Rapid Screening of High Entropy Alloys

We present here some results on our systematic exploration of non‑equiatomic, yet massively alloyed Fe–Mn–Ni–Co–Cr high‑entropy alloys, showing that single‑phase, fcc solid solutions and attractive mechanical properties are accessible over a broad compositional window without maximizing configurational entropy.

Motivation and alloy design concept

We start from the canonical equiatomic CoCrFeMnNi high‑entropy alloy, whose design rationale traditionally relies on maximizing the configurational entropy through equiatomic mixing of multiple principal elements to stabilize single‑phase solid solutions. In earlier work, we had already shown that several strongly non‑equiatomic Fe–Mn–Ni–Co–Cr alloys can form random single‑phase fcc solid solutions with excellent tensile behavior, indicating that equiatomicity is not a necessary condition. Building on this, we deliberately design a compositional series Fe(64−x)MnxNi27.8Co5.7Cr2.3 (at%) with x = 21, 24, 27, 34, 38 (21Mn–38Mn variants), using CALPHAD to select a base composition that retains a high‑temperature fcc phase upon quenching and then systematically varying Mn content while keeping Ni, Co, Cr nearly constant. For each composition, we quantify atomic size mismatch δ, enthalpy of mixing ΔHmix, configurational entropy ΔSconf, valence electron concentration (VEC), itinerant electron concentration (e/a), a (e/a), and Ω = TmΔSmix/|ΔHmix| to benchmark against existing HEA phase‑stability criteria.

We find that ΔSconf of the non‑equiatomic family is reduced by about 17–20% compared to the equiatomic Fe20Mn20Ni20Co20Cr20 case, while δ increases monotonically with Mn content and crosses the classical δ ≈ 4.8 threshold around 34 at% Mn. According to the Zhang/Yang δ–ΔHmix–Ω criteria, only the lower‑Mn variants (21Mn–27Mn) should reliably form single solid solutions, whereas higher‑Mn variants (≥30 at% Mn) should be prone to ordered precipitate formation; our experiments, however, show random single‑phase solid solutions across the entire series. VEC‑based criteria correctly predict fcc stability for both equiatomic and non‑equiatomic alloys, while e/a‑based rules would wrongly suggest bcc formation for the non‑equiatomic compositions, highlighting internal inconsistencies in existing electronic criteria when applied to this system.

Rapid alloy prototyping and processing route

We use a bulk combinatorial rapid alloy prototyping (RAP) methodology to efficiently generate the composition series from a single master heat, enabling metallurgical production of widely varying compositions by controlled sectioning and subsequent thermomechanical treatment. High‑purity elemental feedstock (purity > 99.8%) is induction‑melted under 400 mbar Ar, cast into blocks, hot‑rolled at 900 °C to 50% thickness reduction (10 mm → 5 mm), and homogenized at 1200 °C for 2 h followed by water quenching to eliminate solidification structures and macrosegregation. To tune grain size and mechanical response, we then apply cold rolling up to 64% reduction and short‑time annealing at 900 °C (5–120 min) to achieve fully recrystallized equiaxed grains between roughly 10 and 60 μm, depending on the variant and schedule.

Phase constitution and microstructural stability

X‑ray diffraction on as‑cast samples across the Mn series reveals exclusively fcc Bragg peaks with varying intensities indicative of texture but no detectable second phases; the lattice parameter increases slightly from about 3.60 Å (21Mn) to 3.62 Å (38Mn) with increasing Mn content, consistent with the atomic size effect. Differential scanning calorimetry between 20 and 1300 °C at 5–10 K/min shows no exo‑ or endothermic phase transformation events prior to melting (~1250 °C), for any x‑Mn composition, demonstrating that the as‑solidified single‑phase fcc state is thermally stable over the entire range up to the liquidus. This stability is confirmed at slower heating rates (5 K/min) for the 27Mn alloy, ruling out hidden transformations and emphasizing the robustness of the single‑phase solution.

After homogenization and recrystallization, EBSD phase maps again show exclusively fcc indexing for all alloys, with minor unindexed spots attributable to casting porosity or MnO inclusions along grain boundaries. Inverse pole figure maps reveal fully recrystallized equiaxed grains with typical mean sizes of 36.5, 42.7, 32.3, 33.0, and 26.4 μm for 21Mn, 24Mn, 27Mn, 34Mn, and 38Mn, respectively, along with annealing twins characteristic of low‑SFE fcc alloys. Large‑area EDX maps confirm micron‑scale compositional homogeneity of Fe, Mn, Ni, Co, and Cr, with only limited Ni enrichment and MnO‑related local Mn enrichment at higher Mn contents, typical for high‑Mn fcc alloys.

At the atomic scale, we use site‑specific atom probe tomography (APT) on grain interiors and specific grain/twin boundaries, targeted by EBSD and FIB lift‑out, to assess any elemental partitioning or decomposition. In the representative 27Mn alloy, three‑dimensional elemental maps and binomial frequency distribution analyses show random distributions of Fe, Mn, Ni, Co, and Cr, with normalized parameter m near zero, indicating absence of clustering or short‑range ordering. We detect a weak segregation of trace carbon (~0.039 at%), forming enriched layers at grain boundaries, which confirms boundary position but does not perturb the multicomponent fcc solution. One‑dimensional concentration profiles across these boundaries show no measurable partitioning of the principal elements, corroborating that both grain interiors and boundaries remain compositionally homogeneous single‑phase solid solutions after casting, homogenization, and subsequent processing.

Mechanical properties and Hall–Petch strengthening

Room‑temperature tensile tests on the five homogenized alloys reveal a remarkably similar mechanical response across compositions: all exhibit high ductility with uniform elongation around 38% and total elongation around 58%, comparable to equiatomic CoCrFeMnNi at similar grain sizes. Yield strength and ultimate tensile strength are lower than in the equiatomic alloy by roughly 50% and 25–30%, respectively, which we attribute primarily to reduced solid‑solution strengthening due to lower Co and Cr contents. Within the non‑equiatomic series, increasing Mn content by ~17 at% leads to only modest increases of about 15% in yield strength and 10% in ultimate strength, consistent with the gradual increase in atomic size mismatch δ and associated lattice distortion friction stress.

The strain‑hardening behavior is nearly identical across all compositions: the strain‑hardening rate drops steeply at true strains below ~4% and then decays more gradually at higher strains, supporting a shared deformation mechanism. Vickers microhardness measurements follow the same trend as tensile strengths, with only slight sensitivity to Mn content, reinforcing the notion that Mn variations within this range do not fundamentally alter the strengthening mechanism. We exploit the high ductility and strain‑hardening capacity by cold rolling the 27Mn alloy to 64% thickness reduction and subsequent annealing at 900 °C for 10 min, achieving a recrystallized grain size around 12 μm and demonstrating strong Hall–Petch strengthening: compared to the ~32.3 μm homogenized condition, yield strength increases by ~150% to ~240 MPa and ultimate strength by ~72% to ~645 MPa, while ductility is largely restored relative to the cold‑rolled state.

In the cold‑rolled 27Mn state, we observe heavily deformed grains and high stored dislocation densities, which raise the ultimate strength to ~760 MPa but reduce total elongation to ~16%, reflecting limited strain‑hardening capacity in the pre‑hardened microstructure. The subsequent recrystallization produces a fine equiaxed grain structure that simultaneously enhances strength via grain‑boundary strengthening and recovers ductility through removal of the heavily entangled dislocation network, highlighting the effectiveness of conventional thermomechanical processing in property optimization for non‑equiatomic HEAs.

Deformation mechanisms: planar slip and HDDWs

We monitor deformation microstructures using pre‑polished surfaces analyzed by optical microscopy and electron channeling contrast imaging (ECCI) at different strain levels (≈15% and ≈50%) in representative 21Mn, 27Mn, and 38Mn alloys. At low strains, we consistently observe fine surface steps and slip traces arranged in parallel within individual grains, with orientation changing from grain to grain according to crystallographic orientation, but no evidence of mechanical twinning. At ~15% strain, multiple sets of slip lines appear in most grains, and at ~50% strain we detect severe plastic flow and grain distortion, although slip bands remain discernible in some regions, indicating persistent slip‑controlled deformation.

ECCI analysis in 21Mn and 38Mn at small increments of strain reveals the corresponding dislocation substructures: at ~1% strain we see dislocation pile‑ups at grain boundaries and early development of localized slip bands, already pointing to strong grain‑boundary barriers and planar slip. By ~5% strain, typical planar slip substructures emerge in both alloys, characterized by highly dense dislocation walls (HDDWs) aligned with specific slip planes, along with emerging dislocation cell structures in some grains that indicate limited wavy slip. At ~10% strain, the interaction and entanglement of HDDWs intensify, while dislocation cells become more pronounced in other grains, suggesting that at higher strains additional slip systems activate and cross‑slip becomes more frequent.

Given the random atomic distributions evidenced by APT and the absence of short‑range ordering signatures, we attribute the pronounced slip localization to lattice distortion‑induced friction stress rather than local chemical ordering effects. The coexistence of planar dislocation bands and dislocation cells at higher strains mirrors observations in highly alloyed low‑density Fe–Mn–C steels and equiatomic CoCrFeMnNi, underlining that non‑equiatomic Fe–Mn–Ni–Co–Cr HEAs share similar deformation mechanisms with their equiatomic counterparts. Strain hardening in these non‑equiatomic alloys is thus dominated at early stages by dislocation pile‑ups at grain boundaries and planar slip band formation, and at higher strains by the evolution of HDDWs and cell structures that increase dislocation storage.

Thermodynamic/kinetic analysis and role of sluggish diffusion

To reconcile the experimental single‑phase fcc stability with thermodynamic predictions suggesting possible bcc co‑precipitation at intermediate temperatures (e.g., ~495 °C in CALPHAD for a related Fe32Mn30Ni30Co6Cr2 composition), we perform diffusion‑controlled kinetic simulations using DICTRA with the MOBFE2 mobility database. We model a spherical fcc matrix (1 mm diameter) capable of nucleating a bcc precipitate when energetically favored, starting from a 0.5 nm bcc nucleus at 495 °C and tracking growth over time. The simulations indicate extremely sluggish growth: after ~10^7 s (~115 days) at 495 °C, the bcc particle reaches only ~1.2 nm, and even after 3.2 years it grows to merely ~3.2 nm, with a negligible volume fraction on the order of 10^−7.

These results demonstrate that, although thermodynamics may allow bcc precipitation at intermediate temperatures, the combination of low atomic mobilities and sluggish diffusion effectively freezes the microstructure in its primary fcc state. We interpret the experimentally observed homogeneous single‑phase fcc structure as a consequence of this kinetic stabilization, which prevents significant growth and coarsening of any incipient bcc nuclei that might form during solidification or intermediate‑temperature exposure. This kinetic perspective is consistent with reports of Mn‑ and Cr‑rich precipitation under very long exposure or specific deformation conditions in equiatomic FeCoNiCrMn, but shows that under our processing conditions the non‑equiatomic Fe–Mn–Ni–Co–Cr alloys remain effectively single‑phase.

Implications for HEA design

Our results show that restricting high‑entropy alloy design to equiatomic compositions is unnecessarily limiting and not supported by the observed phase behavior in multicomponent Fe–Mn–Ni–Co–Cr alloys. We demonstrate that a broad class of non‑equiatomic, yet massively alloyed compositions can form stable, random fcc solid solutions with excellent ductility and tunable strength, even though their configurational entropy is not maximized. The conventional reliance on ΔSconf as the primary design driver for HEAs thus needs to be replaced by a more comprehensive criterion that focuses on minimizing Gibbs free energy while explicitly accounting for kinetic constraints and sluggish diffusion in multicomponent systems.

By relaxing the equiatomic constraint, we greatly expand the accessible compositional space, as schematically illustrated in ternary phase‑diagram cross‑sections comparing traditional base‑element alloys, equiatomic HEAs, and non‑equiatomic HEAs. This widened design space allows us to tailor stacking‑fault energy, transformation tendencies, and deformation mechanisms — and thus strain‑hardening behavior — through controlled variations in composition while retaining single‑phase solid‑solution microstructures. In practical terms, our non‑equiatomic Fe–Mn–Ni–Co–Cr alloys provide a versatile platform for property‑oriented design of HEAs for demanding structural applications, where grain‑size refinement, thermomechanical processing, and composition tuning can be combined to achieve high ductility, robust strain hardening, and significantly improved strength without sacrificing phase stability.