Tuning mechanical metastability in FeMnCo medium entropy alloys and a peek into deformable hexagonal close-packed martensite

High and medium entropy alloys (HEAs and MEAs) represent a vibrant field of research in condensed matter physics^1–3 and materials science.^4–6 Unlike their dilute counterparts, HEAs and MEAs are defined by their concentrated compositions, which enable considerable design opportunities^7,8 and trigger the investigations of physicochemical fundamentals.^9,10 The prototypical concept of HEAs and MEAs is to maximize configurational entropy.^11,12 This was originally conceived to stabilize single-phase solid solution microstructure and, thereby, promote solid solution strengthening.¹³ More recently, recognition of compositional and structural metastability in HEAs and MEAs has stimulated further interest in achieving improved properties and revealing more intriguing physical phenomena.¹⁴ Plastic strain-induced martensitic transformation is one example.

The mechanical benefits of this athermic transformation are well-documented:^15–17 It increases strain hardenability and, thereby, promotes homogenous plastic deformation. Among all possible transformation pathways, the face-centered cubic (FCC) to hexagonal close-packed (HCP) transformation is of particular interest. This is because the similar stacking sequence between FCC and HCP lattices enables a well-defined $111FCC$ habit plane, leading to milder plastic accommodation¹⁸ and higher interfacial mobility.^19,20 Because of this, unlike the highly defected $α′$-martensite (body-centered tetragonal, BCT structure) that impedes plastic deformation,²¹ the HCP-martensite, provided its lower crystallographic symmetry, reveals atomistic mechanisms that enable somewhat deformability. Early research confirmed the intersection between HCP-martensite bands can trigger $α′$-martensite nucleation by atomic shuffle.^22,23 More recent literature reported that displacive transformations are also possible in HCP-martensite.^24,25 This enables a peculiar FCC-HCP-FCC sequential martensitic transformation chain²⁴ driven by plastic loading. These physical insights motivate the present study: to better understand the compositional dependency of mechanical metastability. More specifically, we aim to contribute to the understanding of the atomistic processes governing the plasticity and stability of the HCP-martensite.

(Fe₆₀Mn₄₀)_100-xCo_x MEAs were fabricated by vacuum arc melting, followed by cold-rolling, homogenization, and recrystallization treatment. Alloy processing, microstructural characterization, and mechanical testing details are summarized in supplementary material Notes 1–3 and Figs. S1–S3. The design of this ternary MEA system is primarily motivated by two factors: first, the compositional dependency of deformation mechanisms in Fe–Mn binary alloys. To suppress the formation of $α′$-martensite (BCT structure), a relatively high Mn content (usually 15–30 wt. %) is necessary.^15,26 Second, the intrinsic FCC-HCP transformation nature of Co. Among the very few elements (He, Fe, Co, Tl, Pb, and Yb) that can undergo direct FCC-HCP transformation,^19,27 Co exhibits peculiarity because of the absence of body-centered cubic (BCC) structure in the phase diagram.²⁸ However, understanding towards its role in affecting the strain-induced FCC-HCP martensitic transformation for concentrated Fe-Mn alloys is lacking. These considerations motivate the study detailed in this Letter. For simplicity, we denote each MEA by its Co content (i.e., Co_x-MEA). Microstructural investigation through backscatter diffraction (EBSD) and synchrotron x-ray diffraction (SXRD) confirms single FCC-phase microstructures in all four MEAs together with random texture [Figs. 1(a)–1(d)]. These results suggest that Co content increase from 2 to 15 at. % does not lead to martensitic transformation driven by rapid thermal quenching. It can be worthwhile modeling the thermodynamic properties of these alloys in future research, as the change in Co content may affect the thermal stability of the FCC-phase. Although all four MEAs were processed under the same conditions, a discernable grain size reduction can be seen within Co₁₀ and Co₁₅ MEAs [Figs. 1(c) and 1(d)]. While this phenomenon is not the main scope of the current research, it can be plausibly explained by the more sluggish recrystallization kinetics resulting from HCP-martensite formation during cold-rolling.^29,30 An extended discussion about the grain size effect on yield strength (i.e., the Hall–Petch effect) is provided in supplementary material Note 4. The rest of this Letter focuses on plastic strain-induced HCP-martensite, and the starting point is phase transformation kinetics.

Figure 2(a) reveals the SXRD patterns of the Co₁₅-MEA with respect to local plastic strain level. An evident mechanical metastability effect is present, as featured by the discernable HCP peaks as local plastic strain increases. Similar characteristics are also observed in the Co₁₀-MEA (supplementary material Fig. S7). SXRD results also confirm the absence of transitional structure in these two MEAs. The Co₂ and the Co₅ MEAs, on the other hand, both preserve single FCC phase constituents at all surveyed deformation levels, implicating their mechanical stability in response to plastic straining. The HCP-martensite phase fraction was determined from the SXRD diffractograms for the Co₁₀ and the Co₁₅ MEAs using Rietveld refinement.³¹ As seen in Fig. 2(b), highly accelerated transformation kinetics exists in the Co₁₅-MEA: At similar local plastic strain levels, the HCP-martensite fraction is roughly two times higher than the Co₁₀-MEA. Note that the term kinetics is adopted by following the convention of the theory of strain-induced martensitic transformation,^32,33 which actually refers to the increase in the martensite fraction as a function of plastic strain revealed here. The local plastic strain level is adopted to quantify the deformation level in a sense to explore the corresponding phase transformation characteristics. Based on the acquisition method of the local plastic strain detailed in supplementary material Note 2 and Fig. S7, it does not exhibit a point-wise correlation with macroscopic strain level and cannot be utilized to interpret the strain hardening response (supplementary material Fig. S8). Future work could be carried out by an in situ tensile test under SXRD, neutron diffraction, or EBSD to quantitatively address the correlation between HCP-martensite fraction and the resultant strain hardening response.

A similar mechanical metastability was also documented in ternary CoCrNi MEAs.^34,35 However, the strain-induced FCC-HCP martensitic transformation tends to take place at cryogenic temperatures.³⁴ The different temperature-dependent transformation potencies between FeMnCo and CoCrNi MEAs imply the distinctions in intrinsic stacking fault energy, which may be worth exploring by ab initio simulation for future work. By combing Figs. 1 and 2, it is recognized that although all four alloys do not exhibit martensitic transformation during rapid thermal quenching (Fig. 1), the mechanical stability of the parent FCC-phase, however, is correlated with the increasing Co content. Following this sort of compositional dependency, future work could be carried out by fine-adjusting Co content in the current 2–15 at. % range or exploring higher Co content in a sense to further optimize the strength-ductility combination.

The HCP-martensite fractions (⁠$f$⁠) in the Co₁₀ and the Co₁₅ MEAs are further assessed by two well-documented kinetic models: first, the classical Johnson–Mehl–Avrami–Kolmogorov (JMAK) model³⁶ in which the growth rate and the progression of transformation are independent and nucleation is homogenous [Eq. (1)]; and second, the Olson–Cohen model,³² although primarily applied in $α′$-martensite formation, parameterizes the inhomogeneous nucleation contributed by plastic straining [Eq. (2)]. In both equations, $ε$ represents the plastic strain value. $α$ in Eq. (2) is related to the HCP-martensite band formation rate, while $β$ describes the potency of HCP-martensite band intersection. The exponent $n$ in Eq. (2) implies the density of HCP-band intersection, and a higher $n$ value suggests a burst-like development of HCP-band intersection,

As seen from the dotted lines in Fig. 2(b), both MEAs exhibit discernable deviations from the JMAK predictions, implicating two possible kinetic mechanisms. First, HCP-martensite nucleation in these two MEAs may not be ideally homogenous because plastic strain distribution can be highly inhomogeneous at the microstructural level.^37,38 Second, a strong interdependency could exist between the transformation rate and the progression of the transformation, which is plausibly due to deformation hardening of the untransformed FCC phase.²⁹ In contrast, better correlations are seen in the Olson-Cohen model, as depicted by the solid lines in Fig. 2(b). A much higher $α$ value of 8.28 achieves in the Co₁₅-MEA than the Co₁₀-MEA (⁠$α=4.25$⁠), validating the higher HCP-martensite formation rate as Co content increases. The $β$ factor, although moderate in both MEAs, is slightly higher in the Co₁₅-MEA (0.62 vs 0.35), which indicates higher HCP-band intersection probability. Finally, a smaller $n$ value presents in the Co₁₅-MEA (2.83 vs 3.03), implying the seemingly less burst-like development in HCP-band intersections. One interesting point should also be mentioned that, in both Co₁₀ and Co₁₅ MEAs, the transformation almost saturates at a local true strain level of ∼0.50, beyond which the increase in the HCP-martensite phase fraction is subtle. While future work is needed to systematically assess such a phenomenon, the origin of it could still be understood from the following two major respects. First, finite excess free energy. The starting microstructure, although single phase, is metastable and possesses excess free energy, yet a finite amount, which is compositionally dependent.³⁹ This intrinsically dictates how much martensite can form during plastic deformation. Unless the excess free energy is infinite, martensite formation driven by plastic deformation will terminate at a certain deformation level, where the alloy system is thermodynamically equilibrium. Second, strong grain neighborhood effect. In polycrystalline alloys, although the nucleation of the strain-induced martensite mostly follows the Schmid's law (i.e., it favors the orientation where the resolved shear stress is the highest), the subsequent growth process can be impeded by unfavorably oriented neighboring grains.^26,40,41 Because of this, strain-induced martensite formation in polycrystalline alloys, in general, can scarcely be complete.

The foregoing quantitative assessments underpin the positive contribution of Co addition in expediting plastic strain-induced FCC-HCP transformation kinetics. Because of this, uniaxial tensile properties of the Co₁₅-MEA stand out among all four MEAs [Fig. 2(c)]. It yields at ∼195.3 Mpa and then undergoes a salient strain hardening process (see supplementary material Fig. S8), reaching an ultimate tensile strength of ∼742.8 MPa with ∼0.60 fracture elongation. Compared with the coarse-grain single-phase FeMnCoCr-type quaternary metastable HEAs,^24,42 the present Co₁₅-MEA exhibits a ∼40 MPa increase in yield strength, ∼174 MPa increase in ultimate tensile strength, and ∼0.9 increase in fracture elongation. Note that these properties were achieved in an un-optimized condition, aiming to study the compositional dependency of mechanical metastability. Improved properties can be further accessed, for example, via grain refinement⁴³ or partial recrystallization.⁴⁴ One interesting aspect of the Co₁₅-MEA is that provided the highly accelerated FCC-HCP transformation kinetics, the resultant ductility is not significantly impaired as some HCP-phase-rich metastable MEAs/HEAs revealed.⁴⁵ This motivates a further investigation of the underlying phase transformation pathways and deformation micro-mechanisms.

Figure 3 details the in situ scanning electron microscopy (SEM)/EBSD investigation of the strain-induced FCC-HCP martensitic transformation and subsequent deformation processes within the HCP-martensite. At the undeformed state, the selected area of interest solely consists of the FCC-phase [Figs. 3(a1) and 3(b1)]. To track the deformation micro-events in the HCP-martensite, magnified backscatter electron (BSE) micrographs of a local region (see the white box) are provided in Figs. 3(c1)–3(c4). Note that the spherical particles seen in the in situ BSE micrographs are colloidal SiO₂ used for strain computation intended for analyses not discussed here. At a global stress of 390.4 MPa, plastic deformation takes place, which is indicated by noticeable surface steps [Figs. 3(b2) and 3(c2)]. EBSD phase map acquired at the same region confirms the formation of HCP-martensite in both grains [Fig. 3(a2)], and only one HCP-martensite variant nucleates per grain. The thinner traces close to the bottom of Fig. 3(b2) are slip traces of perfect dislocations in the parent FCC-phase. As plastic straining proceeds, the nucleated HCP-martensite plates undergo growth and an increasing number of slip traces also start to appear. It is suggested by crystallographic calculation that the HCP-martensite variant belongs to the $(111)FCC$ plane in the lower grain and the $(111¯)FCC$ plane in the upper grain [also see Fig. 3(d2)]. The perfect dislocation slip traces all belong to the $(1¯11)FCC$ plane. The magnified BSE micrograph in Fig. 3(c3) also verifies the absence of other HCP-martensite variants (also see supplementary material Fig. S9). When the global stress increases to 699.4 MPa, an extensive amount of plastic deformation has taken place. This can be qualitatively inferred from the grain's shape distortion [Fig. 3(b4)]. In both grains, given the massive HCP-martensite, no evident cracking occurs in the grain interior, which implies the deformability of the HCP-martensite in the Co₁₅-MEA. An interesting spindle-like feature forms in the upper grain interior [Fig. 3(c4)] exhibiting a convex surface topology. High magnification EBSD analysis verifies that such a feature reveals an FCC structure [Fig. 3(d1)]. However, according to pole figure [Fig. 3(d2)], its crystallographic orientation is different from the parent FCC-phase, and no twin relationship is found between the new FCC and the parent FCC phases. These in situ analyses highlight that the strain-induced HCP-martensite within the Co₁₅-MEA is highly deformable and can even further transform, realizing an FCC-HCP-(new)FCC transformation pathway. Note that this phenomenon should not be confused with pseudoelasticity or shape-memory effect. In the latter case, martensitic transformation is assisted by elastic stress and the reverse transformation, which recovers the parent phase orientation, is indispensable of load removal and/or temperature increase.^46,47 In contrast, the FCC-HCP-(new)FCC martensitic transformation pathway reported here is achieved purely in the plastic region under a quasi-static monotonic loading condition. The (new)FCC and the parent FCC phases also do not exhibit the identical crystallographic orientation. Detailed considerations of the thermodynamics of this FCC-HCP-(new)FCC martensitic transformation pathway is provided in supplementary material Note 5. Semi-quantitative assessments (based on SEM/EBSD analyses) of the new FCC-phase fraction evolution as a function of the deformation level are provided in supplementary material Fig. S10. It is seen that although the FCC-HCP-(new)FCC transformation can be activated in the present Co₁₅-MEA, its area fraction only reaches an order of magnitude of $10−4$⁠. Because of this, an evident inflection point in the strain hardening rate curve (supplementary material Fig. S8) at the similar deformation level of Fig. 3(b4) is absent.

To uncover the atomistic mechanisms for this FCC-HCP-(new)FCC martensitic transformation chain, scanning transmission electron microscopy (STEM) analyses were carried out for HCP-martensite. High-angle annular dark-field (HAADF)-STEM micrographs acquired along the $112¯0HCP$ zone axis [Fig. 4(a1)] reveal the prototypical $…ABABABAB…$ stacking sequence of the HCP-martensite in a majority of the sample area [Fig. 4(a3)]. A closer inspection of the atomistic structures in Fig. 4(a3) highlights the presence of basal stacking fault within the vast HCP region, suggesting the local atomic stacking sequence changes into $…ABABA|C|BAB…$(also see the colored atoms). Geometric phase analysis (GPA)⁴⁸ also cross-confirms the localized shear strain (⁠$εxy$ component) elevation along the basal faulting plane [Fig. 4(b2)]. This is ascribed to the $a/3⟨101¯0⟩$-type of partial dislocation [see Fig. 5(b1) as a reference] emission that enables the faulted $|C|$-layer. Before detailed discussions on the implications of basal stacking fault on the HCP-(new)FCC transformation mechanisms, a few other insights need to be mentioned.

HAADF-STEM micrographs also evidence the presence of dislocations in the HCP-martensite [Figs. 4(a2), 4(a3), and 4(b1)]. Based on definition, the Burgers circuit in Fig. 4(a3) shows that the “near-edge” dislocation core has both $c$ and $a$ components. Although cross-validation may be necessary via $g·b$ analysis to check the residual contrast under the $0002HCP$ reflection, the present observation is informative to better understand the favorable deformability of the HCP-martensite. Like all other HCP-metals, a stable plastic flow in HCP-martensite requires at least five independent slip systems.⁴⁹ In terms of perfect dislocations, basal-$a$ and prismatic-$a$ slip can maximally enable four independent slip systems. As such, additional plasticity mechanisms shall be involved to accommodate plastic strain along the non-basal directions,^49–51 which was proved critical for promising deformability in numerous HCP-metals.^38,52,53 The mixed $c$ and $a$ property of the dislocation observed here suggests deformation micro-events that enable effective plastic strain accommodation along the $0001HCP$ axis, which in turn contributes to the deformability of the HCP-martensite [Figs. 3(b3) and 3(b4)]. However, considering the debate over the actual slip pathways of non-basal dislocations,^52–54 future in situ TEM studies are needed to unambiguously resolve dislocation plasticity events in HCP-martensite.

The last part of this Letter discusses plausible atomistic mechanisms for the FCC-HCP-(new)FCC martensitic transformation. Suppose a perfect FCC crystal with all atoms projected along its $110FCC$ direction [Fig. 5(a1)], an $…ABCABC…$ stacking sequence can be expected as Fig. 5(a2). The first part of the transformation chain, i.e., the FCC-HCP transformation, takes place by glissile Shockley partial dislocation (⁠$a/6⟨1¯12⟩$⁠) emission on every other $1¯11FCC$ plane⁵⁵ [Fig. 5(a3)]. This will eventually change the stacking sequence to $…ABABAB…$ [Fig. 5(a4)] and bring about a triplex Burgers orientation relationship [Fig. 5(a1)]:²⁴ $1¯11FCC//0001HCP$⁠, $110FCC//112¯0HCP$⁠, and $1¯12FCC//11¯01HCP$⁠. Such characteristics are consistent with the in situ EBSD results [Fig. 3(a2)].

To understand the second part of the transformation chain, i.e., the HCP-(new)FCC transformation, we resort to the HAADF-STEM micrograph [Fig. 4(a3)] that confirms basal stacking fault within the HCP-martensite. This suggests that one glissile HCP partial dislocation (⁠$a/3⟨101¯0⟩$⁠) has emitted, accommodating shear strain [Fig. 4(b2)], while resulting in a faulted $|C|$-layer. The HCP stacking sequence locally changes into $…ABA|C|BAB…$⁠, as sketched in Fig. 5(a5) and observed in Fig. 4(a3). Such a structure is equivalent to one FCC-layer (⁠$…BAC…$⁠) embedded in HCP. Once this FCC-embryo grows, the HCP-(new)FCC transformation takes place. Based on the experiment, two extreme atomistic mechanisms can be plausibly conceived: purely mono-partial emission (MPE) and purely random-partial emission (RPE). Suppose that the emitted partial in HCP-martensite is $a1$ [Fig. 5(b1)], the MPE pathway means that on every other $0001HCP$ plane above the faulting plane, the same type of $a1$ partial emits [Fig. 5(b2)] and leads to FCC formation. This is one extreme situation because the macroscopic shear strain is maximum, i.e., same as the FCC-HCP transformation. The RPE scenario describes the other extreme. As sketched in Fig. 5(b3), instead of both emitting $a1$ partials, the second and the fourth $0001HCP$ planes above the faulting plane, respectively, emit $a2$ and $a3$ partials. This will also lead to FCC-phase formation [Fig. 5(b3)]. However, the macroscopic shear strain is minimum, i.e., ideally zero, because the net shear in RPE $a1+a2+a3=0$⁠.

Besides the difference in shear strain accommodation, the second distinction between MPE and RPE lies in crystallography. Comparing Figs. 5(b2) and 5(a2), any new-FCC phase formed purely through the MPE pathway will exhibit a twin relationship with the parent FCC-phase [Fig. 5(b2)]. In the RPE pathway, however, a well-defined orientation relationship (i.e., a habit plane) between parent- and new-FCC phases is absent. Coming back to the in situ EBSD results [Fig. 3(d2)], no twin relationship is seen between the two FCC phases in the present observation, which rationally excludes the MPE mechanism. However, whether or not the present transformation is accomplished purely through the RPE pathway may still need future exploration. This is because, depending on local chemical environment (short-ranged ordering, for example) or stress state, HCP partial emission may become be a somewhat mixture of both MPE and RPE processes. Furthermore, future STEM characterization may also be needed to clarify the habit plane property resulting from the RPE mechanisms.

In summary, we reveal the feasibility of tuning mechanical metastability in (Fe₆₀Mn₄₀)_100-xCo_x medium entropy alloys. This was accomplished by keeping the Fe-to-Mn ratio as 3:2 while increasing the Co content up to 10 and 15 at. %. SXRD results confirm the positive correlation between Co content and the FCC-HCP transformation kinetics in response to plastic straining. An FCC-HCP-(new)FCC transformation chain was identified in the Co₁₅-MEA by in situ SEM/EBSD experimentation. Atomic resolution characterization of the deformed Co₁₅-MEA confirms the presence of basal-stacking faults within its HCP-martensite. Based on these results, two plausible atomistic processes are postulated for the HCP-(new)FCC transformation, i.e., MPE and RPE. Comparison between HAADF-STEM and in situ EBSD results suggests that MPE is less likely to account for the present transformation. Either pure RPE or a mixed MPE-RPE pathway can more rationally explain the current observation. Future in situ STEM is expected to precisely resolve the participating HCP partials and, thereby, the extent of MPE vs RPE. A “near-edge” dislocation with both $c$ and $a$ components is also seen in the HCP-martensite, which could help to understand the favorable plastic deformability.

See the supplementary material for the processing details and the complementary dataset for the (Fe₆₀Mn₄₀)_100-xCo_x MEAs.

The authors express their gratitude to the reviewers for their tremendous effort in providing constructive feedback. Synchrotron x-ray diffraction experiments were performed on Beamline 11ID-C, Argonne National Laboratory, Chicago, USA. S.L.W. and C.C.T. thank Dr. Y. Ren and his team for their assistance in remote synchrotron x-ray measurement during the COVID19 shutdown. M.X. and J.M.L. acknowledge support for STEM characterization from the National Science Foundation (No. CMMI-1922206). This work utilized the MIT Characterization.nano Facility. The authors express their sincere gratitude to Raith Application Scientist Dr. Y. Yu for the support on the Raith VELION FIB-SEM system (Award No. DMR-2117609).