Bulk spinodal-architected compositionally complex alloy with enhanced energy absorption across a wide temperature range

Abstract

Bulk mechanical energy-absorbing materials are critically needed for various engineering applications. However, existing state-of-the-art materials face significant limitations: architected systems such as 3D-printed nano- and micro-lattices suffer from scalability constraints, while conventional foams often exhibit a strength-ductility trade-off that limits energy absorption. Here, we overcome these challenges by fabricating bulk architected alloys via electrochemical dealloying of a machine learning-identified compositionally complex spinodal alloy. These materials display a hierarchical structural architecture spanning seven orders of magnitude – from atomic-scale lattice distortion, nanoscale precipitates and amorphous oxide layers, microscale ligaments, to macroscale network dimensions. This multi-scale integration enables synergistic deformation mechanisms, yielding energy absorption capacities of ~106 MJ/m³ in bulk and ~ 305 MJ/m³ in micro-samples. Crucially, this enhanced performance is retained from room temperature to 873 K. Our approach provides an effective strategy for designing scalable, high-performance architected materials for demanding condition energy absorption.

Here, researchers fabricated bulk architected alloys via electrochemical dealloying of a ML-identified compositionally complex spinodal alloy, achieving high energy absorption across a wide temperature range via a seven-order hierarchy.

Introduction

Energy-absorbing materials that simultaneously achieve high strength and toughness are essential for structural and life protection in aerospace, automotive, and machinery applications^1–3, where lightweight designs must endure demanding mechanical and thermal loads. Metals, with their innate strength-ductility balance, outperform polymers and ceramics in those roles. Yet, conventional metallic absorbers remain constrained by a persistent strength-toughness trade-off and rapid thermal softening at elevated temperatures⁴. Conventional metallic foams (e.g., Al, Mg, Ni, et al.^5,6) rely on internal friction, ligament plasticity, and pore collapse for energy dissipation. Their stochastic pore structures enabled progressive structural crushing and flow stress plateaus in deformation curves, but their performance is ultimately limited by low yield stresses from poorly optimized architectures⁷, porosity-driven exponential strength decay⁸, as well as rapid softening and oxidation^4,9 at elevated temperatures.

Recent breakthroughs in additive manufacturing, from selective laser melting¹⁰, direct-ink writing¹¹ to two-photon lithography¹², have enabled control over energy-absorbing material architectures^13,14. These techniques now permit the precise fabrication of lattice materials with truss¹⁵, plate¹⁶, and shell¹⁷ unit cell, as well as complex topologies like triply periodic minimal surfaces, redefining the limits of energy absorption. Yet, despite their high performance^18,19, such meticulously engineered materials face an intrinsic trade-off, i.e., the challenge of preserving nanoscale precision while scaling to macroscale dimensions. In contrast, nanoporous metals, usually fabricated through dealloying of precursor alloys²⁰, differ from the layer-by-layer approach of additive manufacturing. This approach enables multi-scale structural fabrication from nanoscale ligaments to bulk materials, such as previously extensively studied nanoporous Au²¹. The naturally evolved non-periodic topologies circumvent the defect sensitivity typical of periodic structures^22,23, while nanoscale ligaments provide high mechanical behavior via pronounced size effects^24–26. Therefore, expanding this structural material from current simple alloys to a broader composition space may enable achieving high performance.

In this study, we introduce a scalable method to create lightweight, bulk micro- and nano-architected alloys using machine learning identified spinodal compositionally complex alloys (CCAs) as precursors. Through controlled electrochemical dealloying²⁰, we transform these alloys into centimeter-scale samples featuring 3D micro/nano-ligament networks with oxide passivation, achieving low densities of 2.77–3.06 g/cm³. The multi-component chemistry enables hierarchical nanostructuring within ligaments while preserving the global spinodal architecture. The resulting materials demonstrate high energy absorption capacities, reaching ~106 MJ/m³ ( ~ 35 J/g) in bulk forms and ~305 MJ/m³ ( ~ 100 J/g) in microscale samples, while maintaining high performance across an extensive temperature range (298–873 K).

Results

Architected alloy fabrication

To identify spinodal alloy precursors, we employed our recently developed physics-informed machine learning method²⁷ (see “Methods”). This method integrates physics informed data descriptors into an artificial neural network architecture (see Supplementary Fig. 1), enabling efficient exploration of the Al-Co-Cr-Fe-Ni system. The algorithm identified Cr_24.2Co_21.8Al_21.4Fe₂₀Ni_12.6 (in atomic percentage) as the spinodal composition (see Supplementary Note 1), which forms a B2/BCC spinodal structure (Supplementary Fig. 2). Thermal annealing at 1373 K (0.5–48 h, see “Methods”) produced tunable spinodal domains with characteristic sizes spanning 270 ± 150 to 1550 ± 950 nm (Supplementary Figs. 3). Subsequent electrochemical dealloying selectively removed the B2 phase, yielding centimeter-scale architected alloys with preserved spinodal network (see Methods and Supplementary Note 2).

The architected bulk alloys exhibit mosaic-like surface patterns under optical microscopy (Fig. 1a), arising from their characteristic micro- or nano-scale spinodal architectures (Fig. 1b, Supplementary Fig. 6). With densities of 2.77–3.06 g/cm³, approximately half of that of their precursor alloy (6.76 g/cm³) (see “Methods”), these lightweight materials demonstrate tunable ligament diameters spanning 270 ± 80 nm to 1320 ± 370 nm, directly correlated with the spinodal domain sizes controlled through thermal annealing (Fig. 1c). Energy-dispersive X-ray spectroscopy (EDS) reveals a final composition of Cr_44.4Fe_27.0Co_18.5Ni_5.4Al_4.7 (see “Methods”, Supplementary Table 1), confirming successful architectural control while maintaining complex alloy characteristics. Interestingly, X-ray diffraction (XRD) patterns (Fig. 1d) demonstrate that the architected CCAs exhibit a dual-phase crystalline structure comprising a body-centered cubic (BCC) phase and a B2 phase.

Fig. 1. Structural characterization of our architected compositional complex alloy (CCA).

a Photograph of bulk architected CCAs showing different light reflections due to surface micro- and nano-structures. b SE-SEM images of architected CCAs obtained from dealloying different heat-treated precursors. c The statistical analysis of ligament size (D) of the architected CCAs. Lognormal fits are included for each histogram. d XRD pattern of the architected CCAs with different ligament sizes. e 3D reconstruction of the morphology of a typical bulk architected CCA with the ligament size of 1320 ± 370 nm. f The connectivity network of ligaments shown in (e). g The polycrystalline-like structure of the bulk architected CCA. h The statistical analysis of the coordination number of ligaments. The inset shows the statistical analysis of the aspect ratio (L/D) of ligaments where a lognormal fit is used. Source data are provided as a Source Data file.

X-ray tomography (XRT) reveals three-dimensional stochastic networks in our bulk architected alloys which exhibit an average ligament size of 1320 ± 370 nm (Fig. 1e, Methods). These dealloyed spinodal CCAs form quasi-periodic, interconnected networks that contrast sharply with the periodical architectures of 3D-printed architected materials². The dealloying process introduces structural features reflecting the polycrystalline precursor: crack-like defects resembling grain boundaries and micro-sized casting voids (Supplementary Fig. 8). Despite these imperfections, the architecture maintains structural integrity through a continuous network of tortuous ligaments (Fig. 1f) and interconnected porosities (Supplementary Fig. 9). Especially, the fabricated architected CCAs inherit the polycrystalline structure from precursors (Fig. 1g, Supplementary Fig. 8), with each ligament preserving single-crystalline character (Fig. 2a, Supplementary Fig. 10). This monocrystalline nature resembles that observed in dealloyed nanoporous gold but differs from additive manufacturing architectures where ligaments typically exhibit a polycrystalline microstructure (e.g., CoCrNiTi_0.1 nanolattice²⁸). Through analyses of approximately 140,000 ligaments and 80,000 nodes, we quantify two defining topological characteristics, i.e., nodal coordination number predominantly ranging from 3 to 5, and ligament aspect ratios following a lognormal distribution with a mean value of 4.4 and a standard deviation of 3.6 (Fig. 1h).

Fig. 2. Nanostructural characterization of spinodal-derived ligaments.

a The dark-field TEM image of an individual ligament was acquired by selecting the B2 superlattice diffraction spot (inset: corresponding selected-area electron diffraction pattern). b Elemental mapping of the ligament region shown in (a). c High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HAADF-STEM) image of the coherent B2-BCC interface probe from a nanoparticle of about 50 nm in size along the <001> zone axis (inset: FFT patterns from the BCC matrix and B2 nanoprecipitates). d Lognormal distribution of nanoprecipitation size (D_NP) shown in (a). e High-resolution TEM (HRTEM) image of the amorphous oxide-BCC matrix interface along the <001> zone axis (insets: FFT patterns from the BCC matrix and the oxide layer regions). f HAADF-STEM image of the multicomponent matrix showing chemical inhomogeneity along the <001> zone axis (insets: Z-intensity variation of the dashed white line). g the contour map of the Von Mises strain obtained via geometric phase analysis (GPA) in (f) (insets: the distribution of Von Mises strain). Source data are provided as a Source Data file.

Furthermore, dark-field transmission electron microscopy (DF-TEM) and energy-dispersive X-ray spectroscopy (EDS) analyses reveal a distinctive hierarchical nanostructure in the spinodal-derived ligaments (Fig. 2a, b, Supplementary Fig. 11). Each ligament features two key characteristics: (i) B2 nanoprecipitates (Al/Ni/Co-enriched) coherently embedded within the BCC matrix (Fig. 2a, c), exhibiting a lognormal size distribution with a mean diameter of ~20 nm and extending up to 80–150 nm (Fig. 2d); (ii) a continuous amorphous passivation layer ( ~ 40% of the ligament diameter) encapsulating the structure (Fig. 2e). In fact, the dealloying process leads to oxidation-induced amorphization on the surface of the ligament, forming the oxide layer²⁹. Meanwhile, the numerous nanoprecipitates within the ligaments originate from the microstructure of the precursor (see Supplementary Fig. 12) and subsequently preserved after dealloying. X-ray photoelectron spectroscopy (XPS) surface profiling further identifies chromium oxide enrichment in the near-surface region (Supplementary Fig. 13). Especially, the multicomponent matrix exhibits significant chemical inhomogeneity and lattice distortion (Fig. 2f, g and the insets). This multiscale architecture, integrating chemically complex crystalline phases with a protective amorphous sheath, represents a unique structural motif of spinodal-derived materials.

Temperature-resistant energy absorption capacity

To evaluate the energy absorption capacity (EAC) of our architected CCAs, we first performed microcompression tests on micro-samples free of casting defects and grain-boundary cracks. Focused ion beam (FIB) milling was employed to fabricate (001)-oriented micropillars ( ~ 10 × 10 × 10 μm³) with controlled dealloying depths of ~10 μm (see “Methods”), creating a functionally graded structure comprising a porous top region (50–60%) and a solid base. This design strategically confines plasticity to the porous region, mimicking conventional test geometries where porous structures are compressed between platens. To eliminate potential substrate effects, we tested non-dealloyed monolithic base cubic pillars approximately 10 μm in size and found their yield strength remained above the stress of the porous region up to the densification stage (Supplementary Fig. 14). Therefore, after subtracting the contribution of the substrate’s elastic deformation, we obtained the stress-strain curves of the architected CCAs (Fig. 3a). Microcompression testing conducted with a strain rate of 4 × 10⁻³s⁻¹ at room temperature (RT, 298 K) (see “Methods”) revealed consistent mechanical behaviors across ligament sizes, exhibiting a 0.2% offset yield stress at 305–320 MPa, characteristic stress plateaus at 531–623 MPa followed by progressive strain hardening and densification strains of 0.513–0.545 (Supplementary Table 3). Analysis of the stress-strain profiles following the literature³⁰ revealed an high EAC of approximately 269–305 MJ/m³ (see Supplementary Note 3). This mechanical performance stems from the spinodal topology formed by nanoscale ligaments²⁴. SEM analyses demonstrate that widespread distributed plasticity occurred in the porous architecture, evidenced by ligament twisting/bending, pore collapsing and densification without any visible sign of overall fracture (Fig. 3b). This behavior starkly contrasts with conventional BCC/B2 metals which typically fracture under similar strains under tension or bending³¹. Especially, the fabricated architected CCAs exhibit a limited size effect, due to their similar topology (Supplementary Fig. 15) and nanostructure.

Fig. 3. Temperature-resistant mechanical properties of our architected CCAs.

a Microcompression stress-strain curves for a non-dealloyed base and (001)-oriented cubic micropillars (side length ~ 10 μm) with varying ligament sizes. b SE-SEM images showing micropillar morphology before and after compression for different ligament sizes. c Stress-strain responses of bulk samples (ligament size = 1320 ± 370 nm) across a wide range of temperatures (inset: photograph of bulk sample geometry). d Energy-absorbing capacity (EAC) versus density (ρ) comparison with previously reported energy-absorbing materials, e Compressive yield stress (σ_y) versus strain characteristics, where ε_d represents densification strain for ductile materials and ε_f indicates fracture strain for brittle materials. f EAC versus temperature (T) performance demonstrating superior thermal stability of our architected CCAs compared to metallic foams, nanoporous metals and lattice metamaterials (comparison data in Supplementary Table 5). Error bars represent standard deviation (note that some error bars are smaller than the datapoints). Source data are provided as a Source Data file.

Next, we systematically evaluated the mechanical performance of bulk samples with the dimension of ~3 × 3 × 3 mm³ under compression across a broad temperature range (298–1073 K) at a strain rate of 4 × 10⁻³s⁻¹ (see “Methods”). At RT, bulk samples exhibited yield strengths of 177–246 MPa ( ~ 55–75% of micropillar values) while maintaining comparable densification strains (0.419–0.473), yielding an EAC of ~100 MJ/m³ (Supplementary Figs. 16-17 and Supplementary Table 4). This strength-size effect likely originates from casting defects and grain-boundary cracks inherent to bulk processing. The yield strength of our bulk samples demonstrated high thermal stability, showing only marginal softening ( < 20%) up to 873 K (Fig. 3c, Supplementary Fig. 18a). This moderate strength reduction was counterbalanced by enhanced densification strains (Supplementary Fig. 18b), maintaining EAC within the 101–148 MJ/m³ range. Microstructural analysis revealed that this temperature resilience correlates with ligament surface roughening from mild oxide-layer growth (Supplementary Fig. 19). Above 873 K, we observed a transition in failure mechanisms. Accelerated oxide growth at 1073 K caused significant ligament embrittlement, particularly pronounced in samples with finer ligaments (270 ± 80 nm), which resulted in EAC reduction due to compromised structural integrity by severe oxidation.

When benchmarked against the state-of-the-art energy-absorbing materials, including metallic foams^4,9,32–36, bulk nanoporous metals^37,38 and nano-/micro-lattice metamaterials^{17,18,28,39–45} (Fig. 3d, Supplementary Table 5), our architected bulk CCAs demonstrate superior energy absorption capacities approaching ~35 J/g despite containing processing defects—a performance matching even the previously reported defect-free micro-samples, such as Ni-B microlattices⁴⁰, glassy carbon nanolattices³⁹, and CoCrNiTi_0.1 nanolattices²⁸. Notably, defect-free microsamples of our architected CCAs exhibit a specific energy absorption capacity reaching the value of ~100 J/g. This high performance stems from an optimal combination of low density, high yield strength and pronounced plasticity, as evidenced by the high densification strain (Fig. 3e). Our architected CCAs maintain their high EAC across a wide temperature range (Fig. 3f), in sharp contrast to previously reported energy-absorbing materials (Supplementary Table 5) that typically show significant thermal degradation. This unique combination of high energy-absorbing performance and thermal stability suggests effective potential for demanding environmental applications.

Mechanisms for high energy absorption

To elucidate the mechanisms underlying the high EAC of our architected CCAs, we conducted micro-pillar compression tests at progressively higher strain levels (see Supplementary Fig. 20). The results revealed that during deformation, dislocations accumulated at the interface between the oxide layer and the metallic core. With ongoing deformation, localized delamination occurred between the oxide layer and specific ligaments, yet the oxide nanolayers also exhibited significant bending, indicating inherent plasticity. Meanwhile, the ligaments exhibit distinct stress states, leading to progressive rather than catastrophic failure in the overall structure. Consequently, the mechanical behavior of individual ligaments significantly influences the compression response, prompting us to perform further nanomechanical characterization via nanoindentation (see “Methods” and Supplementary Note 4). To ensure data integrity, we excluded indents located on ligament sidewalls, which could introduce measurement artifacts (Supplementary Figs. 21-22). Using the Oliver-Pharr method⁴⁶, we extracted the reduced modulus and hardness from valid indents within the ligaments. Both properties exhibited broad distributions across ligament sizes (Fig. 4a), likely due to structural heterogeneities observed in the ligament microstructure (Fig. 2). Especially, the average reduced modulus and hardness of ligaments remained consistent at ~76 GPa and ~4.3 GPa, respectively, independent of ligament size.

Fig. 4. Nanomechanical properties and FEM simulation of architected CCAs.

a Distributions of reduced modulus (E_r) and hardness (H) of spinodal-derived ligaments across varying ligament sizes. b Comparison of experimental microcompression stress-strain data with FEM model prediction (Homo-EPP, Homo-SH, Hetero-SH constitutive laws). Inset is the FEM model consisting of the architected structure extracted from 3D reconstruction data and upper and lower rigid platens. c 3D von Mises stress distribution in FE models at 10% strain. Note that these stresses are normalized for clarity. d Cross sectional 2D contour plots of von Mises stresses. Error bars represent standard deviation. Source data are provided as a Source Data file.

To complement our experimental findings, we extracted 15 micro-samples (10 × 10 × 10 μm³) from the 3D reconstruction of our bulk sample and used them as geometric models for finite element method (FEM) simulations (see “Methods”). These micro-samples exhibited consistent geometric and topological features, including ligament size, aspect ratio and coordination number (Supplementary Fig. 23). Given the complex multiscale deformation mechanisms, a fully predictive model is computationally prohibitive due to the vast disparities in temporal and spatial scales. We therefore adopt a phenomenological approach to capture the essential mechanical response and gain mechanistic insights. For constitutive modeling, we considered three materials behaviors: (1) homogeneous elastic-perfect plastic (Homo-EPP), (2) homogeneous power-law strain hardening (Homo-SH), and (3) heterogeneous power-law strain hardening (Hetero-SH), the latter accounting for the broad distribution of nanomechanical properties observed in nanoindentation (see Methods, Supplementary Figs. 21-22). All three models successfully captured the elastic regime of the experimental stress-strain curves (Fig. 4b). Fitting with the homogenous models yielded an elastic modulus of ~45 GPa and yield strength of ~1.5 GPa (Supplementary Table 6). The fitted modulus ( ~ 45 GPa) was slightly lower than the average modulus of individual ligaments ( ~ 68 GPa, assuming a Poisson’s ratio of 0.3), likely due to oxide layers encapsulating the ligaments⁴⁷. The fitted yield strength corresponded to 30–40% of the measured hardness, consistent with the typical strength-to-hardness ratio observed in metals⁴⁸. In contrast, for the Hetero-SH model, we defined 21 material parameters and assigned them to the elements within the meshed model according to a log-normal probability distribution inspired by nanoindentation results. The mean values of its elastic modulus and yield strength were consistent to those obtained from the homogeneous model (see Supplementary Table 7 and Supplementary Fig. 24).

The post-yielding behavior of our architected CCAs highlights a critical distinction between heterogenous and homogeneous constitutive models. While neither the Homo-EPP nor the Homo-SH model captures the experimental trend beyond yielding, the Hetero-SH model—employing the same strain hardening exponent (n = 0.5) as the Homo-SH model—successfully reproduces the post-yielding response of the architected CCA micropillars (Fig. 4b). This agreement suggests that the high EAC of our architected CCAs arises from the interplay between structural heterogeneity and an unusual strain-hardening behavior of BCC ligaments containing B2 nanoprecipitates. Further insight emerges from the von Mises stress distributions in our FE models (Fig. 4c, d). Homogenous models exhibit pronounced stress concentrations at geometrical singularities (e.g., sharp corners, ligament junctions), which are known to nucleate fracture and degrade EAC in energy absorbing materials^22,23. In stark contrast, the Hetero-SH model effectively mitigates these stress concentrations. Mechanical heterogeneities promote more uniform stress redistribution across the ligaments, preventing localized plasticity. Such delocalization, as reported in prior studies^49,50, enhances materials’ damage tolerance and underpins the observed EAC. Further microhardness analysis (see Supplementary Fig. 25) supports this, as the presence of defects did not cause a significant reduction in hardness or destructive crack propagation.

Discussion

To elucidate the high-temperature performance of our architected CCAs, we conducted nanoindentation measurements of the reduced modulus and hardness of individual ligaments across a range of temperatures (see “Methods”, Supplementary Fig. 26). As depicted in Fig. 5a, b, both the modulus and hardness of our ligaments decrease at a significantly slower rate with increasing temperature compared to conventional alloys^{19,31,51–72} (Supplementary Table 8). This relative thermal insensitivity aligns with the behavior reported in other highly distorted BCC/B2-type high entropy alloys, such as Co₂₅Ni₂₅(HfTiZr)₅₀^31,69, suggesting that the substantial lattice distortion present in our ligaments (Fig. 2g) contributes substantially to the retention of modulus and strength at elevated temperatures in our architected CCAs. Further insights were gained through TEM characterization of ligaments deformed at room temperature. Dislocation pile-ups were observed near the oxide-layer interface (Fig. 5c), indicating that the oxide layer effectively impedes dislocation escape to the surface, thereby mitigating surface crack initiation and delaying ligament rupture⁷³. In addition, nanoscale precipitates dispersed throughout the ligament act as potent obstacles to dislocation motion. The presence of dislocation loops encircling these precipitates provides clear evidence of the Orowan strengthening mechanism (Fig. 5d), resulting in a high density of geometrically necessary dislocations (GNDs). These observations offer direct microstructural validation for the heterogeneous strain hardening model used in our FEM simulations (Fig. 4). Especially, similar dislocation structures—including pile-ups and Orowan loops—were observed even after deformation at 873 K (Supplementary Fig. 27), demonstrating that both the external oxide layer and intra-ligament precipitates remain effective dislocation barriers at high temperatures.

Fig. 5. High-temperature mechanical properties and deformation mechanisms of ligaments.

Comparison of normalized mechanical properties with other materials: a elastic modulus (E/E₀) versus temperature (T); b yield stress/hardness (σ_y/σ_y0 or H/H₀) versus homologous temperature (T/T_m). Data for comparison alloys are provided in Supplementary Table 8. c, d Bright-field TEM analysis of deformation mechanisms in a room-temperature-tested ligament (viewed along <001 > , two-beam condition g = (110)): c dislocation pile-ups at an oxide layer. d Dislocation loops within the ligament interior. e Dynamic mechanical analysis (DMA) of architected CCAs, showing the normalized storage modulus (E’/E’₀) and loss factor (tanδ) as functions of temperature for different ligament sizes. Error bars represent standard deviation. Source data are provided as a Source Data file.

According to strain gradient plasticity theory^74,75, the flow stress σ_p of cubic crystals (e.g., FCC and BCC) containing GNDs and Orowan-strengthening nanoprecipitates can be described by:

$${\sigma }_p={\sigma }_f+Gb\left(\alpha \sqrt{{\rho }_{SSD}+{\rho }_{GND}}+\beta \frac{1}{\overline{l}}\right)$$ 1

Here, σ_f represents the lattice friction stress; G is the shear modulus; b is the magnitude of the Burgers vector; ρ denotes the density of either statistically stored dislocations (SSDs) or GNDs; $\overline{l}$ is the average inter-precipitate spacing; and α and β are dimensionless constants. Equation (1) clearly indicates that both GNDs and nanoprecipitates enhance the flow stress—consistent with the behavior observed in our architected CCAs. Furthermore, this framework provides a theoretical basis for the high-temperature mechanical properties exhibited by our materials. In conventional crystals, both lattice friction (σ_f) and shear modulus (G) exhibit pronounced temperature dependence, resulting in significant thermal softening. In contrast, in severely distorted high entropy alloys, such as Co₂₅Ni₂₅(HfTiZr)₅₀^31,69, these properties have been shown to be less sensitive to temperature. It is therefore reasonable to conclude that an analogous distortion-induced mechanism operates in our architected CCAs, sustaining their flow stress and enhancing mechanical performance at elevated temperatures.

However, the macroscopic stress-strain curves of our architected CCAs (Fig. 3c) reveal a pronounced decrease in overall modulus with increasing temperature. To elucidate this apparent discrepancy, we conducted dynamic mechanical analysis (DMA) on bulk samples (Methods). The measured storage modulus exhibits progressive elastic softening as temperature rises (Fig. 5e). Especially, near 800 K, a sharp decline in storage modulus occurs concurrently with a rapid increase in the loss tangent – a behavior characteristic of glass transition⁷⁶. Considering that the passivating amorphous oxide layer comprises approximately 50 vol % of the architected CCAs, particularly for ligaments with a submicron width (Fig. 2), the macroscopic modulus reduction can be attributed to the onset of glass transition within the amorphous oxide layers. According to ref. ⁷⁷, although amorphous oxides generally possess high oxidization resistance, severe oxidation may occur above their glass transition temperature due to accelerated mass transport of cations and anions. This insight offers a plausible explanation for the accelerated oxidation observed in our architected CCAs when deformed above 873 K (Supplementary Fig. 19).

Having demonstrated the high mechanical performance of our fabricated architected CCAs, it is noteworthy that our ML-guided precursor identification strategy exhibits generality. Selecting another precursor within the Al-Co-Cr-Fe-Ni system (Al₂₃Co₁₅Cr₃₂Fe₁₅Ni₁₅), we successfully fabricated an additional architected CCA with a distinct topology and composition (Supplementary Fig. 28). This result confirms that our approach is insensitive to the precursor, enabling broader application and further development of this materials design strategy.

In summary, this work presents an effective and scalable strategy for fabricating bulk architected alloys with nano-scale features, leveraging a machine learning-identified compositionally complex spinodal system. In contrast to existing architected materials, such as 3D-printed metallic micro- and nano-lattices^2,3, the electrochemically dealloyed bulk architected alloys developed here exhibit hierarchical structural integration spanning seven orders of magnitude: from severe lattice distortion ( ~ 1 nm), B2 nano-precipitates ( ~ 10 nm), and amorphous oxide layers ( ~ 100 nm), to submicron- and micro-scale ligaments (100 nm–1 μm), and finally macroscale network dimensions ( ~ 1 cm). The synergistic interplay of these multiscale heterogeneities leads to simultaneous enhancement in strength, strain hardening capability, and damage tolerance, culminating in high energy dissipation across a broad temperature range. Our findings thus establish a technological pathway for the design of future high-performance architected materials with promising applications in aerospace and automotive sectors.

Methods

Physics-informed machine learning

The dataset for machine learning comprises 484 alloy compositions, including spinodal alloys (150), solid solutions (180), and multi-phase (154), covering binary alloys to compositionally complex alloys with five or more principal elements. We used 0 and 1 to label spinodal and non-spinodal alloy compositions in the dataset. The dataset was randomly divided into 70% training set, 15% test set, and 15% validation set for model training. Data descriptors were selected based on the minimum eigenvalue (λ_min) derived from the Hessian matrix of a random solid solution, combined with 13 traditional data descriptors to construct a multidimensional feature space. The artificial neural network (ANN) adopted a typical three-layer structure (input layer-hidden layer-output layer), and the input data were normalized, and each layer was connected by weights, biases and activation functions. Subsequently, the machine learning model systematically screened the Al-Co-Cr-Fe-Ni alloy system, covering 42,801 compositions. Through experimental validation, three candidate precursors with spinodal decomposition structures were successfully identified (Supplementary Fig. 29). For this study, the Al_21.4Co_21.8Cr_24.2Fe₂₀Ni_12.6 composition was selected for analyses.

Preparation of precursors

The spinodal compositional complex alloy Cr_24.2Co_21.8Al_21.4Fe₂₀Ni_12.6 was prepared by arc melting using high purity aluminum, cobalt, chromium, iron and nickel elements ( > 99.9 wt%) and remelted at least five times under a Ti-gettered high purity argon atmosphere to ensure chemical homogeneity, subsequent cast into a copper mold with dimensions of approximately 5*12*60 mm. The precursor ingots were subsequently annealed at 1373 K (about 0.8 of its melting temperature) for 0.5, 3, 12, and 48 h to eliminate solidification-induced compositional inhomogeneities while adjusting the spinodal microstructure. Thereafter, the annealed ingots were wire-cut to the required size, followed by sequential grinding with SiC sandpaper from 120 to 2500 grit, and then polished with 1 μm aluminum oxide suspension. All samples were ultrasonically cleaned with deionised water, alcohol and dried with cold air before subsequent test.

Electrochemical test

The electrochemical tests were performed using an electrochemical workstation (Iviumstat Technology, Vertex™, Eindhoven, The Netherlands) under ambient conditions (298 K, atmospheric pressure) in a 1 M HCl electrolyte. A standard three-electrode system was utilized, consisting of the test sample as the working electrode, a saturated calomel electrode (SCE) as the reference electrode, and a platinum sheet serving as the counter electrode. Open circuit potential (OCP) data were recorded during a one-hour test prior to the electrochemical tests to reach stabilized values. Electrochemical impedance spectroscopy (EIS) was then conducted at the stabilized OCP with an alternating current (AC) amplitude of 10 mV over a frequency sweep range from 100 kHz to 10 mHz. Potentiodynamic polarisation tests were performed with a scan rate of 1 mV/s, covering a potential window from −0.3 V to +1.5 V versus the OCP.

Fabrication of architected CCAs

Electrochemical dealloying was carried out in a three-electrode electrochemical cell (annealed precursors as working electrode, a SCE reference electrode and Pt sheet counter electrode) containing 1 M HCl electrolyte under ambient conditions, with constant direct current (DC) voltage control. For the 0.5 h, 3 h, 12 h, and 48 h annealed samples, electrochemical dealloying was carried out by applying voltages of −0.1 V, 0 V, 0 V and 0 V (vs. SCE), respectively. Basically, the complete removal of one phase via electrochemical dealloying is determined via two aspects: the change of corrosion current and apparent density. For millimeter-thick specimens fabricated in this study, corrosion current density decays from ~10⁻² A to ~10⁻⁵ A usually signifies the completion of dealloying process. Additionally, the apparent density of bulk samples undergoes a significant decrease from 6.76 g/cm³ (precursor) to a range of 2.77–3.06 g/cm³.

Apparent density measurement

The apparent density of micro- and nano-architected CCAs was determined through mass-volume measurements of dealloyed samples with regular external dimensions of 1 × 10 × 10 mm³. The test sample were ultrasonic cleaned with deionised water, following vacuum-dried at 353K for 24 h to eliminate adsorbed moisture before cooling to ambient temperature. Post-drying mass quantification was performed using an electronic analytical balance (FA2204, Shanghai Puchun Measure Instrument Co., Ltd.) with an accuracy of 0.1mg, while the volume was calculated by measuring the geometric dimensions with a digital micrometer (Yantai Greenery Tools Co., Ltd.) with an accuracy of 0.001 mm. All measurements were repeated three times to ensure the reliability of the data. The tested apparent densities exhibited good repeatability, with a standard deviation below 1%.

Structural and compositional characterization

The crystal structure was characterized via a Rigaku MiniFlex 600 X-ray diffractometer (XRD) with Cu Kα radiation, operating in the 2θ range of 20–100° at a scanning rate of 4°/min. The microstructural features of the architected CCAs were examined by field-emission scanning electron microscopy (SEM, FEI Quanta 450FEG) equipped with energy-dispersive X-ray spectroscopy (EDX). The distribution of the ligament sizes was measured from the SEM images via AQUAMI^78,79. This approach first binarizes the SEM image, then combines a central axis transformation to extract the ligament skeleton and with a distance transformation to calculate local radius. It automatically measures the diameter at each pixel point along the skeleton line, yielding extensive statistical data on ligament sizes. Surface oxide characterization was conducted through high-resolution X-ray photoelectron spectroscopy (XPS). Three-dimensional structural reconstruction was performed non-destructively using X-ray microscopy (XRM, Zeiss Xradia 620 Versa) employing dual-stage magnification optics and a high-flux X-ray source, achieving 500 nm true spatial resolution with 40 nm minimum voxel size. The high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) observations were conducted on Titan Themis G2 and JEM-ARM300F Cs-corrected microscopes operated at 300 kV. The semi-collection angle ranges for HAADF-STEM observations are 48 (inner)−200 (outer) mrad. The dislocation characterizations were performed on JEOL 2100 F equipped with double-tilt holder operated at 200 kV. TEM specimen was prepared by focused ion beam (FIB, FEI Scios DualBeam system). A 2 μm thick carbon protective layer was initially deposited on the surface, followed by pre-cutting of a 10 × 7 × 1.4 μm³ rectangular lamella and transferred to a Cu grid. Sequential thinning was performed using 30 kV/0.1 nA Ga⁺ ion beam, reducing the lamella thickness to approximately 50 nm. Final surface refinement was conducted using a low-energy 5 kV/48 pA Ga⁺ ion beam to minimize amorphous damage layers.

Mechanical characterization

Micropillar compression specimens with approximate dimensions of 10 × 10 × 10 μm³ were fabricated via FIB milling along the [001] crystallographic orientation on bulk samples exhibiting about 10 μm dealloying depth. The micropillars were first coarse milling at 50 nA beam current for rapid material removal, followed by progressive refinement using 5 nA and 1 nA currents. Uniaxial micro-compression tests were performed using a TriboIndenter system (TI 950, Hysitron) equipped with a 50 μm flat indenter, employing a constant strain rate of 4 × 10⁻³s⁻¹. Each sample with different ligament sizes was tested at least twice. Uniaxial compression experiments of bulk architected CCAs were performed on a universal testing machine (CMT5105, MTS). Similarly, architected CCAs with different ligament sizes were tested at least twice at each temperature condition. All samples were first wire-cut into approximately 3.2 × 3.2 × 3.2 mm³ in size, then finely ground, polished, and electro-chemically dealloyed. The dimensional sizes of all samples were re-measured with a digital micrometer before testing. High-temperature compression tests (473 K, 673 K, 873 K, 1073 K) were conducted using the same testing machine (CMT5105, MTS) equipped with a three-section split-type atmospheric furnace (maximum operating temperature 1373 K) and thermocouples positioned at the upper, middle, and lower sections of the chamber for temperature control (temperature fluctuation ± 2 K). The data acquisition rate during testing was 60 pts/sec. Prior to test, specimens were thermally equilibrated for ten minutes, followed by a constant strain rate of 4 × 10⁻³s⁻¹. It is noteworthy that the densification strain was determined using the energy absorption efficiency method, where the onset of densification corresponding to the strain at maximum efficiency. This criterion provides a more reproducible approach than the tangent method, which may cause variations due to subjective selection of the tangent line (Supplementary Fig. 30). Mechanical properties of individual ligaments were investigated using the TriboIndenter system (TI 950, Hysitron) equipped with a Berkovich indenter. Nanoindentation employed displacement control with indentation depth limited to 1/10 of the statistical ligament diameter. 100 indentations were performed in a 10 × 10 array configuration with 5 μm spacing. Considering the contact conditions during nanoindentation tests (i.e., complete or partial/no contact with ligaments), we adopted maximum load and stiffness as parameters to distinguish the data, these parameters are higher when indent into ligaments, while decrease when indent into pore regions (see detail in Supplementary Note 4). High-temperature nanoindentation testing was also performed using the Hysitron TI 950, equipped with a high-temperature sample stage (xSol platform, maximum operating temperature 923 K). Temperature control was achieved via thermocouples positioned at the top and bottom of the chamber (temperature fluctuation ± 2 K), with a data acquisition rate of 200 pts/sec. Dynamic mechanical analysis (DMA) experiments were conducted on macroscopic samples with external dimension of about 3 × 3 × 3 mm³ by applying a sinusoidal displacement with a frequency of 1 Hz and an amplitude of 20 μm under a constant heating rate of 5 K/min. The test samples were fabricated with dimensions of about 3 × 3 × 3 mm³. The loss factor (tanδ) was derived from the measured storage modulus (G’) and loss modulus (G”) via the formula tanδ = G”/ G’.

Finite element simulation

The finite element (FE) simulations in this work employ a phenomenological constitutive model and do not explicitly account for microscale physical mechanisms. This simplification is justified by the scope of our study: the simulations are primarily intended to fit the experimental data obtained at room temperature. Thus, the oxide layer remains solid-like and does not undergo phase transitions. While a fully predictive model incorporating all observed physics remains beyond the current model, our approach effectively captures the essential mechanical response and provides valuable insights into the underlying deformation mechanisms. The material properties of individual ligaments used in FE simulations were estimated under the homogeneous model by fitting the experimental stress-strain curves of the micropillar compression test. For the heterogeneous model, we defined 21 material parameters that follow a lognormal distribution, which is inspired by nanoindentation results. And such distribution possesses a mean elastic modulus and yield strength consistent with those obtained from the homogeneous model. Subsequently, using a Python-based random number generator, we assigned each meshed element a random index drawn from the lognormal distribution, which was then mapped to the above-mentioned predefined list of material parameters to construct the heterogeneous model. All simulations were conducted using the commercial software Abaqus/CAE 2023. The models used for FE simulations were extracted from the 3D reconstructed data by randomly selecting multiple representative volume elements of 10 × 10 × 10 mm³. This approach guaranteed statistical reliability and accounted for microstructural heterogeneity. The extracted FE model was discretized using second-order tetrahedral elements (C3D10M). To capture the failure behavior of ligaments during large deformation, a shear damage model was incorporated to characterize their mechanical response. Rigid platens were positioned at the top and bottom of the model: the bottom platen was fully constrained in all degrees of freedom while in contact with the model, and the top platen applied uniaxial compression under displacement control. The contact between the platen and the architected CCA model, as well as the architected CCA model itself, were set to hard contact. Quasi-static loading conditions were ensured by monitoring the system’s energy balance, maintaining kinetic energy below 5% of internal energy throughout the compression process.

Author contributions

Y.Y. supervised the project and conceived the idea. H.G. fabricated the architected CCAs and performed the primary macro- and micro-mechanical experiments. Y.S.G., Q.W., and H.G. performed the TEM characterization. Q.W. carried out the 3D reconstruction. H.G., Z.Q.C., S.J.H., and A.D.W. performed the high temperature compression test. B.S.G. performed the XPS characterization. Z.X.L. and S.J.H. performed the XRD characterization. H.G. performed the FEM simulation and nanoindentation experiments. H.G., Y.S.G., Q.W., Z.Q.C., Z.X.L., and S.J.H. contributed to the data analysis. H.G. wrote the manuscript. Y.Y. reviewed and edited the manuscript.

Peer review

Peer review information

Nature Communications thanks Haofei Zhou and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

mlY.Y. discloses support for the research of this work from Research Grants Council, the Hong Kong government, through the general research fund with grant numbers CityU11207325 and CityU11202924. Q.W. discloses support for the research of this work from the National Natural Science Foundation of China with grant number NFSC U23A2065.

Data availability

The data generated in this study are provided in the Supplementary Information, Supplementary Dataset and Source Data file. Source data are provided with this paper.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-73884-6.