Atomic-scale strain waves for stronger and more ductile lightweight steels

Domain: chemistry
Published: 2026-03-17
Editorial outcome: minor_revision

Abstract
Reducing weight to save energy and enhancing mechanical properties to increase safety level are both vital for structural materials in modern engineering. The lightweight steels have been promising for addressing these needs. However, the significant loss of ductility and strength in lightweight steels by localized accumulation of dislocations when strengthened by nanoprecipitates is a crucial problem. Here, we show an approach to overcome this dilemma by significant atomic-scale strain waves with extremely small wavelengths (<1 nm) and high amplitudes (up to 3%) in Fe-Mn-Al-C lightweight steels. Such atomic-scale strain waves render the dislocation lines wavy and paired, which tangle into dense hexagonal dislocation networks via cross-slip at medium and late deformation stages, significantly enhancing defect-storage capacity and strain hardening ability. The atomic-scale strain waves also promote the dynamic refinement of slip bands upon deformation. These mechanisms are active in both steel variants with and without nanoscale coherent κ-carbides, enabling unprecedentedly strong and ductile lightweight steels. The strategy of tuning atomic-scale strain waves thus provides an important avenue for designing stronger and more ductile lightweight materials for key structural engineering.

Introduction
The reduction of weight while maintaining or even enhancing strength and ductility of metallic materials is a burning task for saving energy, reducing carbon dioxide emissions and ensuring sustainable reliability for safety-critical parts in various industries1,2. The strength and ductility also act as decisive indexes for the measurement of many other mechanical properties including fatigue resistance3,4 and fracture toughness5. The lightweight Fe-Mn-Al-C steels with face-centered cubic (FCC) austenitic matrix are one of the most promising candidates for addressing the demand of low mass density at excellent strength-ductility synergy1,6-9. The mechanical properties of lightweight steels can be substantially contributed by the precipitation strengthening from different types of nanoprecipitates, e.g., coherent L1 -(Fe, Mn) AlC κ-carbide with ordered FCC structure, and incoherent NiAl B2 phase with ordered body-centered cubic (BCC) structure8-10. However, the shearing of the κ-carbide during plastic deformation at higher stress leads to the local softening, which can cause localized dislocation accumulation and significantly deteriorate the ductility of austenitic lightweight steels6,11,12. Moreover, the κ-carbides at grain boundaries are incoherent with austenitic matrix, which promotes crack initiation and propagation, leading to embrittlement13,14. The B2 (ordered BCC) particles are usually hard to be sheared and hence dislocations need to bypass them9, which leaves additional dislocation loops around the particles behind, leading to remarkable strengthening effect. However, this is usually accompanied with a significant expense of ductility due to dislocation pile-up and stress localization at the intrinsically brittle B2 intermetallic phase13,15.

Recently, a dual-nanoprecipitation approach has been proposed to further enhance the mechanical properties of lightweight steels by simultaneously triggering both nanosized shearable κ-carbides and non-shearable B2 particles1. However, the Orowan looping mechanism in this dual-nanoprecipitation system still increases the stress concentrations and leads to a substantial reduction in ductility13. Another shearable α-phase (disordered BCC) from γ decomposition (γ→ γ+α) has also been introduced into lightweight steels to enhance the mechanical properties16,17.

Such duplex lightweight steels can exhibit multi-stage strain hardening characteristics with sequential activation of deformation mechanisms in the α-phase and γ-matrix18. However, the different deformability of the α- and γ-phases leads to decohesion with stress concentrations at their interphases, which are susceptible to crack nucleation and can cause a substantial reduction in damage tolerance19.

Linear lattice defects carry the plasticity in the lightweight steels. However, their accumulations cause stress concentrations, acting as the fundamental mechanism in restricting the enhancement of mechanical properties. To overcome this dilemma, in this work we propose a strategy to tune the atomic-scale strain waves to alleviate the micro- and nano-scale stress concentrations in lightweight steels, which is validated by the significantly enhanced strength-ductility synergy. This concept is demonstrated in a prototype lightweight steel with nominal composition Fe Mn Al C (at.%) designed through thermodynamic calculations using FactSage software with the FSstel steel database (Supplementary Figure 1). Guided by the calculated phase diagrams, thermomechanical processing steps (e.g., hot-rolling, homogenization, cold-rolling, annealing and aging) with proper parameters were performed to tailor the subnanoscale κ'-carbides (present as local chemical orders) which enable the tuning of atomic-scale wave-like strain distribution. Accordingly, the otherwise damage-prone stress concentrations can be relieved by the well-tuned atomic-scale strain waves. This approach can also boost planar slip, further promoting the strain hardening ability in the loading stages. The present study thus suggests a promising path toward the development of strong and ductile lightweight steels for advanced structural engineering applications.

Results
The present lightweight steel in homogenized condition is characterized by a single-phase face-centered cubic (FCC-γ) austenitic structure, showing homogeneous elemental distribution at the micro-scale without any grain boundary (GB) precipitates (Supplementary Figure 2). The stacking fault energy (SFE) of the steel is relatively high, i.e., ~82 mJ/m2 according to the weak-beam dark-field (DF) STEM characterization (Supplementary Figure 3) and ~78 mJ/m2 calculated by the subregular solution model6,20 (see Supplementary Information). The atomic-scale strain wave in the material was tuned via adjusting the time periods of annealing after cold-rolling. The samples annealed at 900 oC for short time (3 min) and that for longer time (30 min) are denoted as SA and LA, respectively. The X-ray diffraction (XRD) patterns (Supplementary Figure 4) and electron backscatter diffraction (EBSD) phase maps (Fig. 1a, b) reveal the FCC structure in both LA and SA bulk steels. As shown in Fig. 1a-b, abundant annealing twin boundaries (TBs) are present in both steels. The average grain sizes excluding annealing TBs in steels LA and SA are 15.0 ± 9.7 μm and 7.5 ± 5.4 μm, respectively, according to EBSD analysis from multiple areas in each sample. The bright-field (BF) scanning transmission electron microscopy (STEM) images (Supplementary Figure 5a, c) and corresponding energy-dispersive X-ray spectroscopy (EDS) mappings (Supplementary Figure 5b, d) suggest that the steels LA and SA show homogeneous elemental distribution at the micro- and nano-scales. In the selected area electron diffraction (SAED) patterns (inserts in Fig. 1c, d) taken along the zone axis of [001] , the inherently faint γ diffraction spots from specific {100} superlattice diffraction signal of κ'-carbide are visible in both steels LA and SA. More specifically, dark-field (DF) imaging was used to visualize the κ'-carbide domains and the results are shown in Fig. 1c, d, which indicates that the average sizes of κ'-carbide are 0.4 nm and 0.5 nm with average area fractions of 8.5% and 16.5% in steels LA and SA, respectively. The abnormal decreases of fraction and size of the sub-nanoscale κ'-carbides with increasing annealing time from 3 min to 30 min is related to the formation kinetics of κ'-carbide. Specifically, the high atomic mobility promoted by crystalline defects induced in the prior deformation strongly facilitates the formation kinetics of sub-nanoscale κ'-carbides during annealing at the first few minutes, leading to the deviation of associated crystal lattice from thermodynamic equilibrium. However, upon further increasing annealing time, the prolonged exposure of the fully recrystallized microstructure at 900 oC can lead to the partial dissolution of the previously formed sub-nanoscale κ'-carbide, rendering the crystal lattice closer to the thermodynamic equilibrium state.

Atomic-resolution high-angle angular dark field (HAADF) STEM technique was performed in the exploration of the κ'-carbide domains in steels LA and SA. The atomic-resolution HAADF-STEM images overlapped with the inverse fast Fourier transform (IFFT) maps in Fig. 1e, f outline the distribution of κ'-carbide domains in the FCC lattices of the two steels, whereas the contrasts of the different atomic columns indicates that the elements are nonuniformly distributed at the atomic-scale. The atomic-resolution HAADF-STEM image of steel LA acquired along [011] γ zone axis in Supplementary Figure 6a and the EDS analysis result in Supplementary Figure 6b, c suggest that Al tends to be enriched in specific atomic columns. The atomic-scale distributions of Fe and Mn are also inhomogeneous, but are more uniform compared to that of Al. Specifically, Fe-rich columns are Mn-depleted, and the two types of atomic columns are adjacent to each other. This may arise from the zero mixing enthalpy between Fe and Mn, and thus they neither attract nor repel each other21,22. The negative mixing enthalpies of Fe-Al (-11 KJ/mol) and Mn-Al (-19 KJ/mol)23 provide the thermodynamic driving force for the formation of κ'-carbide. In the κ'-carbide domains, the average atomic fractions of Fe, Mn and Al for atomic columns on the (11̅1) plane show wave-like fluctuations with wavelength doubling the spacing of the crystal plane (Supplementary Figure 6d).

Atom probe tomography (APT) was also performed to analyze chemical features of the κ'-carbides. The 3D reconstruction maps of typical cubes in Supplementary Figure 7e, f show the clustering behavior in steels LA and SA, respectively. The calculated radial distribution functions (RDFs) of Fe and Mn around Al atoms (Supplementary Figure 7g) show bulk-normalized Al-(Fe/Mn) concentration ratios exceeding unity at the subnanoscale. Notably, these ratios are higher in steel SA than that in steel LA, indicating that more Al-(Fe/Mn) bonds contribute to the formation of κ'-carbide domains in steel SA. This is consistent with the statistical results for the fractions of κ'-carbides from the DF-TEM images in Fig. 1c, d. The average Al concentration within the κ'-carbides is ~18.1 at. % and ~22.3 at. % for steels LA and SA, respectively. Since the atomic radius of Al (0.143 nm) is remarkably larger than Fe/Mn (0.124 nm), significant lattice expansion and contraction can occur at the Al-rich κ'-carbide domains and Al-depleted FCC-γ matrix, respectively, which can further induce atomic-scale strain fluctuations in the steels.

The atomic-scale strain fluctuation was further explored by the geometric phase analysis (GPA) method25,26 based on HAADF-STEM images, e.g., shown in Fig. 1g, h. The ε strain maps xx show the atomic-scale tension-compression strain distributions in steels LA and SA with statistical average strain values (total pixels) of 0.26% nm-2 and 1.06% nm-2, respectively (Fig. 1g, h). This indicates that steel LA undergoes greater lattice expansion than steel SA. Further, the results suggest that the atomic-scale strain waves are primarily derived from the lattice expansion and contraction at the sub-nano-sized Al-rich κ'-carbide domains and Al-depleted FCC-γ matrix, respectively, resulting in a fluctuating tension-compression strain distribution at atomic scale. Fig. 1i shows the line profiles of atomic-scale strains along the [200] γ direction, revealing the wave-like distribution with crests and valleys. The average wavelength of atomic-scale strains along the [200] γ direction in steel SA (0.84 ± 0.27 nm) is smaller than that in steel LA (0.98 ± 0.38 nm), while the average amplitude in steel SA (1.71 ± 0.70%) is higher than that in steel LA (0.82 ± 0.32%). The ε strain maps in Supplementary Figure 8 also shows the higher strain amplitude and smaller wavelength of the atomic-scale strains in steel SA than those in steel LA. This can be attributed to the higher Al concentration and larger fraction of κ'-carbides in steel SA, as discussed above.

Further, the original steels LA and SA were aged at 600 oC for 40 min to trigger the formation of nanosized L1 -(Fe, Mn) AlC (x<1) κ-carbide, and the resultant materials are denoted by LA-A and SA-A, respectively. XRD patterns (Supplementary Figure 4) and EBSD phase maps (Supplementary Figure 9a, e) confirm the FCC structure in both LA-A and SA-A bulk steels. The average grain sizes excluding annealing TBs in steels LA-A and SA-A are equal to steels LA and SA, respectively, according to EBSD analysis from multiple areas in each sample. This confirms that the aging treatment did not change the grain sizes in the steels. The EDS mappings (Supplementary Figure 9d, h) for the areas captured by BF-STEM images (Supplementary Figure 9c, g) suggest homogeneous elemental distribution at the micro-scale in both steels. However, in the SAED patterns in Fig. 2a, b taken along the zone axis of [001] γ, the {100} superlattice diffraction spots of κ'- and κ-carbides with ordered structures are distinctly visible in both steels LA and SA. This is consistent to the previous finding that the κ'-carbide can serve as a precursor for the formation of κ-carbide by further ordering of C into the body-centered octahedral interstitial positions via spinodal decomposition 6,7. The DF images stemming from the diffraction spot of (110) κ'/κ in Fig. 2c, d light up the κ- and κ'-carbide domains. The average sizes of κ-carbide in steels LA-A and SA-A are 6.1 ± 1.7 nm and 6.0 ± 1.2 nm, respectively. The HAADF-STEM images in Fig. 2e and f reveal the atomic-scale structures of κ-carbides in steels LA-A and SA-A, respectively. The ε xx strain maps in Fig. 2g, h by GPA method using the vectors of (200) γ and (020) γ also show the wave-like tension-compression strain fluctuations in atomic scale. The statistical strain values (total pixels) are 16.87% nm-2 and 6.5% nm-2 in steels LA-A and SA-A, respectively. Fig. 2i shows the line profiles of atomic-scale strains along the [020] γ direction. The matrixes containing sub-nano-sized κ'-carbide domains show atomic-scale strain waves with the average amplitude of 1.84 ± 0.89% and 1.01 ± 0.48% in steels SA-A and LA-A, respectively, similar to those in the as-annealed steels without aging (SA and LA). Moreover, the interiors of aging-induced nano-sized κ-carbide phase regions in steels SA-A and LA-A also exhibit wave-like periodic fluctuations with the average amplitude of 1.59 ± 0.42% and 1.16 ± 0.58%, respectively. For the steel LA-A, the atomic-scale strain waves in the κ-carbide phase are almost tension with average value of wave peaks and troughs to be about 1.58%, which is higher than that in the matrix (~0.06%), suggesting that the atomic-scale strain distributions in the κ-carbide and matrix are distinctly different. However, in the steel SA-A, the atomic-scale strain distributions in the κ-carbide and matrix are fairly similar as indicated by the small differences in average amplitudes (1.59% and 1.84%, respectively) and average strain values (0.09% and -0.24%, respectively).

Fig. 3a shows the tensile engineering stress-strain curves of the steels at room temperature. The steel SA characterized by atomic-scale strain waves with high amplitude and small wavelength exhibits a yield strength value (𝜎 y) of 687 ± 13 MPa, an ultimate tensile strength (𝜎 u) of 1154 ± 4 MPa and a total elongation (𝜀 f) of 67.8% ± 4.0%, which are significantly higher than those values of steel LA (610 ± 10 MPa, 1035 ± 9 MPa and 37.8% ± 2.3%, respectively) with atomic-scale strain waves of lower amplitude and larger wavelength. The enhancements in strength and ductility achieved by tuning atomic-scale strain waves can also be observed when comparing the steels SA-A and LA-A with κ-carbide precipitation strengthening effect. More specific, the steel SA-A has a yield strength (𝜎 y) of 1073 ± 10 MPa and an ultimate tensile strength (𝜎 u) of 1325 ± 8 MPa at a total elongation (𝜀 f) of 50.4% ± 3.2%, which are superior than those of steel LA-A (1051 ± 8 MPa, 1242 ± 13 MPa and 20.1% ± 1.3%, respectively). The steels SA and SA-A exhibit not only enhanced strength and ductility but also superior work-hardening abilities compared to steels LA and LA-A, respectively (Fig. 3b). This is correlated with the modulated dislocation behaviors via tuning atomic-scale strain waves, as specifically discussed next. The above results suggest that the current strategy of tuning atomic-scale strain waves can allow for overcoming the strength-ductility trade-off that are presented in previous steels. Moreover, this strategy can be combined with the coherent nanoprecipitation approach to jointly enhance the strength-ductility combination, as can be confirmed by comparing the tensile curves of the present aged steels containing nano-sized κ-carbides (SA-A, LA-A) and that of the as-annealed variants free of nano-sized κ-carbides (SA, LA).

To avoid sample size effect, the uniform elongation values were used in the comparison of strength-ductility combinations shown in Fig. 3c (see details in Supplementary Table 3). Evidently, the strength-ductility combinations of the present lightweight steels SA and SA-A surpass that of previous lightweight steels, including those with κ-carbide precipitation strengthening 11,12,17,27,28, κ-carbide plus B2 particles strengthening 1,9,13,15,29, and duplex structure composed of FCC-γ and BCC-α phases with κ-carbide precipitation strengthening 18,19,30,31. Further, the products of specific ultimate tensile strength (SUTS) and uniform elongation (UE) of the steels SA and SA-A reach 8.5 and 7.4 GPa·g-1·cm3·%, respectively, which are unprecedentedly high compared to those obtained in previous studies, as shown in Fig. 3d. We also converted the total elongation values from references and our work into those corresponding to identical standard specimen dimensions by the Barba’s law, and accordingly the converted total elongation (CTE) is used in the additional comparison (see the calculation details in Supplementary Information) 32-34. As presented in Supplementary Figure 11, the products of SUTS and CTE of the present lightweight steels SA and SA-A surpass that of the previous lightweight steels.

The atomic-scale strain waves can also modulate the lattice constants of the present lightweight steels (Supplementary Table 2) and thus affect the elastic moduli. As displayed in Supplementary Table 4, the elastic moduli of steels SA and SA-A are higher than those of steels LA and LA-A, respectively. Further, shear modulus associated with the elastic modulus is of significance for determining the Peierls-Nabarro (P-N) stress that required to make a dislocation glide in a crystal without the assistance of thermal activation. Accordingly, the yield strength values for steels SA and LA ascribed from the significant lattice friction are estimated to be ~590 MPa and ~581 MPa, respectively (see the calculation details in Supplementary Information). Grain boundary strengthening also act as an effective mechanism that contribute to the yield strength of the steels, and the corresponding values for steels SA (average grain size of ~7.5 μm) and LA (average grain size of ~15.0 μm) are ~208 MPa and ~147 MPa, respectively (see Supplementary Information). In addition, the κ-carbide can provide significant precipitation strengthening as can be demonstrated by the observation that the yield strength values of steels LA-A and SA-A are higher than steels LA and SA, respectively. Further calculations suggest that the precipitation strengthening contributions from the κ-carbide for steels LA-A and SA-A are ~468 MPa and ~460 MPa, respectively (see Supplementary Information).

To elucidate the underlying deformation mechanisms responsible for the enhanced mechanical properties of the present steels, the deformed microstructures in the tensile-tested samples were characterized and compared at the identical deformation stages with various local strain levels at micro-, nano- and atomic scales. At the medium uniform deformation stages of steels LA and LA-A (i.e., local strains of ~20% and ~10%, respectively), the microstructures are characterized by a series of discrete planar slip bands along {111} γ planes with statistical average spacing of 411.6 ± 168.6 nm and 94.2 ± 86.3 nm, respectively, as shown in Fig. 4a and b. The intense dislocations that progressively tangled into high-density dislocation walls (HDDWs) along intersecting {111} γ slip planes are also observed. With increasing local strain to ~45% for steel LA at the late uniform deformation stage, the deformation microstructures are characterized by the progressive refinement of slip bands with a statistical average spacing reduction to 54.8 ± 35.8 nm (Fig. 4c). For steel LA-A, when local strain increases to ~15% (late uniform deformation stage), it maintains comparable slip band spacing of 93.4 ± 79.2 nm relative to prior strain levels (Fig. 4d). During the necking stages, upon further increasing local strain to ~70% and ~30% for steels LA and LA-A, the average spacings of slip bands are 54.4 ± 20.1 nm and 91.6 ± 58.3 nm, respectively (Supplementary Figure 12 and 13), suggesting that further slip band refinement in both steels is insignificant. Also, the distribution of slip bands is relatively heterogeneous, particularly in steel LA-A (Supplementary Figures 12 and 13).

The deformation microstructures of steels SA and SA-A are shown in Fig. 4e-h. At local strains of ~15% and ~10% (early uniform deformation stages) for steels SA and SA-A, respectively, the paired dislocations are regularly arranged within the matrix (Fig. 4e, f). The planar slip bands are also observed along {111} γ planes in the steel SA as displayed in Fig. 4e, with a statistical average spacing of 121.7 ± 49.7 nm. The increase of local strains to ~50% and ~30% at late uniform deformation stages for steels SA and SA-A, respectively, leads to the significant multiplication of planar slip bands and the increase in the number density of dislocations within individual bands, as displayed in Fig. 4g, h. At these strain levels, the statistical average spacings of slip bands in steels SA and SA-A are 39.3 ± 14.0 nm and 76.8 ± 47.5 nm, respectively. The nanoscale well-organized hexagonal dislocation networks on {111} γ planes are observed in both steels SA and SA-A. Further increasing local strains to ~75% and ~50% for steels SA and SA-A during necking stages leads to the reducing of slip band spacings to 34.3 ± 14.1 nm and 48.8 ± 30.7 nm, respectively (Supplementary Figures 12 and 13).

According to the above results, the morphologies of dislocations in plastically deformed steels SA and SA-A at early and medium uniform deformation stages are distinctly different. This is clearly illustrated by the amplified LAADF-STEM images in Supplementary Figure 14 which shows paired dislocations in steel SA and long dislocation lines in steel LA. This suggests that the atomic-scale strain waves in the steels significantly affect the slip of dislocations and thus their configuration. When the slip of leading dislocation is barriered by the strain wave peaks or troughs, the succeeding dislocation is likely to pile up and aggregate around the nearby region, which facilitates the formation of paired dislocations35. Also, in front of a dislocation line, the strain waves can induce the fluctuations of driving force levels. Thus, the dislocations slip by nanoscale segments that cut through the peaks or troughs of the strain waves. This results in a variant of stick-slip, and the moving dislocation lines become wavy as each segment responds differently. The conversion of an initially straight dislocation line into a wavy configuration also shortens the length to minimize the total energy of the dislocations. This rationalizes the shorter paired-dislocations in steel SA compared with the longer and smoother dislocation lines in steel LA (Supplementary Figure 14). The mechanisms for the formation of short and wavy paired dislocations can also be activated in steel SA-A. Thus, the atomic-scale strain waves with high amplitude and small wavelength lead to the local pinning effect that makes overall dislocation movement sluggish, improving the strength levels of steels SA and SA-A.

In the present study, typical planar slip bands are observed in the deformed microstructures of the steels at various local strain levels, which are also commonly found in previous lightweight steels12,36,37. The inverse fast Fourier transform (IFFT) images in Fig. 4i, j shows the planar slip planes marked by red arrows and the edge dislocations with the Burgers vector of 𝑎/2 [01̅1] for steels LA and SA (with local strains of ~20% and ~15%, respectively). The formation of slip bands by dislocation planar slip is closely related to the stacking fault energy (SFE). The generalized SFE of the present lightweight steel estimated by thermodynamic calculation is ~78 mJ/m2 and the experimentally measured value is ~82 mJ/m2 (see Supplementary Information), which are comparably high. This SFE level would facilitate the planar slip in the steel during plastic deformation38. Notably, the local SFE can be variable from one site to another in the present lightweight steels due to the chemical fluctuation caused by the κ'-carbide. More specific, high Al concentration zones at κ'-carbide domains can be incorporated to push the magnitude of SFE up, while Fe/Mn-rich zones are particularly effective in reducing the local SFE39,40. The lower local SFE can widen the dissociate distance of two Shockley partial dislocations, which promotes the planar slip of dislocations on the initial slip plane. Thus, the atomic-scale strain waves with high amplitude and small wavelength in steels SA and SA-A can bring in drastic fluctuations of local SFE and promote the planar slip of dislocations during plastic deformation. The planar slip of shorter paired dislocations in steels SA and SA-A bring finer slip bands than that in steels LA and LA-A (Supplementary Figure 13). Then the formation and refinement of planar slip bands during plastic deformation can provide significant dynamic Hall-Petch effect for enhancing strain-hardening ability over the deformation process, which significantly contributes to the high ductility at high strength levels41.

During plastic deformation, when the movement of dislocations is hindered on its primary slip plane, the increasing strain can promote a propensity for cross-slip of dislocations to accommodate plastic flow. The possibility of dislocation cross-slip strongly depends on the SFE. The relatively high SFE of the present steels can facilitate dislocation cross-slip by narrowing the dissociation width of perfect dislocations. This also helps to store dislocations and promotes their reactions in the steels. In the steels LA and LA-A, the cross-slip of long dislocation lines can facilitate the formation of HDDWs during plastic deformation, which can induce stress localization and is certainly adverse to the ductility42. Notably, the short paired dislocations in steels SA and SA-A can cross-slip and lead to the formation of dense hexagonal dislocation networks43. This corresponds to shorter dislocation lines and hence lower energy, which can significantly improve the tolerance for dislocation accumulation in the steels during plastic deformation. With the increased dislocation storage capacity, the dynamic formation of hexagonal dislocation networks significantly enhance the strain hardening ability and strength-ductility synergy.

In summary, we have developed unprecedentedly strong and ductile lightweight steel by inducing significant atomic-scale alternating tension-compression strain waves, which are formed by lattice expansion in Al-rich short-range ordered κ'-carbide domains and contraction in Fe/Mn-rich FCC-γ matrix. Upon mechanical loading, these atomic-scale strain waves with high amplitude and small wavelength significantly increase the lattice friction, contributing to the high yield strength. During plastic deformation, the atomic-scale strain waves convert the straight dislocation lines into wavy and paired. The increase of engineering strains can force the paired dislocations tangle into dense hexagonal dislocation networks via cross-slip, which significantly enhances the defect-storage capacity of the steel. The atomic-scale strain waves can also promote the dynamic microstructure refinement with the reduction in the average spacing of planar slip bands during plastic deformation. These mechanisms jointly suppress localized stress concentrations and promote strain hardening ability, rendering the steels ultra-strong and ductile. The demonstrated strategy of tuning atomic-scale strain waves is thus promising for guiding the development of ultra-strong and ductile lightweight materials for advanced structural engineering applications.

Methods
Thermodynamic calculations
The thermodynamic calculations by Factsage software 8.3 with the FSstel database were carried out to design the Fe-Mn-Al-C lightweight steel. The phase diagrams illustrating the phase evolution with respect to the variations of C, Al and Mn contents and temperature are given in Supplementary Figure 1a-c, respectively. The C content of 5 at.% was selected to achieve a single FCC-γ phase above ~900 °C and κ-carbide precipitation below ~650 °C. To avoid the presence of BCC-α ferrite, the Al content of 15 at.% was chosen for the design. Additionally, a relatively high Mn content of 30 at.% was selected due to its role in stabilizing austenitic matrix and reducing the precipitation temperature of κ-carbide. As illustrated in Supplementary Figure 1d, the predicted phase configurations in the designed Fe Mn Al C lightweight steel indicate the high potential to achieve a microstructure consisting of austenite matrix and κ-carbide precipitates.

Material processing
A 5 kg Fe Mn Al C lightweight steel ingot, prepared using a commercial vacuum-induction furnace by melting pure Fe, Mn, Al and graphite (purity >99.9 wt.%), was ordered outside. The exact chemical compositions of the lightweight steel measured by inductively coupled plasma mass spectrometry (ICP-MS) and carbon-sulfur analyzer (CS744) are listed in Supplementary Table 1. A piece of lightweight steel with a thickness of 10 mm was cut from the ingot followed by hot rolling at 900 oC with a thickness reduction of 50%. Then the plate was homogenized at 1200 oC for 2 h followed by water quenching. Cold-rolling was conducted with a thickness reduction of 70%. Recrystallization annealing processes with short time (3 min) and longer time (30 min) were conducted at 900 oC followed by water quenching, and the annealed steel samples are denoted as LA and SA, respectively. Precipitation aging was performed at 600 oC for 40 min based on steels LA and SA, and the aged steel samples are denoted as LA-A and SA-A, respectively. During homogenization, annealing and aging, the lightweight steel samples were hermetically sealed in vacuum quartz tubes to avoid oxidation. The heat treatments were carried out in a box furnace and ended with water quenching in a water bath.

Mechanical characterization
Rectangular dog-bone-shaped tensile specimens with a gauge length of 8 mm and a gauge width of 2.5 mm were machined inhouse by electrical discharge machining (DK 7720, China) according to the standard of ASTM E8 (different specimen sizes are allowed) 44. Room temperature uniaxial tensile tests were conducted by a Sansi 10 kN machine with an engineering strain rate of 1×10-3 s-1. The digital image correlation (DIC) method using the Aramis system (GOM GmbH) was used to precisely determine local strain evolution during tensile testing.

The product of specific ultimate tensile strength (SUTS) and tensile elongation (TE) was calculated as (UTS×TE)/𝜌, where 𝜌 is the mass density. The mass density of the present steel are estimated based on the regression formula45:
1/𝜌 = ∑ 𝐶𝑖/𝜌𝑖 (1)
where 𝜌𝑖 is the mass density of element i and 𝐶𝑖 is the mass fraction of element i.

The elastic modulus and nanohardness values were determined by nanoindentation at room temperature using a KLA G200X indentation tester with a Berkovich tip. During nanoindentation test, 16 indents were arranged in a square with the spacing between adjacent indents of 5 μm to avoid the overlap of plastic zones.

Microstructural characterization
The phase constituents of the steel samples were measured by X-ray diffraction (D/max-B 2550, Rigaku, Japan) with Cu-Kα radiation (λ = 0.154 nm). Electron backscatter diffraction (EBSD) analysis with Hough transform was carried out using a Tescan Clara scanning electron microscope (SEM) with EDAX OIM data collection software at a voltage of 20.0 keV and 7.0 nA with a working distance of 15.0 mm and a step size of 100 nm. Back-scattered electron (BSE) imaging and electron channeling contrast imaging (ECCI) were performed at a voltage of 30.0 keV and 3.0 nA with a working distance of 10.0 mm. Energy dispersive spectrometry (EDS) analysis based on the SEM was carried out with a working distance of 15.0 mm. The average grain sizes of the steels were determined based on EBSD measurements using TSL OIM 8.0 analysis software, with all data points above a threshold CI (Confidence Index) value of 0.1. The samples for SEM observations were prepared by grinding using silicon carbide paper from 400 to 5000 granulation and polishing using 3 μm diamond suspension and 20 nm silica dioxide suspension.

For transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) analysis, a ThermoFisher Talos F200X instrument was operated at a voltage of 200 kV. The probe convergence angle was 10.6 mrad for STEM imaging. High-angle annular dark-field (HAADF), low-angle annular dark-field (LAADF) and bright field (BF) STEM images were obtained at collecting angles of 50-200 mrad, 30-50 mrad, and 0-30 mrad, respectively. The ThermoFisher Spectra 300 instrument was also used for atomic-resolution STEM observation operated at a voltage of 300 kV. The probe convergence angle and collecting angle for the atomic-resolution HAADF-STEM images were 25.0 mrad and 50-200 mrad, respectively. To prepare samples for S/TEM analysis, disc specimens with a diameter of 3 mm were cut from the gauge region of tensile-tested samples at various local strain levels and non-deformation samples and ground to a thickness of ~50 μm followed by electron polishing using a twin-jet electron-polisher at a temperature of -30 °C. The electrolyte used for the electron polishing was a solution of 90% methanol and 10% perchloric acid. The atomic-scale strain maps were obtained by the geometric phase analysis (GPA) method based on the atomic-resolution HAADF-STEM images using the strain++ 1.7.1 software. To ensure high reliability of the strain results, HAADF-STEM imaging was performed with drift correction by the piezo stage controller. The image was reconstructed after filtering out high-frequency noise to improve the signal‐to‐noise ratio, thereby enhancing the precision and accuracy of atomic-scale strain measurements 24.

For atom probe tomography (APT) analysis, the tips were prepared inhouse by a two-stage electro-polishing method. In the first stage, the samples with dimensions of 0.5×0.5×10 mm were polished using a 25 vol% perchloric/acetic acid solution at 15 V under the D.C. condition to prepare a rough needle. Then the needle samples were polished to a suitable sharpness using 2 vol% perchloric acid in 2-butoxyethanol solution at 5 V under the D.C. condition. APT analysis was carried out using CAMECA LEAP 5000 XR in voltage-pulsing mode with a repetition rate of 200 kHz and a pulse fraction of 15% at 50 K.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This article addresses an important issue: achieving increased strength and ductility in light-weight steels. More specifically,\nthe authors attempted to develop a physical mechanism that determines the dynamics of dislocations in the structure of steel\ncontaining atomic-scale strain waves. The idea is novel, and the methods used by the authors allow them to solve the\nproblem. I must note that, in my opinion, the experimental studies were not conducted with sufficient care. This calls into\nquestion the main results and conclusions of the article. For this reason, I cannot recommend it for publication.\nComments:\n1. Page 3, line 69. The steel composition is incorrect.\n2. A very important limitation, in my opinion, is the chosen heat treatment regime. In particular, this applies to the 900°C\ntreatment for 3 minutes. It's unclear whether this duration is sufficient to uniformly heat the sample and form the described\nstructure. It's also unclear how to scale the results to larger samples than those used in this study. Does such a short-term\ntreatment have any practical application? Will it be possible to reproduce the obtained data?\n3. Page 4, lines 106-107. It requires clarification that after SA treatment, the size and volume fraction of k-carbide are greater\nthan after LA treatment. The treatment temperature is the same; why does a longer annealing period result in a smaller\nparticle size and their fraction?\n4. Page 5, lines 113-117. The text, in my opinion, contains contradictory data. On the one hand, it states that the distribution\nof iron and manganese is uniform, but later, columns depleted in iron and enriched in manganese are described.\n5. Why does the article provide approximate rather than precise data on mechanical properties (e.g., in lines 209, 210, 211,\n212, 216, 217, 218 and other). What number of samples were used in the mechanical tests? Why are average data with an\nerror not provided?\n6. In general, the method for selecting the tensile specimen sizes (p. 18) requires clarification. According to what standards\nwere the specimen sizes selected? Figure 3c and d shows a comparison of the mechanical properties of the specimens\nunder study with other materials. Were the materials shown in the figures prepared similarly (had the same dimensions)?\nWere the strain rates the same (or close) for the data presented in these figures? Specimens for which an unfavorable\nlength-to-area ratio was selected may exhibit greater ductility than those manufactured in accordance with the standards.\nAre the described effects of increased flatness and ductility caused by the size factor? All these questions require an\nanswer. It will likely be necessary to re-examine the mechanical properties using more appropriate working part dimensions.\n7. Why were specimens deformed to different degrees of strain used to describe the differences in dislocation structure for\nthe two types of treatments (on pages 14 and 15)? In my opinion, it's correct to compare the dislocation structure of\nspecimens deformed to identical strains. Can we draw valid conclusions about structural differences if, for example, we're\ncomparing strains of 30% and 50%?\n8. Page 13. Again, the statistical averaged spacings are approximate. Statistical analysis requires a precise description of\nthe quantities.", "reviewer_2": "The concept of utilizing atomic-scale strain waves in carbide phases within lightweight steel is novel and intriguing. The\nauthors present substantial evidence supporting the existence of the newly reported κ’ carbide after aging, which contributes\nto a simultaneous enhancement in both strength and ductility. However, several questions remain that, if addressed, could\nfurther strengthen the manuscript.\n1. The terminology “atomic-scale strain waves” appears to be relatively new. Could the authors clarify how this concept\ndiffers from more established phenomena such as short-range order or periodic lattice distortion, which are more frequently\nreported in high entropy alloys and other complex alloys?\n2. In the supplementary materials, the authors refer to statistical results when estimating precipitation strengthening,\nspecifically mentioning the number of pile-up dislocations. Could the authors provide direct evidence or representative\nexamples of pile-up dislocations around the κ carbide? Including such microstructural observations would help validate the\nassumptions used in the strengthening calculations.\n3. Regarding the nanoindentation measurements, could the authors specify the indentation depth at which hardness values\nwere extracted for all samples? Additionally, in the supplementary materials, the authors note that the theoretical yield\nstrength exceeds the experimental value and attribute this discrepancy to “the inevitable influence of annealing twin\nboundaries (TBs) and grain boundaries (GBs) on elevating the elastic modulus values up when using the nanoindentation\ntesting.” This statement is unclear. Since yield strength is obtained from tensile testing, how does nanoindentation relate to\nthe theoretical versus experimental yield strength comparison?\n4. Do the authors expect the κ carbide to transform from the existing κ’ carbide, or to precipitate independently within the\nmatrix after aging at 600 °C? This distinction is important for understanding the phase evolution pathway. A brief discussion\nwould be valuable, especially in light of prior studies on short-range order in other alloy systems that may offer relevant\ninsights into transformation mechanisms or nucleation behavior.\n5. In lines 190–195 of the manuscript, the authors state that the matrix and the κ carbide in the SA-A sample exhibit similar\nstrain distributions. However, no explanation is provided for this observation. Could the authors elaborate on the underlying\nmechanism or microstructural factors that might account for this similarity?"}, "author_response": "Response to Reviewers' Comments\nNCOMMS-25-72731\nWe would like to thank the editor and reviewers for the valuable suggestions and\ncomments. Our response is structured as follows: The comments from the reviewers\nare copied below (black, italic font). For each comment, we present a response and the\ncorresponding manuscript modifications (blue font). The amended manuscript is\nenclosed. The changes therein are shown in red font.\nReviewer #1\nThis article addresses an important issue: achieving increased strength and ductility in\nlight-weight steels. More specifically, the authors attempted to develop a physical\nmechanism that determines the dynamics of dislocations in the structure of steel\ncontaining atomic-scale strain waves. The idea is novel, and the methods used by the\nauthors allow them to solve the problem. I must note that, in my opinion, the\nexperimental studies were not conducted with sufficient care. This calls into question\nthe main results and conclusions of the article. For this reason, I cannot recommend it\nfor publication.\nResponse: We sincerely thank the reviewer for acknowledging the importance and\nnovelty of our work, and for raising pertinent comments and suggestions which are\nimportant for us to improve the manuscript. We have carefully re-analyzed the\nexperimental data and checked all related conclusions. Accordingly, the manuscript has\nbeen carefully revised to address the concerns proposed by the reviewer and to robustly\nstrength our manuscript. We hope it now meets the expected standards for publication.\n1. Page 3, line 69. The steel composition is incorrect.\nResponse: Thanks for the very careful reading and the helpful comment. We have\ncorrected the steel composition on page 3 as suggested by the reviewer.\nModifications: Please see the updated sentence on page 3: “This concept is\n1\ndemonstrated in a prototype lightweight steel with nominal composition\nFe Mn Al C (at.%) designed through thermodynamic calculations using FactSage\n50 30 l5 5\nsoftware with the FSstel steel database (Fig. S1).”\n2. A very important limitation, in my opinion, is the chosen heat treatment regime. In\nparticular, this applies to the 900°C treatment for 3 minutes. It's unclear whether this\nduration is sufficient to uniformly heat the sample and form the described structure. It's\nalso unclear how to scale the results to larger samples than those used in this study.\nDoes such a short-term treatment have any practical application? Will it be possible to\nreproduce the obtained data?\nResponse: We appreciate the reviewer for the valuable comments. We have carefully\nconfirmed the microstructures of the steel SA annealed at 900 oC for 3 min with the\nlow-magnification BSE image (field view of 733 × 550 μm) prior to the EBSD analysis,\nwhich shows the fully recrystallized grains. We have added the overview BSE image\nof the steels LA (annealing at 900 oC for 30 min) and SA (annealing at 900 oC for 3 min)\nin the Supplementary materials. It is then confirmed that our experimental results of the\nfully recrystallized microstructure of the steel SA can be reproduced.\nThe short-time annealing process at 900 oC for 3 min was used for constructing\nthe special atomic-scale strain waves of high amplitude and small wavelength in the\nlightweight steel. It is worth noting that such annealing process was performed on the\ncold-rolled plate with a thickness of 1.5 mm. The corresponding microstructures in Fig.\nS5 demonstrate that this short duration is sufficient to uniformly treat the sample,\ncausing recovery of dislocations and building recrystallized grains with annealing twins.\nWhen considering hot-rolled or cold-rolled sheets with relatively small thickness in\npractical application (e.g., thickness of 1.5 mm in this study), this short-time annealing\nprocess can be adopted, as it enables rapid and uniform temperature distribution along\nthe thickness direction. However, for practical applications involving parts with large\nthickness, this short-time duration annealing process is likely to be not suitable as\nconcerned by the reviewer. In the present study, the high amplitude and small\nwavelength atomic-scale strain waves can be triggered by the short-time annealing\nprocess, which is of significance to modulate the dislocations behavior. The main\nfindings can provide insights for designing stronger and more ductile materials with\nsuch atomic-scale structures by various annealing process with different temperatures\nand durations. Namely, the specific annealing temperature and duration can be finely\ntuned for material parts with different dimensions to obtain the similar structures.\nThe short-time annealing process has been applied in various alloys, with the aim\nof constructing different micro- or nano-structures to meet various requirements of\nmechanical properties. For example, in Cu alloys, a balance of strength-ductility\nsynergy and residual stress can be modulated by annealing at 200 oC for 1 min [Journal\nof alloys and compounds, 2023, 941: 168705]. The fine structure within β phase in Ti-\n6Al-4V alloy, which is highly sensitive to the solution heat treatment temperature, can\nbe optimized by annealing at 915 °C/120 s and 570 °C/180 s, significantly enhancing\nthe strength [Materials Science and Engineering: A, 2025, 926: 147787]. The short-\ntime annealing process, akin to ultra-fast heating technique in steel industry, has been\nproposed to meet the requirements for energy and production efficiency with high-\nquality. The short time exposure at a certain temperature significantly increases strength\nwithout sacrificing a substantial amount of ductility, which worked by effectively refine\nthe grain size, induce the heterogeneous structure, stabilize the austenite and inhibit the\nformation of brittle phase [Materials & Design, 2024, 238: 112658]. It has also been\nreported that the ultra-fast heating at 730 oC for 100 s leads to the formation of retained\naustenite grains, inheriting the chemical composition of strain-induced martensite with\na high density of dislocations in middle-Mn steel, which significant increases yield\nstrength by 270 MPa and the product of strength and elongation up to 55 GPa% due to\nthe enormous work hardening capacity [Journal of Materials Science & Technology,\n2022, 97: 54-68].\nIn summary, the microstructures of steel SA are uniform with fully recrystallized\ngrains. Such a short-time annealing process can be applied to the hot-rolled or cold-\nrolled sheets with relatively small thickness (e.g., thickness of 1.5 mm in this study).\nSimilar short-time annealing process has been widely applied for various materials with\nthe aim of tuning microstructures to enhance the mechanical properties.\nmicrostructures of the steels LA and SA in the Supplementary materials on page 9.\nFig. S5. The micro- and nano-scale morphologies and elemental distributions of the steels LA and\nSA. a Overview BSE image showing the uniform recrystallized microstructure in steel LA. b BF-STEM\nimage showing GBs without precipitates in steel LA. c EDS mappings corresponding to the sample\nregion of a showing the uniform distribution of each element at microscale. d Overview BSE image\nshowing the uniform recrystallized microstructure in steel SA. e BF-STEM image showing GBs without\nprecipitates in steel SA. f EDS mappings corresponding to the sample region of e showing the uniform\ndistribution of each element at microscale.\n3. Page 4, lines 106-107. It requires clarification that after SA treatment, the size and\nvolume fraction of k'-carbide are greater than after LA treatment. The treatment\ntemperature is the same; why does a longer annealing period result in a smaller\nparticle size and their fraction?\nResponse: We thank the reviewer for the comment. Indeed, we confirmed by multiple\ntimes of measurements that the average sizes of κ'-carbide are 0.4 nm and 0.5 nm with\naverage area fractions of 8.5% and 16.5% in steels LA and SA, respectively. Such\n4\nabnormal decreases of fraction and size of sub-nano κ'-carbide with increasing\nannealing time from 3 min to 30 min is related to the formation kinetics of κ'-carbide\nunder thermodynamic conditions in both steels. During annealing of the cold-rolled\nsteel, there are complex structural evolution process including atomic diffusion-\ncontrolled recovery of dislocations, nucleation and growth of subnano-sized structures\nand/or nano-sized precipitates, re-construction of new grains. The atomic diffusion\nplays a crucial role in the formation of subnano-sized κ'-carbide in the present\nlightweight steel during annealing process. Very importantly, the atomic diffusion\noccurs more easily along the crystal defects, e.g., dislocations and grain boundaries due\nto high activity and mobility of atoms at the defects. Among all crystal defects in the\ncold-rolled samples, dislocations account for the largest proportion. Therefore, the\ntangled dislocations offer the pipe diffusion pathway that strongly promote the mobility\nof atoms, which significantly facilitates the kinetics to the formation of local chemical\ninhomogeneity. These local regions in the current Fe-Mn-Al-C steel tend to have\nregular atomic arrangement due to the negative mixing enthalpies of Fe-Al (-11 KJ/mol)\nand Mn-Al (-19 KJ/mol), which renders the formation of subnano-sized κ'-carbide.\nHowever, the recovery of dislocations also proceeds rapidly during annealing. After the\n3 min annealing at 900 oC (steel SA), the previous deformation-induced dislocations\nare absent as the microstructure is fully recrystallized, which suggest that the atomic\nmobility would decrease with further increasing annealing time at 900 oC. Nevertheless,\nthe atomic diffusion at newly constructed grain boundaries remains and continuously\ncoarsens the grains with the increasing annealing time. This results in the larger grain\nsize for 30 min annealed steel (LA: 15.0 ± 9.7 μm) than that for 3 min annealed steel\n(SA: 7.5 ± 5.4 μm). Accordingly, the high mobility of atoms during annealing at the\nfirst few minutes strongly facilitates the formation kinetics of subnano-sized κ'-carbides,\nwhich urger the deviation from thermodynamic equilibrium in perfect crystal lattice. In\nthe 30 min annealed steel, although the annealing at the first few minutes favors the\nformation of κ'-carbide domains, the subsequent prolonged exposure at 900 oC can lead\nto the partial dissolution of the previously formed κ'-carbide to be closer to the\nthermodynamic equilibrium state of the crystal lattice. Therefore, both the fraction and\n5\nsize of κ'-carbides in steel SA are greater than that in steel LA.\nModifications: Please see the updated parts on pages 4-5 of the revised manuscript:\n“The abnormal decreases of fraction and size of the sub-nanoscale κ'-carbides with\nincreasing annealing time from 3 min to 30 min is related to the formation kinetics of\nκ'-carbide. Specifically, the high atomic mobility promoted by crystalline defects\ninduced in the prior deformation strongly facilitates the formation kinetics of sub-\nnanoscale κ'-carbides during annealing at the first few minutes, leading to the deviation\nof associated crystal lattice from thermodynamic equilibrium. However, upon further\nincreasing annealing time, the prolonged exposure of the fully recrystallized\nmicrostructure at 900 oC can lead to the partial dissolution of the previously formed\nsub-nanoscale κ'-carbide, rendering the crystal lattice closer to the thermodynamic\nequilibrium state.”\n4. Page 5, lines 113-117. The text, in my opinion, contains contradictory data. On the\none hand, it states that the distribution of iron and manganese is uniform, but later,\ncolumns depleted in iron and enriched in manganese are described.\nResponse: We thank the reviewer for the helpful comment. Indeed, there was\nvagueness in the original description of the atomic-scale elemental distribution on page\n5. For the specific part, we intended to convey that the distributions of Fe and Mn are\nmore uniform compared to that of Al. The original sentence in the manuscript might\nhave led to an inappropriate implication. Therefore, we have revised and reconstructed\nthe sentence to ensure it accurately reflects the experimental results.\nModifications: We have modified the sentence on page 5 of the revised manuscript:\n“The atomic-resolution HAADF-STEM image of steel LA acquired along [011] zone\nγ\naxis in Fig. S6a and the EDS analysis result in Fig. S6b, c suggest that Al tends to be\nenriched in specific atomic columns. The atomic-scale distributions of Fe and Mn are\nalso inhomogeneous, but are more uniform compared to that of Al.”\n6\n5. Why does the article provide approximate rather than precise data on mechanical\nproperties (e.g., in lines 209, 210, 211, 212, 216, 217, 218 and other). What number of\nsamples were used in the mechanical tests? Why are average data with an error not\nprovided?\nResponse: We thank the reviewer for the helpful comment. As we previously\nmentioned in the manuscript, at least three identical tests were conducted for each\nsample condition to ensure the reproducibility of mechanical properties. In the original\nmanuscript, we only provided the average values with approximation. As suggested by\nthe reviewer, in the revised manuscript we have added the standard errors to the average\nvalues based on our experimental data.\nModifications: Please see the updated sentences on page 11 in the revised manuscript:\n“The steel SA characterized by atomic-scale strain waves with high amplitude and small\nwavelength exhibits yield strength (𝜎 ) of 687 ± 13 MPa, ultimate tensile strength (𝜎 )\n𝑦 𝑢\nof 1154 ± 4 MPa and total elongation (𝜀 ) of 67.8% ± 4.0%, which are significantly\n𝑓\nhigher than those values of steel LA (610 ± 10 MPa, 1035 ± 9 MPa and 37.8% ± 2.3%,\nrespectively) with atomic-scale strain waves of lower amplitude and larger wavelength.”\nand “More specific, the steel SA-A has yield strength (𝜎 ) of 1073 ± 10 MPa and\n𝑦\nultimate tensile strength (𝜎 ) of 1324 ± 8 MPa at total elongation (𝜀 ) of 50.4% ± 3.2%,\n𝑢 𝑓\nwhich are superior than those of steel LA-A (1051 ± 8 MPa, 1241 ± 13 MPa and 20.1%\n± 1.3%, respectively).”\n6. In general, the method for selecting the tensile specimen sizes (p. 18) requires\nclarification. According to what standards were the specimen sizes selected? Figure 3c\nand d shows a comparison of the mechanical properties of the specimens under study\nwith other materials. Were the materials shown in the figures prepared similarly (had\nthe same dimensions)? Were the strain rates the same (or close) for the data presented\nin these figures? Specimens for which an unfavorable length-to-area ratio was selected\nmay exhibit greater ductility than those manufactured in accordance with the standards.\nAre the described effects of increased flatness and ductility caused by the size factor?\nmechanical properties using more appropriate working part dimensions.\nResponse: We thank the reviewer for the helpful comment. In the present study, the\ntensile specimens were prepared according to the standard of ASTM E8. We have added\nthis standard in the revised manuscript.\nAs suggested by the reviewer, we have carefully checked the strain rates\ncorresponding to the mechanical data that we chose for the comparison. While most of\nthe reference data are with a same strain rate of 1.0 × 10-3 s-1, we found that two data\npoints from the references [Materials & Design, 2021, 198: 109315 and Materials\nCharacterization, 2022, 190: 112042] are with strain rates of 2.5 × 10-4 s-1 and 1.0 ×\n10-4 s-1, which are remarkably different from the strain rate used in the others and our\nwork (1.0 × 10-3 s-1). Therefore, we have replaced the two reference data points by two\nsuitable ones from the references [Nature, 2015, 518: 77-79 and Journal of Materials\nResearch and Technology, 2024, 33: 2164-2182], which employed strain rates of 1.0 ×\n10-3 s-1.\nAlso, we have carefully checked the dimensions of the tensile specimens\ncorresponding to the mechanical data that we chose for the comparison. The specific\ndimensions of tensile testing specimens from the references and our work are\nsummarized in Table S3. Various dimensions of tensile testing specimens were used in\nthe references. Correspondingly, the length-to-area ratios are also different, which may\ninfluence the total elongation at increased flatness stages. The size effect in tensile\ntesting has been established for miniaturized specimens [International Journal of\nMachine Tools and Manufacture, 2021, 167: 103755]. For homogeneous materials with\nfully recrystallized microstructure, strength properties measured from miniature and\nstandard-sized specimens show good agreement [Theoretical and Applied Fracture\nMechanics, 2024, 131: 104410]. However, the total elongation is inversely proportional\nto the ratio of the gauge length to the square root of the cross-sectional area (𝐿 /√𝐴 )\n0 0\n[Materials Science & Engineering A, 2023, 883: 145464; Scientific Reports, 2025, 15:\n13846]. For the total elongation, it consists of uniform elongation (independent of\n8\ngauge length) and post-necking elongation (increases with decreasing gauge length).\nAccordingly, we have converted the amount of post-necking elongation from specimens\nwith different gauge lengths and cross section areas to those corresponding to standard\nspecimens with a reference ratio of gauge length to square root of cross-sectional area\n(𝐿 /√𝐴 ) based on the Barba’s law according to standard ASTM A 370 [Theoretical\n𝑟 𝑟\nand Applied Fracture Mechanics, 2024, 131: 104410; Fusion Engineering and Design,\n2020, 161: 112006]:\n𝜀 = 𝜀 +(𝜀 −𝜀 )(𝐿 /√𝐴 )×(√𝐴 /𝐿 ) (1)\n𝑟 𝑢 0 𝑢 0 0 𝑟 𝑟\nwhere 𝜀 , 𝜀 and 𝜀 are the total elongation of the reference standard specimen, total\n𝑟 0 𝑢\nelongation and uniform elongation of the miniaturized specimen. Generally, the Barba’s\nlaw can be directly used for tensile tests with miniaturized specimens, which is mostly\nused in academic fields. Consequently, we have converted the total elongation values\nfrom references and our work to those corresponding to the identical standard specimen\ndimensions, which enables the reliable comparisons of the converted total elongation\n(CTE) and the products of specific ultimate tensile strength (SUTS) and CTE. In\naddition, the uniform elongation (independent of gauge length) as the function of\nultimate tensile strength values have also been plotted to compare the mechanical\nproperties of the various steels.\nModifications: please see the detailed modifications ⅰ-ⅴ in the following.\nⅰ: Please see the updated sentence on page 12 in the revised manuscript: “To avoid\nsample size effect, the uniform elongation values were used in the comparison of\nstrength-ductility combinations shown in Fig. 3c (see details in Table S3).”, “We also\nconverted the total elongation values from references and our work into those\ncorresponding to identical standard specimen dimensions by the Barba’s law, and\naccordingly the converted total elongation (CTE) is used in the additional comparison\n(see the calculation details in Supplementary materials) 32-34. As presented in Fig. S11,\nthe products of SUTS and CTE of the present lightweight steels SA and SA-A surpass\nthat of the previous lightweight steels.” And on page 19: “Rectangular dog-bone-shaped\n9\ntensile specimens with a gauge length of 8 mm and a gauge width of 2.5 mm were\nmachined by electrical discharge machining with reference to the standard of ASTM\nE8 44.”\nⅱ: Please see the updated table S3 on page 21-23 in the revised Supplementary materials：\nTable S3 Detailed dimensions of tensile test, yield strength (YS), ultimate tensile strength\n(UTS), uniform elongation (UE), total elongation (TE), converted total elongation (CTE), mass\ndensity, the calculated product of specific ultimate tensile strength (SUTS) and CTE, product\nof SUTS and UE for various types of lightweight steels.\nLength ×\nwidth × Product of Product\nLight\nthickness Mass SUTS and of SUTS\nweig YS UTS UE TE CTE Refere\nof tensile density CTE and UE\nht (MPa) (MPa) (%) (%) (%) nces\ntest (g/m-3) (GPa·%·g/ (GPa·%·\nsteels\nspecimens cm-3) g/cm-3)\n(mm)\n8 × 2 × 792 916 52 67 59 6.62 8.1 7.1\n17\n1.5 927 1043 40 55 47 6.62 7.4 6.3\n25 × 3 × 1300 1419 5.3 17.4 17.6 6.32 3.9 1.2\n27\n1.5 917 1025 27.5 46.5 46.8 6.32 7.5 4.5\n1146 1386 27 34 32 6.62 6.7 5.6\n20 × 4 × 2 1347 1425 19 30 27 6.62 5.7 4.1 18\n1363 1481 18 25 23 6.62 5.1 4.0\nκ in γ\n1124 1183 32.9 38.2 35.6 6.5 6.5 5.9\n15 × 4 × 2 929 1059 41.8 55.1 48.7 6.5 7.9 6.8 20\n983 1080 40.5 52 46.5 6.5 7.7 6.7\n1047 1300 26 30 29 6.79 5.6 4.9\n950 1210 34 41 30 6.79 7.1 6.0\n20 × 6 × 1 19\n1171 1410 20 25 24 6.79 5.0 4.2\n680 1027 46 53 52 6.79 7.8 6.9\n1205 1400 29 38 31 6.6 6.7 6.2\n4 × 2 × 1 7\n1631 1700 11 13 12 6.6 3.0 2.8\n1567 1672 14.6 18.0 16.5 6.6 4.2 3.7\nκ 12.6 × 5 × 720 1091 43.2 52.9 48.5 6.6 8.0 7.1\n29\nplus 1 1251 1411 25.4 29.0 27.4 6.6 5.8 5.4\nB2 in 1167 1347 24.3 34.0 29.6 6.6 6.1 7.0\nγ 18 × 2.5 × 1446 1507 16.3 24.3 25.2 6.79 5.6 3.6\n28\n1 1600 1622 13.0 20.2 21.0 6.79 5.0 3.1\n1540 1671 9 15 12 6.6 3.1 2.3\n8 × 2 × 1 30\n970 1200 30 38 34 6.6 6.3 5.5\n10\n1357 1548 18.0 20.3 21.2 6.82 4.8 4.1\n50 × 12.5 1207 1486 22.0 24.7 25.7 6.82 5.6 4.8\n31\n× 1 1009 1350 27.6 31.8 33.4 6.82 6.6 5.5\n1186 1473 22.7 25.6 26.7 6.82 5.7 4.9\n1173 1311 12.7 14.2 13.5 6.79 2.6 2.5\n20 × 6 × 1064 1205 16.7 19.4 18.1 6.79 3.2 2.9\n34\n2.5 824 1056 28.3 35.5 31.9 6.79 5.0 4.4\n687 983 36.4 44.9 40.7 6.79 5.9 5.3\nκ in γ 1348 1444 4.9 14.8 14.8 6.56 3.3 1.1\nplus 25 × 6 × 1 1390 1478 4.4 13.9 13.9 6.56 3.1 1.0 32\nα 1398 1494 3.9 11.5 11.5 6.56 2.6 0.9\n1300 1309 17.9 22.0 22.0 6.85 4.2 3.4\n25 × 6 × 1 33\n1060 1288 12.7 13.1 13.1 6.85 2.5 2.4\n50 × 10 × 1008 1202 30 41 45.5 6.66 7.4 5.4\n35\n1 883 1092 22 32 36.1 6.66 5.2 3.6\n8 × 2.5 × This\nSA 687 1158 49.2 69.9 61.0 6.67 10.0 8.5\n1.5 work\n8 × 2.5 × This\nSA-A 1073 1324 39.0 52.8 46.9 6.67 9.3 7.7\n1.5 work\nⅲ: Please see the updated Fig. 3 in the revised manuscript：\ncurves at room temperature. b Strain hardening rate and true stress with respect to true strain. c Plot\nof uniform elongation (UE) with respect to ultimate tensile strength (UTS) for the present steels and\nthe reference lightweight steels. d Plot of the products of specific ultimate tensile strength (SUTS)\nand UE with respect to yield strength (YS) for the present steels and the above reference lightweight\nsteels. The data for previous FCC-γ-based lightweight steels including those with κ-carbide\nprecipitation strengthening (κ in γ) 11,12,17,27,28, κ-carbide plus B2 particles strengthening (κ plus B2\nin γ) 1,9,13,15,29 and duplex structure composed of BCC-α phase and FCC-γ matrix with κ-carbide\nprecipitation strengthening (κ in γ plus α) 18,19,30,31 are provided for references. “Amp.” and “Wav.”\nin a refer to amplitude and wavelength, respectively.\nⅳ: Please see the added calculation details of converted total elongation (CTE) on page\n3-4 in the revised Supplementary materials：\nCalculation of converted total elongation\nThe tensile testing specimens with various dimensions were used in the references, as\nsummarized in Table S3. Consequently, the ratios of the gauge lengths to the cross-sectional areas\n12\nare also different, which can influence on the measured total elongations 22,23. The total elongation\nconsists of uniform elongation (independent of gauge length) and post-necking elongation. Usually,\nthe post-necking elongation increases with decreasing the ratio of the gauge length to the square\nroot of the cross-sectional area (𝐿 /√𝐴 ) 24. In the present study, we use the Barba’s law according\n0 0\nto standards ASTM A 370 to convert the amount of post-necking elongation from specimens with\ndifferent gauge lengths and cross-sectional areas into those corresponding to standard specimens\nwith a reference ratio of gauge length to square root of cross-sectional area (𝐿 /√𝐴 ) 25,26:\n𝑟 𝑟\n𝜀 =𝜀 +(𝜀 −𝜀 )(𝐿 /√𝐴 )×(√𝐴 /𝐿 ) (11)\n𝑟 𝑢 0 𝑢 0 0 𝑟 𝑟\nwhere 𝜀 , 𝜀 and 𝜀 are the total elongation of the reference standard specimen, total elongation\n𝑟 0 𝑢\nand uniform elongation of the miniaturized specimen. Generally, Barba’s law can be directly used\nfor tensile tests with miniaturized specimens, which is mostly applied in academic fields.\nConsequently, we have converted the total elongation values from references and our work\naccording to the statistical data in Table S3 into those corresponding to the standard specimen\ndimensions, which enables the reliable comparisons of the converted total elongation (CTE) and the\nproducts of specific ultimate tensile strength (SUTS) and CTE.\nⅴ: Please see the added Figure S11 on page 15 in the revised Supplementary materials：\nFig. S11 a Plot of converted total elongation (CTE) based on Barba’s law with respect to ultimate\ntensile strength (UTS) for the present steels and the reference lightweight steels. b Plot of the\nproducts of specific ultimate tensile strength (SUTS) and CTE with respect to yield strength for the\npresent steels and the above reference lightweight steels. The data for previous FCC-γ-based\nlightweight steels including those with κ-carbide precipitation strengthening (κ in γ) 17-20,27, κ-\ncarbide plus B2 particles strengthening (κ plus B2 in γ) 7,28-31 and duplex structure composed of\nBCC-α phase and FCC-γ matrix with κ-carbide precipitation strengthening (κ in γ plus α) 32-35 are\nprovided for references.\n13\n7. Why were specimens deformed to different degrees of strain used to describe the\ndifferences in dislocation structure for the two types of treatments (on pages 14 and 15)?\nIn my opinion, it's correct to compare the dislocation structure of specimens deformed\nto identical strains. Can we draw valid conclusions about structural differences if, for\nexample, we're comparing strains of 30% and 50%?\nResponse: We thank the reviewer for the helpful comment. As the ductility values of\nsteels with the two types of treatments are different (Fig. 3a), the corresponding strains\nat the identical deformation stages (e.g., medium uniform deformation stage, late\nuniform deformation stage and post-necking stage) are also different. For the steels LA\nand LA-A, the medium uniform deformation stages correspond to the local strains of\n~20% and ~10%, respectively, in Fig. 4a and b. Similar for other deformed\nmicrostructures in Fig. 4, their corresponding deformation stages are identical, although\nthe specific strain values are different. To avoid possible confusion, we have modified\nthe sentences in the revised manuscript to further clarify this point.\nModifications: Please see the updated sentence on page 14 in the revised manuscript:\n“To elucidate the underlying deformation mechanisms responsible for the enhanced\nmechanical properties of the present steels, the deformed microstructures in the tensile-\ntested samples were characterized and compared at the identical deformation stages\nwith various local strain levels at micro-, nano- and atomic scales.”\n8. Page 13. Again, the statistical averaged spacings are approximate. Statistical analysis\nrequires a precise description of the quantities.\nResponse: We thank the reviewer for the helpful comment. In the revised manuscript,\nwe have added the standard errors based on our experimental data.\nModifications: Please see the updated sentence on page 14-15 in the revised\nmanuscript: “…with statistical average spacing of 411.6 ± 168.6 nm and 94.2 ± 86.3\nnm, respectively, as shown in Fig. 4a and b.”, “…with a statistical average spacing\nreduction to 54.8 ± 35.8 nm (Fig. 4c). …slip band spacing of 93.4 ± 79.2 nm relative to\n14\nprior strain levels (Fig. 4d). …the average spacings of slip bands are 54.4 ± 20.1 nm\nand 91.6 ± 58.3 nm, respectively.”, “…with a statistical average spacing of 121.7 ± 49.7\nnm. …slip bands in steels SA and SA-A are 39.3 ± 14.0 nm and 76.8 ± 47.5 nm,\nrespectively.” and “…slip band spacings to 34.3 ± 14.1 nm and 48.8 ± 30.7 nm,\nrespectively.”\nReviewer #2\nThe concept of utilizing atomic-scale strain waves in carbide phases within lightweight\nsteel is novel and intriguing. The authors present substantial evidence supporting the\nexistence of the newly reported κ’ carbide after aging, which contributes to a\nsimultaneous enhancement in both strength and ductility. However, several questions\nremain that, if addressed, could further strengthen the manuscript.\nResponse: We are very grateful to the reviewer for the positive assessment of our work\nand for the suggestions to further improve our manuscript. We have carefully\nconsidered and addressed all the comments point-by-point. The related parts have been\ncarefully revised with the aim to further strengthen the manuscript.\n1. The terminology “atomic-scale strain waves” appears to be relatively new. Could\nthe authors clarify how this concept differs from more established phenomena such as\nshort-range order or periodic lattice distortion, which are more frequently reported in\nhigh entropy alloys and other complex alloys?\nResponse: We thank the reviewer for the helpful comment. The atomic-scale strain\nwave in the present study is primarily derived from the lattice expansion and contraction\nat the sub-nano-sized Al-rich κ'-carbide domains and Al-depleted FCC-γ matrix,\nrespectively, resulting in a fluctuating tension-compression strain distribution. The sub-\nnano-sized Al-rich κ'-carbide is a special type of short-range ordered structure, which\nalso has remarkable lattice distortion. Therefore, we can consider that the atomic-scale\nstrain wave in the present Fe-Mn-Al-C lightweight steels is associated with the short-\nrange ordered structures with lattice distortion, yet it is still essentially distinct from\nprevious ordinary short-range orders and lattice distortion. As suggested, we have\n15\nfurther clarified this in the revised manuscript.\nModifications: Please see the updated sentence on page 7 in the revised manuscript:\n“Further, the results suggest that the atomic-scale strain waves are primarily derived\nfrom the lattice expansion and contraction at the sub-nano-sized Al-rich κ'-carbide\ndomains and Al-depleted FCC-γ matrix, respectively, resulting in a fluctuating tension-\ncompression strain distribution at atomic scale.”\n2. In the supplementary materials, the authors refer to statistical results when\nestimating precipitation strengthening, specifically mentioning the number of pile-up\ndislocations. Could the authors provide direct evidence or representative examples of\npile-up dislocations around the κ carbide? Including such microstructural observations\nwould help validate the assumptions used in the strengthening calculations.\nResponse: We thank the reviewer for the helpful comment. The number of pile-up\ndislocations were estimated according to our experimental observations and related\nreferences. We have further clarified this part in the revised Supplementary materials.\nModifications: Please see the updated sentence on page 3 in the revised Supplementary\nmaterials: “N is the number of pile-up dislocations. We estimated an appropriate\nnumber to be 6 based on the references 12,17 and the TEM observations (Fig. S14).”\nReferences:\nFeMnAlC lightweight steels. Acta Mater. 198, 258-270 (2020).\nSi-alloying in medium-Al FeMnAlC lightweight steels. Acta Mater. 245, 118611 (2023).\nPlease see the updated Fig. S14 in the revised Supplementary materials:\nin the steels. The long dislocation lines are present in steel LA, while the paired dislocations in steel\nSA. And the dislocations in the steel LA are smoother than those in the steel SA. Dislocation pile-\nup can be observed both in steels LA-A and SA-A as marked by red arrows.\n3. Regarding the nanoindentation measurements, could the authors specify the\nindentation depth at which hardness values were extracted for all samples? Additionally,\nin the supplementary materials, the authors note that the theoretical yield strength\nexceeds the experimental value and attribute this discrepancy to “the inevitable\ninfluence of annealing twin boundaries (TBs) and grain boundaries (GBs) on elevating\nthe elastic modulus values up when using the nanoindentation testing.” This statement\nis unclear. Since yield strength is obtained from tensile testing, how does\nnanoindentation relate to the theoretical versus experimental yield strength comparison?\nResponse: We thank the reviewer for the helpful comment about nanoindentation test.\n200 nm to ensure reliable while minimizing the influence of the surface effects. This\ndetail has been explicitly stated in the Supplementary materials on page 24.\nThe theoretical yield strength values in our study were calculated as the sum of\nlattice friction stress and grain boundary strengthening. The lattice friction stress is\nderived from the Peierls-Nabarro stress, which is the inherent resistance that\ndislocations must overcome to slip in perfect and static crystal lattice. We obtained the\nelastic module values of the steels via nanoindentation to determine the Peierls-Nabarro\nstress. However, the real crystals contain vacancies and other dislocations, which\nfacilitates the slip of dislocations bypassing the full resistance of the ideal lattice. And\nthe thermal vibration of real atoms also helps dislocations in overcoming the Peierls-\nNabarro stress for dislocation motion. Thus, the calculated lattice friction stress based\non the Peierls-Nabarro stress may be overestimated for real materials. We have\nmodified the corresponding explanations for this part in the revised Supplementary\nmaterials.\nModifications: Please see the updated sentence on page 3 in the revised Supplementary\nmaterials: “This may be related to the overestimation on Peierls-Nabarro stress due to\nthe presence of vacancies, dislocations and atomic vibration in the real materials.”\nPlease see the updated Table S4 on page 24 in Supplementary materials:\nTable S4 Vickers-hardness, nanoindentation hardness and elastic modulus of the steel samples\nin the present study. The depth for hardness values is extracted from 100-200 nm.\nLA- SA-\nLightweight steels LA SA HM\nA A\nVickers-hardness (HV) 357.2 399.6 441.3 459.2 307.8\nNanoindentation\n3.779 4.227 4.668 4.858 3.256\nhardness (GPa)\nElastic modulus (GPa) 163.8 166.1 164.9 169.2 157.5\n18\n4. Do the authors expect the κ carbide to transform from the existing κ’ carbide, or to\nprecipitate independently within the matrix after aging at 600 °C? This distinction is\nimportant for understanding the phase evolution pathway. A brief discussion would be\nvaluable, especially in light of prior studies on short-range order in other alloy systems\nthat may offer relevant insights into transformation mechanisms or nucleation behavior\nResponse: We thank the reviewer for the helpful comment. The κ'-carbide can be\nconsidered as the ordered structure with Al atoms located at corner positions and Fe/Mn\nat face-centered positions. Further ordering of C to the body-centered octahedral\ninterstitial positions, leading to the formation of κ-carbide. During the aging process,\nthe spinodal decomposition takes place, which promotes the diffusion of C atoms into\nordered κ'-carbide, thereby transforming it into κ-carbide. With prolonged exposure at\n600 oC, the κ-carbide continues grow up with ongoing spinodal decomposition. Thus,\nthe κ'-carbide serves as a precursor for the formation of κ-carbide during the aging\nprocess. A brief discussion has been added to the manuscript.\nModifications: Please see the updated sentence on page 8 in the revised manuscript:\n“This is consistent to the previous finding that the κ'-carbide can serve as a precursor\nfor the formation of κ-carbide by further ordering of C into the body-centered\noctahedral interstitial positions via spinodal decomposition6,7.”\n5. In lines 190–195 of the manuscript, the authors state that the matrix and the κ carbide\nin the SA-A sample exhibit similar strain distributions. However, no explanation is\nprovided for this observation. Could the authors elaborate on the underlying\nmechanism or microstructural factors that might account for this similarity?\nResponse: We thank the reviewer for the helpful comment. For steel SA-A, the average\namplitudes of atomic-scale strain waves at matrixes (containing sub-nano-sized κ'-\ncarbide domains) and nano-sized κ-carbide are 1.84 ± 0.89% and 1.59 ± 0.42%,\nrespectively. The average values of wave peaks and troughs at matrixes and κ-carbide\nare -0.24% and 0.09%, respectively, which are fairly small. Therefore, the matrix and\nthe κ carbide in the SA-A sample exhibit fairly similar strain distributions. We have\n19\nadded the detail descriptions in the revised manuscript.\nModifications: Please see the updated sentence on page 9 in the revised manuscript:\n“However, in the steel SA-A, the atomic-scale strain distributions in the κ-carbide and\nmatrix are fairly similar as indicated by the small differences in average amplitudes\n(1.59% and 1.84%, respectively) and average strain values (0.09% and -0.24%,\nrespectively).”\nDear Editor,\nWe cordially thank you for kindly letting us know that we need to have a minor revision of the\npaper for final publication. As suggested, the detailed point-to-point response to the additional\ncomments are provided below.\nComment 1:\nOn page 1: Suggest starting with a different beginning:: Reducing weight to save energy and\nenhancing mechanical properties are both necessary to increase...\nResponse: As suggested, we have revised the beginning of abstract: “Reducing weight to save\nenergy and enhancing mechanical properties to increase safety level are both vital for structural\nmaterials in modern engineering.”\nComment 2:\nOn page 3: Is it linear?Fix the spelling\nResponse: As suggested, we have corrected the misspelling and further checked the other parts to\nexclude oversights.\nComment 3:\nOn page 3: When it comes to heat treatment, please address following comments:\n1. Was the sample encapsulated or wrapped in the foil to prevent oxidation? Its a general practice\nto encapsulate samples to prevent contamination/ oxidation. 2. Was the heat treatment carried out\nin a tube or a box furnace? 3. The most important thing how was quenching carried out? Was\nquenching media a water bath, ice , brine or other media? List details.\nResponse: We thank the reviewer for the helpful comment. The alloy samples for homogenization,\nannealing and aging were hermetically sealed in vacuum quartz tubes to avoid oxidation. The heat\ntreatment was performed in a box furnace. The heat treatment process ended with quenching in a\nwater bath. As suggested, we have listed the details in the Methods part of the revised manuscript:\n“During homogenization, annealing and aging, the lightweight steel samples were hermetically\nsealed in vacuum quartz tubes to avoid oxidation. The heat treatments were carried out in a box\nfurnace and ended with water quenching in a water bath.”\nComment 4:\nOn page 18: Names of some of the equipment are missing at several places. In some places\nequipment names are clearly listed. In others, they are left out. Please list the equipment in all\ncases to maintain uniformity. I have commented where it needs to be added\nResponse: As suggested, we have added the names of the equipment for electrical discharge\nmachining and X-ray diffraction.\nComment 5:\nOn page 19: Was this ingot ordered from outside? If so please list it clearly. Such novel\ncompositions in such a quantity are usually ordered commercially\nResponse: The ingot was ordered from outside. As suggested, we have added the details on page\n19: “A 5 Kg Fe Mn Al C lightweight steel ingot, prepared using a commercial vacuum-\n50 30 15 5\ninduction furnace by melting pure Fe, Mn, Al and graphite (purity >99.9 wt.%), was ordered\noutside.”\nComment 6:\nOn page 19: List if inhouse and name of the EDM\nResponse: We thank the reviewer for the helpful comment. The rectangular dog-bone-shaped\ntensile specimens were machined inhouse by electrical discharge machining. We have added the\ncorresponding details in the revised manuscript: “Rectangular dog-bone-shaped tensile specimens\nwith a gauge length of 8 mm and a gauge width of 2.5 mm were machined inhouse by electrical\ndischarge machining (DK 7720, China) according to the standard of ASTM E8 44.”\nComment 7:\nOn page 20: List name of XRD equipment\nResponse: As suggested, we have added the details on page 20: “The phase constituents of the\nsteel samples were measured by X-ray diffraction (D/max-B 2550, Rigaku, Japan) with Cu-Kα\nradiation (λ = 0.154 nm).”\nThank you again very much for your kind patience and efforts invested in our paper.\nSincerely,\nZhiming Li"}, {"round": 2, "reviewer_comments": {"reviewer_2": "The authors have addressed all of my concerns and have made appropriate revisions to the manuscript. I am happy to\nrecommend this manuscript for publication.", "reviewer_3": "The concept of utilizing atomic-scale strain waves in carbide phases within lightweight steel is novel and intriguing. The\nauthors present substantial evidence supporting the existence of the newly reported κ’ carbide after aging, which contributes\nto a simultaneous enhancement in both strength and ductility. We worked in HEA where we studied unique compositions,\nthe authors have translated that to a much simpler alloy Steel with alloy additives which make the work novel."}, "author_response": ""}]

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