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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Directed energy deposition additive manufacturing of functionally graded Al-W composites

Directed energy deposition using laser heat sources (DED-L) is a metal additive manufacturing method that can be used to fabricate functionally graded materials by feeding multiple powder streams directly into a laser-generated melt pool. Additionally, the composition can be spatially varied by independent control of the materials feed rates. DED-L additive manufacturing is used in this work to create continuously graded Al/W composites that span 0–55 vol% W in Al over length scales from 0.6 to 1.2 mm with individual layers on the order of 0.1 mm and powder particle sizes on the order of 10 µm. The obtained composition and thickness ranges are comparable to those typically achieved using conventional powder metallurgy approaches and enables fabrication of composites to be used as a high impedance graded density impactor (GDI) in dynamic ramp compression experiments to study matter under extreme conditions. DED-L additive manufacturing of a GDI presents an opportunity to reduce GDI fabrication time to less than a day compared to many weeks by conventional methods. It is also possible to scale the deposition by DED-L to essentially unlimited dimensions in the lateral directions, whereas conventional methods become limited.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Harnessing dimethyl ether with ultra-low-grade heat for scaling-resistant brine concentration and fractional crystallization

Solvent-driven separations may enable scalable concentration of hypersaline brines, supporting a circular resource economy from the extraction of lithium and rare earth elements from spent battery and magnet leachates. This work analyses a novel solvent-driven water extraction (SDWE) system employing dimethyl ether (DME) and ultra-low-grade heat for brine concentration and fractional crystallization. SDWE exploits DME’s unique properties: (1) a low dielectric constant that promotes water solubility over charged solutes by a factor of 10 3 , and (2) a high volatility that facilitate efficient DME reconcentration with ultra-low-grade heat. The techno-economic viability of SDWE is assessed with a computational framework that encompasses a liquid–liquid separator and a solvent concentrator. We integrate the extended universal quasichemical model with the virial equation of state to predict the compositions of the complex three-phase DME-water mixture at vapor–liquid and liquid–liquid equilibrium. Subsequently, we optimize the thermodynamic and economic performance of SDWE, by controlling the interstage flash pressure, heat source temperature, and the number of concentrating stages. DME-based SDWE concentrates an input saline feed to 5.5 M and regenerates over 99 % of the DME using ultra-low-grade heat below 50 °C, with a DME/water selectivity ratio of 125. Here our calculations reveal that optimal performance is achieved at interstage flash pressures of 0.4 – 0.5 bar for heat source temperatures between 323–373 K, with improved exergetic efficiencies at lower temperatures. At a heat source temperature of 323 K and an interstage pressure of 0.489 bar, DME-driven SDWE achieves an optimal thermodynamic efficiency of 20.5 % and a projected specific cost of US$ 1.93 m -3 . These specific costs suggest that SDWE is competitive with commercialized thermal distillation technologies, while mitigating the traditional risks associated with scaling in heat and mass exchangers with hypersaline brines.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The 3D printing and modeling of functionally graded Kelvin foams for controlling crushing performance

Mechanical impact protection is an important consideration in many applications, ranging from product transportation to sports. Cellular materials are typically used due to their desirable energy absorption properties and light weight. However, their large deformation and rate dependent responses (especially of polymer foams) are challenging to consider in design. Additionally, the use of foams with uniform properties, such as uniform density and uniform stiffness, often restricts the designed foams to only be suitable for a narrow range of mechanical impact conditions whereas real applications commonly face unpredictable situations. 3D printing offers fabrication flexibility and thus opens the door to create foams with tailored properties. In this work, we investigate the feasibility of using 3D printing for functionally graded foams (FGFs) that are optimal over a broad range of mechanical environments. The foams are fabricated by the recently developed grayscale digital light processing (g-DLP) method which can print parts with locally designed properties. These foams are tested under drop test conditions and with slower displacement control. We also model the large deformation behavior of FGFs using finite element analysis in which we account for the different viscoelastic behaviors of the distinct grayscale regions. We then use the model to examine the impact mitigation capabilities of FGFs in different loading scenarios. Finally, we show how FGFs can be used to satisfy real-world design goals using the case study of a motorcycle helmet. In contrast to prior work, we investigate continuous, functionally graded foams of a single density that differ in their viscoelastic responses. This work provides further insight into the benefits of viscoelastic properties and modulus graded foams and presents a manufacturing approach that can be used to produce the next generation of flexible lattice foams as mechanical absorbers.

3D printing↗
DOE OSTI2020

Thermodynamic analysis and optimization of supercritical carbon dioxide Brayton cycles for use with low-grade geothermal heat sources

The transcritical carbon dioxide Rankine cycle has emerged as an alternative for power generation in low-grade heat applications. However, the low heat rejection temperatures required for condensing the carbon dioxide is almost prohibitive for many locations. A simple solution is the adoption of a supercritical carbon dioxide Brayton cycle which does not need such low temperature heat sinks. This power cycle has been poorly studied previously in low-grade heat applications. Therefore, with the aim of determining the performance and feasibility of the supercritical carbon dioxide Brayton cycle from thermodynamic viewpoint, using a low-grade geothermal heat source, this paper presents a comparative thermodynamic analysis between four different supercritical carbon dioxide Brayton cycles. For this purpose, detailed models were developed and solved by coupling the thermodynamic model with the thermal-hydraulic model of a Printed Circuit Heat Exchanger. Subsequently, simulations of a base case, a parametric analysis, and an optimization using Genetic Algorithms, were carried out. Results show that there is a combination of operating conditions that maximizes the electrical output of the system. Besides, some values of the minimum pressure of the cycles can increase substantially the precooler cooling water pumping power. At the optimum design point, using a 20 kg/s geothermal brine stream at 150 °C as heat source with a minimum allowable reinjection temperature of 70 °C, the Intercooled Recuperated Brayton Cycle achieved the highest electric power output, energy and exergy efficiencies, obtaining values of 779.99 kW, 11.51%, and 52.49%, respectively. The other feasible alternatives were the Recuperated Brayton Cycle, the Simple Brayton Cycle and the Intercooled Brayton Cycle, ranked, in that order.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Performance analysis of functionally graded multifunctional piezoelectric energy harvesting microgyroscopes

Functionally graded materials (FGMs) are composite materials with varying material properties in one or more directions. These materials possess distinct characteristics compared to their constituent components. The ability to control material distribution and compositions in FGMs offers improved constraints over the natural frequencies of the system, making them highly suitable for energy harvesting applications. In this study, we focus on a piezoelectric FGM composed of Platinum (Pt) and Lead Titanate Zirconate (PZT). By utilizing FGMs for energy harvesting, we simplify the system from a multilayer structure to a single-layer system, thereby increasing power density by reducing volume. In this work, a power law distribution is used to model the material variation throughout the thickness of the single-layered beam. The governing equations of motion and boundary conditions for FG energy harvesting microgyroscope are derived using Euler-Bernoulli beam theory, the constitutive piezoelectric principle, and the extended Hamilton's principle. To simulate the nonlinear motion of the FG energy harvester, we employ the differential quadrature method (DQM). Subsequently, an investigation is carried out to examine the effects of various factors including material distribution, platinum percentage, base rotation, DC voltage, and electrical load resistance on the energy harvesting microgyroscope with functionally graded materials. Here, the findings suggest that functionally graded energy harvesting gyroscopes can be adjusted to obtain effective energy harvesting and sensing capabilities by carefully selecting the material distribution, input voltage, and electrical load resistance.

42 ENGINEERING↗
DOE OSTI2025

Directed energy deposition of functionally graded V-4Cr-4Ti to Fe-9Cr transition for fusion power systems

This study proposes a graded structure via additive manufacturing for divertor and first wall blanket applications in fusion reactors. Materials were selected based on thermodynamic calculations to operate from 1100 °C at the plasma-facing level to 550 °C at the structural steel level. Conventional joining methods often lead to failures due to discrete reaction layers with significant mechanical property differences. Using laser beam-directed energy deposition (LB-DED), this study demonstrates the fabrication of a VCrTi-Gr91 steel functionally graded component through a novel process parameter optimization framework. A systematic approach included powder characterization, single-track depositions, and construction of printability maps. Near full-density specimens of each interlayer were additively manufactured, and a transition from V-based alloys to reduced activation ferritic martensitic steels was achieved. Computational material selection of interlayer alloys and thermodynamic/diffusion kinetics simulations prevented most interface incompatibilities. A brittle intermetallic formed at one interface, causing cracking, which was not predicted by current thermodynamic models. Transition alloy design approach was updated with a more recent database and a mitigation strategy has been proposed to eliminate the formation of deleterious intermetallic phases. Ultimately, LB-DED has proven effective for producing multi-material graded systems for fusion applications, with the demonstrated process parameter optimization framework applicable to various materials.

Additive manufacturing↗
DOE OSTI2021

Enhanced mechanical properties of additive manufactured Grade 91 steel

High temperature stability of the mechanical properties, including creep behavior, are important factors to consider in certifying additive manufactured (AM) steels for reactor operation. AM-Grade 91 steel, tested at RT is shown to possess high yield strength, strain hardening and ductility even after high temperature aging for extended hours. Enhanced creep resistance at 650 ⁰C is also evident in the AM Grade 91 steel compared to wrought Grade 91 steel tested at the same conditions. In conclusion, the diverse and complex microstructure of this AM steel allows for both enhanced strength and ductility but increases the ductile-to-brittle transition temperature in these steels.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Leveraging Sequential Doping of Semiconducting Polymers to Enable Functionally Graded Materials for Organic Thermoelectrics

With the ability to modulate electronic properties through molecular doping coupled with ease in processability, semiconducting polymers are at the forefront in enabling organic thermoelectric devices for thermal energy management. In contrast to uniform thermoelectric material properties, an alternative route focuses on functionally graded materials (FGMs) where one spatially controls and optimizes transport properties across the length of a thermoelectric material. While primarily studied in the context of inorganic materials, the concept of FGMs for organic thermoelectrics has not been explored. Herein, we introduce how molecular doping of semiconducting polymers enables spatial compositional control of thin-film FGMs. Specifically, we utilize sequential vapor doping of poly[2,5-bis(3-tetradecylthiophen-2-yl) thieno [3,2-b]thiophene] (PBTTT) with the small molecule acceptor 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F4TCNQ) to fabricate the simplest form of FGMs – double- segmented thin films. The two thin-film segments are of equal length (7.5 mm), but each set to different doping levels. Our study focuses on understanding the thermoelectric properties (Seebeck coefficient, α, and electronic conductivity, σ) and structural properties (through X-ray scattering, UV-vis-NIR spectroscopy, and Raman spectroscopy) within and across the two segments. We observe the presence of a small diffuse interfacial region of 0.5 – 1 mm between the two segments where the doping level and transport properties vary continuously. Despite the diffuse interface, the measured effective Seebeck coefficient (αeff) across the two segments is simply the average of α within each segment. Importantly, this experimental result is consistent with reported mathematical models describing αeff in graded thermoelectric materials. Finally, our results demonstrate the facile fabrication and characterization of functionally graded organic thermoelectric materials, providing guidelines for further development on more complex FGMs.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Characterization of textile-grade carbon fiber polypropylene composites

In this work, we consider low-cost carbon fiber produced with a textile-grade precursor. The objective of the study is to investigate textile-grade carbon-fiber-reinforced-polypropylene composites (TCF-PP) from compounded pellets for mechanical and thermal characterization. Four sets of pellets with 1%, 5%, 10%, and 15% reinforcement were manufactured using textile-grade carbon fiber (TCF) and polypropylene (PP) by twin-screw compounding. The addition of TCFs through gravimetric feeder directly in the extruder resulted in lower fiber content; however, side feeder has shown good potential. The pellets were further processed in extrusion compression molding to manufacture plaques. An increase in fiber loading has a negligible effect on fiber attrition as fiber length distribution variation between 1% and 15% reinforced pellets was very small. The addition of TCFs in PP showed a significant improvement in mechanical properties. The tensile strength and modulus of the composite were 26% and 161%, respectively, improved by the addition of 10 wt% TCF. Similar results were observed in the flexure test. However, the impact properties were reduced by 25.54% by the addition of 15% TCF.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Hardness Prediction by Incorporating Heat Transfer and Molten Pool Fluid Flow in a Multi-pass, Multi-layer Weld for Onsite Repair of Grade 91 steel

Introduction: In the current fleet of fossil-fired power plants, creep strength enhanced ferritic steels (CSEF) are used to sustain the harsh service conditions. Enhanced properties of Grade 91 steel result from tempered martensite with a fine distribution of MX and M23C6 carbides. Grade 91 steel is subjected to onsite welding repair to remedy their degradation due to extreme service condition. Knowledge of weld repairability of these steels, such as as-welded hardness distribution, is essential to establishing sound repair procedures. Experimental trial and error tests can consume a lot of time as many welding variables need to be studied. For numerical modelling, most of the multi-pass multi-layer models are based on finite element method, which are limited to solve the heat conduction equation and ignore convective heat transfer due to melt flow. Moreover, the mesh has to be pre-built based on a known or assumed weld cross-section geometry. These finite element based models thus have limited predictive capability as defects are not considered and nugget size are pre-assumed. This research aims at developing a thermal and microstructure evolution model incorporating molten pool dynamics in a multi-pass multi-layer material deposition to predict the as-welded hardness distribution. Technical Approach: All the thermal, physical, and metallurgical properties of Grade 91 as a function of temperature are collected from the literature and inputted into the thermo-fluid model based on Flow-3D, a computational fluid dynamics software. A multi-pass, multi-layer material deposition is simulated where the melting of filler wire into the molten pool is directly considered based on the volume of fluid (VOF) method. The flow behaviour of the molten pool is used to understand the formation of deposition geometry and defects. The temperature profiles during the multi-pass, multi-layer welding are calculated. The results computed using the new model are compared against the experimental data of fusion zone geometry and thermal cycles. Hardness prediction in the heat-affected zone (HAZ) are made using Johnson-Mehl-Avrami (JMA) equation for solid-state phase transformation kinetics. The JMA parameters are extracted from the experimental data available in the literature. For comparison, a standard finite element heat conduction model is also developed to predict the thermal cycles and hardness distribution in the multi-pass, multi-layer weld. Expected Result: Results obtained using the molten pool dynamic simulation versus the finite element heat conduction model are compared. Specifically, the effects of convective heat transfer on the accuracy of the calculated thermal history, bead shape and size, and HAZ hardness distribution are examined.

Modeling, Grade 91 steel, Multi-pass multi-layer d↗
DOE OSTI2024

Dynamic Modeling and Characterization of Nuclear-grade Graphite

Idaho National Labs serves as the spearhead for many innovative energy solutions to the world's energy crisis. One such solution is the INL's Microreactor which is designed to deploy to extreme/remote environments where other sources of power are either unavailable or unreliable. In order to best design these energy solutions for their operational environments, it is crucial to understand how the design, components, and materials will respond to the environmental conditions. One key material in these innovative designs is a nuclear-grade graphite known as PCEA. This study examines the behavior of PCEA graphite under dynamic loading, similar to that which may occur in extreme environments. The objective is to characterize the dynamic behavior and produce an accurate, reliable constitutive model suitable for use in simulation tools such as INL's MOOSE. Graphite specimens were tested using a Split Hopkinson Pressure Bar (SHPB) to administer the dynamic compressive load. The SHPB was charged at various pressures to produce a range of strain rates on the material in compression. Data was acquired via strain gauges on the SHPB setup, from which stress, strain, and time data were collected. Analysis revealed the stress-strain behavior of the material as well as insights into the material behavior's relationship to strain rate. Further work must continue to characterize the various other dynamic behaviors of the material which will combine to create a substantially trustworthy constitutive model for this grade of nuclear-grade graphite. Ultimately, this will allow for realistic simulation of the material in reactor designs, allowing for prediction of design weaknesses and leading to improved designs for increased resilience, security, and reliability.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Sensitivity and Detection Limit of Spectroscopic-Grade Perovskite CsPbBr 3 Crystal for Hard X-Ray Detection

We report spectroscopic-grade single crystal detectors can register the energies of individual X-ray interactions enabling photon-counting systems with superior resolution over traditional photoconductive X-ray detection systems. Current technical challenges have limited the preparation of perovskite semiconductors for energy-discrimination X-ray photon-counting detection. Here, this work reports the deployment of a spectroscopic-grade CsPbBr 3 Schottky detector under reverse bias for continuum hard X-ray detection in both the photocurrent and spectroscopic schemes. High surface barriers of approximate to ≈ 1 eV are formed by depositing solid bismuth and gold contacts. The spectroscopic response under a hard X-ray source is assessed in resolving the characteristic X-ray peak. The methodology in enhancing X-ray sensitivity by controlling the X-ray energies and flux, and voltage, is described. The X-ray sensitivity varies between a few tens to over 8000 μC Gy air -1 cm -2 . The detectable dose rate of the CsPbBr 3 detectors is as low as 0.02 nGy air s -1 in the energy discrimination configuration. Finally, the unbiased CsPbBr 3 device forms a spontaneous contact potential difference of about 0.7 V enabling high quality of the CsPbBr 3 single crystals to operate in "passive" self-powered X-ray detection mode and the X-ray sensitivity is estimated as 14 μC Gy air -1 cm -2 . The great potential of spectroscopic-grade CsPbBr 3 devices for X-ray photon-counting systems is anticipated in this work.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Understanding ERE and iVOC Metrics for Graded CdSeTe Absorbers

PL-based external radiative efficiency (ERE) and implied open-circuit voltage (iVOC) metrics were introduced for thin-film solar absorbers to better understand the voltage deficit and diagnose losses in solar cells. Traditionally, elevated ERE and iVOC measurements are associated with diminished recombination within the solar device, a rationale heavily reliant on the assumption of a uniform bandgap and high carrier mobilities in the absorber. Recently, very low mobilities in CdSeTe absorbers (< 1 cm2/(V.s)) were measured using the light-induced transient grading technique. In this study, we use a detailed numerical model of iVOC to investigate the possible reasons of elevated iVOC in realistic CdSeTe absorbers with a graded Se profile. In particular, we examine how the bandgap nonuniformity and the reduced hole mobility in graded CdSeTe absorbers affect iVOC measurements. We show that high iVOC may result from inflated quasi-Fermi level splitting in the high-Se region in the front part of a CdSeTe absorber with slow hole transport. We reproduce the experimentally reported 360 mV increase in iVOC-VOC gap with reduced doping using a model with sub-1 cm2/(V.s) hole mobility in the high-Se region. Based on our results, we conclude that the iVOC metric (or ERE metric) should not be used as a sole metric of CdSeTe absorber quality. We discuss possible ways to extract useful information from the iVOC-VOC gap by supplementing the front-side illumination measurements with back-side illumination measurements.

14 SOLAR ENERGY↗
DOE OSTI2021

Testing and Modeling of Functionally Graded Aluminum-Doped Zinc Oxide Using Spark Plasma Sintering and Discrete Powder Layers of Varying Composition

Functionally graded material (FGM) ZnO is made via spark plasma sintering/field-assisted sintering technique (SPS/FAST) by varying the Al dopant content along the z-axis or pressing direction. A wide range of Al content (0–5 wt%) is used by adding Al powder to nanosized ZnO powder. Thermoelectric (TE) measurements are done on the FGM and individual layers made separately. X-ray diffraction (XRD) shows two phases, ZnO and spinel phase (ZnAl 2 O 4 ). High-resolution Raman spectroscopy reveals doped ZnO and spinel phase (ZnAl 2 O 4 ) spatially and shows segregation in the layer with highest Al content. Electron backscatter diffraction (EBSD) reveals noticeable grain growth with decreasing Al content, and there is a common, random preferred orientation in all layers. The tested properties are used to simulate efficiency curves for a discretely graded, five-layer FGM as well as a homogenous material, where both graded structures provide an opportunity to widen the current density ranges and therefore the temperature range of useful energy conversion.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Investigation of W-SiC compositionally graded films as a divertor material

W-SiC composite material is a promising plasma-facing material candidate alternative to pure W due to the low neutron activation, low impurity radiation, and low tritium diffusivity of SiC while leveraging the high erosion resistance of the W armor. Additionally, W and SiC have high thermomechanical compatibility given their similar thermal expansion rates. The present study addresses the synthesis and performance of compositionally graded W-SiC films fabricated by pulsed-DC magnetron sputtering. Compositional gradients were characterized using transmission electron microscopy (TEM) and energy-dispersive X-ray spectroscopy (EDS), and crystallographic information was obtained using electron diffraction and X-ray diffraction (XRD). Samples were exposed to L-mode deuterium plasma discharges in the DIII-D tokamak using the Divertor Material Evaluation System (DiMES). Post-mortem characterizations were performed using scanning electron microscopy (SEM) and XRD. Electron diffraction and XRD showed that the compositionally graded W-SiC films were composed of polycrystalline W and amorphous SiC with amorphous W+SiC interlayers. No macroscopic delamination or microstructural changes were observed under mild exposure conditions. Here, this study serves as a preliminary examination of W-SiC compositionally graded composites as a potential candidate divertor material in future tokamak devices.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Strain-Mediated Sn Incorporation and Segregation in Compositionally Graded Ge 1– x Sn x Epilayers Grown by MBE at Different Temperatures

We investigated the process of Sn incorporation and surface segregation for compositionally graded Ge 1–x Sn x epilayers grown on high-quality Ge (001) substrates. Here, the growth resulted in pseudomorphic GeSn layers with a ~6% maximal Sn fraction at a constant substrate temperature. The maximal fraction of Sn was increased to 9.0% when the growth temperature was continuously lowered while increasing the Sn flux. The analysis of surface droplets and SIMS profiles of elemental composition give evidence of Sn rejection during the growth, potentially associated with a critical energy of elastic strain. The intentional reduction of the coherent strain by decreasing the Sn flux near the sample surface has been shown to trap a higher fraction of Sn in the Ge 1–x Sn x layer and lower surface segregation. Our results demonstrate that strain relief by misfit dislocations in the compositionally graded layer is inhibited, which leads to Sn segregation. Specifically, the compressive strain in the graded Ge 1–x Sn x epilayer is effectively “zero” near the interface with the Ge substrate and increases up to about –1.5 × 10 –2 near the surface. Thus, although the nucleation of a dislocation may reduce the compressive strain for the top region of the epilayer, it is not beneficial for the bottom region.

42 ENGINEERING↗
DOE OSTI2025

Sustainable potassium sorbate production from triacetic acid lactone in food-grade solvents

This study advances the production of potassium sorbate (KS) from triacetic acid lactone (TAL) utilizing food-grade solvents, ethanol (EtOH) and isopropyl alcohol (IPA). Here, we have previously demonstrated the route to produce KS from TAL in tetrahydrofuran (THF) as the main solvent, but the use of THF is associated with environmental and health risks especially for food applications. The process employs a catalytic approach in food-grade solvents and includes three main steps: hydrogenation, etherification and hydrolysis, and ring-opening hydrolysis to produce KS from TAL. In the synthesis of KS from TAL, the use of IPA leads to higher yields and reduced reaction times compared to EtOH. As a result, the overall reaction time in IPA was reduced to 35.7 h, compared to 42.1 h in our previous study using THF and EtOH, while achieving a comparable KS yield of 84% from TAL. The synthesized KS exhibits a trans-2, trans-4 geometrical configuration, identical to that of commercially available KS. Through techno-economic analysis (TEA) and life cycle assessment (LCA), we estimated full-scale production of KS from sugarcane with the developed process in IPA could achieve a minimum product selling price (MPSP) of $\$8.27$ per kg with a range of $\$7.06$–10.16 per kg [5th–95th percentiles from 6000 Monte Carlo simulations] and a carbon intensity (CI) of 13.7 [9.6–18.6] kg CO 2 -eq per kg. This study highlights the synthesis of KS from TAL using food-grade solvents, demonstrating improved economic viability and environmental sustainability compared to our previous research (MPSP of $\$9.68$ per kg [$\$8.47$–11.45 per kg] and CI of 16.2 [12.0–21.2] kg CO 2 -eq per kg), as the total required reaction decreases while achieving the comparable overall yield of KS from TAL.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Hamiltonian systems, Toda lattices, solitons, Lax pairs on weighted Z -graded graphs

In this study, we consider discrete one-dimensional nonlinear equations and present the procedure of lifting them to Z -graded graphs. We identify conditions that allow one to lift one-dimensional solutions to solutions on graphs. In particular, we prove the existence of solitons for static potentials on graded fractal graphs. We also show that even for a simple example of a topologically interesting graph, the corresponding non-trivial Lax pairs and associated unitary transformations do not lift to a Lax pair on the Z -graded graph.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗