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DOE OSTI2025

Equilibrium Fe isotope fractionation between olivine, pyroxene, spinel and MORB glass: Implications for mantle partial melting to generate MORBs

Primitive mid-ocean ridge basalts (MORBs) exhibit Fe isotopic compositions heavier than the upper mantle by +0.074 ± 0.028 ‰ for δ 56 Fe. The processes responsible for this isotopic difference remain unclear. Modeling of Fe isotope fractionation during mantle partial melting requires reliable equilibrium Fe isotope fractionation factors between minerals and melts, for which consistent data are still lacking. Here, in this study, we used Nuclear Resonant Inelastic X-ray Scattering (NRIXS) technique to measure Fe force constants for a MORB glass (ALV 519-4-1) and natural mantle minerals (olivine, orthopyroxene, clinopyroxene, and spinel) to determine the equilibrium Fe isotope fractionation factors between them. The force constants determined in this study, in increasing order, are 167 ± 26 N/m for spinel, 175 ± 17 N/m for olivine, 176 ± 20 N/m for MORB glass, 205 ± 26 N/m for clinopyroxene, and 219 ± 36 N/m for orthopyroxene. We evaluated the previously proposed mechanisms for the heavy Fe isotopic composition of MORBs, including (i) mantle partial melting, (ii) mantle lithological heterogeneity, with pyroxenite in the source, (iii) mantle metasomatism by low-degree melts, and (iv) fractional crystallization of olivine from melts. For (i), we used the pMELTS program to simulate adiabatic decompression melting of mantle peridotites, and calculated Fe isotope fractionation based on Fe 3+ –Fe 2+ equilibrium-controlled fractionation, where Fe 3+ forms stronger bonds and is more incompatible than Fe 2+ . At 10 wt% peridotite melting, corresponding to MORB generation, only +0.03 ‰ Fe isotope fractionation between the melt and the original bulk composition (Δ 56 Fe = δ 56 Fe melt - δ 56 Fe 0 ) was produced, insufficient to account for the observed MORB-upper mantle difference. For (ii), melting of pyroxenites yields smaller Fe isotope fractionation than melting of peridotites, making it unlikely the cause for the MORB-upper mantle isotopic difference. For (iii), both the Fe 3+ /ΣFe ratio and the δ 56 Fe of melts increase with the degree of partial melting, indicating that low-degree melts are not isotopically heavy enough to significantly alter the isotopic composition of lithospheric mantle through metasomatism. For (iv), equilibrium isotope fractionation between olivine and melt is near zero. These results suggest that equilibrium Fe isotope fractionation alone cannot explain the MORB isotopic signature, highlighting the potential role of kinetic isotope fractionation. Using a diffusion model, we calculated kinetic Fe and Mg isotope fractionations associated with (iv) olivine crystallization from a melt, and found that the predicted Fe and Mg isotope fractionations were inconsistent with observations in MORBs. Qualitatively, two processes could have induced kinetic Fe isotope fractionation during MORB generation: (a) Fe-Mg interdiffusion between melt and solid during melt migration and (b) reactive melt-rock interactions during melt focusing. However, a quantitative understanding of their role in modifying the melt isotopic composition remains limited and requires further investigation.

Fe isotopes↗

DOE OSTI2021

TEA Modeling to Quantify Economic Implications for Biorefinery Processing of Isolated Anatomical Fractions of Corn Stover

The Feedstock-Conversion Interface Consortium (FCIC; https://www.energy.gov/sites/prod/files/2020/01/f70/beto-fcic-overview-web.pdf), a collaboration of nine national laboratory partners, seeks to understand impacts of feedstock attributes on biorefinery performance. It is hypothesized that different individual anatomical fractions of corn stover vary in composition and recalcitrance, such that processing each fraction on its own through dedicated campaigns may enable better biorefinery economics overall relative to processing the whole stover material. This presentation focuses on techno-economic analysis (TEA) modeling to quantify the yield and cost ramifications for processing isolated anatomical fractions of corn stover through a low-temperature conversion biorefinery, reflecting a biochemical processing pathway consisting of biomass deconstruction through pretreatment and enzymatic hydrolysis, sugar fermentation and upgrading to hydrocarbon fuels, and lignin upgrading to value-added coproducts. Commercial-scale process simulation and economic evaluation leveraged experimental and analytical data from FCIC researchers for conversion of whole corn stover plus three individual anatomical fractions (cobs, husks, and stalks) across key steps of the conversion process. Our assessment found encouraging potential for biorefinery economic gains that may be achieved through this approach. TEA results indicated fuel yields varying from 29-44 gallons gasoline equivalent (GGE)/dry ton for the individual anatomical fractions compared to whole stover at 34 GGE/ton, equating to minimum fuel selling prices (MFSPs) between $6.37-$10.18/GGE for the fractions versus $8.76/GGE for whole stover (when lignin is burned), or $9.15-$15.19/GGE for the fractions versus $13.11/GGE for whole stover (when lignin is upgraded to coproducts, based on current experimental performance levels). Cobs and husks demonstrated the ability to achieve the highest fuel yields and lowest MFSPs, outperforming whole stover, while stalks led to the opposite result, as a composite reflection of compositional differences and process convertibility. Notably, even when taking the weighted average of the results reflecting each anatomical fraction weighted by its corresponding makeup of corn stover, this feasibility TEA screening supports feedstock cost allowances on the order of roughly $22-$29/ton as may reflect accommodating additional biomass fractionation equipment during feedstock pre-processing upstream of the conversion biorefinery gate to separate corn stover into such constituent fractions. Or viewed differently, the weighted average MFSP for the fractions was found to be $0.31-$0.32/GGE lower than the MFSP for the whole stover basis across either lignin scenario, when maintaining a fixed biomass feedstock cost. These findings highlight favorable implications for biorefinery economics as may be achieved by moving to a staged campaign approach for processing different corn stover fractions sequentially. Further opportunities exist for future work to fill in data gaps for remaining anatomical constituents (e.g. leaves) that were not included in the initial experimental studies, though are expected to maintain similar trends.

biochemical processing pathway↗

NASA NTRS2002

Fractionation of the Early Terrestrial Atmospheres: Dynamical Escape

Hydrodynamic escape may have played a significant role in the early fractionation of the atmospheres of the terrestrial planets. This possibility has been demonstrated in the last two decades by numerous models that show radial, transonic flow of hydrogen can occur in the presence of sufficient solar EUV Hydrodynamic escape may have played a significant role in the early fractionation of the atmospheres of the terrestrial planets. This possibility has been demonstrated in the last two decades by numerous models that show radial, transonic flow of hydrogen can occur in the presence of sufficient solar EUV flux, thought to exist in the first 500 My. The models show that the larger the solar flux the greater the mass of the fractionating species, which are accelerated to escape speeds by the hydrogen wind through drag processes. As the atmospheres evolve and the solar EUV flux wanes, the maximum mass of flowing gas constituents decreases until all gases become static. We show that fractionation can continue beyond this point when non-radial flow and dynamically enhanced Jeans escape are considered. For example, the early terrestrial atmospheres are thought to have had large hydrogen contents, resulting in exobase altitudes of a planetary radius or more. In this case, rotational speeds at the exobases of Earth and Mars would be large enough so that light constituents would "spin" off and fractionate, especially at equatorial latitudes. Also, in the presence of transonic flow of hydrogen only, non-radial expansion throws heavier gases to high altitudes in the exosphere, accompanied by strong bulk speeds at the exobase, which results in enhanced thermal escape fluxes and fractionation. flux, thought to exist in the first 500 My. The models show that the larger the solar flux the greater the mass of the fractionating species, which are accelerated to escape speeds by the hydrogen wind through drag processes. As the atmospheres evolve and the solar EUV flux wanes, the maximum mass of flowing gas constituents decreases until all gases become static. We show that fractionation can continue beyond this point when non-radial flow and dynamically enhanced Jeans escape are considered. For example, the early terrestrial atmospheres are thought to have had large hydrogen contents, resulting in exobase altitudes of a planetary radius or more. In this case, rotational speeds at the exobases of Earth and Mars would be large enough so that light constituents would "spin" off and fractionate, especially at equatorial latitudes. Also, in the presence of transonic flow of hydrogen only, non-radial expansion throws heavier gases to high altitudes in the exosphere, accompanied by strong bulk speeds at the exobase, which results in enhanced thermal escape fluxes and fractionation.

Hartle, Richard E.↗

NASA NTRS2002

Fractional Snowcover Estimates from Earth Observing System (EOS) Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS)

The Moderate Resolution Imaging Spectroradiometer (MODIS) on the NASA Earth Observing System (EOS) Terra and Aqua missions has shown considerable capability for mapping snowcover. The typical approach that has used, along with other criteria, the Normalized Snow Difference Index (NDSI) that takes the difference between 500 meter observations at 1.64 micrometers (MODIS band 6) and 0.555 micrometers (MODIS band 4) over the sum of these observations to determine whether MODIS pixels are snowcovered or not in mapping the extent of snowcover. For many hydrological and climate studies using remote sensing of snowcover, it is desirable to assess if the MODIS snowcover observations could not be enhanced by providing the fraction of snowcover in each MODIS observation (pixel). Pursuant to this objective studies have been conducted to assess whether there is sufficient "signal%o in the NDSI parameter to provide useful estimates of fractional snowcover in each MODIS 500 meter pixel. To accomplish this objective high spatial resolution (30 meter) Landsat snowcover observations were used and co-registered with MODIS 500 meter pixels. The NDSI approach was used to assess whether a Landsat pixel was or was not snowcovered. Then the number of snowcovered Landsat pixels within a MODIS pixel was used to determine the fraction of snowcover within each MODIS pixel. The e results were then used to develop statistical relationships between the NDSI value for each 500 meter MODIS pixel and the fraction of snowcover in the MODIS pixel. Such studies were conducted for three widely different areas covered by Landsat scenes in Alaska, Russia, and the Quebec Province in Canada. The statistical relationships indicate that a 10 percent accuracy can be attained. The variability in the statistical relationship for the three areas was found to be remarkably similar (-0.02 for mean error and less than 0.01 for mean absolute error and standard deviation). Independent tests of the relationships were accomplished by taking the relationship of fractional snow-cover to NDSI from one area (e.g., Alaska) and testing it on the other two areas (e.g. Russia and Quebec). Again the results showed that fractional snow-cover can be estimated to 10 percent. The results have been shown to have advantages over other published fractional snowcover algorithms applied to MODIS data. Most recently the fractional snow-cover algorithm has been applied using 500-meter observations over the state of Colorado for a period spanning 25 days. The results exhibit good behavior in mapping the spatial and temporal variability in snowcover over that 25-day period. Overall these studies indicate that robust estimates of fractional snow-cover can be attained using the NDSI parameter over areas extending in size from watersheds relatively large compared to MODIS pixels to global land cover. Other refinements to this approach as well as different approaches are being examined for mapping fractional snow-cover using MODIS observations.

Salomonson, Vincent V.↗

DOE OSTI2022

Fractionalization of subsystem symmetries in two dimensions

The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z 2 topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

2-dimensional systems↗

NASA NTRS2015

CALIPSO Observations of Near-Cloud Aerosol Properties as a Function of Cloud Fraction

This paper uses spaceborne lidar data to study how near-cloud aerosol statistics of attenuated backscatter depend on cloud fraction. The results for a large region around the Azores show that: (1) far-from-cloud aerosol statistics are dominated by samples from scenes with lower cloud fractions, while near-cloud aerosol statistics are dominated by samples from scenes with higher cloud fractions; (2) near-cloud enhancements of attenuated backscatter occur for any cloud fraction but are most pronounced for higher cloud fractions; (3) the difference in the enhancements for different cloud fractions is most significant within 5km from clouds; (4) near-cloud enhancements can be well approximated by logarithmic functions of cloud fraction and distance to clouds. These findings demonstrate that if variability in cloud fraction across the scenes used to composite aerosol statistics are not considered, a sampling artifact will affect these statistics calculated as a function of distance to clouds. For the Azores-region dataset examined here, this artifact occurs mostly within 5 km from clouds, and exaggerates the near-cloud enhancements of lidar backscatter and color ratio by about 30. This shows that for accurate characterization of the changes in aerosol properties with distance to clouds, it is important to account for the impact of changes in cloud fraction.

near-cloud aerosol↗

DOE OSTI2021

Iron, magnesium, and titanium isotopic fractionations between garnet, ilmenite, f ayalite, biotite, and tourmaline: Results from NRIXS, ab initio , and study of mineral separates from the Moosilauke metapelite

Interpreting isotopic signatures documented in natural rocks requires knowledge of equilibrium isotopic fractionation factors. Here, we determine equilibrium Fe isotope fractionation factors between several common rock-forming minerals using a comparative approach involving three independent methods: (i) isotopic analyses of natural minerals from a metapelite from Mt. Moosilauke, New Hampshire, for which equilibration temperature and pressure are well constrained to be near the aluminosilicate triple point (T ≃ 500 °C, P ≃ 4 kbar), (ii) Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements of Fe force constants of minerals, and (iii) Density Functional Theory (DFT) ab initio calculations of Fe force constants of minerals. The minerals studied for Fe isotopes include, in increasing order of their β-factors: garnet < ilmenite ≈ fayalite < biotite < tourmaline < muscovite ≈ plagioclase. Some of this ordering is affected by the presence of Fe 3+ in the minerals, which tends to form stiffer bonds and be associated with heavy Fe isotope enrichments relative to Fe 2+ . We are, however, able to assess the magnitude of the effect of the ratio Fe 3+ /ΣFe on equilibrium fractionation factors, notably on the ilmenite-hematite solid solution. Equilibrium Fe isotopic fractionation factors between garnet, ilmenite, biotite, tourmaline and fayalite are determined. We also report Mg and Ti isotopic compositions of selected Moosilauke minerals that allow us to better constrain the equilibrium fractionation factors for garnet-biotite-tourmaline (Mg isotopes) and biotite-ilmenite (Ti isotopes). We show how the newly determined equilibrium fractionation factors can be used to address diverse problems in Earth and planetary sciences, notably (i) Fe and Mg isotopic fractionation during anatexis, (ii) Fe isotopic fractionation in lunar ilmenite, and (iii) Ti isotopic fractionation during fluvial transport of minerals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

The dynamics of suspensions of prolate spheroidal particles—Effects of volume fraction

Here, the effect of volume fraction on the dynamics of a gravity driven suspension of prolate spheroidal solid particles in a fully periodic domain is examined by fully resolved numerical simulations, for relatively modest Reynolds numbers (around 20, depending on the volume fraction). Three systems are examined, for volume fractions of 2.2% (20 particles), 5.5% (50 particles), and 9.9% (90 particles). The results show a transition from flow at low volume fractions dominated by the hydrodynamic interactions between the particles and the fluid, although modified by collisions, to flow dominated by collisions at higher volume fractions. The distribution of the particles with respect to each other, as measured by the probability distribution of nearest distances, is nearly random at low volume fractions but at high volume fractions, there is more clustering than for a random distribution. At lower volume fractions most of the particles fall broadside on whereas at the highest volume fraction, their orientation is essentially random.

42 ENGINEERING↗

NASA NTRS2002

Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartly, Tom T.↗

NASA NTRS2002

Control of Initialized Fractional-Order Systems

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex w-plane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Hartley, Tom T.↗

NASA NTRS2003

The Stable Isotope Fractionation of Abiotic Reactions: A Benchmark in the Detection of Life

One very important tool in the analysis of biogenic, and potentially biogenic, samples is the study of their stable isotope distributions. The isotope distribution of a sample depends on the process(es) that created it. One important application of the analysis of C & N stable isotope ratios has been in the determination of whether organic matter in a sample is of biological origin or was produced abiotically. For example, the delta C-13 of organic material found embedded in phosphate grains was cited as a critical part of the evidence for life in 3.8 billion year old samples. The importance of such analysis in establishing biogenicity was highlighted again by the role this issue played in the recent debate over the validity of what had been accepted as the Earth s earliest microfossils. These kinds of analysis imply a comparison with the fractionation that one would have seen if the organic material had been produced by alternative, abiotic, pathways. Could abiotic reactions account for the same level of fractionation? Additionally, since the fractionation can vary between different abiotic reactions, understanding their fractionations can be important in distinguishing what reactions may have been significant in the formation of different abiological samples (such as extraterrestrial samples). There is however, a scarcity of data on the fractionation of carbon and nitrogen by abiotic reactions. In order to interpret properly what the stable isotope ratios of samples tell us about their biotic or abiotic nature, more needs to be known about how abiotic reactions fractionate C and N. Carbon isotope fractionations have been studied for a few abiotic processes. These studies presumed the presence of a reducing atmosphere, focusing on reactions involving spark discharge, W photolysis of reducing gas mixtures, and cyanide polymerization in the presence of ammonia. They did find that the initial products showed a depletion in I3C with values in the range of a few per mil to as low as -60 % (potentially comparable to that which accompanies the biosynthesis of organic matter). We need to understand what kind of fractionations are observed with reactions under the non-reducing or mildly reducing conditions now thought to be present on the early Earth. While nitrogen is receiving increased attention as a tool for these kinds of analyses, almost nothing is known about the isotope fractionation that one would expect for abiotic sources of fixed/reduced nitrogen. This project will measure the fixation from a series of abiotic reactions that may have been present on the early Earth (and other terrestrial planets) and produced organic material that could have ended up in the rock record. The work will look at a number of reactions, under a non- reducing, or mildly reducing, atmosphere, covering sources of prebiotic organic C & N from shock heating, to photochemistry, to hydrothermal reactions. Some reactions that we plan to study are; Shock heating of a non-reducing atmosphere to produce CO and NO (in collaboration with Chris McKay), formation of formaldehyde (and related compounds) from COY the formation of ammonia from nitrogen oxides (ultimately from NO) by ferrous iron reduction, and the hydrothermal synthesis of compounds including the hydrocarboxylation/hydrocarbonylation reaction (in collaboration with George Cody), reactions of oxalate to form hydrocarbons and other oxygenated compounds and the formation of lipids from oxalic/formic acid (in collaboration with Tom McCollom), and reactions of carbon monoxide & carbon dioxide with N2, ammonia or nitritehitrate to form hydrogen cyanide, nitriles, ammonia/amines and nitrous

Summers, David P.↗

NASA NTRS2019

The Effects of High-Temperature Fractional Crystallization on Calcium Isotopic Composition

We report Ca isotope fractionation among a co-genetic suite of samples from the Mauritanian Guelb el Azib ultramafic-mafic-anorthosite complex (GAC), which represents the fractional crystallization sequence of an igneous magma chamber. We investigate how the composition of an evolving crystallizing liquid and the resultant mineralogy of co-crystallizing assemblages affects inter-phase Ca isotope fractionation. Because the GAC is an Archean metamorphosed complex, we first investigate the resistance of the Ca isotope signature to secondary hydrothermal alteration and to metamorphism. While we cannot conclude here that Ca isotopes are undisturbed at the mineral scale, we show that they are preserved at the bulk rock scale. This is adequate for our study where several samples are almost monomineralic at the bulk scale level. The δ(exp 44/40)Ca (relative to NIST standard SRM 915a) of GAC layers range from −1.53 to 1.61‰, with the earliest-formed ultramafic cumulate layer being isotopically heaviest and the later, more felsic layers being isotopically lighter. For the first time, we show that plagioclase is much more enriched in light Ca isotopes compared to olivine and (Ca-) pyroxene. Monte Carlo simulations suggest that Ca isotopes are fractionated among co-existing silicate minerals during fractional crystallization, possibly in relation with the residual liquid composition. In qualitative agreement with computational models based on first principles lattice dynamics, we observe that Ca isotope fractionation is mineralogically controlled and importantly, that the degree of fractionation can vary according to the CaO composition of the residual liquid. While previous studies have aimed to understand partial melting as a source of Ca isotope fractionation, our results suggest that fractional crystallization is also a source of Ca isotope variability among co-genetic samples.

Maria C. Valdes↗

DOE OSTI2020

Perspective on Technical Lignin Fractionation

Technical lignin extracted from pulping and biorefining processes provides a class of complex and polydisperse phenolic polymers. Preparation of lignin with lower structural complexity and polydispersity through lignin fractionation is one of the primary solutions to engineer lignin into a value-added material. Sequential lignin fraction by pH controlled precipitation from 12 to 1 is one of the primary developed methods. Partial solubility of lignin in organic solvents is another promising method for lignin fractionation. Organic solvents with different polarity and solubility factors are able to fractionate lignin, yielding a more homogeneous chemical structure. As a modification of the lignin fractionation process using solvents, water/organic solvents mixture, such as propan-2-one, alcohols, and acetic acid, from room to high temperature has been proposed as a greener method for lignin fractionation. Using membrane technology is another promising method and current results indicate a good potential for lignin recovery and fractionation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

From acetone fractionation to lignin-based phenolic and polyurethane resins

In this paper, acetone fractionation was used to increase the homogeneity of softwood kraft lignin for product development. The acetone soluble and insoluble fractions were analyzed in terms of elemental composition, chemical structure, and thermal properties. The phenolic hydroxyl content of the acetone soluble fraction increased by 24%. The acetone soluble fraction of kraft lignin was used to fully substitute phenol in phenolic resin formulation. The resulting formulated lignin-formaldehyde adhesive showed higher adhesion strength (4.3 MPa) compared to a lab formulated phenol-formaldehyde resin (3.4 MPa) with 100% wood failure after lap shear test. On the other hand, the acetone insoluble lignin fraction, which had 23% higher aliphatic hydroxyl content compared to the starting lignin, was used to entirely replace petroleum-based polyol in polyurethane resin formulation. Then a bio-derived solvent (dihydrolevoglucosenone, Cyrene) was used to dissolve the acetone insoluble lignin fraction to synthesize lignin-based polyurethane resin. Tailoring the structure of kraft lignin through solvent fractionation resulted in two fractions, which were used to replace 100% of two major petrochemicals (phenol and polyol) in the formulations of phenolic and PU resins, that would otherwise be challenging due to the heterogeneity of softwood kraft lignin.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Accelerating gradient descent and Adam via fractional gradients

Here we propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Manganese sources and rates impact plant Mn concentrations and soil Mn fractions

Manganese (Mn) is an essential micronutrient for all organisms. In plants, Mn plays a critical role in photosynthesis and as a structural component of enzymes. In soils, Mn exists as different fractions of varying availability to plants. Mn fertilizers can be used to increase Mn availability to plants but are easily converted from a plant-available fraction (exchangeable Mn) to an unavailable fraction (Mn-oxides). Little research has been done in agricultural settings on soil Mn fractions; thus, the objective of this experiment was to study the effect of Mn additions on soil Mn fractions and plant Mn concentration. Here, a greenhouse experiment was conducted by growing soybean (Glycine max) treated with three Mn application rates (recommended or 1×, 10×, and 50×) of two sources (MnSO 4 and Mn ethylenediamine tetraacetic acid [MnEDTA]). Soil Mn fractions (Mehlich-1 extractable, exchangeable, organic-bound, Mn-oxide, residual) were quantified via sequential Mn extraction procedures. Bioavailability was evaluated by measuring soybean leaf Mn concentrations. Both fertilizer types increased available soil Mn fractions. Leaf Mn concentration increased with MnSO 4 50× application at the V3 stage and decreased with MnEDTA addition at the V3 and R2 stages. Mn additions likely resulted in the conversion of Mn into unavailable fractions. This was amplified by higher application rates, where total Mn increased by 18.5%, but available Mn decreased by 4.3% relative to initial soil values. Thus, our study showed that adding Mn to soils does not necessarily increase plant-available Mn.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Sulfur isotope fractionation between aqueous and carbonate-associated sulfate in abiotic calcite and aragonite

Sulfate (SO 4 2– ) incorporated into calcium carbonate minerals enables measurements of sulfur (S) isotope ratios in carbonate rocks. This Carbonate Associated Sulfate (CAS) in marine carbonate minerals is thought to faithfully represent the S isotope composition of the seawater sulfate incorporated into the mineral, with little or no S isotope fractionation in the process. However, comparison between different calcifying species reveals both positive and negative S isotope fractionation between CAS and seawater sulfate, and a large range of S isotope ratios can be found within a single rock sample, depending on the component measured. To better understand the isotopic effects associated with sulfate incorporation into carbonate minerals, we precipitated inorganic calcite and aragonite over a range covering more than two orders of magnitude of sulfate concentration and precipitation rate. Coupled measurements of CAS concentration, S isotope composition and X-ray absorption near-edge spectra (XANES) permit characterization and explanation of the observed dependence of S isotope fractionation between CAS and aqueous sulfate (CAS-SO 4 2– isotope fractionation) on sulfate concentration and precipitation rate. In aragonite, the CAS-SO 4 2– isotope fractionation is 1.0 ± 0.3‰ and independent of the sulfate (and CAS) concentration. In contrast, we note the CAS-SO 4 2– isotope fractionation in calcite covaries strongly with the sulfate concentration and weakly with the precipitation rate, between values of 1.3 ± 0.1 and 3.1 ± 0.6‰. We suggest that the correlation between aqueous sulfate concentration and CAS-SO 4 2– isotope fractionation in calcite reflects a dependence of the equilibrium S isotope fractionation on the concentration of CAS, through the effect of the sulfate impurity on the carbonate mineral’s energetic state.

58 GEOSCIENCES↗

DOE OSTI2022

High volume packing fraction TRISO-based fuel in light water reactors

We report that for a decade, fully ceramic microencapsulated (FCM) fuel, containing tri-structural isotropic (TRISO) fuel particles in a silicon carbide (SiC) matrix, has been investigated as an accident-tolerant fuel for light water reactors (LWRs). Other examples exist of TRISO-based concepts for LWR fuels with different matrix materials. Previous studies assumed TRISO particle volume packing of approximately 0.44 in SiC (or another) matrix, the highest realistic packing fractions possible with conventional manufacturing. Recent advances in advanced manufacturing have yielded the development and demonstration of a fuel form that consists of conventionally manufactured TRISO particles in a 3D-printed SiC matrix with significantly higher possible TRISO packing fractions (0.5–0.7). This increased uranium loading enhances the viability of using TRISO-based particle fuel forms in LWRs. The viability of high-packing-fraction TRISO-based particle fuel forms in LWRs is assessed from the perspective of fuel cycle length, achievable fuel burnup, reactivity coefficients, and fuel cycle performance. Higher-packing-fraction TRISO-based fuel enables either longer cycle lengths (by ~25% at a packing fraction of 0.55 relative to 0.44) at a constant enrichment or decreased enrichments (by ~25% at a packing fraction of 0.55 relative to 0.44) at a constant cycle length. Studies of different fuel kernel types (uranium nitride, uranium oxycarbide, and uranium carbide) yield similar results, although the cycle length of uranium oxycarbide is shorter than for uranium nitride or uranium carbide (due to the lower density of uranium oxide). This work also characterized the production of 14 C resulting from neutron absorption in 14 N during operation for uranium mononitride fuel kernels; the ratio of 14 C/N was 1–2 at. % at discharge. For the fuel cycle evaluation, the activity of spent nuclear fuel and high-level waste at 100 and 100,000 years was lower for high-packing-fraction fuels than for conventional LWR fuel. Environmental impact metrics were similar overall, but higher on the front end of the fuel cycle and lower on the back end of the fuel cycle. Reactivity coefficients of higher-packing-fraction TRISO-based fuel were reasonable compared with those of conventional fuels.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗