Influence of Quantum Oscillations in the Thermal Scattering Law of Zirconium Carbide on Neutron Thermalization and Criticality
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Nuclear Science & Technology↗
Engineering topics
Wormald, J. L.
Publications and source records attributed to Wormald, J. L..
Comparative critical mass calculations for NNL and ENDF/B-VIII.0 - Zirconium hydride thermal neutron scattering laws
Zirconium hydride (ZrH{sub x}) is a moderator material for TRIGA reactors and historical space reactor systems, such as SNAP-10A. Thermal neutron scattering laws (TSL) for two phases of this material, δ and ε, have been previously evaluated by Naval Nuclear Laboratory (NNL) and submitted to the National Nuclear Data Center (NNDC) for inclusion in the US national ENDF/B-VIII.1 nuclear data library. In contrast to the current ENDF/B-VIII.0 TSL evaluations, which consider only a single phase, the new evaluations are derived from separate ab initio calculations for both phases and include coherent elastic effects of the zirconium sublattice. To estimate the impact of these changes to the TSL evaluation of this material, comparative critical mass calculations were performed with MC21 for homogenous mixtures of high-enriched uranium (HEU) and ZrH{sub x} in bare and water reflected sphere configurations. These calculations yield an impact on the estimated critical mass as a function of {sup 235}U loading density with maximum differences as large as 1% - 5% for over-moderated thermal spectrum systems. Consequently, the NNL TSL evaluations are anticipated to have a small impact on criticality calculations of thermal reactor systems regardless of the material phase. Nevertheless, characteristic differences exist in the predicted thermal spectra as function of energy for the two sets of TSL evaluations, which are attributed to difference in the underlying phonon density of states of hydrogen bound in ZrH{sub x}. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Thermal Neutron Scattering Law for Beryllium Hydride and Critical Mass Calculations [Slides]
TSLs for H(BeH 2 ) and Be(BeH 2 ) were evaluated in the incoherent approximation using FLASSH. Minimum critical mass estimates were performed using MC21 continuous energy Monte Carlo calculations with the BeH 2 TSLs. Researchers confirmed very low estimated critical mass for BeH 2 -moderated and Be- reflected spheres. These were the lowest critical masses NNL has studied to date. Future work includes relaxation of the incoherent approximation for Be(BeH 2 ). A small increase in critical mass is expected due to increased neutron transmission at sub-Bragg cutoff energies.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Thermal Neutron Scattering Law for Beryllium Hydride and Critical Mass Calculations
The thermal neutron scattering law (TSL) for crystalline beryllium hydride (BeH 2 ) is developed from first-principles ab initio lattice dynamics calculations and the impact of neutron thermalization in this material on critical mass is estimated. BeH 2 has a body-centered orthorhombic crystal structure with 12 molecules per unit cell and a theoretical density of 0.755 g/cm 3 . The vibrational (phonon) densities of states for H and Be bound in BeH 2 are determined using VASP density functional theory and PHONON lattice dynamics calculations. The TSLs for H bound in BeH 2 , H(BeH 2 ), and Be bound in BeH 2 , Be(BeH 2 ), are then evaluated in the incoherent approximation from the calculated H and Be partial phonon density of states using FLASSH. Finally, critical mass as a function of 235 U loading density for bare and reflected BeH 2 moderated spheres is predicted from MC21 Monte Carlo neutron transport calculations using ENDF/B-VIII.0 cross sections and the H(BeH 2 ) and Be(BeH 2 ) TSL evaluations. Comparisons are made to water (H 2 O), polyethylene (CH 2 ), and beryllium oxide (BeO) as moderators. These critical mass predictions are a refinement upon the prior work by Rao and Srinivasan that neglected thermal neutron scattering effects. The minimum critical mass of a BeH 2 moderated assembly is estimated to be 0.207 kg 235 U for a 0.20 m thick BeO reflected sphere and 0.178 kg 235 U for a 0.40 m thick BeO reflected sphere.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Thermal Neutron Scattering Law Evaluation for Zirconium Carbide and Critical Mass Calculations
Zirconium carbide (ZrC) is a candidate material for use in advanced high temperature reactors, including space nuclear thermal propulsion applications. Thermal neutron scattering laws (TSLs) are generated for carbon bound in ZrC, C(ZrC), and zirconium bound in ZrC, Zr(ZrC), using ab initio lattice dynamics methods. These evaluations are to be submitted for inclusion in ENDF/B-VIII.1 and use the incoherent approximation for inelastic scattering as well as the new mixed elastic scattering treatment. The application of disordered alloy theory is introduced to appropriately capture the isotopic composition of Zr and C in the elastic scattering cross section. Localized higher energy vibrations in the C(ZrC) phonon density of states that are separated from lower energy modes result in quantized oscillations in the inelastic contributions to the TSL with a significant likelihood of large energy down-scattering and up-scattering interactions, where the latter increases in probability with temperature. The quanta of energy transfer during neutron thermalization is substantially greater than classically expected within the thermal neutron energy range. MC21 critical mass calculations of ZrC mixtures with high-enriched uranium demonstrate an impact of the TSLs when compared to free-gas treatment for 235 U concentrations less than 0.2 g/cm 3 . Additional MC21 critical mass calculations with homogenous mixtures of ZrC and reactor-grade graphite also demonstrate sensitivity to the ZrC TSL for thermal spectrum driven fission systems.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Thermal Neutron Scattering Law Evaluations for Zirconium Carbide and Critical Mass Calculations [Slides]
Zirconium Carbide (ZrC) is a refractory material currently being investigated for high temperature reactor applications. ZrC was studied as a base of (U,Zr)C solid solution and UC 2 composite fuels for NERVA-type cores during the Rover program. Testing of the material was performed at Nuclear Furnace 1 (NF-1) located at Los Alamos. Thermal Scattering Law (TSL) evaluations generated with FLASSH are a new contribution to ENDF/B-VIII.1.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Comparative Critical Mass Calculations for NNL and ENDF/B-VIII.0 Zirconium Hydride Thermal Neutron Scattering Laws
Zirconium hydride (ZrH x ) is a moderator material for TRIGA reactors and historical space reactor systems, such as SNAP-10A. Thermal neutron scattering laws (TSL) for two phases of this material, δ and ε, have been previously evaluated by Naval Nuclear Laboratory (NNL) and submitted to the National Nuclear Data Center (NNDC) for inclusion in the US national ENDF/B-VIII.1 nuclear data library. In contrast to the current ENDF/B-VIII.0 TSL evaluations, which consider only a single phase, the new evaluations are derived from separate ab initio calculations for both phases and include coherent elastic effects of the zirconium sublattice. To estimate the impact of these changes to the TSL evaluation of this material, comparative critical mass calculations were performed with MC21 for homogenous mixtures of high- enriched uranium (HEU) and ZrH x in bare and water reflected sphere configurations. These calculations yield an impact on the estimated critical mass as a function of 235 U loading density with maximum differences as large as 1% - 5% for over-moderated thermal spectrum systems. Consequently, the NNL TSL evaluations are anticipated to have a small impact on criticality calculations of thermal reactor systems regardless of the material phase. Nevertheless, characteristic differences exist in the predicted thermal spectra as function of energy for the two sets of TSL evaluations, which are attributed to difference in the underlying phonon density of states of hydrogen bound in ZrH x .
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Comparative Critical Mass Calculations for NNL and ENDF/B-VIII.0 Zirconium Hydride Thermal Scattering Laws [Slides]
Zirconium Hydride (ZrH x ) is a moderator material for TRIGA reactors and SNAP-10A.The thermal scattering has the behavior of quantum oscillator favorable for moderator feedback. ZrH x occurs as a corrosion product in LWR. Previously new phase specific TSL evaluations were generated and submitted to ENDF/B- VIII.1. These include the effects of crystal structure on elastic scattering of Zr(ZrH x ), permit flexibility in stoichiometry for use in reactor physics calculations and fuel characterization, and expand the TSL material sub-library. ENDF/B-VIII.0 ZrH TSLs do not distinguish between material phase. Current work involves preliminary validation & verification testing on the effect of TSLs on critical mass and associated thermal flux.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Update on NNL TSL Validation Efforts [Slides]
A new sub-thermal neutron transmission capability at RPI LINAC has been used to validate Be (metal). NNL transmission measurements validated NCSU Be and Be+Sd TSLs for ENDF/B-VIII.1 and showed improvements WRT ENDF/B-VII.1 and ENDF/B-VIII.0. Amplitude differences highlighted the importance of sample characterization. Additional measurement is in progress for CY2022. PNDA is being developed as an alternative to critical experiment validation.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Update on NNL TSL Validation Efforts [Slides]
This presentation covers how a new sub-thermal neutron transmission capability at RPI LINAC is now in use to help validate TSL evaluations. Additionally, NNL has contributed multiple material evaluations to ENDF/B-VIII.1. Lastly, this presentation covers new methods to improve TSL physics and accuracy are being formulated.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗