield strength and good plastic behavior which deviates from the experimental results due to smaller and stronger mechanical properties in nanoscale metamaterials.²⁸ Furthermore, according to the stress–strain curve and through linear fitting, we can obtain Young’s modulus, which is one of the important characterizations of mechanical properties of materials. In classical mechanics, Young’s modulus is defined as:

E = σ/ε (7)

where σ is axial stress, and ε is the strain. According to eqn (7), the values of Young’s modulus are obtained from the slope of linear stress–strain elastic deformation. Here, Young’s modulus of the AlCrFeCuNix HEA is about 125 GPa, which is very close to that of the experimental result, 118 GPa.

Fig. 4 (a) The compressive stress vs. strain curves of AlCrFeCuNix (x from 0.6 to 1.4) HEAs with various content of Ni: x = 0.6 for curve a, x = 0.8 for curve b, x = 1.0 for curve c, x = 1.2 for curve d, and x = 1.4 for curve e in experiment,¹³ and x = 0.6 for curve f, x = 0.8 for curve g, x = 1.0 for curve h, x = 1.2 for curve i, and x = 1.4 for curve j in MD simulation. (b) The true tensile stress–strain curves of Al0.5CrCuFeNi2 in experiment¹⁴ and MD simulation. (c) The compressive stress–strain curves of AlCrCuFeNi2 in experiment¹⁵ and MD simulation.

3.2 Plastic deformation behavior

Fig. 5 depicts the stress vs. strain curve of the AlCrFeCuNi1.4 HEA under uniaxial tensile loading, where the curve can be obtained from the statistical fluctuations of the 10 times MD simulation data for eliminating the randomness inherent to the NPT ensemble. As a result, at the initial deformation stage the stress is a linear increase with the increase of strain, which is similar to the mechanical behavior of the single-crystal metals. On the other hand, the behavior of the AlCrFeCuNi1.4 HEA is closer to the ideal elastic–plastic behavior, indicating a homogeneous plastic flow, and this result agrees with the previous reports.^3,13–15 To understand the plastic deformation, the microstructural evolution for the AlCrFeCuNi1.4 HEA is examined, and a series of snapshots of deformation are shown in Fig. 5a–e. The elastic deformations are illustrated in Fig. 5a in the initial deformation stage (ε < 9.1%), in which the stress increases linearly with the increase of the applied strain. After the yield point, the shape of the substrate has an obvious change, as seen in Fig. 5b–d. The largest plastic deformation of the AlCrFeCuNi1.4 HEA has been observed in Fig. 5e at a strain of 25%, in which the plastic deformation is triggered by the nucleation and motion of dislocations. Further analysis of the deformation mechanism will be revealed in a later section.

Fig. 5 The tensile stress–strain curve, and the sequence of snapshots capturing the atomic deformation process for the AlCrFeCuNi1.4 HEA under z-direction uniaxial tension in a–e.

According to the local crystalline classification visualized by common neighbor analysis (CNA), each atom is colored for identifying the defects of the AlCrFeCuNi1.4 HEA.²⁹ Based on this coloring method, different atomic structures can be distinguished, for example, green represents FCC atoms, blue represents BCC atoms, red represents HCP atoms and gray stands for disordered atoms that do not satisfy any kind of fundamental atomic structures, as illustrated in Fig. 6. It is well known that a single layer composed by HCP atoms means a twin boundary (TB), two adjacent HCP layers mean an intrinsic stacking fault (ISF), and two HCP layers with a FCC layer mean an extrinsic stacking fault (ESF) between them. As shown in Fig. 6, the embryos of ISF occur with the increase of strain. The formations of deformation twinning and ESF are observed in Fig. 6b–d. In addition, twin growth can be found in further plastic deformation stages (Fig. 6a–d and 7c), and secondary ISF and ESF can be formed in the primary ISF (Fig. 6b–d). It is observed that the secondary partial dislocations can be blocked by primary ISF. Hence, the propagation of deformation twinning enhances the plasticity of the AlCrFeCuNi1.4 HEA. In addition, dislocations impact the TB (see, Fig. 6c–e), and detwinning occurs (see, Fig. 7b–i). With modeling and analysis of defect evolution, it may provide an in-depth mechanism for the plastic deformation of the HEA materials.

Fig. 6 The microstructure of AlCrFeCuNi1.4 under different strains: (a) 9.1%, (b) 11.7%, (c) 15.2%, (d) 18.8%, and (e) 25%.

Fig. 7 Zoomed-in atomic image showing the deformation twinning in single-crystal Cr (a) at a strain of 25%, the deformation twinning and detwinning in HEA at a strain of 14.3% (b and c), 21.2% (d and g), 23.3% (e and h), and 24.3% (f and i).

A comparison of microstructure evolution in the AlCrFeCuNi1.4 HEA and single element metals is shown in Fig. 8 and 9. A large number of ISFs are found to occur in the AlCrFeCuNi1.4 HEA. More slip systems are activated in the AlCrFeCuNi1.4 HEA, and a slip occurs on a series of connected {1 1 1} planes for AlCrFeCuNi1.4 HEA and single element metals, resulting in good plastic behavior. The presence of slip bands for different metals are seen in Fig. 8. Deformation twinning in the HEA occurs at a strain of 14.3% (see, Fig. 7b and c), while the reversible detwinning is observed on further loading (see, Fig. 7b–i). For a large strain of 25%, there is a presence of twin formation in Cu, Ni, and Cr (see, Fig. 7a and 8). In addition, ESFs are mainly concentrated in the AlCrFeCuNi1.4 HEA. Compared with single element metals, a significant amount of cross-slip occurs in the AlCrFeCuNi1.4 HEA under a 25% strain (Fig. 8 and 9), allowing dislocation to move in other (1 1 1) planes. This phenomenon is found in BCC single-crystal Fe nanopillars under compression.³⁰ The AlCrFeCuNi1.4 HEA can form a FCC solid solution over a wide range of compositions^13–15 (see, Fig. 7a–c and 8), and has low stacking fault energy (SFE).³¹ The low SFE in HEA causes an atom slip easily during the deformation process, as shown in Fig. 8. For the low SFE HEA, perfect dislocation dissociates more energetically into partial dislocations, and the stacking fault width is larger, resulting in difficulty to cross-slip and climb.³¹ This reason leads to the plasticity of the HEA being better than that of traditional crystalline metals, which is quite consistent to the experimental results of previous work.^3,31

Fig. 8 Comparison of the microstructure in the AlCrFeCuNi1.4 HEA (a) and single element metals Al (b), Cu (c), Fe (d), Ni (e), and Cr (f) at a 25% strain (green atoms are FCC while atoms are at dislocation cores, and red atoms are at stacking faults).

Fig. 9 Comparison of the microstructure evolution in the AlCrFeCuNi1.4 HEA (a) and single element metals Al (b), Cu (c), Fe (d), Ni (e), and Cr (f) at a 25% strain. All non-FCC atoms are removed by CNA (while atoms are at dislocation cores, and red atoms are at stacking faults).

Fig. 10 demonstrates atom displacement with the increase of strain. The atoms are colored according to the atom displacement, where red atoms illustrate higher displacement. Fig. 10a represents deformation near the yield point, Fig. 10b corresponds to deformation after the yield point, Fig. 10c means the peak value of sawtooth fluctuation in the stress curve, Fig. 10d shows the bottom value of sawtooth fluctuation in the stress curve, and Fig. 10e corresponds to the largest strain of 25%. The atoms in the substrate move non-linearly, resulting in a jagged shape in the surface of the AlCrFeCuNi1.4 HEA. The more overlapping zigzag shape reveals the dislocation slipping dependent atom displacement (Fig. 7 and 10). The comparison of atom displacement in the AlCrFeCuNi1.4 HEA and single element metals is reported in Fig. 11. The low value of atom displacement is concentrated in the middle region of the substrate, and the high value of that is located in the end of the substrate. The jagged shape in atom displacement shows the anisotropic slip amplitude of the AlCrFeCuNi1.4 HEA and single element metals. The region of high displacement is largest in Al, and the region of low atom displacement is larger in the AlCrFeCuNi1.4 HEA and Fe. This is due to interactions between dislocations and solute atoms inducing the dislocation pining effect.³²

Fig. 10 Atom displacement of the AlCrFeCuNi1.4 HEA under different strains: (a) 9.1%, (b) 11.7%, (c) 15.2%, (d) 18.8%, and (e) 25%.

Fig. 11 Comparison of atom displacement in the AlCrFeCuNi1.4 HEA (a) and single element metals Al (b), Cu (c), Fe (d), Ni (e), and Cr (f) at a 25% strain.

The shear localization under uniaxial loading using MD simulations is demonstrated in Fig. 12. According to the local atomic shear strain,³³ atoms are colored in Fig. 12, where the red atoms have high local atomic shear strains. It is well known that when plastic deformation of alloys occurs, the deformation transformation from the essentially smooth deformation pattern to the highly localized deformation leads to the formation of a shear band (SB). As shown in Fig. 12, a series of SB formations and propagations occur. It can be seen that the SB always initiates from the end of the substrate and subsequently propagates rapidly across the substrate in Fig. 12b, leading to a sudden stress drop (see Fig. 5). From Fig. 12b–e, many shear bands and shear transformation zones are found to extend. The substrate eventually ruptures when the SB penetrates into the whole substrate. The stress concentration contributes to the formation of the SB, causing a reduction of the strength of the HEA. Hence, the dislocation gliding is the main mechanism of plastic deformation. The AlCrFeCuNi1.4 HEA is composed of various kinds of elements with equimolar and high chemical disordering. The plastic deformation mechanism depends on the just location in between the conventional alloys and the single element metals. In Fig. 13, atomic strain distribution shows that a significant amount of dislocation slipping occurs in the AlCrFeCuNi1.4 HEA and single element metals under a tension of 25%. Compared to single element metals, the AlCrFeCuNi1.4 HEA has a significant shear band due to the dislocation and solute atom interaction inhibiting the movement of dislocations and activating more slip systems.

Fig. 12 Shear strain of the AlCrFeCuNi1.4 HEA at (a) 9.1%, (b) 11.7%, (c) 15.2%, (d) 18.8%, and (e) 25% tensile strain.

Fig. 13 Comparison of shear strain in the AlCrFeCuNi1.4 HEA (a) and single element metals Al (b), Cu (c), Fe (d), Ni (e), Cr (f) at a 25% strain.

Based on the dislocation extraction algorithm (DXA),³⁴ the tension mechanism of the AlCrFeCuNi1.4 HEA is clearly the dislocation–dislocation interaction, as shown in Fig. 14, where dislocation structures obtained at different strains are observed. As a result, the dislocation number increases rapidly for strains from 9.1% to 11.7%, followed gradually for strains from 11.7% to 25%. It means that the dislocation number depends significantly upon the strain. After reaching a critical stress, partial dislocation emission is observed in slip planes (1 1 1), (1 −1 1), and (−1 1 1), as shown in Fig. 14a. Followed by nucleation of dislocation, a slip caused by dislocation gliding in the three slip planes reduces the stress concentration. In Fig. 14, the reflected dislocations meet with the emitted dislocations, and then either annihilate or react with each other, resulting in the formation of some defects, such as vacancies and new dislocations.¹⁷ The relatively complete and long Shockley partial dislocations appear at a strain of 25%, while the short Shockley partial dislocations concentrate upon low strain. In addition, there are massive perfect dislocations at high strain compared with the low strain. Fig. 15 shows the dislocation evolution in the AlCrFeCuNi1.4 HEA and single element metals under tension. The dislocations themselves are effective obstacles for dislocation motion, resulting in strengthened materials.³⁵ Hence, the dislocation density ρ on the flow stress of the deforming material is studied, which is defined in the ratio of the total length of dislocation lines L and the volume of the crystal V (ρ = L/V). As a result, dislocation density of the HEA is 8.469 × 10²⁷ m⁻², that of Cr is 3.122 × 10²⁷ m⁻², that of Al is 2.902 × 10²⁷ m⁻², that of Cu is 6.539 × 10²⁷ m⁻², that of Fe is 5.720 × 10²⁷ m⁻², and that of Ni is 4.763 × 10²⁷ m⁻². It can be seen that the dislocation density in the HEA has a maximum value, casing a strong work hardening. It can reveal that the dislocation mechanism plays a key role in the high strength of the AlCrFeCuNi1.4 HEA. In addition, compared with the single element metals such as Al and Cr, there are the massive Hirth dislocations and stair-rod dislocations in the AlCrFeCuNi1.4 HEA, to further enhance the strength of the HEA because of the Lomer–Cottrell lock.

Fig. 14 Dislocation evolution of the AlCrFeCuNi1.4 HEA under different strains: (a) 9.1%, (b) 11.7%, (c) 15.2%, (d) 18.8%, and (e) 25%. Dislocation segments extracted by DXA, colored by the magnitude of Burgers vector. The blue line represents perfect dislocation, the green line is Shockley partial dislocation, the red line other, the sky blue line is Frank partial dislocation, the pink line is stair-rod dislocation, and the yellow line is Hirth dislocation.

Fig. 15 Comparison of dislocation evolution in the AlCrFeCuNi1.4 HEA (a) and single element metals Al (b), Cu (c), Fe (d), Ni (e), Cr (f) at a strain of 25%.

4. Conclusions

In summary, plastic deformation mechanisms of the AlCrFeCuNi1.4 HEA under different strains are revealed using MD simulations, in terms of the strain–stress relationship, dislocation evolution, shear strain, and atomic displacement. It is noted from MD simulations that the distributions of shear strain and atomic displacement are sensitive to high strain. Atomistic simulation also has been carried out to investigate the dislocation evolution in the AlCrFeCuNi1.4 HEA. The dislocation pinning due to the severe lattice-distortion effect and solid solute effect is the principal mechanism of plastic deformation in the AlCrFeCuNi1.4 HEA. In addition, the partial dislocation and stacking fault interaction may produce the Lomer–Cottrell lock, causing hardening effects with the increase of strain. The plastic deformation mechanism of the AlCrFeCuNi1.4 HEA with equi-molar elements and high chemical disordering depends on the just location in between the conventional alloys and the single element metals. This study could contribute to atomic-scale insights into the deformation mechanisms of the AlCrFeCuNi1.4 HEA, which may provide guidance for the future development of robust HEA materials.

Acknowledgements

The authors deeply appreciate the support from the NNSFC (11372103 and 11572118), the Hunan Provincial Science Fund for Distinguished Young Scholars (2015JJ1006), the Fok Ying-Tong Education Foundation, China (141005), the project of Innovation-driven Plan of Central South University, the State Key Laboratory of Powder Metallurgy, the Doctoral Research Innovation Projects of Hunan Province (CX2015B086) and the China Scholarships Council program (CSC, no. 201506130055).

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