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Single atom, low valent transition metals are important for heterogeneous catalysis but are challenging to generate and stabilize in a well-defined manner. Herein, we explored the functionalization of silica with well-defined N-heterocyclic phosphenium (NHP) ions to heterogenize low-valent metals. The surface electro-statically bound [NHP] + coordinate to Pt(0) precursors resulting in well-defined, chemisorbed [(NHP)Pt(0)L n ] + sites. The resulting materials catalyze the hydrosilylation of alkynes and exhibit activities and selectivities that rival the current industry standard homogeneous catalysts. The catalysts leach Pt limiting their recyclability; however, recycling studies support that the high regioselectivities arise from heterogeneous sites and Pt particles do not form on the surface. Here we suspect that this phosphenium-based immobilization strategy will result in stable, tunable, low valent heterogeneous transition metal catalysts in a wider array of catalytic reactions.
Capillary heterogeneity has been identified over the last decade as a key control on subsurface CO 2 flow behavior during geological CO 2 sequestration. These heterogeneities can be formed in all sedimentary rocks, ranging from slight variations in the sand grain sizes to extensive sequences of interbedded sands, shales, and limestones. Capillary heterogeneity has been largely, although not entirely, overlooked in subsurface flow modeling because it is assumed to only directly influence fluid redistribution over scales of centimeters to meters. However, even small-scale fluid movements can result in dramatic impacts on the mobility and trapping of the CO 2 over kilometers. Therefore, neglecting capillary heterogeneity at multiple scales could potentially lead to errors in modeling and predicting field-scale plume migration. In this review paper, we aim to provide a consistent overview to (1) establish that capillary heterogeneity can have a major impact on CO 2 plume migration, (2) establish the respective length scales at which capillary heterogeneity matters, and (3) provide guidance for numerical modeling. This review covers pertinent literature and extracts key observations from the core to the field scales. Experimental studies have shown that millimeter-decimeter scale capillary heterogeneity can cause the so-called capillary heterogeneity trapping in addition to pore-scale residual trapping. Even at such a small scale, capillary heterogeneity can already lead to complex upscaled constitutive relationships, such as flow-rate dependent and anisotropic relative permeability, which affects field-scale CO 2 migration even when field-scale heterogeneities are present. Under gravity-dominated flow regimes, centimeter-meter scale capillary heterogeneity can entrap a significant amount of CO 2 at field scale, not just after imbibition but also during drainage. In certain cases, the presence of capillary heterogeneity can even completely stop the vertical movement of the CO 2 plume, hence greatly reducing leakage risks. At meter-kilometer scale, the influence of capillary heterogeneity is more pronounced and can hinder or redirect CO 2 migration in both lateral and vertical directions. The impact of capillary heterogeneity across multiple spatial scales poses a great challenge in modeling CO 2 migration at field scale, because it is practically impossible to build a field-scale earth model with grid blocks at millimeter scale. We recommend a hierarchical modeling approach to address this challenge. At field scale, earth models are built to capture geological features and heterogeneities in high but still practical grid resolutions. For each facies or rock type of the field-scale model, high- resolution meter-scale “conceptual” models are built with millimeter-scale grid blocks to capture representative fine-scale bedding geometries and heterogeneities in various environments of deposition, bridging the gap from subcore scale to the size of a field-scale simulation grid block. Upscaling is then used to preserve the smaller-scale flow dynamics of various rock types in field-scale simulations. Here, future work is needed to (1) refine, improve, and validate the hierarchical modeling approach; (2) build libraries of fine-scale bedding models for facies in various environments of deposition; (3) quantify multiscale capillary heterogeneity effects under subsurface uncertainties; (4) gain learning from different storage formations; and (5) establish best practices that balance accuracy and computational speed.
Small-scale heterogeneities can significantly affect the fate of the CO 2 plume and trapping during CO 2 migration. We conducted geologic carbon storage field-scale simulations to investigate the impact of small-scale heterogeneities on plume dynamics and trapping performance. Small-scale heterogeneities have been shown to increase the amount of trapped CO 2 during buoyancy-driven flow. The trapped CO 2 saturation is validated by previous sandbox experimental work during buoyancy-driven flow in realistic heterogeneous domains and is implemented through the critical CO 2 saturation parameter (i.e., the first non-zero value in the drainage CO 2 relative permeability curve). Depending on the type and degree of heterogeneity, various critical CO 2 saturation values are exhibited. Furthermore, we investigated the effect of small-scale heterogeneities when multiple capillary pressure models are employed. This study demonstrates that an increase in critical CO 2 saturation reduces the CO 2 plume size and lateral extent, accompanying an increase in residual trapping and a decrease in solubility trapping. Lastly, we show that independent of the capillary pressure model used, an increase in critical saturation leads to similar CO 2 plume dynamics distribution and trapping performance. These results emphasize the importance of quantifying the effect of small-scale heterogeneity as they affect the large-scale behavior of the CO 2 plume.
Task-based programming models and execution paradigms provide a means to decompose a computation by expressing it as a graph in which each node represents a specific computation operating on memory objects and the edges define the dependencies in the execution flow. In this execution model, independent nodes in the graph can be executed concurrently in different computing devices, making it suitable for heterogeneous systems in which computing devices with different architectures coexist. However, careful memory orchestration across heterogeneous devices is needed because copies of the same memory object may reside in multiple devices during execution. Manually ensuring such an orchestration is quite challenging. Not only must an application developer guard against race conditions, but they must also optimize data movement between the host and devices because unnecessary data movement significantly impacts performance. To mitigate these challenges, we enhance the IRIS heterogeneous runtime and introduce IRIS-MEMFLOW–a data flow–enabled portable memory abstraction for seamlessly orchestrating memory in diverse heterogeneous computing environments. By using data-flow analysis, IRIS-MEMFLOW guards against race conditions while multiple heterogeneous devices access memory objects. IRIS-MEMFLOW also optimizes data movement between the host and devices without manual intervention. As a result, IRIS provides improved programming productivity, performance, and portability for multidevice heterogeneous executions in high-performance computing and cloud systems that run diverse architectures from different vendors. The efficacy of IRIS-MEMFLOW is evaluated through experiments that show its capability in terms of programming productivity, multidevice heterogeneity, portability, and low overhead versus the state of the art.
In the rapidly evolving field of high-performance computing (HPC), effectively leveraging heterogeneous devices through asynchronous task programming is paramount. This paper presents a robust asynchronous task programming model tailored for a multi-device, multi-stream execution environment that incorporates a diverse array of heterogeneous computing units, including GPUs from various vendors and other accelerators. Current state-of-the-art task programming models provide methodologies to support asynchronous task executions, but they typically handle homogeneous devices using native programming languages, while support for heterogeneous devices is limited to frameworks like OpenCL. This gap presents significant challenges in abstracting heterogeneous devices to harness their true asynchronous capabilities effectively using their native programming languages. By implementing asynchronous task execution, our model significantly boosts the performance of tiled algorithm task graphs through overlapping data transfers with computation and enabling the simultaneous execution of multiple kernels. We integrate this approach into a heterogeneous Intelligent Runtime System (IRIS) and assess its performance using a suite of tiled algorithm benchmarks from the heterogeneous math kernels library (MatRIS) based on IRIS. Experimental results demonstrate a performance improvement ranging from 1.6 × to 2 × over IRIS without asynchronous support, and a notable 22% performance enhancement compared to established runtime systems such as StarPU and PaRSEC. This approach significantly improves computation efficiency of HPC workflows and provides a solid base for future exploration and development in the area of asynchronous task programming in heterogeneous systems.
Distinguishing whether a seismic event is an earthquake or an explosion is a core problem in explosion monitoring. For simplistic models, earthquakes produce a predictable S-wavefield based on their radiation pattern, while an explosion produces no S-wavefield. However, observations from nuclear tests show that explosions can produce significant S-wave energy on both horizontal components. We perform numerical experiments using SPECFEM to constrain when an S-wavefield generated from an explosion might differ from one produced by an earthquake. We generate the S-wavefield for our explosions by placing the source location within a small region consisting of large velocity heterogeneities. For the 2D cases investigated here, a crucial condition is that the size of the region of heterogeneities must be much smaller (approximately 1/12th) than the minimum wavelength of the wavefield for our simulation setups. We investigate both isotropic heterogeneities and anisotropic heterogeneities. Initial results demonstrate that the heterogeneous region lowers the P/S amplitude ratios of an explosion. The presence of strong anisotropic heterogeneities near the source can also produce an S-wavefield with similar amplitudes to the P-wavefield. Lastly, we show that S-wave polarization angles vary as a function of azimuth and distance for explosive sources in the presence of small-scale heterogeneities.
Synergizing wire arc-directed energy deposition (WA-DED) additive manufacturing (AM) with particle-strengthened creep strength-enhanced ferritic (CSEF) steels enables fabrication and repair of critical power-plant components. Investigations focused on fusion-welded particle-strengthened CSEF steels, such as Grade 91 steel, have linked microstructurally heterogeneous regions—forming due to heat affected zones (HAZ)—with premature failure during elevated temperature service. Fusion-based AM, including WA-DED, likewise generates microstructurally and plastically heterogeneous regions due to spatiotemporally varying thermokinetics during deposition. However, works investigating such microstructural heterogeneities, their implications for mechanical behavior, and strategies to mitigate their formation remain scarce. This work identifies microstructurally and plastically heterogeneous regions within the WA-DED-processed Grade 91 steel. Spatial microhardness variations in the as-fabricated specimen correlate with the variation in the attributes of grain, martensitic microstructure, and precipitates across the fusion zone and HAZ. Digital image correlation-enabled tensile tests performed at 500 °C revealed pronounced deformation localization and a wave-like strain distribution, with wavelength close to the melt pool depth, indicating susceptibility of the as-fabricated components to premature creep failure. Such heterogeneity in microstructural and mechanical behavior was attributed to recurring solid-state phase transformations. Subsequently, an interlayer temperature control strategy was implemented, wherein maintaining interlayer temperature above the martensitic start temperature mitigated the heterogeneous microstructural and plastic response in the as-fabricated condition. Findings open pathways to achieving deformation-localization- and creep-resistant microstructures in WA-DED fabricated particle-strengthened CSEF steel components, reducing reliance on post-welding heat treatments—conventionally required to enhance creep resistance—and enabling on-demand, short lead-time fabrication of next-generation power-plant components.
Li metal anode is a promising candidate for next-generation energy storage systems and is widely explored in Li-ion and solid-state batteries. Despite its potential, Li metal anodes face instabilities during long-term cycling, especially when paired with NMC or sulfur-based cathodes, where Li is cycled at high capacities of 6-8 mAh/cm2, equivalent to a thickness of 30-40 µm. During such extensive utilization, degradation mechanisms such as excessive solid electrolyte interphase (SEI), dendrites, and dead Li emerge, and ultimately lead to sudden failure and reduced cycle life. The origin of the degradation mechanisms stem from surface heterogeneities introduced during Li foil manufacturing and storage [1, 2]. As cycling progresses, the local heterogeneities propagate, resulting in uneven Li utilization and degradation-prone regions across the electrode [3], which consequently induce performance variations at the cell level. This heterogeneity propagation is particularly pronounced in large-format pouch cells in practical applications, where the surface effects are magnified. Without a clear understanding of the multi-scale heterogeneities and the development of surface homogenization methods, the performance consistency will be compromised, hindering the commercialization of Li metal batteries. In this presentation, we investigate the evolution of surface heterogeneity propagation on commercially available Li foils. We discover that inhomogeneous Li utilization appears as early as the first half-cycle of formation, manifesting as localized clusters and pits. In pouch cell configurations, these features exhibit areal density variations across the electrode on a scale of millimeters. To improve Li utilization homogeneity, a scalable mechanical brushing method is introduced to remove the chemically heterogeneous surface passivation layer. Furtherore, the influence of utilization homogeneity on cell-to-cell consistency is evaluated using 32 Li-NMC811 pouch cells divided into as-received and brushed Li groups. On the brushed Li, clusters and pits are no longer observable, and the cells exhibit significantly improved consistency in discharge capacity trajectories and cycle lifetime. Overall, this study highlights the role of Li surface utilization homogeneity on long-term cycling performance. Our research provides a pathway for improving large-area electrode uniformity and establishing evaluation methods for cell-to-cell consistency, both are key steps toward the commercialization of Li metal batteries and beyond. [1] Otto, Svenja-K., et al. "In-depth characterization of lithium-metal surfaces with XPS and ToF-SIMS: toward better understanding of the passivation layer." Chemistry of Materials 33.3 (2021): 859-867. [2] Hatzell, Kelsey, et al. "Aligning lithium metal battery research and development across academia and industry." Joule (2024). [3] Kim, Sangwook, et al. "Calendar life of lithium metal batteries: Accelerated aging and failure analysis." Energy Storage Materials 65 (2024): 103147.
Submeter-scale geologic heterogeneity greatly affects CO 2 plume migration and retention. In this work, we present meter-scale laboratory experiments that can capture the impact of realistic submeter-scale geologic heterogeneity on multiphase flow and trapping. We produce realistic sedimentary formations consisting of ripple deposits with varying grain size contrast and wettability in a meter-scale slab chamber. Then, we conduct multiphase flow experiments with analog fluids through these structures and measure the saturation patterns, capillary heterogeneity trapping (CHT), and overall trapping performance. When we alter the ripple bedform architecture, variations in trapped saturation and CHT (10–20%) increment are exhibited. Similar growth in trapping performance is also observed when grain size contrast increases. Finally, wettability changes (water- to oil-wet) can increase nonwetting saturation and CHT up to 5% and 10–20%, respectively. These results emphasize the importance of correctly characterizing the impact of small-scale heterogeneities and wettability changes. We believe this is the first time that multiphase flow experiments were conducted in meter-scale domains with realistic ripple bedforms and heterogeneous wettability to investigate plume migration and trapping.
Considering the vast component design space enabled by fusion-based additive manufacturing (F-BAM) processes, e.g., directed energy deposition (DED), the scale-up manufacturing of Nb-alloys with F-BAM is advantageous for structural applications. However, varying thermokinetic parameters-induced microstructural heterogeneities are prevalent within the F-BAM processed alloys. Such microstructural heterogeneities can have significant implications for the room and elevated temperature mechanical behavior. While a few studies investigating F-BAM processed alloy C103 are available, none of these studies investigate the microstructural heterogeneities – including those associated with solidification growth modes and second phase particles – and the effect thereof on the mechanical behavior. To this end, we investigate the microstructurally heterogeneous regions with varying solidification growth morphologies, segregation behavior, and second phase particle attributes within the laser-DED processed alloy C103. The implications of such heterogeneous regions for room- and elevated-temperature tensile behavior and damage mechanisms are revealed. Particularly, the interface between the cellular and planar region is identified as susceptible to deformation localization. The implications of hot isostatic pressing (HIP) for the consolidation behavior, microstructural evolution, and resulting mechanical behavior are also discussed. Although the recrystallization and grain growth led to a reduced yield strength in the HIPed condition, the homogenization of microstructure alleviated the deformation localization sites, such as the planar/cellular interface within the melt pool. The homogenized microstructure alongside the enhanced consolidation upon HIP led to an enhanced elongation to failure. Findings establish microstructural design considerations in F-BAM processed Nb alloys and also facilitate design of post-processing heat treatments for achieving improved mechanical properties.
Heterogeneity is intrinsic to the dynamic process of a chemical reaction. As reactants are converted to products via intermediates, the nature and extent of heterogeneity vary temporally throughout the duration of the reaction and spatially across the molecular ensemble. The goal of many biophysical techniques, including crystallography and spectroscopy, is to establish a reaction trajectory that follows an experimentally provoked dynamic process. It is essential to properly analyze and resolve heterogeneity inevitably embedded in experimental datasets. We have developed a deconvolution technique based on singular value decomposition (SVD), which we have rigorously practiced in diverse research projects. In this review, we recapitulate the motivation and challenges in addressing the heterogeneity problem and lay out the mathematical foundation of our methodology that enables isolation of chemically sensible structural signals. We also present a few case studies to demonstrate the concept and outcome of the SVD-based deconvolution. Finally, we highlight a few recent studies with mechanistic insights made possible by heterogeneity deconvolution.
Thawing permafrost has the potential to dramatically alter the physical and ecological structure of northern landscapes. Warming of the Arctic and subsequent degradation of permafrost have created a need to assess the stability and movement of soils on hillslopes and the potential impacts on ecosystem structure. In this work, we explore the relationships among vegetation heterogeneity, soil temperature, and soil surface displacements observed from 2019 to 2022 in a watershed in the discontinuous permafrost region on the Seward Peninsula of Alaska. Vegetation heterogeneity was measured as the standard deviation (SD) of the normalized difference vegetation index (NDVI) from 3 m PlanetScope satellite imagery around each soil temperature and active layer thickness observation. Locations of observations were clustered into three soil thermal groups, warm, intermediate, and cold, based on soil temperature and active layer thickness. Average annual horizontal surface displacements were significantly lower for soils within the warm thermal group (median = 0.033 m yr −1 ) compared to soils within the cold thermal group (median = 0.090 m yr −1 ; p < 0.001). Conversely, vegetation heterogeneity was significantly higher in the warm (median = 0.014 SD NDVI; p = 0.002) and intermediate (median = 0.015 SD NDVI; p = 0.002) groups compared with the cold thermal group (median = 0.012 SD NDVI), suggesting a warming-induced shift in vegetation community complexity. Because of the observed associations of ground surface displacement rates and vegetation heterogeneity with soil thermal state, we hypothesize that warming soil conditions induce changes in the rates and patterns of hillslope erosion due to an increase in surface movement as near-surface permafrost thaws, followed by a decrease as the permafrost table deepens and excess ice content diminishes. The transition to warm soils promotes surface ecosystem transformation, shifting the dominant vegetation at the site, given the warming climatic conditions of the region. We integrated our observations of soil temperature, vegetation heterogeneity, and soil surface displacements into a conceptual model that describes the co-evolution of hillslopes and vegetation in warming permafrost environments, which is currently unrepresented in earth system models.
To understand a system is to understand its components and their sum. Cascading interactions between catalyst, solvent, and reagent create a complex web of influences when heterogeneous catalysis meets the condensed phase. Due to the importance of heterogeneous catalysis in chemical manufacturing, and the present and growing potential of condensed phase chemistries, the understanding of these interactions is of paramount importance. To develop condensed phase heterogeneous catalysis, the field needs to develop understanding of the role of solvent in heterogeneous catalytic hydrogenation. While no small feat, fields such as biofuel and petroleum refining have established certain applicable generalities that can bridge the knowledge gap in emerging technologies such as integrated carbon capture and conversion to materials (IC 3 M). In this review, we thoughtfully probe the current paradigm of condensed phase catalysis by challenging the idea that catalyst and solvent are independent reaction design choices. Challenges such as lack of experimental stability studies and poor resolution on our conceptualization of the condensed phase environment are discussed. Parameters such as viscosity and the dielectric constant, and their role on reaction activity and stability are explored. Knowledge gained from established biomass and petroleum processes is discussed and used to anticipate behavior in novel processes.
Single-site heterogeneous catalysts offer an attractive route to unite the molecular precision of homogeneous catalysis with the durability and practical advantages of solids. Surface organometallic chemistry (SOMC) provides a particularly powerful strategy for this purpose by grafting molecular precursors onto tailored surfaces and converting support functionalities into ligand environments for isolated metal centers. As a result, SOMC brings the language and logic of coordination chemistry to heterogeneous catalysis, where the support becomes an integral part of the active site coordination sphere. This Review surveys recent progress in the rational design of SOMC-derived single-site catalysts, with emphasis on synthetic routes, post synthetic transformations, and the deliberate tuning of catalytic behavior through metal-support interactions. Discussions are made on how support identity, hydroxyl topology, acidity, and redox activity shape the geometry, electronic structure, and oxidation state of supported metal sites, as well as how these factors determine activity, selectivity, and stability. We also examine a central limitation of these systems: despite their molecularly informed design, supported single sites often exist as structurally distributed ensembles rather than uniform species, particularly on amorphous supports. This site heterogeneity, along with catalyst dynamics under operating conditions, remains a major barrier to definitive structure-activity relationships. Therefore, emerging approaches that combine advanced characterization, first-principles modeling, ensemble kinetics, and machine learning to resolve active-site structure and guide catalyst development are highlighted. Together, these advances position SOMC as a versatile coordination chemistry framework for the predictive design of heterogeneous catalysts with well-defined molecularly tailored active sites.
Heterogeneous catalysts are crucial in modern societies as they promote sustainability by enabling lower-energy pathways for various chemical reactions. While Density Functional Theory (DFT) computations can provide critical insights into how heterogeneous catalysts operate at the atomic level, they are limited by computational costs and unfavorable scaling with system size. Recently, machine learning interatomic potentials (MLIPs) have emerged as a promising alternative to DFT, offering near-DFT accuracy at significantly reduced cost. Here, in this perspective, we discuss the application of MLIPs in heterogeneous catalyst modeling as a surrogate for DFT. We detail how MLIPs have been applied in thermal catalysis to probe active sites, enable studying complex metallic and nanoporous catalysts, and investigate the reconstruction of catalytic surfaces. We review the use of MLIPs in electrocatalysis and photocatalysis, emphasizing their capabilities in studying transition metal oxide surfaces and solid–liquid interfaces. We also discuss the current limitations of MLIPs, particularly their challenges with transferability and description of non-local interactions. Finally, we conclude by identifying promising and underexplored domains in which MLIPs can further advance our understanding of heterogeneous catalysts.
Natural manganese (Mn) oxide coatings, resulting from the heterogeneous nucleation on foreign substances, have garnered interest based on their importance in the reaction with organic substances and in environmental systems. However, the heterogeneous nucleation of the natural Mn oxide coatings still remains elusive. Here, via fast photochemical oxidation of Mn 2+ (aq), we show that Mn(IV) oxide nuclei form and aggregate on quartz in three distinct successive stages: (i) a nanocrystalline film of unaligned grain forms, (ii) nanoislands develop on the film, and (iii) nanorods form on the nanoislands. Each stage has different crystalline structures and forms by aligned attachment of nanoscale precursors on the preceding surface. Crystal lattice analyses confirm the crystalline development, from the short-range order of the Mn oxide film to the long-range order of the nanorods. Also, the heterogeneous nucleation observed in this work produced groutellite-like tunnel structures of Mn oxide on quartz. Furthermore, this revealed pathway of the heterogeneous nucleation can offer a new perspective on the variety of poorly crystalline structures of natural Mn oxides found in the environment, which can affect elemental redox cycles, contaminant sequestration and removal, and soil carbon storage.
Traditional entropy-based methods—such as cross-entropy loss in classification problems—have long been essential tools for representing the information uncertainty and physical disorder in data and for developing artificial intelligence algorithms. However, the rapid growth of data across various domains has introduced new challenges, particularly the integration of heterogeneous datasets with intrinsic disparities. To address this, we introduce a zentropy-enhanced neural network (ZENN), extending zentropy theory into the data science domain via intrinsic entropy, enabling more effective learning from heterogeneous data sources. ZENN simultaneously learns both energy and intrinsic entropy components, capturing the underlying structure of multisource data. To support this, we redesign the neural network architecture to better reflect the intrinsic properties and variability inherent in diverse datasets. We demonstrate the effectiveness of ZENN on classification tasks and energy landscape reconstructions, showing its superior generalization capabilities and robustness-particularly in predicting high-order derivatives. In image and text classification tasks, ZENN demonstrates superior generalization by introducing a learnable temperature variable that models latent multisource heterogeneity, allowing it to surpass state-of-the-art models on CIFAR-10/100, BBC News, and AG News. As a practical application in materials science, we employ ZENN to reconstruct the Helmholtz energy landscape of Fe3Pt using data generated from density functional theory and capture key material behaviors, including negative thermal expansion and the critical point in the temperature–pressure space. Overall, this work presents a zentropy-grounded framework for data-driven machine learning, positioning ZENN as a versatile and robust approach for scientific problems involving complex, heterogeneous datasets.