Verification of the Re-Released ENDF/B VIII.0 Based Thermal Scattering Libraries
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Structure-Dependent Doppler Broadening Using a Generalized Thermal Scattering Law [Banner Highlight]
Banner Highlight for Structure-Dependent Doppler Broadening Using a Generalized Thermal Scattering Law [DOI 10.3390/jne2020013].
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Data Testing of Polyethylene Thermal Scattering Law with New Thermal Epithermal eXperiments (TEX) Plutonium Baseline Benchmark, PU-MET-MIXED-002
Five plutonium baseline experiments completed in September of 2018 from the Thermal Epithermal eXperiments (TEX) program have been accepted by the International Criticality Safety Benchmark Evaluation Project as PU-MET-MIXED-002 and will be included in the 2020 version of the handbook. The experiments were made up of stacked layers of plutonium Zero Power Physics Reactor (ZPPR) plates moderated by polyethylene (PE, chemical formula C2H4) to varying degrees to create configurations with five different neutron spectra, including one fast configuration, one thermal configuration, and three mixed configurations. Calculations of the benchmark show overprediction of k eff when using the most recent release of the Evaluated Nuclear Data File Version B (ENDF/B) library release (VIII.0) cross sections, particularly when compared to the previous ENDF/B-VII.1 results. One potential source of overprediction was hypothesized to be the new Molecular Dynamics (MD) generated PE Thermal Scattering Law (TSL). The overprediction was shown via calculation to not be caused by the new ENDF/B-VIII.0 thermal scattering law, and in fact the overprediction was mitigated by the new PE TSL.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Generation of the Thermal Scattering Law of Uranium Dioxide with Ab Initio Lattice Dynamics to Capture Crystal Binding Effects on Neutron Interactions
Scattering of thermal neutrons and Doppler broadening of epithermal neutron resonances in uranium and its compounds may be sensitive to crystal binding. The thermal scattering law (TSL) for uranium dioxide, which captures crystal binding effects, has been reevaluated for ENDF/B-VIII.0. Phonon spectra were generated using ab initio lattice dynamics for the paramagnetic phase and validated against experiment. Improved agreement with the Debye-Waller coefficient as a function of temperature is found relative to the spectrum used for the ENDF/B-VII.1 evaluation. The TSL was generated using the phonon expansion method within the NJOY nuclear data processing package and was found to be in reasonable agreement with inelastic neutron scattering measurements. The present evaluation predicts a reduction in the inelastic scattering cross section relative to ENDF/B-VII.1 and a total scattering cross section consistent with neutron transmission experiments
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Generation of high-resolution thermal scattering laws for solid moderators using fast Fourier transforms
Not provided.
Nuclear Science & Technology↗
On a measurement approach to support evaluation of thermal scattering law data
Inelastic thermal neutron scattering in materials that act as neutron moderators, reflectors, and filters results in shaping the neutron spectrum at low energies. This phenomenon is described using differential scattering cross sections calculated from three components including the bound atom (i.e., nuclear) scattering cross section of the neutron, the ratio of the outgoing and incoming neutron energy, and the thermal scattering law (TSL), i.e., S(α,β), where α and β represent dimensionless momentum and energy exchange variables, respectively. To date, no TSL libraries are generated using measured data. However, valuable information may be derived from measurements and “targeted” experiments that can validate TSL data and the related inelastic scattering cross sections. As a demonstration, a suite of coordinated measurements and experiments is described that was designed and used to support the evaluation of the TSL for “nuclear” graphite. This experimental suite includes neutron powder diffraction (for structure analysis), positron annihilation (for nano porosity assessment), inelastic neutron scattering measurements using a chopper spectrometer, transmission experiments using neutrons with energy below the Bragg cutoff thereby accessing the total (inelastic) cross section, and a slowing-downtime experiment to observe the developing neutron spectrum in the material. We find that this experimental suite was key to understanding the difference in TSL between “nuclear” and “ideal” graphite and for the inclusion of “nuclear” graphite in the ENDF/B-VIII.0 nuclear data library release.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Adjusted Graphite Thermal Scattering Data Applied to Fluoride-Salt-Cooled Reactors
Thermal scattering data is a key component of fission reactor simulation. While most materials can be reasonably modeled with a free gas approximation, the moderators in thermal systems require a more rigorous treatment to sufficiently capture their specific neutron interaction physics. Graphite does not typically feature as a principle moderator in power reactors in service today, but remains an attractive prospect for a number of new reactor concepts currently in development. In comparison to light water, a material nearly ubiquitous in thermal reactors, graphite offers a better neutron economy by way of a small absorption cross section, high thermodynamic stability and can be incorporated into the structure of the core itself. Graphite in its purest form is a crystalline material composed of stacked layers of graphene, a hexagonal planar lattice of carbon atoms. In-plane, each carbon atom is covalently bonded to 3 neighbouring carbon atoms, creating a strong bond, while between planes only a weak van der Waals force exists. Pure graphite has a density of 2.26 g/cm{sup 3}. However, reactor-grade contains a significant amount of carbon binder, leading to a porous bulk medium with randomly oriented micro crystals. Densities of 1.5 - 1.9 g/cm{sup 3} are typical for reactor-grade graphite, corresponding to porosities on the order of 10-30%. This deviation from pure crystalline graphite should be accounted for in the thermal scattering data. When an incident neutron is in or near the thermal region, its de Broglie wavelength is the same order as the molecular bond lengths, leading to elastic scattering. At similar energies, the dynamics of the moderator lattice (in the case of solid moderators) can cause inelastic scattering. For these moderators, special cross sections should be calculated and used in reactor simulations. To generate this thermal scattering data, parameters pertaining to the properties and structure of the material in question are fed into a nuclear data processing code, such as NJOY. Within NJOY is a module called LEAPR which is used to generate the thermal scattering law S(α,β), which is in turn is fed into another module THERMR which is used to generate thermal cross sections that factor in the molecular-scale scattering phenomena. The core of the thermal scattering law is the phonon spectrum ρ(β) which describes the modes of excitation of the material lattice. An investigation into the phonon frequency spectrum was conducted at North Carolina State University (NCSU) for reactor-grade graphite which accounts for porosity. This phonon spectrum was calculated using the ab initio density functional theory (DFT) code VASP. The inelastic cross section calculated using this spectrum was found to have good agreement with relevant experimental data. The resulting spectra differed from the benchmark spectrum produced by Young and Koppel, the same data used in current nuclear data evaluations. The latter uses the lattice dynamics of perfect crystalline graphite with four force constants fitted to the model from thermodynamics data from reactor-grade (porous) graphite, which yields a reasonable approximation to the phonon spectrum of reactor-grade graphite.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Dynamical screening of α − α resonant scattering and thermal nuclear scattering rate in a plasma
Not Available
Yao, Xiaojun↗
Benchmarking of ENDF/B-VIII.1 Thermal Scattering Library for Hydrogen
In correctly characterizing the energy and momentum transfer at thermal and cold energies between neutrons and its interacting medium, thermal scattering libraries, which details energy states due to the intra- and inter-molecular bond effects for the medium materials, are applied in place of free-gas cross section libraries in a particle transport simulation code. They are essential to the neutron performance of a neutron facility like SNS, where thermalized neutrons from 20 K liquid hydrogen and ambient (~300 K) water are transported to the beamlines for neutron scattering experiments in studying materials. Recently, a new version of thermal scattering library for parahydrogen and orthohydrogen at 14-20 K was developed and to be released in ENDF/B-VIII.1. It is, therefore, important to benchmark its impacts on the prediction of moderator performance due to the updates in the thermal scattering library. In this study, the recent ENDF/B-VIII.1 thermal scattering library was compared to the current ENDF/B-VII.1 one in the neutron performance calculations for the decoupled and coupled hydrogen moderators at SNS under theorized and real working conditions. In addition, the predictions using both thermal scattering libraries were benchmarked to the measurements of moderator performance. The consistency between the libraries was observed mostly for parahydrogen and the difference in orthohydrogen at cold neutron energies was noted.
Lu, Wei↗
Design of a neutral thermal scattering (NeTS) module for hydrogen in light water
The accurate representation of thermal scattering law (TSL) data is integral to the design and characterization of many modern nuclear systems, particularly those using light water as a moderator/coolant. As a material-dependent distribution over energy-momentum phase space, the TSL may exhibit a variety of unique and relevant conditional (e.g., temperature, pressure) and compositional (e.g., porosity, stoichiometry, radiation damage) dependencies. Currently, there are various approaches to incorporate temperature dependence, which is especially important in coupled neutronic-thermal hydraulic simulations. In each approach, there is an inherent tradeoff between memory consumption and accuracy. Some techniques require tens to hundreds of MBs or more, while others fail to reproduce the underlying data to within 10% error over the considered input domain, despite having a reduced storage burden. This work aims to address both sides of the tradeoff simultaneously by implementing a novel deep learning (DL) approach to TSL representation. The neural thermal scattering (NeTS) concept, which is amenable to an arbitrary number of dependencies, is demonstrated via the inclusion of temperature dependence into a highly compact, highly accurate functional form of the multi- variate TSL (i.e., S(α, β, T)) for hydrogen in light water. Resulting storage requirements are on the order of 100 kB, and median and maximum percent deviations are on the order of 0.1% and 1%, respectively. These measures represent a step improvement over previous techniques. Notably, the developed neural network and feature methodology build on those employed in prior work on beryllium oxide. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Comparison of MCNP thermal scattering laws to inelastic neutron scattering data
Neutron transport computations employ thermal scattering laws (TSLs) to account for the influence of material structure and collective excitations at low energy (≲ 10 eV). Recent work has been undertaken to improve TSL accuracy and expand the number of available materials in the Evaluated Nuclear Data File (ENDF). However, comparison of TSL to measured data is often sparse. In this work, we present a method to evaluate TSL accuracy in the Monte Carlo N-Particle (MCNP) code by simulating inelastic neutron scattering (INS) measurement and comparing to data. The method is briefly described with example application to the recently released ENDF-VIII TSL library for polyethylene as well as a cryogenic PE TSL we are separately developing.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Evaluation of Thermal Scattering Law for U 3 Si 2 Using Temperature-Dependent Phonon Density of States
The thermal scattering law for uranium silicide, a candidate material for high-density nuclear fuel, was evaluated from the temperature-dependent phonon density of states obtained using the quasi-harmonic approximation. For uranium silicide model systems of various volumes near the equilibrium volume, Hellmann-Feynman forces were calculated by performing ab initio lattice dynamics simulations based on density functional theory. Subsequently, the quasi-harmonic approximation was applied by interpolating the results of the harmonic approximation for each volume system. As a sensitivity test, the phonon density of states was calculated for the structures with temperature-dependent volumes at 298 K and 1000 K, obtained by the quasi-harmonic approximation, and the corresponding thermal neutron scattering cross section was evaluated. The temperature-dependent volume and heat capacity of uranium silicide obtained by the quasi-harmonic approximation showed reasonable agreement with experimental data while lattice thermal expansion showed deviation from experimental observations. Thermal scattering cross sections evaluated from 0 K and temperature-dependent phonon density of states exhibited differences of up to 4.1% at 1000 K. This study examines the impact of temperature on the thermal scattering law, employing ab initio lattice dynamics simulations through the quasi-harmonic approximation.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
A Novel Methodology For Generating Thermal Scattering Cross Sections and Uncertainties
With the rise in interest of GEN-IV reactor systems, newer, and more accurate thermal scattering nuclear data are needed. Both GEN-IV reactors and current light water reactors applying for license extensions require high fidelity cross sections and uncertainties to better thermal margins and thereby maximizing energy production and improving economics and safety. Thermal moderator data play a key role in both reactor physics and nuclear criticality safety analyses. Due to the lack of uncertainties data for thermal scattering material, there is no way to quantify the effects of thermal scattering uncertainties in quantities of interest (e.g., k eff ) in reactor or criticality safety systems.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
FLASSH 1.0: Thermal Scattering Law Evaluation and Cross Section Generation
The Full Law Analysis Scattering System Hub ( FLASSH ) is an advanced code which evaluates the thermal scattering law (i.e. TSL, S(α,β)) for thermal scattering cross sections and resonance Doppler broadening. The ability to accurately capture these two key cross section features is dependent on accurate, high fidelity TSL evaluations. FLASSH 1.0 provides advanced physics capabilities resulting in an improved, generalized TSL to most accurately represent the lattice dynamics within any material. This improved TSL will allow for consistent analysis in both the thermal and epithermal energy ranges. The features for TSL analysis are packaged within the FLASSH GUI for easy user interface along with data output in many file formats including ENDF File 7 and ACE files.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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↗
FLASSH 1.0: Thermal scattering law evaluation and cross section generation for reactor physics applications
The Full Law Analysis Scattering System Hub (FLASSH) is a modern, advanced code which evaluates the thermal scattering law (TSL) along with accompanying cross sections. FLASSH features generalized methods which accommodate any material structure. Historical approximations including the incoherent and cubic approximations have been removed. Instead, the latest release of FLASSH features advanced physics options including distinct corrections (1-phonon contributions) and non-cubic formulations. The non-cubic elastic and inelastic contributions are necessary to accurately evaluate 1-phonon contributions. Both non-cubic and 1-phonon calculations require high-density sampling of the various scattering directions. Optimization and parallelization of these routines were therefore necessary to produce results in a reasonable timeframe. With these notable improvements to the generalized TSL, FLASSH 1.0 meets benchmark requirements, demonstrating noticeable agreement with experiment for both TSLs and the resulting integrated cross sections. Additional features including a graphical user interface (GUI), plotting diagnostics, and formatted output options including ACE files allow users to complete a TSL evaluation with minimal input and maximum flexibility. The user GUI creates input files for FLASSH, reducing user error and also providing built-in error checks. Autofill options and suggested input values help make TSL evaluation accessible to novice users. The FLASSH code is compiled to run on both Windows and Linux platforms with automatic parallelization. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Thermal scattering law of C 2 H 4 n : Integrating experimental data with DFT calculations
Improvements in determination of the thermal scattering law of moderator materials (measuring, calculating and validating) are important for accurate prediction of neutron thermalization in nuclear systems. In this paper a methodology for producing thermal scattering libraries from the experimental data for polyethylene C 2 H 4 n is discussed. Double differential scattering cross section (DDSCS) experiments were performed at the Spallation Neutron Source of Oak Ridge National Laboratory (SNS ORNL). New scattering kernel evaluations, based on phonon spectrum for C 2 H 4 n , are created using the NJOY2016 code. Two different methods were used: direct and indirect geometry neutron scattering at ARCS and SEQUOIA, and VISION instruments, respectively, where the phonon spectrum was derived from the dynamical structure factor S(Q, ω ) obtained from the measured DDSCS. In order to compare and validate the newly created library, the experimental setup was simulated using MCNP6.1. Compared with the current ENDF/B-VII.1, the resulting RPI C 2 H 4 n libraries improved both double differential scattering and total scattering cross sections. A set of criticality benchmarks containing C 2 H 4 n from HEU-MET-THERM resulted in an overall improved calculation of K eff , although the libraries should be tested against benchmarks more sensitive to C 2 H 4 n . The DFT + oClimax method is used and is shown to be most comprehensive method for analysis of moderator materials. Finally, the importance of DFT + oClimax method lies in the fact that it can be validated against all data measured at VISION, ARCS and SEQUOIA, and experimental total scattering cross section measurements.
74 ATOMIC AND MOLECULAR PHYSICS↗
NJOY Processing of ENDF/B VIII.0 Thermal Scattering Files
“ENDF/B-VIII.0 provides a major update to the ENDF thermal scattering library. Indeed, it is nearly a completely new sub-library. Only the legacy evaluations for Al, Fe, liquid and solid methane, ortho- and para-hydrogen and deuterium and benzene and the ENDF/B-VII.1 evaluations for SiO 2 are unchanged.”
36 MATERIALS SCIENCE↗