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Computational Materials Design for Ceramic Nuclear Waste Forms Using Machine Learning, First-Principles Calculations, and Kinetics Rate Theory

Ceramic waste forms are designed to immobilize radionuclides for permanent disposal in geological repositories. One of the principal criteria for the effective incorporation of waste elements is their compatibility with the host material. In terms of performance under environmental conditions, the resistance of the waste forms to degradation over long periods of time is a critical concern when they are exposed to natural environments. Due to their unique crystallographic features and behavior in nature environment as exemplified by their natural analogues, ceramic waste forms are capable of incorporating problematic nuclear waste elements while showing promising chemical durability in aqueous environments. Recent studies of apatite- and hollandite-structured waste forms demonstrated an approach that can predict the compositions of ceramic waste forms and their long-term dissolution rate by a combination of computational techniques including machine learning, first-principles thermodynamics calculations, and modeling using kinetic rate equations based on critical laboratory experiments. By integrating the predictions of elemental incorporation and degradation kinetics in a holistic framework, the approach could be promising for the design of advanced ceramic waste forms with optimized incorporation capacity and environmental degradation performance. Such an approach could provide a path for accelerated ceramic waste form development and performance prediction for problematic nuclear waste elements.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Influence of nonstatistical properties in nuclear structure on emission of prompt fission neutrons

We report the Hauser-Feshbach fission-fragment decay (HF 3 D) model is extended to calculate the prompt fission neutron spectrum (PFNS) for the thermal-neutron-induced fission on 235 U, where the evaporated neutrons from all possible fission-fragment pairs are aggregated. By studying model parameter sensitivities on the calculated PFNS as well as nonstatistical behavior of low-lying discrete level spin distribution, we conclude that discrepancies between the aggregation calculation and the experimental PFNS seen at higher neutron emission energies can be attributed to both the primary fission-fragment yield distribution and the possible high spin states that are not predicted by the statistical theory of nuclear structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The Extension of the Hauser-Feshbach Fission Fragment Decay Model to Multi-chance Fission and its Application to 239 Pu

The Hauser-Feshbach fission fragment decay model, HF3D, calculates the statistical decay of fission fragments through both prompt and delayed neutron and γ-ray emissions in a deterministic manner. While previously limited to the calculation of only first-chance fission, the model has recently been extended to include multi-chance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input prescission quantities–fission probabilities, pre-fission neutron energies, and the average energy causing fission– and post-scission quantities–yields in mass, charge, total kinetic energy, spin, and parity. From those fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions. The evaporation of the prompt neutrons and γ rays is calculated through the Hauser-Feshbach statistical theory, taking into account the competition between neutron and γ-ray emission, conserving energy, spin, and parity. The delayed emission is taken into account using time-independent calculation using decay data. This whole formulation allows for the calculation of prompt neutron and γ-ray properties, such as multiplicities and energy distributions, both independent and cumulative fission yields, and delayed neutron observables, in a consistent framework. Here, we describe the implementation of multi-chance fission into the HF 3 D model, and show an example of prompt and delayed quantities beyond first-chance fission, using the example of neutron-induced fission on 239 Pu. This expansion represents significant progress in consistently modeling the emission of prompt and delayed particles from fissile systems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Efficient method for estimation of fission fragment yields of $\textit{r}$-process nuclei

Background: More than half of all the elements heavier than iron are made by the rapid neutron capture process (or $\textit{r}$ process). For very-neutron-rich astrophysical conditions, such at those found in the tidal ejecta of neutron stars, nuclear fission determines the $\textit{r}$-process endpoint, and the fission-fragment yields shape the final abundances of 110 ≤ $\textit{A}$ ≤ 170 nuclei. The knowledge of fission-fragment yields of hundreds of nuclei inhabiting very-neutron-rich regions of the nuclear landscape is thus crucial for the modeling of heavy-element nucleosynthesis. Purpose: In this study, we propose a model for the fast calculation of fission-fragment yields based on the concept of shell-stabilized prefragments defined with help of the nucleonic localization functions. Methods: To generate realistic potential-energy surfaces and nucleonic localizations, we apply Skyrme density-functional theory. In this work, the distribution of the neck nucleons among the two prefragments is obtained by means of a statistical model. Results: We benchmark the method by studying the fission yields of 178 Pt, 240 Pu, 254 Cf, and 254,256,258 Fm and show that it satisfactorily explains the experimental data. We then make predictions for 254 Pu and 290 Fm as two representative cases of fissioning nuclei that are expected to significantly contribute during the $\textit{r}$-process nucleosynthesis occurring in neutron-star mergers. Conclusions: The proposed framework provides an efficient alternative to microscopic approaches based on the evolution of the system in a space of collective coordinates all the way to scission. It can be used to carry out global calculations of fission-fragment distributions across the $\textit{r}$-process region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Energy Dependent Fission Product Yields (2nd year Milestone and Deliverables)

Introduction to the project: One of the Laboratory missions is to provide consistent, high-precision fission product; yield data critical for testing fission models and maintaining the safety and security of the nation’s nuclear weapons stockpile. However, high-quality, energy-differential fission product yield data is missing for certain actinides and neutron energies important to constrain the new U.S. Nuclear Data Program evaluation effort; It has been shown that the reactor antineutrino anomaly may be at least partially caused by roughly 20 fission products. The fission product yield data is missing or incomplete for many of these isotopes, thus it is necessary to accurately determine these values to better constrain the anomaly; Aitor Bracho is measuring very short-lived (seconds to minutes) fission product yields of 235 U and 239 Pu using monoenergetic neutron beams at E n = 60 and 560 keV; Aitor Bracho is using a direct approach utilizing a state-of-the-art rabbit transfer system, superior HPGe detector, and digital acquisition systems for fission decay measurements. The goals of this project: lop experimental capabilities and data analysis techniques to carry out the gamma-ray spectra analysis necessary for fission product yield calculation; Provide high-precision and energy-dependent fission product data supporting fission theory, neutrino physics, and applied physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Statistical Tests for Diagnosing Fission Source Convergence and Undersampling in Monte Carlo Criticality Calculations [Slides]

There is a very strong need for statistical testing to determine fission source convergence in Monte Carlo criticality calculations. Automation of such tests will greatly streamline and support the work carried out by NCS practitioners. Recent R&D work has shown that no single statistical test for convergence is sufficiently reliable, robust, and “guaranteed.” However, a combination of several standard statistical tests for the similarity of distributions, coupled with a high-fidelity estimate of the fission-matrix source is sufficiently robust, reliable, and repeatable that convergence can be “guaranteed.” During the course of the EG-AMCT studies, a number of statistical metrics and tests were proposed for diagnosing clustering and undersampling. None of these was robust and reliable enough for practical use in production codes. However, the expert group efforts came close. Some recent R&D work stemming from those past efforts has been very successful and promising. This Sub-Group will provide international input and collaboration on the development and implementation of statistical tests for convergence, with the primary goal of having the MC codes automatically detect convergence (or lack thereof). Newly proposed statistical tests to detect undersampling (after convergence) will also be reviewed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Isomeric Yield Ratios of fission products: a missing piece in reactor antineutrino summation calculations

The calculation of the spectrum of antineutrinos ( $\overline{V}$ e ) from a reactor is a complicated problem requiring several nuclear data and physics inputs. Many of these have been investigated thoroughly to improve calculations and properly account for uncertainties. One input which has heretofore escaped consideration is the fission yield distribution between ground and isomeric states. In this work, we explore the effect of incorporating newly evaluated isomeric yield ratios (IYR) for 43 fission products into summation calculations and identify the disproportionate importance of certain isotopes, particularly at higher energies. Our analysis indicates that updated IYRs contribute to a significant increase in the $\overline{V}$ e spectrum around and above 7 MeV, with increases of more than 50% at higher energies. Through a detailed sensitivity study, we highlight a number of isotopes for which the IYR has a substantial effect on the $\overline{V}$ e spectrum. This work stresses the critical role of isomeric yields in calculations of reactor $\overline{V}$ e spectra and points to the necessity for their accurate experimental determination, especially for key fission products, in order to refine our understanding and address the observed anomalies between measured and calculated $\overline{V}$ e spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Isomeric yield ratios of fission products: A missing piece in reactor antineutrino summation calculations

The calculation of the spectrum of antineutrinos ($\bar{v}_e$) from a reactor is a complicated problem requiring several nuclear data and physics inputs. Many of these have been investigated thoroughly to improve calculations and properly account for uncertainties. One input which has heretofore escaped consideration is the fission-yield distribution between ground and isomeric states. Here, in this work, we explore the effect of incorporating newly evaluated isomeric yield ratios (IYR) for 43 fission products into summation calculations and identify the disproportionate importance of certain isotopes, particularly at higher energies. Our analysis indicates that updated IYRs contribute to a significant increase in the $\bar{v}_e$ spectrum around and above 7 MeV, with increases of more than 50% at higher energies. Through a detailed sensitivity study, we highlight a number of isotopes for which the IYR has a substantial effect on the $\bar{v}_e$ spectrum. This work stresses the critical role of isomeric yields in calculations of reactor $\bar{v}_e$ spectra and points to the necessity for their accurate experimental determination, especially for key fission products, in order to refine our understanding and address the observed anomalies between measured and calculated $\bar{v}_e$ spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Electronic couplings for singlet fission: Orbital choice and extrapolation to the complete basis set limit

Abstract For the search for promising singlet fission candidates, the calculation of the effective electronic coupling, which is required to estimate the singlet fission rate between the initially excited state (S 0 S 1 ) and the multiexcitonic state ( 1 TT, two triplets on neighboring molecules, coupled into a singlet), should be sufficiently reliable and fast enough to explore the configuration space. We propose here to modify the calculation of the effective electronic coupling using a nonorthogonal configuration interaction approach by: (a) using only one set of orbitals, optimized for the triplet state of the molecules, to describe all molecular electronic states, and (b) only taking the leading configurations into consideration. Furthermore, we also studied the basis set convergence of the electronic coupling, and we found, by comparison to the complete basis set limit obtained using the cc‐pV n Z series of basis sets, that both the aug‐cc‐pVDZ and 6–311++G** basis sets are a good compromise between accuracy and computational feasibility. The proposed approach enables future work on larger clusters of molecules than dimers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Solving the one-dimensional penetration problem for the fission channel in the statistical Hauser-Feshbach theory

Here we solve the Schrödinger equation for an arbitrary one-dimensional potential energy to calculate the transmission coefficient in the fission channel of compound nucleus reactions. We incorporate the calculated transmission coefficients into the statistical Hauser-Feshbach model calculation for neutron-induced reactions on 235,238 U and 239 Pu. The one-dimensional model reproduces the evaluated fission cross section data reasonably well considering the limited number of model parameters involved. A resonance-like structure appears in the transmission coefficient for a double-humped fission barrier shape that includes an intermediate well, which is understood to be a quantum mechanical effect in the fission channel. The calculated fission cross sections for the neutron-induced reactions on 235,238 U and 239 Pu all exhibit a similar structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Comparison of Fission Product Release Predictions using PARFUME with Results from the AGR-2 Irradiation Experiment

The PARFUME (PARticle FUel ModEl) code was used to predict fission product release from tristructural isotropic (TRISO) coated fuel particles and compacts during the second irradiation experiment (AGR-2) of the Advanced Gas Reactor Fuel Development and Qualification Program. The PARFUME model for the Advanced Gas reactor (AGR)GR-2 experiment used the fuel compact volume average temperature for each of the 560 days of irradiation to calculate the release of fission products of silver, cesium, and strontium from a representative particle for a select number of AGR -2 compacts. In addition, safety tests were performed on 15 compacts ranging from 1500 to 1800°C to determine fission product release at temperatures that bound reactor accident conditions. PARFUME was used to calculate the fission product release of silver, cesium, strontium, and krypton during these safety tests. Post-irradiation examination (PIE) measurements provided the data on release of fission products from the fuel compacts and fuel particles, and retention of fission products in the compacts outside the silicon carbide (SiC) layer. The predicted fraction release from PARFUME was then compared to PIE measurements.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Measurements of Irradiated Low Enriched Fuel with a Gamma-Ray Scanning System (ANIMMA 2023 Conference Presentation)

A gamma-ray scanning system was designed to perform post-irradiation measurements of nuclear fuel at Idaho National Laboratory (INL). The system is composed of a coaxial high-purity germanium (HPGe) detector, a collimator, and mechanical positioning stages that translate the fuel sample across the front of the collimator. A Monte Carlo N-Particle code simulation of the system and the fuel were created with vendor-supplied design specifications, dimensional measurements, and x-ray radiographs of the HPGe detector as well as all available fuel specifications. Benchmark measurements were performed by scanning an irradiated fuel rodlet containing eight pellets of 0.74% enriched UO2 in zirconium alloy. This fuel rodlet was part of the Environment Rodlet Transient Test Apparatus (SERTTA) testing campaign in the Transient Reactor Test Facility (TREAT). These results were compared to simulated spectra to help characterize the detector model and establish fidelity. One goal of the system is to determine the number of fissions per gram of UO2 in the fuel. This article documents the modeling, benchmarking measurements, and the calculated number of fissions per gram in the SERTTA-A rodlet which was previously irradiated at TREAT.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Fragment Intrinsic Spins and Fragments’ Relative Orbital Angular Momentum in Nuclear Fission

In this work, we present the first fully unrestricted microscopic calculations of the primary fission fragment intrinsic spins and of the fission fragments’ relative orbital angular momentum for 236 U*, 240 Pu*, and 252 Cf using the time-dependent density functional theory framework. Within this microscopic approach, free of restrictions and unchecked assumptions and which incorporates the relevant physical observables for describing fission, we evaluate the triple distribution of the fission fragment intrinsic spins and of their fission fragments’ relative orbital angular momentum and show that their dynamics is dominated by their bending collective modes in contradistinction to the predictions of the existing phenomenological models and some interpretations of experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Diffusion of alloying and fission atoms in α-U investigated by first-principles calculation

Stability and diffusion of small defect clusters containing alloying or fission atoms (“F” is used to represent both atoms) in an α-uranium (U) crystal are investigated using first-principles calculations. Here, results indicate that different stable defect structures are observed for an interstitial defect and a cluster (F n V m ) containing different alloying or fission atoms and vacancies. An interstitial defect is found to be most stable either at the center of a pyramid pentahedron or in a 〈010〉 mixed dumbbell configuration and the latter one is reported for the first time. Formation energy of a small F n V m cluster depends on the distribution of vacancies. Based on these stable defects, new migration energies and paths have been explored in this work. Anisotropic migration of an interstitial defect by jumping between nearest centers of two pyramid pentahedrons or jumping between two mixed U-Zr dumbbells has been suggested. Furthermore, a new migration-rotation mechanism has been explored for the first time for a FV 2 cluster, resulting in a 3D diffusion. Finally, the effect of substitutional Pu atoms on the migration of a FV 2 cluster suggests that optimizing the Pu concentration may prohibit the diffusion of some alloying or fission atoms, increasing the safe performance of metallic fuels.

3D diffusion↗

Thermal Model for Horizontal In-Water and In-Air Mini-Plate Experiments in the Advanced Test Reactor

Mini-Plate (MP) irradiation tests are a fueled experiment designed for irradiation in multiple test locations in the Advanced Test Reactor (ATR) at the Idaho National Laboratory (INL). MP experiments are considered a non-instrumented drop-in test where small aluminum-clad fuel plate samples are cooled directly by the ATR Primary Coolant System (PCS) water. These fueled experiments contain aluminum-clad fuel mini plates consisting of monolithic U-10Mo. Previous thermal analyses have been documented concerning oxide growth[1] and thermal safety margin[2] for the MP-2 experiment. A thermal analysis has been performed on the MP-2 experiment using a new technique for calculating the necessary time after the experiment has been irradiated and reactor shutdown necessary to not exceed the 95% lower bound blister threshold temperature for the fuel in a horizontal in air configuration. A horizontal in water model has also been analyzed and will be discussed. After the experiment is irradiated in the ATR, it is necessary to calculate the fuel meat temperatures at 12 hours after shutdown. This is done to assure that at the 12 hour mark, if this experiment is removed from the reactor and accidentally dropped onto the working tray and is in the most severe geometrical configuration of horizontal (minimum heat transfer) that fission products will not be released. The blister threshold temperature is considered this safety limit. The horizontal in air analysis is also performed considering that the experiment is horizontal in a drained canal and filled with air and natural convection heat transfer with air on the outside. The initial mini-plate testing campaign known as MP-1 [3] has been irradiated and its purpose was to form the base fuel specimens fabricated by various processes so that a single process can be down-selected for qualification. MP-2 will then serve to populate a comprehensive fuel performance data set for the down-selected fabrication process. The MP-2 experiment will be irradiated in several locations of the ATR as shown in Figure 1. The fuel plate thickness and geometry is identical to the MP-1 experiment [3], with the only variable being the fuel meat thickness. This model of the B-12 position is treated as encompassing the I-21, I-24, and B-9 positions since it has more fuel and higher total heat than the other positions. Since the blister threshold temperature is a function of fission density, a series of fission densities is calculated for the B-12 position to cover the other three positions. The B 12 position specifically uses fuel meat that is 0.016 in thick by 3.25 in long and 0.75 in tall. The total plate thickness is 0.050 in. Aluminum cladding forms the barrier between the PCS and the fuel meat. The purpose of this paper is to demonstrate this new technique developed to calculate the necessary decay time after shutdown for a series of fission densities using the ABAQUS [4] finite element and heat transfer code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Specifications of FIPD Fission Gas Release Data

All fission gas release data stored in the Fuels Irradiation & Physics Database (FIPD) was originally measured using the Gas Assay, Sample and Recharge (GASR) System in the Hot Fuel Examination Facility (HFEF). It is therefore called GASR data in FIPD. During the measurement of a sample, such as an irradiated EBR-II fuel element/capsule, a pinhole-sized region near the top of the element plenum was melted by a laser. Plenum gas then expanded into a calibrated volume (note: in this document, “sample” and “capsule/element” are used interchangeably consistent with GASR documents in FIPD). The pressure rise in the volume was recorded. Helium backfilling and expansion was then performed to determine the sample (e.g., fuel element plenum) volume using Boyle’s Law and assuming ideal gas behavior at constant temperature. With the plenum volume and the recorded pressure rise, the sample (e.g., fuel element plenum) pressure was derived with assumption of ideal gas law behavior. The plenum volume and pressure as well as the cladding temperature during the measurement were collected (GASR data in FIPD). Other records associated with the fission gas release data include: raw GASR data records including volumes and post-puncture pressures of seal head/sealing head and manifold, calibration data, backfilling gas pressure data, and the data analysis records. A sample(s) of the fission gas released from the plenum was collected by the GASR system into sample bottles. The chemical and isotopic composition of the gas sample was analyzed separately from GASR data, and will be discussed in a separate specification. The plenum volume, pressure, and cladding temperature during the measurement are typically utilized to determine the number of moles of gas in the plenum. This quantity is often compared to the number of moles of gas generated by fission events. However, calculating these values and their associated uncertainty is beyond the scope of this document, as it necessitates additional assumptions. The most important document to understand the FIPD fission gas data is the GASR operational manual (title: Gas Assay, Sample and Recharge System (GASR) operation and maintenance manual, HFEF/N OMM 4381, DOC. NO. W0018-0032-ES-00). This manual provides: (1) description of the GASR and the functions of each component (laser drilling, welding, seal head/sealing head, manifold, vacuum system, sample system, purge and gas tag system, etc.); (2) step-by-step guidance on calibrations, operations, and measurements; and (3) maintenance procedures and other details relating to the structure and operation of the GASR. Note that the original GASR operated until 2020. A new GASR with the same design and measurement methodology was installed in 2021. The specifications of the GASR presented on the HFEF website at this time are consistent with the ones given in the operational manual. The methods to calculate the plenum volume and pressures were not included in the operational manual, but were recorded in the legacy data analysis files. Details of the methods are given in Chapter 3.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Quantum entanglement in nuclear fission

Nuclear fission presents a unique example of quantum entanglement in strongly interacting many-body systems. A heavy nucleus can split into hundreds of combinations of two complementary fragments in the fission process. The entanglement of fragment wave functions is persistent even after separation and impacts the partition of particles and energies between fragments. Based on microscopic dynamical calculations of the fission of 240 Pu, this work finds that dynamical quantum entanglement is indispensable in the appearance of sawtooth distributions of average excitation energies of fragments and thus neutron multiplicities, but not in average neutron excess of fragments. Both sawtooth slopes from particle-number projections are found to be steep – a feature which can be alleviated by random fluctuations. The persistent entanglement is mainly due to non-adiabatic dynamics since the final splitting is so fast that the non-localization of wave functions is kept during the separation. These findings may impact the understanding of quantum entanglement more broadly in mesoscopic systems

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗