A novel D022 precipitation-hardened Ni2.1CoCrFe0.5Nb0.2 high entropy alloy with outstanding tensile properties by additive manufacturing

ABSTRACT To introduce D022 superlattice (noted as γ′′ phase) precipitation strengthening in additive manufacturing, a design strategy of combining the overall valence electron concentration with the calculation of phase diagrams is proposed, and Ni2.1CoCrFe0.5Nb0.2 HEA is designed. The wall-shaped samples were prepared by AM, and after solution at 1100 °C for 2 h and aging at 650 °C for 120 h, the γ′′ phase with volume of 14% causes yield strength increase by 727 MPa, the yield strength increased dramatically to ∼1005 MPa, the ultimate strength increased dramatically to ∼1240 MPa, the tensile elongation maintained at ∼20%. The high strength results from the precipitation strengthening of the γ′′ phase, and the large ductility are primarily attributed to an evolution of multiple stacking fault structures. The present study will not only promote the development of high-performance HEAs by AM but also provides a pathway for achievement of AM technology industrial applications.


Introduction
High-entropy alloys (HEAs) composed of multiple principal components have gained extensive attentions due to their unexpectedly simple phase compositions and extraordinary properties (Ye et al. 2016;Tsai and Yeh 2014;Zhou et al. 2020;Miracle and Senkov 2017).In recent decades, significant efforts on the composition design, heterostructure construction, strengthening mechanisms, preparation processes of HEAs have been performed (Gludovatz et al. 2014;Gludovatz et al. 2016).Nevertheless, in various preparation processes, additive manufacturing (AM) has been conceived as an advanced method for the fabrication of HEAs (Zhou et al. 2020).There are seven processes in AM technology, including directed energy deposition (DED), powder bed fusion (PBF), vat polymerisation, binder jetting, sheet lamination, material jetting, and material extrusion (Han et al. 2020).Among them, laser DED and PBF are typical processes for printing HEAs from powder.Due to their merits of design freedom and net-shape manufacturing capability, it is convenient to obtain parts of complex geometry directly from computer-aided design (CAD) models (Kok et al. 2018;Wu et al. 2022).Simultaneously, the flexibility of HEAs in compositional design could provide more opportunities for the industrial application of AM.Laser DED is the most popular printing process for developing HEA products, which can be prepared using not only HEA powder but also different primary elemental powders fed simultaneously through multiple hoppers.Uniform element distribution can be obtained by optimizing the process parameters of laser DED, and the solidified HEA melt pool can be achieved by in situ alloying (Han et al. 2020).However, the laser DED process is accompanied by a complex material-energy interaction and a rapid thermal cycle process different from the traditional process, which leads to defects such as pores, poor fusion and cracks in the formed body, and further affects the mechanical properties of the HEAs (Martin et al. 2017).These defects are difficult to completely eliminate through optimization of process parameters, so they must be solved from the source of alloy composition (Zhou et al. 2019).Therefore, it is very urgent to design highperformance HEAs that can be used for AM.
Many research works have been made to improve the mechanical properties of HEAs prepared by AM (Guan et al. 2019;Gao and Lu 2019;Chew et al. 2019;Li et al. 2018;Brif, Thomas, and Todd 2015;Sun et al. 2019;Guo et al. 2020;Dang et al. 2021;Gu et al. 2021;Nartu et al. 2020;Wu et al. 2021).The commonly used strengthening methods are solid solution strengthening, dislocation strengthening, grain boundary strengthening and precipitation strengthening (He et al. 2014;Jiang et al. 2014;Park et al. 2015;Liu et al. 2013;Li et al. 2016;Deng et al. 2015;Li et al. 2019;He et al. 2016).Among them, precipitation strengthening has an outstanding advantage (Wei, He, and Cem Tasan 2018;He et al. 2016).In precipitation-enhanced HEAs, Al/Ti and Nb elements are successfully introduced to form two types of precipitated phases named the γ ′ and γ ′′ phases, respectively (Zhou et al. 2020).Several groups have attempted to prepare γ ′ precipitated AlCoCrFeNi high-entropy alloy systems by AM.Unfortunately, the appearance of visible cracks suggests the performance destruction (Joseph et al. 2015;Karlsson et al. 2019) because the high Al/Ti content usually produces a large amount of γ ′ -Ni 3 (Al,Ti) strengthening phase during the laser deposition process, which easily leads to the formation of cracks under the action of internal stress (Sistla, Newkirk, and Liou 2015).In contrast, the γ ′′ phase has a slower precipitation rate in the deposition process, and generally requires subsequent aging treatment to precipitate, which means that the deposited samples maintain high plasticity and is not easy to be cracked due to internal stress concentration (Chaturvedi and Chung 1981).Therefore, the strengthening mechanism contributed by γ ′′ precipitation is very suitable for AMed HEAs.
The printability of HEAs, being a target to evaluate the completeness of AM samples, was not only dependent on the optimization of the preparation parameters but also most critical by the alloy composition (Johnson et al. 2019).Researchers have confirmed that the printability of Co-Cr-Fe-Ni-Nb system HEAs possessed the best performance (i.e. the yield strength is ∼896 MPa, the tensile strength is ∼1127 MPa, and the tensile elongation is ∼17%) (Zhou et al. 2020).However, this performance still cannot meet the requirements of aerospace, automotive and energy industries.In order to further enhance the tensile performance of HEAs by AM, the γ ′′ phase precipitation strengthening is introduced.Simultaneously, researchers have demonstrated that the γ ′′ phase with D0 22 structure tended to precipitate in HEAs with the overall valence electron concentration above 8.4, and Ni 3 Nb can exist as a metastable form (He et al. 2019).In addition, the γ ′′ phase typically has a higher lattice mismatch and anti-phase boundary energy, resulting in a higher strengthening capacity (Ardell 1985).Therefore, printable γ ′′ phase precipitation strengthening HEAs based on the Co-Cr-Fe-Ni-Nb system were designed for the outstanding tensile properties of AM-prepared HEAs.
In the present work, the design of γ ′′ phases precipitated Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA is according to the overall valence electron concentration (OVEC) principle and the calculation of phase diagrams (CALPHAD) technique.And the wall-shaped samples without defects successfully made by AM.Subsequently, the nanosuperlattice γ ′′ phase is precipitated in the FCC matrix by aging treatment.The wall-shaped HEA has a yield strength of ∼1005 MPa, an ultimate strength of ∼1240 MPa, and a tensile elongation of ∼20%, which is prior to alloys the reported AM-prepared alloys.

Design of HEAs with D0 22 superlattice
To obtain γ ′′ phase in HEAs and to ensure that the HEAs forms a single-phase FCC matrix during the laser DED and can precipitate γ ′′ phase in subsequent aging treatment.In this work, the Co-Cr-Fe-Ni-Nb system HEAs was selected and the content of Nb was fixed at 0.2, the OVEC principle was used to design the γ ′′ precipitation strengthening phase.The OVEC value of NiCoCrFeNb 0.2 and Ni 1.6 CoCrFeNb 0.2 HEAs is 8.09 and 8.33 by calculation, respectively.Obviously, the OVEC values of those two alloy compositions was lower than 8.4, therefore the D0 22 structure cannot be mainly formed.To improve the OVEC value of the alloy, the content of Ni with high VEC is increased to ensure OVEC of alloy was above 8.4.Meanwhile, the CALPHAD technique was applied to determine alloy composition and predict precipitation behaviour.Figure 1(a) showed the calculated the phase diagram of the NiCoCrFeNb 0.2 HEA, indicating that the Laves phase appears during the laser deposition process.Figure 1(b) exhibited the simulation results of the phase diagram of the Ni 1.6 CoCrFeNb 0.2 HEA, indicating that the Laves phase decreased with the increase of the Ni content.It's well known the Laves phase was harmful to material.In order to eliminate the Laves phase and promote the formation of the γ ′′ phase, our strategy was to further increase Ni content and in turn decreased the content of Fe, the final the Ni 2.1 CoCrFe 0.5- Nb 0.2 HEA composition with an OVEC of 8.54 was designed.Figure 1(c) demonstrated the simulation results of Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA.A single-phase FCC structure was formed during the laser deposition process and γ ′′ phase was precipitated in subsequent aging treatment.The Laves phase was disappeared.Meanwhile, Figure 1(c) provided a theoretical reference for the solution and aging treatment of as-deposited HEA.

Experimental details
The wall-shaped samples with a nominal composition of Ni 2.1 CoCrFe 0.5 Nb 0.2 were printed using laser AM.The process used in AM was laser DED, the process schematic as shown in Figure 2(a), after a number of experiments, the optimized technological parameters as shown in Figure 2(b).The AM system was composed of a 6000 W continuous wave fibre laser, a six-degree-offreedom robotic arm control working table, powder feeders with four coaxial nozzles.The raw material included pure Co, Cr, Fe, Ni and Nb alloy powders with particle size ranging from 45 μm to 105 μm.Afterward, the well-weighed powder was homogeneously mixed in a ball mill for 2 h.After being sifted, the mixed HEA powder was dried in a box vacuum dryer at 80 o C to prevent oxidation.The wall-shaped HEA was prepared using AM in a treatment chamber filled with argon to reduce the oxygen content (below 50 ppm).After repeated experiments, the optimal process parameters were determined: laser power of 1000 W, laser spot diameter of 3 mm, laser scanning speed of 15 mm/s, powder feeding speed of 2 r/min, and Z-direction uplift distance of 0.35 mm.The AISI 304 stainless steel plates with the dimensions of 100 × 100 × 10 mm 3 were selected as substrates.The final printed product was wall-shaped with dimensions of 70 × 3 × 40 mm 3 , which entire morphology as shown in Figure 2(c).Subsequently, according to the predicted result of CALPHAD, the as-deposited sample was conducted by solution treatment at 1100 o C for 2 h and aged at 650 o C for various keeping hours to investigate the precipitation behaviour of γ ′′ phase.
The phase of the HEA samples was characterised through an X-ray diffractometer (X'Pert PRO), using monochromatic Cu Kα (λ = 1.54060Å) radiation, scanning angles ranging from 20°to 80°, and a scanning speed of 5 °/min.The microhardness was measured by a JMHV-1000AT microhardness tester at a loading force of 1.98 N for 10 s.To minimise the error, each sample was tested at 20 different locations along the samples building direction.Rectangular dog-bone-shaped tensile text specimens with standard dimensions of 8 × 2 × 1 mm 3 were used for tensile testing.At room temperature, the tensile properties are tested by material testing machine (MTS CMT5205) with a nominal strain rate of 1 × 10 −3 s −1 .The SEM samples were ground and polished, then etched with dilute aqua regia, and finally characterised by scanning electron microscopy (Zeiss Sigma500).Electron backscatter diffraction (EBSD) was characterised using an Oxford Nordlys Max3, and test results were processed using Channel-5 commercial software.The crystal structure of the samples was analyzed using transmission electron microscope (TEM FEI Talos F200s).The two samples from 120 h of aging and tensile fracture were analyzed by TEM.An Image-Pro Plus software was used to measure the volume fraction of the γ ′′ phase from the micrographs.
The elemental distribution of HEA samples aged at 650 o C for 120 h was investigated using an energy  dispersive X-ray spectroscopy (EDX) and atom probe topography (APT).Needle-shaped samples for APT analysis were prepared by focused ion beam (Helios G4 CX) ring milling.The APT characterisation was performed using a CAMECA LEAP 5000 XR instrument.The equipment equipped with UV laser of a wavelength of 355 nm and a spot size of 2 μm.There is a 52% detection efficiency for this state-of-the-art microscope.The APT data were analyzed in the laser pulsing mode at a specimen temperature of 50 K with pulsing rate of 200 kHz, laser pulse energy of 40 pJ and target evaporation rate of 5 ions/1000 pulses.The commercial AP Suite 6 software was used for 3D reconstruction and composition of APT data.

Microstructures and elemental distribution
The microstructure and phase of Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA in the as-deposited state, solid solution state and 120 h aging state is displayed in Figure 3. Figure 3(a 1 ) demonstrates that the microstructure of the as-deposited HEA exhibits dendritic microstructure.In addition, a Nb-rich (shown in Figure 4 by element surface scanning) second phase exists at the grain boundaries.Figure 3 (b 1 ) exhibits the microstructure of the HEA after solid solution treatment.The dendrites are decomposed, and the Nb-rich phase at the grain boundary enters the matrix.
Figure 3(c 1 ) demonstrates the microstructure of the HEA after aging, and particles exist in the grains.Figure 3(a 2 -c 2 ) exhibits the XRD profiles of Ni 2.1 CoCrFe 0.5- Nb 0.2 HEA under the three treatment states, respectively, which clearly identify that all samples have a single FCC crystalline structure, and it can be further seen that the only single phase is showed after aging treatment despite the particle phase exists on matrix.Despite the precipitation of the γ ′′ phase or the dissolution of the Nb-rich phase can lead to changes in the Nb element distribution, the particles phase is too fine to detect by XRD, which ultimately does not lead to significant changes in lattice parameters (He et al. 2019).Meanwhile, previous studies have shown that the lattice parameters of γ and γ ′′ phases are similar, and it is quite difficult to identify them by XRD, because some diffraction peaks of γ and γ ′′ phases may partially overlap (Pan et al. 2022).
The elemental mapping of the deposited samples detected by energy dispersion spectroscopy (EDS) is shown in Figure 4.It is seen from Figure 4(a) that the percentage of different elements after EDS analysis, indicating that the deposited samples chemical composition is close to the design composition (see Table 1).Figure 4

APT characterisation
To quantitatively reveal the assignment of elements at the atomic scale, needle tips taken from samples aged at 650 o C for 120 h were analyzed using APT. Figure 8 (a) demonstrates a typical atomic map of all elements in a random test area.A 7 at.%Nb iso-concentration surface is also displayed to delineate the outline of the γ ′′ phase.The average size of the γ ′′ phase is consistent with the TEM observation (Figure 6).The γ ′′ phase is enriched in Ni and Nb, whilst Cr, Fe and Co are largely depleted.In addition, the chemical composition difference between the γ ′′ phase and matrix is larger.In Figure 8(b), the elemental partitioning is shown in a proximity histogram constructed across the interface between the γ ′′ phase and matrix.Table 2 shows the chemical composition values of the matrix and γ ′′ phase received by APT analysis.The thermodynamic model proves that Co and Cr tend to replace Ni sites and Fe can replace Nb or Ni sites in a Ni 3 Nb phase (Chaturvedi and Chung 1979).Previous work has demonstrated by APT that the γ ′′ phase of the D0 22 structure exhibits a stoichiometry of (Ni, Co, Cr, Fe) 3 (Nb, Fe) in the FeCoCrNiNb HEA system (Han et al. 2018;Fan et al. 2020).Therefore, in this work, we identified this nanoscale γ ′′ phase based on the stoichiometry of (Ni, Co, Cr, Fe) 3 (Nb, Fe) by APT analysis.

Mechanical properties
The variation of hardness with aging time is shown in Figure 9(a).The hardness tends to increase with increasing aging time, reaching a peak of 481 HV at 120 h.According to the hardness results, HEA specimens in the deposited state, solid solution state, and aged for 72, 120, and 144 h are selected to test their room temperature tensile properties.The room temperature tensile properties of the specimens are tested in the building direction (BD) and scanning direction (SD), respectively, as shown in Figure 9(b,c).The tensile properties of BD and SD remain almost consistent, proving that the HEA prepared by AM is isotropic.The as-deposited HEA exhibits a yield strength of ∼278 MPa, a tensile strength of ∼720 MPa, and a fracture elongation of ∼50%.The asdeposited HEA has better strength and ductility, which is attributed to the advantage of rapid solidification of AM.After solid solution treatment, the specimens show better ductility (∼58%) but a slight decrease in strength (∼647 MPa), which could be attributed to the homogenisation of the Nb-rich phase [see Figure 3 (b 1 )].After various aging treatments, the strength of the specimens increased significantly, especially after aging for 120 h, and yield and ultimate tensile strength is reached ∼1005 MPa and ∼1240 MPa, respectively.Meanwhile, with the extension of aging time, the plasticity of the specimens decreases, and the best combination of strength of 1240 MPa with elongation of 20% is obtained under aging for 120 h.The tensile properties of the currently reported additive manufacturing of alloys (Zhou et al. 2020;Martin et al. 2017;Zhou et al. 2019;Gao and Lu 2019;Chew et al. 2019;Li et al. 2018;Nartu et al. 2020;Zhu et al. 2018;Zhou et al. 2018;Park et al. 2020;Zhu et al. 2019;Joseph et Zhou et al. 2019;Zhou et al. 2019;Qiu et al. 2018;Greitemeier et al. 2016;Ivanov et al. 2017;Han et al. 2019;Tan et al. 2020) is compared with our work [shown in Figure 9(d)], and it is obviously seen that superior mechanical properties are achieved.
Figure 9(e) illustrates the work-hardening behaviour versus true strain for the solid solution state aged for 72 and 120 h.It can be seen that the work-hardening behaviours of the specimens in all three states decreases sharply at the beginning of plastic deformation and then decreases slowly as strain further increases.In addition, the work-hardening rate of the age-treated specimens is superior than that of the solution treatment, and the aging for 120 h is higher than the aging for 72 h.In precipitation-hardened HEAs, the precipitates can either hinder dislocation movement to advance the add to dislocation density or act as a dislocation emitter to advance increase in dislocation density again (Ardell 1985).Therefore, in the homogeneous deformation stage, the work-hardening behaviours of the HEA by solid solution is lower than that of the precipitation strengthened HEA.
Figure 9(f-h) exhibits the tensile fracture of the deposited state, solid-solution state, and aged samples for 120 h, respectively.A hybrid fracture with a combination of raised edges and dimples is shown in Figure 9(f) due to the Nb-rich phase at the grain boundaries.Figure 9(g) demonstrates ductile fracture with many deep dimples owing to the decomposition of the Nbrich phase at the grain boundaries after solid solution treatment.Figure 9(h) shows ductile fracture with more and smaller dimples.After γ ′′ phase precipitation strengthening, the increase in the probability of microcracks and the decrease in fracture area promote the reduction of dimple size.The phase boundary between the γ ′′ phase and the matrix increases the crack formation rate, thereby reducing the crack size.

Evolution of deformation substructure
Figure 10 exhibits the TEM results of the specimen after tensile fracture, which clearly demonstrates the evolution of the deformation mechanism.Figure 10(a) demonstrates that the γ ′′ phase is sheared by dislocations or stacking faults (SFs).The dislocation undergoes multifaceted slip along two {111} slip surfaces and shears the precipitated γ ′′ phase, as shown in Figure 10(b).These dislocations can easily evolve into high-density SFs, which hinders cross-slip during deformation (Lu et al. 2020).In the deformed microstructure, multiple SFs are observed in Figure 10(c).The highdensity Lomer-Cottrell (L-C) lock and nanopitch SFs networks are observed in Figure 10(d), and the strain  hardening effect is improved due to dislocation storage capability of the L-C lock (Fan et al. 2020).Figure 10(e) shows the HRTEM in the parallel stretching direction, and the inset shows the corresponding FFT results, which show that there are two directional SFs.In Figure 10(f), rare microtwins and a high-density of SFs are found.After an examination of 200 sites in a sampling, it is found that only 2% of the sites examined have microtwins, while the other sites demonstrate SFs.
In conclusion, the strengthening mechanism of our Ni 2.1- CoCrFe 0.5 Nb 0.2 HEA is Shearing, not Orowan, and the deformation process is mainly stacking-fault-mediated mode, instead of mechanical twinning deformation.
Considering the superiority of elongation, it is closely related to the strain hardening capacity (Sun et al. 2018).The high-density of SFs present in tensile specimens not only plays an important role in strain hardening, but also serve as remarkable plastic carriers to promote good plasticity.Meanwhile, a small amount of microtwins is present in the specimen as shown in Figure 10(f).These extra twin boundaries provide a wide space for the aggregation of dislocations and act as a channel to promote the movement of dislocations along the twin boundaries, thus reducing stress concentration and leading to high ductility (Zhang et al. 2021).

Crystallographic features of the γ
The γ ′′ phase precipitated in Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA exhibits a typical D0 22 superlattice structure (Figure 6), which is essentially consistent with the stoichiometry of Ni 3 Nb (Sundararaman and Banerjee 1992).The D0 22 superlattice can be seen as consisting of two FCC cells placed along the [001] direction.Because the [001] axis of the D0 22 superlattice can be parallel to the <100 > directional family of the matrix, three type γ ′′ variants can frequently be discovered in the matrix.In our work, the diffractograms of Figure 6(b1) demonstrate the presence of three type γ ′′ variants, and in the DF and HRTEM maps [Figure 6(a,c)] also prove that the disc-like γ ′′ has different orientations.The γ ′′ variant and its ordered structure are further analyzed through the fast Fourier transform (FFT) and the inverse fast Fourier transform (IFFT).Figure 11(a 1 ) demonstrates the IFFT maps of the variant 1, and the corresponding FFT maps is exhibited in Figure 11(a 2 ).The crystallographic relationship of [100] γ ′′//[001] m was determined from Figure 11(a 2 ).In  Figure 11(a 1 ), it can be observed that the lattice of the matrix has the same contrast, while the lattice of γ ′′ has varying contrasts.The illustration in Figure 11(a 1 ) shows the variation of contrast of the lattice γ ′′ and matrix represented by different colours and sizes of the spheres.The brighter spot is marked with a green sphere, while the darker spot is represented with a grey sphere.It can be seen that the green spherical layer recurs every four floor {420} planes, leading to superlattice diffraction points at the ( 10) and ( 210) crystal plane positions [see Figure 11(a 2 )] (Ardell 1985), indicating that Nb in the γ ′′ mainly occupies the corner and central positions in the D0 22 structure.Figure 11(b 1 -b 2 ) shows γ ′′ variant 2 observed in HRTEM images.A crystallographic relationship of [010] γ ′′ //[001] m is determined from the FFT maps, and it can be seen that the green spherical layer recurs every four {240} crystal planes.Figure 10  (c 1 -c 2 ) shows the γ ′′ variant 3 observed in HRTEM images with the crystallographic relation [001] γ ′′// [001] m .It can be seen that the green spherical layer recurs every two floor {110} planes, causing superlattice diffraction points at the (110) γ ′′ plane [see Figure 11(c 2 )].In conclusion, the γ ′′ phase has a large lattice distortion energy and anti-phase boundary energy, which can introduce a larger precipitation strengthening effect.Meanwhile, the γ ′′ phase and the matrix are coherent interfaces, which does not change the dislocation movement path and can avoid dislocation plugging, thus favouring plasticity.
5.2.The reason for strengthening of γ ′′ ′′ ′′ ′′ ′′ phase Generally, strengthening mechanisms for polycrystalline alloys are mainly contributed by dislocation strengthening (s d ), grain boundary hardening (s g ), solid solution hardening (s s ) and precipitation hardening (s p ).In AM, the combination of thermal and strain fields elicits the formation of high-density dislocations (Liu et al. 2022).The contribution of dislocation strengthening to the strength can reach several hundred MPa (Wu et al. 2022).However, we focus the γ ′′ phase precipitation strengthening behaviour in this work.To obtain high volume fraction of precipitated particles, the specimens were recrystallized by solid solution at 1100 o C for 2 h, subsequent aging at 650 o C for 120 h.The as heat-treated HEAs was fully recovered, resulting in the essential reduction of dislocation density.Therefore, the dislocation strengthening could be neglected (He et al. 2019;Lu et al. 2020).The amount of contribution of each mechanism is superimposed to calculate the yield strength (s 0.2 ), which can be expressed by the following equation, where s 0 is the intrinsic strength (Ardell 1985).s 0.2 = s 0 + Ds s + Ds g + Ds p (1) For Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA after precipitation strengthening, the atomic radius of Nb is much larger than that of Ni, Co, Cr and Fe, therefore the addition of Nb into the Ni 2.1 CoCrFe 0.5 alloy will result in lattice distortion strengthening.However, the evaluation of the strengthening effect of the HEA in this study using the conventional solid solution strengthening mechanism is challenging.In this work, we evaluated the lattice distortion strengthening effect.The Ni , where k y is the strengthening coefficient.Therefore, the influence of grain average size variation on yield strength can be expressed as ).In our current research, we set the value of k y as 840 MPa μm 1/2 according to the tensile test of the CoCrFeNi alloy (Wu et al. 2014), and calculated Ds g = 14.41 MPa.Thus, the yield strength increased through solid solution strengthening can be expressed as s s = s  For the precipitation γ ′′ phase, researchers have demonstrated that coherent strengthening (Ds coherency ) and ordered strengthening (Ds ordering ) common domination the strengthening effect (Oblak, Paulonis, and Duvall 1974;Sundararaman and Banerjee 1988).Oblak et al. reported computational equations for the coherent and ordered strengthening of the γ ′′ phase (Oblak, Duvall, and Paulonis 1974). (2) where G [following Ni718 alloy (Oblak, Paulonis, and Duvall 1974), taken to be 70 GPa] is the shear modulus, M (3.06 for FCC matrix) is Taylor factor, ε (calculated to be 0.013 from HRTEM image) is the tetragonal lattice misfit, R and h are diameter and half thickness of γ ′′ phase (measured to be 9.5 and 3.1 nm from DF image, respectively), f (measured to be 14% from DF image) is the volume fraction of γ ′′ phase, b is Burger's vector (b = 0.254 nm), β is the constant (β = 1/3, when three variants of the γ ′′ phase exist in HEA), g APB is the antiphase boundary energy g APB = 0.296 J/mm 2 , following Oblak, Paulonis, and Duvall (1974), and T is the line tension (T = 0.5 Gb 2 ).According to the above equation for coherency strengthening, the contribution value is calculated to be 256 MPa.By the equation for ordered strengthening, the contribution value is calculated to be 492 MPa.The calculated results (748 MPa) are in good agreement with the experimental results (727 MPa).

Strain field around the
To further analyse the contribution of the precipitation γ ′′ phase to strengthening effect, it is necessary to measure the strain field at around the γ ′′ phase.The HRTEM image of the tensile fracture is obtained to measure the strain field using geometric phase analysis (GPA), as shown in Figure 13.The corresponding FFT map is inserted in the HRTEM image, and the diffraction spots show that the region is sheared by SFs, and the spots marked by white are sites of the GPA analysis.
Figure 13(a-c) shows the strain fields of the γ ′′ phase, phase boundary and matrix, respectively.The lattice strain fields were calculated and are shown in the corresponding images for horizontal positive strain (ε xx ), vertical positive strain (ε yy ) and shear strain (ε xy ).The colour scale near each graph indicates the change in strain, where positive values represent tensile strain and negative values represent compressive strain, alternating between positive and negative.A large strain gradient and strain field exist in the γ ′′ phase.The distribution of the γ ′′ phase strain field is random on the nanoscale, but the tensile and compressive strain fields alternate, leading to larger local internal stresses that resist dislocation slippage, thus improving the strengthening effect (Ding et al. 2019).Figure 13(b) demonstrates that the strain at the phase boundary is greater than that of the matrix, whereas it is less than that of the precipitation γ ′′ phase.Since a certain lattice mismatch exists between the γ ′′ phase and the matrix, resulting in an increase in strength, the strain field becomes larger (Chen et al. 2020).In summary, the main strengthening mechanism of Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA is precipitation strengthening.
In this work, the γ ′′ phases precipitation strengthening was introduced into AM, HEAs with excellent tensile properties were obtained.Although the morphology and composition of γ ′′ phase were analyzed by APT, the specific atomic occupation is still the blind spot of research.it has been reported that the volume fraction of precipitated γ ′′ phase is smaller than that of L1 2 phase, less than 20%.Therefore, to further improve the mechanical properties, the thermodynamics and kinetics of γ ′′ phase transition still need to be further clarified.In addition, there is little research on the AM of HEAs in application of high and low temperature environment, the research mainly focuses on the traditional manufacturing process.Therefore, to realise large-scale industrial application of AM-ed HEAs, systematic efforts are still needed to study in the atomic occupation and transformation thermodynamics and kinetics of γ ′′ phase, the strengthening mechanism of low temperature as well as HEAs design of stabilising γ ′′ phase under high temperature, etc. in the future.

Conclusions
To obtain stable single-phase FCC structure during the laser deposition process and precipitate γ ′′ phase in subsequent aging treatment, a combination of OVEC theory with phase diagram simulations is proposed to design HEAs with high-strength plasticity for AM.Based on this approach, the Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA is designed.The HEAs with γ ′′ phase is investigated using XRD, EBSD, TEM, APT, and GPA.The strengthening mechanism of the γ ′′ phase has been deeply discussed.The conclusions can be drawn as follows.
(1) A design strategy of combining OVEC with phase diagram simulation is proposed for the design of the high-performance printable HEAs, solving defects such as holes and cracks during the preparation.
(3) The γ ′′ phase conforms the (Ni,Co,Cr,Fe) 3 (Nb,Fe) stoichiometry using APT analysis.After aging treatment at 650 o C for 120 h, the disk shaped γ ′′ phase with volume fraction of 14% causes yield strength increase by 727 MPa, the yield strength increased dramatically to ∼1005 MPa, the ultimate strength increased dramatically to ∼1240 MPa, the tensile elongation maintained at ∼20%.The high strength results from the precipitation strengthening, and the large ductility are primarily attributed to an evolution of multiple stacking fault (SF) structures.(4) The GPA analysis shows that the strain at the phase boundary is greater than that of the matrix, whereas it is less than that of the γ ′′ phase.From the perspective of strain energy, it is clarified that the main strengthening mechanism is the precipitation strengthening of the γ ′′ phase.

Figure 2 .
Figure 2. (a) The process schematic of laser DED.(b) Laser DED process parameters.(c) Deposition wall-shaped Ni 2.1 CoCrFe 0.5- Nb 0.2 and its direction of taking out of tensile specimens.
Figure3(c 1) demonstrates the microstructure of the HEA after aging, and particles exist in the grains.Figure3(a 2 -c2 ) exhibits the XRD profiles of Ni 2.1 CoCrFe 0.5- Nb 0.2 HEA under the three treatment states, respectively, which clearly identify that all samples have a single FCC crystalline structure, and it can be further seen that the only single phase is showed after aging treatment despite the particle phase exists on matrix.Despite the precipitation of the γ ′′ phase or the dissolution of the Nb-rich phase can lead to changes in the Nb element distribution, the particles phase is too fine to detect by XRD, which ultimately does not lead to significant changes in lattice parameters(He et al. 2019).Meanwhile, previous studies have shown that the lattice parameters of γ and γ ′′ phases are similar, and it is quite difficult to identify them by XRD, because some diffraction peaks of γ and γ ′′ phases may partially overlap(Pan et al. 2022).The elemental mapping of the deposited samples detected by energy dispersion spectroscopy (EDS) is shown in Figure4.It is seen from Figure4(a) that the percentage of different elements after EDS analysis, indicating that the deposited samples chemical composition is close to the design composition (see Table1).Figure4(b-e) demonstrates element mapping scanning of Ni, Co, Cr, and Fe.These elements are homogeneously distributed in the microstructure.However, the distribution of Nb is not homogeneous [see Figure 4(f)].

Figure 5
Figure 5(a 1 -c 1 ) shows the electron backscattered diffraction (EBSD) results of Ni 2.1 CoCrFe 0.5 Nb 0.2 HEA in three treatments, and the grain size of the microstructure under three treatments is shown.Figure 5(a 1 )

Figure 4 .
Figure 4.The high-magnification backscattered electron (BSE) micrograph and corresponding EDS element mappings of the asdeposited.

Figure 8 .
Figure 8.(a) Atom maps of different elements and 3D construction with the 7 at.%Nb iso-concentration surface, (b) Proximity histogram of concentration profiles.

Figure 9 .
Figure 9. (a) The hardness variation of solid-solution HEA upon aging at 650 o C, (b-c) Tensile properties of the as-deposited, solidsolution, and different-hour-aged obtained at room temperature, (d) The map of ultimate tensile strength-ductility combinations of existing AM-fabricated HEAs including our work, (e) The strain hardening rate vs true strain plots, (f-h) the fracture morphologies.

Figure 10 .
Figure 10.(a) TEM dark field (DF) image of the specimen after tensile fracture, (b) TEM images showing the dislocation slip has a planar characteristic, (c) HRTEM picture showing the multiple SFs, (d) HRTEM image showing the hierarchical SF network and L-C locks, (e) HRTEM image and the corresponding FFT results, (e) Representative HRTEM images of SF and micro-twin.

′0
− s 0 −Ds g = 278 − 195 − 14.41 = 68.59MPa.Substituting the above data into Equation (1), the yield strength improved by precipitation strengthening can be calculated as s p = s 0.2 -s 0 -s s -Ds g = 1005 -195 -68.59 -14.41 = 727 MPa.The contribution of various strengthening methods to the strength of Ni 2.1- CoCrFe 0.5 Nb 0.2 HEA is shown in Figure 12.It can be concluded that precipitation strengthening is dominant in the four strengthening mechanisms.

Figure 12 .
Figure 12.Contributions of different strengthening mechanisms.

Figure 13 .
Figure 13.(a) The strain fields of the γ ′′ phase, (b) The strain fields of boundary and matrix, (c) The strain fields of matrix.

Table 1 .
Chemical composition of nominal and EDS.

Table 2 .
Chemical compositions obtained from APT.