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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

Here we develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Insights into Sustainable Nitrogen Fixation by Gas-phase Spectroscopic Measurements and Global Modeling of Reaction Intermediates in Humid Nitrogen Plasma

In this article, there is growing interest in reacting molecular nitrogen and water to sustainably synthesize fixed forms of nitrogen such as ammonia. In particular, low-temperature plasmas can activate these relatively inert feedstocks at or near room temperature without a catalyst. However, because of the enhanced reactivity and nonequilibrium chemistry, a diverse range of products is formed, and the underlying reaction mechanisms are exceedingly complex. In this work, we studied a simplified reactor consisting of a gaseous plasma containing controlled mixtures of nitrogen gas and water vapor. Densities of key chemical species such as N, H, OH, NH, and NO were measured by emission and laser-based spectroscopy as a function of the relative humidity. A global model was constructed and the reaction network was validated by comparing calculated species densities with experiments. We discover that N, a key initial intermediate for ammonia, strongly decreases in the presence of water vapor, and as a result, ammonia formation becomes limited at high relative humidity. This decrease is surprisingly not because N itself reacts, but because one of its main sources, an excited molecular nitrogen state, is reacted away. In addition, oxidation pathways for nitrogen, which lead to NO and related products, are found to be favored over reduction pathways because the corresponding reverse reactions are less significant. Together, this understanding helps explain previously reported observations of selectivity toward nitrogen oxides over ammonia, particularly at higher relative humidities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

HIGH-FIDELITY SIMULATION OF SOOT FORMATION AND THERMAL RADIATION IN A LABORATORY-SCALE RICH-QUENCH-LEAN BURNER

High-fidelity simulations of a swirl-stabilized turbulent spray flame in a laboratory-scale aero-combustor have been performed to evaluate the predictability of state-of-the-art models in capturing soot formation. The simulations employ a complex chemical mechanism developed for Jet-A with PAH chemistry, coupled with the Hybrid Method of Moments (HMOM) soot model, and a Lagrangian dilute spray model for the fuel injection. Two simulations are performed to compare the results when thermal radiation is neglected or included in the solution with a mean spectral model. Modeling closures for the soot differential diffusion effects in mixture fraction space, as well as turbulence-radiation interaction are also evaluated using the data generated by the simulations. Given the degree of complexity of the simulation, the results showed good agreement with experimental measurements of the spatial distribution of the soot volume fraction ensemble average. A closer agreement with the experiment is observed when thermal radiation is included in the solution. Thermal radiation is observed to reduce the flame temperature and increase the flame intermittency, denoted by the increase in the temperature standard deviation in mixture fraction space. The reduction in temperature also leads to a reduction in PAH production and soot volume fraction. Turbulence is observed to have different effects on radiative emission depending on the mixture fraction. Turbulent scalar fluctuations significantly enhance radiative emission in fuel lean mixtures and can also play a role for fuel rich conditions. The statistical description of the turbulence-radiation interaction, previously proposed in the literature, was observed to correctly reproduce the high-fidelity results. Model coefficients were provided for swirl-stabilized flames. The soot differential diffusion model, previously proposed in the literature, based on the residual between the exact term and its model approximation, was also evaluated. The residual correction term further improved the agreement with exact differential diffusion term evaluated with the high-fidelity simulation data in mixture fraction space. The results suggest that the effective turbulent Lewis number can be equal to unity in simulations of turbulent non-premixed recirculating flames.

Soriano, Bruno [Sandia National Laboratories (SNL)↗
DOE OSTI2021

Ab initio Molecular Dynamics Assessment of Thermodynamic and Transport Properties in (K,Li)Cl and (K, Na)Cl Molten Salt Mixtures

Molten salt mixtures are integral part of highly important technological applications such as nuclear reactors. However, due to inherent difficulties associated with experiment at high temperatures and the intrinsic complexity of liquid-phase multi-component systems, understanding their properties at a molecular level remains a challenge. Here, we report on an ab initio molecular dynamics investigation on structural, electronic, transport, and thermal properties of two common molten salt mixtures, (K, Li)Cl and (K,Na)Cl, at five different compositions and three temperatures. Most of the properties were found to depend on both composition and temperature. While properties, like atomic charges, show additive behaviors, other properties, such as electrical conductivity, show considerable deviations from additivity. We shall show that the mixing of the molten salt mixtures is mainly driven by entropy, and that the KCl and LiCl mix better than KCl and NaCl. Our computational results are in general consistent with available experimental data. Comparison with available theoretical data is also provided.

Nguyen, Manh Thuong↗
DOE OSTI2021

Understanding protein-complex assembly through grand canonical maximum entropy modeling

Inside a cell, heterotypic proteins assemble in inhomogeneous, crowded systems where the abundance of these proteins vary with cell types. While some protein complexes form putative structures that can be visualized with imaging, there are far more protein complexes that are yet to be solved because of their dynamic associations with one another. Nevertheless, it is possible to infer these protein complexes through a physical model. However, it is often not clear to physicists what kind of data from biology is necessary for such a modeling endeavor. Here, we aim to model these clusters of coarse-grained protein assemblies from multiple subunits through the constraints of interactions among the subunits and the chemical potential of each subunit. We obtained the constraints on the interactions among subunits from the known protein structures. We inferred the chemical potential that dictates the particle number distribution of each protein subunit from the knowledge of protein abundance from experimental data. Guided by the maximum entropy principle, we formulated an inverse statistical mechanical method to infer the distribution of particle numbers from the data of protein abundance as chemical potentials for a grand canonical multicomponent mixture. Using grand canonical Monte Carlo simulations, we captured a distribution of high-order clusters in a protein complex of succinate dehydrogenase with four known subunits. The complexity of hierarchical clusters varies with the relative protein abundance of each subunit in distinctive cell types such as lung, heart, and brain. When the crowding content increases, we observed that crowding stabilizes emergent clusters that do not exist in dilute conditions. We, therefore, proposed a testable hypothesis that the hierarchical complexity of protein clusters on a molecular scale is a plausible biomarker of predicting the phenotypes of a cell.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Performance of concrete under accelerated physical salt attack and carbonation

Conventional testing of physical salt attack (PSA) on concrete does not consider concomitant factors that may exist in service and alter the mechanisms and kinetics of PSA. This study adopted a combined testing approach where concrete was concurrently investigated under accelerated PSA and carbonation, simulating elements serving in heavy traffic and industrial zones, while implementing ambient conditions similar to that in geographic locations with previous cases of PSA. Based on the tested mixture design parameters [water-to-binder ratio, cement type, and supplementary cementitious materials], potential performance improvement and risks were identified. Thermal, mineralogical, and microscopy analyses elucidated the co-occurrence of complex degradation processes in concrete subjected to accelerated PSA and carbonation, which were distinctive from that induced by the single-factor PSA exposure. The synoptic results from this study may informatively improve guidance on mixture design of concrete when dual exposure to PSA and carbonation is expected in the field.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Atomic-scale mechanism of carbon nucleation from a deep crustal fluid by replica exchange reactive molecular dynamics simulation

Here we present a mechanistic model of carbon nucleation and growth from a fluid at elevated temperature (T) and pressure conditions, typical of those found in the shallow Earth’s lithosphere. Our model uses a replica exchange reactive molecular dynamics framework in which molecular configurations are swapped between adjacent T replica at regular intervals according to underlying statistical mechanics. This framework allows predicting complex molecular structures and thermodynamics while remaining computationally efficient. Here we simulate the reactivity of an unstable mixture of CO 2 and CH 4 at 1000 K and 1 GPa. We find that the path to thermodynamic equilibrium is initially entropy-driven, producing a diversity of short-lived species, including various alcohols with intermediate carbon oxidation states. Cyclic and polycyclic radicals that are sometimes resonance-stabilized form next and set the stage for carbon nucleation. The carbon exsolution process releases abundant water, is exothermic and starts with the nucleation of a large aggregate of hydrogenated graphene flakes from covalently bonded polycyclic units. The carbon backbone of this nucleus subsequently grows into a hydrogen-depleted fullerene-like structure, before evolving toward a partially bilayered graphene layer. Overall, our results show that the mechanism of graphitic C formation is certainly not bimolecular, and that it may involve a combination of key condensation and radical chain reactions. This will help understand the isotopic, and reactive characteristics of carbon-bearing fluids during their upward transit through the Earth’s mantle and crust. Moreover, the mechanistic insights outlined here present intriguing similarities with the process of soot and interstellar dust formation, which suggests that the widespread distribution of abiotic polyaromatic and graphitic material on Earth and beyond may reflect the prevalence of a fundamental chemical pathway.

58 GEOSCIENCES↗
DOE OSTI2025

Structurally Driven Selective Adsorption of Hydrocarbons by Metal Substitution in Isostructural Rare-Earth Metal–Organic Frameworks

The design and realization of highly selective nanoporous materials are necessary to target critical separations across industries. By leveraging pore size, pore shape, and linker functionalization, the design of nanoporous solid adsorbents will enable the rapid production of energy efficient separation materials for high-value gas mixtures. This study uses a combination of modeling, synthesis, and gas adsorption testing to investigate a new class of small-pore isostructural rare-earth (RE) 2,5-dihydroxyterephthalic acid (DOBDC) metal–organic frameworks (MOFs) (RE: Pr-, Gd-, Er-, Yb; DOBDC = 2,5-dihydroxyterephthalic acid) and their adsorption selectivity for acetylene/ethylene mixtures. Density functional theory simulations identified that selective binding of acetylene over ethylene in the Gd-, Er-, and Yb-DOBDC MOFs was due to hydrogen-bonding between acetylene and the linker hydroxyl. Adsorption experiments validated the computational results by identifying mechanisms that control the acetylene/ethylene adsorption selectivity and high acetylene adsorption. Furthermore, dynamic column breakthrough experiments with the Gd-DOBDC MOF validated the simulations and indicated that ethylene can be separated from acetylene in a mixture containing 1 vol % acetylene and 39 vol % ethylene (balance argon). In conclusion, the results highlight the complexity of gas binding in functional porous materials and how combining modeling and experiment enables a fundamental understanding of gas–framework interactions that can be leveraged for the design of future separation materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Butyltin Keggin Ion with a Rare Four-Coordinate Ca Center

Alkyltin clusters are exploited in nanolithography for the fabrication of microelectronics. The alkyltin Keggin family is unique among Keggin clusters across the periodic table; its members appear to favor the lower-symmetry β and γ isomers rather than the highly symmetrical α and ε isomers. Therefore, the alkyltin Keggin family may provide important fundamental information about the formation and isomerization of Keggin clusters. In this study, we have synthesized and structurally characterized a new butyltin Keggin cluster with a tetrahedral Ca 2+ center, fully formulated [(BuSn) 12 (CaO 4 )(OCH 3 ) 12 (O) 4 (OH) 8 ] 2+ (β-CaSn 12 ). The synthesis is a simple one-step process. Extensive solution characterization including electrospray ionization mass spectrometry, small-angle X-ray scattering, and multinuclear ( 1 H, 13 C, and 119 Sn) nuclear magnetic resonance shows β-CaSn 12 is essentially phase-pure and stable. This differs from the previously reported Na-centered analogues that always form a mixture of β and γ isomers, with facile interconversion. Therefore, this study has clarified prior confusion over complex spectroscopic and crystallographic characterization of the Na-centered analogues. Density functional theory calculations showed the following stability order: γ-CaSn 12 < γ-NaSn 12 < β-CaSn 12 < β-NaSn 12 . The β analogue is always more stable than the γ analogue, consistent with experiment. Notable outcomes of this study include a rare tetrahedral Ca coordination, a Na-free alkyltin cluster (important for microelectronics manufacturing), and a better understanding of Keggin families built of different metal cations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

DECAL MDN Resolution Calibration

The simulated pixelated calorimeter uses 0.1 mm × 0.1 mm silicon pixels (0.0001 cm²) silicon pixels as active layers — far finer than current concepts like HGCAL (~0.5 cm²) — improving energy resolution through much finer segmentation. While the standard resolution formalism fits three numbers to a handful of discrete test-beam energies, this work is a first try at a more data-efficient alternative: learning the full response shape continuously in energy with a mixture density network. This continuous, differentiable surrogate is a natural building block for fast simulation of extremely complex calorimeters.

Wang, Peter [U. Chicago (main)]↗
DOE OSTI2024

Mixture-of-Experts for Multi-Domain Defect Identification in Non-Destructive Inspection

Composite materials are widely used in aircraft structures because of their superior mechanical properties. However, their complex failure modes require sophisticated inspection methods to ensure structural integrity. Ultrasonic testing (UT) is a common non-destructive inspection (NDI) technique for aircraft composites that can detect internal and external defects with high resolution and accuracy. Despite their effectiveness, traditional UT methods rely on the manual interpretation of ultrasonic signals, which is time-consuming, labor-intensive, and subjective. Furthermore, processing such large-scale data, particularly across materials of varying thicknesses, significantly increases the computational demands of deep learning model optimization. To overcome these challenges, we propose an efficient sparse mixture-of-experts (MoE) model with a multi-level loss function and introduce four novel training objectives to improve computational efficiency and accuracy in identifying surface defects in composite aircraft materials. Here, we evaluated our approach on material with multiple thicknesses or domains comprising various defects. Our experimental results demonstrate higher accuracy and F1-Score, with only 10% training epochs compared to baseline MoE.

composite materials↗
DOE OSTI2021

A New Complex Borohydride LiAl(BH4)2Cl2

A new mixed alkali metal–aluminum borohydride LiAl(BH4)2Cl2 has been prepared via mechanochemical synthesis from the 2LiBH4–AlCl3 mixture. Structural characterization, performed using a combination of X-ray powder diffraction and solid-state NMR methods, indicates that the LiAl(BH4)2Cl2 phase adopts a unique 3D framework and crystallizes in an orthorhombic structure with the space group C2221, a = 11.6709(6) Å, b = 8.4718(4) Å, c = 7.5114(3) Å. The material shows excellent dehydrogenation characteristics, where hydrogen evolution starts at Tons = 70 °C, releasing approximately 2 wt.% of nearly pure (99.8 vol.%) hydrogen and a very small amount (~0.2 vol.%) of diborane. When compared to halide-free mixed alkali metal–aluminum borohydrides, the presence of Al‒Cl bonding in the LiAl(BH4)2Cl2 structure likely prevents the formation of Al(BH4)3 upon decomposition, thus suppressing the formation of diborane.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Data-driven prediction of the output composition of an atmospheric pressure plasma jet

Cold atmospheric plasma (CAP) in open air hosts numerous chemical species engaged in thousands of chemical reactions. Comprehensive diagnosis of its chemical composition is important across various fields from medicine, where reactive oxygen and nitrogen play key roles, to surface modification. In applications, a centimeter-scale helium–air jet operates for minutes, featuring micrometer-sized streamers and an atmospheric pressure-induced collision frequency in the hundreds of GHz range. To address this intricate multi-scale issue, we introduce a machine learning approach: using a physics-informed neural network (PINN) to tackle the multi-scale complexities inherent in predicting the complete list of species concentrations, gas temperature, and electron temperature of a CAP jet supplied with a mixture of helium and air. Experimental measurements of O 3 , N 2 O, and NO 2 concentrations downstream of the plasma jet, combined with fundamental physics laws, the conservation of mass and charge, constrain the PINN, enabling it to predict the concentrations of all species that are not available from the experiment, along with gas and electron temperatures. The results, therefore, obey all the physical laws we provided and can have a chemical balance with the measured concentrations. In conclusion, this methodology holds promise for describing and potentially regulating complex systems with limited experimental datasets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Performance and community structure dynamics of microbial electrolysis cells operated on multiple complex feedstocks

Microbial electrolysis is a promising technology for converting aqueous wastes into hydrogen. However, substrate adaptability is an important feature, seldom documented in microbial electrolysis cells (MECs). In addition, the correlation between substrate composition and community structure has not been well established. This study used an MEC capable of producing over 10 L/L-day of hydrogen from a switchgrass-derived bio-oil aqueous phase and investigated four additional substrates, tested in sequence on a mature biofilm. The additional substrates included a red oak-derived bio-oil aqueous phase, a corn stover fermentation product, a mixture of phenol and acetate, and acetate alone. The MECs fed with the corn stover fermentation product resulted in the highest performance among the complex feedstocks, producing an average current density of 7.3 ± 0.51 A/m 2 , although the acetate fed MECs outperformed complex substrates, producing 12.3 ± 0.01 A/m 2 . 16S rRNA gene sequencing showed that community structure and community diversity were not predictive of performance, and replicate community structures diverged despite identical inoculum and enrichment procedure. The trends in each replicate, however, were indicative of the influence of the substrates. Geobacter was the most dominant genus across most of the samples tested, but its abundance did not correlate strongly to current density. High-performance liquid chromatography (HPLC) showed that acetic acid accumulated during open circuit conditions when MECs were fed with complex feedstocks and was quickly degraded once closed circuit conditions were applied. The largest net acetic acid removal rate occurred when MECs were fed with red oak bio-oil aqueous phase, consuming 2.93 ± 0.00 g/L-day. Principal component analysis found that MEC performance metrics such as current density, hydrogen productivity, and chemical oxygen demand removal were closely correlated. Net acetic acid removal was also found to correlate with performance. However, no bacterial genus appeared to correlated to these performance metrics strongly, and the analysis suggested that less than 70% of the variance was accounted for by the two components. This study demonstrates the robustness of microbial communities to adapt to a range of feedstocks and conditions without relying on specific species, delivering high hydrogen productivities despite differences in community structure. The results indicate that functional adaptation may play a larger role in performance than community composition. Further investigation of the roles each microbe plays in these communities will help MECs to become integral in the 21st-century bioeconomy to produce zero-emission fuels.

09 BIOMASS FUELS↗
DOE OSTI2025

Combining MicroED and native mass spectrometry for structural discovery of enzyme–small molecule complexes

With the goal of accelerating the discovery of small molecule–protein complexes, we leverage fast, low-dose, event-based electron counting microcrystal electron diffraction (MicroED) data collection and native mass spectrometry. This approach, which we term electron diffraction with native mass spectrometry (ED-MS), allows assignment of protein target structures bound to ligands with data obtained from crystal slurries soaked with mixtures of known inhibitors and crude biosynthetic reactions. This extends to libraries of printed ligands dispensed directly onto TEM grids for later soaking with microcrystal slurries, and complexes with noncovalent ligands. ED-MS resolves structures of the natural product, epoxide-based cysteine protease inhibitor E-64, and its biosynthetic analogs bound to the model cysteine protease, papain. It further identifies papain binding to its preferred natural products, by showing that two analogs of E-64 outcompete others in binding to papain crystals, and by detecting papain bound to E-64 and an analog from crude biosynthetic reactions, without purification. ED-MS also resolves binding of the CTX-M-14 β-lactamase, a target of active drug development, to the non-β-lactam inhibitor, avibactam, alone or in a cocktail of unrelated compounds. These results illustrate the utility of ED-MS for natural product ligand discovery and for structure-based screening of small molecule binders to macromolecular targets, promising utility for drug discovery.

MicroED↗
DOE OSTI2022

High manganese redox variability and manganate predominance in temperate soil profiles as determined by X-ray absorption spectroscopy

Manganese speciation is a key to understanding the fate of contaminants, nutrients, and organic matter in soils. To date, quantification of Mn species in bulk soils has been performed mainly by sequential extraction methods and rarely supported by spectroscopic analysis. In order to obtain quantitative information on the Mn species inventory of soils, we investigated 46 soil horizons (<2-mm fraction, 45.1–2,280 mg/kg Mn) of nine typical Central European soils (Cambisols, Chernozems, Luvisols, Podzol, Stagnosol) by chemical Mn analyses and Mn K-edge X-ray absorption spectroscopy, and related speciation results to major soil properties. Amounts of Mn 2+ , Mn 3+ , and Mn 4+ and the average oxidation state of Mn were evaluated by linear combination fitting (LCF) of X-ray absorption near edge structure (XANES) spectra. Additionally, we used extended X-ray absorption fine structure (EXAFS) spectroscopy to identify and quantify major Mn species. For this, EXAFS spectra of 20 organic and mineral soil samples from five soils (Cambisols, Chernozem, Luvisol) were analyzed by LCF and shell fitting. XANES analyses revealed a high Mn redox variability in organic surface layers, with Mn 2+ being most abundant (≤100%, $\overline{x}$ = 54%), followed by Mn 3+ (≤80%, $\overline{x}$ = 32%) and Mn 4+ (≤55%, $\overline{x}$ = 14%). Mineral soil horizons contained significantly less Mn 2+ (≤56%, $\overline{x}$ = 23%), about equal quantities of Mn 3+ (≤68%, $\overline{x}$ = 31%), and were enriched in Mn 4+ (≤89%, $\overline{x}$ = 46%). EXAFS analyses implied the presence of six major Mn species groups: manganates, organically complexed Mn, Mn(III) oxyhydroxides, silicate-bound Mn, Mn oxides without tunnel- or layer structure, and physisorbed Mn. In litter horizons, Mn was mainly present in organic complexes (58–91%, $\overline{x}$ = 78%) and as physisorbed Mn (≤15%), but individual horizons also comprised manganates, Mn(III) oxyhydroxides, and silicate-bound Mn. Manganates, likely mixtures of phyllomanganates with hexagonal layer symmetry and tectomanganates, dominated in all mineral soil horizons (37–94%, $\overline{x}$ = 67%). Correlation analysis showed that manganates dissolve completely during dithionite-citrate and acid ammonium oxalate extractions, and suggested that Mn 4+ -rich manganates preferentially form under less acidic soil conditions, partly by oxidation of organically complexed Mn(II), and that they are enriched in the soil clay fraction. Mineral soil horizons also contained minor quantities of organically complexed Mn (≤39%, $\overline{x}$ = 11%), silicate-bound Mn (≤30%, $\overline{x}$ = 8%), Mn(III) oxyhydroxides (≤37%, $\overline{x}$ = 7%), Mn oxides without tunnel- or layer structure (≤18%, $\overline{x}$ = 5%), and physisorbed Mn (≤14%, $\overline{x}$ <1%). The detection of Mn(III) oxyhydroxides such as feitknechtite (β-MnOOH) or groutite (α-MnOOH) as well as the spinel hausmannite (Mn 3 O 4 ) in acidic soils is remarkable, since their formation is normally linked to neutral or alkaline pH conditions. Minor contributions of silicate-bound Mn indicate the release of Mn from primary minerals already at early stages of soil formation, and low concentrations of physisorbed Mn suggest that exchangeable Mn is rapidly converted into manganates in oxic soils. In conclusion, the predominance of manganates in mineral soils has far-reaching implications for the functioning of soils and biogeochemical element cycles, as these minerals play an important role in metal binding, plant nutrition, and redox-related processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗