Uniaxial pulling and nano-scratching of a newly synthesized high entropy alloy

Multicomponent alloys possessing nanocrystalline structure, often alluded to as Cantor alloys or high entropy alloys (HEAs), continue to attract the great attention of the research community. It has been suggested that about 64 elements in the periodic table can be mixed in various compositions to synthesize as many as ∼ 10 8 different types of HEA alloys. Nanomechanics of HEAs combining experimental and atomic simulations are rather scarce in the literature, which was a major motivation behind this work. In this spirit, a novel high-entropy alloy (Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 ) was synthesized using the arc melting method, which followed a joint simulation and experimental effort to investigate dislocation-mediated plastic mechanisms leading to side flow, pileup, and crystal defects formed in the sub-surface of the HEA during and after the scratch process. The major types of crystal defects associated with the plastic deformation of the crystalline face-centered cubic structure of HEA were 2,3,4-hcp layered such as defect coordination structures, coherent ∑ 3 twin boundary, and ∑ 11 fault or tilt boundary, in combination with Stair rods, Hirth locks, Frank partials, and Lomer–Cottrell locks. Moreover, 1/6 < 112 > Shockley, with exceptionally larger dislocation loops, was seen to be the transporter of stacking faults deeper into the substrate than the location of the applied cutting load. The (100) orientation showed the highest value for the kinetic coefficient of friction but the least amount of cutting stress and cutting temperature during HEA deformation, suggesting that this orientation is better than the other orientations for improved contact-mode manufacturing.


I. INTRODUCTION
High entropy alloys (HEAs) are multicomponent alloys comprising at least five elements from the periodic table, with each element within a concentration range of 5%-35%.HEAs were formally reported by Yeh et al. 1 and Cantor et al. 2 in 2004, although Cantor developed them long ago in the 1990s through a student project and left academia to join the industry, and it is in his honor that HEAs are also referred to as Cantor alloys.HEAs are endowed with exceptional properties compared to conventional solid-solid solution alloys, which has led to an accelerated global effort in exploring the potentials of HEAs as structural materials, 3 functional materials, 4 smart materials, and sensors 5 as well as biocompatible materials, 6,7 to name a few.Many of these aspects of HEAs are discussed in a recent review paper written by the authors, focusing on the use of machine learning in predicting the crystal structure of HEA. 8 HEAs are now being explored in various engineering applications, including superb ultra-high temperature materials for exhaust nozzle, 9 combustion chambers, 10 compressors, 11 gas turbine case applications in the aerospace engine, 12 and excellent superconductor magnetic materials to create magnets powerful enough to levitate trains with low-loss transmission of electricity. 13Additionally, the exceptional abrasive resistance of HEAs is significant for the use of moving components in industrial applications, e.g., bearings and gears.The higher strength and better deformation resistance characteristics of HEAs are significant for all these applications.Moreover, these applications are governed by the nanotribology of ARTICLE scitation.org/journal/apmHEA, hitherto poorly understood.This is acutely important, given the responsible use of mined materials, as some of the constituent metals required to synthesize HEAs are at critical import risk, which is often referred to as critical raw materials (CRMs). 14umerical solvers, such as ab initio and finite element methods, 15 are unsuitable for studying the tribology of HEA due to the length scale problem and the lack of appropriate material constitutive models.In this sense, molecular dynamics (MD) 16,17 is an appropriate tool to understand plasticity mechanisms in HEA.Combining this simulation-led discovery with an experimental campaign of contact loading study on HEA using nanoscratching 18 was the key highlight of this work.
Recent works have reported some aspects of plastic deformation in HEAs, such as Al 0.1 CoCrFeNi, 19,20 FeCoCrNiCu, 21 AlCr-CuFeNi, 22 and CrMnFeCoNi, 23,24 by using the classical EAM potential function in MD simulations in conjunction with experimental methods such as in situ transmission electron microscope (TEM) uniaxial stress. 25,26The uniaxial stress situation differs from the deviatoric stress condition often witnessed in contact conditions, such as scratching, and since the studies in this area are scarce, this nanoscratching investigation on the newly synthesized HEA is novel.
A study such as this one is necessary to answer open questions to address concerns such as (i) the supercell of HEA developed using the special quasi-random structure (SQS) method does not introduce large prediction errors, (ii) the EAM potential energy function available to simulate the HEA alloy can still be used reliably for performing nanomechanical studies, and (iii) whether a face-centered cubic (FCC) structure of HEA deforms akin to normal FCC metals, such as copper and aluminum, or shows distinct deformation mechanisms.In pursuit of the answers to these questions, a novel high entropy alloy (Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 ) was first prepared in the lab, and experiments were then performed alongside the MD simulations to explain the nanomechanical behavior of this unique FCC HEA.The Ni, Cu, Fe, Co, and Al metal buttons were purchased from Thermofisher Scientific ® with 99.99% purity.All metal buttons were melted together by arc melting in an inert gas (Ar) environment.The melted matrix was solidified, remelted, and resolidified multiple times to ensure homogeneity.The mixing ratio was chosen selectively to obtain Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 .The HEA button was vacuum sealed in a quartz tube, homogenized at 1000 ○ C for 10 hours, and then quenched into the water to freeze the hightemperature phase.The sample thus obtained was analyzed using x-ray diffraction analysis (see Fig. 1), which confirmed that the alloy stabilized into a single-phase FCC alloy.

B. Nano-scratching experiments
In this paper, an instrumented nano-scratching apparatus from Micromaterials Limited (Platform 5, NanoTest Vantage, based at London South Bank University, UK) was used to carry out the nanomechanical testing (see Fig. 2).The loading mechanism comprises a pendulum that rotates around a pivot and is loaded electromagnetically.The test sample was mounted vertically, and the test probe displacement was measured with a parallel plate capacitor with sub-nm resolution.
During nano-scratching, a spheroconical diamond indenter with an end radius of 5 μm and an included angle of 90 ○ was used, as shown in Fig. 3 The atomic model construction of HEA is a complex process.The two schemes available to perform this task are cluster expansion and special quasi-random structures (SQS).Of these methods, the SQS method is more popular and is implemented in software such as Atomsk. 27Once a structure of HEA, either in the form of a cylindrical wire (for nano-tensile tests), or a cubic block (for nanoscratching tests), is made, it can be fed to software, such as LAMMPS (a large-scale atomic/molecular massively parallel simulator), 28 to perform the MD simulations.The visualization of the modeling data were performed using the Open Visualization Tool (OVITO).In OVITO, an automated "dislocation extraction algorithm" (DXA) implementation facilitates in situ analysis of various dislocations and crystal defects, which provides a rapid assessment of the MD data. 18,29,30

MD model parameters
The MD model comprises two types of geometries, namely, a cylindrical wire and a cubical block containing HEA atoms.Two types of cylindrical wires with the same aspect ratio of 0.66 were constructed: one short wire with a diameter of 7.2 nm and a length    110) plane oriented on the z axis; and (iii) the (100) plane oriented on the z axis (see Fig. 4).These wires were subjected to a nanoscale tensile test by pulling them in the z direction.A periodic boundary condition was prescribed in the z direction, and a shrink-wrapped condition was used in the X and Y directions.The model was thermally equilibrated at 300 K, and then a strain rate of 5 × 10 8 s −1 was used to perform the tensile testing.
As for the scratch test, a work piece of size 51.42 × 36.05 × 31.81nm 3 was modeled, containing 4 998 400 (five types) total atoms of high-entropy alloys [see Figs.5(a)-5(c)].The bottom part of this work piece was made rigid by prescribing a fixed boundary condition to hold the workpiece in place during scratching, and a small thermostatic layer was added next to the rigid layer to allow smooth heat dissipation from the workpiece during scratching.As for the indenter, a strong repulsive 31 and rigid-type spherical indenter of 8 nm diameter was modeled.This assumption was necessary due to the lack of a potential energy function parameterized for interactions between carbon atoms (tool) and  workpiece (HEA atoms).The indenter was given a velocity at the beginning of the simulation to travel a certain distance into the workpiece using LAMMPS NVE dynamics.During this motion, each atom in the indented material interacts with the idealized indenter to experience a force of magnitude F(r) = K(r-R) 2 , where K is the force constant (1 KeV/Å 3 ), R is the radius of the spherical indenter, and r is the distance of an atom of the work piece from the center of the spherical indenter.This implies that F(r) remains repulsive if R > r or becomes zero otherwise.Further parameters used to perform the scratch simulation are shown in Table I.

Verification of the HEA model developed using the SQS method
After the initial model development following the SQS method, the radial distribution function was estimated [see Fig. 5(c)].The radial distribution function (RDF) signifies that the workpiece was a long-range, crystalline-ordered structure.Simulated x-ray diffraction (XRD) in LAMMPS was also obtained for this structure to gather experimentally comparable data as evidence to prove that the modeled HEA had the same crystal structure that was synthesized experimentally.This becomes particularly clear from comparing Fig. 5(d) with Fig. 1, which is a direct comparison between experimental and simulated XRD of the high-entropy alloy synthesized for the first time in this work.

Potential energy function and stacking fault energy assessment
An EAM potential developed by Zhou et al. 32 at Sandia Labs was used to describe the interactions between the five atoms of Ni, Cu, Fe, Co, and Al that make up the HEA.Since the stacking fault energy is important to mechanical deformation, it was appropriate to assess the generalized stacking fault energy (GSFE) on the Shuffle plane (111) <−110> of the high-entropy alloy Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 .Generalized stacking fault energy was first proposed by Vitek 33 in 1966 and recently has been proven as a critical criterion for dislocation slip, twinning, and plastic deformation mechanisms. 34GSFE can be computed as 35 where A represents the defect area, E 0 means the energy of a perfect crystal structure, and E(d) is the total energy of the deformed crystal.Intrinsic stacking fault is a planar defect that is a common occurrence in face-centered cubic (FCC) metals during their deformation.The natural stacking arrangement for FCC metals on the closed-packed (111) plane is ABCABCAB. .., but if an intrinsic stacking fault is introduced, the stacking arrangement changes to ABCBCABC. ... It is as if one closed plane, A in this case, has been removed, disrupting the otherwise perfect stacking.Since the modeled high entropy alloy resides in an FCC phase, it was considered appropriate to obtain the generalized stacking fault energy for this alloy, which is shown in Fig. 6.The unstable stacking fault energy (γ us ), which is the first maximum point on the GSFE curve based on Rice's brittle-to-ductile transition model, 36 was found to be 0.02 eV/ Å 2 .γ us represents the energy barrier for defect nucleation.The second maximum point of GSFE is the unstable twinning fault energy (γ ut ).The intrinsic stacking fault energy γ isf was estimated to be about 0.005 eV/ Å 2 .From Fig. 6, it was seen that the GSFE trend for HEA possessed some similarity with other FCC metals, such as copper, as reported previously by other researchers.The slope of GSFE with respect to the displaced atoms obtained from Fig. 6 suggested that about 4.8 GPa shear stress will cause the first instability in the structure, paving the way for the defect nucleation to occur.

III. RESULTS AND DISCUSSION
A. MD simulation of the uniaxial tensile test of the HEA nanowires A video was made from the simulated data (provided as complimentary data) to better understand the emission and propagation of the defects during tensile pulling.It was noticed that as soon as the HEA wire was subjected to tensile stress, an intrinsic stacking fault with a two-hexagonal close-packed (HCP) layer like coordination structure emitted from the surface of the wire, traveling at an angle inside the wire until reaching the circumference at the other end of the wire, as shown in Fig. 7 the other end of the nanowire of HEA is provided as supplementary information.We suggest that the emission of the intrinsic stacking faults relieves the stress intermittently, causing the cyclic drop in the uniaxial stress-strain curves.

B. Experimental measure of scratch force, kinetic coefficient of friction, and specific cutting energy
The scratch experiments were carried out using a ramp loading function on the polycrystalline HEA prepared in the lab, as discussed previously.The experimental scratching results are plotted in Fig. 8, showing the measurement of scratched forces (friction and normal forces), evolution of the kinetic coefficient of friction, evolution of the scratched area, and specific cutting energy (work done by the scratching tool in removing unit volume of material).The normal force was seen to vary from 0 to 500 mN, and it stayed at this magnitude during the course of nano-scratching.The maximum scratch depth at 500 mN force was of the order of 8 μm, and the friction force approached a value of about 225 mN.During steadystate nano-scratching, the kinetic coefficient of friction, which is the ratio of friction and normal forces (Fx/Fy), showed a value close to 0.45.

FIG. 12.
Topography of the HEA workpiece after scratch (i) obtained from MD simulation using a spherical indenter under depth-or velocity-controlled scratching and (ii) nanoscratching experiments with a spheroconical indenter (a) under a constant load of 500 mN and (b) under a ramped load from 0 to 500 mN as per the load function shown earlier in Fig. 3(b).

C. MD simulation estimates of scratch force, kinetic coefficient of friction, stress, and specific cutting energy
Figures 9(a) and 9(b) show the variation in the scratching forces (along the direction of the scratch and normal to the surface) in all three crystallographic orientations obtained from the MD simulations.In the initial state of scratching, the material initially experiences pure compression, and at this stage, the scratch force increases monotonically.After the material undergoes sufficient compression, the material removal process begins as soon as the compression is dominated by shear.In this state, the combined action of shear and compression paves the way for the material to flow plastically in the solid state.During this stage, steady-state scratching leads to a saturated regime of forces, which is an ideal regime to calculate and estimate the average scratch forces and kinetic coefficient of friction.The ratio of the two scratch forces, i.e., Fx (friction force) and Fy (normal force), is also referred to as the kinetic coefficient of friction, which is an important measure for the assessment of the tribology of the surface.From the MD data of the scratch forces, the kinetic coefficient of friction obtained from the simulation for the different orientations was seen to vary from 0.6 to 0.9, while it was minimum for the (110) orientation and maximum for the (100) orientation [See Fig. 9(c)].The value of the experimentally measured coefficient of friction was close to 0.45.The corresponding temperature peak values in the stressed zone are shown in Fig. 9(d).The (111) orientation was seen to be hotter than the (100) and the (110) orientations.
Figure 10 provides a comparison between the simulations and the experiments by way of measuring the kinetic coefficient of friction and the specific cutting energy.The specific cutting energy obtained from MD was found to be maximum for the [100] orientation and minimum for the [110] orientation.The experimental specific cutting energy was estimated to be 6.04 GPa, as illustrated in Fig. 10(b), close to the MD values.The average kinetic coefficient of friction from simulations deviates relatively from the experimental value, as shown in Fig. 10(a).This phenomenon was also noticed by the authors of this paper during the cutting of singlecrystal GaAs. 30Note that the differences in the kinetic coefficient of friction can have numerous origins: (i) the specimen used in the experiments was polycrystalline, whereas the simulations were performed on a single crystal material, (ii) the length scales used in experiments and simulations were dramatically different, and (iii) the specimen used in experiments may contain surface oxides and contamination, which do not exist in simulations.In view of these, we consider specific cutting energy as a more appropriate measure to compare experiments and simulations, especially because this property is independent of the geometry of the scratching tool used in simulations and experiments.
From the scalar measure of the stress tensor in the scratch zone, we estimated the peak average of Tresca stress, von Mizes stress, principal stresses (minor and major), and octahedral shear stresses, as shown in Fig. 11.The relevant formulas for calculation are provided in the supplementary material.Except for the major principal stress criterion, all criteria seem to indicate that the [100] orientation deforms at a lower stress than the other two orientations.The von Mizes stress in the scratched zone of the [100] orientation was about 10.5 GPa, while for the other orientations, it was of the order of 16 GPa.The octahedral shear stress on the [100] orientation was close to 5 GPa, which was close to the value of shear stress (4.8 GPa) obtained from the GSFE curve.D. Side flow, pileup, and crystal defects seen during nano-scratching MD simulations of HEA

Side flow and pileup
The topography of HEA scratches obtained from MD simulations is shown in Fig. 12.One can see a pileup of HEA atoms as well as the side flow on both sides of the nanogrooves on all crystallographic planes.The (010) crystal orientation showed the maximum height of the pileup, whereas the (111) orientation showed the maximum extent of dislocation activities in front of the scratching tool, which is evident on the top part of the scratched surface.The post-scratching surface topography obtained from simulations for all three orientations suggests that HEA exhibits strong anisotropic effects akin to other commonly known FCC metals such as copper and aluminum.In the case of (110), most HEA atoms pile up on both sides of the nanogroove and reach evenly up to 3.5 nm above the surface.In terms of material removal, it can be said that the material pileup for the (010) orientation occurred at an angle in a south-west direction from the front of the cutter, whereas for the (110) orientation, the pileup was equally divided on both sides of the scratching tool.The (111) orientation showed a somewhat uniform pileup on all sides of the surface, with a slightly higher amount in the front of the cutter as seen in the (010) orientation.On the experimental side, two nanoscratch images obtained from the SEM are provided, which were under a constant load of 500 mN and a ramp load from 0 to 500 mN, as per the load function shown earlier in Fig. 3(b).From this simple comparison, it is easier to see that for about 10-15 μm, the HEA showed full elastic recovery during scratching for the applied load conditions.HEA can be seen to flow on both sides of the scratching tool, albeit the extent of side flow can be seen to increase significantly from Fig. 12 (ii) (b) beyond a scratch length of 220 μm.Planar defects near the scratched surface and the sub-surface govern the quality of cutting as well as the plasticity mechanisms by which most of the material is transported during the material removal process.As for the FCC material, the commonly known planar defect templates for deformation are shown in Fig. 13.These include the {111} free surface, the coherent ∑3 twin boundary, the ∑11 <101> {131} symmetric tilt boundary, and the HCP phase with either 2, 3, or 4 layers of thickness.These defects were seen in HEA to not only be limited to the scratched area but also along the side of the scratch, where the stress was not sufficient to cause the material to flow.In some cases, the side flow or piled-up structures also showed additional types of faults.The other forms of defects observed were associated with intrinsic and extrinsic stacking faults, and the extent of these varied with the orientation of the HEA substrate.These planar defects result from the propagation of partial dislocations.Figure 13 highlights the portion of scratched material where these defect types were observed in the simulations.A more detailed visualization of these defects, directly extracted from the simulated nanoscratched specimens, is shown in Figs. 14 and 15.
The FCC structure has 12 non-equivalent partial dislocation slip systems ⟨110⟩/2-{111}.However, not all of these slip systems are operative during scratching.Based on tensor rotation, we can convert the applied shear (scratching) stress to each of the slip systems.The slip systems with the maximum conversion factors (analogous to the Schmid factor) are operative.We found that the (010) scratching has eight most likely operative slip systems

IV. CONCLUSIONS
This paper reports the mechanical properties of a novel highentropy alloy (Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 ) using nano-scratching experiments and MD simulations.This new alloy was synthesized for the first time and was found to reside in the FCC structure.
1.A novel mechanism of cyclic drop in the tensile test of the HEA nanowire was seen from the MD simulations.It was noticed that as soon as the HEA nanowire starts to deform, an intrinsic stacking fault emits from the surface of the wire, traveling at an angle inside the wire until reaching the other end of the wire.Emission of these intrinsic stacking faults relieves the stress intermittently, which revealed a unique insight into the deformation of HEA nanowires in contrast to other FCC metal nanowires.2. The generalized stacking fault energy (GSFE) curve obtained for HEA on the Shuffle set showed the unstable stacking fault energy (γ us ) as 0.02 ev/ Å 2 and intrinsic stacking fault energy γ isf of 0.005 eV/ Å 2 .The corresponding slope of GSFE with respect to the displaced atoms indicated that about 4.8 GPa shear stress triggers first instability in the FCC-HEA structure, paving the way for the defect nucleation.3.During scratching of Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 , several crystal defects were identified, such as {111} free surface atoms, coherent Σ3 grain boundaries, Σ11 faults or tilt boundaries, stacking faults (SF), and the HCP phase with various layer thicknesses.Additionally, Hirth locks and Lomer-Cottrell (LC) locks were also observed.1/6 <112> Shockley was seen as the longest dislocation governing the plasticity in FCC HEA.Aside from this, 1 /2<110> (perfect), 1/6 <110> (stair-rod), 1/3 <100> (Hirth), and 1/3 <111> Frank partials were seen in the sub-surface and pileup portion of the scratched HEA. 4. On comparing the MD simulations with the experiments, the specific cutting energy (work done by the scratching tool in removing a unit volume of material) showed a strong agreement, whereas the kinetic coefficient of friction differed.The observation was not only seen in this work for the FCCphase high-entropy alloy but was also seen during the AFM scratching of GaAs reported recently.This suggests that specific cutting energy is a more suitable parameter to compare MD simulation with experiments.
5. A strong anisotropy was seen from the MD simulations of tensile and scratching testing on HEA in terms of uniaxial tensile stress, scratch force, kinetic coefficient of friction, pile up, and side flow during scratching.The (111) orientation showed the highest uniaxial stress, while the (100) orientation showed the highest kinetic coefficient of friction, requiring maximum specific cutting energy.

SUPPLEMENTARY MATERIAL
See the supplementary material for the formulas used to generate Fig. 11 from the stress tensor obtained from the MD data.
SIMULATION SETUP A. Experimental synthesis and characterization of Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 alloy
(a).As shown in Figs.3(a) and 3(b), the load function in a load-control mode (with a low load head) at room temperature (∼20 ○ C) was used to perform the nano-scratching experiments.With this load function, the tip created a total scratch length of 480 μm such that the initial 250 μm length of scratch at the start used a ramping load of 0-500 mN and the 230 μm length of remaining scratch was performed at a constant load of 500 mN.C. MD simulation model development of the high-entropy alloy Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25

FIG. 7 .
FIG. 7. Stress-strain curves for (a) short and (b) long wires of HEA obtained from the MD simulations for all three crystal orientations, namely [111], [110], and [100].Higher yield stress for the shorter wire than the longer wire signifies the size effect.(c) Crystal defect analysis reveals periodic formation of slip bands (in blue), accounting for the periodic drops in the stress-strain curves.

FIG. 9 .FIG. 10 .
FIG. 9. Variation of (a) scratch force (Fx) and (b) normal force (Fy) on all three crystallographic orientations, (c) evolution of the kinetic coefficient of friction on all orientations, and (d) temperature peak values in the scratch zone of HEA in all three different orientations obtained from MD simulations.

Figures 7 (
Figures 7(a) and 7(b) show the engineering stress-strain curves for the two wires of HEA simulated using MD.The highest yield stresses occur during the [111] loading, yielding about 5 GPa and 4 GPa for the short and long wires, respectively.The lowest yield stresses occur during the [110] loading.The tensile stress-strain curves of the short and long nanowires showed close similarity in both magnitude and trend; however, frequent drops in the stresses (almost periodically) were noticedthis was unique in the HEA nanowire compared to other FCC nanowires that have been

FIG. 11 .
FIG. 11.Peak average stresses during scratching processes obtained from MD simulations for three crystallographic orientations.

TABLE I .
Detailed parameters used for the MD simulation of the Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 HEA alloy.Dimensions of the HEA workpiece 144a × 100a × 88a, where 'a' is 3.615 Å, which is the equilibrium lattice parameter of the Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 at 300 K of 10.8 nm, and one large wire with a diameter of 21.6 nm and a length of 32.4 nm.The nanowires were built in three orientations: (i) the (111) plane oriented on the z axis; (ii) the (