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At least 19 records

Characterizing the solid hydrolysis product, UF 4 (H 2 O) 2.5 , generated from neat water reactions with UF 4 at room temperature

Uranium tetrafluoride (UF 4 ) is an important intermediate in the production of UF 6 and uranium metal. Room temperature hydrolysis of UF 4 was investigated using a combination of Fluorine-19 nuclear magnetic resonance spectroscopy ( 19 F NMR), Raman and infrared spectroscopy, powder X-ray diffraction, and microscopy measurements. UF 4 (H 2 O) 2.5 was identified as the primary solid hydrolysis product when anhydrous UF 4 was stirred in deionized water. Static NMR and 19 F magic angle spinning NMR measurements revealed that a small amount of uranyl fluoride can also form when anhydrous UF 4 is left in water, although this species comprises less than 5% of the total sample with the remaining parts being UF 4 (H 2 O) 2.5 . Since UF 4 is generally considered to be stable under ambient conditions, these findings mark the first time that a room temperature reaction between UF 4 and water has been detected and analyzed without interference from additional chemical reagents. The Raman characterization of UF 4 (H 2 O) 2.5 presented herein is the first on record. Since UF 4 is one of the most used intermediates during chemical conversion of uranium ore to uranium metal for nuclear fuel and weapons, the results presented herein are applicable to numerous nuclear science fields where solid state detection of uranium is of value, including nuclear nonproliferation, nuclear forensics, and environmental remediation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sensitivity of the simulation of passive neutron emission from UF 6 cylinders to the uncertainties in both 19 F(α,n) energy spectrum and thick target yield of 234 U in UF 6

Interest in safeguards verification measurements using passive thermal neutron counting to assay 235 U content in large 30B UF 6 canisters has grown in recent years. Here, the prohibitively high cost and impracticality of using reference 30B calibration cylinders extensively will likely make accurate simulations of increasing interest. Accuracy of the simulated response will define the confidence in the predicted response and the extent to which simulations can reasonably be relied upon. With 234 U driven 19 F(α, n) reactions being the main neutron source in low enriched UF 6 the uncertainties of the 19 F(α, n) energy spectrum and the thick target yield of 234 U in UF 6 propagate into the uncertainty in the predicted response and represent a major influence of basic nuclear data. Here sensitivity of the simulated total (Singles) and coincidence (Doubles) count rates are assessed for the Passive Neutron Enrichment Meter using six potential 19 F(α, n) neutron energy spectra over a range of enrichments and material distributions. The results indicate that variations in the Singles and Doubles due to simulated (α, n) neutron spectrum are less than 1.5% for this set of simulated neutron spectra, with dependence varying inversely with enrichment. Singles uncertainty is only slightly less than that of the thick target 19 F(α, n) yield corresponding to the primary neutron source, whereas the 19 F(α, n) yield dependence of the Doubles is reduced by the non-negligible 238 U(SF) coincident neutron emissions. Based on available thick target 19 F(α, n) yield estimates the uncertainty is on the order of 5%, establishing this as the main nuclear data limitation when simulating thermal neutron detectors response for 30B UF 6 storage cylinders. Based on these findings, it appears that the measurement and evaluation of the thick target 19 F(α, n) yield for uranium hexafluoride is due.

19F(α,n) neutron spectrum↗

Credible Criticality Safety Margin in the 30B Package with LEU+ UF 6 and Hypothetical Water Ingress

The commercial nuclear industry is pursuing advancements in fuel and reactor design that increase the uranium enrichment above 5 wt. % 235 U. These advancements will necessitate the ability to transport bulk quantities of UF 6 at increased enrichments. Currently, the 30B cylinder is the primary container used by the industry for UF 6 storage and transportation and has a long history of successful shipments. This container can support up to 2,277 kg of UF 6 at a maximum enrichment of 5 wt. % 235 U. Previous evaluations have assessed the potential impact of criticality safety for 30B transport at higher enrichments but assumed moderator intrusion would not require evaluation. Although current regulations allow for the exception of moderator intrusion for UF 6 packages through the design and quality control of the package content, this exception is limited to enrichments up to 5 wt. % 235 U. Thus, an investigation of moderator intrusion into a 30B cylinder should be performed. Moderator intrusion into a 30B cylinder is a unique condition for criticality safety evaluation in transportation because of the violent chemical reactions that occur between UF 6 and H 2 O. The resulting intrusion is strongly dependent on the breach size, breach location, breach interface solid/ullage of the UF 6 content, the UF 6 distribution (which is temperature dependent), and temperature/pressure conditions which are dynamic in accident conditions. Additionally, the complexity of the HF-UO 2 F 2 -H 2 O interface that occurs during the event can influence the potential solubility of uranium in the system, as well as influence the amount of UF 6 reaction with H 2 O. With the operating experience from Orano Federal Services LLC, the UF 6 chemical expertise from Oak Ridge National Laboratory (ORNL), and the criticality safety expertise from ORNL, this paper evaluates the neutronic conditions (i.e., k eff ) that apply the understood chemistry and experimental conditions that occur during moderator intrusion of a breached 30B cylinder under postulated accidents. This report examines the historical evaluations of UF 6 transport and expands these evaluations for the enrichments expected for nuclear industry advancement. These simulations primarily feature a homogeneous mixture of UF 6 and H 2 O as an infinite media system and as a sphere with water reflection given an impurity limit of 0.5 wt. % UF 6 . This report demonstrates that this H/U limit is valid up to 8 wt. % enrichment for both H 2 O and HF as the moderating mixture. The water-reflected homogeneous mixed spheres evaluated demonstrate the amount of safety margin applied by restricting the 30B cylinder impurity limit to 0.5 wt. %. Additionally, this report evaluates moderator ingress scenarios of a 30B cylinder. The 30B cylinder simulations vary the cylinder orientation, the mass of UF 6 in the system, the mass of H 2 O in the system, and how much H 2 O has reacted with UF 6 . The moderator ingress of a 30B cylinder was evaluated for the water-reflected homogeneous mixed spheres to demonstrate the amount of safety margin applied by restricting the 30B cylinder impurity limit to 0.5 wt. %. These simulations are standard practice and are independent of the UF 6 -H 2 O reaction. This work also explored more complex simulations that layer the H 2 O over the UF 6 , which incorporates the amount of reacted UF 6 as a separate layer and considers solubility limits of UO 2 F 2 in H 2 O as it is produced. This approach is intended to simulate the postulated event of a large hairline crack occurring on a submerged cylinder. Finally, this work considers the potential of H 2 O mixing into the UF 6 solid heterogeneously using a sponge-like model. The water ingress into the UF 6 is treated as random size spheres, and the reaction products form into a layer over the spheres.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Structural Characterization of Uranium Tetrafluoride Hydrate (UF 4 ·2.5H 2 O)

Uranium tetrafluoride is an important intermediate in the nuclear fuel cycle. Facile synthesis of its hydrate, uranium tetrafluoride hydrate (UF 4 ·2.5H 2 O), has recently been reported. The hydrate forms by contacting anhydrous UF 4 with neat H 2 O at room temperature for 24 h or by exposing anhydrous UF 4 to high relative humidity (>90%) conditions for several weeks. These pathways are of clear environmental relevance. Further understanding of the structure and optical spectra of UF 4 ·2.5H 2 O, especially of the water molecules, is therefore necessary. Herein, the structure of UF 4 ·2.5H 2 O was probed using time-of-flight neutron powder diffraction to improve understanding of the crystalline water environments in the structure. The complete structure was elucidated and compared to a previously reported partial structure for UF 4 ·2.5H 2 O and a predicted complete structure from density functional theory. The crystalline structure exhibits three distinct water environments: two of the three water sites are bound to uranium, and the third water is unbound or “free”. Furthermore, the completed structure reveals an extensive hydrogen bonding network involving water–fluorine and water–water interactions. One bound water site participates in hydrogen bonding with nearby fluoride ligands (O–H···F–U), and the second bound water site participates in hydrogen bonding with the unbound water (O–H···O) and a nearby fluoride ligand (O–H···F–U); the unbound water participates in hydrogen bonding with bound water (O–H···O–U). Low-temperature experiments and thermal analysis indicate UF 4 ·2.5H 2 O is thermally stable from 10 to 358 K, undergoes dehydration at higher temperatures, and is nearly dehydrated at 473 K. Structural measurements provide foundational understanding and will inform future investigations of the thermal and environmental stability of UF 4 ·2.5H 2 O.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Probing the hydrolytic degradation of UF 4 in humid air

This manuscript describes the chemical transformations that occur during hydrolysis of uranium tetrafluoride (UF 4 ) due to its storage in humid air (85% and 50% relative humidity) at ambient temperatures. This hydrolysis was previously reported to proceed slowly or not at all (depending on the percent relative humidity); however, previous reports relied primarily on X-ray diffraction methods to probe uranium speciation. Here, we employ a battery of physiochemical probing techniques to explore potential hydrolysis, including Raman spectroscopy, powder X-ray diffraction, 19 F nuclear magnetic resonance spectroscopy, scanning electron microscopy, and focused ion beam microscopy with energy-dispersive X-ray spectroscopy. Of these, only Raman spectroscopy proved to be particularly useful at observing chemical changes to UF 4 . It was found that anhydrous UF 4 slightly oxidizes over the course of thirteen days to Schoepite-like uranium complexes and possibly UO 3 . In contrast, UF 4 exposed to 50% relative humidity slightly decomposes into UO 2 F 2 , Schoepite-like uranium complexes, and possibly a high order uranium oxide that eluded chemical assignment (U x O y ). Despite the rich chemical speciation observed in our Raman spectroscopy measurements, X-ray diffraction and 19 F NMR measurements on the same material showed no changes. Microscopy measurements suggest that the observed reactions between UF 4 and water occur primarily on the surface of UF 4 particulates via a method that is visually similar to surface corrosion of metals. Therefore, we postulate that NMR spectroscopy and X-ray diffraction, which are well-suited for bulk analysis, are less suited than Raman spectroscopy to observe the surface-based reactions that occur to UF 4 when exposed to humid air. Considering the importance of UF 4 in the production of nuclear fuel and weapons, the results presented herein are widely applicable to numerous nuclear science fields where uranium detection and speciation in humid environments is of value, including nuclear nonproliferation and nuclear forensics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Radiation hot spot formation on UF 6 30B cylinders

The accurate material accountancy of a country's enriched uranium hexafluoride (UF 6 ) stockpiles is imperative to the International Atomic Energy Agency (IAEA) for determining appropriate material safeguards. Uranium hexafluoride is typically stored in large cylinders with enrichment verification typically performed with a NaI gamma detector using the enrichment meter method. This approach for calculating enrichment assumes that the UF 6 is homogeneous inside the cylinder. Here, the measurements and tests presented in this manuscript show that the UF 6 in cylinders left outside in the elements can experience fractionation, leading to inhomogeneity, and subsequent development of radiation hot spots. These hot spot locations can produce errant enrichment measurements. In dark-colored cylinders that experience significant surface heating from the sun, UF 6 sublimates off the cylinder walls, leaving only the uranium daughter products in a horizontal patch (stripe) along the cylinder's midline. This daughter patch is hypothesized to be the source of the radiation hot spots. The patch forms during the summer and tends to decay away during the winter, when solar intensity and temperatures are reduced.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Anion Photoelectron Spectroscopy and Ab Initio Studies of the UF – Anion

A synergistic anion photoelectron spectroscopic and ab initio computational study of photodetachment of UF – is reported. The measurement determined a vertical detachment energy of 0.63(03) eV, which is consistent with a spinor-based relativistic coupled-cluster CCSD(T) value of 0.61 eV. The complex spectral features due to excited electronic states and vibrational progressions of UF are analyzed and assigned with the help of spin–orbit-coupled multireference perturbation theory and spinor-based relativistic coupled-cluster calculations. UF and UF – are confirmed to be dominated by ionic bonding. Furthermore, the usefulness of the spinor CCSD(T) approach is demonstrated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ion temperature and rotation fluctuation measurements with ultra-fast charge exchange recombination spectroscopy (UF-CHERS) in the DIII-D tokamak

An upgraded detector and several optimizations have significantly improved the Ultra-Fast Charge Exchange Recombination Spectroscopy (UF-CHERS) diagnostic sensitivity to ion temperature and parallel velocity fluctuations at turbulence relevant spatio-temporal scales. Normalized broadband ion temperature and parallel velocity fluctuations down to x̃x∼1% (x = Ti, v∥) and up to ∼450 kHz have been measured in a variety of plasmas. The multi-field nature of the CHERS technique also allows measurements of the cross-phase angles of the fluctuating fields. UF-CHERS is optimized to observe emissions from the electron exchange reaction between intrinsic C6+ and hydrogenic neutral beam injected particles near 529 nm. UF-CHERS consists of two chords separated by ∼1 cm radially, less than the turbulence correlation length in DIII-D plasmas, which enables correlated measurements to suppress incoherent electronic and photon noise. The optical components of the spectrometer include a volume-phase-holographic grating with >90% transmission between 528 and 530 nm and f/2 200-mm lenses, selected to maximize the optical efficiency and photon flux. Diffracted light from each chord is collected in eight spectral bins, each with a bandwidth of ∼0.25 nm, and detected and amplified by chilled avalanche photodiodes and custom high-gain, wide bandwidth low-noise preamplifiers to achieve the optimal signal-to-noise ratio. The resulting signals are digitized at 1 MHz, 103–104× faster than the conventional CHERS diagnostics. Spatial coverage is achieved by repositioning a motorized fiber tray between plasmas. UF-CHERS measurements will advance the understanding of turbulent ion transport and contribute to the validation of transport models and simulations.

Truong, D. D. (ORCID:0000000285732539)↗

Nuclear Safeguards: Feature Extraction for Machine Learning Enrichment Analysis of UF 6 Cylinders

With the increasing international interest in using nuclear material as sources of energy, comes the growing concern that we may see an increase in proliferation threats. Uranium hexafluoride (UF 6 ) is used in the nuclear fuel cycle for uranium enrichment. Inspectors from the International Atomic Energy Agency (IAEA) monitor the enrichment levels of UF 6 stored in transportation cylinders, to ensure the enrichments match that of a facility operator’s declarations. However, only a characteristic subset of UF 6 cylinders can be measured by inspectors from the IAEA during these inspections. In turn, the inspector may not identify a cylinder whose enrichment levels do not match the facility declarations. Therefore, our team attempts to develop a machine learning network that could determine the enrichment percentage of cylinders as they enter and exit facilities. The machine learning model must be robust against spectral variations due to factors that are internal and external to the UF 6 cylinder. Such factors include but are not limited to the speed and distance of the moving vehicle, cylinder type, cylinder orientation, and fill level. Many features in the spectral continuum can be used to identify and correct for some of these variations. As a consequence, the model must extract numerous features in the continuum. We investigate new approaches in continuum subtraction to verify enrichment percentage: interpolation and extrapolation of lines at the notable characteristic spectral peaks. It was determined that there was no clear answer on which method proved superior, therefore the decision was made to implement both new methods into the current codebase. We currently rely on synthetic training and testing data to analyze the results and fine tune our models but hope to test the system on measured data soon.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Evaluating Barcode Size and Metal Surface Treatment Options for a Global UF 6 Cylinder Identifier

A team at Oak Ridge National Laboratory tested various barcode sizes, materials, surface finishes, and marking techniques to determine suitable direct part marking techniques and barcode specifications for a new uranium hexafluoride (UF 6 ) cylinder global identifier. This paper describes testing those variables at different read distances and angles with several commercial off-the-shelf direct part mark or barcode readers. This research concluded that a 1.4 in. 2D Data Matrix barcode with a 0.1 in. quiet zone would be appropriate for the machine-readable feature on the proposed UF 6 cylinder global identifier. Testing suggests that this size barcode could be read from an angle of up to 30° over the range of 10–100 cm using multiple commercial off-the-shelf handheld direct part mark or barcode readers. Testing also suggested that barcodes marked on ball-blasted stainless steel with CerMark laser marking ink may be a good choice for the proposed UF 6 cylinder global identifier because they exhibited high contrast and were readable from a desirable range of distances and angles.

42 ENGINEERING↗

Density functional theory (DFT) study of UF 6 hydrolysis: reaction pathways, spectroscopy, and chemical kinetics

Depleted uranium hexafluoride (UF 6 ), a stockpiled byproduct of the nuclear fuel cycle, reacts readily with atmospheric humidity, but the gas-phase reaction mechanism and associated chemical kinetics are poorly understood. During the performance period we undertook development of a state-of-the-art ab initio gas-phase chemical kinetics simulation workflow to model the hydrolysis of uranium hexafluroride (UF 6 ). In doing so, we addressed several outstanding issues in the theoretical treatment of uranium-containing systems. At the outset it was unclear how to generate accurate estimates of kinetic and thermodynamic data for U-containing chemical reactions. Generation of such data has been made routine. Prior to our work, the literature associated with UF 6 hydrolysis were disparate and inaccurate. This body of work provides a modern and comprehensive theoretical assessment of the reaction mechanism, molecular clustering towards deposition, and chemical kinetics. New methodological implementations and software integrations resulting from this work are also highlighted. As much as possible, our predictions were validated against experimental data including particle morphologies, vibrational spectroscopy, atomization enthalpies, and kinetic rate constants. Nevertheless, we were unable to reconcile kinetic measurements with high-accuracy simulations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Morphological Characterization of UO 2 F 2 and UF 4 Hydrolysis Products

Bulk samples of UO 2 F 2 and UF 4 were aged for 3 weeks under various relative humidity (RH) conditions to examine morphological changes associated with the hydrolysis of the materials. Aged samples were analyzed using scanning electron microscopy (SEM) to examine morphological changes, and Raman spectroscopy was used to correlate these changes with chemical composition. Little to no effect was evident for either material under lower RH conditions (i.e., 16% and 33%–38% RH). Under higher RH conditions (83% and 99%), multiple morphological changes were evident within the UO 2 F 2 samples because of the formation of hydrolysis products and possible interactions at the solid–vapor interface. Only one major morphological change was observed over the aging period—within the UF 4 system at 99% RH. This change can be attributed to the initial formation of anhydrous UO 2 F 2 and, subsequently, its hydrolysis products. After 37 weeks, UO 2 F 2 persisted as a hydrolysis product of UF4; however, no further hydrolysis products were observed. These results suggest that further research into a possible divergence of UF 4 and UO 2 F 2 degradation pathways is warranted.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Heterogeneity effects on nondestructive assay measurements of enrichment in UF 6 cylinders

A set of measurements were performed using multiple mechanically cooled HPGe detectors at six positions around a cylinder uranium hexafluoride to assess if matrix inhomogeneity is detectible and effects the determined apparent uranium enrichment. These measurements were performed on nine 30B cylinders of uranium hexafluoride. Six of the cylinders appeared to be homogeneous and had similar apparent measured uranium enrichment, as calculated by the FRAM software, at all positions. However, three cylinders appeared to have local inhomogeneity based on the observed results. This was manifested as very low apparent enrichments, often <10% of the declared enrichment, on select positions. The side with a low apparent enrichment shows elevated daughter isotope activity (e.g., elevated 1001 keV and 766 keV peak count rate) and slightly reduced 235 U activity (lower 185.7 keV count rate). We hypothesize that these heterogenous cylinders may have experienced asymmetric solar heating, which caused volatile UF 6 to sublime preferentially away from the warmed side. A similar phenomenon was observed at a second facility where dose rate measurements confirm that the “low-enriched side” of cylinders show elevated gamma ray dose rates, likely from the removal of UF 6 attenuation and concentration of daughter-products. Care should be taken during uranium enrichment verification when applying methods that include gamma-rays associated with daughter nuclides to the determination of uranium enrichment on cylinders that are stored in sunlight and have asymmetric dose readings around the cylinder.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Applications of HPGe-detected high energy gamma rays toward quantifying neutron emission rates and 234 U enrichment in UF 6 cylinders

This study presents a 234 U enrichment meter that uses high energy gamma and neutron count rate as measured by a portable, high-purity germanium gamma ray detector. Twenty-one 30B cylinders containing UF 6 of varying origin were analyzed with an HPGe detector for high-energy gamma ray and neutron counts. Excellent correlations (R 2 0.95) between various regions of 3.0 MeV gamma rays, neutron count rate, and uranium enrichment were found. These neutron and high-energy gamma data are used to create calibration-dependent enrichment meters for 234 U. The 234 U enrichment calculated from the neutron count rate and 4 – 6 MeV gamma count rate is more accurate than methods that rely on the 120.9 keV peak which is strongly attenuated inside commercial sized UF 6 cylinders. These neutron and high-energy gamma enrichment calculators can also be used to determine a 235 U enrichment, assuming mass-based enrichment from natural uranium, but the results are not as accurate as the traditional 185.7 keV peak enrichment meter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Coupled Cluster Study of the Heats of Formation of UF 6 and the Uranium Oxyhalides, UO 2 X 2 (X = F, Cl, Br, I, and At)

The atomization enthalpies of the U(VI) species UF6 and the uranium oxyhalides UO 2 X 2 (X=F, Cl, Br, I, At) were calculated using a composite relativistic Feller-Peterson-Dixon (FPD) approach based on scalar relativistic DKH3-CCSD(T) with extrapolations to the CBS limit. The inherent multideterminantal nature of the U atom was mitigated by utilizing the singly charged atomic cation in all calculations with correction back to the neutral asymptote via the accurate ionization energy of the U atom. The effects of SO coupling were recovered using full 4-component CCSD(T) with contributions due to the Gaunt Hamiltonian calculated using Dirac-Hartree-Fock. The final atomization enthalpy for UF 6 (752.2 kcal/mol) was within 2.5 kcal/mol of the experimental value, but unfortunately the latter carries a ±2.4 kcal/mol uncertainty that is predominantly due to the experimental uncertainty in the formation enthalpy of U atom. The analogous value for UO 2 F 2 (607.6 kcal/mol) was in nearly exact agreement with experiment, but the latter has a stated experimental uncertainty of ±4.3 kcal/mol. The FPD atomization enthalpy for UO 2 Cl 2 (540.4 kcal/mol) was within the experimental error limits of ±5.5 kcal/mol. FPD atomization energies for the non-U-containing molecules (used for reaction enthalpies) H 2 O and HX (X=F, Cl, Br, I, At) were within at most 0.3 kcal/mol of their experimental values where available. The FPD atomization enthalpies, together with FPD reaction enthalpies for two different reactions, were used to determine heats of formation for all species of this work with estimated uncertainties of ±4 kcal/mol. The calculated heat of formation for UF 6 (-511.0 kcal/mol) is within 2.5 kcal/mol of the accurately-known (±0.45 kcal/mol) experimental value.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Classification of gaseous UF 6 assay by femtosecond LIBS in the 424.4 nm spectral region using numerical HOGSVD-DTW features

This technical note presents experimental results using numerical features of fs-LIBS data to classify the assay value of a gaseous UF 6 material. Here, the data-driven feature vectors are computed by Higher Order Generalized Singular Value Decomposition (HOGSVD) and Dynamic Time Warp (DTW). The method achieves 96.97% accuracy in spectral classification testing with fs-LIBS samples obtained from a UF 6 material with five known assay values ranging from 0.287% to 61.740%, with 100% accuracy for the four largest assay values ranging from 4.615% to 61.740%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

The insufficiency of the charge transfer model for resonant $\text{XES}$ in $\text{UF}$ 4

Recently, it was suggested that the single-electron charge transfer model (ligand 2p to Uranium 5f transition) could be used to explain the U M 4,5 Resonant X-ray Emission Spectroscopy (XES) of uranium dioxide (UO 2 ) and uranium tetrafluoride (UF 4 ). Here in this report, it is shown that this model produces results inconsistent with a joint consideration of both of the bandgaps of UO 2 and UF 4 and is thus insufficient to explain the observed behavior. An alternative Raman-based model is proposed.

36 MATERIALS SCIENCE↗