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Converging towards atomic and nuclear pressures (Final Report)

his report details the development of transformational tools and techniques, allowing the accurate characterization of matter at the most extreme conditions yet studied in the high energy density (HED) domain. Before this work, most experiments quantitatively mapping the nature of matter in the HED realm were performed using planar geometry, which allows for the isolation and measurement of variables in a single thermodynamic state. Such measurements include equation of state variables, optical conductivity, heat transport and more. However, due to a variety of plasma processes, such experiments are limited to below ~10 TPa (100 Mbar) pressures. To achieve higher pressures, convergent experiments are needed. Historically, convergent experiments have not been used for benchmark data because they are integral measurements. That is each part of a convergent target undergoes a time dependent wide range of states, making it difficult to accurately isolate any particular quantity for a given thermodynamic state. This effort developed innovative convergent HED platforms and techniques enabling the exploration of matter from atomic to nuclear scale pressures. This effort also performed pioneering experiments that yielded the first rigorous benchmark data at these extreme conditions. This funding award began with the overarching goal to understand the behavior of matter at extreme (atomic-to-nuclear scale) pressures. The motivation for these goals lie in the fact that every time scientists explore matter beyond the threshold of an atomic unit, there is a fundamental shift in science. The atomic unit for energy, mass, charge, length, and time have each been explored, and each time such a threshold was crossed, a new sequence of discoveries was made resulting in significant awards such as the Nobel Prize. The only unexplored atomic unit is pressure, and this effort set the course for exploring matter at and beyond such pressures. That most of the recently discovered extrasolar planets and stars, as well as matter in the late implosion stages of inertial fusion targets, have deep internal pressures at and beyond atomic pressures amplifies the importance of this effort. Much of the initial work in developing techniques to create these atomic-to-nuclear pressures already existed within the HED community, predominantly at large scale laser facilities such as the National Ignition Facility (NIF) and the Omega60 laser the University of Rochester and although these experiments were routinely performed the ability to extract information about the underlying physical states and processes remained elusive due to the complexity of the experiments, extreme scales in both time and space, and the integrated nature of all the measurements. This work built a rigorous framework so such measurements can routinely be made. This was done in part through the introduction of Bayesian inference techniques into the field of HED science. These techniques allow for the self-consistent extraction of the relevant variables and their explicit and implicit correlations, so as to make use of integrated experimental data to constrain physical models and provide accurate uncertainty bounds for the data. The techniques developed here are fully transparent and proved immediately useful providing quantitative rigorous benchmarks for physical states and processes at some of the most extreme conditions yet explored on Earth. This funding is directly or partly responsible for 7 publications in major peer-reviewed scientific journals, a doctoral thesis, 3 invited talks at major conferences, and the training of a post-doc, 2 graduate students, and 1 undergraduate student. Beyond the effort supported by this award launched the introduction of Bayesian inference into the HED physics community and helped push the usage if modern data-science techniques within the physics community at large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Computational multiphysics modeling of radioactive aerosol deposition in diverse human respiratory tract geometries

The evaluation of aerosol exposure relies on generic mathematical models that assume uniform particle deposition profiles over the human respiratory tract and do not account for subject-specific characteristics. Here we introduce a hybrid-automated computational workflow that generates personalized particle deposition profiles in 3D reconstructed human airways from computed tomography scans using Computational Fluid and Particle Dynamics simulations. This is the first large-scale study to consider realistic airways variability, where 380 lower and 40 upper human respiratory tract 3D geometries are reconstructed and parameterized. The data is clustered into nine groups using random forest regression. Computational fluid and particle dynamics simulations are conducted on these representative geometries using a realistic heavy-breathing respiratory cycle and radioactive iodine-131 as a source term. Monte Carlo radiation transport simulations are performed to obtain detailed energy deposition maps. Our findings emphasize the importance of personalized studies, as minor respiratory tract variations notably influence deposition patterns rather than global parameters of the lower airways, observing more than 30% variance in the mass deposition fraction.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Constraining AGN Torus Sizes with Optical and Mid-infrared Ensemble Structure Functions

We propose a new method to constrain the size of the dusty torus in broad-line active galactic nuclei (AGNs) using optical and mid-infrared (MIR) ensemble structure functions (SFs). Because of the geometric dilution of the torus, the MIR response to optical continuum variations has suppressed variability with respect to the optical that depends on the geometry (e.g., size, orientation, opening angle) of the torus. More extended tori have steeper MIR SFs with respect to the optical SFs. We demonstrate the feasibility of this SF approach using simulated AGN light curves and a geometric torus model. While it is difficult to use SFs to constrain the orientation and opening angle due to the insensitivity of the SF on these parameters, the size of the torus can be well determined. Applying this method to the ensemble SFs measured for 587 SDSS quasars, we measure a torus R–L relation of $\mathrm{log}\,{R}_{\mathrm{eff}}(\mathrm{pc})={0.51}_{-0.04}^{+0.04}\times \mathrm{log}({{L}}_{\mathrm{bol}}/{10}^{46}\,\mathrm{erg}\ {{\rm{s}}}^{-1})-{0.38}_{-0.01}^{+0.01}$ in the WISE W1 band and sizes ~1.4 times larger in the W2 band, which are in good agreement with dust reverberation mapping measurements. Compared with the reverberation mapping technique, the SF method is much less demanding in data quality and can be applied to any optical+MIR light curves for which a lag measurement may not be possible, as long as the variability process and torus structure are stationary. While this SF method does not extract all information contained in the light curves (i.e., the transfer function), it provides an intuitive interpretation for the observed trends of AGN MIR SFs compared with optical SFs.

79 ASTRONOMY AND ASTROPHYSICS↗

Preliminary Report on Compositional Specification for Printed 316SS

The Advanced Materials and Manufacturing Technologies Program is focused on accelerating the development and deployment of advanced materials and components fabricated via additive manufacturing (AM). A key challenge for the widespread adoption of AM is the variability in material properties, which can originate from powder feedstock, process parameters, geometry, and the machine. AM powder feedstock compositions are based on those developed for conventional manufacturing. However, the smaller melt pools combined with multiple melt cycles over the course of a build can have substantial effects on the local phase selection resulting from minor batch-to-batch feedstock variability. Therefore, this report focuses on coupling CALPHAD calculations with data mining and visualization to aid the development of compositional specifications for stainless steel 316, an important alloy for nuclear applications and suitable for AM. This work reports that δ-ferrite formation has a stronger dependence on the amount of nickel in the alloy despite nickel being an austenite stabilizer. These findings show the need for exercising a tighter control on the amount of nickel in the alloy compared with the amount of chromium, which is a ferrite stabilizer.

36 MATERIALS SCIENCE↗

Monte Carlo Simulation of Background and Source Measurements with CSG and CAD Geometries

Detecting radioactive sources in an urban environment is difficult due to the large magnitude and variability of the background radiation. To support the search mission of the National Nuclear Security Administration, a project was undertaken to determine if first-principles modeling and simulation could be used to accurately predict the response of radiation detectors in urban environments. This study demonstrates that the simulated detector responses to photon radiation from both an isotopic source and the background compare well to benchmark-quality measurements in a large urban-like test environment. Simulation results using a traditional combinatorial solid geometry and a CAD model generated from LiDAR measurements gave very similar detector responses. With this validation, further simulations could be used to predict detector responses for various situations in real urban settings.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Electromagnetic total- f algorithm for gyrokinetic particle-in-cell simulations of boundary plasma in XGC

We report the simplified δf mixed-variable/pullback electromagnetic simulation algorithm implemented in XGC for core plasma simulations by Cole et al. [Phys. Plasmas 28, 034501 (2021)] has been generalized to a total- f electromagnetic algorithm that can include, for the first time, the boundary plasma in diverted magnetic geometry with neutral particle recycling, turbulence, and neoclassical physics. The δf mixed-variable/pullback electromagnetic implementation is based on the pioneering work by Kleiber and Mischenko et al. [Kleiber et al., Phys. Plasmas 23, 032501 (2016); Mishchenko et al., Comput. Phys. Commun. 238, 194 (2019)]. An electromagnetic demonstration simulation is performed in a DIII-D-like, H-mode boundary plasma, including a corresponding comparative electrostatic simulation, which confirms that the electromagnetic simulation is necessary for a higher fidelity understanding of the electron particle and heat transport even at the low- β pedestal foot in the vicinity of the magnetic separatrix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effects of ionising radiation exposure in offspring and next generations: dosimetric aspects and uncertainties

The impact of the exposure to ionizing radiation in the offspring and next generation has been investigated in the last decades and currently is the subject of study of the ICRP Task Group 121. Studying the effects of radiation exposure in pre-conceptional and post-conceptional phases can be a challenge since potential effects to the fetus vary depending on the stage of fetal development. Epidemiology and radiobiology studies are the two sources of information one can use to correlate the radiation dose to the human body and tissues and the resulting effects. For a proper evaluation of the outcomes of such studies, and a correct appraisal of the exposure/dose-effect relationship, (i) reliable dosimetry, (ii) accurate reporting, and (iii) reproducibility of results are required. Although variables related to dose, including for instance source of radiation, geometry of irradiation, dose rate etc., are usually known, especially in radiobiology studies, often important details of the irradiation are not reported. In conclusion, based on standards developed by the National Cancer Institute (NCI), the National Institute of Allergy and Infectious Disease (NIAID) and the National Institute of Standards and Technology (NIST), a review of the scientific studies used by the UNSCEAR to estimate the risk of hereditary effects, and by the ICRP in its current recommendations, was conducted to evaluate the way dosimetry was reported. Dosimetry and the related uncertainties were not adequately described in the vast majority of those studies. This does not necessarily mean that they do not provide relevant information, however it prevents from a thorough verification and reproduction of their findings. In order to guarantee the reliability and robustness of the process of revision of the estimates of risk and detriment it is therefore considered mandatory to include a careful check of the new relevant literature with regard to the criteria on the completeness and reproducibility of the dosimetric information.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Impact of external screening on the valence and core level photoelectron spectra of monolayer W⁢S 2

Transition metal dichalcogenides (TMDs) represent an emerging class of layered materials with applications in microelectronics, optoelectronics, photonics, and catalysis. The confinement of charge carriers within the highly anisotropic, quasi-two-dimensional geometry of one-layer (1L) TMDs leads to reduced, variable dielectric screening, giving rise to a quasiparticle band gap that is highly susceptible to the surrounding dielectric environment. Here, exploiting the contrasting external dielectric environments of gold-supported and suspended 1L W⁢S 2 , we show how the electronic states of W⁢S 2 under the effective and ineffective screening environments align at a junction made within the same sheet of material. Photoelectron spectra point to the close alignment of the charge neutrality levels of W⁢S 2 in both environments, and the breakdown of rigid shifts between the valence states and core levels with the core levels shifting more than twice as much as the valence states. Furthermore, the effectively screened W⁢S 2 exhibits a valence state with the photoemission linewidth twice as large as the ineffectively screened suspended W⁢S 2 , presumably originated from the locally varying W⁢S 2 -Au distance and substrate disorders. Collectively, these findings provide key insights into the electronic behavior of W⁢S 2 and its photoemission process with the electronic states renormalized according to the external screening environments.

Dielectric properties↗

Hypercomplex Automatic Differentiation in the Eulerian Hydrocode PAGOSA

Enabling the computation of partial derivatives or sensitivities in production hydrocodes is beneficial for design, optimization, sensitivity analysis, and uncertainty quantification. Traditional finite difference approximations of these sensitivities are inefficient since convergence studies of the step size is required for each parameter of interest. For these reasons, HYPercomplex Automatic Differentiation (HYPAD) was implemented in the Eulerian hydrocode PAGOSA. HYPAD is analogous to forward-mode automatic differentiation except hypercomplex numbers (numbers with multiple imaginary parts) are used instead of dual numbers. Accurate partial derivatives can be computed of all state variables with respect to multiple input variables in a single run. The method was implemented using operator overloading to handle hypercomplex algebra. HYPAD was demonstrated and verified on Sod’s shock tube problem to compute derivatives of the state variables with respect to a material parameter, initial conditions, and geometry.

97 MATHEMATICS AND COMPUTING↗

AEOLUS: Advances in Experimental Design, Optimal Control, and Learning for Uncertain Complex Systems

Sustained advances in the mathematics of modeling and simulation have resulted in the capability today for routine simulation of a number of large scale complex DOE-relevant systems. As remarkable as this capability for solving the so-called forward problem is, it is typically only the first step-an inner loop within an outer loop that explores the simulation model's parameter space and decision space to characterize uncertainty in the model's predictions, learn unknown model parameters from data, design the most informative experiments, determine optimal control strategies, and create optimal designs. Broadly, what unifies all of these outer loop problems is that they are, in one form or another, optimization problems over parameter/control/design space that are constrained by complex uncertain models. To fully realize the power of scientific simulation as a basis for scientific discovery, technological innovation, and rational decision-making, it is imperative to move beyond simulation to tackle the outer loop of optimization for learning from data, experimental design, and control with complex uncertain models. When the models under consideration are large-scale and complex, and when the optimization variable and uncertain parameter spaces are high (or infinite) dimensional, this constitutes a grand challenge of the highest order, and is intractable with conventional methods. To overcome these challenges, the AEOLUS Center was established to develop a unified mathematical, computational, and statistical framework for (1) Learning predictive models from complex data via Bayesian inference and optimization, and (2) Optimizing experiments, processes, and designs using the resulting uncertain models. These problems are intractable with conventional methods, for several reasons: (1) The simulation problems that govern the inner loops of the optimization problems are expensive to execute (due to severe nonlinearity, heterogeneity, multiphysics/multiscale coupling); (2) The optimization variable and uncertain parameter spaces are high dimensional, often stemming from discretizations of infinite dimensional fields such as initial conditions, sources, or material properties. We argue that the key to overcoming these challenges is to develop new mathematical, computational, and statistical methods that exploit the structure of the Bayesian inference and optimization problems mediated by their underlying complex uncertain models. This structure includes the regularity, sparsity, geometry, low intrinsic dimensionality, and multifidelity nature of the maps from uncertain parameter/optimization variable spaces to the specific objectives targeted: Bayesian inference, optimal experimental design, and optimal control design. Black box methods developed as generic tools are incapable of exploiting this structure. To be successful, we must create, integrate, and cross-fertilize ideas across multiple areas of applied math--including approximation theory, Bayesian inference, data science, experimental design, information theory, machine learning, model reduction, optimal control theory, parallel algorithms, PDE-constrained optimization, randomized algorithms, stochastic optimization, and uncertainty quantification--all while exploiting the structure of the problems at hand. With this goal in mind, we have marshaled a team of leading authorities in these areas. While the methods we develop will be broadly applicable across a wide spectrum of DOE problems in which experiments inform models and the systems those models describe must be optimized under uncertainty, we have chosen a specific area, advanced manufacturing and materials, to drive our work. AMM is characterized by complex models across multiple scales, and is a rich source of challenging problems in inference, experimental design, and optimal control, requiring multifaceted and integrated advances in applied mathematics. As such, AMM serves as an excellent vehicle to motivate and demonstrate the advances in applied mathematics developed by our center.

97 MATHEMATICS AND COMPUTING↗

3D printing of void-free glass monoliths: rheological and geometric considerations

Direct ink writing (DIW) is a versatile additive manufacturing technique capable of printing 3D architectures from a broad range of materials. The key advantage of DIW is the ability to spatially control both the architecture and the composition of the printed part, which enables the production of components with previously unachievable combinations of functionalities. One emergent application space for DIW has been in additively manufactured glass optics, where a “green body” is patterned layer-by-layer by extruding a silica-based slurry through a microfluidic nozzle and then thermally consolidated to transparent glass. A critical aspect of the process is ensuring that the printed part is completely free of voids that can occur in the interstitial spaces between the extruded filaments. This outcome is governed by the interplay between ink rheology and strains imposed by the printing process and geometric packing of the filaments. Here, we explore the strain- and rate-dependent deformation events in the DIW process to determine conditions that enable the printing of void-free monoliths without sacrificing shape fidelity. We focus on yield stress fluids consisting of fumed silica nanoparticles dispersed in organic solvents at varied volume fractions to control the rheological properties. We investigate the printability of these ink materials as a function of print process variables and devise the appropriate dimensionless parameters that capture the geometry-dependent and rate-dependent effects on the deformation of the extruded ink. Lastly, we use these scaling arguments to construct a phase diagram for void-free monolith printability.

36 MATERIALS SCIENCE↗

Mechanical evaluation of WC-Co materials with varying microstructures

Tungsten carbide–cobalt materials are useful in a variety of extreme applications due to a desirable blend of properties, yet the technology has not significantly changed since their initial development in the 1920s. The mechanical properties of this class of materials is highly dependent on two variables, the size of the tungsten carbide grains, and the amount of binder phase present in the final body. In this study, the amount of binder phase is isolated across three commercial materials from the same manufacturer with three different grain sizes to investigate the effect on mechanical properties. The mechanical properties investigated are indentation hardness, flexure and tensile strength, as well as fracture toughness. In general, an increase in hardness and tensile strength with decreasing grain size was observed, while the fracture toughness showed the opposite trend with toughness increasing with increasing grain size. The flexure strength results did not show a correlation to grain size. Fractographic analysis identified the dominant strength-limiting flaw for each sample, which largely were in the form of porosity. Other flaws types, such as inclusions from the milling process, clusters of large grains, and machining cracks from the surface finishing process, were also identified. Finally, Weibull analysis was performed and deemed appropriate for analysis of these materials, but strength-size scaling was not conducted due to the variability in the strength-limiting feature between the different specimen geometries.

36 MATERIALS SCIENCE↗

FY24 Integrated Results for High-Temperature Mechanical Testing of LPBF 316H Stainless Steel

This report provides the mechanical test data of laser powder bed fusion (LPBF) 316H stainless steel (SS) collected during Fiscal Year 2024 (FY 24) under the US Department of Energy, Office of Nuclear Energy’s Advanced Materials and Manufacturing Technologies program, along with the current state of microstructural-based understandings of the behaviors. Materials with variabilities in manufacturing site, machine, laser parameters, powder chemistry, porosity, specimen geometry and heat treatment were tested in high-temperature tension, creep, fatigue and creep-fatigue. Electron microscopy and optical microscopy were performed on selected materials before and after the tests to provide microstructural-based understandings to the mechanical behavior. It was discovered that the as-built (AB) and stress-relieved (SR) materials exhibit similar behaviors in tension and creep, as do the solution-annealed (SA) and hot-isostatic pressed (HIP) materials. The AB and SR materials are softer but more ductile than the SA and HIP materials in tension. In creep, the LPBF materials have comparable rupture times but lower rupture strains compared to the wrought materials. The AB and SR materials have low creep rupture strains (<10%) when tested at 720°C and 800°C, while the SA and HIP materials are much more ductile. The LPBF materials exhibit large scatter in fatigue and creep-fatigue lives. The cyclic lives of creep-fatigue tests are lower than those of fatigue tests. In fatigue and creep-fatigue, SR materials outperform SA materials. A common observation from the cyclic tests is that, given the same post-build heat treatment, a lower initial peak stress generally results in a longer cyclic life regardless of hold time. It was also discovered that the batch variation can be more impactful than heat treatment, as demonstrated by the overall better performance of one batch of material than another, regardless of the heat treatment. The results provided insights into how different factors impact the behaviors of LPBF 316H SS. An outlook to FY 25 work scope is provided.

36 MATERIALS SCIENCE↗

Irradiation and corrosion testing of laser powder bed fusion-manufactured materials in the AMMT program

The Advanced Materials and Manufacturing Technologies (AMMT) program operating under the Department of Energy Office of Nuclear Energy is accelerating the qualification and deployment of additively manufactured materials in advanced reactor environments. Laser powder bed fusion (LPBF) has emerged as a promising additive manufacturing technique to fabricate complex components with the potential of tailored material properties. In the nuclear industry, metal additive manufacturing can offer numerous advantages, such as reduced lead times, streamlined quality assurance, and cost-effective low-volume production of new and replacement components with conventional or novel materials and geometries. The rapid and effective qualification of the effect of processing variability on the performance and degradation of additively manufactured materials is essential for the deployment of these components into advanced reactor environments. As part of this effort, AMMT is performing irradiation and corrosion testing of several materials built by LPBF, including 316L and 316H stainless steels. Our efforts encompass neutron irradiation testing, ion irradiation testing, and advanced modeling to provide a robust technical basis for understanding the effect of process variability on materials degradation and developing a sound methodology for accelerated ion irradiation testing. We develop focused irradiation test plans that align well with risk-informed and technologically inclusive approaches to licensing. We will also discuss our plans and specific concerns for corrosion testing additively manufactured material, with a primary focus on molten salt and liquid sodium environments.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Environmental Degradation in Advanced Reactor Environments

The Advanced Materials and Manufacturing Technologies (AMMT) program operating under the Department of Energy Office of Nuclear Energy is accelerating the qualification and deployment of additively manufactured materials in advanced reactor environments. Laser powder bed fusion (LPBF) has emerged as a promising additive manufacturing technique to fabricate complex components with the potential of tailored material properties. In the nuclear industry, metal additive manufacturing can offer numerous advantages, such as reduced lead times, streamlined quality assurance, and cost-effective low-volume production of new and replacement components with conventional or novel materials and geometries. The rapid and effective qualification of the effect of processing variability on the performance and degradation of additively manufactured materials is essential for the deployment of these components into advanced reactor environments. This talk presents an overview of the Environmental Effects area activities within AMMT. AMMT is performing irradiation and corrosion testing of several materials built by LPBF, including 316L and 316H stainless steels. Our irradiation efforts encompass neutron irradiation testing and ion irradiation testing to provide a robust technical basis for understanding the effect of process variability on materials degradation. We develop focused irradiation test plans that align well with risk-informed and technologically inclusive approaches to licensing. We will also discuss our plans and specific concerns for corrosion testing additively manufactured material, with a primary focus on molten salt and liquid sodium environments.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Here, this paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate conformal meshes, this work uses an extended finite element method (XFEM) to discretize the governing equations on non-conforming, embedding meshes. A flexible approach to create truncated hierarchical B-splines discretizations is presented. This approach enables the refinement of each state variable field individually to meet field-specific accuracy requirements. To obtain an immersed geometry representation that is consistent across all hierarchically refined B-spline discretizations, the geometry is immersed into a single mesh, the XFEM background mesh, which is constructed from the union of all hierarchical B-spline meshes. An extraction operator is introduced to represent the truncated hierarchical B-spline bases in terms of Lagrange shape functions on the XFEM background mesh without loss of accuracy. The truncated hierarchical B-spline bases are enriched using a generalized Heaviside enrichment strategy to accommodate small geometric features and multi-material problems. The governing equations are augmented by a formulation of the face-oriented ghost stabilization enhanced for locally refined B-spline bases. We present examples for two- and three-dimensional linear elastic and thermo-elastic problems. The numerical results validate the accuracy of our framework. The results also demonstrate the applicability of the proposed framework to large, geometrically complex problems.

42 ENGINEERING↗

A Novel Variable Extensometer Method for Measuring Ductility Scaling Parameters From Single Specimens

Abstract Macro-scale ductility is not an intrinsic material property but is dependent on the overall geometry of the specimen. To account for variety in specimen geometries, multiple ductility scaling laws have been developed, which scale ductility between different specimen sizes. Traditionally, these ductility laws rely on testing multiple different specimens of varying sizes to obtain material parameters, often done by varying gauge lengths. With the use of digital image correlation (DIC), this study presents a technique where multiple different gauge lengths are extracted from a single specimen to obtain ductility scaling parameters from a single experiment. This technique provides orders of magnitude more data from each specimen than previous techniques. This variable extensometer method is then validated by testing multiple different geometries, and select scaling laws are then compared.

Mechanics↗