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↗
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↗
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 for ice based on neutron time-of-flight experiments carried out at the SEQUOIA spectrometer at the Oak Ridge National Laboratory
Precise estimation of neutron thermalization in moderators relies on high-fidelity thermal scattering cross-section data governed by the thermal scattering law (TSL). The Institut de Radioprotection et de Sûreté Nucléaire (IRSN) has been working on the development of improved TSL for light water ice. Many polymorphic phases of light water ice exist depending on the thermodynamic conditions. The most common type of ice at standard pressure and temperature below water freezing point (273.15 K) is ice-Ih. It is essential to have high-resolution experimental double differential data for developing and/or validating TSL for moderator materials.Existing experimental double-differential scattering data for ice-Ih are extremely sparse and of limited quality. New high-quality double-differential measurements for ice-Ih over multiple temperatures and incident neutron energies would directly support the validation and improvement of ice-Ih TSL models for criticality safety applications.Series of time-of-flight (TOF) inelastic neutron scattering experiments on ice-Ih at temperatures starting at 271 K and down to 6 K, have been carried out at the SEQUOIA spectrometer at the Spallation Neutron Source (SNS) at the Oak Ridge National Laboratory (ORNL), United States. The experiments have been performed for incident neutron energies, Ei= 11, 55, 160, 250, and 600 meV, to explore different excitation energies in the vibrational phonon spectrum. This paper presents the thermodynamic conditions and the details of the TOF measurements on ice-Ih and the derived phonon spectrum from the experimentally measured double differential data. A study of the variation of the phonon spectrum of ice-Ih as a function of temperature is highlighted, and a preliminary TSL evaluation is developed based on the experimental phonon spectrum.
Jaiswal, V↗
Validation of Thermal Scattering Laws for Light Water at Elevated Temperatures with Diffusion Experiments
Light water is the most important neutron moderator in many reactor applications. Thermal neutron scattering kernels for H bound in H 2 O are represented by ENDF-format thermal scattering laws (TSLs) evaluated at discrete temperatures T . Nuclear data evaluations are conventionally validated utilizing a combination of critical benchmarks and experimental cross section data. Existing public critical benchmarks may be inadequate for testing water TSLs over the full range of T of interest in reactor applications, and experimental thermal scattering cross section data for water is sparse at elevated T . In this work, MC21 is used to simulate the decay of the equilibrium thermal neutron flux in light-water spheres of several radii. The fundamental-mode time eigenvalue $\mathcal{a}$ is calculated at 22 °C and 227 °C (at saturation pressure) for each sphere using three different H-H 2 O TSLs. Fitting $\mathcal{a}$ to a polynomial function of geometric buckling allows calculation of the thermal neutron diffusion length L . Extrapolation lengths are treated as a function of the transport mean free path and geometry. Experimental L data from 25 publications at 49 temperatures (from 10 °C to 295 °C), computed by several different time-dependent and space-dependent decay methods, is used to develop an empirical fit of L vs. T . The MC21-calculated L for the TSLs tested are within ±1% of the predicted values at 22 °C and 227 °C. This validation approach, which may be repeated at arbitrary T , constitutes an integral benchmark specific to and characterizing the detailed physics of the thermal scattering kernel applied.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Thermal scattering law for structure-dependent-Doppler broadening in FLASSH
Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
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↗
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)↗
Uranium Carbide and Uranium-Metal Thermal Scattering Law Evaluations and Cross Sections [Slides]
New Uranium Carbide and Uranium Metal evaluations have been developed using the FLASSH platform. Ab initio LD/MD models converged electronic, magnetic, and dynamical properties and demonstrate good agreement with experimental data. Thermal scattering cross sections generate inelastic and elastic thermal neutron scattering libraries in FLASSH . New TSL evaluations occurred in the production of ENDF File 7 data for Uranium Carbide and Uranium Metal submitted to NNDC for ENDF/B-VIII.1 release.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗