Fluctuations in stacking fault energies improve irradiation tolerance of concentrated solid-solution alloys

Journal Pre-proof Fluctuations in stacking fault energies improve irradiation tolerance of concentrated solid-solution alloys Shijun Zhao PII:

S0022-3115(19)30559-8

DOI:

https://doi.org/10.1016/j.jnucmat.2019.151886

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NUMA 151886

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Journal of Nuclear Materials

Received Date: 29 April 2019 Revised Date:

5 November 2019

Accepted Date: 6 November 2019

Please cite this article as: S. Zhao, Fluctuations in stacking fault energies improve irradiation tolerance of concentrated solid-solution alloys, Journal of Nuclear Materials (2020), doi: https://doi.org/10.1016/ j.jnucmat.2019.151886. 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. © 2019 Published by Elsevier B.V.

Fluctuations in stacking fault energies improve irradiation tolerance of concentrated solid-solution alloys Shijun Zhaoa,∗ aDepartment

of Mechanical Engineering, City University of Hong Kong, China

Abstract Concentrated solid-solution alloys (CSAs) have stimulated great interest over recent years because of their excellent mechanical properties and irradiation tolerance. However, since their compositional space can be tuned vastly by varying elemental species and concentrations, it is of great significance to explore the relationship between their mechanical and irradiation performance with their intrinsic properties. In this work, we show that there is a link between the irradiation resistance of CSAs and the fluctuations in their intrinsic stacking fault energies (SFEs). Based on four CSA systems with distinct SFE properties, we find that large fluctuations in SFE distributions, together with the unique heterogeneity of defect diffusion process, can effectively suppress defect number and defect cluster growth under accumulated cascade conditions. We further demonstrate that the reason responsible for the enhanced damage tolerance is that the fluctuations in SFE distributions can effectively impede dislocation movement by increasing the onset stress required for dislocation motion. Our results thus provide evidence that the improved mechanical and irradiation properties of CSAs can be predicted by monitoring their intrinsic SFE characteristics. Keywords: Concentrated alloys, Radiation damage, Stacking fault energy, Defect evolution, Molecular dynamics 1. Introduction In contrast to traditional alloys, the recent development of concentrated solid-solution alloys (CSAs), including high-entropy alloys (HEAs), has opened the possibility of tuning alloying properties by changing alloy compositions from a large set of metallic elements [1, 2, 3, 4]. CSAs are composed of multiple principal elements all at high concentrations. In particular, single-phase CSAs can form solid–solutions on a simple crystal lattice, i.e. face-centered cubic (fcc), ∗Corresponding

author Email address: [email protected] (Shijun Zhao)

Preprint submitted to JNM

November 5, 2019

body-centered cubic (bcc), or hexagonal close-packed (hcp). Different from traditional alloys which are located at an edge or corner of the phase diagram, the alloy compositions of CSAs extend to the center of the phase diagram in the multiple component composition spaces. Therefore, in CSAs, both alloying elements and their concentrations can be adjusted vastly. It has been demonstrated that, depending on compositions, CSAs can exhibit excellent mechanical properties [4, 5], good corrosion resistance [6, 7], and improved radiation resistance [8, 9, 10]. These properties make CSAs strong candidates as structural materials in the extreme environment. For practical applications, both high mechanical strength and irradiation tolerance are desired. Depending on compositions (both alloying elements and concentrations), some CSAs exhibit outstanding mechanical properties, especially at cryogenic temperature. This property has been attributed to the transition of deformation mechanism from conventional dislocation glide at room temperature to twining at low temperatures [1, 4]. Since the deformation mechanism is closely related to stacking fault energies (SFEs), much effort has been devoted to study the nature of SFEs in CSAs. Indeed, theoretical results show that SFEs in CSAs decrease with decreasing temperature [11], suggesting that the high strength of CSAs at low temperature may associate with their low SFEs. Due to chemical disorder, SFE values in CSAs vary at different local atomic environments and therefore, exhibit distributions [12, 13]. Such variations lead to fluctuations in dislocation segments along the dislocation line, as observed experimentally [12]. It has been demonstrated that these fluctuations help to impede dislocation motion and thus contribute to the mechanical strength of CSAs [14]. Indeed, atomistic simulations show that the critical stress to move a dislocation is much higher in CSAs and the dislocation velocity is lower compared to those in pure Ni due to the fluctuations [13, 15, 16]. These results underline the importance of fluctuations of SFEs and dislocation segments in determining the properties of CSAs. The fluctuations result from the extreme disorder inherent to CSAs, which are the main reasons responsible for the good radiation resistance of CSAs. Because of the disorder, every atom in CSAs is unique in terms of the local atomic environment. Hence the defects will exhibit different energy states depending on local configurations [17, 18, 19, 20, 21, 22, 23, 24, 25]. The potential energy landscape for defect migration is, therefore, rougher than that in pure metals, creating significant atomic traps and then improving the irradiation performance. In particular, the low dislocation velocity in CSAs is proposed as the mechanism of radiation damage reduction in CSAs [15, 26]. A correlation between the edge dislocation mobility and the accumulated defect amount in CSAs is observed [15]. These works indicate that there is a strong correlation between dislocation motion and the damage state in CSAs. The slower dislocation motion in CSAs has been interpreted as the result of chemical disorder, which causes locally different SFEs. It is therefore of great interest to reveal the relations among the radiation damage buildup, SFEs and dislocation properties in CSAs, especially the role of fluctuations. Such relations will also enable alloy design with high radiation tolerance by tailoring their intrinsic SFE properties. 2

In this study, the role of chemical fluctuations plays in the irradiation response of single-phase CSAs is examined. With four carefully-chosen CSA systems, i.e. Ni0.5Fe0.5, Ni0.1Fe0.8Cr0.1, Ni0.4Fe0.4Cr0.2, and Ni0.8Fe0.1Cr0.1, the relationship between SFE distributions, radiation damage buildup and dislocation properties are exploited based on molecular dynamics (MD) simulations. These four alloy systems were picked up according to available experiment results, their different SFE properties, and the fcc phase stability regime. Previous experiments have studied irradiation performance of Ni0.5Fe0.5 and Ni0.4Fe0.4Cr0.2[27, 28], which can help us to validate simulation results. The other two were chosen due to their different SFEs and SFE fluctuations. All these considered alloys are stable in fcc structures according to the employed empirical potential and experimental evidence [29]. Our results indicate that alloys with larger fluctuations in SFEs exhibit less damage buildup during accumulated cascades. We further show that the reduction of radiation damage is due to the impedance of dislocation movement, rather than lower dislocation velocities at steady state. The high onset stress for dislocation motion is a result of the large fluctuations in SFE distributions. 2. Method Molecular dynamics simulations were performed using the open-source Largescale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code [30]. The interatomic interactions were described by the Embedded-Atom Method (EAM) parameterized by Bonny et al. [29]. This potential has been proved to yield accurate stacking fault energies and reasonable description of defect production and accumulation in the Ni-Fe-Cr alloy systems [26, 31]. 2.1. Stacking fault energy calculations In order to calculate SFE in different considered alloys, a simulation cell oriented in the [112], [1¯10] and [1¯1¯1] directions was constructed. The SFE is calculated by the energy difference between the defective supercell containing an intrinsic stacking fault and the perfect supercell (ESF−E 0), scaled by the stacking fault area (A): γ = (ESF − E0)/A. (1) Here the stacking fault is created by shifting the upper half of the system by a Burgers vector b=[112]/6 with respect to the lower half. In the calculations, 60 [1¯11¯ ] layers were considered, but with different sizes in the [112]-[1¯10] plane to study the area-dependence of calculated SFE. 2.2. Cumulative cascade simulations The damage accumulation is simulated by 5 keV overlapping cascades, since this energy is the most probable energy in the recoil spectra for MeV-ion irradiation in the considered CSAs [8]. Simulations were carried out in a 34 × 34× 34 fcc supercell containing 157,216 atoms. The system was first relaxed for 10 ps at 300 K in an NPT (constant atom number, pressure, and temperature) 3

ensemble. After that, a primary knocked-on atom (PKA) was chosen randomly from a cubic region with a dimension of 10 × 10 × 10 ˚ A3 located in the center of the simulation box. The PKA was given kinetic energy of 5 keV to initiate the displacement cascade, with the velocity directed in random directions. A variable time step scheme was adopted, in which the maximal displacement of all atoms was restricted within 0.01 ˚ A. The total simulation time for the cascade is around 30 ps, which has been shown long enough to cool down the system [31, 26]. During the cascade simulations, a Brendsen thermostat was applied to the boundary layers in order to remove the excess heat produced by the PKA. In the present study, electronic stopping is not taken into account since an accurate description of electronic stopping within the MD framework is not available. Although it may change the absolute defect number that is calculated in conventional MD, the general trend will not be affected, as we will discuss below. After each cascade, a relaxation run was performed in an NPT ensemble in order to take the stress out of the system [32]. Then the central cubic region in the simulation system was updated, from which the second PKA was chosen randomly and the second cascade was initiated. The process described above was repeated and a total of 500 cascades was simulated. This corresponds to 0.2 dpa (displacement per atom) based on the NRT standard [33]. The final defect structures were determined using the Wigner-Seitz defect analysis as implemented in the Ovito software [34]. Based on the generated defect configurations, different defect clusters were categorized by their sizes. For each alloy, three independent simulations were performed and the final results are averaged. 2.3. Dislocation velocity The velocity of an edge dislocation in the considered CSAs is calculated to reveal how different SFE characteristics can affect dislocation properties. The simulation details are similar to our previous work [13]. Briefly, an edge dislocation was introduced into a box oriented along the [110], [1¯11], and [11¯ 2] directions. The cell dimensions were about 30×24 × 22 nm3 and contains around 1.5 million atoms. Periodic boundary conditions were applied in both the [110] and [1¯12] directions. Fixed boundary conditions were used along the [1¯11] direction. Along this direction, the upper and lower regions of several atomic layers were fixed while the atoms in the central part were mobile[35]. The system was first relaxed using a NPT ensemble, and then the stress-controlled loading was applied by adding external forces to the atoms in the upper and lower regions along the [110] direction. The magnitude of force was F = ±σA/N±, where A was the area of [110]-[1¯12] plane, N± was the number of atoms in the upper or lower region respectively, and σ was the stress applied to the dislocation. The positive and negative sign denoted the opposite force exerted in the upper and lower region, respectively. After relaxation, the edge dislocation dissociates into two Shockley partial dislocations; the dissociation distance depends on the values of SFE. The following simulations were performed in the NVE ensemble with the temperature controlled by a Berendsen thermostat[36]. A time step 4

of 1 fs was used. The position of dislocations was identified using the local structure analysis proposed by Ackland et al [37]. The total simulation time is around 1 ns with a timestep of 1 fs. 3. Result 3.1. Stacking fault energy Because of chemical disorder, the SFE calculated using the supercell model depends on the local atomic environment [25]. As a result, different elemental arrangement near the stacking fault region will lead to different SFEs; the SFE in CSAs becomes a distribution related to the random arrangement of elements. This distribution depends on the stacking fault area that is considered in simulations. For the considered Ni0.5Fe0.5, Ni0.1Fe0.8Cr0.1, Ni0.4Fe0.4Cr0.2 and Ni0.8Fe0.1Cr0.1alloys, the area-dependent SFE distributions are calculated by varying elemental arrangement using different random seeds in the simulations. The results are provided in Supplementary Materials. Here the distribution of SFE calculated within a 20 × 40 supercell in the [112]-[1¯10] plane are shown in Fig.1. At a given box size and alloy composition, a total of 3000 random realizations were performed. We approximate the obtained SFE distribution with a Gaussian function γ−µ C ), (2) exp( f (γ) = √ − 2σ2 2πσ in which the values of C, µ, and σ describe the distribution of SFEs. The fitted mean value (µ) and standard deviation (σ) are provided in Fig.1. Here the value of σ represents the fluctuation in SFEs distributions. Fig. 1 shows that Ni0.1Fe0.8Cr0.1has the lowest SFE among all these alloys considered (Note that the SFE of pure Ni is calculated to be 130.0 mJ/m2 with the same potential). This result is consistent with the experimentally stable fcc phase region for Fe-Ni-Cr compositions [29], in which low SFEs are found when both Ni and Cr concentrations are low. Another feature that can be noticed from Fig. 1 is that these alloys exhibit different standard deviations as can be seen from the Gaussian fitting result. In particular, the highest σ is observed in Ni0.4Fe0.4Cr0.2, whereas it is the lowest in Ni0.1Fe0.8Cr0.1. Since SFE distribution depends on the area investigated, the obtained σ varies with different stacking fault sizes. To characterize such dependence, the full width at half maximum (FWHM) of the fitted Gaussian distribution at different areas is calculated for all considered alloys. The results are shown in Fig. 2. The dependence of calculated FWHM on stacking fault area for all considered alloys is consistent, i.e. FWHM decreases with increasing area. In principle, the FWHM should become zero for infinitely large areas so that the SFE is a single value. Among the four CSAs, Fig. 2 shows that Ni0.4Fe0.4Cr0.2 always exhibits the highest FWHM at a given area. The relationship between FWHM and stacking fault area can be fitted by FWHM= kAm, where k and m are fitting parameters. The obtained m, as indicated in Fig.2, are around −0.48 5

for all four alloys, suggesting that the fluctuation of SFE scales approximately inversely with the square root of the area. In fact, if we consider a canonical ensemble, the energy fluctuation of the system should scale inversely with the square root of the particle number. Since the particle number is proportional to the√area in the scenario of stacking fault calculations, the relationship FWHM∼ 1/ A is reasonable. The consistent results in Fig.2 indicate that the FWHM of SFE can be considered as an intrinsic property of CSAs, since the value of FWHM can be characterized by two parameters, k and m. 3.2. Damage accumulation Accumulated cascade simulations are performed to study the irradiation performance of considered alloys. The accumulation of point defects with increasing recoil events is demonstrated in Fig. 3. The defect number in these alloys first increases linearly and then exhibits different characteristics. Consistent with previous MD results in Ni, Ni0.5Fe0.5 and Ni0.4Fe0.4Cr0.2 [28, 15], the number of point defects is the lowest in Ni0.4Fe0.4Cr0.2, whereas Ni shows the highest defect number under prolonged ion irradiation. This result helps to validate our simulation scheme. In previous simulations, the electronic stopping effects were considered using a friction force acting on atoms with high kinetic energies. The agreement between their results and ours indicates that the electronic stopping considered by friction forces has limited influence on the damage accumulation in considered CSAs. Among these alloys, we find that the generated defect number after 500 cascade simulations is in the order of Ni0.1Fe0.8Cr0.1>Ni0.8Fe0.1Cr0.1>Ni0.5Fe0.5> Ni0.4Fe0.4Cr0.2. The result indicates that both elemental composition and concentration have a significant influence on irradiation tolerance of CSAs. Compared to the SFE results shown in Fig. 1, we can see that the damage buildup has a weak relationship with the magnitude of averaged SFEs (γ¯ ). For exam- ple, Ni0.4 Fe0.4 Cr0.2 exhibits the lowest defect number, but has a higher γ¯ than Ni0.1 Fe0.8 Cr0.1 . Therefore, a lower γ¯ does not necessarily cause a better radiation performance of CSAs. Since SFEs are closely related to dislocation properties, it is therefore of great importance to analyze the defect cluster structures in these different alloys, especially for interstitial defect clusters. To this end, we have made a statistic about the interstitial cluster distributions in different considered CSAs after 500 cascades, and the results are shown in Fig. 4. Fig. 4 shows different clustering properties of point defects in the considered alloys under irradiation. In pure Ni, only a few isolated interstitials are observed; most interstitials form medium to large defect clusters (containing >2 interstitials). On the other hand, in Ni0.5Fe0.5 and Ni0.4Fe0.4Cr0.2 where defect number is much lower than that in other alloys, small- and medium-size defect clusters containing 2-30 interstitials are dominant. In particular, the number of large defect clusters (>51) in Ni0.4Fe0.4Cr0.2is the lowest among them. The behavior of defect clusters in Ni0.1Fe0.8Cr0.1 and Ni0.8Fe0.1Cr0.1 is similar to that in pure Ni, but with a higher number of interstitials in small clusters but a smaller number of interstitials in large clusters. Generally, these results are consistent with experiments which show small defect clusters in CSAs [28]. The 6

low defect number under cascade is in accordance with the observed small defect clusters. Comparing the SFE distribution in Fig.1, we find that the small defect clusters observed in CSAs are associated with their large fluctuations in SFEs. 3.3. Dislocation velocity The observed different defect accumulation behavior in different alloys is related to the mobility of various defects that are produced under ion bombardment. In particular, previous studies have demonstrated that less damage accumulation in alloys is a result of the sluggish diffusion of interstitials and large vacancy clusters, which tends to suppress defect cluster growth, especially dislocations [26, 38, 39]. For the CSAs considered here with different SFE characteristics, it is expected that the properties of dislocations are different. Therefore, we have investigated the mobility of edge dislocations in these CSAs by applying different external shear stresses, as described in our earlier work [13]. The velocity of dislocations is calculated by fitting the position of the two Shockley partial dislocations after they reach steady movement to the simulation time. The results are shown in Fig.5. Consistent with previous results, Fig.5 shows that there is no threshold stress required to initiate the motion of an edge dislocation in pure Ni [13, 15]. However, the motion of dislocation in alloys all depends on threshold stress (σth) below which the dislocation can hardly move or can only partially move. At low stresses, the dislocation velocity increases almost linearly with increasing applied stress, which defines the dislocation friction coefficient B = bσ/v, where b is the Burgers vector and σ is the applied stress [40, 13]. Among these materials, the velocity of an edge dislocation in pure Ni is the highest at given external stress. Compared to all CSAs considered here, the dislocation velocity in Ni0.8Fe0.1Cr0.1 is the highest. Notably, the velocities of dislocations in Ni0.5Fe0.5, Ni0.4Fe0.4Cr0.2 and Ni0.1Fe0.8Cr0.1 are very similar at a steady movement. The data in Fig.5 is calculated when a steady movement of the dislocation is obtained. When the applied stress is less than 300 MPa, the dislocation behavior is quite different in these alloys. We have studied dislocation movement at lower stresses to investigate how the dislocation responds to external stresses. A detailed comparison of the dislocation motion at 200 and 300 MPa is provided in Fig.6, where the dependence of dislocation gliding distance on the simulation time is given. In pure Ni, the steady movement of dislocation has already been observed at 200 MPa, as can be seen from the linear relation between the gliding distance and time. However, the dislocation movement in CSAs behaves differently. Generally, the dislocation movement in CSAs is not continuous, especially in Ni0.5Fe0.5, Ni0.4Fe0.4Cr0.2, and Ni0.8Fe0.1Cr0.1. In these alloys, the dislocations can only move a short distance, and then being stuck at some positions for a long time before they can move again or just stay at the original position for the rest of simulation. The dislocation movement in Ni0.1Fe0.8Cr0.1 is an exception, where dislocation can move for long distances, though the movement is discontinuous as seen by the serrations in the gliding distance–time curve. When

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the applied stress increases to 300 Mpa, the dislocation can move continuously in all alloys, except in one case for Ni0.4Fe0.4Cr0.2. The discontinuous motion of dislocations in CSAs at 200 MPa suggests that the dislocation may get trapped in a specific local environment, which is related to the atomic configurations around the dislocation. For example, in Ni0.4Fe0.4Cr0.2, the dislocation can only move slightly at the beginning of the simulation and then stay in the same location for the rest of the simulation time. Nevertheless, the dislocation line indeed exhibits fluctuations trying to escape from the local trap, as can be seen by the small increase of gliding distance in some dislocation segments (Fig.6(a)). The motion of an edge dislocation involves two dissociated partial dislocations and the stacking fault area between them. To enable continuous dislocation movement, new stacking faults need to be created constantly. As SFEs in CSAs exhibit large fluctuations, the dissociated distance, i.e. stacking fault area also show fluctuations. Here, large fluctuations in SFEs for Ni0.5Fe0.5 and Ni0.4Fe0.4Cr0.2 as indicated in Fig.1 correspond to their discontinuous movement of dislocations, whereas small fluctuations in SFEs for Ni0.1Fe0.8Cr0.1 is related to the ease of dislocation movement (Fig.6(a)). Notably, the dislocation can hardly move in Ni0.4Fe0.4Cr0.2 which exhibits the largest fluctuations in SFEs among these considered CSAs under the same simulation conditions. It should be noted that the dislocation movement in CSAs would depend on the dislocation length since the fluctuations in SFE lead to variations along the dislocation line which act as obstacles for dislocation movement. In this study, the simulated dislocation length is around 21.5 nm, which corresponds to 86| b[111]/2| . This length is long enough to ensure saturated flow stress and therefore, typical configurations around the dislocation are sampled [16]. 4. Discussion Previous studies have established that the good irradiation resistance of CSAs may arise from the slower dislocation motion [26]. In addition, it is shown that the generated defect number in CSAs due to accumulated cascade is in proportional to the steady dislocation velocity [15]. These results indicate that there is a strong correlation between dislocation motion and irradiation resistance of CSAs. The slower dislocation motion in CSAs has been interpreted as the result of chemical disorder, which causes locally different stacking fault properties [13, 16]. Therefore, it is expected that such local fluctuations should be responsible for the peculiar dislocation motion in CSAs. In this work, we show that the slow dislocation motion is related to the fluctuations in SFEs, the role of which increase the threshold stress for dislocation motion. Besides, such impediment of dislocation motion directly correlates with the defect number produced in cascade: larger SFE fluctuations tend to suppress defect production in CSAs. The fluctuations in SFEs (can be measured by the FWHM) can be regarded as an intrinsic property of CSAs associated with the chemical disorder. Therefore, this study provides a direct link between the irradiation performance and 8

intrinsic properties for chemically-complexed concentrated alloys. The lower damage accumulation is related to the difficulty of dislocation motion in CSAs. Specifically, in Ni0.4Fe0.4Cr0.2 where the lowest defect number is obtained under accumulated cascade simulations, the dislocation motion is also the most difficult. Under ion irradiation, plenty of interstitials and vacancies are produced. At room temperature as simulated here, the migration and diffusion of interstitials are dominated, which leads to the formation of dislocations. Our simulation indicates that the difficulty of dislocation motion governs the following defect accumulation. In Ni0.4Fe0.4Cr0.2, the dislocation movement is the most difficult, which efficiently suppresses defect cluster growth. As demonstrated in Fig.4, no large clusters (>51 defects) in Ni0.4Fe0.4Cr0.2 are found. In contrast, the dislocation can move almost freely even at low stresses in pure Ni, and in Ni0.1Fe0.8Cr0.1, which facilitates defect cluster growth, as manifested by the predominant large defect clusters (Fig.4). Comparing the alloy systems studied in this work, we find that a lower damage accumulation is not necessarily associated with the low dislocation velocity. This is the case for Ni0.1Fe0.8Cr0.1. While the defect number in Ni0.1Fe0.8Cr0.1 is as high as that in pure Ni under accumulated cascades (Fig.3), the dislocation velocity is as low as that in Ni0.4Fe0.4Cr0.2 when steady movement of dislocation is reached (Fig.5). In fact, a recent study suggests that the dislocation movement in CSAs can be considered as two modes: an obstacle-dominated regime at low stresses, and a smooth behavior (steady movement) similar to that in pure Ni at high stresses [16]. Our study thus suggests that it is the first mode of dislocation motion that plays a decisive role in influencing defect accumulations. The fluctuations in SFEs are induced by the variations in local composi- tions. Such local fluctuations have been proved to improve the onset stress for dislocation movement. In particular, previous dislocation dynamics simulations suggest that the yield stress of CSAs increases with the increase of local fluctuations of SFEs [14]. Based on the solid solution hardening model, it is argued that the onset stress increase scales with (∆γ)3/2 and (∆γ)4/3 according to the theories of Friedel and Labusch, respectively [14]. Thus large fluctuations in SFEs can effectively suppress dislocation movement, and contribute to the high strength of CSAs. Indeed, large fluctuations in SFE distributions have been found in NiCoCr from both ab initio calculations [11, 25] and experimental measurements [41], which are in accordance with its high strength and good irradiation tolerance as observed in experiments [8]. Defect evolution in CSAs is also related to the defect energy landscape when defect migration starts [9]. To elaborate on the differences among considered alloys, we have calculated the distribution of migration energies in these alloys and show the results in Fig.7. These results are obtained in a 8× 8×8 supercell containing 2048 atoms. Consistent with previous findings, Fig.7 demonstrates that the migration energies in CSAs exhibit broad distributions, with different characteristics in different alloys [42, 24]. Specifically, there is a considerable overlap region between the migration energies of vacancies and interstitials. Such overlap is a result of the large spread in the distributions, an indication of the heterogeneity in defect diffusion[9]. Among these alloys, Ni0.4Fe0.4Cr0.2exhibits 9

the largest overlap region and the widest energy distributions, which can facilitate defect recombination [43] and contribute to the low defect level as observed in cascade simulations. This heterogeneous defect diffusion is also a reason for the improved irradiation resistance found in CSAs. 5. Conclusion The relationship between radiation damage tolerance and intrinsic SFEs in several concentrated alloys is explored based on MD techniques. Because of chemical disorder, the SFEs in CSAs exhibit distributions with different fluctuation amplitude. Through accumulated cascades simulations, we show that the CSA with the largest fluctuations in SFEs demonstrates the highest damage tolerance, as evidenced by the low defect number and small defect clusters. The motion of an edge dislocation in these different CSAs is then studied, and we find that larger fluctuations in SFEs make dislocation motion more difficult by increasing the onset stress required for dislocation movement. Our results also show that a low damage buildup is not necessarily associated with a low dislocation velocity in CSAs. This work provides a link between irradiation performance and intrinsic SFE properties of CSAs, which is essential for understanding the distinct irradiation properties of various CSAs. These insights are also an important step towards irradiation-resistant alloy design. Acknowledgments This work was supported by City University of Hong Kong (No. 9610425), Research Grants Council of Hong Kong (No. 21200919), and National Natural Science Foundation of China (No. 11975193). References [1] D. Miracle, O. Senkov, A critical review of high entropy alloys and related concepts, Acta Materialia 122 (2017) 448–511. [2] J.-W. Yeh, S.-K. Chen, S.-J. Lin, J.-Y. Gan, T.-S. Chin, T.-T. Shun, C.H. Tsau, S.-Y. Chang, Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes, Advanced Engineering Materials 6 (5) (2004) 299–303. [3] B. Cantor, I. Chang, P. Knight, A. Vincent, Microstructural development in equiatomic multicomponent alloys, Materials Science and Engineering: A 375 (2004) 213–218. [4] B. Gludovatz, A. Hohenwarter, D. Catoor, E. H. Chang, E. P. George, R. O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, Science (New York, N.Y.) 345 (6201) (2014) 1153–1158.

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(a) Ni0.5Fe0.5 2

Count Count

µ=31.97 mJ/m 2 σ= 3.50 mJ/m2 µ= 2.54 mJ/m 2 σ= 1.99 mJ/m

(b) Ni0.1Fe0.8Cr0.1 (c) Ni0.4Fe0.4Cr0.2 2

Count Count

µ=28.27 mJ/m 2 σ= 2 4.09 mJ/m µ=82.95 mJ/m 2 σ= 2.66 mJ/m

(d) Ni0.8Fe0.1Cr0.1 0

20

40

60

80

100

2

SFE (mJ/m ) Figure 1: Distribution of stacking fault energies in different CSAs within a supercell size of 20 × 40 in the [112]-[1¯ 10] plane. The results are obtained from 3000 calculations with 60 [1¯ 1¯ 1] layers. The mean and standard deviation derived from a Gaussian fitting are provided in each

case.

15

2

10

1

2

FWHM (mJ/m )

10

Ni0.5Fe0.5 (m1=−0.48) Ni0.1Fe0.8Cr0.1 (m2=−0.44) Ni0.4Fe0.4Cr0.2 (m3=−0.47) Ni0.8Fe0.1Cr0.1 (m4=−0.46)

10

0

10

1

10

2

10

3

10

4

10

5

2

Area (Å )

Figure 2: Full width at half maximum (FWHM) of SFE distributions for different alloys calculated at different stacking fault area. The relationship can be fitted by FWHM= kAm, where k and m are fitting parameters. The obtained m is indicated.

16

800

Ni Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

Defect number

700 600 500 400 300 200 100 0 0

100

200

300

400

500

Number of recoils Figure 3: Damage buildup in different CSAs under accumulated 5 keV cascade simulation. The defect number denotes the number of Frenkel defects based on the Wigner-Seitz defect analysis.

17

Number of interstitials

800 Ni Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

600 400 200 0 1

2−20 11−30 31−50

51+

Cluster size Figure 4: Distribution of interstitial defect clusters after 500 cascades in different CSAs. The size is categorized by the defect numbers.

18

25

Velocity (Å/ps)

20 15 Ni Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

10 5 0 500

1000

1500

2000

Stress (MPa) Figure 5: Calculated velocities of an edge dislocation at steady state in considered alloys at different external shear stress. Below 300 MPa, the dislocation movement in alloys becomes discontinuous and its velocity is difficult to be extracted.

19

(a)

200 100

300

(e)

1400

Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

Gliding distance (Å)

300

1600

(c)

400 Gliding distance (Å)

Gliding distance (Å)

400

200 100

1200 1000 Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

800 600 400 200

0

0

Gliding distance (Å)

Gliding distance (Å)

3000

(d)

4000

Ni Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

2000 1000 0

3000 2000 1000 0

0

200

400

600

Time (ps)

800 1000

(f)

4000

Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

Gliding distance (Å)

(b)

4000

0 Ni0.5Fe0.5 Ni0.1Fe0.8Cr0.1 Ni0.4Fe0.4Cr0.2 Ni0.8Fe0.1Cr0.1

3000 2000 1000 0

0

200

400

600

Time (ps)

800 1000

0

200

400

Figure 6: Dependence of the gliding distance of an edge dislocation on simulation time in the considered alloys at different applied shear stress (a, c, and e) 200, and (b, d, and f) 300 MPa. At each stress, the results from three independent simulations with different initialization of the random elemental distribution are presented. For CSAs, the dislocation is divided by 10 segment with a length of 8 ˚ Aalong the dislocation line, which results in fluctuations in the gliding distance since each segment behaves differently along the dislocation line.

20

600

Time (ps)

800 1000

(a)

(c)

0

0.5

1

(b)

1.5

2

0

0.5

1

(d)

0

0.5

1

1.5

2

Migration energy (eV)

0

1.5

2

0.5

1

1.5

0

2

Migration energy (eV)

0

(g)

VNi VFe VCr

0.5

1

(f)

INi IFe ICr

Count

INi IFe

(e)

VNi VFe VCr

Count

VNi VFe

1.5

2

1

1.5

0.5

2

Migration energy (eV)

0

1.5

2

INi IFe ICr

0.5

1

1.5

2

Migration energy (eV)

Figure 7: Distributions of migration energies for vacancies (The first row) and interstitials (the second row) in considered alloys. From left to right, these four columns represent energies calculated in Ni0.5Fe0.5, Ni0.1Fe0.8Cr0.1, Ni0.4Fe0.4Cr0.2, and Ni0.8Fe0.1Cr0.1.

21

1

(h)

INi IFe ICr

0.5

0

VNi VFe VCr

Conflict of Interest The authors declare no conflict of interests.