Mechanism of Radiation Damage Reduction in Equiatomic Multicomponent Single Phase Alloys

Recently a new class of metal alloys, of single-phase multicomponent composition at roughly equal atomic concentrations (“equiatomic”), have been shown to exhibit promising mechanical, magnetic, and corrosion resistance properties, in particular, at high temperatures. These features make them potential candidates for components of next-generation nuclear reactors and other high-radiation environments that will involve high temperatures combined with corrosive environments and extreme radiation exposure. In spite of a wide range of recent studies of many important properties of these alloys, their radiation tolerance at high doses remains unexplored. In this work, a combination of experimental and modeling efforts reveals a substantial reduction of damage accumulation under prolonged irradiation in single-phase NiFe and NiCoCr alloys compared to elemental Ni. This effect is explained by reduced dislocation mobility, which leads to slower growth of large dislocation structures. Moreover, there is no observable phase separation, ordering, or amorphization, pointing to a high phase stability of this class of alloys.

is, from a principal point of view, a simple way to increase energy efficiency, but requires, in practice, materials that can withstand the increased operation window.Many of the new energy production concepts considered, such as concentrated solar energy and several Generation-IV nuclear concepts, include components with flowing liquid salts or metals, posing serious corrosion challenges [1][2][3].Both electric power generators and nuclear fusion power plants involve high magnetic fields [4], adding a further class of materials properties that needs to be considered.With respect to these requirements on the materials, a recently developed class of metal alloys shows high promise to exhibit greatly improved properties.Most traditional metal alloys involve one principal element alloyed by much lower concentrations of others, or mixtures of several different phases.Systematic synthesis and study of alloys with multiple elements at equal (called "equiatomic" [5] or, in case they contain at least 5 elements, "high-entropy" alloys) or roughly equal concentrations in a single phase structure has, however, started only recently [5,6].Intense recent work has revealed that these alloys have the ability to maintain good mechanical properties both at cryogenic conditions [7] and up to very high temperatures (∼1000 °C), as well as a good corrosion resistance [8].Hence, they are strong candidates to resolve many challenges imposed by extreme environments.However, in the particular case of nuclear reactors, there is the additional complication of radiation damage.In particular, realization of new Generation IV fission reactor concepts [9,10], that will have many improved features (e.g., the capability to burn used nuclear fuel), as well as tokamaklike fusion power plants [10,11], will both subject materials in the reactors to very high neutron irradiation loads.Hence, to realize the great potential of equiatomic and high-entropy alloys in nuclear environments, it is crucial to consider also radiation damage and its buildup in these materials.Recently, preliminary estimations of the possible reduction of radiation damage in Ni equiatomic alloys were done based on analysis of formation of point defects and initial damage structures [12].Here we, in these multicomponent single phase alloys, focus on the issue of damage buildup and its mechanisms, crucial for practical applications.
Even though some classes of steels and other metal alloys are known to have high radiation tolerance, their properties do start to change immediately after the onset of irradiation [10,13].This has motivated an intense ongoing search for new classes of materials with improved radiation hardness.New materials, shown to have high radiation tolerance include nanocrystalline materials [14][15][16], multilayered nanomaterials [17], and nanofoams [18,19].Although all of these are promising for some applications, the high fraction of surface or interface, which are thermodynamically unstable, makes nanostructures in general unreliable for long operational times at elevated temperatures.For such conditions, typical for nuclear reactors, it is very valuable to find homogeneous and stable materials with improved radiation tolerance, and equiatomic or high-entropy alloys could become such a class of materials.
In this Letter, we examine the radiation tolerance of single-phase equiatomic alloys of two and three components: NiFe and NiCoCr, by experiments and molecular dynamics computer simulations, with particular emphasis on the damage buildup effects.The materials are not chosen for any specific application in mind, but to investigate the radiation hardness of equiatomic alloys in general.We show that the multielemental composition of the equiatomic materials slows down dislocation motion in them, leading to a strong (factor of ∼2-3) reduction in radiation damage.Understanding of the actual mechanisms of reduction of radiation damage in the equiatomic metal alloys will allow for a focused search of other combinations of alloying metals with even more improved radiation tolerance.
For our study, we chose the NiFe and NiCoCr alloys since they could be synthesized experimentally as highquality single crystals [20], while maintaining a completely random atom arrangement within a well-defined facecentered cubic (fcc) crystal.(see methods section in the Supplemental Material [21]).Moreover, interatomic potentials for the same alloy composition were readily available [22][23][24].We investigated the radiation response in these materials in comparison to pure Ni, which has the same crystal structure.We emphasize that the outcome of radiation in these materials is by no means a priori clear: while in elemental metals the damage levels saturate at a relatively low defect concentration, around 1% [25], some metal alloys are known to amorphize under irradiation [26], indicating a major increase in damage production.
The experimental pure Ni and equiatomic alloy samples were irradiated with Ni and Au ions with the energies 1.5 and 3 MeV, respectively, producing damage in the dense cascades similar to those produced by neutron recoils in nuclear reactors [25].The damage was analyzed by Rutherford backscattering and channeling (RBS/C; see methods section in the Supplemental Material [21]).The results in Fig. 1 show that there is a major (a factor 2-3) reduction in the damage in the NiFe and NiCoCr equiatomic alloys, as compared to the pure element Ni.Moreover, the three elemental NiCoCr alloy shows a still lower damage level than the two elemental NiFe.
Our cross-sectional transmission electron microscopy (TEM) analysis (Figs. 2 and 3) of Ni and NiFe irradiated by 3 MeV Au ions to 2 × 10 13 and 1 × 10 14 ions=cm 2 at room temperature shows that the depth distribution of defect clusters strongly depends on the ion fluence and the composition of the material.As expected from previous works showing that dislocations have a crucial role in irradiated metals [27][28][29][30][31][32], we observe typical features of dislocation loops and vacancy-type stacking fault tetrahedra (SFT) in all investigated samples.However, comparison of the NiFe micrographs with the Ni ones shows clearly that there is less damage in NiFe, and the feature sizes are smaller.This is confirmed by quantitative comparison of the defect cluster sizes [Figs.2(b) and 3(b)].Moreover, no signs of phase separation or ordering is observed even at the highest doses studied.No cracking was observed in the samples, which gives promise that there is no drastic reduction of ductility under irradiation.Systematic studies of the mechanical property change after irradiation are in progress.
To establish the origin of the damage reduction and reason for a strong dislocation signal, we turn to molecular dynamics (MD) computer simulations, a method widely used to examine radiation damage production in metals [27,33,34] (see methods section in the Supplemental Material [21]).We carried out simulations of radiation collision cascades consecutively in the same simulation cell to reach the high doses of about 0.57 displacements per atom (dpa [35]) that can be compared with the experiments.The simulations were carried out by running 1500-1800 recoils at a typical subcascade energy of 5 keV in a segment of material far from the surface, to mimic damage production at the experimental depths of hundreds of nanometers.
The MD results of damage production under prolonged irradiation show three results of direct relevance to interpret the experiments.First, the point defect damage level saturates with a dose at about 0.3 dpa, consistent with previous experiments in elemental metals [25].The results up to the same dose as in the experiments [see Fig. 4(a)] demonstrate, in agreement with the TEM and RBS measurements, that equiatomic alloys are well resistant to amorphization and do not show any signs of separation or ordering.Second, the defect clustering analysis showed that after the cascade damage started to overlap with preexisting defects, recombination effects [36,37] tended to remove point defects, while defect clusters grew in size and started to form ordered defect structures known as (partial and perfect) dislocation loops.These can be The reduced fraction of damage in the large (≥10 defects) dislocation structures was observed with two different MD interatomic potentials used (see methods section in the Supplemental Material [21]), and is fully consistent with the experimental observations on the differences between the materials.The diameter of the defects are also smaller in the alloys than in pure Ni, see Fig. 4(b) inset, and have a similar size distribution peaked stronger at small cluster sizes for the alloys NiFe and NiCoCr.Thus, we conclude that the reason for the damage reduction in the equiatomic alloys studied here [Fig.4(a)] is that the dislocation structures are in these materials smaller than in the elemental material.
To determine the mechanism by which the dislocation structures observed in the simulations are smaller in NiFe and NiCoCr compared to Ni, we separately analyzed the mobility of edge dislocations in these materials, following the approach in Ref. [38].Lattice distortions caused by the different atomic types in equiatomic alloys can be expected to affect the dislocation mobility in these materials.We found that the edge dislocation in NiCoCr is indeed less mobile than that in NiFe, which in turn is less mobile than that in Ni.The difference in dislocation mobility in the alloys and pure Ni depended on the strain rate used, but was clearly at least a factor of 2. The onset stress for movement is also much higher for the alloys compared with that in the pure element.Hence, we conclude that distortion of the crystal lattice structure in the equiatomic alloying materials is able to hinder the dislocation movement, resulting in smaller damage structures in NiFe and NiCoCr, making them also less likely to grow.This deduction is further supported by the movies provided in the Supplemental Material [21], which show visually that the damage evolution involves extensive discontinuous motion of different dislocation structures, all induced by the radiation condition.The velocity v of a dislocation, once it becomes mobile, depends on an external macroscopic stress σ as [39] where M d is the dislocation mobility constant and b the Burgers vector of the dislocation.Our results show that the mobility of dislocations in equiatomic alloys, M ea d are smaller than those in pure elements M el d .Because permanent deformation of metals is driven by dislocation motion ∝ v in metals, Eq. ( 1) implies that equiatomic alloys can be expected to be able to withstand higher macroscopic stresses σ than the corresponding pure elements.Moreover, we also compared our results qualitatively with similar runs carried out in widely used ferritic Fe-Cr alloys [3,10].In spite of different lattice structures, we observe a similar relative damage reduction compared to the pure element, but find that it is larger in the equiatomic alloys (see Supplemental Material [21]).
We note that the simulated dose rate is orders of magnitude higher than the experimental one due to the limited time scale available for conventional MD simulations.In particular, at experimental dose rates, there would be much more time for point defects to move between the subcascade events.However, most of the point defects would be absorbed by the dislocations, and hence the effect of practically all defects being in damage clusters would be achieved at even lower doses than in the simulations.Hence the main conclusion of the difference in damage production at higher doses (≳0.1 dpa) being due to different dislocation sizes and mobility is not affected by the underestimation of point defect migration in the MD simulations.
To summarize, our combined experimental and simulation results show consistently that equiatomic metal alloys may be more resistant to radiation damage than the corresponding pure elements.Moreover, our analysis of the underlying mechanism of different equiatomic alloys establishes that alloy effects on significant reduction of dislocation mobility is generic and not specific to the current choice of materials or number of elements in the system.Further study is needed to establish whether additional damage reduction is possible with increasing number of elements and to find combinations of alloy composition and materials processing routes that would enable minimizing damage evolution in an engineering material at reasonable cost.Moreover, in nuclear fusion systems, the elements Co and Ni used in the currently studied equiatomic metal alloys would be needed to be replaced, to find alloys without elements that exhibit high activation under neutron irradiation.However, the difference between the NiFe and NiCoCr results already shows that a reduction will depend on material choice, and suggests that there may be alloys with even larger damage reduction than the currently observed one-especially in more chemically disordered alloys with increasing number of principal elements at significant concentrations (not necessarily at equiatomic concentrations), where the number of possible element combinations and alloy compositions are practically limitless.and part of this damage is absorbed by the preexisting defects.The dislocation structures are also made mobile by the lattice heating and distortion caused by additional irradiation, evident from the rapid motion of defective regions.At the highest doses, the damage level has saturated (compare Fig. 4 in main Letter).
Comparison of the Ni and NiFe movies show that the defect structures in NiFe tend to be smaller than those in Ni (cf.detailed discussion in main Letter).

Synthesis of equiatomic alloys.
Polycrystalline ingots of Ni metal and Ni-based equiatomic alloys were prepared using high-purity elemental metals (> 99.9% purity) by arc melting and drop casting into cylindrical copper molds.The phase stability and the formation of single phases were carefully examined and confirmed using X-ray diffraction and microstructure characterization techniques [1].The phase diagram for the investigated alloys, showing their phase stability, can be found for Ni and NiFe in Ref. 2 and the theoretical prediction of the phase stability of NiCoCr in Ref. 3. Face-centered cubic crystal Ni and alloys were grown in an optical floating zone furnace from the polycrystalline drop-cast ingots under an Ar atmosphere [4].The quality and orientation of all crystals were inspected using backscatter Laue diffraction, re-oriented and cut normal to the <100> directions.Disks with thickness of ∼ 1 mm were electrochemically polished to remove the damage layers of the machining in order to produce damage-free surfaces, essential for ion channeling measurements.

Ion irradiation.
Irradiation response at room temperature of Ni, NiFe and NiCoCr were investigated with 3 MeV Au ions to fluences of 2 × 10 13 , 5 × 10 13 and 1 × 10 14 cm −2 and 1.5 MeV Ni ions to 6 × 10 13 , 1 × 10 14 and 2 × 10 14 cm −2 .Raster beam was used to ensure a homogeneous irradiation.The irradiation-induced damage peak was located at ∼ 155 nm and 370 nm for the Au and Ni cases, respectively.These energies were chosen to produce damage within a few hundreds of nanometers from the sample surface, where the damaged region can be readily characterized by microstructural analysis and ion channeling measurements with good depth resolution, but deep enough to avoid complication from surface effects.Predictions of local dose in displacements per atom (dpa) [5] and ion stopping range in Ni were estimated using the Stopping and Range of Ions in Matter (SRIM) code [6] under option of quick calculation of damage with a displacement threshold energy of 40 eV.The measured density of 8.908 g cm −3 is used in the SRIM calculation for pure Ni.

Rutherford backscattering and ion channeling analysis.
Rutherford backscattering spectrometry technique along major channel directions is used to verify the crystal quality and also to determine lattice distortion.A parallel 3.5 MeV He + beam that was well aligned along the <001> crystal direction was employed in the measurements.Following the ion energy deposition by either energetic Au ions or Ni ions, in-situ channeling measurements were subsequently carried out with a Si detector located at a scattering angle of 155 • relative to the incoming He beam to record the increase of the backscattering yield due to irradiation-induced damage.

Microstructural characterization.
The cross-sectional TEM samples were prepared using focused ion beam (FIB) lift-out techniques utilizing the FEI Helios 650 Nanolab Dualbeam workstation.FIBinduced damage and sample thinning were performed by Ga + beam initially with energy of 30 keV and a current of 2.5 nA to 30 pA at an incident angle of ±1.5 • and sequentially down to 5 keV at the angle of ±7 • for 5 min.A flash polishing was conducted to remove residual damage from sample preparation.Bright field imaging of the same samples was done in a JEM 3011 TEM operating at 300 kV.Images were taken at an exposure time of 2 seconds.

Simulations.
The collision cascades in metals were simulated by means of molecular dynamics [7,8] using the fully parallel PAR-CAS code developed within the group in Finland and extensively used for studies of cascades previously [9,10].We used two different potentials to describe the interatomic interactions in NiFe and NiCoCr alloys to verify that there is no significant dependence of the results on the choice of the interatomic potential.To describe the Ni-Co-Cr system, we combined the multi-elemental potentials by Zhou et al. [11] for Ni-Co with the Cr potential in the same formalism developed by Lin et al. [12].To describe the interactions between the different elements in this system, we used the mixing scheme proposed in [11] between all the elements Ni-Co-Cr.For Fe-Ni, we used both the Fe-Ni potential formed in the same Zhou et al. set of potentials [11], and the completely independently developed pair-specific Fe-Ni potential by Bonny et al. [13].Neither of the used potentials ex-plicitly accounts for magnetism.Nevertheless it is implicitely taken into account, for instance, in the fitting of the cohesive energy.This remark is important with respect to results on damage buildup in FeNi, which is a magnetic material.However, previous simulation results on damage production in Fe with an explicit magnetic potential showed no significant difference compared to non-magnetic potentials.[14,15] This justifies the use of potentials, where the magnetism is only implicitly accounted for.Both the Fe-Ni potentials were found to give similar results with respect to the damage production, showing that the results are not specific to a certain interatomic potential.
All three elemental compositions, Ni, NiFe and NiCoCr were simulated up to the dose ∼ 0.57 dpa by running 1500 consecutive 5 keV recoils.Each set of the 1500 recoils was repeated three different times for each system using different seed numbers in the random number generator and different initial random cells, to show that the obtained results are not due to stochastic anomalities.
We dealt with the high energy effects associated with collision cascades by employing well established simulation methods for irradiation effects, namely an adaptive time step algorithm [16], electronic stopping power [17] and the ZBL repulsive potential [6] smoothly joined to the equilibrium potentials to describe the short distance interactions [9].
We used simulation cells comprising about 110 000 atoms to ensure that the heat spikes induced by the 5 keV recoils were fully developed within the cell, and that the periodic boundary conditions (applied at the cell sides in all dimensions) did not affect the final results.The simulation cell is too small for the largest defect structures seen in experiments (can be larger than 10 nm) to be represented, but a separate simulation setup, in FeCr, on a three times larger system showed that the damage level saturates at similar doses and defect levels, indicating that the key results are not sensitive to the system size.
During the cascade simulations, we controlled the temperature only at the sides of the simulation cell by applying Berendsen temperature control [18] on the border atoms.After about 25 ps (of the simulated 30 ps), no visible change in the damage structure was observed any more and the entire cell had cooled down to the ambient temperature (300 K).This will, as mentioned in the Letter, yield a much higher dose rate than that used in the experiments.However, the previous studies with similar approaches to simulate the damage buildup in semiconductors have shown a good agreement with experiments, although there was a similarly large difference in the dose rates [19,20].We ensured the homogeneous irradiation of the simulation cell by shifting the entire cell prior to the subsequent recoil event by a vector of random length (between zero and the cell size) and in a random direction.After the shift, atoms that were outside the cell boundaries were returned inside via the periodic cell boundaries.We monitored the development of stress in the simulations, and found no significant buildup of stress during the prolonged irradiation.A separate simulation was performed where a step of pressure relaxation to 0 kbar between the recoil events was added.This simulation gave identical results within statistical fluctuations to those without the extra step of pressure control.
Defects were analyzed with the Wigner-Seitz cell method [9] as well as with the program OVITO [21] and an adaptive common neighbor analysis implemented in the program.

Comparison with ferritic alloys
Currently a leading candidate class of materials for high radiation environments are ferritic steels based on about 10% Cr in a body-centered cubic (Fe) matrix [22,23], which have been shown to exhibit good radiation resistance, likely due to the Cr slowing down dislocation loop migration [24,25].Hence, even though the Fe-Cr crystal structure is different to the currently studied facecentered cubic systems, it is of some interest to qualitatively compare the current results to those in Fe-10%Cr alloys.Hence we ran a set of similar cumulative 5 keV simulations for this Fe-Cr system modelled with the Olsson et al. potential [26].The results of the comparison, Fig. 1, show that reduction in irradiation damage is superior for the equiatomic alloys compared to iron and the Fe-Cr alloy.We emphasize that the numerical values should not be compared directly to each other, due to differences in the crystal structure, but the relative change difference between the pair of element vs. alloys gives a first indication that the damage reductions obtained in equiatomic alloys may be quite comparable, or even better, than those in long-developed Fe-Cr alloys.However, as for the final Fe-Cr based steels which have undergone decades of development, clearly more work will be needed also on testing and optimizing alloying element concentrations and microstructure for equiatomic alloys, before they are ready for use as engineering materials.

SOURCE CODE AND INPUTS
To enable reproduction of the results, the Supplementary material also includes the complete source code of the software used to carry out the simulations 'parcas' [27].The code, its documentation, and sample inputs for The code can be compiled and run on any Linux/Unix distribution that carries, in addition to the standard system environment, an MPI Fortran compiler, following normal practises of Linux software compilation and execution.The file

README.INSTALL
provided in the main directory created by the unpacking contains installation and running instructions.

FIG. 2 .
FIG. 2. Defect cluster distributions in Ni and NiFe at low fluence.(a) High magnification bright-field images of Ni and NiFe samples irradiated using 3 MeV Au ions to a fluence of 2 × 10 13 cm −2 (Peak dose at 155 nm is ∼0.1 dpa) under two beam conditions, g ¼ ½200, and (b) size distribution of defect clusters.Interstitial-type dislocation loops are indicated by the dashed circles, and small triangles marked by the dotted circles are characterized as SFT.The scale bar is 20 nm.

FIG. 3 .
FIG. 3. Defect cluster distributions in Ni and NiFe at high fluence.Bright-field cross-sectional TEM images (g ¼ ½200) showing the overall irradiated region in Ni and NiFe (a) samples after 3 MeVAu ion irradiation to 1 × 10 14 cm −2 (Damage peak at 155 nm is equivalent to 0.57 dpa).(b) Size distribution of defect clusters.
FIG. 4. Molecular dynamics results of damage production in Ni, NiFe, and NiCoCr.(a) Buildup of total number of defects and number of defects in clusters larger or equal to 10, divided into point defects and defect clusters.The lines are fits of a function to the data points to guide the eye.The individual data points show fairly large fluctuations since individual dislocation recombination reactions (see text) can cause large changes in the defect numbers.(b) Average cluster size distribution at the dose from ∼0.4 dpa to the end.The inset shows the same distribution grouped by cluster diameter.(c) Defect structures in Ni and NiFe at a dose of 0.5 dpa.The atoms shown are filtered by removing the perfect structured fcc atoms according to an adaptive common neighbor analysis, to show only atoms that are part of a defective structure.

FIG. 1 .
FIG. 1.Comparison of the results obtained for the equiatomic alloys compared with Fe and Fe0.9Cr0.1