Mechanical Performance and Microstructural Evolution of (NiCo)₇₅Cr₁₇Fe₈C_{x (x = 0~0.83)} Medium Entropy Alloys at Room and Cryogenic Temperatures

Abstract

We investigated the effects of the addition of Co and carbon on the deformation behavior of new medium-entropy alloys (MEAs) designed by increasing the entropy of the conventional NiCrFe-type Alloy 600. The strength/ductility combination of carbon-free (NiCo)₇₅Cr₁₇Fe₈ MEA was found to be 729 MPa/81% at 298 K and it increased to a remarkable 1212 MPa/106% at 77 K. The excellent strength and ductility of (NiCo)₇₅Cr₁₇Fe₈ at cryogenic temperature is attributed to the increased strain hardening rate caused by the interaction between dislocation slip and deformation twins. Strength/ductility combinations of carbon-doped (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 at cryogenic temperature were observed to be 1321 MPa/96% and 1398 MPa/66%, respectively, both of which are superior to those of other high-entropy alloys (HEAs). Strength/ductility combinations of (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 at room temperature were found to be 831 MPa/72% and 942 MPa/55%, respectively and both are far superior to 676 MPa/41% of the commercial Alloy 600. Yield strengths of carbon-free and carbon-doped alloys comprised strengthening components from the friction stress, grain size strengthening, carbide strengthening and interstitial strengthening and excellent agreement between the predictions and the experiments was obtained. A design strategy to develop new MEAs by increasing the entropy of the conventional alloys was found to be effective in enhancing the mechanical performance.

1. Introduction

High-entropy alloys (HEAs) with solid solution single-phase stabilized through the maximized configurational entropy have attracted extensive academic interest [1,2]. Based on this concept, numerous single-phase high-entropy alloys with various crystalline structures have been studied and these alloys were found to exhibit a combination of high strength and ductility [3,4]. Face-centered cubic (fcc) solid solution HEAs have excellent fracture toughness at cryogenic temperatures compared to conventional alloys [5,6,7,8]. In equiatomic CoCrFeMnNi HEA, the excellent cryogenic properties have been attributed to a transition from planar dislocation slip at room temperature to nano-twinning at lower temperatures [7,8,9]. Wu et al. [10] investigated the mechanical properties of ternary and quaternary equiatomic solid solution HEAs and medium-entropy alloys (MEAs) with fcc structures and observed the strong temperature dependence of the yield and ultimate strengths in CoNiCr, CoNiCrMn and CoNiCrFe. It was found that Cr-containing fcc HEAs have stronger temperature dependence than non-Cr-containing fcc HEAs, and the strong temperature dependence can be attributed to temperature dependent chemical and elastic interactions between dislocations and alloying elements [11,12,13,14,15,16] and/or the presence of co-clusters and short-range orders in these alloys [17,18]. Wu et al. [10] found that ternary CoNiCr alloy has the highest tensile strength, and quaternary CoNiCrFe has the next highest strength, higher than the five-element equiatomic alloy, FeNiCoCrMn and other quaternary alloys. It has been suggested that the strength of solid solution HEAs and MEAs is not solely determined by the entropy but also greatly influenced by strain energy contribution and the chemical enthalpy term due to the interaction between elements [1,2,3,10,19].

A convenient way of developing new HEAs or MEAs would be to increase the entropy of the matrix of conventional alloys by adding elements with high solubility in the matrix and enhance the properties. Conventional NiCrFe-type Alloy 600 (Ni(>72 wt.%)-Cr(14–17 wt.%)-Fe(8–10 wt.%)) is known to have excellent corrosion resistance to sulfur compounds and various oxidizing environments because of its chromium content [20]. Alloy 600 has excellent mechanical properties with high strength and good cold-forming characteristics for use from low to elevated temperatures [20]. Since the increase of Co content up to 40% in Cantor-type HEAs and MEAs is known to increase the strength and ductility and stabilize the fcc structure [21], the modified alloy (NiCo)₇₇Cr₁₅Fe₈ is expected to exhibit the stable fcc phase structure. With the increase of Co from 20 at.% to 40 at.% in CoCrNi medium entropy alloys, widely-extended stacking faults and more pronounced planar slip was observed [22] because Co lowers the stacking fault energy. The reports that Co-free equiatomic CrFeNi exhibited the dual phase (fcc + bcc) structure [23] and the reductions of Cr and Fe contents from CoCrFeNi increased the stability of fcc phase [24] supports the stability of fcc phase in the modified alloy (NiCo)₇₇Cr₁₅Fe₈. The yield strengths of equi-atomic single fcc phase CoCrFeNi at various temperatures were observed to be comparable to those of equiatomic single fcc phase CoCrNi [10].

Klimova et al. [25] found that the solubility of interstitial carbon in fcc solid solution increases with a decrease of Cr content. The decrease of Cr content from 20 at.% to 6.3 at.% was reported to increase the carbon solubility from 0.36 at.% to 1.61 at.% in CoCr_xFeMnNi (x = 1, 0.25) at 1000 °C. Carbon atoms are also known to strengthen the steels [26] and HEAs [25,27,28] through solution strengthening, precipitation and/or grain-size strengthening. In this study, mechanical properties and microstructural evolution of non-equiatomic quaternary Alloy-600-type CoNiCrFe with and/or without carbon addition at room and cryogenic temperatures were studied.

2. Materials and Methods

Alloy 600-type non-equiatomic NiCoCrFe alloy ingots with carbon addition up to 0.8 at.% were cast using vacuum induction melting using Co, Ni, Cr and Fe of >99.9% purity. As stated in the “Introduction”, the composition of the alloys in the present study is similar to that of 600-type (Ni-Cr(14–17 wt.%)-Fe(8–10 wt.%)) alloys except that approximately half of major Ni content (72–80%) was substituted by Co. The composition of the alloys in the present study is expressed in at.% to compare it to the conventional medium entropy alloys, but the composition in wt.% is also summarized in

Table 1. Chemical composition of the (Ni,Co)₇₅Cr₁₇Fe₈C_x alloys in atomic percentage (at.%) and weight percentage (wt.%).

Alloys		Co	Ni	Cr	Fe	C
(NiCo)75Cr17Fe8	at.%	36	39	17	8	-
	wt.%	36.95	39.87	15.4	7.78
(NiCo)75Cr17Fe8C0.34	at.%	36.16	38.39	17.01	8.1	0.34
	wt.%	37.25	39.35	15.43	7.9	0.07
(NiCo)75Cr17Fe8C0.83	at.%	36.12	38.2	16.87	7.98	0.83
	wt.%	37.29	39.3	15.4	7.84	0.17

for comparison with Alloy 600. The alloying with carbon was made by adding ferrochrome with high carbon content. The carbon content was measured to be 0.34 at.% and 0.83 at.% using a Leco C/S-844 C/S determinator (St. Joseph, MI, USA). Because of the addition of carbon, the exact chemical compositions of major substitutional atoms, Co, Ni, Cr and Fe varies with the addition of carbon and are summarized in wt.% and at.% in Table 1. However, carbon-free alloy and carbon-containing alloys will be presented as (NiCo)₇₅Cr₁₇Fe₈, (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 in the text. During vacuum induction melting, the vacuum was maintained below 10⁻³ torr. The initial ingots had the rectangular shape with the size measuring 40 × 110 × 140 mm³. The ingots were then cut into a size of 30 × 40 × 15 mm³ and homogenized at 1200 °C for 6 h in a vacuum, followed by cooling in air. After homogenization, the ingots were rolled into plates with a thickness of 1 mm at room temperature. In order to obtain an alloy with a recrystallized microstructure, the rolled plates were annealed at 850 °C for 1 h.

Tensile specimens were machined from the recrystallized sheets with a gage length of 9 mm and a width of 3.4 mm. Tensile tests were performed at room temperature and cryogenic temperature (77 K) at an engineering strain rate of 1 × 10⁻³ mm/s. The 77 K cryogenic testing was carried out after fully immersing the specimens and grips in a bath of liquid nitrogen and stabilizing the cryogenic temperature. Microstructural and phase analyses of the alloys were carried out using X-ray diffraction (XRD), and a scanning electron microscope (SEM) equipped with an electron back-scattering diffraction (EBSD) detector at an acceleration voltage of 15 kV. The grain structure and phase distribution were also characterized using an EBSD system (Oxford Instruments, Oxford, UK) attached to a field-emission scanning electron microscope (FE-SEM; Helios, Pegasus, FEI). Nanostructure and electron diffraction analyses were performed using a transmission electron microscope (TEM) operated at 200 kV (TEM, JEM-2100F, JEOL, Tokyo, Japan). The TEM foils for TEM observation were prepared using twin-jet electro polishing method by South Bay Model 550 in a solution of 90% methanol and 10% perchloric acid with a voltage of 25 V and at 25 °C.

3. Result and Discussion

3.1. Effect of Carbon on the Microstructural Evolution

The solubility of carbon increases with temperature and the mechanical properties of (NiCo)₇₅Cr₁₇Fe₈C_x medium entropy alloys (MEAs) would be influenced by the thermomechanical processing. In order to estimate the effect of carbon interstitial and carbides in the annealed alloy, XRD spectra from the solid solution treated and annealed alloys were analyzed. Figure 1 shows the XRD patterns of the annealed (a) and solid solution treated (b) (NiCo)₇₅Cr₁₇Fe₈C_x with different carbon contents, respectively. XRD spectra from annealed and solution-treated (NiCo)₇₅Cr₁₇Fe₈C_x in Figure 1a,b support the assertion that (NiCo)₇₅Cr₁₇Fe₈ is a single phase fcc alloy with carbon addition stabilized the fcc phase. No noticeable peaks were observed even in the carbon-containing annealed alloys with 0.83 at.% carbon despite the presence of carbides (confirmed by TEM) because of the low volume fraction of submicron sized carbides as in CoCr_0.25FeMnNi. [25]. The shift of XRD peaks with an increase of carbon content was found to be insignificant in the annealed alloys (see inset of Figure 1a), suggesting that either the effect of carbon on the lattice constant is insignificant or the interstitial carbon content is small.

In the solution-treated (NiCo)₇₅Cr₁₇Fe₈, the XRD peaks shifted to the lower angle with an increase of carbon content (see inset of Figure 1b), suggesting the expansion of the lattice with an increase of carbon content. The lattice parameter of the fcc phase matrix was found to increase from 0.3546 nm to 0.3553 nm as the carbon content increased from 0 to 0.83 at.%. In Figure 1c, the variations of lattice parameters of solution treated and annealed alloys as a function of carbon content are exhibited. A nearly linear relationship between the carbon content, C_at.% and the lattice constant, a (a (nm) = 0.3546 + 0.00084 C_at.%) for solution-treated alloys was observed. The linear increase of the lattice constant in the solution-treated alloys and the lower sensitivity of lattice constant to the carbon content in the annealed alloys suggest that most carbon precipitated as carbides in the annealed alloys and the interstitial carbon in the annealed matrix is much smaller than those consumed for carbide formation. It has been reported that the solubility of interstitial carbon in the Cantor-type HEAs at high temperatures increased with a decrease of Cr content [25]. Klimova et al. also reported that the carbon solubility decreased rapidly below 800 °C in CoCr_xFeMnNi (x = 1, 0.25) [25].

EBSD inverse-pole-figure maps of annealed (NiCo)₇₅Cr₁₇Fe₈, (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 are shown in Figure 2. It is apparent that the grain size of (NiCo)₇₅Cr₁₇Fe₈C_x decreased with increasing carbon content, especially when the carbon content is higher (0.83 at.%). The grain size excluding twin boundaries was measured to be 15.1 μm in carbon-free (NiCo)₇₅Cr₁₇Fe₈, and those of carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 were measured as 9.6 μm and 3.1 μm, respectively. The grain size including twin boundaries was measured to be 11.3 μm, 6.4 μm and 1.9 μm for three alloys, respectively. The decrease of grain size with increase of carbon content in (NiCo)₇₅Cr₁₇Fe₈C_x MEAs is attributed to grain boundary pinning effect of carbide particles [25,26,27]. A higher dislocation storage and the lower recovery due to carbon atoms and carbides may have contributed to grain size refinement [27]. Figure 3 shows the change in grain size and annealing twin volume fraction as a function of carbon content. The grain size and annealing twin volume fraction were evaluated by orientation imaging microscopy (OIM) EBSD system (v. 7, EDAX Inc, Sandy, UT, USA). It is apparent that the grain size decreased and annealing twin volume fraction increased significantly with increasing carbon content in the annealed (NiCo)₇₅Cr₁₇Fe₈C_x alloys. The twin volume fraction increased from 0.14 in the carbon-free (NiCo)₇₅Cr₁₇Fe₈ to 0.414 in carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_0.83.

EBSD phase maps of annealed carbon-free (NiCo)₇₅Cr₁₇Fe₈ (a) and carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_0.34 (b) and (NiCo)₇₅Cr₁₇Fe₈C_0.83 (c) are shown in Figure 4. As shown in this figure, carbon-free alloy shows a large-grained single fcc phase structure whereas the carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 show the distribution of submicron-scale carbides. The presence of M₂₃C₆ carbide particles (blue phase) and M₇C₃ carbides (small yellow phase) were confirmed by EBSD phase mapping. It should be noted that the size of carbides in (NiCo)₇₅Cr₁₇Fe₈ type alloys is much smaller than that (0.2–0.5 μm) in the Cantor alloy [27]. The volume fraction of M₂₃C₆ carbides was found to be greater than that of Cr₇C₃. The fractions of both M₂₃C₆ and M₇C₃ carbides increased with increase of carbon. The formation of smaller nanoscale M₇C₃ carbides is compatible with the observation in the equiatomic CoCrFeMnNi [27]. The presence of submicron carbides along the twin and grain boundaries in the present study is due to the increased solubility of carbon above 800 °C and rapid decline of carbon below 800 °C in low Cr content HEA [25]. Since the size of carbides in the grain interior was found to be smaller in TEM analyses, the carbides in grain interiors were hardly observed in the EBSD phase map because of its smaller size. No carbides were observed in the EBSD phase map of solution-treated alloy. Since small carbides are not detected in EBSD, extensive TEM works were carried out. Figure 5a–d exhibit the TEM images of solution-treated (NiCo)₇₅Cr₁₇Fe₈C_0.83 (a), annealed (NiCo)₇₅Cr₁₇Fe₈C_0.34 (b) and annealed (NiCo)₇₅Cr₁₇Fe₈C_0.83 (c, d). In Figure 5a, some dislocations that may form during sample preparation or quenching were observed with no indication of carbide formation, supporting the dissolution of carbides at 1200 °C. In Figure 5b,c, round-shaped submicron particles in the grain interior and at grain boundaries are shown. It is obvious that the carbide population increased significantly with an increase of carbon content from 0.34 at.% to 0.83 at.%. The diffraction pattern from the carbide particle (marked) in Figure 5d suggests that they are mostly Cr₂₃C₆-type carbides.

The presence of closely spaced carbides along some straight grain boundaries and twin boundaries (indicated by arrows) and the decrease of grain size with an increase of carbon content suggests that carbide precipitation and recrystallization took place in the similar temperature range during annealing and cooling. It is interesting to note that M₂₃C₆ carbides (blue in Figure 4) were more frequently observed at twin boundaries than at grain boundaries. Guan et al. [26] directly observed the precipitation along twin boundaries and reported that precipitation occurred concurrently with recrystallization and the combined effect of precipitation and solute segregated to twin boundaries modified the recrystallization behavior. The concurrent precipitation and recrystallization reported by Guan et al. [28] supports the suggestion of this study. Earlier Vaughan [29] also observed the precipitation of submicron carbides at twin boundaries in austenitic stainless steels aged at 800 °C. Nie et al. [30] reported that solute atoms segregated to the twin and grain boundaries, leading to nucleation and growth of the precipitates and relieving the strain energy. The decrease of grain size with increase of content in the present study can be explained by the suggestion of Guan et al. [28] that precipitates and higher solute concentration along original twin boundaries hindered the grain growth of newly formed recrystallized grains.

3.2. Effect of Carbon Addition on the Mechanical Properties

In order to analyze the effect of carbon addition on tensile behavior in (NiCo)₇₅Cr₁₇Fe₈C_x MEAs, a tensile test was performed. Stress-strain responses of (NiCo)₇₅Cr₁₇Fe₈C_x at room and cryogenic temperatures are exhibited in Figure 6. The increase in the carbon content resulted in the pronounced increase in strength of the alloys and the moderate reduction in elongation. At room temperature, the yield strength of (NiCo)₇₅Cr₁₇Fe₈C_x increased from 311 MPa to 650 MPa with the addition of 0.83 at.% carbon. The tensile strength of carbon-free (NiCo)₇₅Cr₁₇Fe₈ at room temperature was measured to be 729 MPa, and the tensile strengths of (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 were found to be 831 MPa and 931 MPa, respectively. The ductility at room temperature decreased with the increase in carbon content. The ductility of (NiCo)₇₅Cr₁₇Fe₈C_0.83 is still greater than 50%. It is interesting to note that both yield strength and elongation increased simultaneously with decrease of the testing temperature to 77 K. It should also be noted that the hardening rates increased significantly at 77 K, resulting in a dramatic increase of the tensile strength. With a decrease of the testing temperature from room temperature to 77 K, the tensile strength increased from 729 MPa to 1212 MPa for the carbon-free alloy, from 831 MPa to 1321 MPa for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and from 942 MPa to 1397 MPa (NiCo)₇₅Cr₁₇Fe₈C_0.83. The more dramatic increases of strength and elongation at cryogenic temperature compared to that of the yield stress suggest that more effective deformation induced strengthening worked at 77 K. Tensile mechanical properties such as yield strength (YS), ultimate tensile strength (UTS) and elongation to fracture (EF) of the (NiCo)₇₅Cr₁₇Fe₈C_x of the present study are summarized in

Table 2. Tensile mechanical properties of the (NiCo)₇₅Cr₁₇Fe₈C_x of the present study along with the data of Alloy 600 for comparison.

Carbon Content	Testing Temperature (K)	YS (MPa)	UTS (MPa)	EF (%)	Processing Condition
(NiCo)75Cr17Fe8	77	491	1212	106	annealed at 850 °C
	298	311	729	81
(NiCo)74.55Cr17.01Fe8.1C0.34	77	583	1321	96
	298	390	831	72
(NiCo)74.32Cr16.87Fe7.98C0.83	77	865	1397	66
	298	650	942	55
Alloy 600 (Ni74Cr17.38Fe7.91C0.71)	298	331	676	41	annealed at 870 °C [31]
Alloy 600 (Ni74Cr17.93Fe8.02C0.05)	298	220	602	52	annealed at 1070 °C [20]

along with the data of Alloy 600 [20,31] for comparison.

In Figure 7, the hardening rates of (NiCo)₇₅Cr₁₇Fe₈C_x alloy with different carbon contents (0, 0.34 and 0.83 at.%) are plotted as a function of true strain at room or cryogenic temperatures. The initial hardening rates of (NiCo)₇₅Cr₁₇Fe₈C_x increased with increasing carbon content at room temperature. Hardening rates of carbon-containing alloys were larger than those of carbon-free alloy up to the true strain of 0.25 at room temperature, suggesting the effect of carbon and/or carbide on the dislocation accumulation. However, the strain range with the sustained work hardening rate (negligible change of hardening rate with strain) is greater in the carbon free alloy, providing excellent ductility (~80%) at room temperature in the carbon-free alloy. At cryogenic temperature, hardening rates of all alloys exhibited higher values than the room temperature hardening rates of their counterparts. The initial hardening rates at 77 K also increased with increase of carbon content. It should be noted that the hardening rates of carbon-free (NiCo)₇₅Cr₁₇Fe₈ and low carbon (NiCo)₇₅Cr₁₇Fe₈C_0.34 alloy even increased with strain in the strain range of 0.1–0.6 at 77 K. The plateau or hump of strain hardening rate in Figure 6 suggests the activation of a new deformation defect which can act as both deformation obstacles and deformation carriers. The increase of strain hardening rate with strain has been observed in various twin-induced plasticity (TWIP) [32,33,34,35] and transformation-induced plasticity (TRIP) alloys [34]. The excellent strength and ductility of (NiCo)₇₅Cr₁₇Fe₈ and low carbon (NiCo)₇₅Cr₁₇Fe₈C_0.34 alloy in Figure 5 is attributed to the increase of strain hardening rate with strain in the strain range of 0.1–0.6 at 77 K. The tensile strength increased significantly up to ~1400 MPa in carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_0.83 with a decent ductility of 106.

3.3. Effect of Carbon on the Deformation Microstructure

TEM microstructures of (NiCo)₇₅Cr₁₇Fe₈ (a), (NiCo)₇₅Cr₁₇Fe₈C_0.34 (b) and (NiCo)₇₅Cr₁₇Fe₈C_0.83 (c) deformed to 20% at room temperature are exhibited in Figure 8a–c. In carbon free (NiCo)₇₅Cr₁₇Fe₈ alloy, a rather homogeneously distributed dislocation structure with a slight tendency of dislocation clustering was observed. The stacking fault energy of Alloy 600 at room temperature was reported to be 28 mJ/m² [36], a little higher than that (21 mJ/m²) of 304 stainless steel. It has been suggested that Cu-13 at.% Zn alloy with the stacking fault energy (SFE) of 29 mJ/m² is in the transition range of the slip mode changes from wavy to planar [37]. A homogeneously distributed dislocation structure with no deformation twinning in Figure 8a suggests that the SFE of Alloy 600-type (NiCo)₇₅Cr₁₇Fe₈ MEA at room temperature is not greatly changed by the alloy modification. In carbon containing (NiCo)₇₅Cr₁₇Fe₈C_0.34 (b) and (NiCo)₇₅Cr₁₇Fe₈C_0.83 (c) MEAs, deformation twins developed in addition to homogeneously distributed dislocations. It should be noted that nanoscale carbides (indicated by arrowheads) were formed in the carbon-containing alloys and their volume fraction and size increased with an increase of carbon content in Figure 8b,c. Deformation twins were observed more profusely in (NiCo)₇₅Cr₁₇Fe₈ (a), (NiCo)₇₅Cr₁₇Fe₈C_0.34 (b) and (NiCo)₇₅Cr₁₇Fe₈C_0.83 (c) deformed to 20% at cryogenic temperature as shown in Figure 9a–c. The presence of deformation twins at cryogenic temperature is evident in both the diffraction patterns and TEM images. The interaction between the dislocation and the deformation twins causes the accumulation of high-density dislocations within the twin lamellas, leading to increased strength with deformation. The accumulated dislocations also act as effective obstacles to dislocation motion, increasing the critical stress required to induce plastic deformation and providing additional strengthening rate.

It should be noted that deformation twins were also observed in the carbon-free alloy at cryogenic temperature in contrast to the absence of deformation twins in the carbon free alloy at room temperature. Dissociated partial dislocations and thin twins were known to interact with nanometer-sized carbides via a bypass mechanism [38] and the large carbides could act as obstacles to the twinning propagation [27,38]. In high carbon (NiCo)₇₅Cr₁₇Fe₈C_0.83 with larger carbides in Figure 9c, the spacing between twin bands increased because larger carbides act as obstacles to crack propagation. It is shown that deformation twin bands were not observed in the path blocked by large carbides as shown in Figure 9c. Instead, the deformation twin bands in the path without large carbides were found to be thicker. Apparently, the activation of twin bands with smaller spacing in (NiCo)₇₅Cr₁₇Fe₈ (a) and (NiCo)₇₅Cr₁₇Fe₈C_0.34 (b) in Figure 9 increased the hardening rate more effectively with strain and also increased the ductility. In (NiCo)₇₅Cr₁₇Fe₈C_0.83 with widely spaced deformation twins, initial hardening rate was high, but it decreased rapidly, resulting in the decrease of ductility. It was suggested that the fraction of deformation twins increased with increase of carbon content up to 0.6% in high Mn steels [39]. The initial enhanced hardening rate and earlier decrease of the hardening rate above 30% strain in the high carbon (NiCo)₇₅Cr₁₇Fe₈C_0.83 are compatible with the observation in carbon-containing CoCrFeMnNi HEA [27]. The decreased strain-hardening rate at later deformation stages and the corresponding decrease in ductility were attributed to the presence of Cr₂₃C₆ [27] and/or the effect of carbon on the deformation twinning or the dynamic recovery [27,35,37]. Arrays of dislocations and deformation twin bands are known to impinge on carbide particles [27,38,40] developing high stress concentrations. It should be noted that the annealing twin fraction increased as shown in Figure 3 since growth of annealing twins are not impeded by the larger carbides because of the concurrent precipitation and recrystallization (including the formation of annealing twins) during the annealing process [28].

Wu et al. [41] suggested that the formation of deformation twinning was enhanced by increasing carbon addition in a CoCrFeMnNi alloy, in contrast to the observation of Stepanov et al. [42]. Wu et al. [41] and Wang et al. [43] suggested the decrease of SFE with increase of carbon content in HEAs, while Stepanov et al. [42] proposed an increase of SFE with carbon content. Ko and Hong [27] asserted that extra caution should be exercised during TEM measurements of SFE of alloys because the distribution of alloying elements can be disrupted by local heating and the distance between partial dislocations can be altered by the internal stress field. Although the roles of interstitial carbon on SFE and twinning are still controversial, a number of experimental observations support the influence of interstitial [27,44,45] and substitutional [27,35,37] atoms on twinning in alloys with insignificant changes of SFE. The effect of carbon on the formation of annealing and deformation twins can also be explained by the effect of the frictional stress of interstitial on the twinnability and stability of twins [35,37]. Ovid’ko and Sheinerman [46] suggested that incoherent twin boundaries with solute atoms segregated at twinning partial dislocations are more stable with respect to detwinning. Hong [35] proposed that increased frictional stress due to solute atoms and the decreased SFE increases the stress needed to join partial dislocations, resulting in the inhibition of cross-slip and inducing deformation twinning. The interaction between solute atoms and twin boundaries and its effect on enhancing twin stability is more generally accepted for various alloys [35,37,44,45]. It has been shown that the addition of interstitials, such as nitrogen and oxygen, promotes deformation planarity [37] in stainless steels and Ti alloys. Interstitials such as carbon, nitrogen, and oxygen were observed to segregate at Shockley partials and hinder cross slipping or the joining of partial dislocations, promoting planar slip and twinning in some alloys [30,46]. The observation that the annealing twin fraction increased with increasing carbon content in the present study was attributed to the effect of carbon on the stability of partials and the enhanced stability of annealing twins.

3.4. Estimation of Carbon Partitioning into Carbides and Interstitial Carbon

The addition of carbon was found to have a beneficial effect on the mechanical properties by decreasing the grain size [27,47], increasing the friction and/or back stress associated with interstitial carbon or carbides [27], and enhancing the stability of deformation twins [27,46]. Two types of carbide, M₂₃C₆ and M₇C₃ carbide particles, were observed in (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 as exhibited in Figure 4 and Figure 5. For the estimation of strengthening effects of carbides on the strengthening due to dislocation–carbide interaction and grain size strengthening due to grain boundary pinning, the size and volume fraction of carbides in the grain interiors and at grain boundaries were analyzed separately irrespective of the types of carbide. In (NiCo)₇₅Cr₁₇Fe₈C_0.34, the average sizes of carbide in the grain interiors and at grain boundaries were estimated to be 85.1 nm and 159.2 nm, respectively. With the addition of 0.83 at.% carbon ((NiCo)₇₅Cr₁₇Fe₈C_0.83), the average carbide sizes present at the matrix and grain boundaries were 79.5 nm and 189.8 nm, respectively. The size of carbide present in the matrix was observed to be smaller than that at grain boundaries. Because of the concurrent formation of carbides and recrystallization, the combined effects of solute segregation and carbide formation could modify the recrystallization behavior and control the grain size [28]. Further grain boundary migration and growth are retarded by the presence of carbide particles.

The precise estimation of interstitial carbon and carbon consumed for carbide formation is important for the prediction of the strengthening mechanism of carbon-containing alloys. The partitioning of carbon into interstitial carbon atoms and carbides in the carbon containing alloys annealed at 850 °C estimated through the comparison of the lattice constant of the carbon containing alloys annealed at 850 °C (Figure 1b) with that of quenched counterpart (Figure 1a) after solution treatment at 1200 °C. The content of interstitial carbon can be calculated using the relationship between lattice constant and the total content of the solution-treated alloys, (a (nm) = 0.3546 + 0.00084 C_at.%) assuming that all carbon atoms are interstitial carbon after solution treatment (at 1200 °C). The effect of carbides on the lattice constant of the matrix would be negligible if there is any. If all carbon content was used for the formation of carbides after annealing, there would be no change of lattice constant of the matrix. The change of lattice constant in Figure 1c suggests that some carbon atoms remained as interstitial atoms and affected the lattice constant. The difference of the lattice constant between the annealed and solution-treated alloy is due to the difference of interstitial carbon and the interstitial content can be calculated using the lattice constant of the annealed alloy in Figure 1c and the equation, a (nm) = 0.3546 + 0.00084 C_at.%. The content of interstitial carbon was calculated to be 0.04 at.% and 0.17 at.% for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively. Therefore, the rest of the total carbon excluding the interstitial carbon was considered to be used for carbide formation. The volume fraction of carbides was calculated using the lattice structure of carbides by assuming that all carbides were Cr₂₃C₆ since we found that the volume fraction of Cr₇C₃ is less than 7% of that of Cr₂₃C₆ in the EBSD phase map.

It should be noted that 80~90% of carbon precipitated out as carbides after annealing at 850 °C. The theoretical carbide volume fraction(f) can be calculated from the phase density, atomic fraction and relative atomic mass assuming that most carbides are M₂₃C₆ type carbides as observed in Figure 4 and Figure 5. The lattice constant of CoNiCrFe alloy (a = 0.355 nm) is used to estimate the density of CoNiCrFe alloy (8.0 g/cm³), while the density of M₂₃C₆ is sourced to Cr₂₃C₆ (7.0 g/cm³) as presented in reference [48]. The relative atomic mass of M in M₂₃C₆ is taken from the average of Co, Ni, Cr and Fe (56.4 g/mol). If the carbon content is partitioned into carbides excluding interstitial carbons (0.04, 0.17 at.%) from total carbon contents (0.34, 0.83 at.%) are used to estimate the theoretical volume fraction of M₂₃C₆ carbide, the estimated volume fractions of M₂₃C₆ carbide is 1.11 vol.% and 2.98 vol.% for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively. The fractions of carbides were also estimated based on the areal distribution of carbides in TEM images (5 images each) and they were calculated to be 0.92% and 3.2% for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively. The experimentally measured fractions were found to be reasonably close to those calculated volume fraction of carbides based on the shift of XRD peaks.

3.5. Strengthening Contribution to Carbon-Free and Carbon Containing Alloys

In order to understand the strengthening mechanisms in the carbon-free and carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_x MEAs, the yield strength can be predicted by estimating the strengthening caused by microscale/nanoscale obstacles to deformation [18,49]. The excellent combinations of strength and ductility of (NiCo)₇₅Cr₁₇Fe₈C_x MEAs is thought to result from the contributions from grain refinement strengthening, precipitation strengthening and solid-solution strengthening by substitutional and interstitial (carbon) atoms. The yield strength, σ_y can be expressed as the summation of various strengthening contributions [50,51]:

$$\begin{array}{cc}\hfill {\sigma }_y& = {\sigma }_0+ \Delta {\sigma }_G+ \Delta {\sigma }_P+\Delta {\sigma }_D+ \Delta {\sigma }_{SS}+ \Delta {\sigma }_{iS}\hfill \\ & ={\sigma }_f+ \Delta {\sigma }_G+ \Delta {\sigma }_P+\Delta {\sigma }_D+ \Delta {\sigma }_{iS}\hfill \end{array}$$

(1)

where ${\sigma }_0$ is the intrinsic strength, $\Delta {\sigma }_G$ from grain refinement, $\Delta {\sigma }_P$ from precipitates/paricles (carbides), $\Delta {\sigma }_D$ from dislocation density increment and $\Delta {\sigma }_{SS}$ is substitutional solution strengthening contributions, and $\Delta {\sigma }_{iS}$ is interstitial solution strengthening by carbon, respectively. Since we are only interested in the additional strengthening by the addition of carbon, the friction stress ${\sigma }_f=({\sigma }_0+ \Delta {\sigma }_{SS }$) was used instead of the intrinsic stress ${\sigma }_0$ in Equation (1). TEM images of fully annealed alloys exhibited very few dislocations, suggesting that the strengthening contribution from dislocation ($\Delta {\sigma }_D$) density is negligible for the annealed alloy. Therefore, strengthening components contributing to the yield strength of the annealed alloy in the present study consist of the friction stress, grain size strengthening, carbide strengthening and interstitial strengthening (${\sigma }_f+ \Delta {\sigma }_G+ \Delta {\sigma }_P + \Delta {\sigma }_{iS}$).

It has been suggested that the grain size refinement in the annealed carbon containing CoCrFeMnNi was mostly associated with the grain boundary-pinning effect of carbides [52]. The population of carbide particles clearly increased with increasing carbon content. The strengthening due grain refinement by carbides can be obtained by the typical Hall–Petch equation $({\sigma }_y= {\sigma }_f+ k_y{d}^{-1/2})$, where d is the grain size and $k_y$ is the Hall–Petch coefficient. The ${\sigma }_f$ of CrFeCoNi alloy was reported to be 90 MPa at room and 286 MPa at cryogenic temperature [10,53], The Hall–Petch coefficient was reported to be 855 MPa μm^1/2 [54] at room and 870 MPa μm^1/2 [10,53] at cryogenic temperature for the CrFeCoNi alloy. We examined the temperature-dependence of the yield strength of (NiCo)₇₅Cr₁₇Fe₈ of the present study and compared this value with that of CoCrFeNi [52,53,54] and found that both alloys have the similar temperature dependence. The grain size versus strength data of (NiCo)₇₅Cr₁₇Fe₈ falls closely on the Hall–Petch equation lines of CoCrFeNi. Therefore, (NiCo)₇₅Cr₁₇Fe₈ is thought to have the similar Hall–Petch behaviors to those of CoCrFeNi. The yield strength increase caused by grain size difference ($\Delta {\sigma }_G$) can be expressed as:

$$\Delta {\sigma }_G= k_y \left(d_p{}^{-1/2}- d_o{}^{-1/2}\right)$$

(2)

where $d_p$ represent the grain size of the processed alloy. The estimated contributions of grain boundary $\left(\Delta {\sigma }_G\right)$ strengthening predicted by Equation (2) are 220 MPa, 276 MPa, 485.6 MPa at room temperature and 223.9 MPa, 280.8 MPa, 494.1 MPa at cryogenic temperature for (NiCo)₇₅Cr₁₇Fe₈, (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively. The concurrent recrystallization and precipitation of submicron carbides at twin and grain boundaries during annealing at 850 °C [38] effectively prohibited the grain growth, resulting in a significant increase in strength, which can be predicted by the Hall–Petch equation.

Strengthening by submicron carbide precipitation caused by the passage of dislocations through non-shearable particles can be predicted by an Ashby–Orowan type equation as follows [48,55]:

$$\Delta {\sigma }_p=0.538\frac{Gb{f}_p{}^{0.5}}{d_p} \ln \left(\frac{d_p}{2b}\right)$$

(3)

where G is shear modulus, b is Burgers vector,$f_p$ is the volume fraction of particles, and $d_p$ is diameter of carbide particles. Shear modulus of quarternary CrFeCoNi alloy at room temperature was reported to be 82 GPa [56], b = 0.357 nm is the Burgers vector of (NiCo)₇₅Cr₁₇Fe₈ alloy, and volume fractions and average sizes of carbide precipitates were calculated from TEM images and the EBSD phase map. The shear modulus of (NiCo)₇₅Cr₁₇Fe₈ at cryogenic temperature was calculated using the temperature dependence of shear modulus in CoCrFeMnNi [57,58]. The average size of carbide present in the matrix was measured to be 85.1 nm and 79.5 nm for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively, and the volume fraction of carbide is 0.2% and 0.32% for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively. The calculated value of $\Delta {\sigma }_p$ due to the carbides in the grain interior, which act as obstacles to dislocation motion is 39.5 MPa and 52.8 MPa at room temperature for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively. The calculated value of $\Delta {\sigma }_p$ increased to 41.5 MPa and 55.4 MPa at cryogenic temperature. Traditional approaches to estimating the effect of in interstitial solution hardening are all based on dilute solution alloys. The increment of shear stress, Δτ₀ caused by interstitial carbon atoms can be estimated using the atomic size misfit ${\mathsf{\epsilon }}_L\left(=\frac{1}{a}\times \frac{da}{dC}\right)$ that was imposed on the matrix, [35,58,59,60], where a is the lattice parameter and C is the interstitial carbon content. The lattice parameters of the solid solution-treated (NiCo)₇₅Cr₁₇Fe₈, (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.8 MEAs were calculated from the XRD data (Figure 1a), which are 0.3546 nm, 0.3548 nm and 0.3553 nm, respectively. The atomic size misfit ${\epsilon }_L$ was calculated to be 0.24 per at.% of carbon, which agrees well with the value of 0.22% reported for CoNiCr [61].

The enhancement of CRSS (MPa) Δτ_0L by interstitial solid solution caused by size misfit can be expressed as [62]:

$$\Delta {\tau }_{iS}=fG\alpha {\epsilon }_L{}^m{c}^n$$

(4)

where ${\mathsf{\epsilon }}_L \mathrm{is}\mathrm{the}\mathrm{misfit}\left(\frac{1}{a}\frac{da}{dc}\right)$, α is a parameter dependent on the character of dislocations (α = 16 for most cases [39,40]), f is the temperature dependent numerical constant. The parameter f increases in proportional to the strength (=4 × 10⁻⁴ at room temperature and 5.7 × 10⁻⁴ at cryogenic temperature [39,40]) In the Fleischer model, the exponent m = 3/2 and n = 1/2 [62]. The interstitial carbon in the matrix was 0.04 at.% and 0.17 at.% for (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, respectively. The strengthening component due to interstitial solution effect by using the interstitial carbon content was calculated to be 4.9 MPa and 10.2 MPa at room temperature and 7.4 MPa and 15.2 MPa at cryogenic temperature, respectively (

Table 3. Strength contributions from different strengthening mechanisms of the annealed carbon-free and carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_x medium-entropy alloys (MEAs). (N/A: not applicable).

	Carbide Size (nm)	Volume Fraction (%)	YS (MPa)		Hall-Petch Equation (MPa)				Precipitation Strengthening (MPa)		Interstitial Solution Strengthening (MPa)		Calculated Strength (MPa)
Alloys			RT	77 K	RT		77 K		RT	77 K	RT	77 K	RT	77 K
					${\sigma }_o$	$\Delta {\sigma }_G$	${\sigma }_o$	$\Delta {\sigma }_G$
(NiCo)75Cr17Fe8	N/A (No carbides)	N/A	311	496	90	220.0	286	223.9	N/A	N/A	N/A	N/A	310	509.9
(NiCo)75Cr17Fe8C0.34	85.1	0.20	397	596	90	276.0	286	280.8	39.5	41.5	4.9	7.4	410.4	615.7
(NiCo)75Cr17Fe8C0.83	79.5	0.32	650	865	90	485.6	286	494.1	52.8	55.4	10.2	15.2	638.6	850.7

). Using Equations (1)–(4), the yield strengths of (NiCo)₇₅Cr₁₇Fe₈, (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83, were calculated as 310 MPa, 410.4 MPa and 638.6 MPa at room temperature and 509.9 MPa, 615.7 MPa and 850.7 MPa at cryogenic temperature, respectively. In Table 3, the strength contributions from different strengthening mechanisms of the annealed carbon-free and carbon-containing (NiCo)₇₅Cr₁₇Fe₈C_x MEAs are summarized. In Figure 10a,b, predicted strengthening components including $\Delta {\sigma }_G$ by grain refinement, $\Delta {\sigma }_P$ by carbides, $\Delta {\sigma }_{iS}$ by interstitial solution strengthening of carbon and the friction stress due to intrinsic stress and substitutional solid solution strengthening $({\sigma }_0+\Delta {\sigma }_{SS }$) for carbon-free and carbon-containing alloys are plotted with the experimental yield strengths of (NiCo)₇₅Cr₁₇Fe₈, (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83. It is apparent that the predicted data are in reasonable agreement with the experimental results. In carbon-free (NiCo)₇₅Cr₁₇Fe₈, the friction stress component consisting of the intrinsic stress and the solid solution strengthening increases significantly with the decrease of temperature, suggesting the strong temperature dependence of substitutional solid solution strengthening as in CoCrFeMnNi HEA [18,63]. The major contribution of carbon to strengthening is caused by grain-size refinement followed by precipitation strengthening by carbide formation in the grain interior as shown in Figure 10. The effect of interstitial carbon on the solution strengthening is insignificant although it increased with the increase of carbon content.

For most metallic materials, tensile strength and tensile ductility usually display the strength–ductility trade-off. In Figure 11a,b, the yield strengths (a) and tensile strengths of (NiCo)₇₅Cr₁₇Fe₈C_x are plotted against the ductility at cryogenic temperature along with the data of other HEAs [3,5,25,43]. Both figures exhibit outstanding combinations of strengths (YS, UTS) and ductility of alloys of the present study compared to HEAs. As can be seen in Figure 10, strength/ductility combinations of carbon-free (NiCo)₇₅Cr₁₇Fe₈ and carbon containing (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 are also superior to those of carbon-free and carbon-containing CoCrFeMnNi [25] Fe_49.6Mn₃₀Co₁₀Cr₁₀C_0.5 [43]. In Figure 11a,b, the yield strengths (a) and tensile strengths of (NiCo)₇₅Cr₁₇Fe₈C_x are plotted against the ductility at cryogenic temperature along with the data of other HEAs [20,21,31,48] and Alloy 600 [31]. Both figures exhibit outstanding combinations of strengths (YS, UTS) and ductility of alloys of the present study compared to HEAs and Alloy 600. It should be noted that the strength/ductility combination of carbon-free (NiCo)₇₅Cr₁₇Fe₈ MEA was found to be 729 MPa/81% at 298K, superior to that (676MPa/41% [31]) of Alloy 600. The higher strength and ductility of (NiCo)₇₅Cr₁₇Fe₈ MEA is thought to be attributed to the effect of Co addition on the deformation behavior. As shown in Figure 10, the friction stress including the substitutional solution hardening contributed to the strength of the alloy significantly. It has been suggested that the decrease of Ni and the increase of Co decreased the stability of fcc phase appreciably, but the balancing Ni and Co content was known maintain the stability of fcc phase [64]. Yuan et al. [65] reported that the SFE decreased to 20–22 mJ/m² at 34 at.% Co in Ni-Co base superalloys, but it increased rapidly to 27 mJ/m² as the Co content increased to 35 at.% in Ni-Co base superalloys. The SFE of (NiCo)₇₅Cr₁₇Fe₈ of the present study is thought to be close to or slightly lower than that of alloy 600 [36]. The strength enhancement of (NiCo)₇₅Cr₁₇Fe₈, compared to Alloy 600 can be attributed to substitutional solution hardening and the effect of alloying on the slip planarity [35,37]. As can be seen in Figure 10, strength/ductility combinations of carbon-free (NiCo)₇₅Cr₁₇Fe₈ and carbon containing (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83(b) are also superior to those of Co-Cr-Ni-Fe HEAs [20,21,31,48,63] because of the strengthening contributions including $\Delta {\sigma }_G$ by grain refinement, $\Delta {\sigma }_P$ by carbides, $\Delta {\sigma }_{iS}$ by interstitial solution strengthening by carbon and the friction stress by intrinsic stress and substitutional solid solution strengthening $({\sigma }_0+\Delta {\sigma }_{SS}$). In this study, a new design strategy to develop a new medium entropy alloy by increasing the entropy of the conventional alloys by adding a new element with high solubility was found to be effective in enhancing the mechanical performance.

4. Conclusions

We investigated the effects of the addition of 35 at.% Co and carbon addition on the deformation behavior and mechanical properties of the conventional NiCrFe-type Alloy 600 at room and cryogenic temperatures.

• Increasing the entropy of the matrix of conventional alloys by adding new elements with high solubility to conventional alloys is proved to be a convenient new design strategy of developing new HEAs or MEAs with the enhanced performance.
• The concurrent recrystallization and precipitation of submicron carbides at twin and grain boundaries during annealing effectively prohibited the grain growth, resulting in a fine-grained structure and a significant increase in strength in carbon-doped alloys.
• In carbon containing (NiCo)₇₅Cr₁₇Fe₈C_0.34 (b) and (NiCo)₇₅Cr₁₇Fe₈C_0.83 MEAs, deformation twins developed in addition to homogeneously distributed dislocations. The nanoscale carbides were observed to be formed both in grain interiors and at grain boundaries. Their volume fraction and size increased with increase of carbon content.
• Strength/ductility combination of carbon-free (NiCo)₇₅Cr₁₇Fe₈ MEA was found to be 729 MPa/81% at 298 K and it increased to remarkable 1212MPa/106% at cryogenic temperature. The excellent strength and ductility of (NiCo)₇₅Cr₁₇Fe₈ at cryogenic temperature is attributed to the increased strain hardening rate caused by the interaction between dislocation slip and deformation twins.
• Carbon-doped (NiCo)₇₅Cr₁₇Fe₈C_0.34 (1321 MPa/96%) and (NiCo)₇₅Cr₁₇Fe₈C_0.83 (1398 MPa/66%) MEAs also exhibited excellent strength/ductility combinations, both of which are superior to those of other HEAs found in the literature.
• Strengthening components contributing to the yield strength of the annealed alloy in the present study consist of the friction stress, grain size strengthening, carbide strengthening and interstitial strengthening (${\sigma }_f+\Delta {\sigma }_G+\Delta {\sigma }_P+\Delta {\sigma }_{iS}$). Excellent agreement between the predictions and the experiments were obtained.
• Strength/ductility combinations (NiCo)₇₅Cr₁₇Fe₈, (NiCo)₇₅Cr₁₇Fe₈C_0.34 and (NiCo)₇₅Cr₁₇Fe₈C_0.83 at room and cryogenic temperatures are superior to those of other HEAs and MEAs because of the strengthening contributions by grain refinement, carbide formation, interstitial solution strengthening and the friction stress by intrinsic stress and substitutional solid solution strengthening.