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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 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Exploring the Influence of Linker Substitution and Ratios on Cooperative Framework Flexibility through the Mixed-Linker Approach

Cooperatively flexible metal–organic frameworks that exhibit step-shaped, or Type V-like, adsorption–desorption profiles can lower requisite pressure–temperature swings and thus energy input, necessary for an array of gas storage, delivery, and separations applications. However, such benefits are lost if the pressure threshold of the adsorption and desorption steps at a given temperature does not match the conditions dictated by the application, such as H 2 storage and delivery or olefin–paraffin separations. Unfortunately, the discovery of cooperatively flexible frameworks remains wholly serendipitous and de novo design remains impossible. Accordingly, there is a great need to further our understanding of flexibility such that we can intuitively derivatize known frameworks and, ultimately, design entirely new ones to meet the requisite conditions of energy-consumptive processes. In this work, we demonstrate that the mixed-linker, or multivariate, approach is a powerful tool for the derivation of a known flexible framework, with variances in linker substitution and ratio giving rise to a family wherein significant changes to the step-shaped adsorption–desorption profiles for multiple adsorbates are observed. Specifically, we report 12 isostructural mixed-linker derivatives of CdIF-13 (sod–Cd(benzimidazolate) 2 ) with six point-modified benzimidazole linkers spontaneously synthesized through prototypical solvothermal conditions. Furthermore, each is shown by PXRD to exhibit similar reversible flexibility to CdIF-13 and by TGA and DSC to be similarly thermally stable. Isothermal gas adsorption measurements with N 2 at 77 K, CO 2 at 195 K, and propane at 298 K demonstrate the wide-ranging, adsorbate-dependent effects of linker substitution and ratio, including dramatic reductions in the adsorption threshold pressure, evolution of multiple steps, and complete absence of observable adsorption. Aided by prior crystallographic characterization of CdIF-13, the observed trends were analyzed in an attempt to resolve the influence of linker substitution and ratios on structural behavior. In total, this work illustrates how the mixed-linker approach enables the synthesis and study of a large catalog of functionally modified frameworks, which can help identify the variables that influence flexibility and sorption behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Anomalous H 2 Desorption Rate of NaAlH 4 Confined in Nitrogen-Doped Nanoporous Carbon Frameworks

Confining NaAlH 4 in nanoporous carbon scaffolds is known to alter the sorption kinetics and/or pathways of the characteristic bulk hydride reactions through interaction with the framework at the interface, increased specific surface area of the resulting nanoparticles, decreased hydrogen diffusion distances, and prevention of phase segregation. Although the nanosize effects have been well studied, the influence of the carbon scaffold surface chemistry remains unclear. Here we compare the hydrogen sorption characteristics of NaAlH 4 confined by melt infiltration in nitrogen-doped/undoped ordered nanoporous carbon of two different geometries. 23 Na and 27 Al MAS NMR, N 2 sorption, and PXRD verify NaAlH 4 was successfully confined and remains intact in the carbon nanopores after infiltration. Both the N-doped/undoped nanoconfined systems demonstrate improved reversibility in relation to the bulk hydride during hydrogen desorption/absorption cycling. Isothermal kinetic measurements indicate a lowering of the activation energy for H 2 desorption by as much as 70 kJ/mol in N-doped frameworks, far larger than the reduction in carbon-only frameworks. Most interestingly, this dramatic lowering of the activation energy is accompanied by an unexpected and anomalously low NaAlH 4 desorption rate in the N-doped frameworks. This suggests that the framework surface chemistry plays an important role in the desorption process and that the rate limiting step for desorption may be associated with interactions of the hydride and host surface. Our results indicate that functionalization of carbon scaffold surface chemistry with heteroatoms provides a powerful method of altering the characteristic hydrogen sorption properties of confined metal hydride systems. Furthermore, this technique may prove beneficial in the path to a viable metal hydride-based hydrogen storage system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A Julia Framework for Graph-Structured Nonlinear Optimization

Graph theory provides a convenient framework for modeling and solving structured optimization problems. Under this framework, the modeler can arrange/assemble the components of an optimization model (variables, constraints, objective functions, and data) within nodes and edges of a graph, and this representation can be used to visualize, manipulate, and solve the problem. In this work, we present a Julia framework for modeling and solving graph-structured nonlinear optimization problems. Our framework integrates the modeling package Plasmo.jl (which facilitates the construction and manipulation of graph models) and the nonlinear optimization solver MadNLP.jl (which provides capabilities for exploiting graph structures to accelerate solution). We illustrate with a simple example how model construction and manipulation can be performed in an intuitive manner using Plasmo.jl and how the model structure can be exploited by MadNLP.jl. We also demonstrate the scalability of the framework by targeting a large-scale, stochastic gas network problem that contains over 1.7 million variables.

Cole, David↗
DOE OSTI2024

Plutonium and Cerium Perrhenate/Pertechnetate Coordination Polymers and Frameworks

Spent nuclear fuel (SNF) contains transuranic and lanthanide species, which are sometimes recovered and repurposed. One particularly problematic fission product, 99 TcO 4 – , hampers this recovery via coextraction with high valence metals, perhaps by complexation during aqueous reprocessing of SNF. There is limited molecular-level knowledge concerning the coordination chemistry between TcO 4 – or its well-known surrogate ReO 4 – and transuranic/lanthanide species. In the current study, we investigated the coordination of ReO 4 – /TcO 4 – with plutonium and cerium cations by structural and chemical characterization of a series of isolated extended solids. In this study, Ce represents both trivalent lanthanides and is considered a surrogate for Pu, respectively, in its common trivalent and tetravalent oxidation states. The structural elucidation of the seven isolated crystalline solids revealed that ReO 4 – /TcO 4 – directly connects to Pu IV , Pu VI O 2 2 + , Ce III , and Ce IV in the terminal and bridging coordination modes, leading to 1-, 2-, and 3-dimensional frameworks. For example, ReO 4 – coordination to Pu(IV) formed a 1D chain or 2D framework, isostructural with previously isolated Th(IV) compounds. However, Pu VI O 2 2 + alternating with ReO 4 – led to a unique 1D chain, different from the prior-reported U(VI)/Np(VI)-ReO 4 – /TcO 4 – structures. Coordination of ReO 4 – /TcO 4 – with Ce(III) promotes the assembly of 3D frameworks. Finally, attempted synthesis of a Ce(IV)-ReO 4 – compound resulted in a 2D framework with a mixed-valence Ce III/IV . The highly acidic reaction conditions supported the reduction of both Ce IV and Tc VII , challenging isolation of compounds featuring these species. Only one TcO 4 -containing structure was obtained in this study (Ce III –TcO 4 3D framework), vs the six total Ce/Pu-ReO 4 compounds. Furthermore, our three Pu-ReO 4 crystal structures are the first reported and translated to atomic-level information about Pu-TcO 4 coordination in nuclear fuel reprocessing scenarios, in addition to broadening our knowledge of bonding trends in the early, high-valence actinides.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2015

Single-crystal-to-single-crystal metalation of a metal-organic framework: A route toward structurally well-defined catalysts

Metal–organic frameworks featuring ligands with open chelating groups are versatile platforms for the preparation of a diverse set of heterogeneous catalysts through postsynthetic metalation. The crystalline nature of these materials allows them to be characterized via X-ray diffraction, which provides valuable insight into the structure of the metal sites that facilitate catalysis. A highly porous and thermally robust zirconium-based metal–organic framework, Zr 6 O 4 (OH) 4 (bpydc) 6 (bpydc 2– = 2,2'-bipyridne-5,5'-dicarboxylate), bears open bipyridine sites that readily react with a variety of solution- and gas-phase metal sources to form the corresponding metalated frameworks. Remarkably, Zr 6 O 4 (OH) 4 (bpydc) 6 undergoes a single-crystal-to-single-crystal transformation upon metalation that involves a change in space group from $Fm\bar{3}m$ to $Pa\bar{3}m$. This structural transformation leads to an ordering of the metalated linkers within the framework, allowing structural characterization of the resulting metal complexes. Furthermore, Zr 6 O 4 (OH) 4 (bpydc) 6 yields an active heterogeneous catalyst for arene C–H borylation when metalated with [Ir(COD) 2 ]BF 4 (COD = 1,5-cyclooctadiene). These results highlight the unique potential of metal–organic frameworks as a class of heterogeneous catalysts that allow unparalleled structural characterization and control over their active sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A Pathway Analysis Framework for Evaluating the Economic and Environmental Viability of Biomass-Based Plastic Production

Plastic production from fossil feedstocks (e.g., naphtha, coal, and natural gas) is not sustainable and causes known environmental impacts such as global warming. A possible solution is to shift production pathways to use biomass, which is a sustainable feedstock that can sequester atmospheric carbon dioxide. This study presents an optimization-based pathway analysis framework for evaluating the carbon footprints of the production of mainstream plastics from biomass and fossil feedstocks. We use the modeling framework to quickly navigate complex interdependencies that exist between the production pathways of different plastics and to determine pathways of minimum production cost under a range of carbon pricing scenarios. The framework interprets carbon prices as an exogenous taxation scheme or an endogenous negative value perceived by producers. The proposed approach reveals the biomass feedstock quantities needed to displace fossil counterparts and the plastics and technologies that should be prioritized. The framework can also be used for evaluating system-wide trade-offs between production costs and carbon footprints that arise from pathway interdependencies. We also evaluate hidden environmental impacts associated with the large-scale use of biomass as a feedstock, such as land use and water eutrophication that results from a significant increase in fertilizer use. Therefore, it is important to highlight that there are trade-offs between decarbonization and other environmental issues. Here, the proposed framework provides an integrative platform for basic techno-economic and life-cycle data that can be used for analyzing diverse scenarios and determining necessary technology targets (e.g., yields, footprints, and costs) to achieve required levels of decarbonization.

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

Combining Theory and Experiment to Map the Atomic-Level Structure–Energy Pathways of Adsorbate-Mediated Phase Changes in a Cooperatively Flexible Metal–Organic Framework

An important subclass of metal–organic frameworks (MOFs) exhibits cooperative flexibility, wherein individual crystallites undergo global structural phase changes in response to external stimuli. Where cooperative flexibility results in reversible changes between crystalline states of distinct accessible porosity, these frameworks can exhibit rare yet desirable behaviors that cannot be explained by local dynamics alone. Yet, the chemical and structural origins of cooperative flexibility and how frameworks undergo these reversible phase changes at the atomic level remain poorly understood. Deliberate design for specific applications is therefore exceedingly difficult, and there is great impetus to develop a fundamental understanding of this phenomenon. Here, an effective and widely accessible computational approach is developed, which is designed to provide microscopic resolution via direct comparison to experimental data along the desorption-guided pathway. The strategy is applied to explain the desorption-induced phase change in an experimentally well-characterized framework, CdIF-13 (sod-Cd(benzimidazolate)2), where experiment alone was unable to resolve the atomistically detailed phase change landscape. Our findings reveal that the cooperative phase change pathways are adsorbate dependent with thermodynamics of intermediate structural states dictated by a nuanced interplay of ligand orientation, skeletal symmetry, and modes of surface adsorption. The results reveal that this isotropically flexible framework is “chaperoned” through a complex energy landscape by specific adsorbates, revealed by the reported computational approach with atomic-level insight and validated by experimentally determined structures. Thus, this work facilitates both understanding and future design of flexible materials for applications in gas storage, transport, delivery, and separation technologies.

03 NATURAL GAS↗
DOE OSTI2016

Olsalazine-Based Metal–Organic Frameworks as Biocompatible Platforms for H 2 Adsorption and Drug Delivery

The drug olsalazine (H4olz) was employed as a ligand to synthesize a new series of mesoporous metal–organic frameworks that are expanded analogues of the well-known M2(dobdc) materials (dobdc4– = 2,5-dioxido-1,4-benzenedicarboxylate; M-MOF-74). The M2(olz) frameworks (M = Mg, Fe, Co, Ni, and Zn) exhibit high surface areas with large hexagonal pore apertures that are approximately 27 Å in diameter. Variable temperature H2 adsorption isotherms revealed strong adsorption at the open metal sites, and in situ infrared spectroscopy experiments on Mg2(olz) and Ni2(olz) were used to determine site-specific H2 binding enthalpies. In addition to its capabilities for gas sorption, the highly biocompatible Mg2(olz) framework was also evaluated as a platform for the delivery of olsalazine and other encapsulated therapeutics. The Mg2(olz) material (86 wt % olsalazine) was shown to release the therapeutic linker through dissolution of the framework under simulated physiological conditions. Furthermore, Mg2(olz) was used to encapsulate phenethylamine (PEA), a model drug for a broad class of bioactive compounds. Under simulated physiological conditions, Mg2(olz)(PEA)2 disassembled to release PEA from the pores and olsalazine from the framework itself, demonstrating that multiple therapeutic components can be delivered together at different rates. The low toxicity, high surface areas, and coordinatively unsaturated metal sites make these M2(olz) materials promising for a range of potential applications, including drug delivery in the treatment of gastrointestinal diseases.

Levine, Dana J.↗
DOE OSTI2014

Three-dimensional periodic supramolecular organic framework ion sponge in water and microcrystals

Self-assembly has emerged as a powerful approach to generating complex supramolecular architectures. Despite there being many crystalline frameworks reported in the solid state, the construction of highly soluble periodic supramolecular networks in a three-dimensional space is still a challenge. In this paper we demonstrate that the encapsulation motif, which involves the dimerization of two aromatic units within cucurbit[8]uril, can be used to direct the co-assembly of a tetratopic molecular block and cucurbit[8]uril into a periodic three-dimensional supramolecular organic framework in water. The periodicity of the supramolecular organic framework is supported by solution-phase small-angle X-ray-scattering and diffraction experiments. Upon evaporating the solvent, the periodicity of the framework is maintained in porous microcrystals. Lastly, as a supramolecular 'ion sponge', the framework can absorb different kinds of anionic guests, including drugs, in both water and microcrystals, and drugs absorbed in microcrystals can be released to water with selectivity.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Phase-enabled metal-organic framework homojunction for highly selective CO 2 photoreduction

Conversion of clean solar energy to chemical fuels is one of the promising and up-and-coming applications of metal–organic frameworks. However, fast recombination of photogenerated charge carriers in these frameworks remains the most significant limitation for their photocatalytic application. Although the construction of homojunctions is a promising solution, it remains very challenging to synthesize them. Herein, we report a well-defined hierarchical homojunction based on metal–organic frameworks via a facile one-pot synthesis route directed by hollow transition metal nanoparticles. The homojunction is enabled by two concentric stacked nanoplates with slightly different crystal phases. The enhanced charge separation in the homojunction was visualized by in-situ surface photovoltage microscopy. Moreover, the as-prepared nanostacks displayed a visible-light-driven carbon dioxide reduction with very high carbon monooxide selectivity, and excellent stability. Our work provides a powerful platform to synthesize capable metal–organic framework complexes and sheds light on the hierarchical structure-function relationships of metal–organic frameworks.

14 SOLAR ENERGY↗
DOE OSTI2021

PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys

Abstract The PRISMS-Fatigue open-source framework for simulation-based analysis of microstructural influences on fatigue resistance for polycrystalline metals and alloys is presented here. The framework uses the crystal plasticity finite element method as its microstructure analysis tool and provides a highly efficient, scalable, flexible, and easy-to-use ICME community platform. The PRISMS-Fatigue framework is linked to different open-source software to instantiate microstructures, compute the material response, and assess fatigue indicator parameters. The performance of PRISMS-Fatigue is benchmarked against a similar framework implemented using ABAQUS. Results indicate that the multilevel parallelism scheme of PRISMS-Fatigue is more efficient and scalable than ABAQUS for large-scale fatigue simulations. The performance and flexibility of this framework is demonstrated with various examples that assess the driving force for fatigue crack formation of microstructures with different crystallographic textures, grain morphologies, and grain numbers, and under different multiaxial strain states, strain magnitudes, and boundary conditions.

Chemistry↗
DOE OSTI2018

SSZ-70 Borosilicate Delamination Without Sonication: Effect of Framework Topology on Olefin Epoxidation Catalysis

Here, we report a scalable delamination procedure for a SSZ-70-framework layered-zeolite precursor, which for the first time does not involve either sonication or long-chain surfactants. Our approach instead relies on the mild heating of layered zeolite precursor B-SSZ-70(P) in an aqueous solution containing Zn(NO 3 ) 2 and tetrabutylammonium fluoride. Powder X-ray diffraction data are consistent with a loss of long-range order along the z-direction, while 29 Si MAS NMR spectroscopy demonstrates preservation of the zeolite framework crystallinity during delamination. The resulting delaminated material, DZ-2, possesses 1.4-fold higher external surface area relative to the nondelaminated three-dimensional zeolite B-SSZ-70, based on N2 physisorption data at 77 K. DZ-2 was functionalized with cationic Ti heteroatoms to synthesize Ti-DZ-2 via exchange with framework B. Ti-DZ-2 contains isolated titanium centers in its crystalline framework, as shown by UV-Vis spectroscopy. The generality of the synthetic delamination approach and catalyst synthesis is demonstrated with the synthesis of delaminated material DZ-3, which is derived from layered zeolite precursor ERB-1(P) with MWW framework topology. Upon catalytic testing for the epoxidation of 1-octene with ethylbenzene hydroperoxide as oxidant, under harsh tail-end conditions that deactivate amorphous Ti-silica-based catalysts, Ti-DZ-2 exhibits the highest per-Ti-site activity, selectivity, and stability for 1-octene epoxidation of all catalysts investigated. This testing includes the prior benchmark delaminated zeolite catalyst in this area, Ti-UCB-4, which possesses similar external surface area to Ti-DZ-2 but requires sonication and long-chain surfactants for its synthesis. The synthesis of DZ-2 is the first example of an economical delamination of layered zeolite precursor SSZ-70(P) and opens up new doors to the development of delaminated zeolites as commercial catalysts.

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

Generalized framework for likelihood-based field-level inference of growth rate from velocity and density fields

Measuring the growth rate of large-scale structures ( f ) as a function of redshift has the potential to break degeneracies between modified gravity and dark energy models, when combined with expansion-rate probes. Direct estimates of peculiar velocities of galaxies have attracted interest as a means of estimating fσ 8 . In particular, field-level methods can be used to fit the field nuisance parameter along with cosmological parameters simultaneously. This article aims to provide the community with a unified framework for the theoretical modeling of the likelihood-based field-level inference by performing fast field covariance calculations for velocity and density fields. Our purpose is to lay the foundations for a nonlinear extension of the likelihood-based method at the field level. We have developed a generalized framework, implemented in the dedicated software flip to perform a likelihood-based inference of fσ 8 . We derived a new field covariance model, which includes wide-angle corrections. We also included the models previously described in the literature inside our framework. We compared their performance against ours, and we validated our model by comparing it with the two-point statistics of a recent N-body simulation. The tests we performed have allowed us to validate our software and determine the appropriate wavenumber range to integrate our covariance model and its validity in terms of separation. Our framework allows for a wider wavenumber coverage to be used in our calculations than in previous works, which is particularly interesting for nonlinear model extensions. Finally, our generalized framework allows us to efficiently perform a survey geometry-dependent Fisher forecast of the fσ 8 parameter. We show that the Fisher forecast method we developed gives an error bar that is 30% closer to a full likelihood-based estimation than a standard volume Fisher forecast.

Ravoux, Corentin↗
DOE OSTI2019

Application usability levels: a framework for tracking project product progress

The space physics community continues to grow and become both more interdisciplinary and more intertwined with commercial and government operations. This has created a need for a framework to easily identify what projects can be used for specific applications and how close the tool is to routine autonomous or on-demand implementation and operation. We propose the Application Usability Level (AUL) framework and publicizing AULs to help the community quantify the progress of successful applications, metrics, and validation efforts. This framework will also aid the scientific community by supplying the type of information needed to build off of previously published work and publicizing the applications and requirements needed by the user communities. In this paper, we define the AUL framework, outline the milestones required for progression to higher AULs, and provide example projects utilizing the AUL framework. This work has been completed as part of the activities of the Assessment of Understanding and Quantifying Progress working group which is part of the International Forum for Space Weather Capabilities Assessment.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Establishing a Numerical Modeling Framework for Hydrologic Engineering Analyses of Extreme Storm Events

In this study a numerical modeling framework for simulating extreme storm events was established using the Weather Research and Forecasting (WRF) model. Such a framework is necessary for the derivation of engineering parameters such as probable maximum precipitation that are the cornerstone of large water management infrastructure design. Here this framework was built based on a heavy storm that occurred in Nashville (USA) in 2010, and verified using two other extreme storms. To achieve the optimal setup, several combinations of model resolutions, initial/boundary conditions (IC/BC), cloud microphysics and cumulus parameterization schemes were evaluated using multiple metrics of precipitation characteristics. The evaluation suggests that WRF is most sensitive to IC/BC option. Simulation generally benefits from finer resolutions up to 5 km. At the 15km level, NCEP2 IC/BC produces better results, while NAM IC/BC performs best at the 5km level. Recommended model configuration from this study is: NAM or NCEP2 IC/BC (depending on data availability), 15km or 15km-5km nested grids, Morrison microphysics and Kain-Fritsch cumulus schemes. Validation of the optimal framework suggests that these options are good starting choices for modeling extreme events similar to the test cases. This optimal framework is proposed in response to emerging engineering demands of extreme storm events forecasting and analyses for design, operations and risk assessment of large water infrastructures.

atmospheric model↗
DOE OSTI2026

Validation of an integrated modeling framework for investigating 3D plasma responses in tokamak plasmas

As contemporary experimental tokamaks are pushed toward reactor-relevant operation, they provide essential testbeds for demonstrating and exploring ELM control strategies for deployment in future fusion pilot plants. Accurate predictions of full plasma responses are essential to guide and optimize these demonstrations. This paper introduces and validates an integrated modeling framework over a historical range of DIII-D operational space. The integrated modeling framework uses only scalar plasma parameters and optional reference boundary to self-consistently and flexibly scan through tokamak operational space and estimate the corresponding ELM-suppression relevant plasma response over 3D coil phase space. The framework generates tightly converged equilibria that satisfy a target set of plasma parameters (I p , β N , l i ), with kinetic profiles constrained by an EPED(NN)-computed pedestal and empirical core model. The plasma response of these modeled equilibria is calculated with GPEC. Validated against 55 distinct DIII-D equilibria, the framework consistently reproduces experimentally constrained equilibrium pressure, q, and other representative profiles using the time-varying information from only evolving scalar plasma parameters; plasma response validation is performed for the n=3 perturbation. In particular, the plasma response of a DIII-D discharge scanning q 95 in search of ELM suppression windows is quantitatively reproduced. By accurately reproducing experimental equilibria and plasma responses across wide parameter variation, the framework supports potential for synthetic parameter scans in key operational, stability, and plasma response dimensions to investigate RMP ELM-suppression experiments and inform predictive RMP scenario optimization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

The art framework

Future Intensity Frontier experiments at Fermilab are likely to be conducted by smaller collaborations, with fewer scientists, than is the case for recent Energy Frontier experiments. art is a C++ event-processing framework designed with the needs of such experiments in mind. An evolution from the framework of the CMS experiment, art was designed and implemented to be usable by multiple experiments without imposing undue maintenance effort requirements on either the art developers or experiments using it. We describe the key requirements and features of art and the rationale behind evolutionary changes, additions and simplifications with respect to the CMS framework. In addition, our package distribution system and our collaborative model with respect to the multiple experiments using art helps keep the maintenance burden low. We also describe in-progress and future enhancements to the framework, including strategies we are using to allow multi-threaded use of the art framework in today's multi- and many-core environments.

Green, C.↗
DOE OSTI2026

Framework for X-ray mirror surface shape fitting

For accurate characterization of grazing-incidence X-ray mirrors, we present a comprehensive framework to fit measured surface shapes (either slope or height) of X-ray mirrors used in synchrotron radiation and free-electron laser facilities. We summarize the closed-form expressions of some typical surface shapes of X-ray mirrors including elliptic cylinders, hyperbolic cylinders, ellipsoids, hyperboloids, and diaboloids. This framework is composed of four layers: definition of standard shapes with closed-form expressions, generation of theoretical surface with pose parameters (six degrees of freedom defining an object's position and orientation relative to a coordinate system), parameter optimization with the ability to select which parameters are fit and which are held constant, and the development of user-friendly fitting function wrappers for particular fitting tasks. A few practical fitting examples are demonstrated to verify the effectiveness of the proposed fitting framework. We discuss the physical meanings of the fitting parameters, and provide several examples using the elliptic cylinder and ellipsoid shapes to highlight some features of the framework. Moreover, we provide the presented framework as open-source codes (MATLAB and Python codes available at https://github.com/nsls2omf/xmf) to the community to encourage academic collaboration and further improvements.

36 MATERIALS SCIENCE↗