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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Spectroscopic Measurements of L X-rays with a TES Microcalorimeter for a Non-destructive Assay of Transuranium Elements

Spectroscopic measurement of the L X-rays emitted from transuranium elements is one of the most useful techniques for the non-destructive assays of nuclear materials. In this study, we fabricated a transition-edge-sensor (TES) microcalorimeter using a 5-μm-thick Au absorber and tested its ability to measure the L X-rays emitted from two transuranium elements, Np-237 and Cm-244 sources. The microcalorimeter was found to successfully measure the L X-rays with an energy resolution (full width at half maximum) below 70 eV. These results confirm that L X-rays can be identified using the proposed TES microcalorimeter to enable non-destructive assays of transuranium elements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Postprocessing Mixed Finite Element Methods For Solving Cahn–Hilliard Equation: Methods and Error Analysis

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Extraction and separation of rare earth elements using LN resins in hydrochloric acid

The separation of the rare earth elements is essential for numerous scientific applications but remains a significant challenge due to the nearly identical chemical properties of the adjacent lanthanide elements. Eichrom’s LN series of extraction chromatographic resins feature organophosphorus extractants and are widely used to achieve adjacent lanthanide separations. While extensive characterization of these resins has been completed for nitric acid matrices, the use of hydrochloric acid is preferred for a variety of applications. Further, the extraction of the rare earth elements, La–Lu and Y, has been characterized on LN and LN2 resins in hydrochloric acid via batch uptake and column chromatographic studies.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2018

Analysis of thermo-elastic problems using the improved element-free Galerkin method

The improved element-free Galerkin method (IEFG) is presented to deal with thermo-elastic problems. This mesh-free method is a combination between the element-free Galerkin method and the improved moving least-square approximation. It has not the Kronecker delta property, and the penalty method is used to impose the essential boundary conditions. In this paper, linear and stationary thermo-elasticity is treated. To solve the thermo-elastic problem, this latter is decoupled into two separate parts: first, the heat transfer problem is analyzed to reach the temperature field, which is used as input in the mechanical problem to calculate the displacement field and then the stress fields. Numerical examples with different boundary conditions are illustrated. The performance and the accuracy of the IEFG method are approved when obtained results are compared to finite-element results and analytical solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Localized harmonic characteristic basis functions for multiscale finite element methods

We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with discontinuous coefficients. These coefficients represent the conductivity of a composite material. We assume a background with a low conductivity that contains inclusions with different thermal properties. Under this scenario, we design a multiscale finite element method to efficiently approximate solutions. The method is based on an asymptotic expansion of the solution in terms of the ratio between the conductivities. The resulting method constructs (locally) finite element basis functions (one for each inclusion). These bases generate the multiscale finite element space where the approximation of the solution is computed. Numerical experiments show the good performance of the proposed methodology.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

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

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

36 MATERIALS SCIENCE↗
DOE OSTI2023

Selective oxidation and nickel enrichment hinders the repassivation kinetics of multi-principal element alloy surfaces

Robust and sustained corrosion resistance in multi-principal element alloys (MPEA) requires rapid repassivation, i.e. regrowth of the passive layer once it is damaged or destroyed at the surface. In this study, we show that the repassivation of Al 0.1 CrCoFeNi MPEA in 0.6 M NaCl solution is hindered at pH of ~ 2.4 - 6.8 due to the formation of a Ni-enriched subsurface layer as a result of selective oxidation and dissolution of several principal elements, which can be fully restored at pH of ~ 14 from the oxidation of all principal elements. Specifically, surface characterization via X-ray photoelectron spectroscopy (XPS), high-angle annular dark-field (HAADF) imaging in scanning transmission electron microscopy (STEM), and atom probe tomography (APT), are coupled with density functional theory (DFT) calculations to determine surface composition, oxidation state, and electron work function to uncover the structural origin of the pH-dependent repassivation mechanisms. It was found that selective oxidation of Cr, Co, and Fe in the acidic to neutral solutions altered the surface composition to be significantly enriched in Ni as compared to the bulk. Once the original passive film is destroyed locally by either pitting or tribocorrosion, this altered surface composition exhibited a much poorer repassivation capability due to the increased electron work function and reduced surface reactivity at higher Ni concentration. Finally, these understandings could shed light on the future compositional design of non-equiatomic MPEAs towards sustained repassivation and corrosion resistance over a wide pH range.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Treatment of domain integrals in boundary element methods

A systematic and rigorous technique to calculate domain integrals without a volume-fitted mesh has been developed and validated in the context of a boundary element approximation. In the proposed approach, a domain integral involving a continuous or weakly-singular integrand is first converted into a surface integral by means of straight-path integrals that intersect the underlying domain. Then, the resulting surface integral is carried out either via analytic integration over boundary elements or by use of standard quadrature rules. This domain-to-boundary integral transformation is derived from an extension of the fundamental theorem of calculus to higher dimension, and the divergence theorem. In establishing the method, it is shown that the higher-dimensional version of the first fundamental theorem of calculus corresponds to the well-known Poincare lemma. The proposed technique can be employed to evaluate integrals defined over simply- or multiply-connected domains with Lipschitz boundaries which are embedded in an Euclidean space of arbitrary but finite dimension. Combined with the singular treatment of surface integrals that is widely available in the literature, this approach can also be utilized to effectively deal with boundary-value problems involving non-homogeneous source terms by way of a collocation or a Galerkin boundary integral equation method using only the prescribed surface discretization. Sample problems associated with the three-dimensional Poisson equation and featuring the Newton potential are successfully solved by a constant element collocation method to validate this study.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2018

A discrete-continuum coupled finite element modelling approach for fibre reinforced concrete

Highlights: • An easy-to-implement but effective meso-scale modelling approach is developed for FRC. • It is capable of simulating and interpreting all main failure mechanisms in FRC. • It is critically validated by experiments with single or multiple random fibres under various loading conditions. • It can be used to optimise key design factors of FRC at meso/material scale by parametric studies. - Abstract: Fibre reinforced concrete (FRC) exhibits complicated failure modes such as fibre breakage, mortar cracking, crushing and spalling, fibre-mortar interfacial debonding, depending on many material properties, geometric dimensions, boundary and loading conditions. Most existing numerical models are unable to reproduce these failure modes that may occur simultaneously or sequentially in a specimen, mainly due to difficulties in generating finite element meshes with a large number of randomly-oriented fibres. Herein we develop a discrete-continuum coupled finite element modelling approach for FRC materials capable of effectively simulating all the major failure modes. The continuum damaged plasticity model is used to simulate damage and fracture behaviour of the mortar, while debonding of fibre-mortar interfaces is modelled by nonlinear cohesive interfacial elements. Unique techniques are devised to generate conforming meshes between fibres and the surrounding mortar so that the randomly-oriented fibres are easily modelled. The modelling approach is validated by simulating single fibre pullout tests with different inclination angles, notched and non-notched direct tensile tests and three-point bending beam tests with randomly-distributed multiple fibres.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Separation of rare earth element radioisotopes by reverse-phase high-speed counter-current chromatography

Analytical scale purification of rare earth element (REE) radioisotopes is typically accomplished using cation-exchange resins (e.g. AG 50W-X8) and high-performance liquid chromatography (HPLC). Despite the variety of improvements made since the development of this separation process in the 1950s, nearest neighbor separations remain a challenge, as does the issue of irreversible sample adsorption. Herein, we report a study that evaluates the potential of high-speed counter-current chromatography (HSCCC) as an alternative method for purifying REE elements, with specific reference to separations of fission product REE of interest to nuclear forensics. Complementary HSCCC REE separation experiments, one spiked with radiotracer and REE fission product activity, allowed for in depth analysis of resulting fractions from both an elemental (inductively coupled plasma atomic emission spectroscopy, ICP-AES) and radiological (gamma-ray spectrometry, beta counting) purity perspective. The highly reproducible nature of separation profiles generated from HSCCC instruments was leveraged to simplify work-up of samples containing radioisotopes. Subsequent radioanalytical evaluation revealed minimal carryover of Eu into neighboring Sm and Tb fractions (as indicated by presence of 150Eu), and trace contamination of the Tb fraction with Y (as indicated by presence of 91Y). Subtle differences in stationary phase retention across the two columns were reflected in significant variations in decontamination factors of duplicate parallel separations. Furthermore, these differences paired with obtained distribution of radioisotopes provided valuable insights into future improvements. Collectively, this study represents a significant step forward in development of HSCCC technology for task specific REE radioisotope purification.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2024

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Distribution of rare earth and other critical elements in lignites from the Eocene Jackson Group, Texas

Coal is increasingly evaluated as a source of rare earth elements (REEs) in the United States to address the overreliance on imported REEs. The objective of this study was to assess the distribution of REEs in lignites from selected mining areas in the Texas Gulf Coastal Plain region. Thirty-one archived lignite and rock samples previously collected by the U.S. Geological Survey were analyzed for their rare earth element and critical mineral content. These include samples from one core (5400 and 5500 lignite horizons) and two opencast lignite mines (Gibbons Creek 3500 and 4500 horizons, and San Miguel horizons A to D) in the Eocene Jackson Group of the Texas Gulf of Mexico Coastal Plain. Some lithologies in the Gibbons Creek 3500 and 4500 lignite-bearing sections have high total rare earth, yttrium (Y), and scandium (Sc) (REYSc) values, up to 7800 ppm (ash basis) REYSc. The lignite lithologies show an enrichment in rare earths, [samarium (Sm) through gadolinium (Gd)]. The basal Gibbons Creek 3500 lignite bench shows a heavy rare earth element enrichment pattern resembling that often seen in peats through high volatile A bituminous coals. The 5500 lignite sequence, overlying the latter lignite sections, shows a light rare earth enrichment. The San Miguel lignite benches have heavy rare earth enrichments with a negative europium (Eu) anomaly.

58 GEOSCIENCES↗
DOE OSTI2025

Chemistry imaging and distribution analysis of rare earth elements in coal using LIBS and LA-ICP-MS instruments

Currently, demand for rare earth elements (REEs) increased significantly. Coal is actively evaluated as potential economic sources for extraction of REEs. Here, in this work, laser-induced breakdown spectroscopy (LIBS) was evaluated for rapid estimation of REEs content and their distribution in the natural coal samples. The results were compared with similar laser ablation–inductively coupled plasma–mass spectrometry (LA-ICP-MS) measurements. Thirteen coal samples (nine standard samples and five natural samples) were used in this study. Powder samples were pressed into pellets while coal chunks were directly ablated for data recording. Pellets of the powder standard samples were used to optimize the data acquisition system and then data recorded with this optimized system was used to identify the proper data acquisition and analysis models. After establishing the proper data acquisition system and analysis model using the standard samples, natural coal samples in powder form and their chunks were utilized to record LIBS and LA-ICP-MS spectra. Multivariate calibration models were developed using four of the natural samples, which were evaluated by predicting the REE content in the fifth sample. Principal component analysis was performed on the LIBS data obtained from the natural samples and it classified all the samples with high accuracy. Two-dimensional (2D) elemental mapping on coal chunk samples was also performed using both LIBS and LA-ICP-MS to study the distribution of REEs in the samples. The resulting elemental images and their correlations can be used to infer mineral distributions.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2016

Partition of unity finite element method for quantum mechanical materials calculations

The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences (FD) and finite-elements (FE) have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative to PW: excessive number of degrees of freedom (basis functions) needed to achieve the required accuracies. In this paper, we present a real-space partition of unity finite element (PUFE) method to solve the Kohn–Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution process using partition-of-unity enrichment techniques in finite element analysis. The method developed herein is completely general, applicable to metals and insulators alike, and particularly efficient for deep, localized potentials, as occur in calculations at extreme conditions of pressure and temperature. Full self-consistent Kohn–Sham calculations are presented for LiH, involving light atoms, and CeAl, involving heavy atoms with large numbers of atomic-orbital enrichments. We find that the new PUFE approach attains the required accuracies with substantially fewer degrees of freedom, typically by an order of magnitude or more, than the PW method. As a result, we compute the equation of state of LiH and show that the computed lattice constant and bulk modulus are in excellent agreement with reference PW results, while requiring an order of magnitude fewer degrees of freedom to obtain.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Detection of rare earth elements in Powder River Basin sub-bituminous coal ash using laser-induced breakdown spectroscopy (LIBS)

We reported our preliminary results on the use of laser-induced breakdown spectroscopy to analyze the rare earth elements contained in ash samples from Powder River Basin sub-bituminous coal (PRB-coal). We have identified many elements in the lanthanide series (cerium, europium, holmium, lanthanum, lutetium, praseodymium, promethium, samarium, terbium, ytterbium) and some elements in the actinide series (actinium, thorium, uranium, plutonium, berkelium, californium) in the ash samples. In addition, various metals were also seen to present in the ash samples

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

Siderophile element constraints on the thermal history of the H chondrite parent body

The abundances of highly siderophile elements (HSE: Re, Os, Ir, Ru, Pt, Pd), as well as 187 Re- 187 Os and 182 Hf- 182 W isotopic systematics were determined for separated metal, slightly magnetic, and nonmagnetic fractions from seven H4 to H6 ordinary chondrites. The HSE are too abundant in nonmagnetic fractions to reflect metal-silicate equilibration. The disequilibrium was likely a primary feature, as 187 Re- 187 Os data indicate only minor open-system behavior of the HSE in the slightly and non-magnetic fractions. 182 Hf- 182 W data for slightly magnetic and nonmagnetic fractions define precise isochrons for most meteorites that range from 5.2 ± 1.6 Ma to 15.2 ± 1.0 Ma after calcium aluminum inclusion (CAI) formation. By contrast, 182W model ages for the metal fractions are typically 2–5 Ma older than the slope-derived isochron ages for their respective, slightly magnetic and nonmagnetic fractions, with model ages ranging from 1.4 ± 0.8 Ma to 12.6 ± 0.9 Ma after CAI formation. This indicates that the W present in the silicates and oxides was not fully equilibrated with the metal when diffusive transport among components ceased, consistent with the HSE data. Further, the W isotopic compositions of size-sorted metal fractions from some of the H chondrites also differ, indicating disequilibrium among some metal grains. The chemical/isotopic disequilibrium of siderophile elements among H chondrite components is likely the result of inefficient diffusion of siderophile elements from silicates and oxides to some metal and/or localized equilibration as H chondrites cooled towards their respective Hf-W closure temperatures. The tendency of 182 Hf- 182 W isochron ages to young from H5 to H6 chondrites may indicate derivation of these meteorites from a slowly cooled, undisturbed, concentrically-zoned parent body, consistent with models that have been commonly invoked for H chondrites. Overlap of isochron ages for H4 and H5 chondrites, by contrast, appear to be more consistent with shallow impact disruption models. The W isotopic composition of metal from one CR chondrite was examined to compare with H chondrite metals. In contrast to the H chondrites, the CR chondrite metal is characterized by an enrichment in 183 W that is consistent with nucleosynthetic s-process depletion. Once corrected for the correlative nucleosynthetic effect on 182 W, the 182 W model age for this meteorite of 7.0 ± 3.6 Ma is within the range of model ages of most metal fractions from H chondrites. Finally, the metal is therefore too young to be a direct nebular condensate, as proposed by some prior studies.

58 GEOSCIENCES↗
DOE OSTI2013

A 2.5D boundary element formulation for modeling damped waves in arbitrary cross-section waveguides and cavities

Highlights: •Dispersive properties of viscoelastic waveguides and cavities are computed using a regularized 2.5D BEM. •Linear viscoelasticity is introduced at the constitutive level by means of frequency dependent complex moduli. •A contour integral algorithm is used to solve the nonlinear eigenvalue problem. •The Sommerfeld radiation condition is used to select the permissible Riemann sheets. •Attenuation of surface waves in cavities approaches the attenuation of Rayleigh waves. -- Abstract: A regularized 2.5D boundary element method (BEM) is proposed to predict the dispersion properties of damped stress guided waves in waveguides and cavities of arbitrary cross-section. The wave attenuation, induced by material damping, is introduced using linear viscoelastic constitutive relations and described in a spatial manner by the imaginary component of the axial wavenumber. The discretized dispersive wave equation results in a nonlinear eigenvalue problem, which is solved obtaining complex axial wavenumbers for a fixed frequency using a contour integral algorithm. Due to the singular characteristics and the multivalued feature of the wave equation, the requirement of holomorphicity inside the contour region over the complex wavenumber plane is fulfilled by the introduction of the Sommerfeld branch cuts and by the choice of the permissible Riemann sheets. A post processing analysis is developed for the extraction of the energy velocity of propagative guided waves. The reliability of the method is demonstrated by comparing the results obtained for a rail and a bar with square cross-section with those obtained from a 2.5D Finite Element formulation also known in literature as Semi Analytical Finite Element (SAFE) method. Next, to show the potential of the proposed numerical framework, dispersion properties are predicted for surface waves propagating along cylindrical cavities of arbitrary cross-section. It is demonstrated that the attenuation of surface waves approaches asymptotically the attenuation of Rayleigh waves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

All-electron Kohn–Sham density functional theory on hierarchic finite element spaces

In this work, a real space formulation of the Kohn–Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule.

97 MATHEMATICS AND COMPUTING↗