Composition Space Research Articles

Integrated design of aluminum-enriched high-entropy refractory B2 alloys with synergy of high strength and ductility.

Refractory high-entropy alloys (RHEAs) are promising high-temperature structural materials. Their large compositional space poses great design challenges for phase control and high strength-ductility synergy. The present research pioneers using integrated high-throughput machine learning with Monte Carlo simulations supplemented by ab initio calculations to effectively navigate phase selection and mechanical property predictions, developing single-phase ordered B2 aluminum-enriched RHEAs (Al-RHEAs) demonstrating high strength and ductility. These Al-RHEAs achieve remarkable mechanical properties, including compressive yield strengths up to 1.7 gigapascals, fracture strains exceeding 50%, and notable high-temperature strength retention. They also demonstrate a tensile yield strength of 1.0 gigapascals with a ductility of 9%, albeit with B2 ordering. Furthermore, we identify valence electron count domains for alloy ductility and brittleness with the explanation from density functional theory and provide crucial insights into elemental influence on atomic ordering and mechanical performance. The work sets forth a strategic blueprint for high-throughput alloy design and reveals fundamental principles governing the mechanical properties of advanced structural alloys.

Physics-coupled Data-driven Design of High-Temperature Alloys

We present a materials design loop, which streamlines physics-coupled machine learning (ML) surrogate models to discover new alloy chemistries with improved properties. The efficacy is demonstrated by discovering a high-temperature alumina-forming austenitic (AFA) stainless steel with enhanced creep, followed by experimental validation. The ML models have been trained using a well-curated, highly consistent experimental dataset augmented with synthetic microstructural features from a computational thermodynamic approach. We have populated a large number of hypothetical AFA alloys to explore the high-dimensional composition space and have predicted their creep properties by providing the same synthetic input features obtained from the trained ML models. Uncertainties from the ML training were taken as thresholds for truncating predicted results to identify alloys with improved or deteriorated creep. Individual elemental compositions have been determined via probability density distribution analysis from the group of alloys at the top and bottom of the predicted creep values for further virtual and experimental validations. We anticipate that this workflow can be applied to screen desired conditions, such as chemistry and processing parameters, in high-dimensional space through physics-guided data analytics.

Exploring the kinetics and thermodynamics of TiFe0.8CrxMn0.2-x hydrogen storage alloys

The influence of Fe substitution by Cr and/or Mn on the hydrogenation properties of TiFe0.8CrxMn0.2-x hydrogen storage alloys was explored for several substitution amounts (x = 0, 0.05, 0.1, 0.15 and 0.2). The synthesized alloys consisted of a dominant TiFe (cubic, CsCl-type) and a secondary C14 Laves phase (hexagonal, MgZn2-type). The increase in Cr content, and consequently in C14 Laves phase fraction, improved the first hydrogenation kinetics and the hydrogen intake after activation (1.60–1.70 wt% H2 at 30 °C within 3 min), while substantially stabilizing the monohydride phase. The reaction enthalpy obtained from pressure-composition-temperature (PCT) curves hence increased along Cr substitution, ranging 24.35 ± 0.34 to 35.39 ± 1.00 kJmol-1 for the absorption, and 31.08 ± 1.39 to36.34 ± 1.99 kJmol−1for the desorption (absolute values). These experimental findings were in good agreement with density functional theory (DFT) predictions performed across the explored composition space. The estimated entropy values on the other hand remained nearly constant, fluctuating between 84.28 ± 4.76 and 102.64 ± 3.12 J mol−1 H2 K−1 for the absorption, and 100.46 ± 9.71 up to 105.45 ± 4.31 J mol−1 H2 K−1 for the desorption. Solid-gas reaction modeling showed that, under practical service conditions, the hydrogenation of activated alloys was interface-controlled followed by diffusion-controlled mechanisms as the reaction proceeded.

How to Produce Cultural Space for Sustainable Development Towards Rural Revitalization: A Case Study of China

Cultural revitalization is a key factor in the sustainable development of the countryside and is included in the five-dimensional indicators of China's rural revitalization strategy. Although established studies have examined the spatial dimension of rural cultural revitalization, the internal structure of spatial production and the logic of action are still not entirely clear. Based on an interview survey in villages in northern Henan, China, this paper conducts a qualitative study of the structured characteristics of rural cultural spatial production and the actor logic behind it using a grounded theory research method. The results show that the production of local cultural space, socio-cultural space, mass recreational space, and cultural industries space constitute a composite structured rural cultural space. Public power, intellectual elites, residents' rights and industrial capital have demonstrated a “co-constructive” cooperative relationship This paper provides a theoretical and empirical basis for promoting rural cultural revitalization and sustainable development through the production of rural cultural space.

Can Hume-Rothery rules predict single-phase high-entropy rocksalt oxide phases?

ABSTRACT In the quest for understanding and tailoring the formation and properties of entropically stabilised ceramics, rocksalt-structured (MgNiCoCuZn)O occupies a central place. To date, most of the reported high-entropy rocksalt oxides (HERSOs) are derivatives of the original (MgNiCoCuZn)O, and only a couple of other novel HERSOs have been synthesised. To pave the way for the discovery of new HERSOs, we seek rapid and effective methodologies for screening large compositional spaces such as those associate with high entropy oxides. In this letter, we analyse modifications of the Hume-Rothery (HR) rules that govern the formation of solid-solution metallic alloys. We propose that HERSOs can form based on maintaining an oxidation state of +2 for all cations and a low value for the coefficient of variation associated with the lattice constants of the unmixed constituent oxides in a (hypothetical or actual) rocksalt phase. As a result of applying Hume-Rothery-inspired rules, we provide an heuristic explanation for the synthesizability of three experimentally realised HERSOs, and list a significant number of other HERSO compositions that can potentially be realised via similar methodologies. The rules devised in this work for HERSOs should provide guidance for future synthesis efforts, and we expect that community use could lead to further refinements as well as to modifications for application-specific screening.

Unraveling symmetric hierarchy in solid-state reactions of tungsten-based refractory metal carbides through first-principles calculations

Refractory metal carbides, usually fabricated via solid state reactions, require precise control of their reactants and temperature, especially when they enter a complex compositional space, like high-entropy (multi-component) carbides. In this work, the solid-state reactions of tungsten based refractory metal carbides M-W-C (M = Ti, Zr, Hf, V, Nb, Ta) are systematically studied through first-principles thermodynamic calculations and percolation simulations, and its relationship with symmetric principles is unraveled. Symmetric hierarchy is defined by the group-subgroup Bärnighausen tree and the gap in their space group number. It suggests MC and WC/W2C are two possible reactants to form the highest symmetric M-W-C ternary carbides, and indicates the larger the gap in their space group number, the harder the reactions. From the symmetric hierarchy, we found the reaction path from MC to M-W-C ternary carbides is the most probable, supported by the Gibbs reaction free energy. Carbon percolation within the metal framework plays another role in the solid-state reactions of tungsten based refractory metal carbides. It reveals the phase transition from M6W6C to M3W3C undergoes a transient M2W2C. The success in predicting the phase relationship of M-W-C ternary system offers a new paradigm for the design and synthesis of high-entropy carbides, nitrides, and oxides.

Spinel oxide enables high-temperature self-lubrication in superalloys

The ability to lubricate and resist wear at temperatures above 600 °C in an oxidative environment remains a significant challenge for metals due to their high-temperature softening, oxidation, and rapid degradation of traditional solid lubricants. Herein, we demonstrate that high-temperature lubricity can be achieved with coefficients of friction (COF) as low as 0.10-0.32 at 600-900 °C by tailoring surface oxidation in additively-manufactured Inconel superalloy. By integrating high-temperature tribological testing, advanced materials characterization, and computations, we show that the formation of spinel-based oxide layers on superalloy promotes sustained self-lubrication due to their lower shear strength and more negative formation and cohesive energy compared to other surface oxides. A reversible phase transformation between the cubic and tetragonal/monoclinic spinel was driven by stress and temperature during high temperature wear. To span Ni- and Cr-based ternary oxide compositional spaces for which little high-temperature COF data exist, we develop a computational design method to predict the lubricity of oxides, incorporating thermodynamics and density functional theory computations. Our finding demonstrates that spinel oxide can exhibit low COF values at temperatures much higher than conventional solid lubricants with 2D layered or Magnéli structures, suggesting a promising design strategy for self-lubricating high-temperature alloys.

Accelerated Exploration of Empty Material Compositional Space: Mg-Fe-B Ternary Metal Borides.

Borides are a family of materials with valuable properties for various applications. Their diverse structures and compositions, yet disparity in the constituent chemical elements for the known compounds, give elemental substitutions for prototypes great potential for material discovery. To explore uncharted material compositional space, we develop a workflow that joins high-throughput crystal structure prediction and automated diffraction pattern matching to discover new compounds with significant prediction and synthesis hurdles. Utilizing the workflow, we explore the empty Mg-Fe-B ternary compositional space, previously uncharted largely due to the immiscibility of Mg and Fe, as a paradigm. A total of 275 ternary boride prototypes are classified, using which we predict 23 (158) stable and metastable ternary phases within 50 (200) meV/atom above the convex hull. We identify Gd2(FeB)7-type Mg2Fe7B7 and ZrCo3B2-type MgFe3B2 to match previously unsolved experimental powder X-ray diffraction (PXRD) patterns. The discovered Mg2Fe7B7 and related channeled structures feature mismatched Mg and (FeB) sublattice periods, for which we conduct structural analyses with respect to the PXRD. They are predicted to exhibit exceptionally fast superionic transport of Mg and outstanding electrochemical performance, which serve as post-Li-ion battery candidate electrode materials. This result opens a new avenue for borides' potential applications as electrode materials and fast ionic conductors. This work also portrays the map and landscape of ternary metal borides with similar chemical environments. With high efficiency, the prototype- and PXRD-assisted crystal structure prediction workflow opens a new avenue for exploring various material compositional spaces across the periodic table.

Data-driven design of novel lightweight refractory high-entropy alloys with superb hardness and corrosion resistance

Lightweight refractory high-entropy alloys (LW-RHEAs) hold significant potential in the fields of aviation, aerospace, and nuclear energy due to their low density, high strength, high hardness, and corrosion resistance. However, the enormous composition space has severely hindered the development of novel LW-RHEAs with excellent comprehensive performance. In this paper, an machine learning (ML)-based alloy design strategy combined with a multi-objective optimization method was proposed and applied for a rational design of Al-Nb-Ti-V-Zr-Cr-Mo-Hf LW-RHEAs. The quantitative relation of “composition-structure-property” was first established by ML modeling. Then, feature analysis reveals that Cr content greater than 12 at.% is a key criterion for alloys with high corrosion resistance. The phase structure, density, melting point, hardness and corrosion resistance of the alloys were screened layer by layer, and finally, three LW-RHEAs with superb hard and corrosion resistance were successfully designed. Key experimental validation indicates that three target alloys have densities around 6.5 g/cm3, and all alloys are disordered bcc_A2 single-phase with the highest hardness of 593 HV and the largest pitting potential of 2.5 VSCE, which far exceeds all the literature reports. The successful demonstration in this paper clearly demonstrates that the present design strategy driven by the ML technique should be generally applicable to other RHEA systems.

Bayesian Learning Aided Theoretical Optimization of IrPdPtRhRu High Entropy Alloy Catalysts for the Hydrogen Evolution Reaction.

The complex compositional space of high entropy alloys (HEAs) has shown a great potential to reduce the cost and further increase the catalytic activity for hydrogen evolution reaction (HER) by compositional optimization. Without uncovering the specifics of the HER mechanism on a given HEA surface, it is unfeasible to apply compositional modifications to enhance the performance and save costs. In this work, a combination of density functional theory and Bayesian machine learning is used to demonstrate the unique catalytic mechanism of IrPdPtRhRu HEA catalysts for HER. At high coverage of underpotential-deposited hydrogen, a d-band investigation of the active sites of the HEA surface is conducted to elucidate the superior catalytic performance through electronic interactions between elements. At low coverage, a novel Bayesian learning with oversampling approach is then outlined to optimize the HEA composition for performance improvement and cost reduction. This approach proves more efficacious and efficient and yields higher-quality structures with less training set bias compared with neural-network optimization. The proposed HEA optimization theoretically outperforms benchmark Pt catalysts' overpotential by ≈40% at a 15% reduced synthesis cost comparing to the equiatomic ratio HEA.

Ultrafast complete dechlorination enabled by ferrous oxide/graphene oxide catalytic membranes via nanoconfinement advanced reduction

Chlorinated organic pollutants widely exist in aquatic environments and threaten human health. Catalytic approaches are proposed for their elimination, but sluggish degradation, incomplete dechlorination, and catalyst recovery remain extremely challenging. Here we show efficient dechlorination using ferrous oxide/graphene oxide catalytic membranes with strong nanoconfinement effects. Catalytic membranes are constructed by graphene oxide nanosheets with integrated ultrafine and monodisperse sub-5 nm nanoparticles through simple in-situ growth and filtration assembly. Density function theory simulation reveals that nanoconfinement effects remarkably reduce energy barriers of rate-limiting steps for iron (III)-sulfite complex dissociation to sulfite radicals and dichloroacetic acid degradation to monochloroacetic acid. Combining with nanoconfinement effects of enhancing reactants accessibility to catalysts and increasing catalyst-to-reactant ratios, the membrane achieves ultrafast and complete dechlorination of 180 µg L−1 dichloroacetic acid to chloride, with nearly 100% reduction efficiency within a record-breaking 3.9 ms, accompanied by six to seven orders of magnitude greater first-order rate constant of 51,000 min−1 than current catalysis. Meanwhile, the membranes exhibit quadrupled permeance of 48.6 L m−2 h−1 bar−1 as GO ones, because nanoparticles adjust membrane structure, chemical composition, and interlayer space. Moreover, the membranes show excellent stability over 20 cycles and universality for chlorinated organic pollutants at environmental concentrations.

Additive manufacturing of multiscale NiFeMn multi-principal element alloys with tailored composition

Abstract Nanostructured multi-principal element alloys (MPEAs) have been explored as next-generation engineering materials due to unique mechanical and functional properties which have significant advantages over traditional dilute alloys. However, the practical applications of nanostructured MPEAs are still limited due to the lack of scalable processing approaches to prepare a large quantity of nanostructured MPEAs, as well as lack of an efficient pathway for high-throughput discovery of better functional nanostructured MPEAs within their vast compositional space. Here we tackle these challenges by presenting an integrated approach by combining direct-ink-writing-based additive manufacturing, solid-state sintering, and chemical dealloying to manufacture hierarchically porous MPEAs. The hierarchical structure is comprised of macro- and micro-scale pores introduced via extrusion printing and polymer decomposition during sintering, as well as nanoscale pores formed via chemical dealloying. The macro- and micro-scale pores allow efficient dealloying of a large mass of material as the diffusion length that the corroding medium must penetrate remains at the scale of the ligaments formed after sintering (∼10 μm), despite the large volume of the 3D-printed samples. In addition, this integrated approach enables versatile control of the alloy composition via precisely tuning the ratio of elemental powders in the starting ink, thus offering a pathway for high-throughput discovery of novel functional MPEAs. As a case study, multiscale macro/micro/nanoporous NiFeMn MPEAs with three different compositions were investigated as catalysts to reduce the overpotential of oxygen evolution reaction (OER), where NiFeMn-based electrocatalysts display composition-dependent performance such that the overpotential measured at a current of 0.5 A g−1 for OER increases in the order of Ni58Fe29Mn13 ⩽ Ni64Fe26Mn10 < Ni76Fe18Mn6. This introduced manufacturing process offers new opportunities for scalable fabrication and rapid screening of nanostructured multi-component complex alloys.

Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning

AbstractDiverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discretized compositions and possible neighbor-to-neighbor transitions. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and order in procedurally generated simplex grids, keeping the algorithm $${\mathcal{O}}(N)$$ O ( N ) , with minimal memory, enabling rapid construction of graphs with billions of transitions in seconds. Additionally, we demonstrate how such graph representations can be combined to homogeneously express complex path-planning problems, while facilitating efficient deployment of existing high-performance gradient descent, graph traversal, and other optimization algorithms.

Toward Accelerating Discovery via Physics-Driven and Interactive Multifidelity Bayesian Optimization

Abstract Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and often nondifferentiable parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, processing spaces, and molecular embedding spaces. Often these systems are expensive or time consuming to evaluate a single instance, and hence classical approaches based on exhaustive grid or random search are too data intensive. This resulted in strong interest toward active learning methods such as Bayesian optimization (BO) where the adaptive exploration occurs based on human learning (discovery) objective. However, classical BO is based on a predefined optimization target, and policies balancing exploration and exploitation are purely data driven. In practical settings, the domain expert can pose prior knowledge of the system in the form of partially known physics laws and exploration policies often vary during the experiment. Here, we propose an interactive workflow building on multifidelity BO (MFBO), starting with classical (data-driven) MFBO, then expand to a proposed structured (physics-driven) structured MFBO (sMFBO), and finally extend it to allow human-in-the-loop interactive interactive MFBO (iMFBO) workflows for adaptive and domain expert aligned exploration. These approaches are demonstrated over highly nonsmooth multifidelity simulation data generated from an Ising model, considering spin–spin interaction as parameter space, lattice sizes as fidelity spaces, and the objective as maximizing heat capacity. Detailed analysis and comparison show the impact of physics knowledge injection and real-time human decisions for improved exploration with increased alignment to ground truth. The associated notebooks allow to reproduce the reported analyses and apply them to other systems.2

Performance Prediction of High-Entropy Perovskites La0.8Sr0.2MnxCoyFezO3 with Automated High-Throughput Characterization of Combinatorial Libraries and Machine Learning.

Perovskite oxides form a large family of materials with applications across various fields, owing to their structural and chemical flexibility. Efficient exploration of this extensive compositional space is now achievable through automated high-throughput experimentation combined with machine learning. In this study, we investigate the composition-structure-performance relationships of high-entropy La0.8Sr0.2MnxCoyFezO3±𝞭 perovskite oxides (0 < x, y, z <1; x+y+z≈1) for application as oxygen electrodes in Solid Oxide Cells. Following the deposition of a continuous compositional map using thin-film combinatorial pulsed laser deposition, compositional, structural, and performance properties are characterized using six different techniques with mapping capabilities. Random forests effectively model electrochemical performance, consistently identifying Fe-rich oxides as optimal compounds with the lowest area-specific resistance values for oxygen electrodes at 700 °C. Additionally, the models identify a statistical correlation between oxygen sublattice distortion-derived from spectral analysis of Raman-active modes-and enhanced performance.

Bayesian optimization of 7-component (AlVCrFeCoNiMo) single crystal alloy’s compositional space to optimize elasto-plastic properties from molecular dynamics simulations

Abstract Exploring the vast compositional space of high-entropy alloys (HEAs) promises materials with superior mechanical properties much needed in industrial applications. We demonstrate on the 7-component alloy AlVCrFeCoNiMo system with randomly ordered atoms that this exploration of the compositional space can be accelerated by combining molecular dynamics simulations with Bayesian optimization. Our algorithm is tested on maximizing the shear modulus, resulting in pure Mo, an unsurprising result based on Mo’s large density. Maximizing the yield stress results in Co-, Cr- and Ni-based alloys with the optimal composition varying depending on the presence of defects within the crystal. Finally, we optimize the plastic behaviour by aiming for high stresses while minimizing the deformation fluctuations, and find that a predominantly NiMo alloy’s high lattice distortions ensure a smooth stress response. The results suggest that mechanical properties of 2- to 4-component alloys with optimized composition may be superior to those of equiatomic HEAs without short-range order.

Hydrated silicate ionic liquids: Ionic liquids for silicate material synthesis

The development of Hydrated Silicate Ionic Liquids, which are hypo-hydrated room temperature melts of alkali silicates, has created new opportunities for synthesizing porous silicates. Their discovery also allows to reinterpret the role of an ionic liquid for zeolite synthesis and offer unique opportunities to study crystallization in situ. The reduced complexity of HSILs renders them excellent model systems yielding a large space of zeolite phases and framework compositions, and even allowing computer simulations. This work summarizes the impact of alkalinity, hydration, and cation type on silicate speciation and provides physicochemical data spanning relevant temperatures and compositions for zeolite formation. The data is meant as a reference point to further accommodate and verify (computational) models.

Machine learning-assisted design of CaBi2Nb2O9-based ceramics with high piezoelectricity and thermal stability

Calcium bismuth niobate CaBi2Nb2O9 (CBN)-based ceramics are promising candidates for high-temperature piezoelectric applications due to its high Curie temperature. However, the traditional trial-and-error method cannot realize fast design of high-temperature piezoceramics over a wide range of composition space. Based on small sample datasets, a machine learning model was proposed to accelerate the design of CBN-based ceramics with high piezoelectricity and thermal stability. Using the trained gradient boosting regression model, the piezoelectric coefficients are predicted for CBN-based ceramics with different compositions. Based on the machine learning prediction results, we prepared the co-doped Ca1-2x(NaCe)xBi2Nb2-x(W0.75Mn0.25)xO9 (CBNCWM-x) by solid phase reaction method. The results show that co-doping changes the lattice distortion, grain size and domain structures of CBN-based ceramics, realizing the enhanced piezoelectric properties. CBNCWM-0.03 ceramics exhibit an optimum piezoelectric coefficient (d33 ∼ 17.2 pC/N) that is quite close to the predicted result by machine learning model. Moreover, the CBNCWM-0.03 ceramics possess a Curie temperature of 913 °C and maintain 90.7 % of its original d33 value after annealing at 900 °C for 2 h, demonstrating excellent thermal stability. The present work not only provides an approach for the rapid discovery of CBN-based ceramics with high piezoelectricity but also obtains excellent thermally stable ceramics for high-temperature applications.

Research on Spatial Morphological Characteristics and Influencing Factors of Industrial Heritage: A Case Study of Nine Industrial Heritages in Guizhou Province

Industrial heritage, recognized as a significant aspect of historical and cultural heritage, has garnered considerable attention from scholars globally. To elucidate the spatial morphological characteristics and the underlying influencing factors of industrial heritage within karst regions, this study employs methods such as the interstice index, fractal dimension analysis, and spatial syntax. It conducts research on the spatial morphological characteristics of nine typical industrial heritages in Guizhou Province. The primary factors contributing to the variations in layout forms are the intricate karst topography and the functional requirements of production. The functional zoning of industrial heritage aligns with its layout, characterized by straightforward functional zones that have not developed into composite spaces. The overall connectivity of industrial heritage is relatively low, exhibiting weak integration, significant disparities in control values, low average depth values, and a deficiency in comprehensibility and diversity of options. This indicates that the internal connectivity of industrial heritage spaces is generally inadequate, with low accessibility, strong interrelations, average convenience, limited connectivity, and generally acceptable passage. The overall spatial, architectural, and roadway configurations of industrial heritage predominantly exhibit a uniform pattern. Importantly, industrial heritage reveals a highly variable overall spatial form, with an average fractal dimension of 1.57, complex architectural layouts (average fractal dimension of 1.50), and simplistic road network designs (average fractal dimension of 1.43), which collectively suggest high spatial complexity and irregular characteristics. This study can provide a reference for the analysis of spatial characteristics and influencing factors of other material cultural heritages, and it is of great significance for the systematic protection and revitalization of industrial heritage.

Elastic constants from charge density distribution in FCC high-entropy alloys using CNN and DFT

While high-entropy alloys (HEAs) present exponentially large compositional space for alloy design, they also create enormous computational challenges to trace the compositional space, especially for the inherently expensive density functional theory calculations (DFT). Recent works have integrated machine learning into DFT to overcome these challenges. However, often these models require an intensive search of appropriate physics-based descriptors. In this paper, we employ a 3D convolutional neural network over just one descriptor, i.e., the charge density derived from DFT, to simplify and bypass the hunt for the descriptors. We show that the elastic constants of face-centered cubic multi-elemental alloys in the Ni–Cu–Au–Pd–Pt system can be predicted from charge density. In addition, using our recent PREDICT approach, we show that the model can be trained only on the charge densities of simpler binary and ternary alloys to effectively predict elastic constants in complex multi-elemental alloys, thereby further enabling easier property-tracing in the large compositional space of HEAs.