Anisotropic plasticity mechanisms in a newly synthesised High Entropy Alloy investigated using atomic simulations and nanoindentation experiments

This work used atomic simulations and nanoindentation experiments to investigate hardness, modulus alongside sub-surface crystal defects and dislocation mediated plasticity mechanisms leading to anisotropic pile up and local entropy variation in high entropy alloys. The experimental campaign began from Thermo-Calc phase prediction of Ni 25 Cu 18.75 Fe 25 Co 25 Al 6.25 HEA which followed experimental synthesis of the material using arc melting method and experimental nanoindentation using a Berkovich indenter under load-controlled conditions. Through MD simulations, the value of ℎ 𝑓 /ℎ 𝑚𝑎𝑥 in monocrystalline HEA was consistently found to be larger than 0.7 which suggested pile-up behaviour to dominate and sink-in behaviour to be unlikely. In the case of (110) and polycrystalline HEA substrates, the elastic work in the indentation hysteresis loop was seen to be larger than the (100) and the (111) orientations which explains that the (110) orientation substrate showed least elastic modulus and hardness while the (111) monocrystalline HEA showed the highest elastic modulus and hardness. From the simulations, a “lasso” type loop on the (110) orientation and cross-over of shear loops on the other orientations accompanied by dislocations of type 1/

To further enhance the gas and steam turbine efficiency in comparison with traditional Ni-based superalloys, recently, a new HEA Ni25Cu18.75Fe25Co25Al6.25 has been reported through the machine learning method which was experimental synthesised using vacuum arc melting under inert gas environment [16].Similar to other engineering materials, HEA also possess strong anisotropy, however, these aspects of anisotropic deformation behaviour of HEA have just begun to be investigated.This is important for instance, if HEA is being promoted for its use as a potential bond coating material for gas turbine engines, then deploying HEA with preferable orientation can improve coating lifetime.Also, it is unknown at this stage whether FCC phased HEAs and BCC phased HEAs follow same extent of anisotropy as monoatomic elemental metals such as copper (FCC) and Tantalum (BCC) or the presence of different type of atoms makes HEA behave differently during its plastic deformation?
Computation calculations offer new possibilities to obtain faster predictions about the material behaviour.On this front, the use of machine learning and data driven models, offer new avenues and much work in this area is being undertaken at present [16].On the contrary, atomistic computational tools such as molecular dynamics (MD) simulation use physics-based rationale to provide theoretically accurate predictions.Researchers can now use MD to probe crystal defects, dislocation mediated plasticity and preferential directions of deformation with a greater level of certainty [17] [18].On course to such an investigation, a recent study investigated the influence of alloy composition and grain size on the mechanical behaviour of AlCoCrFeNi HEA [19].However, this study did not focus on investigating anisotropy in HEA.Similarly, another MD simulation was employed to investigate FeNiCrCoCu HEA and it reported about the complementary roles of dislocation activity and twinning in controlling plasticity during nanoindentation response [20].
These studies provides a good basis to build on the initial work and in that process, it is the first investigation which provides a comparison of the MD simulation with the nanoindentation experiments on Ni25Cu18.75Fe25Co25Al6.25 high entropy alloy to better understand the anisotropic behaviour during nanoindentation.

Theoretical phase prediction of HEA
The CALPHAD methodology was utilised to minimise the global Gibbs free energy of a multicomponent system as a function of temperature and composition, thereby enabling the prediction of phase equilibria for Ni25Cu18.75Fe25Co25Al6.25.To visually represent the phase equilibria of this alloy in terms of phase percent as a function of temperature, a one-dimensional step diagram was employed using Thermo-Calc software (2023a) with TCHEA6 database [21], as shown in Fig 1.  inhomogeneities that arise from the partitioning of slow-diffusing/high-melting point elements from fast-diffusing/low-melting point elements [22].These inhomogeneities introduce variations not only in the composition but also in the solidus (incipient melting) temperature.The equilibrium diagram illustrates the phases that emerge when the alloy is annealed at a sufficiently high temperature for a long duration to allow for complete atomic diffusion and the attainment of the most thermodynamically stable configuration with the lowest possible Gibbs free energy.The CALPHAD approach plays a critical role in predicting the compositional evolution during solidification by coupling databases of thermodynamic parameters with diffusional kinetics parameters.

Experimental synthesis of HEA
To begin the experimental synthesis, the metal buttons were procured.Various metal buttons of Ni, Cu, Fe, Co and Al elements (purities> 99.99%) were purchased from Thermofisher Scientific®.All elemental metals were melted together by vacuum arc melting under inert gas (high purity Ar) environment.The ingot formed in the process was melted and solidified multiple times to ensure chemical homogeneity, and then the HEA button was vacuum sealed in a quartz tube, homogenised at 1000ᐤC for 10 hours, and then quenched into water for stabilising high-temperature phase.The detailed description of this high-entropy alloy is provided in Table 1.

Nanoindentation experiments on HEA
Nanoindentation experiments were conducted under load controlled conditions on a NanoTest Vantage machine (V5) machine from Micromaterials, UK.A Berkovich indenter tip (radius ~140 nm) was used to indent the HEA substrate using a velocity of 0.5 μm/s.The Berkovich indenter tip was prescribed with a peak load of 10 N in 4 s and the load was held for 20 s followed by unloading in 10 s as per the load function shown in Fig 3.

MD simulation setup
The MD simulations were carried out using the "Large-scale Atomic/Molecular Massively Parallel Simulator" (LAMMPS) software [23].A series of MD simulations consisted of nanoindentation on the (100), ( 110), (111) and polycrystalline Ni25Cu18.75Fe25Co25Al6.25 substrates were performed.The crystal structure of the HEA substrate was built by employing special quasi-random structures (SQS) approach in the Atomsk software [24].algorithm [26] to identify crystal defects, origins of dislocations and their Burgers Vector.The MD simulations were performed using the NVE ensemble at an equilibrated temperature of 300 K by applying the Nose-Hoover method [27] for 30 ps.The boundary conditions were set to be p, s and p type in X, Y and Z directions respectively [28][29].
For robust description of the chemical atoms containing five types of atoms (Ni, Cu, Fe, Co and Al), an EAM potential developed by Zhou et al. [30] was used.Further details of the process parameters used to perform the MD simulation of Ni25Cu18.75Fe25Co25Al6.25 in this work are provided in Table 2. Ensemble used in the simulation NVE at 300 K

Indenter type
An imaginary spherical shaped rigid indenter of radius R=4 nm described by a repulsive force constant 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 atom of the work piece from the centre of the spherical indenter.This implies that F(r) remains repulsive if R > r or becomes zero otherwise.
Timestep used for the calculation 1 fs

P-h plots obtained from the MD simulation
The P-h curves obtained from the MD simulation for the (100), ( 110 The ℎ  signifies the maximum depth of indentation.The value (ℎ  /ℎ  ) was calculated for each case.It can be seen that the polycrystalline HEA showed the minimum ℎ  /ℎ  of 0.398 while the (100), ( 110) and (111) monocrystalline HEA substrate showed this ratio to be 0.733, 0.493 and 0.721, respectively.To quantify the reduced modulus of the HEA substrate (  ), Oliver and Pharr (O&P) method was used [31]: where Er is the reduced elastic modulus, S is the slope of the top 1/3 rd part of the unloading curve, β=1 a constant for spherical indenter, A is the projected area (m 2 ) which varies with the depth of indentation.For this work, since a purely repulsive indenter was used, the value of Eindenter is infinite; the equation to obtain Especimen then simplifies to: where the value of υspecimen (Poisson's ratio) was taken as 0.26 for the Ni25Cu18.75Fe25Co25Al6.25 substrate [32].The estimated projected contact area was computed by employing geometry-based area function approach [33], as shown in Eq. ( 4).
where R is the radius of the indenter and h is the instantaneous displacement of the indenter Additionally, hardness is a measure of a material's resistance to plastic deformation which can be obtained as where  ℎ represents the loading force during loading process.
The MD results obtained from the simulations revealing the length scale dependent elastic modulus and nanoindentation hardness are shown in Fig 6.It may be noted that in the MD simulations performed here, a purely repulsive indenter was used so the values of indentation hardness and modulus extracted from the simulations are not comparable to the experimental values.This is because as opposed to a diamond indenter, an imaginary repulsive indenter had infinite modulus and a frictionless repulsive surface.This aspect was already reviewed by the authors in their previous work [33] so the value of elastic modulus and hardness obtained from a pure repulsive indenter is only indicative but the approximation about the dislocation and plasticity mechanisms obtained from MD are still valuable to understand the origins of the plasticity mechanisms.

P-h plot and the anisotropic pile up seen from the nanoindentation experiments
The P-h plot from the nanoindentation experiments performed on the indigenously synthesised polycrystalline HEA composition Ni25Cu18.75Fe25Co25Al6.25HEA [34] is been shown in

Anisotropy in HEA deformation obtained from the MD simulations
The residual indentation showed strong anisotropy on the (100), ( 110  For ease of understanding, the polycrystalline configuration has been compared pre and post indentation deformation by bringing an EBSD equivalent colour scheme.It can be seen from Fig 9 that the indenter made contact in the region which is at the intersection of several grains with orientations (310), ( 111), ( 101) and (210).As opposed to a perfect spherical symmetry, the lines of plastic deformation can be seen to be traversing through these grains carrying different propensity of deformation.Of those grains, the (210) orientation can be seen to be affected the most showing that the extent of dislocation propagation has affected a good half part of the grain, thus confirming that this orientation is most amenable compared to the other three grains in the ease of its plastic deformation.
(a) Before indentation (b) After indentation

3.3.Mechanism of plastic deformation in Ni25Cu18.75Fe25Co25Al6.25 HEA
The entropy based fingerprint calculation within OVITO is highlighted in Fig 10 which distinguishes ordered and disordered structure.When the value of location entropy is more negative, then it is better ordered [38].In the case of HEA indentation, the degree of disoardering can be seen to grow in the areas affected by the stress exerted by the indenter as well as in the grain boundaries.Also, the growth of the dislocation loops deeper on the (110) orientation can be seen to change the measure of local entropy which in other words indicates the local disordering in the crystalline structure of FCC HEA.
An extended analysis of these disordered structures was made using the CAT algorithm which is discussed further.the indentation load as also reported experimentally through TEM observations [39].
On indentation of the (110) orientation, a "lasso" type dislocation loop can be seen to emerge, which was not evidenced in any other case of indentation [40][41].The (110) orientation showed multiple shear loops which were seen to advance under the stress caused by the indenter into the HEA material by the advancement of their edge components.The formation process of "lasso" type dislocation loop is explained further using the analytical model of dislocation evolution through Fig 12, where a octahedron dislocation loop is used to indicate the formation process of "lasso" type dislocation loop., Hirth dislocations are also known as Hirth locks [42] and Frank dislocations are known as Lomer-Cottrell (LC) locks [43].
However, not all these slip systems are operative during contact loading experiment such as boundary obstructs the growth and propagation of shear loops leading to form a complex and concentrated junction of stacking faults in the indented area.Thus, in the case of (110) and polycrystalline HEA substrates, the elastic work in the indentation hysteresis loop was seen to be larger than the (100) and the (111) orientations.

Conclusions
The paper report novel insights into the anisotropic plastic deformation mechanisms of a high entropy alloy (HEA) with composition Ni25Cu18.75Fe25Co25Al6.25.In line with the Thermo-Calc prediction, the XRD experiments revealed that this HEA composition stabilises in FCC phase.Nanoindentation experiments using a Berkovich indenter under load-controlled conditions showed its hardness and reduced modulus to be about 1.32 GPa and 155 GPa respectively.A broad list of conclusions from this study can be summarised as below: 1.The (100) orientation monocrystalline showed atomic pileup with a clear 4-fold symmetry.The value of ℎ  /ℎ  from the MD simulations on monocrystalline HEA was consistently found to be larger than 0.7 which suggested pile-up behaviour to dominate during indentation of HEA and sink-in behaviour to be unlikely.In the case of (110) and polycrystalline HEA substrates, the elastic work in the indentation hysteresis loop was seen to be larger than the (100) and the (111) orientations.It was learned that the (110) orientation was softer while the (111) monocrystalline HEA showed the highest elastic modulus and hardness.3. The defects accompanying these dislocations in the sub-surface were identified to be FCC intrinsic stacking faults (ISF), adjacent intrinsic stacking faults (quad faults), coherent ∑3 twin boundary and a coherent twin boundary next to an intrinsic stacking fault (triple fault).From EBSD analysis applied to the MD data, an acute information learned was that the (210) orientation and the<110> family of directions were seemed to be preferable for the plastic deformation in FCC phased HEAs.

Figure 1 :
Figure 1: Phase composition of Ni25Cu18.75Fe25Co25Al6.25 alloy as a function of temperature calculated by Thermo-Calc software with TCHEA6 database.

Fig 1
Fig 1 shows key characteristics of the phase equilibria, including the width of the single-phase face-

Figure 2 :
Figure 2: Experimental X-ray diffraction pattern along with the simulated X-ray diffraction pattern of the newly synthesised high entropy alloy Ni25Cu18.75Fe25Co25Al6.25.

Figure 3 :
Figure 3: (a) Schematic of the Berkovich indenter tip and (b) load function used for the nanoindentation.
The schematic model of the monocrystalline and polycrystalline HEA built in this work are shown in Fig 4. The polycrystalline HEA specimen of size 36.1 nm × 36.1 nm × 35.9 nm containing 30 number of grains was modelled and visualised using Open Visualization Tool (OVITO) [25] as shown in Fig 4(b) and Fig 4(c).The post processing of LAMMPS data was performed with an automated "dislocation extraction algorithm" (DXA)

Figure 4 : 2 :Case 1 :
Figure 4: (a) Monocrystalline Ni25Cu18.75Fe25Co25Al6.25HEA model (b) polycrystalline Ni25Cu18.75Fe25Co25Al6.25HEA model (c) Identification of individual grains in the polycrystalline HEA sample ), (111) and polycrystalline HEA obtained from the simulated nanoindentation are shown in Fig 5.A total displacement of 1.8 nm can be seen which include 0.3 nm of free travel before the indenter touches the substrate and then advances into the substrate by 1.5 nm depth.From Fig 5, the loading and unloading processes were accompanied by several pop-in and pop-out events.Fig 5 also revealed that the peak loading forces at 1.5 nm indent depth were 1241.8nN, 511.5 nN, 1286.1 nN and 466 nN for the (100), (110) (111) monocrystalline and polycrystalline HEA substrate respectively.The lowest peak load of 466 nN observed in poly HEA can be attributed to the easy slippage and deformation of the grain boundaries (GBs).The observation of GBs was extensively examined and is discussed in the next sections.The residual depth of indentation ℎ  indicated the extent of permanent plastic deformation of the HEA substrate during the timescale of the simulation.

Figure 5 :
Figure 5: P-h curves obtained from the MD simulation for the HEA (a) (100) orientation (b) (110) orientation (c) (111) orientation and (d) polycrystalline HEA.Violet arrows and orange arrows refer to the Pop-in and Pop-out events respectively.
Fig 6(a) indicated that the polycrystalline HEA substrate showed the lowest magnitude of elastic modulus while the (111) monocrystalline HEA showed the highest elastic modulus.In Fig 6(b), following the same order, the lower nanoindentation hardness was shown by the polycrystalline substrate whilst the (111) orientation showed the highest hardness with (110) orientation being the softer orientations across the three major crystallographic orientations.

Figure 6 :
Figure 6: (a) Variation in the elastic modulus and (b) nanoindentation hardness of Ni25Cu18.75Fe25Co25Al6.25HEA obtained from the MD simulations.

Fig 7 .
An array of 36 indents was made in the HEA sample as shown in Fig 7(a).At a peak load of 10 N, the maximum indentation depth was about ~18 microns.No sink in behaviour was noticed but anisotropic pileup only along one edge of the nanoindentation edge in the SEM imaging of the nanoindentation topography can be seen from Fig 7(a).The departure of the blue line to the yellow line (Fig 7(a)) only on one of the three indented edges suggest strong anisotropy in the pile-up behaviour of HEA.The HEA revealed a reduced elastic modulus of 155 GPa and nanoindentation hardness of 1.32 GPa.ℎ  /ℎ  is a useful parameter to predict pile-up or sink-in behaviour, where a ratio above 0.7 indicates pile-up behaviour and a ratio below 0.7 suggests sink-in behaviour[35][36][37].In case of the newly synthesised Ni25Cu18.75Fe25Co25Al6.25, the experimental ℎ  /ℎ  was 0.922, as indicated inFig 7(b).This value confirms pile up behaviour during nanoindentation.A Hertzian curve was fitted to identify the elastic-plastic transition point.This point coincides at an indentation depth of ~8 µm which is demonstrated inFig 7(b).The area of plastic deformation zone was significantly higher than the area under the elastic deformation zone which is a clear indication that the newly synthesised Ni25Cu18.75Fe25Co25Al6.25HEA deformed predominantly in the plastic mode with minimum elastic recovery.It should be noted that the experimental sample indented was a polycrystalline HEA.

Figure 7 :
Figure 7: (a) SEM of indentation array performed on the polycrystalline HEA (b) Experimental P-h plot and Hertzian fit on the Ni25Cu18.75Fe25Co25Al6.25 polycrystalline substrate highlighting elastic and plastic work involved in the HEA indentation ), (111) orientations as well as on the polycrystalline HEA shown in Fig 8.The (100) HEA showed clear 4-fold symmetry atomic pileup (see Fig 8(a)) along the 〈011〉, 〈01 ̅ 1 ̅ 〉, 〈01 ̅ 1〉 and 〈011 ̅ 〉 directions, which is consistent with the previous report for the Fe-Ni-Cr-Co-Cu high-entropy alloy [20].The (110) monocrystalline setup showed evenly distributed deformation shown in Fig 8(b) with somewhat a 4-fold symmetry.In the case of (111) orientation, material flow and pileup shown in Fig 8(c) did not indicate any clear preferential direction of deformation.Interestingly, for the polycrystalline HEA model, the 4-fold or 3-fold symmetry atomic pileup was less clearer due to the interaction of several grains which can be seen from Fig 8(d).To further study this, the polycrystalline dump file was post-processed by removing the top lattice layers using the polyhedral template matching algorithm within OVITO which leaves a clear visibility of the individual grains as shown in Fig 9.

Figure 9 :
Figure 9: The state of various grains (a) before indentation and (b) after indentation on the polycrystalline HEA.

Figure 12 :Figure 13 :
Figure 12: Analytical models of dislocation evolution (a) Emission of shear loop (b-d) Cross-over of screw components (e-f) Formation of octahedron "lasso" type dislocation loop.

Figure 14 :
Figure 14: The evolution of microstructure at depths of 0.5 nm, 1.5 nm and after unloading.