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At least 289 records · Page 16

Local bilinear computation of Jacobi sets

Abstract We propose a novel method for the computation of Jacobi sets in 2D domains. The Jacobi set is a topological descriptor based on Morse theory that captures gradient alignments among multiple scalar fields, which is useful for multi-field visualization. Previous Jacobi set computations use piecewise linear approximations on triangulations that result in discretization artifacts like zig-zag patterns. In this paper, we utilize a local bilinear method to obtain a more precise approximation of Jacobi sets by preserving the topology and improving the geometry. Consequently, zig-zag patterns on edges are avoided, resulting in a smoother Jacobi set representation. Our experiments show a better convergence with increasing resolution compared to the piecewise linear method. We utilize this advantage with an efficient local subdivision scheme. Finally, our approach is evaluated qualitatively and quantitatively in comparison with previous methods for different mesh resolutions and across a number of synthetic and real-world examples.

97 MATHEMATICS AND COMPUTING↗

Accelerated screening of functional atomic impurities in halide perovskites using high-throughput computations and machine learning

The pressing need for novel materials that can serve rising demands in solar cell and optoelectronic technologies makes the nexus of halide perovskites, high-throughput computations, and machine learning, very promising. Ever increasing amounts of data on the structure, fundamental properties, and device performance of halide perovskites provide opportunities for learning chemical rules and design principles that make these materials attractive, and applying them across wide chemical spaces. In this work, we show that impurity properties of halide perovskites computed using density functional theory (DFT) can be combined with machine learning (ML) to deliver predictive models and quick identification of optoelectronically active impurity atoms. Our computation lead to the largest reported dataset of the formation energies and charge transition levels of Pb-site impurities in methylammonium lead halide (MAPbX 3 ) perovskites. Descriptors are defined to uniquely represent any impurity atom in any MAPbX 3 compound and mapped to the computed impurity properties using regression techniques such as Gaussian process regression, neural networks, and random forests. We use the best optimized predictive models to make predictions for hundreds of impurities across 9 MAPbX 3 compounds and create lists of dominating impurities, that is, impurities that can shift the equilibrium Fermi level in the perovskite as determined by native point defects. Finally, this accelerated screening powered by computations and machine learning can guide the identification of problematic impurities that may cause undesired recombination of charge carriers, as well as impurities that can be deliberately introduced to tune the perovskite conductivity and resulting photovoltaic absorption.

36 MATERIALS SCIENCE↗

Interpreting the Lipidome: Bioinformatic Approaches to Embrace the Complexity

Background Improvements in mass spectrometry (MS) technologies coupled with bioinformatics developments have allowed considerable advancement in the measurement and interpretation of lipidomics data in recent years. Since research areas employing lipidomics are rapidly increasing, there is a great need for bioinformatic tools that capture and utilize the complexity of the data. Currently, the diversity and complexity within the lipidome is often concealed by summing over or averaging individual lipids up to (sub)class-based descriptors, losing valuable information about biological function and interactions with other distinct lipids molecules, proteins and/or metabolites. Aim of review To address this gap in knowledge, novel bioinformatics methods are needed to improve identification, quantification, integration and interpretation of lipidomics data. The purpose of this mini-review is to summarize exemplary methods to explore the complexity of the lipidome. Key scientific concepts of review Here we describe six approaches that capture three core focus areas for lipidomics: (1) lipidome annotation including a resolvable database identifier, (2) interpretation via pathway- and enrichment-based methods, and (3) understanding complex interactions to emphasize specific steps in the analytical process and highlight challenges in analyses associated with the complexity of lipidome data.

Kyle, Jennifer E.↗

A Neural Network Approach to Predict Gibbs Free Energy of Ternary Solid Solutions

Here, we present a data-centric deep learning (DL) approach using neural networks (NNs) to predict the thermodynamics of ternary solid solutions. We explore how NNs can be trained with a dataset of Gibbs free energies computed from a CALPHAD database to predict ternary systems as a function of composition and temperature. We have chosen the energetics of the FCC solid solution phase in 226 binaries consisting of 23 elements at 11 different temperatures to demonstrate the feasibility. The number of binary data points included in the present study is 102,000. We select six ternaries to augment the binary dataset to investigate their influence on the NN prediction accuracy. We examine the sensitivity of data sampling on the prediction accuracy of NNs over selected ternary systems. It is anticipated that the current DL workflow can be further elevated by integrating advanced descriptors beyond the elemental composition and more curated training datasets to improve prediction accuracy and applicability.

42 ENGINEERING↗

Enhanced Radiation Damage Tolerance of Amorphous Interphase and Grain Boundary Complexions in Cu-Ta

Amorphous interfacial complexions are particularly resistant to radiation damage and have been primarily studied in alloys with good glass-forming ability, yet recent reports suggest that these features can form even in immiscible alloys such as Cu-Ta under irradiation. In this work, the mechanisms of damage production and annihilation due to primary knock-on atom collisions are investigated for amorphous interphase and grain boundaries in a Cu-Ta alloy using atomistic simulations. Amorphous complexions, in particular amorphous interphase complexions that separate Cu and Ta grains, result in less residual defect damage than their ordered counterparts. Stemming from the nanophase chemical separation in this alloy, the amorphous complexions exhibit a highly heterogeneous distribution of atomic excess volume, as compared to a good glass former like Cu-Zr. Complexion thickness, a tunable structural descriptor, plays a vital role in damage resistance. Thicker interfacial films are more damage-tolerant because they alter the defect production rate due to differences in intrinsic displacement threshold energies during the collision cascade. Overall, the findings of this work highlight the importance of interfacial engineering in enhancing the properties of materials operating in radiation-prone environments and the promise of amorphous complexions as particularly radiation damage-tolerant microstructural features.

36 MATERIALS SCIENCE↗

Temperature-Dependent Mechanical Properties of Ni-Based Concentrated Alloys: Insights from First-Principles Calculations

The present work focuses on predicting temperature-dependent mechanical properties of Ni-based concentrated alloys Ni 18 Cr 10 Co 10 Fe 6 M 4 (abbreviated by X 44 M 4 , with M = Al, V, Mn, Fe, Nb, Mo, and W) using density functional theory (DFT). These predictions are based on shear (plastic) and elastic deformations, utilizing the special quasirandom structure (SQS), the phonon-based quasiharmonic approach (QHA), and the quasistatic approach. The resulting properties include coefficient of thermal expansion via QHA, ideal shear strength (τ IS ), and stable and unstable stacking fault energies (γ SF and γ US ) through pure alias shear deformation, and elastic constants (c ij ), bulk modulus (B 0 ), and shear modules (G 0 ) via elastic deformation. Notably, predicting accurate γ SF is challenging due to uncertainties that can exceed the γ SF values. τ IS and γ US exhibit a strong linear relationship, enabling the accurate prediction of γ US based on the precisely determined τ IS . All mechanical properties of X 44 M 4 decrease with increasing temperature, except for some γ SF cases such as X 44 M 4 with M = V, Mn, Fe, Mo, and W. Among the X 44 M 4 alloys, X 44 Nb 4 exhibits the lowest τ IS , γ US , and G 0 values, and the highest B 0 /G 0 ratio, while X 44 Mn 4 has the lowest B 0 and B 0 /G 0 ratio. We found that volume is a crucial descriptor for understanding and modeling mechanical properties (except B0 and maybe also γ SF ) affected by alloying elements and temperature. Ni-based dilute alloys (e.g., Ni 11 M 1 and Ni 31 M 1 ) and concentrated alloys (e.g., X 44 M 4 ) show similar trends in mechanical properties influenced by alloying elements and temperature, simplifying the analysis and design of Ni-based alloys.

Elastic properties↗

Quantitative study of the effect of grain boundary parameters on the slip system level Hall-Petch slope for basal slip system in Mg-4Al

Several theoretical studies have reported that the geometry and structure of grain boundaries in polycrystalline materials could impose a significant effect on the Hall-Petch slope. However, experimental observations are primarily limited by the ability of the techniques to accurately quantify the grain boundary strength and validate these theoretical models. Using high-resolution electron backscatter diffraction (HR-EBSD), the local stress tensor ahead of a slip band blocked by a grain boundary was quantified and coupled with a continuum dislocation pile-up model to assess the barrier strength of specific grain boundaries to specific slip systems, referred to as micro-Hall-Petch coefficient. For basal slip system in a deformed Mg-4Al alloy, the micro-Hall-Petch coefficient ($k^{basal}_{μ}$) varied significantly, from 0.054 to 0.184 MPa - m 1/2 for nine different grain boundaries. These results were correlated with geometric descriptors of the respective grain boundaries, with three-dimensional GB profile additionally measured via focused ion beam milling. It was found that the angle between the two slip plane traces on the grain boundary plane was the most sensitive parameter affecting $k^{basal}_{μ}$, followed by the angle between the slip directions. A functional form for calculation of $k^{basal}_{μ}$ depending on these two angles is proposed to augment crystal plasticity constitutive models with slip resistance dependent on some measure of the grain size. The method allows a new pathway to calibrate grain size strengthening parameters in crystal plasticity models, allowing further computational investigations of the interrelationship between texture, grain morphology, and the Hall Petch effect.

36 MATERIALS SCIENCE↗

A complete grain-level assessment of the stress-strain evolution and associated deformation response in polycrystalline alloys

Polycrystalline alloys are used pervasively across structural applications contingent upon extensive experimental testing. A statistically representative number of tests are required to expose the variability in the material's performance, as a result of non-uniform microstructures and associated micromechanical fields. In a more direct means of capturing this pertinent information, multi-modal experimental techniques are presented to measure and track the complete micromechanical state, evolving during loading, of each and every grain within the regions of interest. Specifically, a combination of high-energy X-ray diffraction microscopy and digital image correlation coupled with electron backscatter diffraction are conducted on a specimen for each of the alloys, Haynes 282 and Ti7Al. The results of the multi-modal analysis definitively demonstrate that the degree of heterogeneity increases with deformation level and is used to assess the number of grains necessary for a representative volume element description of the stress state for each of these materials. Moreover, higher resolution imaging is used for identification of the slip system activity and subsequently used to study slip transmission events. An accurate knowledge of the resolved shear stress in adjacent grains (grain interactions) is demonstrated to be a key descriptor of the slip transmission events.

36 MATERIALS SCIENCE↗

Machine-learning enabled thermodynamic model for the design of new rare-earth compounds

We employ a descriptor based machine-learning approach to assess the effect of chemical alloying on formation-enthalpy of rare-earth intermetallics. Application of machine-learning approaches in rare-earth intermetallic design have been sparse due to limited availability of reliable datasets. In this work, we developed an ‘in-house’ rare-earth database with more than 600 + compounds, each entry was populated with formation enthalpy and related atomic features using high-throughput density-functional theory (DFT). The SISSO (sure independence screening and sparsifying operator) based machine-learning method with meaningful atomic features was used for training and testing the formation enthalpies of rare earth compounds. The complex lattice function coupled with the machine-learning model was used to explore the effect of transition metal alloying on the energy stability of Ce based cubic Laves phases (MgCu 2 type). The SISSO predictions show good agreement with high-fidelity DFT calculations and X-ray powder diffraction measurements. Our study provides quantitative guidance for compositional considerations within a machine-learning model and discovering new metastable materials. The electronic-structure of Ce-Fe-Cu based compound was also analyzed to get an in-depth understanding of the electronic origin of phase stability. The interpretable analytical models in combination with density-functional theory and experiments provide a fast and reliable design guide for discovering technologically useful materials.

36 MATERIALS SCIENCE↗

Rapid discovery of high hardness multi-principal-element alloys using a generative adversarial network model

Multi-principal element alloys (MPEAs) continue to gain research prominence due to their promising high-temperature microstructural and mechanical properties. Recently, machine learning (ML) and materials informatics have been used extensively for screening MPEAs, however, most of these efforts were focused on constructing classification and regression models for predicting phase stability and mechanical properties of known compositions. These approaches may accelerate the screening process but optimizing new compositions with desirable properties within a practical time frame from an infinitely large design space of MPEA systems remains a grand challenge. To tackle this composition optimization challenge, a generative adversarial network coupled with a neural-network ML model was utilized to design MPEAs by filtering compositions that have high hardness. Even in a high-dimensional space with 18 elements as descriptors, the ML model was able to generate optimized compositions from which one composition was found to have 10% higher hardness (941 HV) than the maximum in the training data (857 HV). Density-functional theory was used to provide thermodynamic and electronic insights to higher hardness of the new MPEA found. The present work can optimize compositions from a wide design space of 18 elements (including W, Ta and Nb) that presents an opportunity to synthesize new compositions for applications ranging from corrosion-resistant alloys to nuclear materials. Here the findings suggest that generative ML can greatly accelerate materials discovery by identifying novel compositions, which can serve as a data-informed tool to guide experiments.

36 MATERIALS SCIENCE↗

Atomistic simulations and machine learning of solute grain boundary segregation in Mg alloys at finite temperatures

Understanding solute segregation thermodynamics is the first step in investigating grain boundary (GB) properties, such as strong yttrium (Y) effects on grain growth and texture evolution in micro-scale polycrystalline magnesium (Mg) alloys. To estimate the average GB segregation behavior in low-solute-concentration Mg alloys (e.g., 2 at.% Y), a state-of-the-art spectral approach is applied based on a per-site segregation energy spectrum for Y solute atoms at zero K obtained from molecular statistics (MS) simulations of ~10 4 GB sites in Mg symmetric tilt GBs (STGBs). Although selected MS simulation results are consistent with verification by density functional theory (DFT) calculations, estimates of average segregation tendency based on the zero-K energy spectrum deviate from experimental observations. To resolve this problem, thermodynamic integration (TI) methods based on molecular dynamics (MD) simulations are used to determine the per-site segregation free energies of Y at representative GB sites, which show contributions beyond harmonic approximations can be important for certain GB sites at high temperatures. A surrogate model of per-site segregation free energy is constructed from a small set of TI data points using stacking cross-validation regressors and physics-informed descriptors. This model is applied to predict the Y segregation free energy spectra for thousands of GB sites in Mg STGBs with uncertainty quantification. Finally, the average segregation tendency predicted by the spectral approach based on the free energy spectra agrees well (within the uncertainty range) with experimental observations for micro-scale polycrystalline Mg alloys at typical thermomechanical processing temperatures (500 ~ 800 K), where thermodynamic equilibrium states are likely to be achieved due to fast diffusion.

Atomistic simulations↗

Solute clustering in polycrystals: Unveiling the interplay of grain boundary junction and long-range solute attraction effects

Spectral analysis of local atomic environments has become a powerful tool for studying solute atom segregation and interactions at grain boundaries in nanocrystalline alloys. When applied to individual grain boundaries, the spectral analysis has shown that solute-solute interaction can be either attractive or repulsive, with long-range relative attraction enhancing the likelihood for solute atoms to begin clustering. In this article, we combine this analysis with a new grain-boundary structure descriptor based on grain-boundary atom coordination, to investigate the impact of grain-boundary junctions on solute atom segregation in polycrystals. Specifically, we systematically characterize the tendency of solute clusters to begin forming at various types of ordinary grain boundaries, triple junctions, and high-order junctions in Ag polycrystals containing either Ni or Cu solute atoms. Our findings demonstrate that the formation of solute clusters at grain boundaries is primarily driven by long-range relative solute attraction, rather than short-range solute-solute interactions. Furthermore, this effect is most pronounced near grain-boundary junctions. Our study highlights the multiscale nature of solute segregation at crystalline interfaces and provides new insights into the complex phenomena governing heterogeneous solute segregation in grain-boundary networks.

Grain-boundary junction↗

DuctGPT: A Generative Transformer for Forward Screening of Ductile Refractory Multi-Principal Element Alloys

Designing ductile materials for extreme environments such as fusion reactors requires a deep understanding of the complex interplay between electronic structure, mechanical stability, and wide compositional space. Here, in this work, we introduce DuctGPT, a physics-informed, GPT-powered machine learning platform that enables rapid and accurate prediction of ductility across a wide range of refractory multi-principal element alloys (MPEAs). Trained on both experimental and high-fidelity computational data, DuctGPT integrates descriptors such as density of states at the Fermi level, elastic constants, and valence electron concentration to capture the fundamental mechanisms governing ductile versus brittle behavior. Using this framework, we screen over 1000 compositions in of body-centered cubic (BCC) MPEAs, including two new alloy classes, i.e., NbTa-rich (NbTa $>$ 50 at.%) NbTa-Ti-V and W-rich ($>$ 50 at.%) W-Ti-V MPEAs, to rapidly identify promising alloy compositions with enhanced ductility. Validation against experimental data confirms the model's ability to predict ductility with high fidelity and low uncertainty. By leveraging conversational AI and robust physical modeling, DuctGPT provides a blueprint for the next generation of alloy design assistants, enabling human-AI collaboration in the accelerated discovery of ductile, high-performance materials for fusion, aerospace, and advanced manufacturing.

AI/ML↗

Effects of spatial energy distribution-induced porosity on mechanical properties of laser powder bed fusion 316L stainless steel

Laser powder bed fusion (LPBF) additive manufacturing (AM) offers a variety of advantages over traditional manufacturing, however its usefulness for manufacturing of high-performance components is currently hampered by internal defects (porosity) created during the LPBF process that have an unknown impact on global mechanical performance. By inducing porosity distributions through variations in print energy density and inspecting the resulting tensile samples using computed tomography, nearly 50,000 pores across 75 samples were identified. Porosity characteristics were quantitatively extracted from inspection data and compared with mechanical properties to understand the strength of relationships between porosity and global tensile performance. Useful porosity characteristics were identified for prediction of part performance. Results indicate that ductility and strain at ultimate tensile strength are the global tensile properties most significantly impacted by porosity and can be predicted with reasonable accuracy using simple porosity shape descriptors such as volume, diameter, and surface area. Moreover, it was found that the largest pores influenced behavior most significantly. Specifically, pores in excess of 125 µm in diameter were found to be a sufficient threshold for property estimation. These results establish an initial understanding of the complex defect-performance relationship in AM 316L stainless steel and can be leveraged to develop certification standards and improve confidence in part quality and reliability for the broader set of engineering alloys.

36 MATERIALS SCIENCE↗

Part-scale microstructure prediction for laser powder bed fusion Ti-6Al-4V using a hybrid mechanistic and machine learning model

Laser powder bed fusion (LPBF) Ti-6Al-4V is widely studied for use in structural applications in aerospace and medical industries, but mechanical anisotropy and microstructural inhomogeneity prohibits its wider adoption. Although successful microstructure prediction models have been developed, a remaining challenge is their limited integration across length/time scales and validation by experimental studies. Here, this work proposes a physics-augmented machine learning surrogate model to unite predictions of LPBF temperature, β phase morphology and texture, and α/α’ formation into a single framework that is calibrated and validated with experiments. First, a phase field (PF) model of the martensitic β→α’ transformation is developed and calibrated using data from in-situ synchrotron cyclic heating/cooling studies quantifying the variation of α phase fraction with time. In parallel, an established finite difference-Monte Carlo (FDMC) model predicts the part-scale temperature profile and β grain formation during solidification. A dataset is developed using LPBF cyclic temperature descriptors from the FDMC model as inputs and corresponding α/α’ phase fraction and width from the PF model as outputs. Five machine learning (ML) regression models are tested and optimized, having mean absolute error in testing ≤ 4 %, and the k-nearest neighbors (KNN) model is selected as the best performing. The KNN model is called at the nodal level during post-processing of the FDMC model to replace and downscale the response of the PF model. The combined agility and accuracy of the hybrid FDMC-ML model enables part-scale microstructure predictions that can be further used for property predictions to accelerate AM process optimization.

36 MATERIALS SCIENCE↗

HCOOH Decomposition on Sub-Nanometer Pd 6 Cluster Catalysts: The Effect of Defective Boron Nitride Supports Through First Principles

The catalytic properties of a hexagonal boron nitride- (h-BN) supported Pd 6 sub-nanometer cluster in the context of formic acid (HCOOH) decomposition were studied by means of periodic Density Functional Theory (DFT) calculations. The effect of support defectivity – boron (h-B v N) and nitrogen (h-BN v ) monovacancies – on the competition between the formate (HCOO)- and carboxyl (COOH)-mediated decomposition pathways was analyzed. Defects are responsible for charge-transfer leading to a positively or negatively charged cluster, and open new reactive channels in which vacancy-mediated dehydrogenation pathways can occur. Pd 6 cluster reconstructions, induced by the adsorption of reaction intermediates and by the presence of monovacancies in the support, greatly stabilize the formation of CO from COOH, which could drastically decrease the selectivity towards hydrogen production. Here, a simplified descriptor-based analysis, based on selected thermochemical quantities calculated on charged cluster models, suggests that Pd 6 sub-nanometer clusters supported on pristine h-BN and h-BN v can be more selective than Pd 6 supported on defective h-B v N towards HCOOH dehydrogenation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydrogenation and C-S bond activation pathways in thiophene and tetrahydrothiophene reactions on sulfur-passivated surfaces of Ru, Pt, and Re nanoparticles

Thiophene-H2 reactions proceed via sulfur removal and hydrogenation routes on dispersed metal nanoparticles that become decorated by refractory S-adlayers during catalysis. The identity and kinetic relevance of the required elementary steps are described here based on rates measured at S-chemical potentials set by H2S/H2 ratios similar to those prevalent during practical catalysis on Re, ReSx, Ru, and Pt catalysts. Free energies for S adatom formation (from H2S decomposition and H2 evolution) are strongly exothermic (< -50 kJ mol-1 on Pt(111) and < -150 kJ mol-1 on Re and Ru(0001)), but strong repulsions between S adatoms cause adsorption free energies to increase significantly with coverage on all three surfaces, preventing complete monolayer formation. These adlayers, composed of unreactive S-atoms (S') that cover 1/3–2/3 ML leave residual interstitial spaces (*) that bind S-atoms (S*), intermediates, and transition states reversibly, as required for catalytic turnovers. The number and binding properties of these interstices depend on the identity and chemical state of the nanoparticle bulk phase, which influences S'-binding and coverages and cause large differences in direct desulfurization and hydrogenation turnover rates (per exposed metal atom) on dispersed Re, ReSx, Ru, and Pt. The identity and kinetic relevance of elementary steps for desulfurization (to C4¬ hydrocarbons) and hydrogenation (to tetrahydrothiophene; THT) are similar among these catalysts; they involve the kinetically-relevant formation of a thiophene-derived intermediate (monohydrothiophene on Re and ReSx; dihydrothiophene on Ru and Pt) that either cleaves its C-S bond or “over-hydrogenates” to THT in one surface sojourn. THT then undergoes C-S bond cleavage in secondary reactions that correct such over-hydrogenation to form the more unsaturated species that cleave C-S bonds. THT/C4 product ratios are insensitive to H2S/H2 ratios and thiophene pressure, even though active interstitial spaces are covered by kinetically-detectable coverages of S* and thiophene; therefore, primary and secondary reactions must involve the same active surfaces. The observed increase in THT/C4 ratios with H2 pressure shows that THT formation transition states involve a larger number of H-atoms than for C-S cleavage. The requirement for bound species with intermediate unsaturation (between THT and thiophene) for C-S bond cleavage is reminiscent of the H-shuttling required in C-C and C-O hydrogenolysis, reactions that involve the partial dehydrogenation of alkanes and alkanols, respectively, to weaken such bonds and to increase the formation entropy of the relevant transition states via the evolution of H2(g). These mechanistic details challenge prevalent paradigms about different site requirements for hydrogenation and desulfurization pathways and about how metal-sulfur bond energies act as descriptors of reactivity; in fact, such binding energies merely act to define the refractory S-adlayers that enable the formation of weakly-binding interstices that reversibly bind intermediates and transition states, thus allowing catalytic turnovers.

Yik, Edwin↗

Single pot catalyst strategy to branched products via adhesive isomerization and hydrocracking of polyethylene over platinum tungstated zirconia

Hydrocracking is an insufficiently explored route for chemical recycling of plastics waste. Platinum tungstated zirconia (Pt-WZr) was used in a batch reactor at low temperatures of 250 °C and 30 bar H 2 pressure for 1-24 h reaction times using low-density polyethylene (LDPE, M w ~76 kDa). We find Pt-WZr is a bifunctional catalyst for LDPE hydrocracking leading to higher value branched fuel- and lubricant-ranged alkanes. Here we demonstrate that the catalyst metal-to-acid site molar ratio (MAB) shifts the product distribution to larger cracked products and increases the isomerization degree in the residual polymer. We propose a new adhesive isomerization mechanism between the metal and Brønsted acid sites in parallel with slow polymer chain cracking, caused by competitive adsorption of the polymer over the liquid products and stereochemical hindrance of methines. This study provides a blueprint on how to engineer effective catalysts for hydrocracking polyolefin plastic wastes using the MAB as a catalyst descriptor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗