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DOE OSTI2022

Evaluation of Thermal Neutron Scattering Law and Cross Sections for Calcium Hydride

Presented in this paper are the calculated thermal scattering law (TSL) and thermal neutron scattering cross sections for Calcium Hydride, hereafter referred to by its chemical symbol CaH 2 . The only other such data prior to this evaluation are thermal neutron scattering libraries in the JEFF database, which suffer from nonphysical features and inaccuracies. The data in this evaluation are calculated from first principles; Density Functional Theory (DFT) is used to calculate the phonon density of states (DOS), which is the primary input required to calculate the TSL. The TSL and cross sections have been evaluated for the three non-equivalent atom cites in the CaH 2: Ca, H 1 , and H 2 . Each evaluation has been submitted to the NNDC for consideration in the next ENDF/B release.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Thermal neutron scattering cross sections for amorphous carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm{sup 3}. From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical optical peak at 0.25 eV for the ideal graphite disappears for amorphous carbon, in good agreement with the expected structure. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Thermal Neutron Scattering Cross Sections for Graphitic Amorphous Carbon

Carbon materials are commonly found in both nuclear reactors and experimental systems. Various carbon structures occur in nuclear applications ranging from crystalline and nuclear graphite to the amorphous carbon seen in next-generation advanced reactor designs. Amorphous carbon is based on a randomized graphite-like structure and offers the unique ability to disperse impurities throughout the bulk composition. A graphite-like amorphous carbon system was modeled using the classical molecular dynamics (MD) code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). An improved version of the temperature-dependent Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential was used to model the carbon-carbon atomic interactions for the temperature at 300 K along with densities 1.60, 1.70, 1.85, and 2.23 g/cm 3 . From the normalized velocity autocorrelation function (VACF), the phonon density of state (DOS) was then calculated as the Fourier transform of the normalized VACF. This DOS was then used as the primary input for the evaluation of the thermal scattering law (TSL, i.e. S(α,β)) and associated neutron thermal scattering cross sections. The TSL was analyzed using the Full Law Analysis Scattering System Hub (FLASSH). The amorphous structure results in shifts of the phonon DOS to lower energy modes than typically displayed for ideal crystalline graphite. This impact on the DOS is directly reflected in the TSL. Furthermore, the typical features and the optical graphitic peak at 0.25 eV for the ideal graphite DOS disappear for graphite-like amorphous carbon, which shows good agreement with the expected structure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Rossi-α Measurements on a System Consisting of Weapons Grade Plutonium Moderated by Polyethylene [Poster]

A series of experiments nicknamed "TEX," standing for Thermal-Epithermal eXperiments, were performed at the National Criticality Experiments Research Center (NCERC) on the Planet critical assembly. The TEX experiment campaigns are a collaboration between Los Alamos National Laboratory (LANL) and Lawrence Livermore National Laboratory (LLNL) and funded by the Nuclear Criticality Safety Program (NCSP). The TEX experiment consists of several campaigns; this work specifically discusses measurements made on one series of TEX experiments designed to examine the thermal scattering law (TSL) for polyethylene. This series consisted of two different critical configurations which contain plutonium fuel. The plutonium plates are 2 in. by 3 in. by 0.125 in. Zero Power Physics Reactor (ZPPR) plates and are placed in a tray in an array of 6 plates by 4 plates wide creating a 12 in. by 12 in. square. These trays of plutonium are interleaved between polyethylene plates. These measurements differ from previous TEX experiments in that they examine a more thermal neutron spectrum than previously examined by interleaving much thicker interstitial moderating plates than the previous measurements. The two configurations differ in the thickness of polyethylene between the fissile material. While the experiment was designed to examine the TSL, this work only examines the results of Rossi-α measurements on the two different configurations. For both configurations, Rossi-α measurements were performed to experimentally validate the neutron spectrum.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Isotope Effects in Thermal Neutron Scattering [Slides]

AMPX links Thermal Scattering Law (TSL) libraries to isotopes in the resolved resonance region. No guidance is given in the TSL files or the ENDF format if this is acceptable or advised, which can lead to several issues. This presentation discusses these issues and provides suggested solutions.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

TSL Nuclear Fuel Evaluations and Capabilities at NC State University [Slides]

This presentation discusses the purpose of this project which is to provide thermal scattering law (TSL) and cross section data to support advanced reactor modeling and criticality safety. The presentation also examines modeling and simulations, evaluation updates, and benchmark applications in connection with the project. In summation, new and updated uranium fuel evaluations have been submitted to the ENDF/B libraries. These include vital fuel materials U-metal, UC, UN, and UO 2 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Development of a Pulsed Slowing-Down-Time Benchmark of Neutron Thermalization in Graphite

Graphite is a classic neutronic material that has been used as both a reactor reflector and moderator in various nuclear reactor systems. The ability to accurately predict the slowing down and thermalization of neutrons in graphite can have significant implications on the safety and operation of such reactor systems. In reactors, the neutron thermalization process is quantified using the thermal scattering law (TSL) and related cross sections for a given moderator. An ideal approach to assess the validity of TSL data is using benchmark measurement based on the pulsed Slowing-Down-Time technique and its comparison with the appropriate graphite nuclear library. In this work, experimental measurement and computational Monte Carlo simulations were performed to benchmark the slowing down characteristics and thermalization of neutrons in nuclear (reactor-grade) graphite. Given the density of graphite, various graphite libraries were selected for the benchmark analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Ab Initio Evaluation of Uranium Carbide S(α,β) and Thermal Neutron Cross Sections

Uranium Carbide (UC) is a nuclear fuel material which offers better neutron economy and lower fuel-cycle costs compared to conventional mixed-oxide fuels. UC’s lattice binding and dynamical properties impact thermal neutron scattering and low temperature epithermal resonance absorption. The Thermal Scattering Law (TSL) describes the scattering system available energy and momentum transfer states. There is no TSL evaluation for UC in the ENDF/B-VIII.0 database; herein, ab-initio lattice dynamics (AILD) techniques are invoked to calculate the phonon spectrum for UC using spin-orbit-coupling density functional theory (DFT). The TSLs, inelastic and elastic thermal scattering cross sections for Uranium and Carbon in UC, respectively, are calculated in FLASSH for use in higher fidelity reactor design calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Isotope Effects in Thermal Neutron Scattering [Slides]

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2022

Total thermal neutron cross section measurements of hydrogen dense polymers from 0.0005–20 eV

Hydrogen dense polymers, specifically polyethylene, polystyrene, and Plexiglas, have served as neutron moderator and reflector materials in hundreds of separate critical benchmark experiments because of their low cost and abundance of hydrogen. In order to accurately model and simulate these critical benchmarks, the thermal scattering law (TSL) evaluation that governs how neutrons will thermalize must be well understood and rigorously validated. To support this validation, researchers at Rensselaer Polytechnic Institute performed total neutron cross section measurements for high-density polyethylene & polystyrene over the energy range 0.0005–20 eV and for Plexiglas G & Plexiglas G-UVT over the energy range 0.0005–3 eV. Comparisons were made between the measured cross section and that predicted by the ENDF/B-VIII.0 and Oak Ridge National Laboratory/European Spallation Source/Rensselaer Polytechnic Institute TSL evaluations for polyethylene, Plexiglas, and polystyrene, as available. These experiments represent the first total neutron cross section measurements for polystyrene.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Thermal Neutron Scattering Research and Development at Oak Ridge National Laboratory [Slides]

This presentation provides an overview of the project, specifically describing how neutron cross sections can be broken up into several regions. It also discusses how thermal scattering law (TSL) $\textit{S(α, β)}$ is related to dynamic structure factor $\textit{S(q, E)}$ and how $\textit{S(q, E)}$ can be broken up into 2 primary components, incoherent and coherent, and how it can be calculated in several ways, including density functional theory (DFT) and molecular dynamics (MT). Additionally, it states that ENDF currently stores coherent elastic (Bragg edges), incoherent elastic and incoherent inelastic. Also discussed are the experimental capabilities, evaluations, and uncertainty quantification of the project.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Rossi-alpha Analysis of Thermal/Epithermal eXperiments Optimized for Polyethylene Thermal Neutron Scattering

Accurate nuclear data is the foundation for predictive simulations and design of new experimental in the nuclear community. The criticality safety community has particular interest in benchmarking assemblies with thermal neutron data. To address such needs the Nuclear Criticality Safety Program (NCSP) funded the Thermal/Epithermal eXperiments (TEX) campaigns that were to be completed between Lawrence Livermore National Laboratory (LLNL) and Los Alamos National Laboratory (LANL). Specifically, analysis of plutonium with a thermal neutron spectrum expands on previous work to help validate thermal scattering law data, which can have larger impacts in thermal applications. The first of these experiments were successfully conducted in 2018, but this paper will focus on the 2021 measurement focused on investigating the the thermal scattering law (TSL) for polyethylene. These experiments were successfully conducted at the National Criticality Experiments Research Center (NCERC) using the Planet vertical lift critical assembly machine. Polethylene plates were layered with trays of Zero Power Physics Reactor (ZPPR) 24 plates in a 12" by 12" square. The ZPPR plates were 2" by 3" by 0.125" bearing weapons grade plutonium. The polyethylene moderator was either 2" or 1.6875" thick. This work builds on the Rossi-alpha calculations done by McKenzie et al. for the same detector-assembly system and will only focus on the Rossi-alpha neutron noise method. This work will aim to further validate the results of the experiment through a novel neutron noise python package. Following similar methodology to the previous analysis, analysis of TEX evaluated the prompt neutron decay constant at delayed critical, $α_{DC}$ using Rossi-alpha for different polyethylene moderator thicknesses. These results will help improve understanding of TSL in critical experiments. Alpha (α), is the prompt neutron decay constant of the measured system and allows for the evaluation of a systems propensity to sustain fission chains via prompt neutrons. The single value description of the assemblies allow for comparison between experiments regardless of composition, geometry, and reflectors/moderators. Rossi-alpha measurements were performed on the polyethylene moderated TEX experiments to estimate $α_{DC}$.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Advancements in Validation of TSLs through Inelastic Neutron Scattering and Transmission Measurements [Abstract]

Historically, the free gas approximation has been used to treat the thermal scattering of neutrons with energies below a few electron-volts (eV) in unevaluated materials. However, this method inadequately reproduces neutron scattering at these energies. Until recently, only a limited number of materials had available thermal scattering law (TSL) files/libraries in the ENDF nuclear data libraries in this energy range. With advancements in atomistic modeling techniques, such as molecular dynamics, ab-initio molecular dynamics, and density functional theory, TSL libraries have become available for many more materials. This is particularly relevant due to the rising interest in several advanced reactor systems that require novel moderator and reflector materials. While quasi-integral and integral benchmarks have been designed to validate historically important moderator materials (such as light water and polyethylene), there is currently a lack of standard validation methods for TSLs, especially when multiple conflicting TSLs exist. To address this issue, the Oak Ridge National Lab Nuclear Data group has been working on utilizing inelastic neutron scattering (INS) measurements combined with transmission (i.e., total cross section) measurements to evaluate and validate TSLs for different materials. We plan to demonstrate how this method has worked on materials such as polyethylene, lucite, and polystyrene. In addition, we will compare the newly created libraries to ENDF libraries for these materials and explain why integral benchmarks should not be used for validation when multiple TSLs exist.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Phonon-informed Neural Thermal Scattering (NeTS) Optimization for Crystalline Graphite and Beryllium Metal

Fast neutrons born from fission lose energy through scattering interactions in the process of slowing-down. As neutrons thermalize to the order of $k$ $b$ $T$ (where $k$ $b$ is the Boltzmann constant, and $T$ is the temperature of the medium), their de Broglie wavelength and energy approaches the order of inter-atomic spacing and quantized lattice vibrations, i.e., phonons. At thermal energies, the thermal scattering law (TSL), i.e., $S$($α, β$), captures crystal binding contributions to the total reaction rate, or cross section. This dimensionless material property describes the energy ($β$) and momentum ($α$) exchanges available in a medium. Currently, $S$($α, β$) is evaluated in the Full Law Analysis Scattering System Hub (FLASSH) code for discrete inputs and stored as ENDF/B File 7 for 0-phonon elastic (MT 2) and n-phonon inelastic (MT 4) processes. Further processing recasts $S$($α, β$) into cumulative distribution functions for sampling post-collision scattering kinematics. In practice, interpolation schemes are employed to access data between tabulated values. An improvement to this juncture of the nuclear data pipeline is supplying cross sections on-the-fly (OTF), as has been developed for the un-resolved resonance region to minimize non-physical interpolation errors. This capability may improve simulation accuracy for accident and transient analyses, where rapidly varying changes in temperature and pressure are difficult to predict beforehand. To do so, deep artificial neural networks (ANNs) can be employed which collapse non-linear, complex data into a lightweight dictionary of neural weights and biases. This has been successfully demonstrated for the hydrogen in light water $S$($α, β$) dataset in the form of a Neural Thermal Scattering (NeTS) module. In this work, the NeTS framework is extended to consider the impact of material-dependent dynamical features on optimal neural pre-processing and architecture design decisions, such as number of neurons per hidden layer, residual skip connections and neural depth. New NeTS modules for crystalline graphite and beryllium metal illuminate a novel correlation between dynamical nonlinearity and optimal neural parametrization when deploying $S$($α, β$) on-the-fly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Thermal Scattering Law Data Development for Paraffin Wax

Paraffin wax is often used as a nuclear moderator to slow down the fast neutrons in experimental critical assemblies [1]. It is a colorless and soft solid material that consists primarily of straight-chain alkanes (n-alkanes), which are hydrocarbons with the general formula CnH2n+2 [2-3]. The length of the hydrocarbon chain ranges from C20 to C30 and higher [2]. It is distinguished by its solid state at room temperature and begins to melt above approximately 310 K [4]. Paraffin wax is a commonly employed substance in the manufacture of shielding. One of its noteworthy characteristics is its ability to effectively absorb the neutrons. Also, it possesses a high macroscopic cross section, which enables it to efficiently moderate neutrons. As a result, paraffin wax is extensively utilized in various applications where moderation and shielding of neutrons are needed. For simulations, it is necessary to evaluate its thermal scattering law (TSL) and cross sections. Computationally, classical molecular dynamics (CMD) simulations provide the capability of simulating atomic details. For example, several unary, binary, and few multi component mixtures have been investigated of the paraffin model by using molecular dynamics simulations [5-12]. An assessment of thermal neutron scattering in a heavy paraffinic oil treated both as a solid and a viscous fluid containing 25% linear branched paraffin (C30H62), 35% one ring cycloalkane (C30H60), 15% two rings cycloalkane (C30H58), and 25% aromatic (C30H60) chains has been studied using CMD simulations for producing TSL data [13]. Nevertheless, there is lack of TSL and cross section data for paraffin wax as most of the reported analyses focus on the unary and binary mixture of n-alkanes, which is not consistent with actual paraffin wax [2]. In this work, we applied the equilibrium CMD simulations technique to explore the structure and dynamical properties of wax, which are fundamental input to calculate the TSL. A paraffin wax system was modeled using the CMD code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) [14-15] with the semi-empirical COMPASS [16] force field. The density of state (DOS) was calculated from the normalized velocity autocorrelation function (VACF), which is the Fourier transform of the normalized VACF. The DOS was used for the calculation of the TSL and thermal scattering cross sections. The paraffin wax atomic system was constructed by using the MedeA material design platform [17], and was benchmarked using available properties (i.e., density, bond lengths, angles, diffusivity, and viscosity).

Nuclear Criticality Safety Program (NCSP)↗

DOE OSTI2023

Thermal Cross Section Measurements At The RPI LINAC

Recently, a cold moderator was designed and developed for use at the Rensselaer Polytechnic Institute Linear Accelerator (RPI LINAC). This cold moderator proved to easily and safely couple to an existing neutron producing target, while enhancing neutron flux below 0.02 eV by up to a factor of 8 by cooling polyethylene down to 29 K. This cold moderator capability allowed for significantly improved counting statistics below 0.02 eV not previously possible due to a poor signal to background ratio. Additionally, testing was performed to characterize the energy resolution of the new cold moderator system and found the system easily capable of resolving resonances in Ta-181 at 4 and 10 eV, while also clearly resolving the Bragg edges found in Be metal below 0.01 eV. Furthermore, following the design and development of a cold polyethylene moderator, a series of thermal total cross section measurements were performed for polyethylene, polystyrene, Plexiglas and yttrium hydride in the thermal region. These measurements serve to help validate thermal scattering law (TSL) evaluations in the 0.0005 – 1 eV energy range. For polyethylene and polystyrene, two sets of experiments were performed – one with the Enhanced Thermal Target (ETT) and another with the ETT plus the new cold moderator capability (ETTC). The yttrium hydride and Plexiglas measurements were only performed with the ETTC. The measurements for polyethylene help to validate the data processing methodology when using the ETTC, while extending the measured range of polyethylene down to 0.0005 eV. Two different Plexiglas, Plexiglas G and Plexiglas G-UVT, and two different concentrations of yttrium hydride, H/Y = 1.85 and 1.68, were measured. Overall, all materials had generally good agreement with their ENDF/B-VIII.0 TSL evaluations, though some discrepancies were noticed. In the case of the yttrium hydride, the high energy oscillations in the hydrogen cross section and the low energy Bragg edges in the yttrium cross section were clearly seen. These measurements represent the first total cross section measurements that encompass the entire thermal region from 0.0005 – 1 eV for polystyrene and yttrium hydride.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Thermal cross section measurements at the RPI LINAC [Abstract]

Recently, a cold moderator was designed and developed for use at the RPI LINAC. This cold moderator proved to easily and safely couple to an existing neutron producing target, while enhancing neutron flux below 0.02 eV by cooling polyethylene down to 29 K. This cold moderator capability allowed for significantly improved counting statistics below 0.02 eV not previously possible due to a poor signal to background ratio. Additionally, testing was performed to characterize the energy resolution of the new cold moderator system and found the system easily capable of resolving resonances in Ta-181 at 4 and 10 eV, while also clearly resolving the Bragg edges found in Be metal below 0.01 eV. Following the design and development of a cold polyethylene moderator, a series of thermal total cross section measurements were performed for polyethylene, polystyrene, Plexiglas and yttrium hydride in the thermal region. These measurements serve to help validate thermal scattering law (TSL) evaluations in the 0.0006 – 20 eV energy range. For polyethylene and polystyrene, two sets of experiments were performed – one with the Enhanced Thermal Target (ETT) and another with the ETT plus the new cold moderator capability (ETTC). The yttrium hydride and Plexiglas measurements were only performed with the ETTC. The measurements for polyethylene help to validate the data processing methodology when using the ETTC, while extending the measured range of polyethylene down to 0.0007 eV. Two different Plexiglas, Plexiglas G and Plexiglas G-UVT, and two different concentrations of yttrium hydride, H/Y = 1.85 and 1.68, were measured. Overall, all materials had generally good agreement with their ENDF/B-VIII.0 TSL evaluations, though some discrepancies were noticed. In the case of the yttrium hydride, the high energy oscillations in the hydrogen cross section and the low energy Bragg edges in the yttrium cross section were clearly seen. These measurements represent the first total cross section measurements that encompass the entire thermal region from 0.0006 – 3 eV for polystyrene and yttrium hydride.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Experimental Validation of Thermal Scattering Evaluations

In order to test the performance of new neutron thermal scattering law (TSL) evaluations it is desirable to have experimental data that is highly sensitive to the TSL and provides high fidelity information on the energy dependent performance of TSL evaluations. Three relevant experiments are discussed including: accurate thermal total cross section measurements, thermal neutron die-away experiments, and neutron leakage experiments. The experimental setups and results are reviewed, and examples provided for some moderators including polyethylene, Plexiglas, and YHx. For the experiments preformed thus far, there is generally good agreement between the measured total cross section and simulations using current TSL evaluations, however in certain energy ranges differences were observed. Similarly, neutron die-away and leakage measurements for samples at room temperature are in good agreement with data computed from TSLs, however leakage measurements for polyethylene at 29K show discrepancies with TSL evaluations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗