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DOE OSTI2023

Finite temperature properties of uranium mononitride

Uranium mononitride (UN) is a promising nuclear fuel that combines the advantageous properties of readily used UO 2 and uranium alloys, such as high melting temperature and high uranium density, and thermal conductivity, respectively. A better understanding of UN behavior at operating temperatures can be obtained from finite temperature data, such as elastic properties. To get this information, ab initio molecular dynamics (AIMD) simulations were performed at five different temperatures using constant volume (NVT) and constant pressure (NPT) ensembles. Initially, the performance of PBE functional in reproducing experimental crystallographic properties and magnetic ordering is assessed. The finite temperature phonon dispersions are calculated using NVT simulation results, which show a softening of the phonon modes with increasing temperature. The NPT results are used to obtain the thermal expansion of UN and finite temperature electronic properties. The calculated thermal expansion is compared with our measurements using neutron diffraction. Additionally, the temperature dependent elastic properties of UN are evaluated using the strain-stress method in AIMD simulations, indicating that UN becomes softer and more compressible with increasing temperature. Also, the calculated Young’s modulus slope is in very good agreement with the experiment. The finite temperature heat capacity and electronic thermal conductivity are calculated from AIMD simulations, which are in better agreement with the experiment than the heat capacity and thermal conductivity calculated using the structures relaxed at 0K. Finally, the thermal diffusivity from AIMD has opposite temperature dependence compared to experimental results, which we argued comes from the underestimated electronic thermal conductivity.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Lieb-Robinson Bounds with Exponential-in-Volume Tails

Lieb-Robinson bounds demonstrate the emergence of locality in many-body quantum systems. Intuitively, Lieb-Robinson bounds state that, with local or exponentially decaying interactions, the correlation that can be built up between two sites separated by distance 𝑟 after a time 𝑡 decays as exp (𝑣⁢𝑡 −𝑟), where 𝑣 is the emergent Lieb-Robinson velocity. In many problems, it is important to also capture how much of an operator grows to act on 𝑟 𝑑 sites in 𝑑 spatial dimensions. Perturbation theory and cluster expansion methods suggest that, at short times, these volume-filling operators are suppressed as exp (−𝑟 𝑑 ). We confirm this intuition, showing that, for 𝑟 >𝑣⁢𝑡, the volume-filling operator is suppressed by exp (−(𝑟−𝑣⁢𝑡) 𝑑 /(𝑣⁢𝑡) 𝑑−1 ). This closes a conceptual and practical gap between the cluster expansion and the Lieb-Robinson bound. We then present two very different applications of this new bound. Firstly, we obtain improved bounds on the classical computational resources necessary to simulate many-body dynamics with error tolerance 𝜀 for any finite time 𝑡: as 𝜀 becomes sufficiently small, only 𝜀 −O⁡(𝑡 𝑑−1 ) resources are needed. A protocol that likely saturates this bound is given. Secondly, we prove that disorder operators have volume-law suppression near the “solvable (Ising) point” in quantum phases with spontaneous symmetry breaking, which implies a new diagnostic for distinguishing many-body phases of quantum matter.

computational complexity↗

DOE OSTI2018

Degradation of ILW Drums Due to Internal Metallic Corrosion - 18036

Within the British nuclear inventory, metallic Intermediate Level Waste (ILW) is encapsulated in grout and stored in stainless steel drums. Based on recent inspections held in the relevant storage facilities (Sellafield, Cumbria), a proportion of these drums have exhibited considerable distortion, raising concerns about the long-term safety of the packages. Distortion may be caused by the generation of voluminous and potentially flammable substances resulting from metallic corrosion occurring within the drums' core. Potential oxygen influx in the event of steel fracture and consequently drum's failure could potentially cause release or even ignition of the encapsulated radioactive material. The mechanical degradation of the encapsulants (stainless steel and grout) induced from the progressive corrosion of the encapsulated metallic components (and the associated volume expansion) was investigated using both Finite Element Modelling (FEM) techniques as well as experimental trials. A parametric study using simplified 3D FE models was performed to determine their structural integrity under different scenarios. Synchrotron X-Ray tomography (XRT) was used to monitor the behaviour of miniaturized ILW drum-simulants, whilst the latter were subjected to controlled accelerated corrosion in situ. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

Declamped Piezoelectric Coefficients in Patterned 70/30 Lead Magnesium Niobate–Lead Titanate Thin Films

Lateral subdivision of blanket piezoelectric thin films increases the functional properties through both increased domain wall mobility and declamping of the intrinsic response. This work presents the local effects of substrate declamping on the piezoelectric coefficient d 33,f of 300 nm thick, rhombohedral, {001}-oriented lead magnesium niobate–lead titanate thin films at the 70/30 composition (70PMN–30PT). Films grown by chemical solution deposition on platinized Si substrates are patterned into strip structures ranging from 0.75 to 9 µm in width. The longitudinal piezoelectric coefficient, d 33,f , is interrogated as a function of position across the patterned structures by three approaches: finite element modeling, piezoresponse force microscopy, and nanoprobe synchrotron X-ray diffraction. It is found that d 33,f increases from the clamped value of 40–50 to ≈160 pm V -1 at the free sidewall under 200 kV cm -1 excitation. The sidewalls partially declamp the piezoelectric response 500–600 nm into the patterned structure, raising the piezoelectric response at the center of features with lateral dimensions less than 1 µm (3:1 width to thickness aspect ratio). The normalized data from all three methods are in excellent agreement, with quantitative differences providing insight to the field dependence of the piezoelectric coefficient and its declamping behavior.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Simulated effect of defect volume and location on very high cycle fatigue of laser beam powder bed fused AlSi10Mg

This study quantifies the interaction between volumetric defect location and size on the very high cycle fatigue (VHCF) of laser beam powder bed fused (LB-PBF) AlSi10Mg. Crystal plasticity finite element method (CPFEM) simulations were used to investigate the effects of defect location and size on the driving force for crack initiation. The CPFEM model was calibrated against uniaxial and cyclic experimental data of LB-PBF AlSi10Mg. Defect characteristics were informed by experimental data from the specimens produced in various geometries to create realistic representative volume elements (RVEs) with equivalent volume fractions of defects. By embedding defects of varying sizes and locations within the RVEs, fatigue indicator parameters (FIPs) were calculated to analyze the impact of defects’ characteristics on fatigue performance. Different combinations of defect volume and locations were generated for various microstructure instantiations, providing insight into extreme value fatigue responses. Larger defect volumes located on free surfaces consistently generated the highest FIPs, suggesting defect size and boundary proximity intensify stress concentration effects. RVEs with multiple smaller defects produced lower FIPs than those with single large critical defects. These findings underscore the critical role of defect characteristics on fatigue life, providing a foundation for future predictive modeling in fatigue-sensitive AM applications.

AlSi10Mg↗

DOE OSTI2020

Superfluid condensate fraction and pairing wave function of the unitary Fermi gas

The unitary Fermi gas is a many-body system of two-component fermions with zero-range interactions tuned to infinite scattering length. Despite much activity and interest in unitary Fermi gas and its universal properties, there have been great difficulties in performing accurate calculations of the superfluid condensate fraction and pairing wave function. In this paper, we present auxiliary-field lattice Monte Carlo simulations using a lattice interaction which accelerates the approach to the continuum limit, thereby allowing for robust calculations of these difficult observables. As a benchmark test, we compute the ground-state energy of 33 spin-up and 33 spin-down particles. As a fraction of the free Fermi gas energy $E_{\text{FG}}$, we find $E_0/E_{\text{FG}}$ = 0.369(2), 0.372(2), using two different definitions of the finite-system energy ratio, in agreement with the latest theoretical and experimental results. We then determine the condensate fraction by measuring off-diagonal long-range order in the two-body density matrix. We find that the fraction of condensed pairs is α = 0.43(2). Further, we also extract the pairing wave function and find the pair correlation length to be $ζ_pk_F$ = 1.8(3)ℏ, where $k_F$ is the Fermi momentum. Provided that the simulations can be performed without severe sign oscillations, the methods we present here can be applied to superfluid neutron matter as well as more exotic $\textit{P}$-wave and $\textit{D}$-wave superfluids.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2016

Quantitative evaluation of an air-monitoring network using atmospheric transport modeling and frequency of detection methods

A methodology to quantify the performance of an air monitoring network in terms of frequency of detection has been developed. The methodology utilizes an atmospheric transport model to predict air concentrations of radionuclides at the samplers for a given release time and duration. Frequency of detection is defined as the fraction of “events” that result in a detection at either a single sampler or network of samplers. An “event” is defined as a release of finite duration that begins on a given day and hour of the year from a facility with the potential to emit airborne radionuclides. Another metric of interest is the network intensity, which is defined as the fraction of samplers in the network that have a positive detection for a given event. The frequency of detection methodology allows for evaluation of short-term releases that include effects of short-term variability in meteorological conditions. The methodology was tested using the U.S. Department of Energy Idaho National Laboratory (INL) Site ambient air monitoring network consisting of 37 low-volume air samplers in 31 different locations covering a 17,630 km 2 region. Releases from six major INL facilities distributed over an area of 1,435 km 2 were modeled and included three stack sources and eight ground-level sources. A Lagrangian Puff air dispersion model (CALPUFF) was used to model atmospheric transport. The model was validated using historical 125 Sb releases and measurements. Relevant one-week release quantities from each emission source were calculated based on a dose of 1.9 × 10 –4 mSv at a public receptor (0.01 mSv assuming release persists over a year). Important radionuclides considered include 241 Am, 137 Cs, 238 Pu, 239 Pu, 90 Sr, and tritium. Results show the detection frequency is over 97.5% for the entire network considering all sources and radionuclides. Network intensities ranged from 3.75% to 62.7%. Evaluation of individual samplers indicated some samplers were poorly situated and add little to the overall effectiveness of the network. As a result, using the frequency of detection methods, optimum sampler placements were simulated that could substantially improve the performance and efficiency of the network.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Efficient real space formalism for hybrid density functionals

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn–Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space finite-difference Laplacian matrix by leveraging its Kronecker product structure, thereby enabling the time to solution of associated linear systems to be highly competitive with the fast Fourier transform scheme while not imposing any restrictions on the boundary conditions. We implement this formalism for both the unscreened and range-separated variants of hybrid functionals. We verify its accuracy and efficiency through comparisons with established planewave codes for isolated as well as bulk systems. In particular, we demonstrate up to an order-of-magnitude speedup in time to solution for the real space method. We also apply the framework to study the structure of liquid water using ab initio molecular dynamics, where we find good agreement with the literature. Overall, the current formalism provides an avenue for efficient real-space DFT calculations with hybrid density functionals.

Chemistry↗

DOE OSTI2015

Selecting registration schemes in case of interstitial lung disease follow-up in CT

Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information), four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the range of 1.985–2.156 mm and 1.966–2.234 mm, for NLP and ILD affected regions, respectively, excluding schemes with statistically significant lower performance (Wilcoxon signed-ranks test, p < 0.05), resulting in 13 finally selected registration schemes. Conclusions: Selected registration schemes in case of ILD CT follow-up analysis indicate the significance of adaptive stochastic gradient descent optimizer, as well as the importance of combined rigid and nonrigid schemes providing high accuracy and time efficiency. The selected optimal deformable registration schemes are equivalent in terms of their accuracy and thus compatible in terms of their clinical outcome.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Damage development in neutron-irradiated concrete in a test reactor: Hygro-thermal and mechanical simulations

This paper reports the development of a 3D mesoscale hygro-thermal-mechanical simulation approach to predict damage in concrete irradiated in a test reactor. This framework, developed in MOOSE, considers the effects of elevated temperature, moisture content, and high neutron fluence (energy threshold, E > 0.1 MeV) on the mortar and aggregates separately. The first-stage simulation implements hygro-thermal analysis to determine the temperature and RH inside the specimen as a function of imposed radiation energy. These are used as inputs to the second stage, which considers radiation-induced volumetric expansion (RIVE) of aggregates, and creep, shrinkage, and stress-strain response of mortar to predict the expansion, stresses, and damage in specimens made using different coarse aggregates and subjected to different irradiation times. The irradiation time-dependent damage in the mortar is expressed using an isotropic damage parameter. This multi-physics model serves as a predictive tool for damage quantification in concrete due to neutron irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Numerical Simulation of Critical Factors Controlling Heat Extraction from Geothermal Systems Using a Closed-Loop Heat Exchange Method

Closed-loop heat exchange for geothermal energy production involves injecting working fluid down a well that extends through the geothermal resource over a significant length to absorb heat by conduction through the well pipe. The well then needs to return to the surface for energy recovery and fluid re-injection to complete the cycle. We have carried out mixed convective-conductive fluid-flow modeling using a wellbore flow model for TOUGH2 called T2Well to investigate the critical factors that control closed-loop geothermal energy recovery. T2Well solves a mixed explicit-implicit set of momentum equations for flow in the pipe with full coupling to the implicit three-dimensional integral finite difference equations for Darcy flow in the porous medium. T2Well has the option of modeling conductive heat flow from the porous medium to the pipe by means of a semi-analytical solution which makes the computation very efficient because the porous medium does not have to be discretized. When the fully three-dimensional option is chosen, the porous medium is discretized and heat flow to the pipe is by conduction and convection, depending on reservoir permeability and other factors. Simulations of the closed-loop system for a variety of parameter values have been carried out to elucidate the heat recovery process. To the extent that convection may occur to aid in heat delivery to the pipe, the permeability of the geothermal reservoir, whether natural or stimulated, is an important property in heat extraction. The injection temperature and flow rate of the working fluid strongly control the ultimate energy recovery. Pipe diameter also plays a strong role in heat extraction, but is correlated with flow rate. Similarly, the choice of working fluid plays an important role, with water showing better heat extraction than CO2 for certain flow rates, while the CO2 has higher pressure at the production wellhead which can aid in surface energy recovery. In general, we find complex interactions between the critical factors that will require advanced computational approaches to fully optimize.

Oldenburg, Curtis↗

DOE OSTI2018

Modeling the diffusion of heat energy within composites of homogeneous materials using the uncertainty principle

The goal of this paper is to develop a highly accurate and efficient numerical method for the solution of a time-dependent partial differential equation with a piecewise constant coefficient, on a finite interval with periodic boundary conditions. The resulting algorithm can be used, for example, to model the diffusion of heat energy in one space dimension, in the case where the spatial domain represents a medium consisting of two homogeneous materials. The resulting model has, to our knowledge, not yet been solved in closed form through analytical methods, and is difficult to solve using existing numerical methods, thus suggesting an alternative approach. The approach presented in this paper is to represent the solution as a linear combination of wave functions that change frequencies at the interfaces between different materials. It is demonstrated through numerical experiments that using the Uncertainty Principle to construct a basis of such functions, in conjunction with a spectral method, a mathematical model for heat diffusion through different materials can be solved much more efficiently than with conventional time-stepping methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Spectral Quadrature method for accurate O ( N ) electronic structure calculations of metals and insulators

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space O(N) Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the O(N) evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order to exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in O(N) operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established O(N 3 ) planewave results. In conclusion, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Determining Stability Margins in Adiabatic Superconducting Magnets with 3-D Finite Element Analysis

Superconducting magnets play a key role in the development of experiments at Fermilab; understanding the operating stability of these can allow us to utilize more potent magnets for future experiments (like the proposed Muon Collider), optimize the design of magnets in more immediate experiments (like Mu2e), and research the future use of more exotic materials (like high-temperature superconductors). This summer, I developed a 3-D parametric FEA program in ANSYS Mechanical APDL that simulates quench in superconducting magnets, and I also developed a parametric MATLAB program that predicts thermal behavior in magnet quench using the MIITS method. These programs can provide useful quenching parameters (like minimum quench energy and normal zone propagation velocity) for different cases of quench, leading to the previously mentioned objective of magnet design optimization. To test the programs, preliminary cases were run and the data produced was compared and analyzed. The results of these analyses, as well as the program operating methods, are discussed in this project.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Incorporating point defect generation due to jog formation into the vector density-based continuum dislocation dynamics approach

During plastic deformation of crystalline materials, point defects such as vacancies and interstitials are generated by jogs on moving dislocations. A detailed model for jog formation and transport during plastic deformation was developed within the vector density-based continuum dislocation dynamics framework. Here as a part of this model, point defect generation associated with jog transport was formulated in terms of the volume change due to the non-conservative motion of jogs. Balance equations for the vacancies and interstitials including their rate of generation due to jog transport were also formulated. A two-way coupling between point defects and dislocation dynamics was then completed by including the stress contributed by the eigen-strain of point defects. A jog drag stress was further introduced into the mobility law of dislocations to account for the energy dissipation during point defects generation. A number of test problems and a fully coupled simulation of dislocation dynamics and point defects generation and diffusion were performed. The results show that there is an asymmetry of vacancy and interstitial generation due to the different formation energies of the two types of defects. The results also show that a higher hardening rate and a higher dislocation density are obtained when the point defect generation mechanism is coupled to dislocation dynamics.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Asymmetric collapse by dissolution or melting in a uniform flow

An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-Analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-Analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton-Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In conclusion, the model raises fundamental mathematical questions about broken symmetries in finite-Time singularities of both continuous and stochastic dynamical systems.

42 ENGINEERING↗

DOE OSTI2024

Characterization of latent image of electron beam resist via critical-dimension resonant soft X-ray scattering

Metrology plays a crucial role in semiconductor manufacturing by providing accurate and precise measurement and characterization of critical parameters. With the development of high-resolution extreme ultraviolet lithography (EUVL) processes, critical dimensions are shrinking to sub-10 nm. Resist materials encounter the challenge of providing heightened sensitivity and a handle on exacerbating stochastic variations. A comprehensive understanding of the chemical profile of the latent image is pivotal for mitigating stochastic effects and optimizing pattern quality. However, the subtle differences in chemistry between the exposed and unexposed regions of the resists make it extremely challenging to characterize the latent images with sub-nanometer precision. Here, we develop the metrology with critical-dimension resonant soft X-ray scattering (CD-RSoXS) to probe the chemical profiles of latent images stored in resist after exposure. The combination of absorption spectroscopy and enhanced scattering contrast makes it possible to characterize the subtle structural and chemical variations in the latent image. Moreover, the results of the measurements are compared with the simulations with a finite element method–based Maxwell solver to extract a detailed profile of the latent and developed images. We demonstrate that the CD-RSoXS technique can provide valuable insights into the high spatial resolution and local chemical sensitivity simultaneously, which is crucial to understanding the resolution limits and stochastic effects in EUVL processes.

36 MATERIALS SCIENCE↗

DOE OSTI2016

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, relies on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗