Thermal Neutron Scattering Cross Sections Research Articles

Calculation scheme for thermal neutron scattering cross-sections of hydrogenous molecules in liquid and solid phases by molecular dynamics

For systematic analysis of the neutronics properties of various hydrogenous materials that can be candidates for cold moderators, a calculation scheme for thermal neutron scattering cross-sections (TNSCs) of hydrogenous molecules in liquid and solid phases is developed in combination with molecular dynamics simulations. For a feasibility study of the present scheme, TNSCs of liquid and solid mesitylene are calculated, and the neutron spectrum in solid mesitylene is analyzed by using generated thermal scattering law data. Furthermore, by comparing calculated total cross-sections of other 14 hydrogenous molecules with experimental data, a wide usefulness of the present scheme is confirmed.

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

Presented here are the calculated thermal scattering law (TSL) and thermal neutron scattering cross sections for Calcium Hydride, hereafter referred to by its chemical symbol CaH2. The only other such data prior to this evaluation are thermal neutron scattering libraries in the JEFF database, which do not fully capture the scattering physics of the CaH2 system. 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 derive the TSL. The TSL and cross sections have been evaluated for the three non-equivalent atom cites in the CaH2: Ca, H1, and H2. Each evaluation has been submitted to the NNDC for consideration in the next ENDF/B database release.

Thermal scattering law data generation for hydrogen bound in zirconium hydride based on the phonon density of states from first-principles calculations

The thermal neutron scattering cross sections of zirconium hydride (ZrHx) is heavily affected by its lattice structure which can be represented by phonon density of states (DOS). In the past decades, many works tried to get parameterized phonon DOS of ZrHx by fitting certain types of experimental results. In the present work, we adopt the first-principles calculation to obtain the phonon DOS of ZrH1.5 in δ phase and ZrH2 in ε phase. The theoretical phonon DOS is used to calculate the thermal scattering cross sections which are then used in the neutronics simulations of several TRIGA reactors. The numerical results show that the phonon DOS obtained by first-principles calculations can produce more accurate scattering cross sections, and improve the neutronics results of TRIGA reactors compared with the phonon DOS models applied in ENDF/B and JEFF evaluated nuclear data libraries.

THERMAL SCATTERING LAW ENDF LIBRARIES FOR LIQUID FLIBE

Several advanced nuclear reactor concepts have been proposed in the past few years where FLiBe molten salt represents a major constituent of the core. In this case, neutrons produced in fission slow down and moderate in FLiBe (a eutectic with a mixture of 2:1 ratio of LiF and BeF2) until they reach low energies (i.e, below 1 eV). At that stage, the thermalization process becomes dominant and the neutrons achieve a quasi-equilibrium energy state that is dependent on the temperature of the moderator. In neutronic simulations, the description of neutron thermalization is captured using the thermal scattering law (TSL), i.e., S(α,β), of the material in which low energy neutrons are interacting. S(α,β) defines the energy-momentum phase space that is available for an incoming low energy neutron. In addition, it is directly proportional to the double differential thermal neutron scattering cross section. In this work, the TSL of molten salt FLiBe is developed based on a generalized density of excitation states (GDOS) derived from atomic trajectories generated using classical molecular dynamics (MD) simulations that were performed with the LAMMPS code. The MD simulations utilized a Born-Mayer type atomic potential function that was verified to reproduce the properties of FLiBe including density and viscosity. The FLASSH code was used to evaluate the TSL’s ENDF File 7 in a temperature range extending from 773 K to 1673 K. In addition, ACE type cross section libraries are produced and tested with the objective of contributing the data to the National Nuclear Data Center for inclusion in the ENDF/B-VIII database.

Crystal binding effects on neutron scattering and criticality in U–Mo fuels

Using molecular dynamics simulations, we calculate the phonon densities of states of U-10Mo and U-7Mo at different temperatures. The results are then used to calculate the thermal neutron scattering cross sections of both alloys at temperatures that span anticipated reactor operating temperatures and at several 235U enrichment levels. The cross sections are calculated using a modified version of NJOY that is able to calculate coherent elastic cross sections for disordered alloys. The addition of binding effects decreases the cross section by up to a factor of 21 over the free-atom model, resulting in a difference in keff between 3 and 36 pcm for a simple model of a spherical fuel pellet. Based on these results, we conclude that binding effects have a minor impact on criticality, but the qualitative differences between the U–Mo bound-atom and free-atom thermal neutron scattering cross sections may be important in neutron scattering experiments and in the assessment of uncertainties in reactor models and configurations.

Methodology for Generating Covariance Data of Thermal Neutron Scattering Cross Sections

This paper details and implements a framework for evaluating thermal neutron scattering cross sections that provide data and covariance data for hydrogen in light water. This methodology involves perturbing model parameters of molecular dynamics potentials and fitting the simulation results to experimental data. The framework is general and can be applied to any material or simulation method. The fit is made using the Unified Monte Carlo method to experimentally measure double-differential scattering cross sections of light water at the Spallation Neutron Source at Oak Ridge National Laboratory. Mean values and covariance data were generated for model parameters, phonon density of states, double-differential cross sections, and total scattering cross sections. These posterior parameter values were very similar to their prior values with a maximum relative error of 0.54%. This falls within in the Unified Monte Carlo–calculated uncertainties on the order of 2.7%. Additionally, posterior double-differential cross sections agree favorably with ENDF/B-VIII.0 cross sections. The new thermal scattering law was tested by comparing it against benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook, which showed a slight improvement over the ENDF/B-VIII.0 library. Additionally, the covariance matrix of the phonon density of states was validated to confirm that the spread of keff from the density of states used to generate the covariance matrix was similar to the spread of keff from the density of states of the sampled covariance matrix.

Implementation of an adaptive energy grid routine in NDEX for the processing of thermal neutron scattering cross sections

Thermal neutron scattering laws tabulated in File 7 for various materials the ENDF/B database require processing to generate the cross section and distribution data needed for use in Monte Carlo reactor simulations. Typically, the total scattering cross section is calculated on a fixed energy grid and interpolated on this grid. Nevertheless, this method may result in the loss of physical features in the cross section related to the details of the thermal scattering law, especially the oscillatory behavior of solid hydride moderators (e.g., ZrH, YH2). An adaptive energy grid has been implemented in the NDEX nuclear data code, initialized from the tabulated β grid of the processed evaluation. Cross section libraries for Monte Carlo codes generated using this adaptive grid demonstrate greatly improved prediction of oscillations in solid metal hydride moderators when compared to the fixed grid method.

Validation of Thermal Neutron Scattering Cross Sections for Heavy Water based on Molecular Dynamics Simulation

Recently, the thermal scattering libraries of ENDF/B-VIII.0 and JEFF-3.3 for light and heavy water were released with a new water model (CAB model) proposed by Damian. For the CAB model, the molecular dynamics code GROMACS was used to more accurately describe the realistic motions of water molecules. In this paper, to consider the coherent component we also generated the thermal scattering cross section of the deuterium and oxygen bound in the heavy water molecules using the GROMACS code and EPSR code. In addition, the frequency spectrum was also calculated using the GROMACS code. Thermal scattering cross sections based on the newly calculated Sköld correction factor and the frequency spectrum were generated by NJOY2016 code. Finally, the performance of the generated thermal scattering cross sections were validated by performing an ICSBEP benchmark simulation using MCNPX code.

Thermal neutron scattering kernels for uranium mono-nitride: A potential advanced tolerant fuel candidate for light water reactors

The use of uranium mono-nitride (UN) fuel in light water reactors has recently received an increasing interest. Neutronic and thermal-hydraulic performance of UN and associated composite fuels have been studied lately for several types of light water reactors. A comprehensive and detailed analysis of the performance of these reactors using nitride fuels require a complete set of thermal neutron scattering libraries of UN. In this work, the thermal neutron scattering law, the inelastic and coherent elastic scattering cross sections of UN are calculated at different temperatures starting from the phonon density of states obtained from first-principles electronic structure calculations. Excellent agreement between the calculated phonon dispersion relations and the experimental data have been obtained. Due to the huge mass difference between the constituent elements, the calculated nitrogen optic phonon modes are well-separated from those of uranium acoustic phonon modes. The nitrogen scattering law shows a set of well-defined and equally-spaced peaks corresponding to multi-phonon scattering processes, demonstrating that the nitrogen atoms behave as nearly independent three-dimensional quantum harmonic oscillators. The effects of this behavior on the computed inelastic scattering cross sections are thoroughly discussed. As 14N has a large absorption cross section in the thermal energy range and results in a production of 14C, the scattering law and the inelastic scattering cross section of U15N are also calculated. Our calculated scattering cross sections are discussed in comparison with the ENDF/B-VIII.0 thermal neutron scattering cross sections of UN and UO2, and it has been found that U15N fuel can be a viable alternative to the UO2 one.

Thermal neutron scattering cross sections of 238U and 235U in the γ phase

The development of metallic, low-enrichment uranium fuels requires accurate prediction of their neutron transport properties and reactivity parameters, which in turn require thermal neutron scattering data. Accurate prediction of thermal neutron scattering data, including thermal cross sections, requires knowledge of the phonon scattering properties of the medium, but such matrix binding effects in next-generation fuels such as U–Mo, U–Zr, and U–Si are typically neglected because these effects are often difficult to measure or calculate. Using molecular dynamics simulations with previously published interatomic potentials, we calculate the phonon dispersion relations and phonon densities of states for 235U and 238U in the α and γ phases. The performance of these potentials was evaluated using published ab initio simulation data and inelastic neutron scattering data. The phonon densities of states obtained by each potential were then utilized to calculate the thermal neutron scattering cross sections of 235U and 238U at 1113 K using the NJOY program. The resulting thermal neutron scattering cross sections are assessed by comparison to data obtained from available experimental densities of states. The cross sections generated show how the addition of binding effects decreases the cross section by up to a factor of six over the free-atom model. A definite effect on reactivity is also demonstrated by the use of these thermal libraries on a simple core model. As a consequence, the cross sections generated in this work provide a better description of the true cross section than the free-atom data currently available. We also discuss the sensitivity of the thermal scattering cross sections to the phonon density of states.

<em>Ab initio</em> calculation of the thermal neutron scattering cross sections of uranium mononitride

Nuclear design and neutronic analysis of thermal neutron reactor need high reliable thermal neutron cross sections. Uranium mononitride (UN) is a candidate fuel material for advanced power reactor with its better thermodynamics and accident tolerance. However, in thermal neutron region, reliable thermal neutron scattering cross sections are lacked for UN, which is disadvantageous to reactor physics simulations. The scattering law of the UN fuel material may impact the thermal neutron spectrum and criticality of the reactor systems. Neutron cross sections in thermal range are correlated with energy, temperature, physical and chemical properties of the scattering medium, reflecting the phonon spectra of material itself. In this paper, based on the ab initio method of quantum mechanics, phonon density of states in UN are calculated by VASP/PHONON code, and used for integral to obtain UN heat capacity at a constant volume. Adopting this new phonon density of states, NJOY/LEAPR code is used to generate S (, ) data by thermal neutron scattering theory and NJOY/THERMR utilizes these data to produce thermal scattering matrix in order to investigate thermal kernel effect of UN. Subsequently, thermal neutron scattering cross sections of UN are generated with NJOY code system. Comparison with uranium dioxide (UO2) in the traditional PWR is done. Results indicate that optimized lattice parameter are in good agreement with the database; the optical modes are well separated from the acoustic modes compared with UO2; heat capacity at a constant volume is consistent with experimental value; the inelastic and elastic cross sections of 238U in UN are lower than those of 238U in UO2. N in UN only deals with incoherent part in elastic cross sections. As the temperature increases, elastic cross sections of UN decrease while inelastic ones increase, and cross sections approach to free atom cross section at high energies. Considering the limitations of 14N, the scattering law and inelastic scattering cross sections are also under investigation using 15N in UN compound. This paper's conclusion fulfill the vacancy of thermal neutron scattering cross sections of UN, which laid a foundation for systematic study on the neutronics properties of UN fuel in the light water reactors as well as for the design of new neutron moderators and neutron filer.

Application of the CAB evaluation of thermal scattering law for heavy water to ZED-2 critical benchmarks at room temperature

To improve the evaluations in thermal scattering sub-libraries, a set of thermal neutron scattering cross sections (scattering kernels) was developed recently at Centro Atómico Bariloche (CAB) for deuterium and oxygen bound in liquid heavy water, and made available in the ENDF-6 format. These libraries are based on a combination of results of molecular dynamics (MD) simulations and recent experimental data and, when used, result in an improvement of calculations of observables of single neutron scattering experiments, compared to results based on previous evaluations.In this work, we provide additional details on the CAB evaluation of heavy water at room temperature and discuss the important integral characteristics of neutron scattering kernels, such as the cross sections, average scattering cosine, and average secondary energy. Then, the new set of thermal scattering kernels is applied in modelling criticality of the ZED-2 reactor, and the international benchmarks LEU-MET-THERM-003 (ICSBEP handbook) and ZED2-HWR-EXP-001 (IRPhEP handbook) are analyzed in detail. The differences in the estimates of criticality due to changes in the S(α,β) data from the reference one (ENDF/B-VII) to the CAB evaluation are 100–200pcm; they are comparable but smaller than the ZED-2 benchmark uncertainties (≈±300pcm). Changing the reference evaluation of 16O to the recently developed one from the CIELO project (WPEC subgroup 40) results in a decrease of criticality by ∼100pcm. Using different combinations of the improved nuclear data for deuterium, oxygen, and the CAB TSL model, we obtain biases up to 300–400pcm in the estimates of criticality of the selected ZED-2 benchmarks. Application of the new evaluations for 235U and 238U from the CIELO project improves the estimates of keff by decreasing the bias by ∼100pcm that indicates a need for further investigations of the ZED-2 critical assemblies.

Thermal neutron scattering cross section of liquid FLiBe

The molten salt material Li2BeF4 (FLiBe) has been widely proposed as a moderator and coolant material in nuclear applications. Its usage and impact on neutron thermalization in the system requires accurate generation of FLiBe thermal neutron scattering libraries. In this work, liquid FLiBe is modeled using the classical molecular dynamics code LAMMPS. Experimental limits of liquid FLiBe properties are determined from reported databases. Predicted properties of FLiBe from molecular dynamics simulations including density, viscosity, and atomic species diffusivities are computed and compared to experimental data. To initiate the calculation of the thermal neutron scattering law, the velocity autocorrelation functions are calculated from molecular dynamics trajectories and subjected to Fourier transformation to obtain the density of states of possible excitations. Bound modes and diffusive modes of the density of states are separated to calculate the corresponding scattering law Sbound(α,β) and ,Sdiff(α,β) respectively. Thermal neutron scattering cross section libraries of F, Li, Be in FLiBe are generated at temperatures of 873 K, 923 K and 973 K in ENDF/B VII.1 format.

Thermal neutron scattering law calculations using ab initio molecular dynamics

In recent years, methods for the calculation of the thermal scattering law (i.e. S(α,β), where α and β are dimensionless momentum and energy transfer variables, respectively) were developed based on ab initio lattice dynamics (AILD) and/or classical molecular dynamics (CMD). While these methods are now mature and efficient, further advancement in the application of such atomistic techniques is possible using ab initio molecular dynamics (AIMD) methods. In this case, temperature effects are inherently included in the calculation, e.g. phonon density of states (DOS), while using ab initio force fields that eliminate the need for parameterized semi-empirical force fields. In this work, AIMD simulations were performed to predict the phonon spectra as a function of temperature for beryllium and graphite, which are representative nuclear reactor moderator and reflector materials. Subsequently, the calculated phonon spectra were utilized to predict S(α,β) using the LEAPR module of the NJOY code. The AIMD models of beryllium and graphite were 5 × 5 × 5 crystal unit cells (250 atoms and 500 atoms respectively). Electronic structure calculations for the prediction of Hellman-Feynman forces were performed using density functional theory with a GGA exchange correlation functional and corresponding core electron pseudopotentials. AIMD simulations of 1000–10,000 time-steps were performed with the canonical ensemble (NVT thermostat) for several temperatures between 300 K and 900 K. The phonon DOS were calculated as the power spectrum of the AIMD predicted velocity autocorrelation functions. The resulting AIMD phonon DOS and corresponding inelastic thermal neutron scattering cross sections at 300 K, where anharmonic effects are expected to be small, were found to be in reasonable agreement with the results generated using traditional AILD. This illustrated the validity of the AIMD approach. However, since the impact of the temperature on the phonon DOS (e.g. broadening of spectral peaks) was observed in AIMD analysis, this technique may be envisioned as the approach for deriving the needed atomistic data for thermal scattering law calculations under realistic temperature and structural conditions for a given material.

New evaluation of thermal neutron scattering libraries for light and heavy water

In order to improve the design and safety of thermal nuclear reactors and for verification of criticality safety conditions on systems with significant amount of fissile materials and water, it is necessary to perform high-precision neutron transport calculations and estimate uncertainties of the results. These calculations are based on neutron interaction data distributed in evaluated nuclear data libraries. To improve the evaluations of thermal scattering sub-libraries, we developed a set of thermal neutron scattering cross sections (scattering kernels) for hydrogen bound in light water, and deuterium and oxygen bound in heavy water, in the ENDF-6 format from room temperature up to the critical temperatures of molecular liquids. The new evaluations were generated and processable with NJOY99 and also with NJOY-2012 with minor modifications (updates), and with the new version of NJOY-2016. The new TSL libraries are based on molecular dynamics simulations with GROMACS and recent experimental data, and result in an improvement of the calculation of single neutron scattering quantities. In this work, we discuss the importance of taking into account self-diffusion in liquids to accurately describe the neutron scattering at low neutron energies (quasi-elastic peak problem). To improve modeling of heavy water, it is important to take into account temperature-dependent static structure factors and apply Skold approximation to the coherent inelastic components of the scattering matrix. The usage of the new set of scattering matrices and cross-sections improves the calculation of thermal critical systems moderated and/or reflected with light/heavy water obtained from the International Criticality Safety Benchmark Evaluation Project (ICSBEP) handbook. For example, the use of the new thermal scattering library for heavy water, combined with the ROSFOND-2010 evaluation of the cross sections for deuterium, results in an improvement of the C/E ratio in 48 out of 65 international benchmark cases calculated with the Monte Carlo code MCNP5, in comparison with the existing library based on the ENDF/B-VII.0 evaluation.

Thermal neutron scattering cross sections of beryllium and magnesium oxides

Alkaline-earth beryllium and magnesium oxides are fundamental materials in nuclear industry and thermal neutron scattering applications. The calculation of the thermal neutron scattering cross sections requires a detailed knowledge of the lattice dynamics of the scattering medium. The vibrational properties of BeO and MgO are studied using first-principles calculations within the frame work of the density functional perturbation theory. Excellent agreement between the calculated phonon dispersion relations and the experimental data have been obtained. The phonon densities of states are utilized to calculate the scattering laws using the incoherent approximation. For BeO, there are concerns about the accuracy of the phonon density of states used to generate the current ENDF/B-VII.1 libraries. These concerns are identified, and their influences on the scattering law and inelastic scattering cross section are analyzed. For MgO, no up to date thermal neutron scattering cross section ENDF library is available, and our results represent a potential one for use in different applications. Moreover, the BeO and MgO efficiencies as neutron filters at different temperatures are investigated. BeO is found to be a better filter than MgO, especially when cooled down, and cooling MgO below 77K does not significantly improve the filter’s efficiency.

ICONE23-1349 FIRST-PRINCIPLES STUDY ON THERMAL NEUTRON CROSS SECTIONS OF ELECTRON-DOPED LITHIUM HYDRIDE

LiH is designated as a promising moderator and shielding material because of its low density, high melting point and large fraction of H atoms. Previous work was done to produce full and partial phonon spectra of LiH in a primitive cell and then be used to generate thermal neutron scattering cross sections of H in LiH and Li in LiH using the NJOY code system. A re-evaluate work with super cells was done in this paper to modify DFT (Density Function Theory) calculations' error in First Principles. The overall agreement of the lattice constants for pure LiH with the experiments is excellent if the zero-point motion is taken into account. From the theoretical calculation for electron (n)-doped LiH, it is indicated that metallic n-doped LiH was found to be a good superconductor. The phonon spectrum was predicted to be significantly softened, with both Li and H vibrations softened with the introduction of the dopant. Analysis was done in this paper to study thermal neutron scattering cross sections of this electron (n)-doped LiH. A comparison of the generated cross sections shows that accounting for the dopant introduced in the calculations affects the cross sections mainly in some energy range, and the phonon effect mainly occurs at low temperature, which is helpful to study the neutronic properties of LiH, especially for the reactors used LiH moderator.

Improvement on the calculation of D2O moderated critical systems with new thermal neutron scattering libraries

To improve the evaluations in thermal sublibraries, we developed a set of thermal neutron scattering cross sections (scattering kernels) for the deuterium and oxygen bound in heavy water in the ENDF-6 format. These new libraries are based on molecular dynamics simulations and recent experimental data, and result in an improvement of the calculation of single neutron scattering quantities. In this work, we show how the use of this new set of cross sections also improves the calculation of thermal critical systems moderated and/or reflected with heavy water. The use of the new thermal scattering library for heavy water, combined with the ROSFOND-2010 evaluation of the deuterium cross sections, results in an improvement of the C/E ratio in 48 out of 65 benchmark cases calculated with the Monte Carlo code MCNP5, in comparison with the existing library based on the ENDF/B-VII evaluation.

Inelastic Thermal Neutron Scattering Cross Sections for Reactor-grade Graphite

Current calculations of the inelastic thermal neutron scattering cross sections of graphite are based on representing the material using ideal single crystal models. However, the density of reactor-grade graphite is usually in the range of 1.5 g/cm3 to approximately 1.8 g/cm3, while ideal graphite is characterized by a density of nearly 2.25 g/cm3. This difference in density is manifested as a significant fraction of porosity in the structure of reactor-grade graphite. To account for the porosity effect on the cross sections, classical molecular dynamics (MD) techniques were employed to simulate graphite structures with porosity concentrations of 10% and 30%, which are taken to be representative of reactor-grade graphite. The phonon density of states for the porous systems were generated as the power spectrum of the MD velocity autocorrelation functions. The analysis revealed that for porous graphite the phonon density of states exhibit a rise in the lower frequency region that is relevant to neutron thermalization. Using the generated phonon density of states, the inelastic thermal neutron scattering cross sections were calculated using the NJOY code system. While marked discrepancies exist between measurements and calculations based on ideal graphite models, favorable agreement is found between the calculations based on the porous graphite models and measured data.

Modern Techniques for Inelastic Thermal Neutron Scattering Analysis

A predictive approach based on ab initio quantum mechanics and/or classical molecular dynamics simulations has been formulated to calculate the scattering law, S(κ⇀,ω), and the thermal neutron scattering cross sections of materials. In principle, these atomistic methods make it possible to generate the inelastic thermal neutron scattering cross sections of any material and to accurately reflect the physical conditions of the medium (i.e, temperature, pressure, etc.). In addition, the generated cross sections are free from assumptions such as the incoherent approximation of scattering theory and, in the case of solids, crystalline perfection. As a result, new and improved thermal neutron scattering data libraries have been generated for a variety of materials. Among these are materials used for reactor moderators and reflectors such as reactor-grade graphite and beryllium (including the coherent inelastic scattering component), silicon carbide, cold neutron media such as solid methane, and neutron beam filters such as sapphire and bismuth. Consequently, it is anticipated that the above approach will play a major role in providing the nuclear science and engineering community with its needs of thermal neutron scattering data especially when considering new materials where experimental information may be scarce or nonexistent.