Atomistic study on the nano-scratch mechanism of CoCrFeMnNi high-entropy alloy at different morphology densities

The physical nature of the scratch behavior of CoCrFeMnNi HEA and its deformation mechanism at different morphology densities are investigated by molecular dynamics simulations. The results show that the groove morphology contributes to the reduction of surface plastic deformation and exhibits a friction-reducing effect. As the morphology density decreases, the surface deformation and atom pile-up decrease, and the plastic deformation in the scratch region decreases, resulting in a further enhancement of the friction reduction effect. The increase of scratch depth intensifies the plastic deformation of the specimens, and the average scratch coefficient of friction increases with the increase in scratch depth. The dominant plastic deformation mechanism in the scratch deformation of CoCrFeMnNi HEA with different morphology densities is the slip deformation of Shockley partial dislocations. The MD simulations are verified further by qualitatively comparing them with corresponding experimental observations of CoCrFeMnNi HEA.


Introduction
As a new type of engineering material, high-entropy alloys (HEAs) have great application potential in aerospace, civil transportation and weaponry due to their excellent mechanical properties [1][2][3]. In the past two decades, a large number of HEAs have been proposed. Among all the existing HEAs, CoCrFeMnNi HEAs, which are composites of equiatomic elements of Co, Cr, Fe, Mn and Ni, are widely concerned as a result of its superb mechanical properties at various extreme conditions [4][5][6][7]. CoCrFeMnNi HEA devices will inevitably be subjected to scratch loading in service, resulting in the scratch or wear on the surface of the HEA material, thus reducing the assembly accuracy and service reliability of the relevant devices.
Yeh et al [1] and Cantor et al [3] independently reported HEAs with multiple elemental compositions of equal or nearly equal atomic ratios. A large number of uniaxial tensile/compression experiments were conducted to investigate the plastic deformation mechanisms of CoCrFeMnNi HEAs [8][9][10]. Woo et al [11] revealed that the dominant deformation mode of CoCrFeMnNi HEAs at high temperature was the dislocation glide and diffusion-controlled dislocation creep. Wu et al [12] observed that many macroscopic slip bands with different orientations were formed during the deformation of CoCrFeMnNi HEA at room temperature by in situ neutron diffraction experiments. Yao et al [13] further observed with a metallographic microscope that the number of slip lines on the surface of CoCrFeMnNi HEA increased gradually with the increase of strain during the tensile at room temperature, and revealed that the microstructure of CoCrFeMnNi HEAs experienced the evolution process of dislocation clustering, dense dislocation wall formation, and dislocation cell formation. Laplanche et al [14,15], Deng et al [16], Otto et al [17], Smith et al [18] and Kireeva et al [19] showed that dislocation slip was the main deformation mechanism in FCC structured HEAs. Nanoscale deformation twinning was observed by Otto et al [17] after loading the strain to 20% at 77 K, but not in specimens tested at an experiment temperature of 300 K.
As the temperature decreases, the deformation mechanism of CoCrFeMnNi HEA changes from a dislocation slip-dominated deformation mechanism at room temperature to dislocation slip and mechanical twin at low temperatures [12,20]. Otto et al [17] observed by scanning transmission electron microscopy that when the experiment temperature was reduced to 77 K, twinning provided an additional deformation mode to accommodate plasticity in CoCrFeMnNi HEAs. The results of Gludovatz et al [6], Otto et al [17] and Schuh et al [21] showed that the twinning morphology in CoCrFeMnNi HEAs was sheet structure, and the thickness of deformation twin varied from a few nanometers to micrometers. Diao et al [20] revealed that the deformation twin caused a hardening of the stress-strain curve and an increase in the ultimate tensile strength of CoCrFeMnNi HEAs. Aitken et al [8] showed that the formation of twin in FCC HEAs was attributed to the formation of the continuous adjacent fault plane and depended on the stacking fault energy. Recently, Naeem et al [22] used in situ neutron diffraction experiments to further investigate the deformation mechanism of stacking fault in CoCrFeMnNi HEAs at high strain and ultralow temperature.
Tensile experiments at quasi-static to dynamic strain rates were performed by Shabani et al [23] to point out that the dominant plastic deformation mechanisms changed from dislocation slip at the quasi-static strain rate to dislocation slip and twin deformation at impact loading and the ultimate tensile strength and ductility improved with the increase in strain rate due to the activation of deformation nano-twins in HEAs.
In addition to experimental studies, MD simulations had been applied to analyze the plastic deformation mechanism of CoCrFeMnNi HEAs under uniaxial tensile/compressive. Choi et al [24] observed that twins formed along with partial dislocation and severe lattice distortion would promote the formation of dislocations in CoCrFeMnNi HEAs. Fang et al [25] investigated the deformation and plasticity as well as strength in the dualphase nanocrystalline HEAs with a variable volume fraction of FCC (Face-Centered Cubic) and HCP (Hexagonal Close Packed) phases using atomistic simulations during the tensile tests, which revealed that straininduced phase transformation in dual-phase CoCrFeMnNi HEA improved the ductility and strength of nanocrystalline HEA. Qi et al [7,26,27] found that twinning controlled the inelastic deformation at the low temperature and high strain rate, and dislocation slipping gradually became the main plastic deformation mechanism with the increase in temperature and the reduction in strain rate.
In terms of scratch experiments in CoCrFeMnNi HEAs, Nagarjuna et al [28] pointed out that the hardness of the deformed layer showed higher than the matrix owing to grain refinement induced by sliding friction. For MD simulations about scratch in CoCrFeMnNi HEAs, Tang and Li [29] reflected that the correspondingly reduced stress concentration and less lattice deterioration helped to absorb more wearing energy before failure. Qi et al [27,30] further revealed that the inelastic deformation of CoCrFeMnNi HEA was affected by the partial dislocations generated during the scratch. Although the microscopic deformation behavior of CoCrFeMnNi HEA in nano-scratch had been preliminarily investigated, the effect of surface morphology density on the scratch behavior of single crystal CoCrFeMnNi HEA and its deformation mechanism at the atomic scale were not yet reported. Consequently, MD simulations were employed for this work to characterize the effect of surface morphology density on the scratch response of single crystal CoCrFeMnNi HEA under nano-scratch and its deformation mechanism at the atomic scale.

Simulation methodology
As shown in figure 1, the simulation cell is composed of a bulk CoCrFeMnNi HEA and a spherical column diamond scratch tool, and the specimen is classified into newton layer, thermostat layer, and fixed layer, where thicknesses of both the thermostat layer and the fixed layer are 0.40 nm. The X, Y and Z directions in the model correspond to the crystal directions [100], [010] and [001], respectively. The initial lattice constant of the CoCrFeMnNi HEA is 3.59 Å [24,31]. The size of the specimen is 22.40 nm × 12.00 nm × 6.40 nm containing 150750 atoms. The scratch tool radius is set to 2.40 nm, while the center of the scratch tool sphere is 26.80 nm and 6.00 nm from the origin in the X and Y directions, respectively. The simulation cell is subjected to a periodic boundary condition in the Y-direction, while free boundary conditions are applied in the X and Z-directions.
Referring to the research work on nanoscale rough surfaces, the rectangular shape of the substrate surface morphology is chosen [32][33][34]. The geometric features of the surface morphology are characterized by the parameters a, b and h, as shown in figure 1. As shown in figure 2, the h/a values for the five different morphology density specimens (T1, T2, T3, T4 and T5) are 0, 0.5, 1, 1.5 and 2, respectively. Except for the h/a value of 0, where h is zero, b and h are fixed at 2.00 nm for all other morphology densities, and the values of a are set to 4.00, 2.00, 1.33 and 1.00 nm. The substrate morphology density is defined as r = + . a a b The morphology densities of T1, T2, T3, T4 and T5 are 100%, 67%, 50%, 40% and 33%, respectively.
Under the NPT ensemble, the initial thermal equilibrium of the model is achieved by relaxing the simulated cell at the temperature of 300 K with zero pressure. The scratch process is performed under the NVE ensemble. The scratch tool is carried out with a constant velocity of 100 m s −1 and an initial temperature of 300 K from the initial position along the negative direction of the X-axis. The time step during the simulation is set to 1 fs. The interaction between CoCrFeMnNi HEAs is developed based on the second nearest-neighbor modified embedded-atom method [24]. The total atomic potential energy of a system E is expressed as: where F i is the embedded energy of atom i, r i is the background electron density at site i, and S ij and ( ) AE R ij ij are the screening factor and pair potential between atoms i and j separated by a distance R , ij respectively. The interaction between the diamond scratch tool and the substrate is described by the LJ potential: where, e is the energy parameter; s is the distance parameter; and r is the distance between two atoms. According to the universal force field parameters calculated by Rappe et al [35] and the Lorentz-Berthelot mixing rules [36], the interaction parameters between the diamond scratch tool and the substrate are calculated in table 1.
The scratch tool can be regarded as a rigid body during the simulation, and the interaction between diamond atoms (C-C) is ignored [36][37][38][39][40][41]. MD simulations of the scratch behavior were performed by LAMMPS [42] (Large-scale Atomic/Molecular Massively Parallel Simulator), and the simulation results were visualized and analyzed with OVITO (Open Visualization Tool) [43].

Results and discussions
3.1. Scratch behavior at different morphology densities Figure 3 presents the evolution curves of the tangential and normal forces with the scratch distance for the CoCrFeMnNi HEA at different morphology densities and the scratch depth of 2.4 nm. As demonstrated in figure 3, the tangential and normal forces increase from zero gradually as the scratch tool scratches into the specimen initially. After the scratch tool completely scratches into CoCrFeMnNi HEA, the tangential and normal forces generally stabilize. The mean tangential force and normal force after the scratch tool wholly into the specimen (scratch distance up to 6.8 nm) until the scratch distance reaches 20 nm are taken as the average tangential force and average normal force, respectively. Figure 4 is the average scratch force and the average scratch coefficient of friction (SCOF) for various morphology densities. As shown in figure 4(a), the average tangential force and the average normal force exhibit the same trends, which both decrease with the decrease of the morphology density. The ratio of the average tangential force and the average normal force is regarded as the average SCOF. As shown in figure 4(b), the average SCOF of T1, T2, T3, T4 and T5 morphology densities respectively are 0.97, 0.81, 0.64, 0.58 and 0.53. It is clear that the average SCOF decreases following the decline of morphology density; at the scratch tool radius of 2.4 nm, the T5 morphology density exhibits the most significant friction reduction effect, and the T1 morphology density possesses the greatest frictional resistance. This suggests that the texturing treatment on the surface of CoCrFeMnNi HEA can result in a friction reduction. Similar results were observed by Li et al [32] in a nanoscale grinding simulation of single-crystal copper.   Figure 5 shows the temperature variation of specimens with different morphology densities during the scratch. As shown in figure 5, at the beginning of scratch, the temperature curves keep constant owing to a lack of contact between the scratch tool and the specimen; with the increase of the scratch distance, the temperature progressively increases, while the rate of increase gradually drops to 0; after the scratch distance of about 18 nm, a slight drop in temperature is observed. This is because the scratch tool gradually interacts with the substrate at the beginning, generating a great deal of heat, which consequently increases the temperature; subsequently, the temperature depends on the competition between the heat generated during the scratch and the heat absorbed by the thermostat layer [32]. Obviously, when the morphology density is over 40%, the temperature shows a dependence on the surface morphology which increases with the increase of the morphology density, especially after the scratch distance up to 9 nm, the temperature under T1 morphology density is always much higher than the others. Since various morphology densities possess the same thermostat layer, it can be inferred that surface texture can reduce the heat generated by scratch deformation. The above analyses indicate that texturing treatment of the surface of CoCrFeMnNi HEA leads to a reduction in the specimen temperature during the scratch. Figure 6 shows the atomic structure of the longitudinal profile along the scratch direction and the surface atomic structure at different morphology densities after the scratch. As shown in figure 6(a), for the planar morphology (T1) specimen, a large number of atoms accumulate in front of and on both sides of the scratch tool, while for the groove morphology (T2, T3, T4 and T5) specimens, the substrate grooves in the scratch area are completely destroyed after the scratch deformation. As shown in figure 6(b), a great number of atoms pile up around the scratch area after the scratch, and the height of atom accumulation before the scratch tool decreases as the morphology density decreases. It indicates that the groove morphology contributes to the reduction of lattice deformation in the scratch region of CoCrFeMnNi HEA at a scratch depth of 2.4 nm, showing a frictionreducing effect, and the surface plastic deformation and the height of pile-up decrease as the morphology density decreases.

Scratch mechanism at different morphology densities
The dislocation distribution in the simulation cell is analyzed through dislocation extraction algorithm [44]. Figure 7 shows the dislocation distribution of specimens with different morphology densities after the scratch. As shown in figure 7, dislocations around the scratch region intertwine with each other; and most of the dislocations at each morphology density are Shockley partial dislocations with a few other types of dislocations intersperse. This suggests that the dominant plastic deformation mechanism of the CoCrFeMnNi HEA during the scratch at different morphology densities is the slip deformation of Shockley partial dislocations under the scratch action of the scratch tool on the substrate. Figure 8 exhibits the variation of the total length of dislocations in the specimens with different morphology densities during the scratch. Due to the adjustment of atomic positions during the energy minimization and relaxation, lattice misfit occurs at the interface [45], which leads to a non-zero total dislocation length for each specimen at the scratch distance of 0 nm. As shown in figure 8, the total length of dislocations for T1 morphology density after the scratch is higher than that for T2, T3, T4 and T5 morphology density after the scratch; the total length of dislocations at T2 morphology density increases noticeably with the increase of scratch distance, while the rate of change of total length is almost zero for T3, T4 and T5 morphology densities. It indicates that the dislocations of CoCrFeMnNi HEA are suppressed with the decrease of the morphology density during the scratch.
The specimen surface absorbs the dislocations sliding to the surface, which causes the total dislocation length of each specimen to fluctuate as the scratch distance increases. At the same scratch depth, the decrease of the morphological density promotes the annihilation of dislocations that slip into the surface. It results in a decrease in the total dislocation length as the morphology density decreases.
The scratch behavior of CoCrFeMnNi high-entropy alloy with different scratch depths and its deformation mechanism are investigated to further reveal the scratch deformation mechanism at the prescribed morphology density. Figure 9 shows the average scratch force and the average SCOF for T3 morphology density specimens at different scratch depth curves and the scratch depths of 1.2, 2.4 and 3.6 nm. A1, A2 and A3 are employed as abbreviations for the three scratch depths of 1.2, 2.4 and 3.6 nm, respectively. As shown in figure 9, the average normal force and average tangential force increase sharply with increasing in scratch depth; and the average SCOF increases correspondingly with the increase of scratch depth.  Figure 10 shows the atomic structure of the longitudinal profile along the scratch direction and surface atomic structure at the scratch depths of 1.2, 2.4 and 3.6 nm after the scratch. As shown in figure 10, the surface textures in the scratch area are damaged. At the scratch depth of 1.2 nm, the substrate grooves in the scratch area are not completely destroyed and slight atom accumulation is observed in the longitudinal profile; while at the scratch depths of 2.4 and 3.6 nm, the grooves in the scratch area are completely destroyed and significant lattice distortion and pile-up are observed. Furthermore, as shown in figure 10, the height of pile-up around the scratch region increases with the increase of scratch depth. Figure 11 presents the dislocation distribution in the specimen after the scratch for different scratch depths. As shown in figure 11, the dislocations in the specimen are concentrated in both sides of the scratch area, and the dislocations at different scratch depths are entangled together; as the scratch depth increases to 3.6 nm, a large number of dislocations are generated and clustered together; the dislocations in the specimen at different depths are dominated by Shockley partial dislocations. It demonstrates that the dominant plastic deformation mechanism of the CoCrFeMnNi HEA in the scratch deformation at different depths is still the slip deformation of Shockley partial dislocations. Figure 12 shows the total length of the dislocation line versus scratch distance at different scratch depths in the scratch process. The total dislocation line length fluctuates with the increase in scratch distance at the scratch depths of 1.2 and 2.4 nm, while it increases significantly at the scratch depth of 3.6 nm; furthermore, the total dislocation line length at 3.6 nm is notably higher than that at 1.2 and 2.4 nm after the scratch tool completely penetrates the substrate. This indicates that the increase of scratch depth promotes the plastic deformation of CoCrFeMnNi HEA.
Obviously, smaller depths of scratch reduce subsurface damage and can improve grinding efficiency by having a relatively large number of chip atoms [46]. In contrast, a larger scratch depth resulting in more lattice defects and dislocations in the scratch regions, which leads to a stronger sliding friction hindrance, resulting in a significant increase in the required normal scratch force and a reduction in the scratch friction coefficient.
The average SCOF increases with increasing in morphology density and scratch depth for different morphology densities and scratch depths. When the scratch tool enters the substrate and the applied mechanical loading in the scratch area exceeds the nucleation stress of dislocations, dislocations nucleate and grow from atoms around the scratch tool and induce plastic deformation, which in turn causes the removal of atoms in the scratch area. As the plastic deformation in the scratch area intensifies, more atoms accumulate in front of the scratch tool, increasing the SCOF in the scratch area [47]. With the decrease of the morphology density and the scratch depth, the plastic deformation of the scratch area in the groove morphology is suppressed due to the dislocation annihilation, which reduces the SCOF in the scratch area and thus results in a friction reduction effect. As shown in figures 6, 7, 10 and 12, the accumulation height of atom before the scratch tool and the total dislocation line length in the scratch region significantly increase with increasing in morphology density and scratch depth. This indicates that the plastic deformation in the scratch area becomes more severe with the    increase of the morphology density and the scratch depth. Therefore, the SCOFs under different morphology densities are related to the dislocation defects in the scratch area; the more intense for the plastic deformation induced by dislocations, the greater the frictional coefficient of the scratch area. The dominant plastic deformation mechanism of the CoCrFeMnNi HEA during the scratch at different morphology densities is the slip deformation of Shockley partial dislocations under the scratch action of the scratch tool on the substrate. Therefore, it can be determined that the main dislocation defect affecting SCOF during the scratching is Shockley partial dislocation. It also suggests that texturing the surface and reducing the morphology density of the surface at a set scratch depth can significantly decrease the plastic deformation of CoCrFeMnNi highentropy alloy, thus inhibiting the wear of CoCrFeMnNi high-entropy alloy devices.

Validation of simulation results
Since the prescribed time scale in MD simulations is several orders of magnitude lower than the existing experiments, the existing works have mainly qualitatively compared MD simulations with the corresponding experiments [48][49][50]. In the experiments on scratch of CoCrFeMnNi HEA, Nagarjuna et al [28] revealed that the friction coefficient stabilized at a longer sliding time. The tangential force, normal force, and SCOF in CoCrFeMnNi HEA were also observed to stabilize with increasing scratch time in MD simulations [27]. The tendencies of the tangential force, normal force versus scratch distance for CoCrFeMnNi HEA at different morphology densities obtained from MD simulations in this work are consistent with the results revealed by the existing experiments and MD simulations.
Further results available by Laplanche et al [14,15], Deng et al [16], Otto et al [17], Smith et al [18] and Kireeva et al [19] demonstrated that dislocation slip was the dominant plastic deformation mechanism in CoCrFeMnNi HEA. Qi et al [30] also noted that the plastic deformation in the uniaxial tensile of CoCrFeMnNi HEA was dominated by Shockley partial dislocations by MD simulations. Nagarjuna et al [28] found that the severe deformed layer was partially eliminated by excessive sliding and the dislocation slipping in the scratch region of CoCrFeMnNi HEA. In MD simulations of this work, dislocations began to nucleate beneath the indenter tip, and induced the plasticity, which in turn caused the removal of atoms from the scratch area, during the nano-scratch stage. Qi et al [27,30] investigated the mechanical behavior and microstructural evolution of nanocrystalline CoCrFeMnNi HEA under scratch load by MD simulations, and further pointed out that the plastic deformation of CoCrFeMnNi HEA was significantly affected by Shockley partial dislocations generated. Wagner et al [51] revealed that plastic deformation occurred initially by the glide of perfect dislocations dissociated into Shockley partials on {111} planes through transmission electron microscope in the compression test of CoCrFeMnNi HEA. Utt et al [52] also observed the emitted and gliding motion of an array of Shockley partial dislocations under tensile load in the CoCrFeMnNi HEA. These experimental results prove that it is reasonable that the dislocation slipping of Shockley partial dislocation dominates the plastic deformation of CoCrFeMnNi as shown in the MD simulation results of this work. The plastic deformation mechanism for different morphology densities in the scratch region of the CoCrFeMnNi HEA acquired by MD simulations obtained in this work is consistent with the results revealed by the existing experiments and MD simulations. In summary, by comparing the MD simulation results obtained in this work with the corresponding macro and microscopic experiment results, the MD simulations in this work can be determined to be reasonable and further reflect the scratch behavior of CoCrFeMnNi HEA at the atomic scale and its deformation mechanism under different morphology densities.

Conclusions
MD simulations can reveal the physical nature of the scratch behavior of CoCrFeMnNi HEA with different surface morphology densities and provide a mechanism reference for establishing relative theoretical model. The findings indicate that: The average SCOF increases with increasing in morphology density and scratch depth for different morphology densities and scratch depths. With the decrease of morphology density and scratch depth, the plastic deformation of the scratch area in the groove morphology is suppressed due to the dislocation annihilation, which reduces the SCOF in the scratch area and thus results in a friction reduction effect.
The dominant plastic deformation mechanism of the CoCrFeMnNi HEA during the scratch at different morphology densities is the slip deformation of Shockley partial dislocations under the scratch action of the scratch tool on the substrate. The main dislocation defect affecting the friction coefficient during the scratch is Shockley partial dislocation. Texturing the surface and reducing the morphology density of the surface at a set scratch depth can significantly decrease the plastic deformation of CoCrFeMnNi high-entropy alloy, thus inhibiting the wear of CoCrFeMnNi high-entropy alloy devices.