Boron-assisted synthesis of compositionally complex amorphous oxides via short-range-order-constrained generative design

Abstract

Engineering short-range atomic order offers a promising route to design amorphous solids. Here, we establish a boron-assisted amorphization strategy using ApolloX, a theory-guided, short-range-order-constrained generative framework for identifying low-energy configurations in compositionally complex multielement systems. Using FeCoNiMoBO_x as a model platform, ApolloX generates candidate amorphous structures across varied boron contents. Ab initio molecular dynamics simulations reveal that increasing the boron content suppresses atomic diffusion and crystallization, accompanied by the stabilization of BO₃-centered local motifs that favor amorphous structure formation. Guided by these predictions, we synthesize three FeCoNiMoBO_x compositions with distinct boron contents and use synchrotron scattering and electron microscopy to confirm their compositional fidelity, structural homogeneity, and targeted amorphous characteristics, thereby validating the predicted boron-dependent structural evolution. We further extend this strategy to a broader library of multimetal BO_x compositions spanning diverse metal combinations and boron loadings. These results identify boron incorporation as an effective and generalizable means of enhancing amorphization and establish a theory-guided framework for the discovery of compositionally complex amorphous materials.

INTRODUCTION

Amorphous materials play an important role across ceramics, glasses, catalysts, and energy-storage systems. The high compositional tunability makes them an excellent platform for multicomponent solid synthesis at the atomic level and has led to their extensive applications due to their diverse local coordination environments and cocktail effect (1–3). Unlike crystalline solids, which have long-range periodicity, amorphous phases lack long-range order and are instead dominated by short-range order (SRO) (4–7). Consequently, variations in local bonding motifs and coordination statistics often exert a stronger influence on functional properties than the global symmetry. Recent experimental studies have demonstrated that differences in SRO can modulate electrochemical behavior, including oxygen evolution, oxygen reduction, and redox activity in battery cathodes (8–11). These findings highlight the critical importance of understanding and tuning SRO in amorphous systems. Yet, establishing quantitative links between composition, local structure, and amorphization behavior in multicomponent solids remains highly challenging due to the unpredictable nature of the amorphous structure.

Amorphous solids exhibit a rugged energy landscape in which many metastable configurations are accessible even at a fixed global composition (12), and the specific SRO motifs realized experimentally often depend sensitively on the synthesis pathway (13). In practice, melt-quench molecular dynamics (MD) is highly effective for modeling amorphous structures formed under fast annealing conditions, capturing key trends of amorphization and local structural evolution (14–16). However, directly simulating experimentally relevant slow synthesis rates with MD is often computationally prohibitive (17–21). Therefore, identifying low-energy local environments that are accessible under slow synthesis conditions can serve as a practical surrogate for direct slow-rate MD. In 1953, Brown and colleagues (22) first reported the preparation of amorphous catalysts using boron-based chemistry, thus opening up the application of amorphous materials in catalysis. Our previous work also confirmed that B doping can effectively reduce the coordination number of metal sites in metal oxides (23), but the associated boron-centered structural changes could not be fully resolved. Extending these insights to chemically complex, multimetal oxides requires a framework that can systematically explore how composition governs diffusion behavior, local bonding motifs, and the resulting amorphous structure.

In this study, we investigate how boron content regulates SRO and amorphization in multimetal BO_x systems by integrating a boron-assisted synthesis route with ApolloX. ApolloX is a structure-guided, SRO-constrained generative framework designed to identify low-energy and physically plausible amorphous configurations with prescribed compositions and local-order characteristics. In its current implementation, the generative and particle swarm optimization (PSO) framework is designed to optimize structural stability and energetics, with functional properties evaluated in subsequent screening and analysis. Consequently, the generated low-energy structures are evaluated via downstream density functional theory (DFT) calculations to assess their catalytic activity and electronic properties. As a representative testbed, we apply this integrated approach to an oxygen evolution reaction (OER)–relevant transition-metal system containing Fe, Co, Ni, Mo, B, and O (24–26). Boron has a small covalent radius and readily integrates into metal-oxygen networks, whereas B₂O₃ is a well-established glass former that promotes amorphization by disrupting long-range periodicity and suppressing phase separation, crystalline domains, and interfacial boundaries (27, 28). Using FeCoNiMoBO_x as a representative platform, we combined ApolloX with ab initio molecular dynamics (AIMD) to quantify how boron concentration modulates BO₃ formation, metal-oxygen coordination motifs, and atomic diffusion—key factors that collectively control amorphization and can ultimately affect water oxidation activity. Guided by these predictions, we first synthesize three representative compositional groups and perform rigorous, multimodal characterization to confirm compositional fidelity, structural homogeneity, and the targeted amorphous/SRO features, thereby supporting the feasibility of the proposed synthesis strategy and the boron-regulated structural trends predicted by theory. Building on this validation, we further extend the approach to a broad library of distinct multimetal BO_x amorphous compositions (spanning diverse metal combinations and boron loadings), demonstrating the generality and transferability of the boron-assisted route for composition-driven tuning of amorphous structures in multicomponent oxides.

RESULTS

The ApolloX-guided design framework for multielement amorphous solids is schematically summarized in Fig. 1. In this workflow, ApolloX first generates statistically representative local short-range-ordered configurations for chemically complex multimetal BO_x systems (Fig. 1A), providing atomic-level insight into how different metal and boron contents reshape the local coordination environment. These configurations are then used as starting points for AIMD simulations, which reveal the dynamic formation of BO₃ motifs, the associated lower diffusion rates, and the resulting enhancement of amorphization. Guided by these theoretical insights, we design a composition-controlled synthesis strategy (Fig. 1B), in which both the identity or ratio of metal cations and the boron content are tuned so that higher boron loadings promote stronger amorphization. Last, this integrated computational-experimental strategy culminates in synthesizing the predicted compositions and validating their amorphous structure and elemental distributions using electron microscopy and spectroscopy (Fig. 1C). Building on this framework, we next establish a boron-assisted amorphization platform for chemically complex multimetal BO_x catalysts.

Fig. 1. ApolloX-guided design of boron-assisted amorphous multimetal BO_x catalysts.

(A) ApolloX workflow for generating statistically representative local SRO environments in multimetal BO_x compositions, enabling direct visualization of metal-oxygen and boron-oxygen coordination motifs. Dynamic behavior analysis by AIMD based on ApolloX-derived structures, revealing the emergence of BO₃ motifs that act as diffusion-slowing units and promote amorphization. (B) Translation of these insights into a boron-content-programmable synthetic strategy within a controlled compositional window, in which the boron content is systematically tuned while the overall compositional regime is controlled; increasing boron content strengthens BO₃-rich networks and enhances the tendency toward amorphous structures. (C) Experimental realization and validation of the designed multimetal BO_x catalysts, including amorphous nanoparticle morphology, diffuse electron-diffraction halos. Structural visualizations were generated using VESTA (55) and OVITO Basic (56).

ApolloX: An SRO-constrained framework for predicting low-energy local environments in multielement amorphous solids

For amorphous solids, the final structure is highly sensitive to the kinetic pathway of synthesis, with slower assembly generally yielding more relaxed, lower-energy local environments. To efficiently identify the low-energy structural motifs accessible to a specific multicomponent composition, we developed ApolloX (Automatic Prediction by generative mOdel for Large-scaLe Optimization of X-composition materials). Unlike traditional brute-force, atom-by-atom exploration of the full configurational space, ApolloX uses an SRO-constrained conditional generative framework. It predicts physically plausible, low-energy SRO patterns, represented as local coordination environments, that are consistent with prescribed thermodynamic conditions. This strategy transforms amorphous structure discovery into a guided optimization within a reduced SRO space, substantially improving search efficiency.

As outlined in Fig. 2A, the ApolloX workflow comprises four main stages. First, we use the pair density matrix (PDM) as a compact, size-independent K × K descriptor (where K is the number of element types) to capture local chemical environments and SRO statistics (Fig. 2B and Supplementary Text, Section A). Second, an in-house conditional generative model (Cond-CDVAE; Fig. 2C) is trained on 10,000 reference structures to learn the statistical mapping between PDMs and atomic configurations. At inference, the model generates atomic structures conditioned on target PDMs. Third, candidates are rapidly relaxed and screened for thermodynamic stability based on formation enthalpy and configurational entropy (Fig. 2D), using the fine-tuned DPA-2 machine learning interatomic potential (29). Last, a population-based PSO (managed via PySwarms; Fig. 2E) iteratively refines the SRO toward lower-energy configurational manifolds. To preserve structural diversity and prevent trapping in local minima, 60% of the lowest-energy structures are retained in each PSO cycle, whereas the remainder are regenerated.

Fig. 2. Overview workflow of ApolloX.

(A) Main workflow of ApolloX for structural modeling, including the model’s iterative generation process. (B) Structures are represented using the PDM, and a dataset is constructed by mapping each structure to its corresponding PDM. (C) Model architecture of the Cond-CDVAE. An embedding network (EMB) integrates a structure’s composition (Comp.) and PDM into a unified conditioning vector. The graph neural network encoder (PGNNEnc) encodes the structure alongside its conditioning vector into a latent vector, capturing its underlying features. Subsequently, a multilayer perceptron MLPL predicts the lattice parameters based on the latent vector. The graph neural network decoder (PGNNDec) outputs a score function for denoising and reconstruction of a plausible structure. (D) Enthalpy stability is evaluated using the convex hull method, and entropy stability is assessed based on configurational entropy. (E) PSO is used to optimize the PDM, using the PYSWARMS package. Structural visualizations were generated using OVITO Basic (56).

To demonstrate the methodological advantage of ApolloX for compositionally complex disordered materials, we benchmarked it on a chemically diverse boron-rich oxide, Fe₁₂Co₁₂Ni₁₂Mo₁₂B₁₂O₆₀ (120 atoms; Supplementary Text, Section B), chosen as a representative charge-balanced multicomponent amorphous system. Starting from 10,000 randomly generated configurations constructed by elemental substitution on a body-centered cubic parent phase, with analogous tests on face-centered cubic and hexagonal close-packed lattices (Supplementary Text, Section C), ApolloX accurately reconstructed the target SRO, yielding mean relative PDM errors typically below 20 to 25%. Benchmark comparisons with representative baseline approaches, including random initialization, special quasirandom structures, Monte Carlo (MC)–only sampling, and Metropolis Monte Carlo (MMC), further demonstrate its improved efficiency in identifying low-energy structures. Among 1500 evaluated structures, 1.7% of ApolloX-generated configurations fell below an energy threshold of −960 eV, compared with 1.2% for the extensive MMC baseline and below 0.3% for the other methods.

Notably, ApolloX identified five ultralow-energy configurations below −990 eV, whereas such configurations were not observed by the baseline approaches. Beyond introducing PDM as a compact descriptor, the key innovation of ApolloX lies in reformulating amorphous-structure prediction as an efficient, directed search in a fixed-dimensional SRO space. By projecting a large off-lattice amorphous configuration onto a compact K × K PDM representation and coupling this space with conditional generative modeling and PSO searching strategy, ApolloX enables directed exploration of thermodynamically favorable amorphous motifs that would be difficult to access through direct optimization in the full atomic-coordinate space. Consistent with this design, the generated structures exhibit high coverage, uniqueness, and novelty across the configurational landscape (figs. S1 and S2 and table S2), whereas PSO evolution from 100 generated seeds rapidly identifies low-energy amorphous configurations within only a few generations. Furthermore, analysis of 1500 relaxed structures reveals a correlation between PDM deviation from the ground-state motif and the potential energy (fig. S1E), confirming that the PDM-based representation captures the essential energetic information of the amorphous landscape and provides an effective optimization coordinate for low-energy amorphous structure discovery.

Boron-controlled diffusion and amorphization tendency from MD

To investigate how boron influences amorphization and local structure, we combine ApolloX with AIMD to examine a series of multimetal BO_x compositions. ApolloX was used to generate SRO-consistent configurations containing 6, 9, and 12 atomic % (at %) B (Group-1, Group-2, and Group-3, respectively) as representative low-boron, intermediate-boron, and high-boron compositions within an experimentally accessible range. This series was designed to probe boron-dependent changes in amorphization and SRO while maintaining a predominantly multimetal-oxide framework; it was not intended to represent a globally optimized activity window. These structures serve as starting points for assessing how incremental changes in boron concentration affect microstructure and stability. For each composition, 1500 candidate structures are sampled and the lowest-energy configurations, which implicitly reflect both enthalpic and configurational-entropy contributions, are selected for further analysis and to define the composition window later realized experimentally. The predicted local-structure maps and elemental enrichment heatmaps (Fig. 3A) show that increasing boron content drives a transition from dispersed to aggregated metal distributions. Comparison of the atomic structures across the three groups reveals a clear evolution in SRO: In Group-1 (low boron), metal-O-metal connectivity dominates, whereas increasing boron causes oxygen to preferentially coordinate with boron, forming BO₃ motifs in which boron is threefold coordinated (Fig. 3B). At the highest boron level (Group-3), this shift toward BO₃ formation markedly reduces metal-oxygen interactions and promotes metal clustering (Fig. 3A). These trends highlight the pivotal role of boron in reshaping local SRO, driving a crossover from metal-O-metal connectivity toward B-O coordination and direct metal-metal interactions, consistent with experimental bonding analysis that indirectly confirms the presence of BO₃ units.

Fig. 3. SRO evolution and diffusion-limited amorphization mechanism.

(A) Nearest-neighbor statistics heatmaps for three boron contents. (B) Higher boron promotes short-range B-O ordering and metal clustering. (C) MD-derived diffusion coefficients show boron diffuses more slowly than metals (300 to 2050 K, 24 ps). (D) Enriched BO₃ motifs reduce mobility, hinder rearrangement, and favor amorphization. (E) B K-edge XANES of Group-1/2/3 versus B₂O₃: BO₃ (∼194 eV) and BO₄ (∼198 eV); increasing BO₃ indicates trigonal boron enrichment. a.u., arbitrary units. (F) Time-resolved snapshots show BO₃ clusters evolve into a percolating network (structural arrest) before partial breakup at high T. Structural visualizations were generated using VESTA (55).

From a kinetic standpoint, crystallization requires local atomic rearrangements into ordered motifs, and its nucleation and growth rates are therefore set by atomic diffusion. When diffusion is slow, crystallization is hindered and the temperature-time window for forming or retaining an amorphous state expands (30, 31). This diffusion-amorphization relationship is well established in solid-state amorphization and diffusion-couple systems: Reduced atomic mobility (or slower structural relaxation) suppresses crystallization and promotes vitrification, thereby shaping the resulting amorphous structures (32–36). In multicomponent and high-entropy systems, complex chemical environments further suppress diffusion and slow structural relaxation, enhancing amorphous stability (37, 38). In such settings, the slowest diffusing species effectively acts as a kinetic bottleneck for structural restructuring (39–41). To test this diffusion-controlled picture, we perform AIMD simulations with varying boron concentrations, heating each system from 300 to 2050 K over 24 ps (Fig. 3, C, D, and F). Here, the AIMD heating ramp is used as a comparative kinetic probe (relative mobility across compositions), rather than a direct model of experimental synthesis. Quantitative analysis of diffusion coefficients shows that the low-boron group exhibits a higher overall diffusivity (fig. S5). Figure 3C reveals that increasing boron content systematically suppresses metal and boron atomic diffusion; among all elements, boron diffuses the slowest and its mobility decreases most steeply as its concentration increases. The time evolution of the mean squared displacement (MSD) for boron exhibits a pronounced stagnation plateau between 12.5 ps and 20 ps in the high-boron system, coinciding with a transient “frozen” state. Structural snapshots (Fig. 3F) show that, during this plateau, boron atoms form locally stable BO₃ triangular motifs that percolate into a short-range network, strongly restricting boron mobility. Upon further heating, thermal energy disrupts the BO₃ framework and restores diffusion.

Within this framework, boron-regulated SRO, particularly the increasing prevalence of BO₃-centered local environments together with the accompanying metal clustering, is associated with reduced atomic mobility and an enhanced tendency toward amorphization. This behavior suggests that the system can transiently access a low-mobility, short-range-ordered state before further thermal activation drives it toward a more disordered and diffusive regime. Figure 3D summarizes the proposed boron-assisted amorphization mechanism. Specifically, boron incorporation is proposed to introduce local geometric distortion through the formation of BO₃-centered motifs and boron-rich local environments, thereby disrupting long-range structural coherence and kinetically frustrating crystallization, which together favor the formation of an amorphous structure. As shown in Fig. 3E, the B K-edge x-ray absorption near-edge structure (XANES) spectra of Group-1 to Group-3 are dominated by an intense feature at ∼194 eV, which is assigned predominantly to trigonal BO₃ coordination based on comparison with commercial B₂O₃ and previously reported spectra of structurally well-defined borate and borosilicate reference compounds (42–44). Notably, the BO₃-related feature increases progressively from Group-1 to Group-3, consistent with progressive enrichment of trigonal boron environments. Only a weak BO₄-related shoulder is observed at ∼197 to 199 eV. Accordingly, the B K-edge XANES analysis presented here is qualitative rather than quantitative.

To further validate our theoretical model of boron-assisted amorphization and confirm the robustness of the diffusion-based interpretation across a broader compositional space, we constructed an approximately equal-ratio theoretical series containing 0 to 20 at % B (g1 to g11) (fig. S6). Using ApolloX to generate low-energy candidates, we established a controlled framework to systematically quantify the macroscopic effects of boron. These candidate structures were simulated using the fine-tuned DPA-2 potential (29). For each composition, diffusion coefficients and short-range-order descriptors were averaged over 10 independent trajectories. Thermodynamically, formation-energy calculations reveal that the fundamental structural competition lies between local metal-O and B-O configurations (fig. S7). With the exception of molybdenum, the formation energy of B₂O₃ is comparable to or lower than those of the corresponding transition-metal oxides. This confirms that B-O motifs are highly competitive, locally redistributing oxygen from metal environments to borate-like configurations; this oxygen scavenging fragments the continuous metal-oxygen framework and drives the metal aggregation observed in our experiment-constrained maps (Fig. 3A). Kinetically, consistent with the diffusion-controlled mechanism discussed above, our MLP-driven simulations demonstrate a systematic decrease in both overall atomic diffusion (fig. S6A) and bond-orientational order parameters (fig. S6B) as the boron content increases.

Collectively, this broad compositional series confirms that boron promotes amorphization through a synergistic mechanism: Thermodynamically, it introduces robust oxygen competition that disrupts long-range networks of metal oxides; kinetically, it acts as a universal slow-diffusing bottleneck that suppresses overall atomic mobility and stabilizes disordered short-range environments.

Synthesis of amorphous catalysts and experimental validation of boron-driven amorphization

Guided by the dynamical and thermodynamic insights provided by ApolloX, we developed a general boroxide-mediated route for the synthesis of amorphous multimetal oxide catalysts (details of the synthesis method are provided in Supplementary Text, Section I). This protocol could be extended across a broad range of chemical complexities, including binary, ternary, quaternary, quinary, 8-component, 10-component, and even more compositionally complex systems (Fig. 4). The x-ray diffraction (XRD) patterns of all synthesized samples show no sharp crystalline peaks (Fig. 4A), demonstrating that this strategy consistently yields amorphous products over a wide compositional space. For the representative 10-element catalyst, annular dark-field scanning transmission electron microscopy (ADF-STEM) imaging and the corresponding EDS elemental maps further reveal a homogeneous spatial distribution of all constituent elements without obvious phase segregation (Fig. 4D), supporting the chemical uniformity of the resulting amorphous phase. As exemplified by the quinary FeCoNiMoBO_x system, equimolar volumes of 0.2 M Fe(NO₃)₃, Co(NO₃)₂, Ni(NO₃)₂, and (NH₄)₆Mo₇O₂₄ solutions were first prepared and maintained at 4°C, whereas a separately prepared 5 M NaBH₄ solution was refrigerated for 72 hours before use. In an ice bath, the metal-salt solutions were combined, followed by rapid addition of hydrolyzed NaBH₄ at half the total metal-solution volume under vigorous stirring for 30 min; the resulting mixture was then kept at 4°C for 18 hours to complete amorphization. We consider the use of highly concentrated and fully hydrolyzed NaBH₄ to be critical because its hydrolysis generates a strongly alkaline environment rich in boron-oxygen species and reducing borohydride complexes. Control experiments (fig. S12A) further show that prolonged NaBH₄ hydrolysis suppresses the low-binding-energy B-M (M = metal) component, indicating that complete hydrolysis is important for preventing the formation of metal-boron species. Under these conditions, the boron-oxygen species inhibit rapid metal migration while simultaneously coupling to the metal centers, and boron derived from the reducing species can be incorporated into the oxide matrix. These synergistic effects collectively favor the formation of homogeneous amorphous metal borate/oxide networks.

Fig. 4. Universality of the synthetic strategy.

(A) XRD patterns of the synthesized boron-containing multimetal oxides, from medium-entropy to high-entropy compositions, all exhibiting broad diffuse features characteristic of amorphous structures. (B) Linear sweep voltammetry (LSV) curves for the OER measured in 1.0 M KOH without iR compensation. (C) Corresponding overpotentials required to reach a current density of 10 mA cm⁻². (D) ADF-STEM image and corresponding EDS elemental maps of the 10-element high-entropy amorphous catalyst, AlMnFeCoNiCuZnMoSnWBO_x, showing the homogeneous spatial distribution of the constituent elements.

Having established the generality of this synthetic route, we next evaluated the OER performance of the synthesized compositions. Among them, the fully amorphous quinary FeCoNiMoBO_x catalyst exhibited the best activity, delivering an overpotential of only 222 mV at 10 mA cm⁻², markedly lower than those of commercial IrO₂ and crystalline layered double hydroxides (LDHs) (Fig. 4, B and C). The optimal amorphous FeCoNiMoBO_x demonstrates highly competitive OER activity compared with recently reported multimetal amorphous and high-entropy oxide/(oxy)hydroxide catalysts while maintaining excellent durability under industrially relevant current densities (table S6). We therefore selected FeCoNiMoBO_x as it provides both optimal catalytic performance and a well-defined compositional platform for isolating structure-property relationships. Within this system, the boron content could be systematically tuned by varying the reaction time. Specifically, reactions carried out for 3, 6, and 18 hours yielded three FeCoNiMoBO_x samples with distinct boron loadings, denoted as Group-1, Group-2, and Group-3, respectively. ICP-OES (inductively coupled plasma optical emission spectrometry) analysis confirms that the experimentally obtained compositions are highly consistent with the intended designs, with boron contents of 5.87, 8.47, and 11.68 at %, closely matching the nominal 6, 9, and 12 at % levels (table S4). This well-controlled composition series therefore provides an appropriate experimental platform for testing the boron-dependent structural evolution predicted by ApolloX.

We then carried out multimodal structural characterization to benchmark the synthetic strategy and to test the predicted boron-driven amorphization trend. XRD results suggest that weak oxide-related peaks progressively broaden and diminish with increasing boron content (Fig. 5A). Synchrotron XRD further shows that, although all three samples lack sharp Bragg reflections (fig. S8), the diffraction features become progressively broader and weaker from Group-1 to Group-3, consistent with a gradual transition from partially crystalline to predominantly amorphous structures. The corresponding pair distribution functions (PDFs) (Fig. 5B) likewise show the progressive disappearance of weak long-range periodicity with increasing boron incorporation.

Fig. 5. Structural characterization of FeCoNiMoBO_x samples with varying boron contents.

(A) XRD patterns of Group-1, Group-2, and Group-3 samples, showing the disappearance of long-range diffraction peaks and progressive amorphization with increasing boron content. (B) Experimental PDFs [G(r)] revealing changes in local atomic ordering. (C) Short-range G(r) curves highlighting the relative intensities of M-O, M-M, and M-O-M correlations for each group. (D) Fourier-transformed EXAFS fitting curves in the R-space EXAFS spectra of the Co K-edge, showing a decrease in Co-O coordination and an increase in Co-M interactions as boron content increases. (E) Wavelet-transform EXAFS contour plots of Co foil, Co₃O₄, and the three sample groups, where the shift from Co-O-Co to Co-M scattering paths with higher boron levels is evident.

Together, these observations indicate that higher boron contents are associated with a stronger tendency toward amorphization, in agreement with the theoretical predictions. Short-range PDF analysis (Fig. 5C) further suggests that this structural evolution is accompanied by disruption of M-O-M linkages, likely because increasing boron redistributes oxygen from the parent oxide network and promotes M-M interactions. At the same time, the remaining M-O coordination helps maintain structural homogeneity and suppress macroscopic phase separation.

The x-ray absorption measurements provide further support for this local structural evolution. XANES results indicate that the transition-metal elements retain broadly similar average oxidation states across the three groups (fig. S10). In the R-space extended x-ray absorption fine structure (EXAFS) spectra at the Co K-edge (fig. S11), increasing boron content weakens the Co-O contribution while strengthening Co-M coordination, consistent with a progressive breakdown of oxide-like M-O-M connectivity and the emergence of stronger M-M associations. Similar trends are also observed at the Ni and Fe K-edges.

Wavelet-transform analysis of the Co K-edge EXAFS spectra (Fig. 5E) shows a systematic shift of the [χ_(k), χ_(R)] intensity centroid from Co-O-Co to Co-M scattering as the boron content increases, and the corresponding Co EXAFS fits in R space (Fig. 5D) reproduce the experimental features with low R factors (table S5). Consistently, the short-range-order parameter α_ij quantitatively captures the same trend (45), indicating reduced metal-oxygen connectivity and enhanced metal-metal association with increasing boron content from Group-1 to Group-3 (fig. S9). To further examine the boron chemical environment, we performed high-resolution B 1s x-ray photoelectron spectroscopy (XPS) measurements (fig. S12). The final Group-1 to Group-3 samples are dominated by oxidized B-O components, with no detectable low-binding-energy feature characteristic of metal-boron bonding within the experimental sensitivity. This assignment is also supported by the B K-edge XANES spectra (Fig. 3E), which are dominated by the BO₃-related feature. Together, the XRD, PDF, microscopy, XPS, and XAS (x-ray absorption spectroscopy) results support a coherent structural picture in which increasing boron content progressively drives FeCoNiMoBO_x away from oxide-like long-range order toward a more homogeneous amorphous network with modified metal-oxygen coordination and predominantly oxidized boron coordination, broadly consistent with the structural evolution predicted by ApolloX.

Amorphization strategy for multicomponent boroxide catalysts and functional validation in FeCoNiMoBO_x

To probe the boron-dependent structure-property relationships, we investigated three FeCoNiMoBO_x compositions (Group-1 to Group-3) with metal ratios nearly constant for OER performance. The overpotentials at a current density of 100 mA cm⁻² decrease from 515 to 483 and 456 mV from Group-1 to Group-3 (fig. S13), indicating that higher boron content is associated with improved OER performance under demanding operating conditions. To better understand the origin of this trend, electrochemical impedance spectroscopy (fig. S14) was performed. The Nyquist-arc diameter decreases from Group-1 to Group-3, indicating progressively improved interfacial charge-transfer behavior. Together with the simulated enhancement in metal-metal SRO, these results suggest that boron-induced local structural ordering facilitates electron transfer across the catalyst/electrolyte interface. However, the improvement in charge-transfer behavior does not translate proportionally into the polarization observed at industrially relevant current densities, suggesting that the remaining overpotential cannot be explained solely by the local short-range-order motif but likely also involves additional electrode-level processes beyond the atomic-scale structural optimization considered in the present framework. To better understand this trend, we combined operando spectroscopy with electronic-structure analysis. In situ near-ambient-pressure x-ray photoelectron spectroscopy (NAP-XPS) shows that Co undergoes the most pronounced potential-dependent surface-state evolution in the multicomponent FeCoNiMoBO_x matrix, whereas the Fe 2p and Ni 2p spectra change much less (fig. S15). These observations identify Co as the most responsive redox-active surface center under OER conditions and motivate the use of Co-centered electronic descriptors. Within this framework, λ₁ and λ₂ are used as PDOS-derived initial-state descriptors (46) that quantify the degree of unoccupied Co 3d states and the number of electronically accessible active states for interfacial charge transfer, respectively (fig. S16). Both descriptors increase monotonically with boron content, consistent with the experimentally observed decrease in overpotential from Group-1 to Group-3. This agreement suggests that boron incorporation systematically modifies the Co-centered electronic structure in a manner favorable for OER, although it does not by itself identify the full operando active phase or isolate a single microscopic origin of activity.

We further assessed durability in an anion-exchange-membrane water electrolyzer (AEMWE). At 500 mA cm⁻², all three FeCoNiMoBO_x electrodes show stable operation, whereas Group-3 exhibits the lowest voltage increase rate, 0.227 mV hour⁻¹ over 811 hours, substantially better than commercial IrO₂ under identical conditions (fig. S13). Operando Raman spectroscopy (fig. S13C) of Group-3 likewise shows no detectable crystalline metal-oxide vibrational features across the applied potential range while retaining a persistent -OH–related band near 773 cm⁻¹, indicating that the catalyst maintains a structurally robust disordered framework during operation.

Together, these results support a consistent structure-property interpretation for FeCoNiMoBO_x: Increasing boron content correlates with changes in both local structure and electronic structure, including reduced M-O-M connectivity, enhanced Co-M/M-M near-neighbor correlations, and more favorable Co-centered initial-state electronic descriptors. These effects collectively align with the experimentally observed improvements in activity and durability and suggest that boron tunes the local catalytic environment in a cooperative way.

DISCUSSION

Here, we demonstrate that short-range-order-guided generative design provides a practical route to compositionally complex amorphous oxides. By coupling ApolloX with boron-assisted synthesis, we identify a physically interpretable amorphization mechanism in which boron stabilizes BO₃-rich local environments, restricts atomic diffusion, and promotes structural disorder while retaining functionally relevant metal-metal interactions. The agreement between theoretical predictions and experimental observations for FeCoNiMoBO_x suggests that this framework can move amorphous-material discovery beyond empirical trial-and-error toward structure-informed design.

The results for AlMnFeCoNiCuZnMoSnWBO_x further clarify that compositional complexity alone does not guarantee enhanced catalytic performance through a high-entropy or “cocktail” effect. From the perspective of the present SRO framework, increasing the number of constituent elements expands the diversity of accessible local atomic environments but does not necessarily increase the population of catalytically favorable motifs. Although Fe, Co, Ni, and Mo are established components for alkaline OER, the introduction of less active elements such as Al, Cu, and Zn may dilute active-site populations and disrupt favorable interactions among the catalytically relevant metals, leading to lower activity than that of FeCoNiMoBO_x (24, 26, 47). This 10-metal composition was designed to test the compositional scope of boron-assisted amorphization rather than to maximize OER performance. Its successful formation as a chemically homogeneous amorphous material therefore demonstrates the structural generality of the strategy while also showing that compositional generality and catalytic optimization are distinct objectives.

This distinction outlines both the fundamental scope of the present framework and its primary directions for future extension. Now, ApolloX operates as a thermodynamics-driven generative framework, wherein the search logic is governed strictly by structural plausibility and energetic stability rather than targeted functional properties. As a result, property metrics such as the electronic descriptors used in this work are evaluated postgeneration as downstream benchmarks rather than active feedback signals. Structurally, the pair-based PDM representation also leaves room for improvement in capturing higher-order angular correlations and medium-range order. To transition from stable structure discovery to true property-directed inverse design, future extensions should directly incorporate property-predictive models into the SRO-constrained search loop. This integration will enable prospective, function-oriented optimization and broaden the framework’s applicability across diverse amorphous functional materials.

MATERIALS AND METHODS

PDM descriptor

To encode SRO in the Cond-CDVAE framework both efficiently and without bias, we introduced the PDM as the primary structural descriptor. The PDM counts the number of near-neighbor atomic pairs for each element-element combination within a specified cutoff radius and arranges these counts in a K × K matrix, where K denotes the number of distinct element types. This representation maintains a fixed dimensionality regardless of composition while fully capturing local chemical environments. The PDM is formally defined

$${\text{PDM}}_{\mathrm{\alpha \beta }}\left(r_{\mathrm{c}}\right)=\sum _{i<j}\mathrm{\Theta }(r_{\mathrm{c}}-d_{\mathit{ij}})[{\mathrm{\delta }}_{\mathit{si},\mathrm{\alpha },}{\mathrm{\delta }}_{\mathit{sj},\mathrm{\beta }}+{\mathrm{\delta }}_{\mathit{si},\mathrm{\beta }}{\mathrm{\delta }}_{\mathit{sj},\mathrm{\alpha }}]$$ (1)

where N is the total number of atoms in the simulation cell, i,j ∈ {1,...,N}, s_i denotes the chemical species of atom i (e.g., Fe, Ni, or B), and d_ij is the minimum-image interatomic distance under periodic boundary conditions. The cutoff radius is fixed to r_c = 5.0 Å. Θ_(x) is the Heaviside step function [Θ_(x) = 1 for x > 0, else 0] and δ_a,b is the Kronecker delta. This unnormalized PDM is closely related to the pair-probability form of the multicomponent Warren-Cowley/GM-SRO descriptors (48, 49). Furthermore, similar pair-count descriptors are widely used as radial symmetry functions in modern machine learning interatomic potentials (50), emphasizing the general applicability of this construction. Supplementary Text (Section A) provides the pseudocode for calculating the PDM along with a worked example to illustrate the procedure.

Model details of Cond-CDVAE

The initial training set of 10,000 structures was generated by randomly occupying atomic sites in fixed-lattice structures. These configurations are then optimized using a fine-tuned DPA-2 (29), a machine learning potential capable of handling a wide range of elements. After optimization, each structure is labeled by its PDM.

We adapted the Cond-CDVAE model to generate structures conditioned on the PDM. In our scenario, the conditioning variables include both composition and PDM. The element type of each atom is represented by a categorical embedding vector. The composition is then calculated as a weighted average of the element type embedding vectors based on the number of atoms of each type. Meanwhile, the PDM, represented as a matrix of continuous variables, is flattened into a vector and normalized in the training set. The composition vector and PDM vector are concatenated to form the conditional vector. Other model hyperparameters are provided in table S3. Once trained, Cond-CDVAE (51) can generate additional structures conditioned on the specified PDM, offering a versatile framework to explore diverse SRO configurations in high-entropy materials.

During the generation stage, the target composition and PDM should be provided. These conditioning variables, combined with a latent vector sampled from the latent space, are used by the lattice predictor to predict lattice parameters. Subsequently, the PGNNDec reconstructs a valid structure from random atomic coordinates using Langevin dynamics.

Mean relative error of PDMs

To evaluate the reconstruction error distribution, diversity metrics (uniqueness and coverage), and novelty fraction, it is essential to define a standard for structural similarity. A widely used criterion is the StructureMatcher function in the pymatgen library, which compares crystal structures by accounting for lattice parameters, atomic positions, species ordering, and symmetry operations within specified tolerances to determine whether two structures are crystallographically equivalent. However, matching becomes substantially more challenging as the number of atoms increases (51), and for multicomponent alloys, the properties are not always dictated by the precise coordinates of individual atoms. In a 120-atom system, almost none of the structures are identified as equivalent by this method. Instead, we use a parameter related to the local atomic environment, the mean relative error (MRE) of PDMs, to quantify structural similarity. The MRE is computed by evaluating the relative error of corresponding elements in two PDMs and then averaging over all elements. Because the relative error is asymmetric under the exchange of two structures, we define the MRE between two structures as the smaller of the two values obtained. Two structures A and B are considered equivalent if MRE_(A,B) < δ, where δ is a predefined threshold.

Fine-tune details of DPA-2

The structural complexity of the B₁₂Mo₁₂Co₁₂Fe₁₂Ni₁₂O₆₀ system poses substantial challenges for structure optimization using first-principles methods. Although MLPs have emerged as a promising approach to accelerate quantum mechanical calculations, enabling high-throughput, large-scale, and long-timescale atomic simulations at a substantially reduced computational cost, their accuracy and transferability critically depend on the quality of the training set. However, generating training data from scratch is both computationally expensive and labor-intensive, and MLPs often struggle to generalize beyond the scope of their training data. To address these limitations, we fine-tune the pretrained universal DPA-2 model (29), which uses a universal descriptor trained on a diverse dataset computed at different levels of theory and can be further adapted to specific chemical systems of interest. The DPA-2 descriptor consists of a repinit layer to embed the local atomic environment with a cutoff radius of 6.0 Å; the atomic representation is subsequently updated using six message-passing repformer layers. Specifically, we refine the DPA-2 model using trajectories obtained from AIMD simulations consisting of 2789 frames under a random branch, whose fitting network consists of three hidden layers with 240 neurons each. After 80,000 training steps, the resulting model achieves a root mean square error (RMSE) of 7.76 meV/atom in energy, 139.61 meV/ Å in force, and 0.068 meV/atom in virial, demonstrating its efficacy in accurately describing the targeted system (detailed in fig. S4).

Warren-Cowley SRO parameter

To describe the local environment of multielement materials, the Warren-Cowley SRO parameter (45) is often defined as

$${\mathrm{\alpha }}_{\mathit{ij}}\left(r\right)=1-\frac{P_{\mathit{ij}}\left(r\right)}{c_j}$$ (2)

where i and j denote atomic species, P_ij(r) is the conditional probability of finding an atom of type j at distance r (or within a specific neighbor shell) around a central atom of type i, and c_j is the overall molar (or atomic) fraction of species j in the system. If α_ij(r) = 0, it indicates that the distribution of species j around species i matches the global composition; if α_ij(r) > 0, it implies that species j is deficient (repelled) around species i; if α_ij(r) < 0, it implies that species j is enriched (aggregated) around species i. In an ideal random distribution, α_ij(r) = 0 for any i, j, and r. When the system exhibits SRO, α_ij(r) deviates from 0.

DFT and MD calculations

In DFT calculations, the Perdew-Burke-Ernzerhof generalized gradient approximation and projector-augmented wave (PAW) pseudopotentials implemented in VASP (52–54) code were used. For Fe, Co, Ni, Mo, and B, the number of valence electrons of 8, 9, 10, 6, and 3 were explicitly considered, respectively. The corresponding valence electron configurations are Fe (3d⁶ 4s²), Co (3d⁷ 4s²), Ni (3d⁸ 4s²), Mo (4d⁴ 5s²), and B (2s² 2p¹), which are in agreement with the ZVAL values obtained from our pseudopotential setup. Core electrons were treated using PAW potentials. A plane-wave cutoff energy of 650 eV and Γ-point-only Brillouin-zone sampling were used for structural optimizations, with convergence criteria of 1 meV atom⁻¹ in total energy and 10 meV Å⁻¹ in residual forces.

To refine the generated structures, we fine-tune the pretrained DPA-2 model (29) with selected MD trajectories frames to achieve both accuracy and efficiency in searching for local minima. Geometry optimization with the L-BFGS method implemented was used to relax each candidate structure into a DPA-2–based local minima. The fitness function for these simulations was the free energy at T = 0 K, which reduces to enthalpy, ensuring the physical relevance of the predicted configurations. Although local optimization increases computational cost, it reduces noise in the energy landscape, improves configuration comparability, and produces optimized structures for subsequent analysis.

Supplementary Materials

This PDF file includes:

Supplementary Text

Supplementary Algorithm 1

Tables S1 to S8

Figs. S1 to S16

References